Zhou Yi Hang Shi Xue (周易杭氏學)

《易》注自宋以前未嘗有圖也。逮周廉溪傳陳希夷《太極圖》而為之說，遂開理學之宗。但《圖》與《易》猶不相屬也。至朱子《本義》，取邵子河洛、先後天八卦、大小方圓各圖，與其改訂之卦變圖，弁諸經首，歷代宗之。自是圖之與《易》，相為附麗。後之說《易》者，無不有圖。

Before the Song dynasty, those who interpreted the Zhou Changes did not use diagrams. It was not until the Northern Song dynasty when Zhou Dunyi received the Taiji Diagram from Chen Tuan and wrote the Taiji Diagram Explanation that the school of Neo-Confucianism began to take shape; however, at that time, the Taiji Diagram and the Zhou Changes text still spoke separately, and they were not yet connected. It was only when Zhu Xi wrote The Original Meaning of the Zhou Changes that he included the river chart and the Luo square, the positions of the Earlier Heaven and Later Heaven trigrams, and the large and small circular diagrams, along with his own revised diagram of changing hexagrams, all placed at the beginning of the text. Since then, diagrams and the Zhou Changes have become interdependent, and later scholars who interpreted the Zhou Changes have all used diagrams.

漢學家雖力攻河洛先後天之名，而其為說，仍不能廢陰陽四象及五行生成、九宮變化之義。而為之圖者，且層出不窮。蓋數理繁賾，卦爻錯綜，表之以圖，說乃易明。故學《易》者先辨圖書，識其陰陽生化之原，奇偶交變之義，而後觀象玩辭，有所準的。不致眩惑歧誤而靡所適從，亦事半功倍之一道焉。

In the Qing dynasty, scholars who specialized in Han learning strongly criticized terms such as "Heavenly River Chart," "Luo Writing," "Earlier Heaven," and "Later Heaven." However, when they formulated their own theories, they could not do away with the concepts of yin and yang, the Four Symbols, the numerical principles of the Five Phases, and the changes in the Nine Squares system. In fact, those who illustrated these principles with diagrams became more numerous in each generation. This is because the principles of numbers and reason are complex and intertwined, and using charts helps clarify the meaning. Therefore, those studying the Book of Changes should first clearly distinguish the types of diagrams such as the Heavenly River Chart and Luo Writing, understand the fundamental principles of yin and yang transformation, and the meaning of the alternation between odd and even numbers. Only then can they observe the hexagrams and contemplate the line statements, having a clear standard in their minds, and avoid being confused by various conflicting interpretations. This is also an efficient way to achieve greater understanding.

《繫傳》曰“《易》有太極”，又曰“六爻之動，三極之道也”。極者，至極而無對之稱。三極者，天極地極人極也。故曰“太極”者，所以異於三極也。極既無對，極而益之曰“太”，則更無有可以並之而尚之者矣。

The Great Treatise says, "The Book of Changes contains the Supreme Ultimate," and also says, "The movement of the six lines represents the principles of the three extremes." The term "extreme" refers to the highest and ultimate, having nothing else to be its counterpart. The term "three extremes" refers to the heavenly extreme, the earthly extreme, and the human extreme. Confucius deliberately called it the "Supreme Ultimate" in order to distinguish it from the three extremes of heaven, earth, and humanity. Originally, the term "extreme" already had nothing to be its counterpart. By adding the character "tai" (great) to "extreme," it indicates that nothing else can be placed on the same level or above it.

是以太極者，立乎天地之先，超乎陰陽之上，非言詞擬議所可形容。蓋狀之以言則有聲，有聲非太極也。擬之以形則有象，有象亦非太極也。《詩》曰“上天之載，無聲無臭”，庶或似之。然無字為有字之對，有對亦非太極也。

Therefore, the Taiji exists prior to the generation of heaven and earth, and transcends the dual forces of yin and yang. It cannot be described by words or discourse. To describe it with words would involve sound, and anything that involves sound is not Taiji. To compare it with forms would involve images, and anything that involves images is not Taiji. The Classic of Poetry, Great Yamen, attributed to King Wen, says, "The heavens carry on their work silently and without odor," perhaps coming closer to describing the workings of heaven without sound or smell. However, the character "wu" (nothingness) only makes sense in contrast to "you" (somethingness). Anything that involves a contrast or duality is still not Taiji.

孔子於無可形容擬議之中，而形容擬議之曰“太極”，可謂聖人造化之筆，更無他詞足以附益而增損之矣。然而有太極之名，似亦非太極之真諦。乃無礙其為太極者，則以“太極”二字，均無物質無精神可言，更無其他之詞義足以相併相對。可以謂之名，亦可以謂之非名。此聖筆之神化，所以不可思議也。

In a place where there is no way to describe or compare, Confucius managed to use the term "Taiji" to express it. This can be considered the extraordinary skill of a sage in participating in the workings of the universe; there is no other word that can add to or subtract from it. However, once the term "Taiji" is established, it seems that it is no longer the true essence of Taiji. Yet it remains Taiji, because the two characters "Taiji" cannot be classified as either material or spiritual, nor can another term be found to stand in contrast or parallel to it. It can be regarded as a name, or it can be said that it is not a name at all. This is precisely the marvelous and inconceivable skill of the sages' writing.

夫焉能又為之圖？自周子而後，相傳之圖有三。於是“太極圖”三字，流播環寰宇，幾於婦孺皆知。以論傳論，恐學者認《太極圖》為太極，則是非混淆（“《易》有太極，是生兩儀”。《易》曰“辨是與非”，即辨諸此。另有《圖說》見後。）。差以毫釐，謬以千里，而象數終無以明矣。爰詮其義，並列後出諸圖，以資辨別。

So if that is the case, how can we still draw a diagram of the Taiji? Since the time of Zhou Dunyi, there have been three transmitted versions of the Taiji diagram, and the term "Taiji Diagram" has become widely known throughout the world, almost familiar to every man and woman. Following the previous interpretations, the greatest danger for scholars is that they take the "Taiji Diagram" itself as Taiji, thereby confusing the concepts of "is" and "is not." The Great Treatise says, "The Book of Changes has Taiji, from which the two principles arise," and the Book of Changes also says, "distinguish between 'is' and 'is not.'" What needs to be distinguished is precisely this point. There is also a "Diagram Explanation" mentioned later. A slight error at the beginning leads to a great mistake in the end, and thus the study of figures and numbers can never be properly explained. Therefore, first we should explain the meaning of "Taiji," and then list all the various diagrams that have appeared in later generations, for readers to distinguish.

老子曰“有物無形，先天地生”，即謂太極也。以孔子《十翼》告成，老子已出關西去，故未知孔子有此假定之名，而曰“無以名之，強名之曰道”。究竟“道”字，實未能妙合無間，老子亦無可如何，而強名之耳。使老子得見孔子“《易》有太極”一語，必舍其名而從之。《道德經》更可省卻無數語言矣。

Laozi said, "There is something that exists without form, coming into being before heaven and earth," referring to the Taiji. By the time Confucius completed the Ten Wings, Laozi had already left for the western pass of Hangu. Therefore, he did not know that Confucius had already given this concept the name "Taiji." Laozi could not give it a proper name, so he said, "It is impossible to name it, so we must give it a name, calling it Dao." In fact, using the term "Dao" to refer to it can never fully capture its boundless nature. Laozi himself had no other way, so he merely gave it a provisional name. If Laozi had seen Confucius' statement "The Book of Changes contains Taiji," he would have abandoned his own term and adopted this one instead. The "Dao De Jing" would then have saved countless words of argumentation.

《說文》：“極，棟也。”《易·大過》：“棟隆，本末弱也。”棟亦訓極。“建中立極”，故極亦訓中。棟從東從木，木生於東，得木之正，故以室中主幹之巨木謂之棟。蓋上棟下宇，初創宮室之時構造皆甚簡單，以巨木支柱正中而四周下垂，與今日營帳之制略同。故棟必在室之正中，與極字之訓，義可以相通。若以今日之所謂棟者例之，則與“極”字之義不相蒙矣。此亦言太極者不可不知者也。

The "Sayings of the Classic of Characters" explains the character "ji" as "a central beam of a house," referring to the main beam in the center of a building. The "Zhou Yi" (Book of Changes) mentions "dong long" in the "Da Guo" hexagram, and the "Commentary on the Judgment" interprets it as "both beginning and end are weak." This shows that "dong" can also be interpreted as "ji." Ancient sayings also mention "jian zhong li ji," meaning "establishing the center as the standard," so "ji" can also mean "center." The character "dong" is composed of "dong" and "mu," meaning east and wood. Wood is strong in the east and receives the correct energy of wood, so the main central beam of a house is called "dong." In ancient times, when people first built houses, their structures were simple, using only one large wooden beam placed in the center as a support. The covering around it would naturally slope downward, similar to the structure of today's tents. Therefore, the beam was always in the center of the house, which connects with the meaning of "ji" as "center." If we compare it to today's concept of "dongliang" (beam), it would be unrelated to the original meaning of "ji." This is a point that those who discuss the Taiji (Supreme Ultimate) should not be unaware of.

周子《太極圖說》曰“無極而太極。太極動而生陽，動極而靜。靜而生陰，靜極復動。一動一靜，互為其根。分陰分陽，兩儀立焉。陽變陰合，而水火木金土五氣順布，四時行焉。五行一陰陽也，陰陽一太極也，太極本無極也。五行之生也，各一其性。無極之真，二五之精，妙合而凝。乾道成男，坤道成女。二氣交感，化生萬物，萬物生生而變化無窮焉。

The Taiji Tu Shuo by Zhou Dunyi says: From the state of no extreme, Taiji arises. When Taiji moves, yang qi is generated; movement reaches its extreme and turns into stillness; when stillness arises, yin qi is generated; stillness reaches its extreme and turns back into movement. Movement and stillness are the root of each other, and thus yin and yang are separated, establishing the two principles. Yang qi moves and transforms, while yin qi condenses and combines, leading to the sequential arrangement of the five elements: water, fire, wood, metal, and earth. The four seasons, spring, summer, autumn, and winter, follow accordingly. In the end, the five elements are merely one yin and one yang, and yin and yang in the end are merely one Taiji, and Taiji itself is originally the state of no extreme. Each of the five elements generates itself and possesses its own nature. The true essence of the state of no extreme, together with the two yin and yang energies and the essence of the five elements, skillfully combine and condense: the Qian principle generates male, the Kun principle generates female. These two energies interact and respond, giving rise to all things. All things continuously generate and transform, with no end to their changes.

惟人也得其秀而最靈。形既生矣，神知發矣。五性感動，而善惡分萬事出矣。聖人定之以中正仁義，而主靜立人極焉。故聖人與天地合其德，日月合其明，四時合其序，鬼神合其吉凶。君子修之吉，小人悖之凶。故曰‘立天之道曰陰與陽，立地之道曰柔與剛，立人之道曰仁與義’，又曰‘原始反終，故知死生之說’。大哉《易》也！斯其至矣。”

Only those who possess the most refined and spiritual aspect among the Five Phases can attain true virtue. Once the physical form is formed, the spirit and perception become active. The five human qualities—benevolence, righteousness, propriety, wisdom, and faithfulness—are stirred by external influences, leading to the distinction between good and evil, and the origin of all things. The sage establishes principles of the middle, correctness, benevolence, and righteousness to govern these, and advocates stillness as the main approach, thereby establishing the "human extreme." Thus, the sage's virtue harmonizes with heaven and earth, his brightness with the sun and moon, his seasonal changes with the four seasons, and his discernment of good and evil with the spirits. The gentleman follows this principle in self-cultivation and attains good fortune, while the petty person who violates it brings about misfortune. Therefore, the "Commentary on the Changes" states, "The way of heaven is called yin and yang, the way of earth is called softness and hardness, and the way of humanity is called benevolence and righteousness." The "Great Treatise" also says, "To trace back to the beginning and return to the end, thus understanding the doctrine of life and death." How great is the "Zhou Yi"! This is its ultimate meaning.

周子此圖，出自希夷，宋儒諱之甚深。然希夷亦非自作也，實本諸《參同契》。彭曉注《參同契》，有《明鏡圖訣》一卷。（《序》稱：廣政丁未為蜀孟昶廣政十年，漢天福十二年也。彭號真一子，字秀川，蜀人。）

The diagram of the Taiji diagram originated from Chen Tuan, and Song dynasty Confucian scholars kept this origin very secret. However, Chen Tuan himself did not create it; it actually came from the Eastern Han dynasty alchemist Wei Boyang's "Zhouyi Cangtongqi." In the Five Dynasties period, Peng Xiao wrote annotations on the "Cangtongqi" and also composed a separate work called "Mingjing Tu Jue" (his "Preface" is dated "Guangzheng Dingwei," which refers to the tenth year of Guangzheng in the reign of Meng Chang, the ruler of the Later Shu, also known as the twelfth year of Tianfu in the Later Han dynasty). This line of transmission traces the original source of the Taiji diagram back to the alchemical tradition.

毛氏奇齡曰：“《參同契》諸圖，自朱子注後（朱子注《參同契》，隱姓名為鄒欣，號空同道人。），學者多刪之。”徐氏注本已亡（按：徐名景休，東漢人，官青州從事，注《參同契》。桓帝時授淳于叔通。），他本龐雜不足據。惟彭本有《水火匡廓圖》、《三五至精圖》、《斗建子午圖》、《將指天罡圖》、《昏見圖》、《晨見圖》、《九宮八卦圖》、《納甲圖》、《舍元播精圖》、《三五歸一圖》。

In the Qing dynasty, Mao Qiling said that the original set of diagrams accompanying the "Supplement to the Supreme Truth" had, since Zhu Xi made annotations (Zhu Xi annotated the "Supplement to the Supreme Truth" but concealed his real name, signing himself as Zou Xin, with the courtesy name Kongtong Daoren), been mostly deleted by scholars. The annotated edition by Xu Shi of the Eastern Han dynasty has already been lost (Hang noted: Xu Shi was named Jingxiu, a person of the Eastern Han dynasty, who once served as a minor official in Qingzhou, and he made annotations on the "Supplement to the Supreme Truth." During the reign of Emperor Huan, he passed on this discipline to Chunyu Shutong). Other editions are too miscellaneous to be reliable. Only the edition by Peng Xiao still preserves the "Diagram of Water and Fire Encircling," "Diagram of the Three and Five Ultimate Essence," "Diagram of the Celestial Stem and Earthly Branches," "Diagram of Pointing to the Heavenly Gang," "Diagram of the Setting Sun," "Diagram of the Rising Sun," "Diagram of the Nine Palaces and Eight Trigrams," "Diagram of the Stem Assignment," "Diagram of the Dispersal of Essence," and "Diagram of the Three and Five Returning to One." These ten diagrams are the only physical evidence available for tracing the origin of the Taiji Diagram.

今周子之黑白分三層者，即《水火匡廓圖》也。其中間之水火金木土，即《三五至精圖》也。惟圖式雖同，尚末有太極之名也。考唐《真元妙經品》，有《太極先天圖》，合三輪五行為一，而以三輪中一○五行下一○為太極，又加以陰靜陽動男女萬物之象，凡四大○。陰靜在三輪之上，陽動在三輪之下，男女萬物皆在五行之下，則與周子之圖名義皆同，但多“先天”二字耳。

The part of the diagram in Zhou Dunyi's illustration today that shows black and white intermingled divided into three layers is the Peng edition's "Water and Fire Enclosure Diagram." The part in the middle where the five phases of water, fire, metal, wood, and earth are connected is the "Three and Five Ultimate Essence Diagram." Although the diagram format is the same, the term "Taiji" was not yet used at that time. Further examination of the Tang dynasty "Zhenyuan Miaojing Pin," which contains an illustration called the "Taiji Earlier Heaven Diagram," shows that the three-layered circle and the five phases are combined into one. It uses a circle in the middle of the three circles and a circle below the five phases to represent Taiji, and adds images of yin stillness, yang movement, and male and female as well as all things, making a total of four large circles: yin stillness above the three circles, yang movement below the three circles, and male and female as well as all things arranged below the five phases. This shows that it is entirely consistent with Zhou Dunyi's diagram, differing only in the addition of the two characters "Earlier Heaven."

然則此圖，自道家傳出，已無疑義。周子但為之說，並將上下次序略有修改而已。首曰“無極而太極”，終有語病。當時陸梭山已有疑義，與朱子往反辯論累數萬言。朱子雖曲為迴護，並於《太極圖說》注中申明謂“非太極之上覆有無極”，但其圖明明確太極之上有無極，其說終不可通也。其作《本義》，取邵子先天諸圖，而不以此圖列諸卷首，殆亦有所悟歟！

This suggests that the diagram originated from Daoist tradition, leaving no doubt. Zhou Dunyi merely wrote an explanatory commentary on it and slightly adjusted the order of the sections. His opening sentence, "From the boundless void comes the Supreme Ultimate," inevitably left a logical flaw. At the time, Lu Jiushao (Suoshan) raised a question, and they debated back and forth for tens of thousands of words with Zhu Xi. Although Zhu Xi tried to defend it, he still explicitly stated in the annotations to "The Diagram of the Supreme Ultimate" that "there is not another boundless void above the Supreme Ultimate." However, the diagram clearly shows a layer of boundless void above the Supreme Ultimate, making his statement ultimately incoherent. Later, when Zhu Xi wrote "The Original Meaning of the Zhou Changes," he only included Shao Yong's Earlier Heaven diagrams at the beginning, but did not include this diagram of the Supreme Ultimate. Perhaps he himself had some realization about it.

古太極圖，亦名“天地自然之圖”。趙氏撝謙《六書本義》曰：“天地自然之圖，伏羲氏龍馬負之出於滎河，八卦所由以畫也。世傳蔡季通得於蜀隱者，秘而不傳。趙氏得之於陳伯敷氏，熟玩之有太極函陰陽，陰陽函八卦之妙。自明洪武以後，此圖遂盛傳於世。”

The ancient Taiji diagram is also known as the "Diagram of Heaven and Earth in Their Natural State." In his work "Six Classics: Original Meaning" from the Ming dynasty, Zhao Huiqian said that this diagram of heaven and earth is said to have been brought out by a dragon horse from the river Xinghe during the time of Fuxi, and the Eight Trigrams were drawn based on it. It is said that in the Southern Song dynasty, Cai Yuan ding (Jitong) obtained it from a hermit in Sichuan and kept it secret, not passing it on. Zhao Huiqian himself obtained it from Chen Bofu, and after repeatedly contemplating it, he realized the wonderful aspect that Taiji contains yin and yang, and yin and yang contain the Eight Trigrams. Since the Ming dynasty's Hongwu period, this diagram has been widely circulated.

（按：蔡氏晚年得此圖未久即病卒，故朱子亦未之見也。蔡死後秘藏於家，至其孫始傳佈之，已在宋亡之後。胡元一代，尚鮮稱述。至明初劉青田取以繪入八卦之中，遂風行海內，幾於家喻戶曉，無人不知有太極圖矣。）

(Hang氏按：Cai Yuan ding died soon after obtaining this diagram, so Zhu Xi did not see it. After Cai's death, the diagram was kept secret in his family and was only made public by his grandchildren, which was already after the fall of the Southern Song dynasty. During the entire Yuan dynasty, few people mentioned it. It was not until Liu Ji (Qingtian) of the early Ming dynasty included it within the Eight Trigrams that the diagram became widespread throughout the country, almost known to everyone.)

朱子發云：“陳摶以《先天圖》授种放，三傳而至邵雍。則康節之學，實出自希夷。所演《先天圖》，陰陽消長，亦與此圖悉合，故又謂之《太極真圖》。其環中為太極，兩邊黑白回互。白為陽，黑為陰。陰盛於北，而陽起而薄之，故邵子曰‘震始交陰而陽生’。自震而離而兌以至於乾，而陽斯盛焉。

In the Song dynasty, Zhu Zhen (Zi Fa) said: Chen Tuan passed on the "Earlier Heaven Diagram" to Zhong Fang, who passed it on to three generations until it reached Shao Yong. This shows that Shao Yong's learning actually came from Chen Tuan. The "Earlier Heaven Diagram" that Shao Yong deduced discusses the waxing and waning of yin and yang, and it matches the ancient Taiji diagram in every aspect. Therefore, this diagram is also called the "True Taiji Diagram." The center of the diagram is Taiji, with black and white circles interlocking on both sides: white represents yang, and black represents yin. Yin is strongest in the north, and yang arises from here, gradually approaching yin, so Shao Yong said, "Zhen begins to meet yin and yang is born." From Zhen to Li to Dui, and then to Qian, yang gradually becomes stronger.

震東北，白一分，黑二分，是為一奇二偶。兌東南，白二分，黑一分，是為二奇一偶。乾正南全白，是為三奇純陽。離正東，取西之白中黑點，為二奇含一偶，故云‘對過陰在中也’。

Now looking at the scores on the diagram: Zhen is in the northeast, with white occupying one part and black occupying two parts, forming the Zhen hexagram of one odd line and two even lines; Dui is in the southeast, with white occupying two parts and black occupying one part, forming the Dui hexagram of two odd lines and one even line; Qian is in the due south, entirely white, forming the Qian hexagram of three odd lines, all yang; Li is in the due east, where one must take the black dot from the western white part to form two odd lines with one even line, hence it is said 'the yin is in the middle of the opposite,' meaning the yin is contained within oneself, opposite the other side.

陽盛於南，而陰來迎之，故邵子曰‘巽始消陽而陰生’。自巽而坎而艮以至於坤，而陰斯盛焉。巽西南，黑一分，白二分，是為一偶二奇。艮西北，黑二分，白一分，是為二偶一奇。坤正北全黑，是為三偶純陰。坎正西，取東之黑中白點，為二偶含一奇，故云‘對過陽在中也’。

Yang energy is strongest in the south, and Yin energy comes from there to meet it, so Shao Yong said, "Xun begins to reduce Yang and Yin is generated." Starting from Xun, then Kan, then Gen, and finally Kun, Yin energy gradually becomes stronger. Xun is located in the southwest, with black occupying one part and white occupying two parts, making a Xun hexagram with one even and two odd lines; Gen is located in the northwest, with black occupying two parts and white occupying one part, making a Gen hexagram with two even and one odd line; Kun is located in the due north, entirely black, making a Kun hexagram with three even lines and pure Yin; Kan is located in the due west, and one white dot from the east is taken from the black to form two even lines containing one odd line, so it is said, "Yang is in the center opposite."

坎離為日月，升降於乾坤之間，而無定位。納甲寄中宮之戊己，故東西交易，與六卦異也。八方三畫之奇偶，與白黑之質，次第相應，深得陰陽造化自然而然之妙。但既有黑白之分，備陰陽之用，已非太極之真相，不當稱之為《太極圖》。今北方俗呼此圖為‘陰陽魚兒’，‘魚’字實‘儀’字之誤。稱之曰‘陰陽儀圖’，或曰‘兩儀圖’，斯名實相符矣。”

The trigrams Kan (Water) and Li (Fire) symbolize the sun and moon, rising and setting between Qian (Heaven) and Kun (Earth), and originally have no fixed direction. In terms of "Najia" stem assignment, they are associated with the stems Wu and Ji in the Central Palace. Therefore, the eastern and western positions must exchange their symbolic meanings, differing from the method used for the other six trigrams. The odd and even numbers of the three strokes in each of the eight directions correspond precisely with the number of black and white blocks, layer by layer, clearly demonstrating the natural workings of yin and yang. However, once black and white are distinguished and the functions of yin and yang are established, it is no longer the true nature of the Taiji. Therefore, it should not be called the "Taiji Diagram." Now, in northern folk, this diagram is commonly called the "Yin-Yang Fish," but the word "fish" is actually a miswriting of "instrument." It should be called the "Yin-Yang Instrument Diagram" or the "Two Principles Diagram" to match the actual meaning.

此圖流傳甚古，蘊蓄宏深，決非後人所能臆造。大抵老子西出函關，必挾圖書以俱行，故遺留關中，為道家之秘藏。至於唐宋而後，始逐漸傳佈，要皆為三代以上之故物，無可疑也。

This diagram has a very ancient origin, containing profound meaning, and could not have been invented by later people. The general account is that when Laozi left the pass of Hangu, he must have taken these books with him, so such texts remained in the area of Hangu and were secretly kept by the Taoist school. It was only after the Tang and Song dynasties that these texts gradually spread throughout the world. In the end, they are all ancient relics from before the Xia, Shang, and Zhou dynasties, and there is no doubt about this. From this we can conclude that the ancient Taiji diagram dates back far earlier than the Confucian scholars of the Song dynasty, and the Song people merely inherited the old diagram.

惟圖像既顯分黑白，是已生兩儀。分之為四，即成四象。分之為八，即成八卦。可謂之“兩儀生四象，四象生八卦之圖”。但流傳既久且遠，世俗已無人不認此為太極圖者。所謂習非勝是，辨不勝辨。惟學者宜詳究其義理，因名責實，而求得真諦。斯源頭不誤，自能清澈見底。不可以習見而忽之，反為流俗所誤也。

The image, once clearly divided into black and white, signifies the emergence of the Two Principles. Dividing each of black and white again into two results in the Four Symbols; dividing again into eight produces the Eight Trigrams. Therefore, this image can at most be called the "Diagram of the Two Principles generating the Four Symbols, and the Four Symbols generating the Eight Trigrams," not the Taiji Diagram. However, due to its long and widespread transmission, the common people have come to recognize it as the Taiji Diagram. This is what is called "accumulating errors into truth," and no amount of argument can change it. Scholars should only carefully examine its meaning, follow the name to investigate the reality, and thus seek the true essence. If the source is correct, the following will naturally be clear. One should not become careless merely because it is familiar, and be misled by popular misconceptions.

此來瞿塘氏之圖，亦從《古太極圖》研索而出者也。以居中之黑白二線，代兩點，以象陽方盛而陰已生，陰方盛而陽已生，有循環不絕之義。留中空者以象太極，其陰陽之由微而顯，由顯而著，亦悉合消息之自然。與河圖陰陽之數，由微而著，由內而外，亦適相合。來氏另有一圖，以河圖陽數佈於白中，陰數佈於黑中，又以配八卦四時十二辰，及古今治亂盛衰之象。圖多，茲不贅錄。

This is a diagram created by Lai Zhide of the Ming dynasty (Qutang), derived from the ancient Taiji Diagram. He used a single black and white line in the center to replace the original black and white dots, symbolizing that when Yang is at its peak, Yin has already begun to emerge, and when Yin is at its peak, Yang has already begun to emerge, conveying the meaning of continuous cycles. The blank space in the diagram symbolizes the Taiji. The transition of Yin and Yang from hidden to manifest, and from manifest to prominent, fully conforms to the natural principle of waxing and waning. This is consistent with the arrangement of the numbers of Yin and Yang in the Yellow River Chart, which progresses from subtle to prominent and from inner to outer. Lai Zhide also created another diagram in which the Yang numbers of the Yellow River Chart are arranged on the white side and the Yin numbers on the black side. He used this to associate with the Eight Trigrams, the four seasons, the twelve earthly branches, and the changes of prosperity and decline in the world throughout history. There are many such diagrams, but they are not listed here one by one.

來氏此圖，蓋亦悟太極之非圖所可狀，非言語可能形容，故留其外之黑白回互者為兩儀，而空其中以為太極。然“太極”二字之下繫之以圖，終有所難通也。以上三圖，皆稱太極。周子之圖，僅見於性理諸書，習之者今已不多。來氏之圖，傳亦不廣。惟第二圖風行宇內，幾與八卦並傳。圖像雖精，與孔子“太極”二字之義，實不相符。此為學易推原象數之第一步，不可不深思明辨，而求得其至當者也。

Lai Zhide's diagram probably also realized that the Taiji cannot be depicted by a diagram or described by words, so he left the outer black and white interlocking parts as the two principles, and left the center empty as the Taiji. However, beneath the two characters "Taiji," there is still a diagram attached, which remains difficult to explain. The three diagrams mentioned above are all called Taiji: Zhou Dunyi's diagram appears only in books discussing nature and principles, and now few people study it; Lai Zhide's diagram is not widely circulated either; only the second ancient Taiji diagram is widely circulated throughout the world, almost as popular as the Eight Trigrams. Although its image is exquisite, it does not conform to the meaning of "Taiji" as mentioned by Confucius. This is the first step in studying the Book of Changes concerning its symbolic representations and numerical patterns. It is essential to think deeply and discern clearly, seeking the most appropriate conclusion.

太極既不可以圖，然非圖又不足明陰陽顯化之妙，是惟有舍太極而圖兩儀。兩儀既明，則太極自立乎其先。無象之象，亦因象而顯矣。

The Taiji cannot be drawn as a diagram, yet without a diagram it is insufficient to explain the subtle transformations of yin and yang. Therefore, we must abandon the Taiji and instead draw the two principles (liang yi). Once the two principles are clearly drawn, the Taiji naturally stands before them; the formless form is thus revealed through the tangible two principles.

此端木國瑚氏之圖也，於文日正為是。下正北方正而上直日，日中影正。影正，則左右自分為兩。左陽而右陰。故《易》於乾之初爻曰“不見是”，未濟之上爻曰“有孚失是”。全《易》六十四卦，三百八十四爻，以此一“是”為始終，其故可深長思也。

This is a diagram created by Du Mengguo Hu in the Qing Dynasty. In terms of character form, adding "zheng" under "ri" forms the character "shi." The diagram's lower part faces due north directly, while its upper part faces the sun directly. The sun is in the center, and its shadow is straight; when the shadow is straight, left and right naturally divide into two sides, with the left being yang and the right being yin. Therefore, in the Qian hexagram's initial line of the Zhou Yi, the Wenyan Zhuan states, "Not seeing it but without distress." In the Weiji hexagram's upper line, the line statement says, "Having sincerity but losing the correct path." All sixty-four hexagrams and 384 lines in the entire Zhou Yi are unified by this single character "shi." The reason behind this is worth deep contemplation.

有丨畫中央，便分兩列。《繫傳》曰：“乾坤成列，而易立乎其中矣。”是則乾坤左陽儀，右陰儀。從丨生出，是太極，是兩儀。一至而二分（東西分，南北至。），是一是二，易陰陽生，不待再言“太極生兩儀”，此為“《易》有太極，是生兩儀”。

In the diagram, there is a vertical line 「丨」 standing in the center, dividing the space into two columns on either side. The Great Treatise says, "When Heaven and Earth are arranged in order, the Book of Changes stands in the midst." This precisely corresponds to the arrangement here: Heaven (Qian) is on the left as the Yang symbol, and Earth (Kun) is on the right as the Yin symbol. All of this originates from the central vertical line, which is both the Taiji and the two principles (two yi). One "Zhi" (solstice) gives rise to two "Fen" (equinoxes), with the spring equinox and autumn equinox dividing east and west, and the winter solstice and summer solstice marking the extremes of north and south. It is both one and two, and thus the yin and yang of the Book of Changes arise naturally. There is no need to add another sentence such as "Taiji gives rise to two yi," for this is precisely the original meaning of "The Book of Changes has Taiji, which gives rise to two yi."

端木氏此圖，似較舊說更為明顯。不名曰“太極圖”，更無語病。學者與前三圖合而觀之，“太極”二字之義，可瞭然矣。“太極”之上，無能更加以字者。惟孔子曰“《易》有太極”。“《易》有”二字，必須重讀，與《序卦》“有天地”“有萬物”諸“有”字，皆一氣貫注。孔子贊易，皆是從“有”立說，以示與老子之以“無”立說者不同。

The diagram of Duanshu Guohu seems clearer than previous interpretations; since it is not called the "Taiji Diagram," there is no grammatical error. Scholars can view this diagram together with the previous three diagrams, and the meaning of "Taiji" becomes clear. No other words can be added above "Taiji," for only Confucius said "The Book of Changes contains Taiji." The two characters "has" in "has Taiji" must be read with emphasis, and they are connected with the series of "has" in the "Xugua Zhuan" such as "has heaven and earth" and "has all things." Confucius praised the Book of Changes, always starting from the concept of "has," to show the difference from Laozi's approach which started from "nothingness."

故將“有”字直提至“太極”之上，曰“《易》有太極”，而全《易》之生生不已，皆由此“有”字以發生者也。繼之曰“是生兩儀”，此“是”字上貫“《易》有太極”四字，而下澈全章。全《易》六十四卦，皆以此一字作骨，故特於初、終二爻發明之。觀此知孔子贊《易》筆法，一字一義，無不與全書精神貫注，脈絡相通，未可滑口讀過也。

Therefore, Confucius elevated the character "有" (to have, to exist) directly above "太极" (the Ultimate Ultimate), saying "The Book of Changes has the Ultimate Ultimate." All the ceaseless generative principles of the entire Zhou Changes are generated from this single character "有." Then he says "from which the two principles arise." The character "是" (this, that) above inherits the meaning of the previous four characters "The Book of Changes has the Ultimate Ultimate," and below it connects with the entire passage. All sixty-four hexagrams of the Book of Changes take this character as their backbone. Therefore, Confucius deliberately pointed it out in the first line of the Qian hexagram and the top line of the Wei Ji hexagram, which mark the beginning and the end respectively. From this we can see the style of Confucius in commenting on the Book of Changes: each character has its own meaning, and none is disconnected from the spirit of the whole book or the logical flow. When reading, one must not pass it by carelessly.

《繫傳》曰“形而上者謂之道，形而下者謂之器”，太極者實超乎道與器之上，而立乎其先者也。故分言之。形而上者有太極，形而下者亦未始無太極也。故曰“天地一太極”。萬物各有其太極。後儒以太極為形而上者，是與形而下者對待，實失“太極”之本義也（老子曰：“無以名之，強名之曰道。”此道字與形而上之道意義不同。）。

The Great Treatise says, "What is above form is called the Way, and what is below form is called the thing." But the Supreme Ultimate actually transcends both the Way and the thing, and exists prior to them. Therefore, when considered separately: the level above form contains the Supreme Ultimate, and the level below form also contains the Supreme Ultimate. Thus it is said, "Heaven and Earth are a single Supreme Ultimate," and all things also have their own Supreme Ultimate. Later Confucian scholars regarded the Supreme Ultimate solely as what is above form, thus making it a counterpart to what is below form, which actually misses the original meaning of "Supreme Ultimate" (Laozi says, "It cannot be named; force it to be named, call it the Way," but the "Way" here is not the same as the Way above form).

是以天下之事事物物，凡有對待者，皆太極所生之兩儀，非太極也（今世科學家曰精神，曰物質，相對待者也，太極實超乎精神物質之上。曰空間，曰時間，相交午者也，太極實超乎空間時間之外。哲學主唯心論者謂一切唯心所造，主唯物論者謂科學萬能物質不滅。太極則超乎唯心唯物之上，而不可以唯心唯物概之者也。）。

Therefore, all things and matters in the world, whenever they can be presented as opposing aspects that depend on each other, are the two principles (yin and yang) generated by the Taiji. They are not the Taiji itself. (Today's scientists refer to spirit and matter as a pair of opposing concepts; in reality, the Taiji exists beyond both spirit and matter. Similarly, space and time are two intersecting axes, but the Taiji exists beyond space and time. Philosophers who advocate idealism claim that everything is created by the mind, while those who advocate materialism claim that science is omnipotent and that matter is eternal; however, the Taiji exists beyond both idealism and materialism, and cannot be summarized by either of these two perspectives.)

以質言之曰剛與柔，而太極超乎柔剛之外。以氣言之曰陰與陽，而太極立乎陰陽之先。以事理言之曰動與靜，曰善惡吉凶，而太極實幾於動靜善惡吉凶之微，無有而無不有，無在而無不在。《序卦傳》曰“盈天地之間唯萬物”，謂盈天地之間惟太極可也。此天地一太極也。小而至一塵之微，極至於微而不可見之物，亦莫不各具有動靜生滅之機，即莫不有其太極，此物各一太極也。

In terms of quality, there is hardness and softness, but the Taiji exists beyond hardness and softness; in terms of qi, there is yin and yang, but the Taiji exists prior to yin and yang; in terms of principles, there is movement and stillness, good and evil, auspicious and inauspicious, but the Taiji lies hidden in the subtle beginnings of movement and stillness, good and evil, auspicious and inauspicious, before they manifest. It is said to have no existence yet it is present everywhere; it is said to be absent yet it is everywhere present. The "Xugua Zhuan" states, "The fullness of the universe is only the myriad things." If it is said that what fills the universe is only the Taiji, that is also acceptable, which is "the universe is one Taiji." Even as small as a single grain of dust, or as minute as something invisible to the naked eye, each possesses the mechanism of movement and stillness, birth and death, and thus each has its own Taiji, which is "each thing has its own Taiji."

宋儒言太極，不離乎動靜陰陽，已落言詮。牽及五行，則更遠矣。朱子注《太極圖說》，謂“無靜不成動，無動不成靜。譬如鼻息，無時不噓，無時不吸。噓盡則生吸，吸盡則生噓。理自如此，陰陽只是一氣。陰氣流行即為陽，陽氣凝聚即為陰”。其論雖精，總未達一間。程子曰：“動靜無端，陰陽無始。非知道者，孰能識之？”然動靜無端而自有其端，陰陽無始而自有其始也。識此端與始，以言太極，庶乎近矣。

The Song dynasty Confucian scholars discussed the Taiji, always relating it to movement and stillness, yin and yang, which already falls into verbal explanation. When they further involved the Five Phases, they became even more distant. Zhu Xi commented on the "Taisi Tu Shuo" saying: "Without stillness, there can be no movement; without movement, there can be no stillness. For example, the nose breathing, there is always inhalation and exhalation without cease; when inhalation reaches its end, exhalation arises; when exhalation reaches its end, inhalation arises. This is the inherent nature of things. Yin and yang are merely one breath: when yin qi spreads out, it becomes yang; when yang qi condenses, it becomes yin." Although this discussion is precise, it still lacks one layer. Cheng Yi said: "Movement and stillness have no beginning, yin and yang have no origin. Who, except those who truly understand the Dao, can recognize it?" However, although movement and stillness are said to have no beginning, they do have their beginning; although yin and yang are said to have no origin, they do have their origin. Recognizing this beginning and origin, and then discussing Taiji, one is already close to the truth.

《繫傳》曰：“河出圖，洛出書，聖人則之。”《書·顧命》曰：“河圖在東序。”《論語》曰：“河不出圖。”《禮記·禮運》曰：“山出器車，河出馬圖。”鄭康成《易注》引《春秋緯》：“河以通乾出天苞，洛以流坤吐地符。河龍圖發，洛龜書成。河圖有九篇，洛書有六篇。”揚雄《旡靈賦》曰：“大《易》之始，河序龍馬，洛出龜書。”

The Great Treatise says: "The Yellow River produced the chart, and the Luo River produced the writing, and the sage followed them." The Book of Documents, Gu Ming, records "the Yellow River Chart was in the eastern hall," indicating that it was once displayed in the eastern chamber of the royal palace. The Analects records Confucius lamenting "the Yellow River does not produce the chart." The Book of Rites, Li Yun, says "mountains produce vehicles and instruments, and the Yellow River produces horse figures." Zheng Xuan's Commentary on the Changes cites the Spring and Autumn Writings, saying: "The Yellow River, through the communication of Heaven, produces the heavenly symbol, and the Luo River, through the flow of Earth, produces the earthly symbol. The Yellow River Chart arises with the dragon horse, and the Luo Writing is completed with the turtle book. The Yellow River Chart has nine chapters, and the Luo Writing has six chapters." This means that the Yellow River Chart communicates with Heaven and produces the heavenly mandate, while the Luo Writing flows through Earth and produces the earthly symbol, and the two are originally a pair of Heaven and Earth. Yang Xiong's Wu Ling Fu also says: "The beginning of the great Changes is the Yellow River's dragon horse and the Luo River's turtle book."

《漢書·五行志》劉歆曰：“伏犧氏繼天而王，受河圖則而畫之，八卦是也。禹治洪水，錫洛書而陳之，洪範是也。聖人行其道而實其真，河圖洛書，相為經緯；八卦九章，相為表裡。昔殷道弛，文王演《周易》。周道敝，孔子作《春秋》。則乾坤之陰陽，效洪範之咎徵。天人之道粲然著矣。”

The Han Shu's "Five Phases Chapter" cites Liu Xin's words: Fuxi received the mandate of heaven and became king, accepted the Yellow River Chart, and based on it he drew the trigrams, which are the Eight Trigrams. When Da Yu controlled the floodwaters, heaven bestowed the Luo Writing upon him, and based on it he arranged the categories, which is the "Hong Fan" Nine Categories. The sages promoted their teachings and implemented their truths. The Yellow River Chart and the Luo Writing form the vertical and horizontal threads, while the Eight Trigrams and the Nine Categories form the inside and outside. In the past, during the Shang dynasty, when the government became lax, King Wen developed the Zhou Changes; during the Zhou dynasty, when the government declined, Confucius wrote the Spring and Autumn Annals. One drew upon the yin and yang of Qian and Kun, the other verified the omens of the Hong Fan, thus the principle of the connection between heaven and humanity became clearly evident.

河圖洛書之見於經傳者如此，而其內容如何，則無可考。至宋初陳希夷氏，始有龍圖之數。邵康節因之，以五十五、四十五兩數，分為河圖洛書，當時頗多爭議。如范諤昌、劉牧諸氏，以四十五為河圖，五十五為洛書。漢上朱氏因之。朱文公從蔡季通之議，定十為河圖，九為洛書，以冠《本義》之首。更詳演其數，以入《易學啟蒙》，相傳至今。

The accounts of the Yellow River Chart and the Luo Writing found in classical texts are limited to these references. As for their actual content, it has become impossible to verify. It was not until the early Northern Song dynasty that Chen Tuan introduced the concept of "Dragon Diagram" numbers. Shao Yong continued this tradition, assigning the number fifty-five to the Yellow River Chart and forty-five to the Luo Writing. At that time, there was considerable controversy. For example, Fan Echanchang and Liu Mu argued that forty-five belonged to the Yellow River Chart and fifty-five to the Luo Writing, a view also followed by Zhu Zhen, the Han Shang Master. Later, Zhu Xi adopted the opinion of Cai Yuan ding, determining that the number ten belonged to the Yellow River Chart and nine to the Luo Writing. He placed these two diagrams at the beginning of the first volume of The Original Meaning of the Zhou Changes, and elaborately explained their numerical patterns in his work The Awakening of the Study of the Changes, a tradition that has continued to the present day.

復經丁易東、張行成、熊良輔，及勝清江慎修、萬彈峰諸氏之推演，義蘊畢宣。所謂神變化而行鬼神者，無不與易義悉相貫通，而《彖》、《象》所不可解者，亦得以數象相證而通其義。雖未敢謂此即為古之河圖洛書，而數理之神化，則固建諸天地而不悖，質諸鬼神而無疑，百世以俟聖人而不惑者也。

Later scholars such as Ding Yidong, Zhang Xingcheng, Xiong Liangfu, and Qing dynasty figures Jiang Yong (Shenxiu) and Wan Nianchun (Tansheng) further developed these ideas, and it was through their efforts that the deeper meanings were fully revealed. The statement in the Great Treatise that "the divine changes and moves like ghosts and spirits" is fully consistent with the principles of the Book of Changes; even those parts of the Commentary on the Judgment and Image Commentary that were previously difficult to understand could be clarified through the mutual verification of numbers and images. Although we cannot definitively say that this is the original Yellow River Chart and Luo Writing from ancient times, this system of numerical and logical transformations indeed stands in harmony with the heavens and earth without contradiction, and it can be verified against ghosts and spirits without doubt. Even if a sage appears a hundred generations later, he would not be confused by it.

自明季以來，言漢學者雖盡力攻擊，但只能爭河洛之名。而於其數，則無能置喙焉。欲探易道無盡之蘊，發千古神秘之局者，端在於是。乃舍其實而鶩其名，不亦慎哉！茲仍從《本義》、《啟蒙》之名，以五十五者為河圖，以四十五者為洛書，以便稱引。至陳希夷龍圖之說，義甚膚淺，故朱子疑為偽造。然其所謂龍圖者，分合之數皆五十有五，且明明曰龍圖不曰龜圖。劉牧之以九為圖十為書，是顯畔其師說矣。

Since the Ming dynasty, those who study Han learning have vigorously attacked the River Chart and the Luo Square, but they could only dispute over the names; regarding their numbers, they had no say. To explore the boundless depth of the I Ching and to reveal the ancient mystery, the key lies in these numbers. To abandon the substance and chase after the names, should we not carefully reflect? Therefore, we still use the names of The Original Meaning of the Zhou Changes and The Illumination of the Study of Changes, taking fifty-five numbers as the River Chart and forty-five numbers as the Luo Square, for reference. As for Chen Tuan's theory of the Dragon Chart, its meaning is very shallow, so Zhu Xi suspected it was fabricated. However, what he called the Dragon Chart, when separated or combined, always totals fifty-five, and clearly called it the Dragon Chart, not the Turtle Chart. Liu Mu, on the other hand, took nine numbers as the River Chart and ten numbers as the Luo Square, which clearly contradicts his master's teachings.

揚子《太玄》曰：“一六為水，二七為火，三八為木，四九為金，五十為土。一與六共宗（北），二與七為朋（南），三與八成友（東），四與九同道（西），五與五相守（中）。”按：揚子不言十者，五與五即十，太玄用九數，故置十不言。且數止於九，至十則復為一。故河洛以十為盈虛，亦數象關鍵之一。學者宜深思之。

Yang Xiong's "Tai Xuan" says: "One and six belong to water, two and seven to fire, three and eight to wood, four and nine to metal, five and ten to earth. One and six share the same origin (in the north), two and seven are companions (in the south), three and eight are friends (in the east), four and nine are on the same path (in the west), and five and five keep each other (in the center)." Hang's commentary states: Yang Xiong does not mention "ten" because five plus five equals ten; "Tai Xuan" uses nine as the key number, so it omits ten. Moreover, the counting stops at nine, and ten returns to one. Therefore, the He Tu and Luo Shu treat ten as the key to fullness and emptiness: the He Tu includes ten in its total of fifty-five, while the Luo Shu does not include ten in its total of forty-five. The difference lies here. This is a crucial point in numerical symbolism, and scholars should think deeply about it.

鄭康成氏曰：“天地之氣各有五。五行之次：一曰水，天數也。二曰火，地數也。三曰木，天數也。四曰金，地數也。五曰土，天數也。此五者，陰無匹，陽無耦，故又合之地六為天一匹也，天七為地二耦也，地八為天三匹也，天九為地四耦也，地十為天五匹也。”又曰：“布六於北方以象水，布八於東方以象木，布九於西方以象金，布七於南方以象火。”

Zheng Xuan said: The energies of heaven and earth each have five kinds. The order of the Five Phases is: one is water, belonging to the heavenly numbers; two is fire, belonging to the earthly numbers; three is wood, belonging to the heavenly numbers; four is metal, belonging to the earthly numbers; five is earth, belonging to the heavenly numbers. These five generating numbers have no counterparts on the yin side and no pairs on the yang side, so each is given a complementary number: the earthly six pairs with the heavenly one, the heavenly seven couples with the earthly two, the earthly eight pairs with the heavenly three, the heavenly nine couples with the earthly four, and the earthly ten pairs with the heavenly five. He also said: place six in the north to symbolize water, place eight in the east to symbolize wood, place nine in the west to symbolize metal, and place seven in the south to symbolize fire. The arrangement of the completed numbers in the four directions of the He Tu chart originates from this.

朱子曰：“此言天地之數。陽奇陰耦，即所謂河圖者也。中五為衍母，次十為衍子。次一二三四為四象之位，次六七八九為四象之數。二老位於西北，二少位於東南。其數則各以其類，交錯於外也。”按：此非言大衍之數，不必以衍母衍子相牽涉。而四象之數之位，亦為揲蓍得卦之用。於此言之，其義反窄矣。

Zhu Xi said: This passage discusses the numbers of heaven and earth. Yang is odd, and Yin is even, which is what is referred to as the Yellow River Chart. The central five is the mother of the great derivation number, and the next ten is the son of the great derivation number; then one, two, three, and four are the positions of the four images, while six, seven, eight, and nine are the numbers of the four images. The two "old" (old Yang and old Yin) are located in the northwest, and the two "young" (young Yang and young Yin) are located in the southeast. Their numbers are arranged alternately in the outer circle according to their categories. Hang氏 remarked: This passage is not actually discussing the great derivation number, so there is no need to involve the concepts of the mother and son of the derivation; the numbers and positions of the four images have separate uses during the process of divining by means of the yarrow stalks, and placing them here actually narrows the meaning of their significance.

《繫傳》曰：“天一，地二。天三，地四。天五，地六。天七，地八。天九，地十。天數五，地數五，五位相得而各有合。天數二十有五，地數三十。凡天地之數五十有五，此所以神變化而行鬼神也。”揚子《太玄》及鄭注所演其方位與生成之數，均極明晰。雖未繪為圖，已與圖無異矣。陳邵但按其說而圖之耳。

The Great Treatise says: "Heaven is one, Earth is two; Heaven is three, Earth is four; Heaven is five, Earth is six; Heaven is seven, Earth is eight; Heaven is nine, Earth is ten. The numbers of Heaven are five, the numbers of Earth are five. The five positions are paired two by two and each has its union. The total of Heaven's numbers is twenty-five, the total of Earth's numbers is thirty. The total numbers of Heaven and Earth together are fifty-five. It is because of this number that it can produce mysterious transformations and the movement of ghosts and spirits." The directions and the numbers of generation explained in Yang Xiong's Tai Xuan and in Zheng Xuan's annotations are already very clear; although they were not drawn into a diagram, they are essentially the same as if there were a diagram. Chen Tuan and Shao Yong merely drew them according to these statements. This shows that the content of the diagram was not created out of nowhere by the Song people, but was already present in the original texts.

五行之次，始見於《洪範》。而坎水、離火、乾金、巽木，均備載於《說卦》。經傳之互見者，更不勝枚舉。故毛西河雖攻擊河圖洛書之說最力，終不能蔑去此數，謂應改名曰“天地生成圖”。然其數之體用自在，名稱之同異，抑其末耳。

The order of the Five Phases first appears in the Shangshu · Hongfan. The associations of Kan as water, Li as fire, Qian as metal, and Xun as wood are also fully recorded in the Shuogua Zhuan. Examples of mutual reference between the classic text and its commentary are numerous. Therefore, Mao Qilin (Xihé) although most vigorously attacked the theories of the Yellow River Chart and the Luo Writing, could not erase this system entirely, and could only advocate renaming it as the "Heaven and Earth Generating Chart." However, the essence and application of this system have always existed. Whether the name is the same or different is merely a minor detail.

後儒有泥於“龍馬負圖”之文，謂此五十五數，馬體所生之旋毛。黑白五十五點，其陰陽匹耦如今圖，惟當繪圖點為旋毛形。於是有繪馬而寫圖於馬腹者，亦有將五十五點均改作旋毛形者。其拘泥附會，與漢學家之斷斷然徒爭其名稱者，同一蔽耳。更有泥圓方之說，將河圖一六二七三八四九之數，均作弧線成圓形，於義理並無出入，均可不必也。

Later scholars became fixated on the phrase "a dragon horse carried the diagram," claiming that the fifty-five numbers represented the spiraled hairs on a horse's body, with fifty-five black and white dots symbolizing yin and yang. They believed the diagram should be drawn in the form of these spiraled hairs. Some even drew a horse and inscribed the diagram on its belly, while others uniformly transformed the fifty-five dots into spiraled shapes. This kind of rigid and forced interpretation is no different from the Han scholars' insistence on names and arguments, which is a form of obstruction. Others were fixated on the idea of a round heaven and square earth, drawing the numbers 1 and 6, 2 and 7, 3 and 8, 4 and 9 in curved lines to form a circle. Although this does not contradict the meaning, it is entirely unnecessary to do so.

關子明曰：“洛書之文，九前一後，三左七右。四前左，二前右。八後左，六後右。”邵子曰：“圓者星也。曆紀之數，其肇於此乎？（《啟蒙》曰：曆法合三始以定剛柔，二中以定歷律，二終以紀閏餘。是所謂曆紀也。）方者土也，畫州井地之法，其仿於此乎？蓋圓者河圖之數，方者洛書之文，故羲文因之而造《易》，禹箕敘之而作《範》也。”

Guan Lang (Ziming) said: The arrangement of the Luo Book is nine in front, one at the back; three on the left, seven on the right; four in the front left, two in the front right; eight in the back left, six in the back right. Shao Yong said: The circular arrangement relates to celestial phenomena, and the numbers used in the calendar and year reckoning probably originated from this (The "Yixue Qimeng" says: The calendar combines the "three beginnings" to determine yin and yang, combines the "two middles" to determine the calendar and music, combines the "two endings" to record the leap months, which is what is called the calendar system). The square arrangement relates to the land, and the methods of dividing states and managing the well-field system probably imitate this. In general, the circular is the numbers of the He Tu, and the square is the text of the Luo Book, so Fuxi and King Wen used it to create the Book of Changes, and Great Yu and Ji Zi used it to compose the "Hong Fan."

《大戴禮·明堂篇》曰：“明堂者，古有之也，凡九室。二九四七五三六一八。”（其數及位均與此同。明堂九室，故亦稱九宮。）

The Great Dai Ritual Records · Bright Hall Chapter says: The Bright Hall system has existed since ancient times, consisting of nine rooms with numbers arranged in the order of two, nine, four, seven, five, three, six, one, and eight. (These nine numbers and their respective positions are exactly the same as the Luo Writing. Since the Bright Hall has nine rooms, it is also called the Nine Palaces.) This shows that the numbers of the Luo Writing were already embodied in the ancient architectural system.

《易乾鑿度》：“太一取其數以行九宮。”鄭注曰：“太一者，北辰神名也。下行八卦之宮，每四乃還於中央。中央者，北辰之所居，故謂之九宮。天數大分，以陽出，以陰入。陽起於子，陰起於午。

The "Yi Wei Qian Zao Du" says: "The Supreme One takes the numbers to move through the nine palaces." Zheng Xuan's commentary explains that the Supreme One is the name of the deity of the North Star, which moves downward through the palaces governed by the Eight Trigrams. Each time it completes four palaces, it returns to the center. The center is the dwelling place of the North Star, hence the term nine palaces. The heavenly numbers are generally divided into two paths: emerging with yang and returning with yin. Yang energy originates from the Zi position, while yin energy originates from the Wu position.

是以太一下九宮，從坎宮始。自此而從於震宮，自此而從於巽宮，所行半矣。還息於中央之宮，既又自此而從於乾宮，又自此而從於兌宮，又自此而從於艮宮，又自此而從於離宮，則周矣。上游息於太一之星，而反於紫宮。行起從於坎宮始，終於離宮也。”

Therefore, the Supreme One moves through the nine palaces, starting from the Kan palace (North 1), then moving to the Zhen palace (East 3), then to the Xun palace (Southeast 4). This covers half the journey, so it rests in the central palace (5). Then it moves to the Qian palace (Northwest 6), then to the Dui palace (West 7), then to the Gen palace (Northeast 8), then to the Li palace (South 9), completing the full circuit. Finally, it ascends to rest at the Supreme Star, returning to the Ziwei palace. The entire route begins at the Kan palace and ends at the Li palace.

九宮之色：一白，二黑，三碧，四綠，五黃，六白，七赤，八白，九紫，以次遞推。今《曆書》承用不廢，亦猶行古之道也。

The nine palaces are each associated with a specific color: one white, two black, three green, four green, five yellow, six white, seven red, eight white, and nine purple, following this sequence in a cyclic manner. Today's almanac still continues to use this system of flying stars' colors without abandoning it, which can be considered as following the ways of ancient people.

張平子曰：“臣聞聖人明審律曆，以定吉凶。重之以卜筮，雜之以九宮。經天驗道，本盡於此。且河洛六藝，篇錄已定。後人皮傅，無所容竄。律曆卦候，九宮風角，數有徵效，世莫肯學，而競稱不占之書。譬猶畫工惡圖犬馬而好作鬼魅，誠以實事難形，而虛偽不窮也。”觀此可見易象數理之學，在漢時已就式微。宜晉唐而後之言《易》者，失所師承。致悉棄實事，而專尚空談也。

Zhang Heng (Pingzi) submitted a memorial saying, "I have heard that sages carefully examine the laws and calendars, using them to determine auspicious and inauspicious signs, and also employ divination and the Nine Palaces; observing celestial phenomena and verifying the heavenly way, the fundamental principles are all contained here. Moreover, the River and Luo diagrams and the Six Arts have long been established, and later generations can only superficially interpret them, unable to insert false works. The studies of laws and calendars, hexagram atmospheres, seasonal changes, the Nine Palaces, and wind divination all have verifiable evidence and practical effects, yet people are unwilling to learn them, instead competing to praise those books that cannot predict events. This is like a painter who dislikes painting dogs and horses but prefers to paint ghosts and spirits, because real things are difficult to depict, while false things can be freely fabricated without limit." From this, we can see that the branch of the Yi school focusing on images and numbers had already declined in the Han dynasty; it is no wonder that after the Jin and Tang dynasties, those who studied the Yi lost their proper transmission, abandoning the practical aspects entirely and focusing solely on empty talk.

洛書之數，四十有五。與河圖相合，適為一百。凡一百之數，列為平方，對角分之，則一得五十有五，一得四十有五，此亦數理之自然，非人意可為增損其間也。故圖之與書，相為表裡，不能分析。或謂伏羲得河圖而畫卦，禹受洛書而演範，是言其取用之方。伏羲則圖畫卦，以圖為主。禹受書演範，以書為主。非伏羲時未嘗有書，大禹未嘗有圖也。

The total of the Luo Shu is forty-five, and when added to the fifty-five of the He Tu, they make exactly one hundred. If the number one hundred is arranged into a square with ten rows and ten columns, and then divided along the diagonals, one part will be fifty-five and the other forty-five. This is naturally the case in numerical reasoning, and human intention cannot alter it. Therefore, the He Tu and the Luo Shu are interdependent and cannot be considered separately. Some people say that Fuxi obtained the He Tu and used it to draw the trigrams, while Yu the Great obtained the Luo Shu and used it to elaborate the "Hong Fan" (the Nine Codes). This is merely referring to their respective emphasis: Fuxi mainly used the He Tu to draw the trigrams, taking the diagram as the main focus; Yu the Great mainly used the Luo Shu to elaborate the "Hong Fan," taking the text as the main focus. It does not mean that the Luo Shu did not exist in Fuxi's time or that the He Tu did not exist in Yu the Great's time.

朱子《啟蒙》曰：河圖洛書之位與數，其所以不同何也？曰：河圖以五生數，統五成數，而同處其方，蓋揭其全以示人，而道其常，數之體也。洛書以五奇數統四偶數，而各居其所。蓋主於陽以統陰，而肇其變，數之用也。

Zhu Xi's "Yixue Qimeng" presents a question and answer: Why do the Yellow River Chart and the Luo Writing differ in their directions and numbers? Answer: The Yellow River Chart uses five generating numbers to govern five completing numbers, with generating and completing numbers sharing the same direction (one and six are both in the north, two and seven both in the south, and so on). This presents the whole in one place for people to see, discussing the constant way, which belongs to the 'essence' of numbers. The Luo Writing uses five odd numbers to govern four even numbers, with odd and even numbers each occupying their own positions (odds are in the four cardinal directions and the center, evens in the four corners). This uses yang to govern yin, thus initiating change, which belongs to the 'function' of numbers.

曰：其皆五居中何也？曰：凡數之始，一陰一陽而已矣。陽之象圓，圓者徑一而圍三。陰之象方，方者徑一而圍四。圍三者以一為一，故參其一陽而圍三；圍四者以二圍一，故兩其一陰而為二，是所謂參天兩地者也。三二之合則為五矣，此河洛之數所以皆以五為中也。

Question: Why do both the Yellow River Chart and the Luo Writing take five as the central number? Answer: The beginning of numbers starts with one yin and one yang. The image of yang is round, with a diameter of one and a circumference of three; the image of yin is square, with a diameter of one and a circumference of four. For the circumference of three, taking one yang gives three; for the circumference of four, taking half of one yin gives two. This is what the "Sayings of the Hexagrams" refers to as "three in heaven and two on earth." When three and two are added together, it makes five, which is why both the Yellow River Chart and the Luo Writing take five as their central number.

數與位皆三同而二異。蓋陽不可易，而陰可易。成數雖陽，固亦生之陰也。河圖之一二三四，各居其五象本方之外。而二四六八者，又各因五而得數，以附於其生數之外。洛書之一三七九，亦居其五象本方之外。而二四六八者，又各因其類以附於奇數之側。蓋中者為主，而外者為實。正者為君，而側者為臣，亦各有條而不紊也。

The numbers and positions of the two systems have three points in common and two points that differ. This is because the yang cannot be changed, while the yin can be altered; the formed numbers, although belonging to yang, originally arise from the yin generating numbers. In the Yellow River Chart, the numbers one, two, three, and four each reside outside their respective five-element positions, and the numbers two, four, six, and eight are derived by adding to the central five, thus attaching themselves to the outer layer of the generating numbers. In the Luo Writing, the numbers one, three, seven, and nine also reside outside their respective five-element positions, while the numbers two, four, six, and eight are arranged according to their categories, attached to the sides of the odd numbers. The central numbers are primary, while the outer numbers are actual; those in the central positions are like a sovereign, and those in the side positions are like ministers, each with order and without confusion. This is the distinction between the Yellow River Chart emphasizing generation and the Luo Writing emphasizing odd and even.

曰：其多寡之不同何也？曰：河圖主全，故極於十，而奇偶之位均。論其積實，然後見其偶贏而奇乏也。洛書主變，數極於九，而其位於實，皆奇贏而偶乏也。必皆虛其中焉，然後陰陽之數，均於二十，而無偏耳。

Question: Why are the numbers different in quantity? Answer: The Yellow River Chart governs the whole, so the numbers go up to ten, with equal numbers of odd and even positions. However, when considering the actual total sum, even numbers have an excess while odd numbers are deficient (the sum of the even numbers two, four, six, eight, and ten is thirty, while the sum of the odd numbers one, three, five, seven, and nine is twenty-five). The Luo Writing governs change, so the numbers only go up to nine. When looking at the actual positions, odd numbers have an excess while even numbers are deficient. Only when the middle five voids are excluded do the numbers on both yin and yang sides each total twenty, achieving balance without excess or deficiency.

曰：其序之不同何也？曰：河圖以生出之次言之，則始下，次上，次左，次右，以復於中，而又始終下也。以運行之次言之，則始東，次南，次中，次西，次北。左旋一周，而又始於東也。其生數之在內者，則陽居左而陰居上右也。

Question: Why are the orders different? Answer: The Yellow River Chart, if considered according to the sequence of the generating numbers, starts with the lower (Northern one), then the upper (Southern two), then the left (Eastern three), then the right (Western four), then back to the center (five), and then starts again from the lower. If considered according to the order of movement, it begins with the East, then the South, then the Center, then the West, then the North, rotating to the left for a full cycle, and then starts again from the East. As for the generating numbers within, the Yang numbers are arranged on the left, while the Yin numbers are arranged on the upper and right sides.

洛書之次，其陽數，則首北，次東，次中，次西，次南。其陰數，則首西南，次東南，次西北，次東北也。合而言之，則首北，次西南，次東北，次中，次西北，次西，次東北，而究於南也。其運行，則水克火，火克金，金克木，木克土。右旋一周，而土復克水也。是亦各有說矣。

The order of the Luo Writing is based on the yang numbers: first north (one), then east (three), then center (five), then west (seven), and finally south (nine). Based on the yin numbers: first southwest (two), then southeast (four), then northwest (six), and finally northeast (eight). Combined, the order is first north, then southwest, then northeast, then center, then northwest, then west, then northeast, and finally south. As for its movement, water overcomes fire, fire overcomes metal, metal overcomes wood, wood overcomes earth, and earth then turns back to overcome water. This also has its own reasoning.

曰：其七八九之數不同何也？曰：河圖六七八九，既附於生數之外矣，以陰陽老少進退饒乏之正也。其九者，生數一三五之積也。故自北而東，自東而西，以成於四之外。其六者，生數二四之積也。故自南而西，自西而北，以成於一之外。七則九之自西而南者也，八則六之自北而東者也，此又陰陽老少互藏其宅之變也。

Question: Why are the numbers seven, eight, and nine different? Answer: Since the numbers six, seven, eight, and nine in the Yellow River Chart are attached outside the generating numbers, they represent the correct examples of yin and yang's old and young, advancing and retreating, abundance and scarcity. Among them, nine is the product of the generating numbers one, three, and five added together, so it moves from north to east, then from east to west, forming outside the number four. Six is the product of the generating numbers two and four added together, so it moves from south to west, then from west to north, forming outside the number one. Seven is nine coming from the west to the south, and eight is six coming from the north to the east. This is another example of yin and yang's old and young mutually hidden within each other's dwellings.

洛書之縱橫十五，而七八九六迭為消長。虛五分十，而一含九，二含八，三含七，四含六，則參伍錯綜，無適而不遇其合焉。此變化無窮之所以為妙也。又曰：乾無十者，有坤以承之。坤無一者，有乾以首之。（按：洛書偶數，當曰由東南次西南，次西北，次東北。朱子蓋未知陰數逆行，從四起也。）

The Luo Square has numbers that add up to fifteen both across and down, with the numbers seven, eight, nine, and six alternating in their increase and decrease. When the central number five is removed and the ten is split apart, it becomes one containing nine, two containing eight, three containing seven, and four containing six. Thus, the numbers three and five are interwoven, and no matter how they are combined, they can always form a harmonious number, which is the wonderful aspect of its infinite transformations. Zhu Xi also said: Heaven does not have ten, but Earth takes over; Earth does not have one, but Heaven starts it off. (Huang's note: The even numbers in the Luo Square should be said to go from Southeast to Southwest, then to Northwest, and then to Northeast. Zhu Xi probably did not know that the yin numbers move in reverse order, starting from four.)

蔡氏元定曰：古人傳記，自孔安國、劉向父子、班固，固皆以為河圖授羲，洛書錫禹。關子明、邵康節，皆以十為河圖，九為洛書。蓋《大傳》既陳“天地五十有五”之數，《洪範》又明言“天乃錫禹洪範九疇”。而九宮之數，戴九履一，左三右七，二四為肩，六八為足，龜背之象也。

Cai Yuanping said: The biographies of ancient scholars, from Kong Anguo, Liu Xiang and his son Liu Xin to Ban Gu, all held that the Yellow River Chart was given to Fuxi and the Luo Writing was bestowed upon Da Yu. Guan Lang and Shao Yong also regarded the number ten as representing the Yellow River Chart and the number nine as representing the Luo Writing. Since the Great Treatise states "the numbers of heaven and earth total fifty-five," and the Hongfan chapter clearly says "heaven bestowed upon Yu the Hongfan nine categories," while the nine palace numbers are arranged with nine at the top and one at the bottom, three on the left and seven on the right, two and four as shoulders, six and eight as feet, exactly resembling the pattern of a turtle's shell. There is supporting text on both sides, so it was determined that ten represents the chart and nine represents the writing.

劉牧以九為河圖，十為洛書，託言出於希夷。既與諸儒舊說不合，其易置圖書，並無明驗。其實天地之理，一而已矣。伏羲作《易》，不必預見洛書，而已逆與之合。大禹作《範》，不必追考河圖，而已暗與之符。誠以此理之外無他理故也。

Liu Mu took nine numbers as the Yellow River Chart and ten numbers as the Luo Writing, falsely attributing this to Chen Tuan. This contradicts the previous views of various scholars, and his alteration of the charts lacks clear evidence. In reality, the principle of heaven and earth is one: Fuxi composed the Book of Changes without needing to have seen the Luo Writing beforehand, yet naturally it coincided with it; and the Great Yu composed the Hongfan without needing to look back at the Yellow River Chart, yet naturally it corresponded with it. This is because there is no other principle beyond this one.

律呂有五聲十二律，而其相乘之數，究於六十。日有十干十二支，而其相乘之數，亦究於六十。二者皆起於《易》之後，其起數又各不同（按：聲律干支皆始於黃帝，其度數皆出於八卦。《周易》之《象》、《彖》、《爻》詞，根據於聲律干支者正多。故謂二者起於伏羲畫卦之後可也，謂起易後不可也。今之易周文王之易也。）。

There are five tones and twelve musical laws, and when these two are multiplied together, the ultimate number is sixty. The day branches consist of ten heavenly stems and twelve earthly branches, and when these two are combined, the ultimate number is also sixty. Both of these systems originated after the Book of Changes, yet their methods of counting differ. (Hang's note: Both musical laws and heavenly stems and earthly branches began with the Yellow Emperor, and their numerical systems are derived from the eight trigrams. The statements in the Image Commentary, the Commentary on the Judgment, and the Line Statements of the Zhou Changes all frequently refer to musical laws and heavenly stems and earthly branches. Therefore, it is acceptable to say that these systems originated after Fuxi created the trigrams, but it is not acceptable to say they originated after the Book of Changes; the Book of Changes referred to here is King Wen's version.)

然與《易》之陰陽策數多少自相配合皆為六十者，無不若合符契也。下至《運氣》、《參同》、《太一》之屬，雖不足道，（《運氣》、《參同》、《太乙》與《遁甲》、《六壬》皆出於易，皆說易之最精者。不明此而讀《彖》、《象》，爻詞不可解者多矣。舊儒皆以經學自大，以術數為小道，宜易道之終不能明也。蔡氏之說不免囿於積習，學者更不可囿其說以自域也。）然亦無不相通，蓋自然之理也。

However, they all correspond with the number of yin and yang lines in the Book of Changes, and they all amount to sixty, with no discrepancy at all, like a perfectly matching seal. Further down, works such as the "Yunqi" (On the Meridians), "Santongqi" (The Concordance of Three), and "Taiyi" (Supreme Oneness), which Cai believed were not worth mentioning (Hang noted: The "Yunqi," "Santongqi," and "Taiyi" along with "Dun Jia" and "Liu Ren" all originate from the Book of Changes, and are among the most refined interpretations of it. Without understanding these, there would be many difficulties in interpreting the Line Statements. Old scholars regarded classical texts as superior and considered divination techniques as minor pursuits, which is why the principles of the Book of Changes remained unclear. Cai Yuan Ding's view is inevitably limited by traditional habits, and scholars should not be confined by his opinion and set limits for themselves), in reality, they all connect with each other, which is a natural principle.

彭申甫曰：河圖，聖人嘆其不出而已。重典藏於柱下，史府固未嘗亡，適周蓋得見之。河洛之書，漢時猶存。《後漢書》：“楊厚字仲桓，廣漢新都人。臨命戒子統曰：吾娣表中有先祖所傳秘記。統感父遺言，從犍為周循學習先法，又就同郡鄭伯山受河洛書，及天文推步之術。”鄭氏所云九篇六篇，今皆無傳。

Peng Shenpu said: The Yellow River Chart, Confucius was merely lamenting that it no longer appeared. Such important classics were kept by the historian at the gatepost. The history office had never been lost, and when Confucius went to Zhou to inquire about propriety, he might have seen them. Books like the Yellow River Chart and the Luo Writing still existed in the Han dynasty. The "Book of the Later Han" records that Yang Hou, whose name was Zhonghuan, was from Guanghan Xindu. Before his death, he told his son Yang Tong that his sister's box contained secret records passed down by his ancestors. Yang Tong, moved by his father's last words, studied the methods of his ancestors with Zhou Xun from Jianren, and also learned the writings of the Yellow River and Luo River and the techniques of astronomical calculations from Zheng Boshan of the same county. As for the nine chapters of the Yellow River Chart and the six chapters of the Luo Writing mentioned by Zheng Xuan, they are all lost today.

大抵如緯書所傳，真偽參錯。《尚書·中候》曰：“帝堯即政七十載，修壇河洛，仲月辛日禮備至於日稷（按：稷、昃古通用字。豐“日盈則昃”，亦作稷。），榮光出河，龍馬銜甲，赤字綠色，臨壇吐圖。”顧野王玉符瑞圖，虞舜時洛水出黃龍，舜與三公臨觀，黃龍五采，負圖出舜前，頌聖瑞者，固多侈陳。

In general, the accounts found in the so-called "Wei Shu" are mixed with true and false elements. The "Shang Shu · Zhong Hou" states: Emperor Yao ruled for seventy years, and at the banks of the He and Luo rivers, he built an altar. On the 28th day of the second lunar month, he prepared the ceremonial rites. When the sun began to set (Hang notes: "Ji" and "Ze" were used interchangeably in ancient times; the "Feng" hexagram's "the sun reaches its fullness and then wanes" is also written as "Ji"), he saw a brilliant light rising from the river. A dragon horse emerged from the river, carrying a book with jade characters on a green background, and it presented the diagram before the altar. Gu Yewang's "Yu Fu Rui Tu" also mentions that during the time of Emperor Yu Shun, a yellow dragon appeared in the Luo River, and Yu Shun and his three ministers personally came to observe. The yellow dragon was of five colors, and it carried a diagram which appeared before Yu Shun. Such accounts praising the divine signs of sages are naturally full of elaborate descriptions.

然天生神物，不容終秘。洛書文得箕子演之，未聞有圖。河圖有數無文，得夫子繫《易》明著之，蓋有圖而亡於周末矣。歷千五百餘年，邵子因數演圖，因圖立說。雖云得之於陳希夷，實則河圖方位，本之《參同契》。洛書方位，本之《太一·九宮》。點畫陰陽，即揚子《太玄經》，及《漢書·五行志》而神悟變化，自符乎奇偶生成之體用，故朱子宗之，以冠全經。雖疑者猶多，終不可掩也。

However, the divine objects created by Heaven will not remain hidden forever. The Luo Writing contains characters, and King Ji Zi used them to compose the "Hongan Fan" (The Great Plan). But there is no mention of a diagram. The He Tu has numbers but no characters; it was only after Confucius composed the "Xici" (Great Treatise) that the numbers were clearly recorded. This shows that originally there was a diagram, which was lost during the late Zhou dynasty. After more than 1,500 years, Shao Yong deduced the diagram from the numbers and established a system based on it. Although he claimed to have received it from Chen Tuan, the positioning of the He Tu actually comes from the "Cantong Qi" (The Concordance of the Three), and the positioning of the Luo Writing comes from the "Taiyi · Jiugong" (The Great One · Nine Palaces). The division of black and white dots to represent yin and yang is based on Yang Xiong's "Tai Xuan Jing" and the "Wuxing Zhi" (Five Elements Chapter) in the "Hanshu" (Book of Han). From these, he intuitively grasped the principles of change, naturally aligning with the principles of odd and even numbers as both form and function. Therefore, Zhu Xi revered it and placed it at the beginning of the entire text. Although there are still many skeptics, they cannot ultimately obscure its significance.

萬氏彈峰《易拇·更正河圖洛書說》曰：“河圖洛書，邵子朱子闡發無餘蘊矣。但後人所傳，不無少差。如舊河圖一六居北，二七居南，三八居東，四九居西，五十居中，其點皆平鋪無兩折者，而十在中間分二五對置，便失其旨。

Wan Nian Chun (Tan Feng) in "Yi Mu · Correcting the Explanation of the Yellow River Chart and Luo Writing" says: The principles of the Yellow River Chart and Luo Writing have already been thoroughly explained by Shao Yong and Zhu Xi, leaving no further room for elaboration. However, the diagrams passed down by later generations contain some minor errors. For example, the traditional depiction of the Yellow River Chart places one and six in the north, two and seven in the south, three and eight in the east, four and nine in the west, and five and ten in the center. Originally, the points in each direction are arranged in a flat layout, not folded into two rows. Only the number ten in the center is split into two fives, arranged vertically above and below each other, thus losing the original meaning.

蓋河圖外方而內圓，一三七九為一方，其數二十也。二四六八為一方，其數亦二十也。中十五共五十五數，中十點作十方圓布，包五數在內。此外方內圓而五數方布在中者，中一圈，即太極圓形。外四圈分佈四方，為方形。十包五在內，仍然圓中藏方，方中藏圓；陰中有陽，陽中有陰之妙也。而十五居中，即洛書縱橫皆十五之數，是又河圖包裹洛書之象。

The River Chart is square on the outside and round on the inside: the numbers one, three, seven, and nine form one group, totaling twenty; the numbers two, four, six, and eight form another group, also totaling twenty; adding the central numbers ten and five, the total becomes fifty-five. The ten points in the center should be arranged in a circular pattern, with the five numbers contained within. This is called square outside and round inside, with the five numbers arranged in a square in the center. The central circle represents the round shape of the Taiji, while the outer four circles are arranged in the four directions to form a square. The ten contains the five, which again shows the principle of a circle containing a square and a square containing a circle, with yin containing yang and yang containing yin. The ten and five combine to make fifteen, which is exactly the number found in the Luo Square where the sums of the rows, columns, and diagonals all equal fifteen. This is the symbolic relationship of the River Chart enclosing the Luo Square.

河圖點皆平鋪無兩折，洛書亦然。舊洛書圖，二四六八皆兩折。不知河洛本二四六八，亦宜平鋪。洛書外圓而內方，圓者黑白共四十數。圓佈於其外，一三七九為一方，二四六八為一方，仍然河圖本體。此又圓中藏方，洛書包裹河圖之象，而中五又有方中藏圖之妙。

The points of the Yellow River Chart are all laid out flat without being folded into two rows; the Luo Writing should be the same. The traditional depiction of the Luo Writing shows the numbers two, four, six, and eight folded into two rows; but people do not realize that the numbers two, four, six, and eight originally belong to both the Yellow River Chart and the Luo Writing, and they should also be laid out flat. The Luo Writing is round on the outside and square inside: the outer circle contains a total of forty black and white numbers arranged in a circular pattern; within it, the numbers one, three, seven, and nine form one group, and the numbers two, four, six, and eight form another group, which remains the original structure of the Yellow River Chart. This again represents the image of a circle containing a square, with the Luo Writing enclosing the Yellow River Chart. In the center, the number five embodies the subtle aspect of a square containing a circle.

河圖已具洛書之體，洛書實有運用河圖之妙，因將圖書奇偶方圓交互表之以圖。漢劉氏云河圖洛書相為經緯，八卦九章相為表裡，此語自有傳授，非漢儒所能言也。”（二四六八當曰四二八六，萬氏亦未知陰數逆用之序也。）

The Yellow River Chart already contains the form of the Luo Writing, and the Luo Writing actually includes the subtle application of the Yellow River Chart. Therefore, Wan's method combines the odd and even numbers, as well as the square and circle, into a single diagram. In the Han dynasty, Liu Xin said that the Yellow River Chart and Luo Writing are like the meridians and parallels, and the Eight Trigrams and Nine Chapters are like the inside and outside. This statement has its own lineage of transmission, and is not something that ordinary Han Confucian scholars could come up with. (Hang's note: Wan's statement that 'two four six eight' should be 'four two eight six', showing that he still does not understand the reverse order of the yin numbers.)

萬氏之圖，較僅改形式而無意義者（如以河圖為旋毛形，洛書作龜坼形者是也。），自高一籌。然兩數之體用分合，固極明晰。不必改作，意自可見。惟初學得此，未始不可為觸目會心之一助，故特錄之。

Wan's diagram is naturally superior to those changes that merely alter the form without any real meaning, such as drawing the Yellow River Chart in a spiral shape or the Luo Writing in the form of turtle shell cracks. However, the numbers in both systems are already very clear in terms of their essential nature and application, so there is actually no need for such alterations; their meaning is self-evident. Nevertheless, for beginners who come across this diagram, it can serve as a helpful aid to understanding, so it is specially recorded here.

至兩圖之加減除乘，及進退變化之妙，除朱子《易學啟蒙》，邵子《皇極經世》外，有蔡西山之《經世節要》，張行成之《經世演義》、《易通變》，丁翼東之《衍翼》，胡滄曉之《周易函書》，江慎修之《河洛精蘊》，張楚鍾之《易圖管見》。推衍至詳，千變萬化，未能悉錄。

As for the addition, subtraction, multiplication, and division of numbers in the two diagrams, as well as the subtle changes and transformations, besides Zhu Xi's "Yixue启蒙" (Easy Enlightenment in the Study of the Changes) and Shao Yong's "Huangji Jingshi" (The Classic of the Supreme Ultimate), there are also Cai Yuanding's "Jingshi Jieyao" (Essentials of the Worldly Order), Zhang Xingcheng's "Jingshi Yanyi" (Explanations of the Worldly Order) and "Yitongbian" (Variations in the Changes), Ding Yidong's "Yanyi" (Derivative Wings), Hu Xu's "Zhouyi Hanshu" (Commentary on the Zhou Changes), Jiang Yong's "He Luo Jingyun" (Essence of the River and the Luo), and Zhang Chuzhong's "Yitu Guanjian" (Observations on the Diagrams of the Changes). These works elaborate on these topics with great detail, covering countless variations, which cannot all be listed here.

有以圖書配八卦者，多拘執牽滯，不能悉當。其實河圖為體，洛書為用。河圖即先天，洛書為後天。河圖為體而體中有用，洛書為用而用中有體。此即萬氏圖，中分圓分方，方含圓，圓又含方之意也。歷代數理、曆象、推步、占驗、醫學、風鑑諸家，均以洛書為用，其義悉本於易。前人罕有言者，茲特扼要略述如左。

Some people attempt to match the River Chart and the Luo Square with the Eight Trigrams, but their approaches are often rigid and forced, failing to be consistent everywhere. In reality, the River Chart represents the essence, while the Luo Square represents the application; the River Chart corresponds to the Earlier Heaven, and the Luo Square corresponds to the Later Heaven. The River Chart, as the essence, contains within it the application, while the Luo Square, as the application, contains within it the essence. This is precisely the meaning of the Wan Diagram, which divides the circle and the square, with the square containing the circle and the circle containing the square. Throughout history, various schools that deal with numerical principles, astronomy, calendar calculations, divination, medicine, and physiognomy have all used the Luo Square as the application, and their meanings are all based on the Book of Changes. The River Chart arranges the numbers of generation and transformation to establish the essence, while the Luo Square arranges the numbers of the nine palaces to initiate the application; one is still, the other is dynamic; both are indispensable. This point has rarely been discussed by previous scholars, so here I will briefly explain it.

洛書與河圖相異，驟視之似一六與三八未易，而二七四九乃互易其方者，實則惟一三五不動。一三五者，天陽之生數，不可動者也。《周易》乾用九，九即一三五之積數也。故易道扶陽而抑陰，非陽之有待於扶，而陰必於抑也。天地陰陽之數，理本如是。論其體，陽生於陰。言其用，則陰統於陽。

The Luo Book differs from the Yellow River Chart. At first glance, it seems that the pairs one and six, three and eight remain unchanged, while two and seven, four and nine have merely exchanged positions. In reality, only one, three, and five remain fixed. One, three, and five are the yang numbers generated by heaven; they cannot be moved. In the Qian hexagram of the Zhou Changes, the phrase "use nine" refers to the sum of one, three, and five. Therefore, the way of the Changes supports yang and restrains yin—not because yang truly needs support or yin really deserves suppression, but because the principles of yin and yang in heaven and earth are naturally so. In terms of essence, yang arises from yin; in terms of application, yin must be governed by yang.

如河圖之六合一為七，七陽也。二合七為九，九陽也。三合八為十一，一陽也。四合九為十三，三陽也。五合十為十五，五陽也。總數五十有五，亦陽也。洛書之對位，則皆陰也。一九合十，三七合十，二八合十，四六合十，總數四十，皆陰數也。而御之以中五，則縱橫上下交錯無不為十五，總數四十有五，皆陽數矣。

Looking at the Yellow River Chart: six and one combine to make seven, which is a yang number; two and seven combine to make nine, also a yang number; three and eight combine to make eleven, which reduces to one on the units place, also yang; four and nine combine to make thirteen, reducing to three, yang; five and ten combine to make fifteen, reducing to five, yang; the total is fifty-five, also a yang number. Now looking at the Luo Writing's opposite positions added together: one and nine make ten, three and seven make ten, two and eight make ten, four and six make ten, the total is forty, all yin numbers; but once the central five is used to govern them, the vertical, horizontal, and diagonal additions all result in fifteen, and the total becomes forty-five, which then turns entirely into yang numbers.

（此為以陽統陰，君子道長，小人道消，《周易》之大義也。觀天地生成之數，天數二十有五而地數三十，陽少陰多，故古今來恆苦治世少而亂世多。君子少而小人多。聖人參天兩地，建中立極，以五御十，化陰為陽，而以洛書四十五數為用。則天數二十有五，地數二十，陽多陰少，十數不見而潛藏於兩數相合之中。是小人皆化為君子，撥亂反正成燮理陰陽之功，其樞機悉在中。五與十五能御十，則君子道長。五不能御十，則君子道消。五十者，中孚也。故孔子“五十學易，可以無大過”。詳見《學易筆談》。）

This is the principle of governing yin with yang, where the way of the gentleman grows longer while that of the petty person diminishes, which is the great meaning of the Zhou Changes. Observing the numbers of the generation of heaven and earth, the number of heaven is twenty-five and that of earth is thirty. Yang is less and yin is more, so throughout history, the time of good governance has been few and the time of chaos has been many, and the number of gentlemen has been few while that of petty persons has been many. The sage takes the number of heaven as three and that of earth as two, establishing the center and the ultimate standard. Using five to govern ten, he transforms yin into yang, and employs the number forty-five of the Luo Writing: thus the number of heaven remains twenty-five, and that of earth becomes twenty, resulting in yang being more and yin less. The number ten no longer appears separately but is hidden within the combination of the two numbers. This is equivalent to transforming petty persons into gentlemen, rectifying disorder and achieving the harmonization of yin and yang. The key lies in the concept of 'center'. Five and fifteen can govern ten, thus the way of the gentleman increases; if five cannot govern ten, the way of the gentleman diminishes. The combination of five and ten is called 'zhongfu', meaning that five is in the center and can harmonize with ten. Therefore, Confucius said, 'At fifty, one can study the Zhou Changes and avoid great mistakes.' See the author's 'Notes on Studying the Zhou Changes' for details.

洛書之位，一居於北，與河圖同。此為萬數之本，不可動搖，《乾·文言》曰“確乎其不可拔”者此也。由北而東北，而東，而東南，本一二三四之數也。由西北，而西，而西南，而南，本六七八九之數也。古聖於此，但將二八兩數互易其位，遂成今日洛書之數。天地造化之機，陰陽變化之妙，悉在於此。略圖如下。

The Luo Shu arrangement has one at the northern position, the same as the He Tu. This is the fundamental principle of all numbers, unshakable. The "Zhen Yan" of the Qian hexagram says "firmly rooted and unmovable," referring precisely to this. From north to northeast, to east, to southeast, the numbers originally follow the sequence one, two, three, four; from northwest to west, to southwest, to south, they follow the sequence six, seven, eight, nine. The ancient sages based their arrangement on this structure, and only exchanged the positions of the numbers two and eight, resulting in the Luo Shu as we see it today: the northeast position changes from two to eight, and the southwest position changes from eight to two, exactly matching the form described as "nine at the top, one at the bottom, two and four as shoulders, six and eight as feet." The key to the workings of heaven and earth, the subtleties of yin and yang transformation, all lie in this single exchange. A simple diagram is provided below.

此二八兩數，其位之相易，尚易見也，前人亦有言之者。而暗中實為五十之變化，則未易知之，前人亦從無發明者。蓋二八位，在先天卦則巽震也，在後天卦則坤艮也。坤艮皆土，為五十之數。萬物皆生於土，皆歸於土。成始成終，而皆在於艮之一位矣（此須合先後卦位詳玩之）。

The numbers two and eight, when their positions are exchanged, are relatively easy to recognize, as predecessors have mentioned. However, in reality, this exchange is actually a transformation of five and ten, which is not easily understood, and predecessors have never discovered this. Originally, the positions of two and eight in the Earlier Heaven hexagrams are Xun and Zhen, while in the Later Heaven hexagrams they are Kun and Gen. Both Kun and Gen belong to the earth element, which corresponds exactly to the numbers five and ten. All things are born from earth and ultimately return to earth, beginning and ending in the position of Gen. (This point requires a careful consideration of the positions of Earlier Heaven and Later Heaven hexagrams together.)

巽震相易，故雷風恆之《象傳》曰“立不易方”，此言其未易之體也。易則為巽震，故風雷益之《彖傳》曰“自上下下”，曰“天施地生”，此即其已易後之用也。坤艮為謙，《謙·彖傳》曰：“天道下濟而光明，地道卑而上行。”曰：“天道虧盈而益謙，（風雷益）地道變盈而流謙，鬼神（二西南未申，八東北丑寅。西南為神極，東北為鬼藏。）害盈而福謙，人道惡盈而好謙。”《象》曰：“裒多益寡。”

In the Earlier Heaven arrangement, the trigrams Xun (Wind) and Zhen (Thunder) are exchanged, so the hexagram Heng (Duration) with the image of Thunder over Wind says, "Standing firm without changing direction," referring to the nature before change. Once change occurs, it becomes the hexagram Yi (Benefit) with the image of Wind over Thunder. Therefore, the Commentary on the Judgment of Yi says, "Benefiting those above and below," and also "Heaven spreads its virtue and Earth produces growth," which refers to the function after change. In the Later Heaven arrangement, the trigrams Kun (Earth) and Gen (Mountain) combine to form the hexagram Qian (Humility). The Commentary on the Judgment of Qian says, "The way of Heaven descends and brings brightness; the way of Earth is lowly yet ascends." It also says, "The way of Heaven reduces excess and benefits humility (this sentence corresponds to the image of Wind over Thunder in Yi), the way of Earth transforms excess into flow and benefits humility. The spirits (two in the Southwest, belonging to Wei and Shen; eight in the Northeast, belonging to Chou and Yin) harm excess and bless humility. The way of human beings detests excess and favors humility." The Image Commentary says, "Taking much and giving little."

凡此皆指二八兩位，陰陽變化之玄妙。先儒專就坤艮本卦之象以求其義，無論如何附會穿鑿，終不能字字著落也。此即《易》與河洛二數關合之證，亦即二八兩數易位之證。於此求《易》，則《易》彖象之辭，昔之所謂不可解者，亦可十解其五六矣（此理精深微妙，先儒未肯輕洩。邵子《皇極經世》但微露其機，學者宜潛心體會，勿忽視焉。）。

All these discussions concern the subtle transformations of the numbers two and eight, representing yin and yang. Earlier scholars focused solely on the images of the hexagrams of Kūn (Earth) and Gèn (Mountain) to seek meaning, but no matter how they interpreted or forced connections, they could never fully apply the meanings to each word. This is clear evidence of the connection between the Book of Changes and the River and Lake number systems, and also evidence of the interchangeability of the numbers two and eight. By understanding this, one can now interpret the phrases from the Commentary on the Judgment and the Image Commentary, which were previously considered difficult to understand, and now can be resolved to a large extent. This principle is profound and subtle; earlier scholars did not easily reveal it. Shao Yong's "Huangji Jingshi" only slightly hinted at the key, so scholars should deeply study and reflect on it, without being careless.

其兩圖位次，五行順逆生克之序，舊說甚詳，亦淺而易，茲不贅述。惟洛書五行之次，既悉與後天八卦相符，而河圖之四方與中央，亦悉本生生之義，正不必牽扯補湊為也。

As for the positions in the two diagrams, and the order of the Five Phases moving forward or backward, as well as their mutual generation and control, old explanations are detailed and easy to understand, so there is no need to repeat them here. It is only necessary to know that the order of the Five Phases in the Luo Book completely corresponds with the Later Heaven Trigrams, and the four directions and the center in the He Diagram are entirely based on the principle of continuous generation. Therefore, there is no need to involve further fabrication or combination.

孔子曰“河出圖，洛出書，聖人則之”。古籍殘闕，既無從取證，此所謂河圖洛書者，未必為當日所取則之河圖洛書。但其奇偶相得之數，必為天一天二之五十五數。雖有蘇張之舌，決不能指其為非者也。其數之悉符於易象，順逆變化之與天地同流。亦雖有蘇張之舌，不能辨其為否者也。

Confucius said, "When the Yellow River produced the chart and the Luo River produced the book, the sage took them as models." However, ancient texts are incomplete, and there is no way to verify them. What is now called the Yellow River Chart and the Luo Writing may not be exactly the same as the ones the sage took as a model. But the numbers which pair odd and even must certainly be the fifty-five numbers derived from the sequence "Heaven one, Earth two" in the Great Treatise. Even with the eloquence of Su Qin and Zhang Yi, one could not deny this. These numbers are consistent with the imagery of the Book of Changes, and their reversals and transformations correspond with the movement of heaven and earth. Again, even with the eloquence of Su Qin and Zhang Yi, one could not argue against them. In other words, the chart may not be the exact one from ancient times, but the numbers must certainly be the same set as in ancient times.

然則非則圖以畫卦，必則卦以畫圖，所謂相為表裡者也。愚以為龍馬負圖，乾龍坤馬，即乾坤也。靈龜吐書，戴九履一，即坎離也。後人不察，必求龍馬以實之，泥龜形而坼之，不亦傎乎！

So if that is the case, then if one does not take the diagram to draw the hexagrams, one must take the hexagrams to draw the diagram. This is what is meant by being mutually explanatory. I think that "the dragon and horse carrying the diagram" refers to the hexagrams Qian and Kun, since dragon belongs to Qian and horse belongs to Kun. "The spiritual turtle spitting out the book" refers to the hexagrams Kan and Li, since it is said that "nine is on top and one is below." Later people failed to observe carefully, insisting on finding a real dragon and horse to confirm it, and being stuck to the shape of the turtle, cutting the diagram into pieces. Is this not a complete reversal?

二五之精，妙合而凝，實為萬物生化之源。而二八易位，即二五構精之妙用也。古今丹家千言萬語譬喻百端，皆以玄機隱秘，終不肯一語道破，皆由不知圖書易象，早已顯示其端。

"The essence of two and five, mysteriously combining to form a condensation," is indeed the root of the generation and transformation of all things; and the exchange of positions between two and eight precisely represents the subtle function of the union of two and five to form the essence. Throughout history, alchemists have written countless words and set up hundreds of metaphors, all because they regarded the secret as hidden, never willing to reveal it in one sentence. In reality, it is because they did not know that the River Chart and the Luo Square, along with the images of the Book of Changes, have already revealed the beginning of this principle.

學者畏難苟安，不肯從易學根本下手，致枉費心血，暗中摸索，千古長夜。有白首無成者，有終身由之而莫明其妙者，良可慨矣！茲復繪二五構精圖如下，明白淺顯。無論何人，皆可一目瞭然矣。幸勿因其淺近，且得之太易而忽視焉。

Scholars fear difficulty and seek comfort, unwilling to start from the fundamental aspects of easy study, leading them to waste their efforts in blind exploration, as if living in eternal darkness. Some grow old with nothing to show for it, while others follow it all their lives yet never grasp its true essence. It is truly lamentable. Therefore, here I draw another diagram called "The Diagram of the Essence of Two and Five" below, drawn clearly and simply so that anyone can understand it at a glance. I hope people will not look down upon it just because it is simple and easily obtained.

周濂溪《太極圖說》曰：“二五之精，妙合而凝。”《通書》曰：“二氣五行，化生萬物。五殊二實，二本則一，是為萬一。一實萬分，成一各正。”此數語實扼陰陽變化之要，宜注意焉。

The "Taisi Tu Shuo" by Zhou Dunyi says: "The essence of two and five combine in a subtle way and solidify." In his "Tong Shu," he also says: "The two energies and the five phases transform to generate all things. The five are distinct but the two energies are real. The two energies, when traced to their root, are one Taiji. Therefore, all things return to their root as one principle. One principle disperses into myriad differences, and each thing realizes its own oneness and corrects its destiny." These words really grasp the key to the transformation of yin and yang, and should be given particular attention.

（二實者，天以陽生萬物，地以陰成萬物。動而陽，靜而陰，陽變陰合而生五氣，由五氣而生萬物，故曰“五殊”也。五殊本於陰陽，互為其根也。兩儀生，而陽交於陰，陰交於陽而生四象，四象分而生八卦，八卦錯而萬物生焉。是曰“一動一靜，天地之至妙歟”，是以五氣布四時行，萬物生生而無窮，“五行一陰陽也，陰陽一太極也”。太極散而為萬物，則萬物各一其性，各具一太極，渾然全體而靜者，常為主焉。兼有無全體，用涵動靜，為萬化之源，萬有之本者，妙合二五之精焉。）

The so-called "two realities" refer to the fact that heaven generates all things through yang energy, and earth completes all things through yin energy. Motion is yang, stillness is yin; yang changes and yin combines to produce the five elements, which in turn generate all things. Therefore, it is said "five distinct aspects." The five distinct aspects originate from yin and yang, which are each other's root. When the two principles (yin and yang) come into being, yang interacts with yin and yin interacts with yang to produce the four images. The four images further divide to produce the eight trigrams, and the eight trigrams intermingle to give rise to all things. This is what is meant by "one motion and one stillness, the ultimate subtlety of heaven and earth." Thus, the five elements are arranged, the four seasons operate, and all things continuously generate without end. "The five elements are one aspect of yin and yang, and yin and yang are one aspect of the Taiji." The Taiji disperses to become all things, and each thing possesses its own nature and contains its own Taiji. The whole and complete, ever still, is the sovereign. The comprehensive encompassing both existence and non-existence, its function includes both motion and stillness, is the source of all transformations and the fundamental basis of all existence. This is how the phrase "subtle combination and coagulation" is made concrete.

原數左五六而右三二，數偏倚而不平。雖有中五，無從化生。以二五交易其位，則左右皆八。《謙·象》曰：“君子以裒多益寡，稱物平施。”謙為坤艮二八之位。二八交易，即二五交易也。二八合十為土，二五亦合十為土，陰陽生化，因以不窮。數似淺而義蘊極深，二千年來無人道破。會於此用苦功者，必當悉著者之苦心也。

The original numbers have five and six on the left, and three and two on the right, making the weights on both sides uneven and unbalanced; although there is a five in the middle, it cannot initiate transformation and generation. If we exchange the positions of two and five, both sides will become eight. The Image Commentary of the卦 of Humility says: "The superior man uses the method of reducing excess and supplementing deficiency, measuring things and giving fairly." This refers precisely to this principle. The卦 of Humility is composed of the Earth and the Mountain, and it concerns the second and eighth positions; exchanging the second and eighth positions is equivalent to exchanging the second and fifth. The combination of two and eight makes ten, which belongs to earth; the combination of two and five also makes ten, which belongs to earth: thus yin and yang generate endlessly. This number seems simple, but its meaning is profound, and for two thousand years no one has explained it. Those who have worked hard here will surely understand the author's sincere intention.

《周易》八卦方位之有先天後天，雖始於有宋，然推之於數而悉符，求之於象而胥合，證之於《彖》、《象》十翼，而確有可據。是乃易象之所固有，不但《周易》為然，即《連山》、《歸藏》，其經卦別卦既同，恐亦不能有用而無體，有後天而無先天也。

The eight trigrams of the Zhou Changes are arranged in directions according to the Earlier Heaven and Later Heaven systems. Although this classification began in the Song dynasty, when using numbers to calculate, everything fits perfectly; when using images to seek meaning, each corresponds exactly; and when verifying with the Ten Appendices such as the Commentary on the Judgment and the Image Commentary, there is indeed solid evidence to support it. This shows that these concepts were originally part of the divination images of the Zhou Changes. Not only does the Zhou Changes follow this pattern, but also the Lianshan and Guicang, since their three-line primary trigrams and six-line compound trigrams are the same as those in the Zhou Changes, it is likely that they also had both the Earlier Heaven and Later Heaven systems, not only using them but also having their fundamental principles.

漢《易》雖鮮傳書，然如荀氏慈明之升降，虞氏仲翔之納甲，取象於先天卦位者甚多。自朱子本者甚多，而《參同契》尤先後天並用，特未立此先天後天之名目耳。自朱子《本義》，以邵子先後天八卦方位各圖，弁諸經首，遂開後儒攻擊之門。明清以來言漢學者，以排詆宋學為先，乃波及於邵子。

Although few specialized works on the study of the I Ching from the Han dynasty have survived, many concepts such as the rising and falling explained by Xun Shuang (Ciming) and the stem assignment explained by Yu Fan (Zhongxiang) are based on the Earlier Heaven trigram positions. After Zhu Xi, many scholars based their interpretations on the Earlier Heaven trigram positions, and the Shentongqi especially uses both Earlier Heaven and Later Heaven trigrams, though it does not explicitly use the terms "Earlier Heaven" and "Later Heaven." Since Zhu Xi's Zhou Yi Benyi placed the diagrams of the Earlier Heaven and Later Heaven trigrams at the beginning of each chapter, it opened the door for later Confucian scholars to criticize. From the Ming and Qing dynasties onwards, those who studied the Han tradition regarded opposing the Song tradition as the top priority, and thus Shao Yong also suffered as a result.

實則宋季項氏安世，早有平論。謂河洛卦象，體用分明，悉出理數之自然，無可攻擊。所以遭後世之非議者，只以立名未當耳。故謂天地定位為伏羲八卦可也，謂帝出乎震為文王八卦，未免無據。蓋伏羲畫卦，體用一源，當然先後天並有，不能至文王而始有此八卦之用也。

In fact, Xiang Anshi in the late Southern Song dynasty had already made a fair comment: he believed that the River and Lake (He Luo) and the trigrams are clearly distinguished in terms of their principles and applications, arising naturally from reason and numbers, and thus cannot be attacked. The reason they were criticized by later generations is only because their names were improperly established. Therefore, saying that "Heaven and Earth are positioned" belongs to the trigrams of Fuxi is acceptable; but saying that "The Emperor arises from the震 (Zhen)" belongs to the trigrams of King Wen is without sufficient basis. Because when Fuxi drew the trigrams, the principles and applications arose from the same source, so the Earlier Heaven and Later Heaven trigrams both existed naturally. It was impossible for the applications of these trigrams to begin only with King Wen.

故後儒有改伏羲八卦為天地定位圖，改文王八卦為帝出乎震圖者，自較舊名為佳。但改伏羲與文王之名可也，至先天後天之名，則不可改。《序卦》定名，與《彖》、《象》、《繫辭》之明言先後天者甚多，不但“先天而天弗違，後天而奉天時”二語，足為先後天之證也。

Therefore, later people changed the Fuxi Eight Trigrams diagram to be called the "Diagram of Heaven and Earth Positioned" and the Wen Wang Eight Trigrams diagram to be called the "Diagram of the Emperor Emerging from Zhen," which are better names than the old ones. However, it is acceptable to change the names of Fuxi and Wen Wang. As for the terms "Earlier Heaven" and "Later Heaven," they should not be altered. The "Preface to the Sequence of Hexagrams" gives the name "Earlier Heaven" and "Later Heaven," and there are many explicit mentions of "Earlier Heaven" and "Later Heaven" in the "Commentary on the Judgment," "Image Commentary," and "Great Treatise." Not only does the "Wenyan" of the Qian hexagram mention "Earlier Heaven and Heaven does not violate, Later Heaven and it follows the timing of Heaven," which can serve as evidence for the concept of Earlier Heaven and Later Heaven. This shows that the idea of Earlier Heaven and Later Heaven was not fabricated by the Song dynasty scholars.

吳喬《他石錄》謂乾卦先天之先讀去聲，非邵子所謂先天之先，是真世儒之見。孔子贊《易》之時，豈有沈約四聲之譜，已傳異音別義之說哉！《彖》、《象》，《文言》、《繫辭》，無不有韻，分陰分陽，細入毫芒，獨未嘗有異讀改義之例。

Wu Qiao's "Ta Shi Lu" says that in the "Wenyan" of the Qian hexagram, the character "xian" in "Xian Tian" is read in the falling tone, which is not the same as Shao Yong's "Xian Tian." This is truly the view of a vulgar scholar. When Confucius praised the Book of Changes, there was no Shen Yuo's four-tone system in place, and the idea of different pronunciations leading to different meanings was already widespread. None of the "Tuan Zhuan," "Xiang Zhuan," "Wenyan," and "Xi Ci" do not have rhyming, and the distinction between yin and yang is refined to the finest detail, yet there is not a single instance of changing pronunciation to alter meaning.

漢學家博考群籍，亦明知乾坤坎離之先後體用，極陰陽造化之妙，無可非難。於是又遁其辭，指為外道，曰希夷仙也，不妨以外道說《易》。邵子交於二程，何可出此？

Western scholars have thoroughly examined various texts and are well aware that the principles and applications of the trigrams Qian, Kun, Kan, and Li in the Later Heaven arrangement have fully exhausted the subtleties of yin and yang's creative transformations. Therefore, they should not be criticized. However, they resort to another set of evasive arguments, labeling it as an external doctrine, and claim Chen Tuan was a supernatural being and a Taoist priest, thus justifying the use of external doctrines to explain the Book of Changes. But how could Shao Yong, who had close discussions with the two Cheng brothers, engage in such behavior?

“考亭于丹道有所見，是以手注魏伯陽之《參同契》。見邵之圖，欣然會心，入於《本義》，而不計丹道可以倚《易》，《易》不為丹道作也”云云，是非但昧禮失求野之義，且聲聲言易，與易道之相去遠甚。博學雄辯，適見其客氣之盛。茲編去取，一本經傳，準之象數。門戶異同之見，概所不取。

They also say: "Zhu Xi had some understanding of the alchemical practices, so he personally annotated Wei Boyang's Treatise on the Concordance of the Three; upon seeing Shao Yong's diagrams, he was delighted and included them in his 'Original Meaning,' but he did not consider that alchemy can be based on the Book of Changes, yet the Book of Changes was not written for alchemy." Such remarks not only fail to understand the principle of "when rites are lost, seek them in the wild," but also constantly talk about the Book of Changes while being far from its true way. Though they are learned and eloquent, they precisely reveal an excessive display of ambition. The selection and rejection in this book are all based on the classics and their transmitted texts, with the principles of figures and numbers as the standard. All preconceived notions about different schools of thought are entirely rejected.

《說卦傳》曰：“天地定位，山澤通氣。雷風相薄，水火不相射。數往者順，知來者逆。八卦相錯。是故易，逆數也。”

The Sayings on the Trigrams states: Heaven and Earth establish the positions of above and below, mountains and marshes communicate through their energies, thunder and wind interact with each other, and water and fire do not dislike or extinguish each other. Counting the past is in order, knowing the future is in reverse, and the eight trigrams interconnect with each other. Therefore, the Book of Changes is a study of reverse reasoning. This chapter provides the textual basis for the arrangement of the Earlier Heaven Trigrams: Heaven and Earth determine the positions of above and below, mountain and lake communicate through their energies, thunder and wind interact, water and fire face each other, and the eight trigrams are paired and interwoven to function together.

（胡東樵《易圖明辨》曰：按此章與八卦之位無涉。天地定位言乾坤自為匹也，山澤通氣言艮兌自為匹也，雷風相薄言震巽自為匹也，水火不相射言坎離自為匹也，云云。夫《說卦傳》本文明明曰“天地定位”，而曰“與位無涉且自為匹”者，無位又安見其相匹乎？其恣意辯駁，不顧前後如此。）

Hu Wei (Dongqiao) in his work "Yitu Mingbian" says: This chapter has nothing to do with the directions of the Eight Trigrams. "Heaven and earth are positioned" refers to Qian and Kun forming a pair by themselves, "Mountains and marshes communicate with each other" refers to Gen and Dui forming a pair by themselves, "Thunder and wind contend with each other" refers to Zhen and Xun forming a pair by themselves, "Water and fire do not shoot at each other" refers to Kan and Li forming a pair by themselves, and so on. However, the text of "Shu Guan Zhuan" clearly states "Heaven and earth are positioned," yet he says it has nothing to do with directions and is only about each pair forming by themselves; without any position, from where can one see that they are paired with each other? He argues arbitrarily, contradicting himself so much.

邵子曰：“此一節明伏羲八卦也。八卦相錯者，明交錯成六十四卦也。數往者順，若順天而行，是左旋也。皆已生之卦也，故曰數往也。知來者逆，若逆天而行，是右行也。皆未生之卦也，故云知來也。夫易之數由逆而成矣。此一節直解圖意，若逆知四時之謂也。”

Shao Yong said: This section discusses the Eight Trigrams of Fuxi. The phrase "the eight trigrams are interwoven" means that the eight trigrams are combined to form the sixty-four hexagrams. "To count the past is to go with the natural order" is like moving in accordance with the heavenly timing, turning to the left, counting the hexagrams that have already been formed, hence called "counting the past"; "to know the future is to go against the natural order" is like moving against the heavenly timing, turning to the right, pushing forward the hexagrams that have not yet been formed, hence called "knowing the future." The numbers of the Book of Changes are established through reverse reasoning. This section directly explains the meaning of the Earlier Heaven diagram, just as reversing to know the four seasons.

（以次序觀之有乾一而後，有兌二。有兌二而後、有離三震四，而巽五坎六艮七坤八亦以次而生。自圖之左方，震之初為冬至，離兌之中為春分，以至於乾之求而交復。至焉，皆逆而得其已生之日。因自今日而追逆昨日也，故曰“數往者順”。

Looking at the order, first comes Qian one, then Dui two; after Dui two comes Li three and Zhen four, followed by Xun five, Kan six, Gen seven, and Kun eight in sequence. Observing the left half of the diagram, Zhen begins at the winter solstice, between Li and Dui is the spring equinox, and it continues until reaching the end of Qian, where it meets Fu hexagram. All numbers counted up to this point are traced backward to determine past days, just as going back from today to yesterday. Therefore, it is said, "counting the past is in the order of progression."

其右方自巽之初為復，至坎艮之中為秋分。艮至於坤之末而交姤。至焉，皆進而得其未生之日。因自今日而逆訃來日也，故曰“知來者逆”也。按：此但以言邵子之數，至《說卦》所言蘊義甚廣，實不僅此。朱子僅取邵說，故攻擊之者謂取《十翼》為先天卦註腳。然先天圖豈邵子私有哉！）

The right half of the diagram starts from the beginning of Xun (here the original text marks it as "Fu"), proceeding to between Kan and Gen, which corresponds to the autumn equinox. From Gen to the end of Kun, it meets at Guo. Any count reaching here refers to days yet to come, pushing forward from the present, just as predicting tomorrow from today. Therefore, it is said, "knowing the future requires moving backward." Hang's commentary states: this is only referring to Shao Yong's system of numbers. As for the profound meanings discussed in "Shuo Gua," they are extremely vast and extend far beyond this. Zhu Xi only adopted Shao Yong's view, so critics accused him of treating the Ten Wings as annotations to the Earlier Heaven diagram. However, is the Earlier Heaven diagram not a private possession of Shao Yong alone?

邵子《觀物外篇》曰：“震始交陰而陽生，巽始消陽而陰生。兌陽長也，艮陰長也。震兌在天之陰也，巽艮在地之陽也。故震兌上陰而下陽，巽艮上陽而下陰。天以始生言之，故陰上而陽下，交泰之義也。地以既成言之，故陽上而陰下，尊卑之義也。乾坤定上下之位，離坎列左右之門。天地之所闔闢，日月之所出入。是以春夏秋冬，晦朔弦望，晝夜長短，行度盈縮，莫不由乎此矣。”

Shao Yong's "Outer Chapters on Observing Things" says: Zhen is the beginning of Heaven interacting with Yin and the initial emergence of Yang energy; Xun is the beginning of Earth diminishing Yang and the initial emergence of Yin energy. Dui is Yang increasing, and Gen is Yin increasing. Zhen and Dui belong to Yin within Heaven, while Xun and Gen belong to Yang within Earth. Therefore, the top line of Zhen and Dui is Yin while the lower lines are Yang; the top line of Xun and Gen is Yang while the lower lines are Yin. From the perspective of Heaven's initial emergence, Yin is above and Yang is below, reflecting the meaning of mutual harmony and transformation. From the perspective of Earth's completion, Yang is above and Yin is below, reflecting the meaning of hierarchy and respect. Qian and Kun determine the positions of above and below, Li and Kan form the left and right gates, and thus the heavens and earth open and close, and the sun and moon rise and set. Therefore, the four seasons, the phases of the moon, the length of day and night, and the movement and changes of celestial bodies all originate from here.

（《朱子語類》曰：先天圖直是精微，不起於邵子。希夷以前元有，只是秘而不傳，次第是方土輩所相傳授。《參同契》所言，亦有些意思。）

Master Zhu said: The Earlier Heaven diagram is very subtle and profound, and it did not originate from Shao Yong; in fact, it originally existed before Chen Tuan, but was kept secret and not passed down. It was mostly transmitted through generations by alchemists. The discussions in the Treatise on the Integration of the Three Teachings also convey a similar meaning.

先天八卦，以乾坤坎離為四正，震巽艮兌為四維。四正者，所以立體。故河圖之位，亦只列四方。乾坤坎離者，即天地水火（以曆象言，離坎亦為日月。）。水火者，天地之大用。合天地水火，而萬象無不畢舉矣。釋氏言地水火風，西儒言水火土氣，亦即乾坤坎離也（坎水離火。地即土，天即氣也。釋氏言風，風亦為氣也。）。

The Earlier Heaven Trigrams take Qian and Kun as the two main trigrams, and Kan and Li as the four cardinal directions. The four main trigrams are used to establish the fundamental principles, so the Yellow River Chart only marks the four cardinal directions. Qian, Kun, Kan, and Li represent Heaven, Earth, Water, and Fire. If we consider them from the perspective of the calendar and celestial phenomena, Kan and Li also represent Water and Fire, which are the greatest functions of Heaven and Earth. When Heaven, Earth, Water, and Fire are combined, all phenomena are complete. Buddhism speaks of Earth, Water, Fire, and Wind, while Western scholars speak of Water, Fire, Earth, and Air. In reality, these are all the same as the four trigrams of Qian, Kun, Kan, and Li. Water and Fire correspond to Kan and Li, Earth corresponds to Earth, and Heaven corresponds to Air. The Wind mentioned by Buddhism also belongs to Air. Therefore, when discussing the fundamental elements of the universe, both Eastern and Western traditions ultimately cannot escape these four trigrams.

邵子所謂震始交陰而陽生者，謂乾與坤接，而震一陽生於下。《參同契》曰：“三日出為爽，震庚受西方。”言三日之夕，月見庚方，納震一陽之氣也。巽始消陽而陰生者，謂坤與乾交，而巽一陰生於下。《參同契》曰：“十六轉就統，巽辛見平明。”言十六日月旦月退辛方，納巽一陰之氣也。

Shao Yong said, "Zhen begins to meet Yin and Yang is born," referring to the union of Qian and Kun, with the first Yang line of the Zhen hexagram arising at the lower line. The "Three Days' Auspiciousness" in the "Cantong Qi" says, "Three days after the moon appears, Zhen and Geng receive the western direction," referring to the evening of the third day of the lunar month when the new moon appears at the Geng position (west), receiving the first Yang energy of the Zhen hexagram. The statement "Xun begins to eliminate Yang and Yin is born" refers to the union of Kun and Qian, with the first Yin line of the Xun hexagram arising at the lower line. The "Sixteen Days' Transformation" in the "Cantong Qi" says, "On the sixteenth day, the moon moves to the Xin position at dawn," referring to the morning of the sixteenth day of the lunar month when the moon retreats to the Xin position, receiving the first Yin energy of the Xun hexagram.

自震一陽進而納兌之二陽，至乾之陽而滿。兌納丁，乾納甲。此望前之候，明生魄死之月象也。自巽一陰退，而納艮之二陰，至坤三陰而滅。艮納丙，坤納乙，此望後三候魄生明死之月象也。

From the trigram Zhen with one yang, advancing to the trigram Dui with two yang, and finally reaching Qian with three yang fully developed: Dui takes the stem Ding, and Qian takes the stem Jia. This corresponds to the lunar phase before the full moon, when the bright part of the moon is gradually increasing and the dark part is gradually decreasing. From the trigram Xun with one yin, retreating to the trigram Gen with two yin, and finally reaching Kun with three yin completely exhausted: Gen takes the stem Bing, and Kun takes the stem Yi. This corresponds to the lunar phase after the full moon, when the dark part of the moon is gradually increasing and the bright part is gradually decreasing. The eight trigrams each incorporate ten stems through the method of Najia. The waxing and waning of the moon phases correspond one-to-one with the increasing and decreasing of the trigram lines.

此所謂納甲。雖出於《參同契》，虞氏翻說《易》，皆本於此，與先天八卦方位之陰陽消長悉合。可見自漢以前，必有此說。魏伯陽得假之以明丹學，與朝屯暮蒙之候，同為取資於《易》，非伯陽所創造也。

This is what is called "Najia" or "stem assignment." Although it originates from the "Cantongqiqi," Yu Fan said that the entire system of the "Yi" is based on it, and it perfectly aligns with the yin and yang changes in the Earlier Heaven Trigrams. This shows that this system must have existed before the Han dynasty. Wei Boyang merely used it to explain alchemy, just as he used "morning Zun and evening Meng" to determine the timing of fire, which also draws upon the "Yi," not something he created himself.

今指納甲為道家外說，然則屯蒙需訟之次，將因《參同契》定為火候，亦謂之外說耶（今屯蒙需訟，幸有孔子《序卦》一篇得以無紊。使《序卦》不傳，而簡冊紊亂，亦惟有取《參同契》所列朝屯暮蒙之次以定六十四卦之序耳。何獨疑於納甲為哉！）！

Nowadays some people regard Najia as a heretical doctrine of Taoism; then why should the sequence of the hexagrams Zun, Meng, Xu, and Song, which was used by the Shangongqi to determine the timing of fire, also be called heretical? (Today's order of Zun, Meng, Xu, and Song is fortunate to have been clarified by Confucius' Xugua Zhuan. If Xugua Zhuan were lost and the records were disordered, we would only take the order of Zun in the morning and Meng in the evening as listed in Shangongqi to determine the sequence of the sixty-four hexagrams. Why then do we doubt Najia especially?)

《禮運》曰：“播五行於四時，和而後月生也。是故三五而盈，三五而闕。”正合此意。播五行於四時，以一歲中四氣之流行言之，出震齊巽之方位是也。三五而盈三五而闕，以一月中月體之消長言之，乾南坤北之方位是也。

The Li Ji · Li Yun says: "To spread the Five Phases through the four seasons, harmony is achieved and then the moon is born. Therefore, it waxes and wanes in cycles of three and five." This exactly matches the meaning here. The phrase "to spread the Five Phases through the four seasons" refers to the flow of the four energies within a year, which corresponds to the Later Heaven directional system of "the Emperor arises from Zhen, aligns with Xun." The phrase "it waxes and wanes in cycles of three and five" refers to the waxing and waning of the moon's body within a month, which corresponds to the Earlier Heaven directional system of Qian in the south and Kun in the north.

月生明謂陽之進，月生魄謂陰之退者；天地之數，天數二十有五，地數三十。故一月三十日，而月之得光只二十五日（每月二十八日至初二日，月無光也。）。《參同契》曰：“七八數十五，九六亦相當。四者合三十，陽氣索滅藏。”此象數兼資，不能離數以言象，亦不能離象以言數者也。附納甲圖如下。

The concept of "moon being bright" refers to the advance of yang and the retreat of yin. This can also be verified by numbers: in the numbers of heaven and earth, the heavenly number is twenty-five and the earthly number is thirty, so a month is thirty days, yet the moon is only bright for twenty-five days (from the 28th of each month to the second day of the next month, the moon is dark). The "Compendium of the Supreme Ultimate" states: "Seven and eight make fifteen, nine and six also correspond. Four numbers together make thirty, yang energy begins to diminish and retreat." The young yang seven combined with the young yin eight makes fifteen, while the old yang nine combined with the old yin six also makes fifteen. When these four numbers are combined, they total thirty, exactly matching the thirty days of a month, and at this point yang energy begins to retreat and hide. This is a mutual reliance between form and number: one cannot discuss form without number, nor can one discuss number without form. The following is the diagram of Najia.

納甲之說，不但與先天圖之陰陽消長相合，與河圖之數位亦合。河圖三八居東為甲乙木，二七居南為丙丁火，四九居西為庚辛金，一六居北為壬癸水，五十居中為戊己土。乾納甲，坤納乙，東方木也。兌納丁，艮納丙，南方火也。震納庚，巽納辛，西方金也。坎納戊，離納己，中央土也。乾又納壬，坤又納癸，北方水也。漢上朱氏曰：“納甲者，舉甲以該十日也。乾納甲壬，坤納乙癸。震巽庚辛，坎離戊己，艮兌丙丁，皆自下生。聖人仰觀日月之運，配之以坎離之象，而八卦十日之義著矣。”乾坤甲乙，艮兌丙丁，震巽庚辛，坎離戊己，為日月本體，故圖未列。乾又納壬，坤又納癸，乃陽中之陰，陰中之陽。目所不見，故亦不列於圖。

The method of assigning the ten heavenly stems to the eight trigrams, known as "Najia," not only matches the sequence of yin and yang rising and falling in the Earlier Heaven diagram, but also corresponds exactly with the numbers assigned to each direction in the Yellow River Chart. In the Yellow River Chart, the numbers three and eight are located in the east, corresponding to "Jia and Yi" (wood); two and seven are in the south, corresponding to "Bing and Ding" (fire); four and nine are in the west, corresponding to "Wu and Xin" (metal); one and six are in the north, corresponding to "Ren and Gui" (water); and five and ten are in the center, corresponding to "Wu and Ji" (earth). When comparing with Najia, "Qian" (Heaven) takes "Jia," and "Kun" (Earth) takes "Yi," both located in the east, which is wood. "Dui" (Lake) takes "Ding," and "Gen" (Mountain) takes "Bing," both located in the south, which is fire. "Zhen" (Thunder) takes "Wu," and "Xun" (Wind) takes "Xin," both located in the west, which is metal. "Kan" (Water) takes "Wu," and "Li" (Fire) takes "Ji," both located in the center, which is earth. "Qian" also takes "Ren," and "Kun" also takes "Gui," both located in the north, which is water. Zhu Zhen, a Song dynasty scholar known as the "Han Shang Xiansheng" and author of "Han Shang Yichuan," said that "Najia" refers to using the first heavenly stem, "Jia," to represent all ten heavenly stems. "Qian" takes "Jia" and "Ren," and "Kun" takes "Yi" and "Gui," while "Zhen" and "Xun" take "Wu" and "Xin," "Kan" and "Li" take "Wu" and "Ji," and "Gen" and "Dui" take "Bing" and "Ding." These assignments are generated sequentially from the lower trigrams. The sage observed the movement of the sun and moon, using the images of "Kan" and "Li" to correspond with them, thereby making the principle of matching the eight trigrams with the ten heavenly stems clear. As for the heavenly stems assigned to "Qian" and "Kun," "Gen" and "Dui," "Zhen" and "Xun," and "Kan" and "Li," they relate to the forms of the sun and moon themselves, so they are not separately marked on the Najia diagram. The additional stems "Ren" assigned to "Qian" and "Gui" assigned to "Kun" represent the hidden yin within yang and the hidden yang within yin, which are invisible, hence they are not included in the diagram.

《繫傳》曰：“懸象著明，莫大乎日月。”虞氏注謂：“日月懸天成八卦象，三日暮震象月出庚，八日兌象月見丁，十五日乾象月盈甲壬，十六日旦巽象月退辛，二十三日艮象月消丙，三十日坤象月滅乙癸，晦夕朔旦則坎，坎象水流戊。日中則離離象火就己，戊己土位，象見於中。”“日月相推而明生焉。”《坤·象》“西南得朋”。虞曰：“陽喪滅坤，坤終復生。”此指說易道陰陽之大要也。又曰：“消乙入坤，滅藏於癸。”

The Great Treatise says: The celestial phenomena hanging in the sky and shining brightly, none are greater than the sun and moon. Yu Fan, a scholar of the Three Kingdoms period in Wu, explained this saying: The sun and moon hanging in the sky, their movement forms the images of the Eight Trigrams. On the third day of the month, in the evening, the new moon appears at the 'Geng' position in the west, symbolizing the first movement of the Yang trigram 'Zhen'; on the eighth day, the waxing moon appears at the 'Ding' position, symbolizing the trigram 'Dui' with two Yangs; on the fifteenth day, the full moon shines brightly at the 'Jia' and 'Ren' positions, symbolizing the trigram 'Qian' with three Yangs fully present; on the sixteenth day, in the morning, the moon begins to wane at the 'Xin' position, symbolizing the first emergence of the Yin trigram 'Xun'; on the twenty-third day, the waning moon disappears at the 'Bing' position, symbolizing the trigram 'Gen' with two Yins; on the thirtieth day, the moon's light fades completely at the 'Yi' and 'Gui' positions, symbolizing the trigram 'Kun' with three Yins. At the transition between the evening of the last day of the month and the morning of the first day, the moon returns to the trigram 'Kan', which represents water, and the water flows and corresponds to 'Wu'; when the sun reaches its zenith, it corresponds to the trigram 'Li', which represents fire, and the fire corresponds to 'Ji'. 'Wu' and 'Ji' both belong to the central position of the Earth, and their image is manifested in the center. The Great Treatise also says: The sun and moon move in succession, and light is thus produced. The 'Xiang Ci' of the 'Kun' hexagram mentions 'gaining friends in the southwest', and Yu Fan explains that when the Yang energy is completely lost, the 'Kun' body follows and disappears, but when 'Kun' reaches its end, it will again be reborn. These words are all pointing out the main framework of the 'Yi' doctrine of the cycle of Yin and Yang. Yu Fan also said: The moon's light fades at 'Yi' and enters 'Kun', eventually disappearing and being hidden at 'Gui'.

《參同契》曰：“天地設位，而易行乎其中矣。天地者，乾坤之象也。設位者，列陰陽配合之位也。易謂坎離。坎離者，乾坤二用。二用無爻位，周流行六虛。往來既不定，上下亦無常。幽潛淪匿，升降於中。包囊萬物，為道紀綱。”漢以前易字皆從日從月，日上月下。日勿之易後出，遂滋異議。許叔重《說文》“日”字引《秘書》“日月為易”，可見相傳甚古矣。

The Eastern Han dynasty alchemist Wei Boyang in his work "Zhou Yi San Tong Qi" said: Heaven and Earth have established positions of above and below, and the principle of change operates within this. By "Heaven and Earth," he refers to the images of the Qian and Kun hexagrams. By "setting positions," he means arranging the positions of yin and yang to complement each other. Here, the term "Yi" refers to the Kan and Li hexagrams. Kan and Li are the two functions emanating from Qian and Kun. These two functions do not occupy fixed positions on the yao, but instead circulate throughout the six voids of above and below, all directions. They come and go without fixed places, ascend and descend without fixed paths. They are hidden and concealed, moving up and down within Heaven and Earth, encompassing and containing all things, becoming the fundamental principles of the great Dao. As for the term "Yi," in the writing style before the Han dynasty, it was composed of the characters for "sun" above and "moon" below. Later, a different form emerged with "sun" above and "wu" below, leading to various conflicting interpretations. Xu Shen (style name Shuzhong) in his "Shuo Wen Jie Zi" cited the saying from the "Mysteries Secret Records" that "the sun and moon form the Yi," indicating that this interpretation has a very ancient origin.

《虞氏易》卦位，乾坤列東，艮兌列南，震巽列西，坎離居中，與納甲圖同。蓋先天卦位立其體，故天地定位，日東月西。陰陽消長，各循其序。納甲言其用，故卦各從其所納之方，雖異而實同也。離東坎西，至望夕則日西月東。坎離易位，其離中一陰，即是月魄。坎中一陽，即是日光。東西正對，交注於中。此二用之氣，所以納戊己也。故曰“坎戊月精，離己日光。日月為易，剛柔相當。蟾蜍與兔魄，日月氣雙明”也。

Yu Fan's system of the Yu Family Yi uses the same arrangement of trigrams as the "Najia Diagram": Qian and Kun are placed in the east, Gen and Dui in the south, Zhen and Xun in the west, and Kan and Li in the center. This is because the Earlier Heaven arrangement is used to establish the fundamental nature, so the heavens and earth are positioned above and below, the sun is in the east, the moon in the west, and yin and yang change in a fixed order. However, the Najia system refers to function, so each trigram is arranged according to the direction of the heavenly stem it incorporates. Although they appear different, they are essentially the same. Normally, Li (the sun) is in the east and Kan (the moon) in the west, but at the full moon in the evening, the sun sets in the west and the moon rises in the east, so Kan and Li switch positions. The central yin line in Li is the moon's phase, and the central yang line in Kan is the sun's light. The sun and moon are directly opposite, and the two energies meet in the center, which is why Kan and Li incorporate the central earth elements "Wu" and "Ji." Therefore, the "Cantong Qi" says: Kan incorporates "Wu," which is the essence of the moon; Li incorporates "Ji," which is the brilliance of the sun. The sun and moon together form the character "Yi," with exactly the right balance of yang and yin. The moon's toad and rabbit phase, along with the sun's yang essence, make the energies of the sun and moon both bright.

乾納甲而納壬，坤納乙而納癸者，以乾之中畫即太陰之精，望夕夜半月當乾，納其氣於壬方，地中（地中者，即地之下面也。）對月之日也。坤之中畫即太陽之精，晦朔之間日在坤，納其氣於癸方，地中合日之月也。徐敬可曰：“望夕之陽既盈於甲，其夜半日行至壬，而月與為衡。日中原有陰魄，所謂離中一陰者，平時含蘊不出（今西人以遠鏡窺日，見日中有甚大之黑影，與離卦之象適合。），至是盛陽將革，又感正對之陰，乃充溢流滋，而為生陰之本，故其象為⊙，即望夕夜半壬方之日也。

The trigram Qian has already received the heavenly stem Jia, and also receives the stem Ren. The trigram Kun has already received the stem Yi, and also receives the stem Gui. The reason for this is that the central line of the trigram Qian is actually the essence of the yin (moon), and on the night of the fifteenth day of the lunar month, when the moon is at the position of Qian, it channels the energy to the direction of Ren. This is the position of the sun underground, which is directly opposite the moon. The central line of the trigram Kun is actually the essence of the yang (sun), and at the time when the sun is at the position of Kun during the transition between the new moon and the full moon, it channels the energy to the direction of Gui. This is the position of the moon underground, which is directly opposite the sun. Qing dynasty scholar Xu Shimu (style name Jingke) said: On the fifteenth day, the sun's energy has already filled up the direction of Jia, and that night, the sun moves to the direction of Ren, facing the moon opposite as the two ends of a balance. The sun itself contains the yin essence, which is called the "one yin within the fire" (Li trigram). This yin essence is usually hidden and not visible (nowadays, Westerners use telescopes to observe the sun and see large dark spots on its surface, which correspond to the empty center of the Li trigram). At this time, the yang energy is at its peak and about to change, and it feels the opposing yin energy, so the yin essence fills and spreads out, becoming the source of yin generation. Therefore, its image is drawn as a circle "⊙", which represents the sun at midnight in the direction of Ren on the fifteenth day.

晦旦之陽，既盡於乙，其夜半日行至癸，而月與同躔。月中原有陽精（今西人遠鏡窺見月中有類於河流者，其形不定。雖未敢斷為即月中之陽精，然與坎卦之象亦無不合矣。），所謂坎中一陽者，平時胚渾而不分，至是則盛陰將革，又感摩戈之陽，乃剖發迸洩而為生陽之本，故其象為〇，即晦朔間癸方之月也。故曰壬癸配甲乙，乾坤括始終。”此論納甲極精。以證先天卦位，益可見漢人以前，必有相傳之學說。或即許叔重所謂《秘書》（《說文》“日月為易”引《秘書》）之類，不但非陳邵所創造，亦非魏伯陽所能創造也。

On the day of the晦, the yang energy had already exhausted itself at 「Yi」. That night, the sun reached the position of 「Gui」, and the moon traveled along the same path. The moon originally contained yang essence (nowadays westerners have seen with telescopes that there are traces resembling rivers on the moon's surface, which are not fixed in shape; although we cannot confirm that these are the yang essence within the moon, they are not inconsistent with the image of the solid yang in the Kan trigram). This is referred to as 「one yang within Kan」. Normally, it was in a state of confusion and undifferentiated, but at this time, the extreme yin was about to change, and it felt the yang energy that was rubbing against and stimulating it. The yang essence thus split and burst forth, becoming the fundamental source of yang. Therefore, its image is drawn as 「〇」, which is the moon at the 「Gui」 position between the new moon and the full moon. Therefore, it is said that 「Ren」 and 「Gui」 pair with 「Jia」 and 「Yi」, and the Qian and Kun trigrams encompass the beginning and the end. Xu's discussion on the assignment of stems is very precise. Using it to verify the Earlier Heaven trigram positions, we can further see that there must have been another system of transmission before the Han dynasty, perhaps similar to what Xu Shen referred to as the 「Secrets」 (the saying 「the sun and moon are the Book of Changes」 in the Shuowen Jiezi is quoted from the 「Secrets」). Thus, the theory of assigning stems and the Earlier Heaven trigrams were not created by Song dynasty figures such as Chen Tuan and Shao Yong, nor by Eastern Han's Wei Boyang.

（萬氏彈峰曰：天地定位一節，孔子已發明納甲之旨，得《參同契》其義始著。以六卦證月候，而坎離為日月之本體，居中不用。五行家謂初三以後庚金旺，初八以後丁火旺，十五以後甲木旺，十六以後辛金旺，二十三以後丙火旺，三十日後乙木癸水旺。蓋月受日之精光，而五行又受日月之精光，故乘日月所泊之地而旺也。東方朔以納甲五行定人命之吉凶禍福，則其說亦不起於《參同契》也。）

Wan Danfeng said: In the section of the "Sayings on the Trigrams" called "Heaven and Earth are Positioned," Confucius already indicated the purpose of the Najia system. It was only with the "Threefold Concordance" of the Zhou Changes that this meaning became clearly evident. The "Threefold Concordance" uses the six trigrams of Zhen, Dui, Qian, Xun, Gen, and Kun to correspond with the lunar phases within a month, while the trigrams Kan and Li are regarded as the essence of the sun and moon, remaining in the center and not participating in the rotation of the six trigrams. The Five Phases school then developed the theory that after the third day of the month, Geng metal is dominant; after the eighth day, Ding fire is dominant; after the fifteenth day, Jia wood is dominant; after the sixteenth day, Xin metal is dominant; after the twenty-third day, Bing fire is dominant; and after the thirtieth day, Yi wood and Gui water are dominant. This is because the moon receives the light of the sun, and the Five Phases receive the light of both sun and moon, so they each become dominant according to the heavenly stems associated with the positions of the sun and moon. Dongfang Shuo of the Han dynasty used the Najia system combined with the Five Phases to determine the fortune and misfortune of people, showing that this theory did not originate from the "Threefold Concordance."

《繫傳》曰：“雷以動之，風以散之。雨以潤之，日以烜之。艮以止之，兌以說之。乾以君之，坤以藏之。”邵子本此節，繪六十四卦方圖，其中心四卦為震巽恆益，外一層為坎離，再外一層為艮兌，再外一層為乾坤，次序悉合。與其小橫圖（即《本義》所謂《伏羲八卦次序》者）八卦之次序亦合（震巽居中，外為坎離，又外為艮兌，首尾為乾坤）。故邵子《大易吟》曰：“天地定位，泰否反類。山澤通氣，咸損見義。風雷相薄，恆益起意。水火相逮，既濟未濟。四象相交，成十六事（十六事者，四畫之卦即中爻是也）。八卦相蕩，為六十四。”

The Great Treatise says: Thunder is used to move all things, wind to scatter all things, rain to nourish all things, sun to dry all things, mountain to stop all things, lake to make all things joyful, heaven to rule all things, and earth to contain all things. A Song dynasty scholar named Shao Yong drew the "Sixty-Four Hexagram Square Diagram" based on the order of this passage: the central four hexagrams are Zhen, Xun, Heng, and Yi, the next layer are Kan and Li, then Gen and Dui, and the outermost layer are Qian and Kun, with the order exactly matching the text. This is consistent with the arrangement of the eight trigrams in his "Small Horizontal Diagram" (which is the same as the order of the eight trigrams in Zhu Xi's "Original Meaning of the Zhou Changes" known as the "Fuxi Eight Trigram Order")—Zhen and Xun are in the center, then Kan and Li, then Gen and Dui, and Qian and Kun at the ends. Therefore, in his poem "Great Yi Inning," Shao Yong says: Heaven and earth are positioned above and below, forming the hexagrams Tai and Po, which are the result of their reversal; mountain and marsh energies communicate, and the hexagrams Xian and Shen reflect this meaning; wind and thunder interact, giving rise to the hexagrams Heng and Yi; water and fire connect, forming Ji Ji and Wei Ji. The four trigrams interact in pairs, forming sixteen matters (the so-called "sixteen matters" refer to the four-line hexagrams, which are the middle lines of the six-line hexagrams); the eight trigrams interact and generate the sixty-four hexagrams.

此邵子有得於先天之學，而擷其精蘊處也。惟乾一兌二離三震四巽五坎六艮七坤八之數，乃邵子貫澈易理，獨有會心，自成一家之學。與揚子《太玄》，皆足與《易》相發明，而實非《周易》卦象之數也。自《本義》以邵圖弁首，後之說《易》者，以邵子之數為易象之數。如來瞿塘、胡滄曉、張乘槎比比皆是，實屬大誤。故茲編於邵子之小橫圖、大橫圖、大圓圖、方圖，皆不贅錄。間有足資參考者，今所刊行之《易經》皆具此圖，檢尋固極便也。

These sentences clearly show that Shao Yong indeed had profound insights into the Earlier Heaven system, and he extracted the essential aspects from it. However, the system of numbers "Qian one, Dui two, Li three, Zhen four, Xun five, Kan six, Gen seven, Kun eight" was uniquely developed by Shao Yong after he thoroughly understood the principles of the Zhou Changes. It forms his own independent school of thought, similar to Yang Xiong's "Tai Xuan" from the Han dynasty, which can complement the Zhou Changes. Yet, it is not the numerical system inherent in the hexagrams of the Zhou Changes. Since Zhu Xi's "The Original Meaning of the Zhou Changes" placed Shao's diagrams at the beginning, later scholars of the Zhou Changes began to treat Shao's numbers as part of the symbolic system of the Zhou Changes. Many scholars, such as Lai Zhide, Hu Cangxiao, Zhang Chengcha, and others, followed this approach. This is a serious mistake. Therefore, this book does not reproduce Shao Yong's "Small Horizontal Diagram," "Large Horizontal Diagram," "Large Round Diagram," and "Square Diagram." Occasionally, some of these diagrams may be of reference value. Nowadays, most published editions of the "Book of Changes" include these diagrams, making them easily accessible for reference.

《說卦傳》曰：“乾天也，故稱乎父。坤地也，故稱乎母。震一索而得男，故謂之長男。巽一索而得女，故謂之長女。坎再索而得男，故謂之中男。離再索而得女，故謂之中女。艮三索而得男，故謂之少男。兌三索而得女，故謂之少女。”此節明乾坤交生六子之序，《本義》別立為圖，曰“文王八卦次序”，（伏羲八卦因而重之為六十四，豈至文王而始有乾坤六子之序？況後天八卦以坎離為用，乾坤退居，何得以此為文王八卦乎？）實即先天圖。陽始交陰，陰始交陽，由先天八卦，變為後天之樞紐也。學者以先天後天兩圖，並列互觀，詳察其陰陽變化之序，先後更易之次，自有無窮妙境。諸家之說，雖各明一理，非具有心得者，閱之轉無所適從耳。

The Sayings on the Trigrams states: Qian represents Heaven, so it is called the father; Kun represents Earth, so it is called the mother. Zhen is the first son born when Kun seeks Qian once; Xun is the first daughter born when Qian seeks Kun once; Kan is the middle son born when they seek twice; Li is the middle daughter born when they seek twice; Gen is the young son born when they seek three times; Dui is the young daughter born when they seek three times. This passage explains the order in which Qian and Kun generate the six sons. However, Zhu Xi's The Original Meaning of the Zhou Changes presents a separate diagram titled "The Order of the King Wen Trigrams." (If Fuxi's trigrams are overlapped to form the sixty-four hexagrams, how could the order of the six sons of Qian and Kun only appear after King Wen? Moreover, the Later Heaven Trigrams use Kan and Li as the main trigrams, while Qian and Kun have already been set aside, so how can this diagram be called the King Wen Trigrams?) In fact, it refers to the Earlier Heaven Diagram: Yang begins to interact with Yin, and Yin begins to interact with Yang. This is the key point in the transformation from the Earlier Heaven Trigrams to the Later Heaven Trigrams. Those studying the I Ching should compare the Earlier Heaven and Later Heaven diagrams side by side, carefully observing the order and sequence of the changes in yin and yang. This will naturally reveal infinite subtleties. Although various interpretations each explain one aspect clearly, without personal insight, reading them may only confuse which one to follow.

《說卦傳》曰：“帝出乎震，齊乎巽，相見乎離，致役乎坤，說言乎兌，戰乎乾，勞乎坎，成言乎艮。萬物出乎震，震東方也。齊乎巽，巽東南也。齊也者，言萬物之絜齊也。離也者，明也，萬物皆相見，南方之卦也。坤也者，地也，萬物皆致養焉。故曰致役乎坤。兌正秋也，萬物之所說也，故曰說言乎兌（坤地也，不可以一方言，故不曰西南。兌正秋也，舉兌則坎冬震春離夏可知矣。西南為神，神無方而易無體，故獨此兩卦不言方。）。戰乎乾，乾西北之卦也，言陰陽相薄也。坎者水也，正北方之卦也，勞卦也，萬物之所歸也，故曰勞乎坎。艮東北之卦也，萬物之所成終而成始也（艮居丑寅二辰。丑十二月成，終也。寅正月成，始也。），故曰成言乎艮。”

The *Sayings on the Trigrams* says: The "Emperor" who governs the process of generation and nurturing comes forth from the trigram *Zhen* (Thunder), reaches *Xun* (Wind) and becomes orderly, reaches *Li* (Fire) and things meet and recognize each other, reaches *Kun* (Earth) and receives nourishment and service, reaches *Dui* (Lake) and expresses joy and speech, reaches *Qian* (Heaven) and yin and yang contend, reaches *Kan* (Water) and there is toil and exhaustion, reaches *Gen* (Mountain) and the process is completed and comes to an end. All things originate from *Zhen*, which is in the east; reaching *Xun*, which is in the southeast, things become orderly. "Orderly" means that all things grow clean and neat. *Li* is brightness, and at this point all things appear to each other, which is the trigram of the south. *Kun* is earth, and all things receive nourishment here, so it is said "they are served by *Kun*." *Dui* corresponds to autumn, the season when all things are joyful and mature, so it is said "it expresses joy and speech through *Dui*." (*Kun* represents the earth, which cannot be confined to a specific direction, so the text does not specify its position as southwest; *Dui* corresponds to autumn, so *Kan* belongs to winter, *Zhen* to spring, and *Li* to summer can be inferred. The southwest position belongs to "spirit," which has no fixed location, and the *Book of Changes* has no fixed form, so only *Kun* and *Dui* are not assigned specific directions.) "Contending in *Qian*," *Qian* is the trigram of the northwest, meaning yin and yang are here in conflict. *Kan* is water, the trigram of the north, the trigram of toil and exhaustion, and all things here retreat and conceal, so it is said "toil occurs in *Kan*." *Gen* is the trigram of the northeast, where all things complete and end, yet also begin anew (*Gen* occupies the positions of *Chou* and *Yin*: *Chou* is the twelfth month, the end of the year; *Yin* is the first month, the beginning of the year), so it is said "it completes and begins anew through *Gen*."

《觀物外篇》曰：“至哉！文王之作易也。其得天地之用乎？故乾坤交而為泰，坎離交而為既濟也。乾生於子，坤生於午。坎終於寅，離終於申。以應天之時也。置乾於西北，退坤於西南，長子用事，而長女代母，坎離得位，兌震為偶，應地之方。王者之法，其盡於是矣。”

Shao Yong said in his "Outer Chapter of Observing Things": What a great achievement, King Wen's interpretation of the Book of Changes! He must have grasped the functions of heaven and earth. Therefore, the trigrams Qian and Kun interact to form the卦 Tai, and the trigrams Kan and Li interact to form the卦 Ji Ji. The energy of Qian originates from "Zi," and the energy of Kun originates from "Wu"; the energy of Kan ends at "Yin," and the energy of Li ends at "Shen"—this is used to correspond with the seasons of heaven. Place Qian in the Northwest, let Kun retreat to the Southwest, let the eldest son Zhen take charge, and let the eldest daughter Xun act as the mother's representative. Let Kan and Li occupy the positions of Due North and Due South respectively, and let Dui and Zhen pair with each other—this is used to correspond with the directions of the earth. The principles for a ruler to govern the world are all contained within this.

林氏《易稗傳》曰：“先天所以立體也，後天所以致用也。以陰陽之體論之，巽離兌本陽體也，而陰來交之。震坎艮本陰體也，而陽來交之。伏羲之卦，得陽多者屬乎陽，得陰多者屬乎陰。後天之卦，得一陰者為三女，得一陽者為三男。先天之位，三女附乎乾，三男附乎坤。陰附陽，陽附陰也。後天之位，三男附乎乾，三女附乎坤者，陰附陰，陽附陽也。”（按：先天言體，故陰陽從其多者為主。後天言用，故陰陽取其少者為主也。）

Song dynasty scholar Lin Zhi in his work "Yi Bie Zhuan" said: The earlier heaven trigrams are used to establish the essence, while the later heaven trigrams are used to demonstrate function. In terms of the essence of yin and yang, Xun, Li, and Dui originally belong to the yang essence, but have yin lines to interact with them; Zhen, Kan, and Gen originally belong to the yin essence, but have yang lines to interact with them. The trigrams of Fuxi's earlier heaven are such that those with more yang lines are classified as yang, and those with more yin lines are classified as yin. The later heaven trigrams, however, count a single yin line as three females and a single yang line as three males. In the earlier heaven arrangement, three females are attached to Qian, and three males are attached to Kun, representing yin attaching to yang and yang attaching to yin. In the later heaven arrangement, three males are attached to Qian, and three females are attached to Kun, representing yin attaching to yin and yang attaching to yang. (Hang's note: The earlier heaven discusses essence, so yin and yang are discussed based on the side with more lines; the later heaven discusses function, so yin and yang are discussed based on the side with fewer lines.)

《說卦傳》曰：“神也者，妙萬物而為言者也。動萬物者莫疾乎雷，撓萬物者莫疾乎風，燥萬物者莫熯乎火，說萬物者莫說乎澤，潤萬物者莫潤乎水，終萬物始萬物者莫盛乎艮。故水火相逮，雷風不相悖，山澤通氣，然後能變化既成萬物也。”（既讀若概，古字通也。《本義》：此去乾坤而專言六子，以見神之所為然。其位序亦上章之說，未詳其義。朱子不強不知以為知，是其篤實處。但此章為易學綱領，與“帝出乎震”一章並列。全《易》精蘊，悉從此出。不知其義，《易》何從說哉！）

The "Commentary on the Trigrams" says: The term "spirit" refers to its subtle ability to transform and generate all things. Nothing moves and activates all things more swiftly than thunder, nothing moves and stirs all things more swiftly than wind, nothing dries up all things more intensely than fire, nothing brings joy to all things more effectively than marshes, nothing nourishes all things more thoroughly than water, and nothing concludes and begins all things more powerfully than mountains. Therefore, water and fire communicate with each other, thunder and wind do not contradict each other, and the energies of mountains and marshes connect with each other, thus enabling transformation and the completion of all things. ("Ji" is read as "gai," an ancient variant character. Zhu Xi's "The Original Meaning of the Zhou Changes" says: This chapter omits Heaven and Earth and focuses solely on the six trigrams, to illustrate the workings of "spirit"; its order of directions is also the same as in the previous chapter, but the underlying principles are still not fully understood. Zhu Xi's refusal to force an understanding of what he did not comprehend is a reflection of his sincerity. However, this chapter is the essence of the study of the Book of Changes, and it is placed alongside the chapter "The Emperor arises from Thunder," from which all the profound meanings of the Book of Changes flow. Without understanding this, from where would the Book of Changes begin?"

後天八卦，為人用之卦。古聖帝王制作之大原，治平之經緯，皆出於後天八卦之用。下而曆象、推步、運氣、樂律、占卜、風鑑、星命諸術，亦皆後天卦也。《周易》序卦，則以先天為體，後天為用，二者兼行。漢學家之攻擊先天，由於門戶之見過深，未暇取經文而詳玩之耳。《上經》始乾坤終坎離，明明先天卦位也。《下經》始咸恆終既未濟，明明後天之卦位也。而六十四卦之命名，於先後天相關者尤多。

The Later Heaven Trigrams are the trigrams used for human affairs. All the fundamental principles of the ancient sage kings in creating systems and governing the country and pacifying the world originated from the function of the Later Heaven Trigrams. Going further down, in areas such as calendars and astronomy, calculations, the five movements and six qi, music theory, divination, geomancy, and star and destiny studies, none of them are not based on the Later Heaven Trigrams. The arrangement of the sixty-four trigrams in the Zhou Changes takes the Earlier Heaven as its essence and the Later Heaven as its function, using both together. Qing dynasty Han scholars blindly attacked the theory of Earlier Heaven, because they had too deep a sectarian bias and did not have the time and effort to carefully study the classic texts. The Upper Classic begins with Qian and Kun and ends with Kan and Li, clearly indicating the positions of the Earlier Heaven Trigrams. The Lower Classic begins with Xian and Heng and ends with Ji Ji and Wei Ji, clearly indicating the positions of the Later Heaven Trigrams. Moreover, the naming of the sixty-four trigrams is closely related to both Earlier Heaven and Later Heaven.

如天火曰同人，同人親也。水地曰比，比親也。同人比何以親？非以先後天，乾離坤坎之位相合乎？火雷曰噬嗑，噬嗑合也。水澤曰節，節亦符合之意。非離震坎兌，亦先後之位相合乎？此其最顯者也。蠱卦幹父之蠱，幹母之蠱，本卦未嘗有父母之象。虞氏以卦變言之，謂蠱由否來，父母謂否之乾坤。然損亦否變，未嘗言父母，否本卦亦未言父母，何獨著其象於蠱？惟以先後天證之，則先天山風之位，後天以乾坤居之，可不煩言而自解矣。各卦類此者甚多，詳下《卦名》章。

For example, the hexagram with Heaven above and Fire below is called "Tong Ren" (Union), and the "Zaji Guan Zhuan" says, "Tong Ren means to be close to others." The hexagram with Water above and Earth below is called "Bi" (Approach), and "Bi" also means to be close. Why do both "Tong Ren" and "Bi" take the meaning of "close"? It is precisely because the position of Heaven in the Earlier Heaven corresponds to the position of Fire in the Later Heaven, and the position of Earth in the Earlier Heaven corresponds to the position of Water in the Later Heaven. Similarly, the hexagram with Fire above and Thunder below is called "Shi He" (Breaking the Bones), and "Shi He" means to join together. The hexagram with Water above and Marsh below is called "Jie" (Limitation), and "Jie" (a symbol of authority) also implies conformity. This is also because the position of Fire in the Earlier Heaven corresponds to the position of Thunder in the Later Heaven, and the position of Water in the Earlier Heaven corresponds to the position of Lake in the Later Heaven. These are the most obvious examples. Another example is the "Gu" hexagram, whose line statement says, "To renew the father's affairs" and "To renew the mother's affairs." However, the "Gu" hexagram itself does not contain the image of parents. Yu Fan explained this using hexagram transformation, saying that "Gu" comes from the "Pǐ" hexagram, and the parents are the Heaven and Earth in "Pǐ." However, the "Sun" hexagram also comes from "Pǐ," yet it does not mention parents. "Pǐ" itself does not mention parents either. Why does "Gu" specifically have this image? Only by referring to the Earlier and Later Heavens can we understand this clearly: in the Earlier Heaven, the positions of Mountain (Gen) and Wind (Xun) correspond to certain directions, while in the Later Heaven, these directions are occupied by Heaven and Earth. Thus, the meaning becomes clear without further explanation. There are many more such examples, which will be detailed in the chapter on "Hexagram Names" below.

《說卦傳》“帝出乎震”一章，與“神也者”一章，皆言後天八卦之方位及作用。一“帝”字，一“神”字，皆貫澈全章。帝也者，所以主宰此出震齊巽之用者也。神也者，所以變化此雷風山澤之妙者也。帝出乎震而神妙於兌，兌為少女（今西洋相傳上古之神像，類作少女形，其用意與此亦不謀而合者也），兌說言，故曰“妙萬物而為言”者也。先天水火不相射，雷風相薄。至後天二八易位，則水火相逮。雷風不相悖，山澤通氣（山澤通氣，先後天同也。然後天山澤之用，即見於震兌。以震兌反之，即艮巽也。），然後能變化既（既當讀若概）成萬物也。

In the chapter "Di Chu Hu Zhen" and "Shen Ye" from the "Shuo Gua Zhuan," both discuss the positions and functions of the Later Heaven Trigrams. The character "Di" (Emperor) and "Shen" (Spirit) each run through the entire chapter. "Di" is the one who governs the process of "coming forth from Zhen, harmonizing with Xun." "Shen" is what makes the changes of thunder, wind, mountain, and marsh subtle and profound. The Emperor emerges from the position of Zhen, while the Spirit manifests its subtlety at the position of Dui. Dui represents the young maiden (a concept that aligns with the Western tradition of ancient deities often depicted as young women). Dui governs joy and speech, hence the "Shuo Gua Zhuan" states that "Shen" is "wondering at all things and expressing them through words" — the subtlety of all things is revealed through speech. In the Earlier Heaven arrangement, water and fire are incompatible, and thunder and wind clash with each other. In the Later Heaven arrangement, the positions of Kūn (Earth) and Gèn (Mountain) are exchanged, resulting in water and fire being connected, thunder and wind not conflicting, and the energies of mountain and marsh communicating. The phrase "Shan Ze Tong Qi" (mountain and marsh communicate) is the same in both Earlier and Later Heaven. However, in the Later Heaven arrangement, the function of mountain and marsh is actually embodied in Zhen and Dui. Reversing Zhen and Dui gives Gèn and Xun. Only then can transformation fully produce all things. The character "Ji" should be read like "Gai," meaning complete.

“萬物出乎震”，以下“萬物之絜齊也，萬物皆相見，萬物皆致養，萬物之所說，萬物之所歸，萬物之所成終而所成始”，凡七言“萬物”。獨乾曰“陰陽相薄”，不言萬物。以後天乾居戌亥之位，為萬物入無之數，八風不周之方，群龍無首，用藏而不可見（乾無也。《說文》：天屈西北為無。），故不言萬物。至坎藏艮成，終而復始，震出用九，即以長子代父之用也。“神也者”一章，備言六子，皆稱萬物。不言乾坤，以六子之用皆乾坤之用，故始曰“妙萬物”而為言，終曰“既成萬物”。凡言“萬物”者八，雖不言乾坤，而乾坤之用已並舉矣。

Starting from "All things arise from Zhen," the text continues with "All things are pure and orderly," "All things appear together," "All things receive their nourishment," "All things are attracted," "All things return to their resting place," and "All things reach completion and begin anew," mentioning "all things" seven times in total. However, when discussing Qian, it only mentions "yin and yang interact," without referring to "all things." This is because in the Later Heaven arrangement, Qian is located at the position of Xu and Hai, which corresponds to the number representing "nothingness," an area where the eight winds cannot reach. As stated in the "Line Statement" of the Qian hexagram, "All dragons have no leader," indicating that its function is hidden and not visible (Qian represents "nothingness," as explained in the "Shuo Wen Jie Zi": "Heaven is in the northwest but does not reach, hence it is called 'nothingness'). Therefore, "all things" are not mentioned. When reaching the position of Kan, which is about gathering and storing, and Gen, which marks the completion and beginning again, the process starts anew with Zhen, which is the action of the eldest son taking the place of the father. In the chapter discussing "What is the spirit," all six sons are mentioned, and each instance refers to "all things," but does not mention Qian and Kun. This is because the functions of the six sons are all manifestations of the functions of Qian and Kun. Therefore, the chapter begins by saying "wondering about all things and expressing it through words" and ends with "having completed all things." This chapter mentions "all things" eight times; although Qian and Kun are not explicitly mentioned, their functions are implicitly included.

《說卦》自“天地定位”至“神也者”四章，詳言先後天八卦方位功用，備極明顯。雖未有圖，亦與圖無異。而“易逆數也”以下，如“動散潤烜說止君藏”，與下兩節之摹擬虛神，更有非圖之所能描畫者。舊說謂先天卦圓，後天卦方，固未嘗誤。然不可泥於字面，兼玩圖書圓中有方，方中有圓之義，方能得變化活潑之機。

The Sayings on the Trigrams chapter from "Tian Di Ding Wei" to "Shen Ye Zhe" covers in detail the positions and functions of the Earlier Heaven and Later Heaven Trigrams, explaining things clearly. Although the original text does not include a diagram, it is as if it did. The statements following "Yi, ni shu ye" such as "moving it, dispersing it, moistening it, shining it, explaining it, stopping it, ruling it, and concealing it," as well as the later two sections describing that subtle and profound realm, go beyond what a picture can convey. The old saying that "Earlier Heaven Trigrams are drawn in a circular diagram and Later Heaven Trigrams in a square diagram" is not wrong in itself; however, one should not be stuck on the literal meaning. One must also consider the idea of circles containing squares and squares containing circles found in the Yellow River Chart and the Luo Writing, in order to grasp the lively and dynamic vitality.

且所謂圓者，非紙上所畫一圈之平圓，乃如天體之渾圓耳。讀者但認定所畫圓圖之形以為圓，每多窒礙而難通矣。所謂方者，不僅四方，亦兼八方。要亦非紙上所畫之平方，學者詳玩圖書，必先深求其意，得其形而不滯於形，明其體而不囿，先後融貫，兩圖不啻一圖，亦即可以無圖。或有疑吾言者，可取此四章誦讀至百千遍，目追心寫，自悟孔聖神化之筆，真與造物同功，決非後人先天、後天兩圖所能盡。此孔子贊《易》之所以無藉乎圖也。

Moreover, the term "circle" does not refer to the flat circular shape drawn on paper, but rather to a three-dimensional, spherical form like the celestial bodies. If readers take the shape of the circular diagram on paper as the sole definition of a circle, they will often find themselves encountering obstacles and inconsistencies. Similarly, the term "square" is not merely the four cardinal directions, but also includes the eight cardinal directions; it is not simply the flat square shape drawn on paper. Those studying the Book of Changes must carefully examine the meaning behind the Yellow River Chart and the Luo Writing. They must understand the form without being restricted by it, grasp the essence without being limited by it, and integrate the Earlier Heaven and Later Heaven concepts. In the end, the two diagrams become one, and even the diagrams may no longer be needed. If someone doubts this, they should read these four chapters hundreds or even thousands of times, following the text with their eyes and imitating its meaning with their heart. They will eventually realize that Confucius' writing is so skillful and profound that it matches the workings of nature itself, something that later diagrams of Earlier Heaven and Later Heaven cannot fully capture. This is precisely why Confucius did not rely on diagrams when commenting on the Book of Changes.

後天方位，離南坎北。漢學家遂據此以攻擊乾南坤北之先天圖，謂孔子《說卦傳》，明言乾西北之卦，坤雖不言方，居離兌之間，自在西南。故曰“乾寒坤暑”。若乾南坤北，則乾暑坤寒，豈非與孔子之說大悖乎！先天駁議，當以此說為最有根據。後人雖有辨之者，其說仍不出邵氏方圓二圖之外，未足以辨漢學之惑焉。夫《繫傳》曰“天地定位”，曰“天地設位”，皆以天地言，而乾坤在其中。易者，一易而無不易，上下易，陰陽易，此所以成天地之用。而乾坤之位，豈有一定而不易之理？

The Later Heaven arrangement places the trigram Li (Fire) in the south and Kan (Water) in the north. Qing dynasty Han scholars used this to criticize the Earlier Heaven diagram which claims that Qian (Heaven) is in the south and Kun (Earth) is in the north. They pointed out that Confucius' "Commentary on the Hexagrams" clearly states that "Qian is the trigram of the northwest." Although Kun is not explicitly mentioned in terms of direction, it is located between Li and Dui, so it must be in the southwest. Therefore, the "Commentary on the Hexagrams" mentions "Qian represents cold, and Kun represents heat." If Qian were indeed in the south and Kun in the north, then Qian would represent heat and Kun would represent cold, which would contradict Confucius' statements. This argument has been the most convincing among the criticisms of the Earlier Heaven diagram. Later scholars who defended the Earlier Heaven diagram have tried to explain it, but they have not escaped the framework of Shao Yong's square and circular diagrams, and thus have not resolved the Han scholars' doubts. In fact, the "Great Treatise" says "the heavens and earth are positioned" and "the heavens and earth are set in position," which are statements about the heavens and earth. Qian and Kun are included within these. The "Book of Changes" is about change; once there is change in one place, there is change everywhere. Up and down can be reversed, yin and yang can be reversed, and it is precisely because of this that the functions of heaven and earth are realized. Then, how could the positions of Qian and Kun be fixed and unchanging?

乾南坤北者，天地之體，陰陽升降，冬寒夏暑，布五行而成四時。天度一歲而一周，此天地之南北以一年而言者也。而日行一日而一周，子南午北，以分晝夜。卯酉東西，以正昏旦。此晝夜之南北，以一日而言者也。故論卦位，有一年之南北，有一日之南北。一日之南北，子北在夜，午南為晝，午南而子北，離午而坎子，此人人所知者也。而論一年之南北，則冬至日南至，而夏至日北至，體用相錯，則子午不啻易位，坤居南而乾在北矣。是以八卦陰陽，都要活看。先天後天之圖，只存其大體之梗概，萬不可沾滯泥執。以紙上之卦爻，為天地之法象也。

The saying "Qian in the south and Kun in the north" refers to the fundamental nature of heaven and earth: yin and yang rising and falling, winter's cold and summer's heat, distributing the Five Phases to form the four seasons. The entire cycle of the celestial sphere takes one year to complete, which refers to the north-south direction of heaven and earth over the course of a year. However, the sun completes one cycle in a day, with Zi in the south and Wu in the north to distinguish day and night, and Mao and You in the east and west to determine dusk and dawn. This refers to the north-south direction of day and night within a single day. Therefore, when discussing the positions of the trigrams, there are two ways to consider north and south: one based on the annual cycle and the other based on the daily cycle. Based on the daily cycle: the position of Zi is in the north, associated with night, and the position of Wu is in the south, associated with day. Wu is in the south and Zi is in the north, with Li paired with Wu and Kan paired with Zi, which is well known. However, based on the annual cycle: on the day of Winter Solstice, the sun reaches its southernmost point, and on the day of Summer Solstice, the sun reaches its northernmost point. The nature of cold and heat and the function of day and night intersect, causing Zi and Wu to switch positions. Thus, Kun ends up in the south and Qian ends up in the north. This shows that the same concept of "north and south" changes depending on whether we are discussing a day or a year. Therefore, the yin and yang of the eight trigrams must be viewed dynamically. The Earlier Heaven diagram and the Later Heaven diagram only preserve a general outline; they must not be rigidly adhered to, nor should the trigrams and lines drawn on paper be regarded as the actual patterns of heaven and earth.

讀《易》首在明卦。六爻之卦，皆三畫之八卦因而重之，以成六十四卦。不明三畫之卦，何以明《彖》、《象》而識經傳之意義乎？不明先後天之方位體用，何以明象數而識陰陽之變化乎？專言漢《易》者，向無八卦方位之圖。專言宋學者，卦圖皆宗朱子《本義》，全取邵氏之說，均無論矣。其號稱兼取漢宋，如《周易折中》、《來氏集註》、《周易函書》等，皆蒐羅宏富。卦象之圖，多至數百，要皆偏重於宋學者為多。所謂以先天數為易數之誤，均未能免焉。

Reading the I Ching, the first thing to understand is the hexagrams. A hexagram consists of three lines of the eight trigrams overlaid upon each other, forming the sixty-four hexagrams. Without understanding the trigrams, how can one comprehend the Commentary on the Judgment and the Image Commentary, or grasp the meaning of the classic texts? Without understanding the principles and applications of the earlier heaven and later heaven arrangements, how can one understand the symbolic numbers and recognize the changes of yin and yang? Those who specialize in the Han dynasty interpretation of the I Ching have never included the trigram diagrams. Those who specialize in the Song dynasty school all follow Zhu Xi's The Original Meaning of the Zhou Changes and entirely adopt Shao Yong's views—these two schools need not be discussed further. As for those who claim to combine both Han and Song interpretations, such as the Imperially Approved Zhou Changes in the Middle, Lai Zhide's Collected Commentaries on the Zhou Changes, and Hu Xu's Zhou Changes in the Letter, they collect a great deal of material, with hundreds of diagrams of trigrams. However, in general, they still lean more towards the Song school, and they have all failed to avoid the error of taking the earlier heaven numbers as the fundamental numbers of the I Ching.

邵氏之說理非不精也，特皆其悟而自得之理，別有境界。初學於數理尚無端倪，驟讀其說，極易以辭害意。即如“天根”“月窟”諸說，非深造有得，不易領會。若展圖而指之，曰此天根也，此月窟也，乃乾遇巽時地逢雷處也，意非不明，而心得何在？且跡象橫梗胸中，以後更難言進步，實為初學之大患。茲編之有圖，出於萬不得已。因為初學說法，非此不便指講。故陳陳相因之圖，雖有佳者，亦徒割愛。學者能象義觕（同粗）明，然後最求前人之圖說觀之，是非去取，自有成竹。不致以訛傳訛，此著書者之微意也。

Shao Yong's explanations are not without precision, but they are based on his own insights and represent a different level of understanding. Beginners who are just starting to grasp the principles of numbers and patterns may find it difficult to comprehend them at first. If they read his works abruptly, they may easily be misled by the surface meanings and misunderstand the true intent. Take expressions like "the root of heaven" and "the cave of the moon," for example. Without deep insight and personal experience, it is hard to truly understand them. If one simply points out, "This is the root of heaven, and this is the cave of the moon," saying things like "When heaven meets wind" or "When earth meets thunder," the words may be clear, but where is the personal realization? Moreover, if such fixed forms and images remain in one's mind, it will become even more difficult to make progress later on. This is indeed a great hindrance for beginners. The reason I still use diagrams in this book is out of necessity: to explain things to beginners, diagrams are indispensable for guidance. Therefore, I have deliberately omitted all the traditional diagrams, even those that are well-drawn. Scholars should first get a general understanding of the general meaning of the hexagrams and their meanings ("c" is the same as "coarse"). Then they can go on to study the diagrams and explanations of predecessors. In this way, they can judge what is correct and what is not, and decide what to take and what to discard, with a clear understanding in their minds, thus avoiding the spread of errors. This is my intention in writing this book.

程朱《傳》、《義》，宗王《注》，其釋《彖》、《象》，均以卦德卦義卦名為言。來知德氏《集註》言性情，以內卦為性，外卦為情，意非不當，要皆強為之名。實則孔子《繫傳》、《說卦》，當名辨物，已有定稱。《傳》曰：“彖者，才也。才也者，材也。”言材則體用皆賅，德性兼備無餘蘊矣。《說卦》“雷動風散”，“乾健坤順”兩章，皆言八卦之材。知八卦象之材，而後知六十四卦因重交互，無不各因其材。而辨其情偽吉凶，銖兩悉稱，名實相副。《彖》、《象》傳贊，亦無不各因其材以為之辭，無一字之虛設焉。

Cheng Yi's Yichuan Commentary on the Changes and Zhu Xi's The Original Meaning of the Zhou Changes both follow Wang Bi's Commentary on the Zhou Changes. In explaining the Commentary on the Judgment and the Image Commentary, they all use the terms "gua de" (the virtue of the trigram), "gua yi" (the meaning of the trigram), and "gua ming" (the name of the trigram) as their basis. In contrast, Lai Zhide's Collected Commentaries on the Zhou Changes of the Ming dynasty introduced the concept of "xingqing" (nature and emotion), taking the inner trigram as nature and the outer trigram as emotion. Although his intention cannot be considered improper, these are all forced and newly coined terms. In reality, Confucius in the Great Treatise and the Discourse on the Trigrams already established fixed terms through identifying names with things. The Great Treatise says, "Tuan (Commentary on the Judgment) means 'cai' (material or capacity); 'cai' means 'cai' (material)." By using the term "cai," both the essence and function are included, encompassing virtue and nature without omission. In the Discourse on the Trigrams, the passage "Thunder moves it, wind disperses it" and "Qian is strong, Kun is receptive" both discuss the "cai" of the eight trigrams. Understanding that each trigram's image has its own "cai" allows one to comprehend that the sixty-four trigrams are formed by overlapping and interacting trigrams, none of which is not based on their respective "cai." Thus, one can distinguish between genuine and false, good fortune and misfortune, gain and loss with precision, ensuring that names and realities correspond exactly. The commentary in the Commentary on the Judgment and the Image Commentary also never uses a single word without reference to the "cai" of the trigram.

學者宜詳玩經文，而合之於象，準之於數，融會貫通，由一卦以推各卦，而觀一卦，更必遍取各卦，參互比例，而後能得其真確之意義。不可因字義註釋之已明，而不復研求深意之所在焉。健順動入陷麗止說，各一字概一卦之德性功用。而父母男女，亦各因其名，以定一卦之分際。今皆謂之材者，以六十四卦之《彖》、《象》，無不合內外兩卦之材以命辭。而一卦六爻，及內外中爻，亦無不取材於是。

Those who study the Book of Changes should carefully examine the text, aligning it with the trigrams, verifying it with the numbers of the hexagrams, and integrating these elements to understand one hexagram in relation to all others. When observing a single hexagram, one must also refer to all the other hexagrams for comparison, only then can the true meaning be grasped. One must not stop at understanding the words literally, but should delve deeper into their profound implications. "Jian, Shun, Dong, Ru, Xian, Li, Zhi, Shuo"—Qian represents strength, Kun represents receptivity, Zhen represents movement, Xun represents entry, Kan represents depression, Li represents brightness, Gen represents stillness, and Dui represents joy. Each of these terms summarizes the virtue and function of a hexagram with a single character. The terms such as father, mother, eldest son and daughter, middle son and daughter, and youngest son and daughter also define the boundaries of each hexagram according to their names. Now these are collectively referred to as "cai" because the Commentary on the Judgment and the Image Commentary of the sixty-four hexagrams all derive their expressions from the materials of both the inner and outer trigrams. Moreover, the six lines of a hexagram, as well as the inner trigram, outer trigram, and the intermediate lines, all draw their materials from these sources.

《傳》曰：“君子觀其彖辭，則思過半矣。”彖辭因材而施之辭也，且不特內外卦為然。即卦中之一爻，為何卦之爻，即具何卦之材。如為坎爻必有陷義，或險義。為離爻者，必具明義，或麗義。惟乾坤兩卦，不以爻言。而《雜卦》之“震起兌見巽伏艮止”，此“起止見伏”四字，尤為八卦變化之門。觀象玩辭，均不可不於此鄭重注意也。

The Great Treatise says: "A gentleman observes the hexagram statements and thus reflects upon more than half of their meaning." The hexagram statements are conclusions drawn based on the materials of each hexagram, so understanding the hexagram statements means grasping most of their meaning. Moreover, the materials used are not limited to the inner and outer hexagrams; any line within a hexagram, depending on which hexagram it belongs to, possesses the materials of that hexagram. For example, a line belonging to Kan carries the meaning of "trapping" or "danger"; a line belonging to Li carries the meaning of "brightness" or "adhesion." Only Qian and Kun, the pure yang and pure yin hexagrams, are not divided according to their lines. As for what the Miscellaneous Hexagram Treatise says: "Zhen signifies movement, Dui signifies appearance, Xun signifies concealment, and Gen signifies stillness," these four words—"movement, stillness, appearance, concealment"—are especially the gateways of the transformation of the eight trigrams. Observing the hexagram images and contemplating the hexagram statements cannot fail to pay serious attention to these points.

《易》六十四卦，八純卦外，五十六卦，皆合兩卦之象數而立之名。名所由來，兩漢之師說既不盡傳，後人遂不能明其意之所在。為之說者，皆賴《序卦》及《雜卦》之單辭雙義，推衍而申明之。不知《序卦》，但據文王之卦序而貫串之，《雜卦》則專以中爻交錯，明剛柔消長之理，而終之以剛決柔之大用。此皆孔子贊《易》微言大義所在，與當名辨物，別為一義，不容依附牽涉併為一談者也。蓋自《連山》、《歸藏》，經卦別卦，相傳各有其名。文王之序《周易》，有仍其舊名者，有別言新名者。今《連山》、《歸藏》，既無全書，無從參考。而《周易》卦名，各家注《易》者，迄無所發明。

The Zhou Changes contain sixty-four hexagrams. Excluding the eight pure hexagrams (Qian, Kun, Kan, Li, Zhen, Gen, Xun, and Dui, each formed by the repetition of their trigrams), the remaining fifty-six hexagrams derive their names from the images and numbers of two trigrams. The origin of these names has not been fully transmitted through the traditional interpretations of the Han dynasty. Later scholars have therefore been unable to understand the original intent. Those who attempt to explain them rely only on the single-sentence remarks in the "Sequence of Hexagrams" and the "Miscellaneous Hexagrams," which often have dual meanings. They fail to realize that the "Sequence of Hexagrams" merely connects the sixty-four hexagrams in the order established by King Wen, while the "Miscellaneous Hexagrams" focuses on the interaction of the middle trigrams to explain the principle of the waxing and waning of yin and yang, ultimately concluding with the great use of "yang overcoming yin." Both of these texts are places where Confucius conveyed profound meanings in the commentary on the Zhou Changes. They are separate from the principle of "naming things according to their names" (establishing names for hexagrams to distinguish things), and should not be conflated or confused. Using the "Sequence of Hexagrams" and the "Miscellaneous Hexagrams" to explain the origin of hexagram names is like using the principles of one matter to explain the names of another. Originally, since the "Lian Shan" and "Gui Cang," the single-trigram hexagrams and the six-trigram hexagrams were said to have their own names. When King Wen arranged the Zhou Changes, some names were carried over from the old ones, while others were newly established. However, since the "Lian Shan" and "Gui Cang" have not been fully preserved, there is no reference available. And throughout history, those who have commented on the Zhou Changes have never explained the meanings of the hexagram names.

其淺顯易見者，如泰否損益等卦，尚不難顧名思義。若火山之何以名旅，山火之何以名賁，及大過小過之類，則望文生義，即難自圓其說。眾議紛紜，乃無可折中矣。不知名位象數，互相因緣，不能相離。不知名，其何以知《易》？遍徵群籍，兼及古今占筮諸書，始知《周易》卦名，有合內外兩象之名義而成者，如屯蒙需訟等卦是也。有取象於先天卦位者，如大小過等卦是也。有取象於後天方位者，如謙睽家人等卦是也。有合取先後天卦位者，如噬嗑同人節比中孚觀頤大小畜等卦是也。更有取象於八宮世應，及五行順逆者，至不一例，要無不各有其義。舊說只限於內外兩象者，說尚可通。餘皆以不解解之，茲特疏舉所已知者如左，未知者仍闕疑以俟後之君子。

Among the more obvious ones, such as the hexagrams of Tai, Pǒ, Sun, and Yi, it is not difficult to understand their names from their meanings. However, for hexagrams like the Fire Mountain hexagram named Lv, and the Mountain Fire hexagram named Ben, as well as hexagrams such as Da Guo and Xiao Guo, if we merely rely on the literal meaning of their names, it becomes hard to explain them consistently, leading to many conflicting interpretations and no clear resolution. One must understand that the names of hexagrams, the positions of lines, the images, and the numbers of hexagrams are interdependent and cannot be separated. If one does not even understand the origin of a hexagram's name, how can one hope to understand the Yi? For this reason, I have extensively consulted various books, including ancient and modern divination texts, and have come to realize that the origins of the names of hexagrams in the Zhou Yi are roughly divided into the following categories: some are formed by combining the images of the inner and outer trigrams, such as Zun, Meng, Xu, and Song; some are based on the positions of the Earlier Heaven hexagrams, such as Da Guo and Xiao Guo; some are based on the Later Heaven directions, such as Qian, Kui, and Jia Ren; some combine both Earlier and Later Heaven positions, such as Shi He, Tong Ren, Jie, Bi, Zhong Fu, Guan, Yi, Da Xu, and Xiao Xu; and there are also those based on Jing Fang's eight palaces, the World and Response Lines, and the order and reversal of the Five Phases, with very inconsistent examples, yet each has its own meaning. The old interpretations only covered those based on the images of the inner and outer trigrams, which are somewhat reasonable, but the others can only be explained as "un-understood." Here I specially list the ones I have now understood, while those still unclear remain in doubt, waiting for future scholars to resolve.

乾　象辭“天行健”三字盡之。八純卦名，皆不易。既知八卦之方位，象數重卦之名位，象數舉可知矣。　坤　象辭“地勢坤”三字盡之。乾不稱乾而坤稱坤者，此天地陰陽之分際，聖人之物筆也。按：《序卦》不序乾坤，以乾坤為天地，萬物皆覆載於天地之中。全《易》六十四卦皆乾坤六爻所生，故《繫辭》稱為“《易》之門”，“《易》之蘊”，非屯蒙以下六十二卦所能等量而齊觀也。《序卦》首曰“有天地”，天地即乾坤也。

The Qian hexagram: The "Heaven moves with strength" in the Great Image Commentary has already explained it fully. The names of the eight pure hexagrams all retain the old names from the trigrams, without changing them. As long as one understands the positions and numbers of the eight trigrams, the names, positions, and numbers of the compound hexagrams can also be inferred. The Kun hexagram: The "Earth's terrain is receptive" in the Great Image Commentary has already explained it fully. The Great Image of Qian does not say "Heaven moves with Qian" but instead says "Heaven moves with strength," while the Great Image of Kun still uses the word "Kun." This is precisely the difference between heaven and earth, yin and yang, and the careful balance of the sage's writing. Hang's note: The Order of Hexagrams does not include Qian and Kun in the sequence of mutual generation, because Qian and Kun are heaven and earth, and all things are covered and supported by heaven and earth. All sixty-four hexagrams of the Book of Changes are generated from the six lines of Qian and Kun, so the Xici Commentary calls them "the gate of the Book of Changes" and "the essence of the Book of Changes," which cannot be compared with the other sixty-two hexagrams starting from Zun and Meng. The Order of Hexagrams begins by saying "there is heaven and earth," and "heaven and earth" refers specifically to Qian and Kun.

屯　屯，難也，陰陽始交，故為六十二卦之始。按：屯象，草木初出地，而尾猶屈。一陽動於下，而上未應。中爻艮止，故難。此由內外兩象取義以立名者也。　蒙　蒙，物之始生。按：陽氣動於地之下，而二上兩爻包坤，有離象。如日光下燭，則地之上必有氣蒸發，所謂蒙氣是也。故名曰“蒙”。

The hexagram Zun (Obstruction): "Zun" means difficulty. Yin and yang are just beginning to interact, so it comes after Qian and Kun, and is the first of the remaining sixty-two hexagrams. Hang's commentary says: the image of the character "Zun" resembles young grass and trees emerging from the ground with their tips still curled. The hexagram Zun has Zhen below and Kan above, with one yang line at the bottom initiating movement, but no response above yet; the third, fourth, and fifth lines together form Gen, which signifies stopping, hence the name "Obstruction." This is an example of naming a hexagram based on the images of the inner and outer trigrams. The hexagram Meng (Obstinacy): "Meng" refers to the initial state of all things. Hang's commentary says: yang energy is beginning to move underground, and the two yang lines, Nine in the Second and Nine at the Top, enclose the three, four, and fifth lines forming Kun, which is solid on the outside and hollow inside, exactly like the image of Li. Just as sunlight shines from above, there must be rising mist on the ground, which is called "Meng qi," hence the name "Obstinacy."

需　《象》曰：“雲上於天”。《序卦》：“需，養也。”按：需從雨從而。“雨”為坎，“而”與古文天字同，乾也。　訟　《象》曰：“上剛下險。險而健，訟。”言其義也。天與水違行，言其象也。按：天水違行，何以有訟之名？夫乾父也，坎為中男，天與水乎，抑父與子也。聖人不忍斥言父子，而云天水，所謂微言也。《雜卦》“訟不親也”，可互文見義矣。

The hexagram Need: The Great Image says "clouds above the sky," and the Order of Hexagrams says "Need means nourishment." Hang's commentary says: The character "Need" is composed of "rain" and "er." "Rain" corresponds to the trigram Kan, and "er" is similar in ancient form to the character for "sky," corresponding to Qian. The hexagram Need is composed of Qian below and Kan above, so the character and the hexagram correspond. The hexagram Strife: The Commentary on the Judgment says "upper yang and lower danger, dangerous yet strong, hence strife," which explains its meaning. The Great Image says heaven and water are moving in opposite directions, which explains its physical image. Hang's commentary says: Heaven and water moving in opposite directions is called "strife." Why? Because Qian is the father and Kan is the middle son. So "heaven and water" actually refers to father and son. The sage did not say directly that father and son have a lawsuit, so he used the term "heaven and water," which is called "subtle words." The Miscellaneous Hexagrams say "strife means not being close," and these two statements complement each other in meaning.

師　《彖》曰：“地中有水，師。師，眾也。”按：大地所載之物，莫多於水。而地中之水，尤多於地上之水。故云“眾”。　比　《象》曰：比，輔也。按：水地相比，先天卦坤居北方，後天卦坎居北方，坤坎同位，故曰“比”。此合先後天之象而立名者也。

The "Military" hexagram: The "Commentary on the Judgment" says, "Water beneath the earth, military; military means multitude." Hang's note: The earth carries many things, but water is the most abundant; and water beneath the earth is even more than that on the surface, hence the meaning of "multitude." The "Comparison" hexagram: The "Great Image Commentary" says, "Comparison means assistance," meaning the idea of being close and supportive. Hang's note: The "Comparison" hexagram has upper Kan water and lower Kun earth, with water and earth being close and supportive. In the Earlier Heaven arrangement, "Kun" is in the north, and in the Later Heaven arrangement, "Kan" is also in the north. "Kun" and "Kan" share the same position, hence the name "Comparison." This is an example of taking the images of both the Earlier Heaven and Later Heaven arrangements to name the hexagram.

小畜　《象》曰：風行天上，小畜。按：後天巽東南，乾西北，乾巽對宮，畜有相近相合之意。此取後天方位之象以立名者也。月卦乾為四月，與巽辰巳亦同位。　履　《彖》曰：柔履剛也。按：“柔履剛”三字，聚訟不決。或云“乾履兌”，或曰“三履四”，皆非也。柔履剛，坤三柔履乾三剛，此由對卦取象以立名者也。坤曰“履霜”，離曰“履錯然”。始終以履，即始終以禮。先天兌居乾之左，後天兌居乾之右，左右逢源，禮和為貴，合先後天之象觀之，更見象義之精，立名之當也。

The hexagram Xiao Xu says: The Great Image says, "Wind moves over heaven, small accumulation." Hang's commentary notes: In the Later Heaven arrangement, "Xun" (Wind) is in the Southeast, and "Qian" (Heaven) is in the Northwest, with the two trigrams Qian and Xun directly opposite each other. The term "xu" (accumulation) implies closeness and union, as well as gathering and storing. This is an example of naming a hexagram based on the Later Heaven directional imagery. Looking further at the twelve message hexagrams, "Qian" (Heaven) corresponds to the fourth month (the month of Si, or Snake), and the branch associated with the Later Heaven position of Xun is Chen and Si, which also share the same position. The hexagram Li (Steps) says: The Commentary on the Judgment says, "Softness treads on firmness." Hang's commentary notes: The phrase "softness treads on firmness" has been debated throughout history. Some say it refers to "Qian treading on Dui," while others say it refers to "Six in the Third treading on Nine in the Fourth," but neither is correct. The term "softness treads on firmness" actually refers to the three soft lines of the hexagram Kun treading on the three firm lines of the hexagram Qian. This is an example of naming based on the imagery of the opposing hexagrams (Qian and Kun). The hexagram Kun's line statement says "treading on frost," and the hexagram Li's line statement says "treading in disorder," both beginning and ending with the word "treading," which signifies a beginning and an end that both relate to "ritual." Looking at the directions: In the Earlier Heaven arrangement, "Dui" (Lake) is to the left of "Qian" (Heaven), while in the Later Heaven arrangement, "Dui" is to the right of "Qian." In both cases, "Dui" meets "Qian" on either side, which aligns with the meaning of "the use of ritual lies in harmony being most precious." By combining the Earlier and Later Heaven images, we can see the precision of the imagery and the appropriateness of the naming.

泰　《彖》曰：小往大來。否　《彖》曰：大往小來。按：泰否之說，先儒言之詳矣。然其立名，則取象於卦候，及先後天方位者也。玩《坤·文言》自見。　同人　天火同人。《雜卦傳》曰：同人親也。按：先天乾，後天離，先後同位，故曰“同人”，曰“同人親也”。

The hexagram Tai says: The Commentary on the Judgment states, "small things go out and great things come in," meaning the yin energy moves outward and the yang energy comes inward. The hexagram Po says: The Commentary on the Judgment states, "great things go out and small things come in," meaning the yang energy moves outward and the yin energy comes inward. Hang notes: The principles of the hexagrams Tai and Po have been explained in detail by previous Confucian scholars; however, regarding their naming, they are based on the imagery of the hexagram energies and seasonal changes (Tai is the hexagram of the first month, Po is the hexagram of the seventh month) as well as the earlier and later heaven directions. By contemplating the yin and yang waxing and waning discussed in the "Discourse on the Image" of the Hexagram坤, this can be clearly understood. The hexagram Tongren: Heaven above and fire below forms the hexagram Tongren. The Miscellaneous Hexagram Commentary states, "Tongren means to be close to others." Hang notes: In the earlier heaven arrangement, the hexagram Qian is located in the south, and in the later heaven arrangement, the hexagram Li is also located in the south. Both earlier and later heaven arrangements share the same position, hence the name "Tongren." The Miscellaneous Hexagram Commentary therefore says, "Tongren means to be close to others."

大有　《象》曰：火在天上。按：大有亦先後同位，而其立名，不取先後天，而取對卦水地比覆象之地水師，故師眾也，大有眾也。變化不測，精義入神。《學易筆談二集》，述其一端，餘義尚未能盡。　謙　《象》曰：地中有山。按：後天坤艮對宮，坤未艮丑，子正在丑，午正在未，丑二未八。二八易位，天地之數由此勻平，故曰“謙稱平”。

The hexagram Da You: The Great Image says, "Fire in the heavens." Hang's commentary states: Da You also belongs to the category of hexagrams that share the same position in both the Earlier Heaven and Later Heaven systems (in the Earlier Heaven, Qian is in the south; in the Later Heaven, Li is also in the south). However, its name is not derived from the Earlier Heaven or Later Heaven, but from its opposing hexagram Bi (Water on Earth) turned upside down to form Shi (Earth on Water). Shi means "multitude," and Da You also signifies "multitude" — meaning that one possesses many things. This method of deriving meaning through transformation is unpredictable and profound, entering into the realm of the mysterious. I have discussed one aspect of this in my "Pen Talks on the Study of the Book of Changes, Volume Two," but there are still other meanings that I have not fully explained. The hexagram Qian: The Great Image says, "Mountain within the earth." Hang's commentary states: In the Later Heaven system, the positions of the hexagram Kūn (Earth) and Gèn (Mountain) are opposite. Kūn is paired with "Wei," and Gèn is paired with "Chou." The position of "Zi" (Due North) is directly followed by "Chou," and the position of "Wu" (Due South) is directly followed by "Wei." Counting the earthly branches in order, "Chou" corresponds to the number two, and "Wei" corresponds to the number eight. When two and eight exchange positions, the numbers of heaven and earth become balanced, hence the Commentary on the Judgment says, "Qian, to measure things and distribute evenly." The fundamental meaning of "Qian" is to maintain balance.

豫　《象》曰：雷出地奮。按：豫之立名，與大有與師謙與履同例。履以制禮，禮之本在謙。豫以作樂，樂之本在小畜。孟子曰“畜君何尤”，又曰“一遊一豫為諸侯度”，乃深得易象之精意者也。　隨　《象》曰：澤中有雷。按：隨之立名，取象後天之少女長男，陽動陰隨，夫倡婦隨。而六爻未嘗言夫婦，則重在隨時。有孚在道，不以形下之名與器限也。此非熟玩先後天八宮納甲，及六十四卦，上下變通，未易窺測。

The hexagram Yu: The Great Image says, "Thunder arises from the earth and moves forward." Hang's commentary states: The naming of Yu follows the same principle as Da You taking its image from Shi and Qian taking its image from Lu. Lu is used to establish rites, and the foundation of rites lies in "Qian" (humility); Yu is used to create music, and the foundation of music lies in the moderation and restraint of Xiao Xu (small accumulation). The Mencius cites Yanzi's words: "Xu Jun He You" — restraining the faults of the sovereign is not something to be blamed, and "Yi You Yi Yu, Wei Hou Ju Du" — the travels and pleasures of the Son of Heaven should become the standard for the feudal lords. This is precisely a deep understanding of the essence of the Book of Changes. The hexagram Sui: The Great Image says, "Thunder within a marsh." Hang's commentary states: The naming of Sui takes its image from the later heaven positions of the young woman (Dui) and the elder son (Zhen): yang initiates movement while yin follows, like husband and wife in harmony. However, the six lines of Sui do not mention husband and wife, indicating the focus is on "following the times" — the line statement "There is sincerity in the path" relies on sincerity aligned with the right path, not limited by worldly distinctions of rank or objects. This level of understanding cannot be grasped without thoroughly mastering the later heaven positions, Jing Fang's eight palaces, the stem assignment system, and the principles of transformation in the sixty-four hexagrams.

蠱　《象》曰：山下有風。按：山風兩卦，先天在右，後天居左。立名之取象於先後天自無疑義。爻象多取父母，即後天乾坤之證也。所以謂之蠱者，蠱訓事，亦訓故。史稱三皇五帝之故事，亦云“蠱事”，故曰“幹蠱”。陰陽之數，至十八而變化備，蠱次第十八。物之變莫不由於風，實由於蟲。巽之風兼今日之所謂空氣。空氣不可見，於風見之。巽之入，風之無微不入，實氣之無微不入耳。蟲生於氣化，氣非有止之者亦不化。上卦艮止，故蠱能變化。物理之精，一名之微，而鉅細無遺。非造化之筆，其孰能之！

The "Gǔ" hexagram: The "Great Image" says "mountain beneath wind." Hang氏 notes: The hexagrams of "Gèn" (Mountain) and "Xùn" (Wind) are both located on the right side in the Earlier Heaven diagram and on the left side in the Later Heaven diagram. This clearly shows that the naming and imagery of "Gǔ" are based on the positions of the Earlier and Later Heaven diagrams, which is without doubt. Its line statements frequently mention "rectifying the father's affairs" and "rectifying the mother's affairs," which serve as evidence that in the Later Heaven arrangement, the hexagrams of "Qián" (Heaven) and "Kūn" (Earth) occupy the positions previously held by "Gèn" and "Xùn" in the Earlier Heaven diagram. The term "Gǔ" can be interpreted as "affairs" or "old matters." Historical texts refer to the old affairs of the Three Emperors and Five Kings as "gùshì" (old stories), also written as "gǔshì" (affairs of the past). Therefore, the line statements refer to "rectifying the affairs," meaning to manage or reform these old matters. From a numerical perspective, the yin and yang numbers are fully expressed by the number eighteen, and the hexagram "Gǔ" is exactly the eighteenth in the sequence of hexagrams. All changes in the world are due to wind, but actually they are due to insects (microscopic creatures). The wind represented by "Xùn" includes what is today called "air"; air is invisible, but it can be perceived through wind. The virtue of "Xùn" is "entering," as wind penetrates everywhere, which is actually the air penetrating everywhere. Insects are generated from the transformation of air, but if air is not restrained by something, it will not transform. The upper trigram of "Gǔ" is "Gèn," which represents stopping, so "Gǔ" can produce transformation. The principles of things are so subtle; even the subtle aspect of a hexagram's name encompasses everything, large and small. If it were not the brush of nature, who could achieve such a feat!

臨　《象》曰：澤上有地。按：臨為月卦，立名自出於卦候，觀彖辭自見。臨丑月卦，丑數二。丑與子合，為天地始合，故復小臨大。　觀　《象》曰：風行地上。按：巽坤亦先後天同位之卦。名曰“觀”者，觀以目。目上下相合，觀八月卦，故亦兼取卦候。　噬嗑　《象》曰：電雷噬嗑。按：先天離，後天震，故曰“噬嗑合”也。明先後天之相合也。

The hexagram "Qin" (Approach): The Great Image says "Earth over Water." Hang's commentary states: "Qin is one of the twelve message hexagrams. Its name naturally comes from the hexagram's qi and seasonal changes. Looking at its "Tuan Ci" (Commentary on the Image) will clarify this. The hexagram "Qin" corresponds to the month of Chou, which is the second in the sequence of the earthly branches. Chou combines with Zi, indicating the beginning of the meeting between heaven and earth. Therefore, "Fu" (Zi month, one yang) is small, while "Qin" (Chou month, two yangs) is great. The hexagram "Guan" (Observation): The Great Image says "Wind moving over Earth." Hang's commentary states: "In the Earlier Heaven arrangement, 'Xun' (Wind) is located in the southwest, and in the Later Heaven arrangement, 'Kun' (Earth) is also located in the southwest. 'Xun' and 'Kun' are hexagrams that occupy the same position in both Earlier Heaven and Later Heaven. The name 'Guan' (Observation) is derived because observation requires the eyes, and the character 'Guan' itself symbolizes two eyes facing each other. 'Guan' is also the eighth month hexagram, so its name also takes into account the hexagram's qi and seasonal changes. The hexagram "Shihe" (Crushing): The Great Image says "Lightning and Thunder Crushing." Hang's commentary states: In the Earlier Heaven arrangement, 'Li' (Fire) and in the Later Heaven arrangement, 'Zhen' (Thunder) are located in the same position. Therefore, the "Zage Zhuan" (Miscellaneous Hexagrams) says "Shihe, combining," which indicates the convergence of Earlier Heaven and Later Heaven in this position.

賁　《象》曰：山下有火。按：山以草木為飾。賁無色也。山下有火，草木焚山成賁矣。此由內外兩象立名者也。旅之“鳥焚其巢”，象出於賁，所謂上下易之卦也。　剝　《象》曰：山附於地。按：剝為九月卦，當然由卦候立名。陰之消陽以漸，剝與夬相對。履霜堅冰，非至柔變剛，尚不悟其為剝也。

The hexagram of Zhen says: "Fire below the mountain." Hang's commentary says: A mountain is decorated with grass and trees, but when Zhen reaches its extreme, it becomes colorless ("White Zhen, no blame" in the line statement of the top nine). Fire below the mountain burns the grass and trees, and the mountain becomes white Zhen. This is an example of naming a hexagram based on the images of the inner and outer trigrams. The hexagram of Lu, line three "The bird burns its nest," is exactly based on the image of Zhen. Lu and Zhen have their inner and outer trigrams reversed, which is called "reversing upper and lower." The hexagram of Po says: "The mountain attached to the earth." Hang's commentary says: Po is the hexagram of September, so it is named based on the seasonal changes of the hexagram. Yin gradually consumes Yang, and Po and Guai are opposite to each other: Guai is five Yangs deciding to remove one Yin, while Po is five Yins peeling away one Yang. The line statement of the first six in the hexagram of Kun says "Treading on frost, the hard ice comes." If people do not wait until the soft Yin accumulates into a strong force, they will not realize that it has already become "Po."

復　《象》曰：雷在地中。又曰：復其見天地之心乎？按：復為一陽來復，立名即取本卦之一爻為主，而兼取卦候。《傳》曰“復小而辨於物”。辨之於早，所以能見天地之心也。　無妄　《象》曰：天下雷行，物與無妄。按：妄，《說文》“亂也”。馬、鄭、王、蕭皆作望。以剛自外來為主於內，前人都以變卦釋之，而說各不同，未敢妄斷。觀象辭“君子以茂對時育萬物”，則亦有取卦候。故端木氏《周易指》以為對時卦，亦無他書可證，姑闕疑以待博雅君子。

The Hexagram of Fu: The Great Image says, "Thunder in the earth." The Commentary on the Judgment adds, "Fu, can it be the heart of heaven and earth?" Hang's note: Fu represents the return of one yang line. The name of the hexagram is based on the first line, the Nine at the Beginning, and also takes into account the seasonal and climatic changes associated with the hexagram. The Great Treatise says, "Fu, small yet discerning of things." This means that even in the most minute details, one can discern the direction of things. Because of this early discernment, one can see the creative heart of heaven and earth. The Hexagram of Wuwang: The Great Image says, "Thunder moving across the world, things are without error." Hang's note: The character "wang" is explained in the Shuowen Jiezi as meaning "disorder." Ma Rong, Zheng Xuan, Wang Su, and Xiao Shi all wrote it as "wang." The Commentary on the Judgment says, "Yang strength comes from outside and becomes the dominant force within." Previous scholars explained this using hexagram transformation, but the interpretations differ among the various schools. I dare not make an arbitrary judgment. Looking at the phrase "The gentleman thus cultivates himself in accordance with the seasons and nurtures all things" in the Great Image, it is evident that it also takes into account the seasonal and climatic changes associated with the hexagram. Therefore, the Qing scholar Duanguo Hu in his Zhouyi Zhi classified Wuwang as the "seasonal hexagram." However, there is no other source to confirm this, so I will leave it in doubt, awaiting the resolution by learned scholars.

大畜　《象》曰：天在山中。按：艮乾亦先後同位之卦，乾巽以闢卦及後天同位曰“小畜”。故此先後八卦同位者，曰“大畜”。　頤　《象》曰：山下有雷。按：頤亦先後天同位，故取象上下相合。凡頤皆下動而上下動者也。爻取龜息虎視，當為古易相傳之象，為今道家修養之秘龠。孔子非道家之學，故以節言語慎飲食言之，而象數亦無不悉合。所謂殊塗而同歸也。

The hexagram of Great Accumulation: The Great Image says, "Heaven in the mountain." Hang's commentary: The trigrams Guan and Qian are also trigrams that are in the same position in both the Earlier Heaven and Later Heaven systems — in the Earlier Heaven, Guan is in the Northwest, and in the Later Heaven, Qian is also in the Northwest. Previously, the hexagram of Small Accumulation was named because the trigrams Qian and Xun are in the same position according to the twelve gate trigrams and the Later Heaven directions. Here, the entire Earlier Heaven and Later Heaven trigrams are in the same position, so it is called "Great Accumulation." The hexagram of Nourishment: The Great Image says, "Thunder beneath the mountain." Hang's commentary: The hexagram of Nourishment is also a hexagram where the Earlier Heaven and Later Heaven trigrams are in the same position (in the Earlier Heaven, Zhen is in the Northeast, and in the Later Heaven, Gen is also in the Northeast). Therefore, it takes the image of the upper and lower parts combining. Generally, when one chews, it is the lower jaw that initiates movement, with the upper and lower parts moving in coordination. The line statements refer to "the spiritual turtle" inhaling and exhaling, and "the tiger watching intently," which should be old images passed down from the ancient Book of Changes, that is, the secret key of Daoist cultivation today. Confucius did not speak of Daoist studies, so he only spoke of controlling speech and being cautious in diet, yet it is entirely consistent with the principles of numbers and images — this is what is called "different paths leading to the same destination."

大過　《象》曰：澤滅木。按：大過，大者過也。陽大陰小，過者過乎中之謂。大過言大過乎中，即陽過乎中也。此全取象於先天卦位。先天巽兌居乾之左右，皆偏而不中。巽兌皆二陽，所謂陽過乎中（先天以體為主，以二陽者為陽卦，二陰者為陰卦。後天以用為主，以一陰為陰卦，一陽為陽卦。觀大小過立名，先天卦之方位已明白如見矣。）。大者過也。“大過棟橈”，棟極也，極中也，本末弱則合上下兩象而言之。頤中重坤，大過重乾，以結上篇。終以坎主，開後天之局，即以啟下篇之端。故離履錯然，上下篇相錯，六十四卦皆一氣呵成矣。

The Hexagram of Great Excess: The Great Image says "the marsh overcomes the wood." Hang's commentary states: The Hexagram of Great Excess is "greatness exceeding." Yang represents the great, Yin the small, and "excess" means going beyond the center. "Great Excess" refers to the great going beyond the center, that is, Yang exceeding the center. This is entirely based on the Earlier Heaven arrangement: In the Earlier Heaven, Wind and Lake are on either side of Heaven, both leaning to one side rather than being in the center. The two trigrams Wind and Lake each contain two Yang lines, which is exactly what is called "Yang exceeding the center." (The Earlier Heaven focuses on the essence, so a hexagram with two Yang lines is considered a Yang hexagram, and one with two Yin lines is considered a Yin hexagram. The Later Heaven focuses on function, so a hexagram with one Yin line is considered a Yin hexagram, and one with one Yang line is considered a Yang hexagram. Just by looking at the names of the Hexagrams of Great Excess and Small Excess, the positions in the Earlier Heaven are clearly visible.) Therefore, it is said "greatness exceeding." The Hexagram Statement says "Great Excess, the beam is bent." "Beam" refers to the extreme of the roof, and "extreme" means the center. The Commentary on the Judgment says "both beginning and end are weak," which is based on both upper and lower images (the first and top lines are both Yin, so both ends are weak). Now looking at the conclusion of the Upper Canon: The Hexagram of Nourishment has the middle four lines overlapping to form坤 (Earth), and the Hexagram of Great Excess has the middle four lines overlapping to form乾 (Heaven), thus concluding the Upper Canon. Finally, it uses Kan (Water) as the main element (Kan and Li (Fire) are at the end of the Upper Canon), opening up the pattern of the Later Heaven, thereby initiating the Lower Canon. Hence, the first line of the Hexagram of Li (Fire) says "walking in a confused manner," with the Upper and Lower Canons interweaving, and the sixty-four hexagrams flowing seamlessly together.

習坎　《象》曰：水洊至。按：八純重卦，皆不易卦名，獨坎曰“習坎”。先儒論議紛如，各有所見，偏以理想者多。坎勞卦也，後天居坤位，坤“不習無不利”，所謂安而行之者也。非生知之聖，詎足語此？聖人立教，首重時習。坎子一始，故特於重坎著“習”字以明立教之旨，亦為全《易》入門之關鍵也。　離　《象》曰：明兩作。按：“明兩作”者，兼日月而言。月得日光而明，月之明即日之明，故重離以象日月也。離居乾位，而曰“牝牛”，正與《坤·彖》之“牝馬”對。所謂八卦相錯。

The Hexagram of "Progressing Water" (Xí Kǎn): The Great Image says, "Water flows continuously." Hang's commentary states: After eight pure hexagrams are superimposed upon each other, their names remain unchanged, except for the Hexagram of Kan, which is called "Progressing Water." Previous scholars have debated this issue extensively, each with their own views, but most of their interpretations are based on speculation. Kan is referred to as the "Toil Hexagram" in the Sayings of the Trigrams. In the Later Heaven arrangement, it occupies the position of the Hexagram of Kun. The line six in the second of the Hexagram of Kun says, "Without learning, there is no disadvantage," indicating a state of effortless and natural action. If one is not a sage who knows by birth, how could such a state be achieved? Sages emphasize teaching, starting with "learning and reviewing regularly." Kan is associated with the position of Zi, which signifies the beginning of a year and a day. Therefore, the character "Progressing" is specially added above the double Kan to highlight the purpose of establishing education, which is also the key to understanding the entire Book of Changes. The Hexagram of Li: The Great Image says, "Two lights are shining." Hang's commentary states: The phrase "two lights are shining" refers to both the sun and the moon. The moon becomes bright only when it receives the light of the sun; the brightness of the moon is actually the brightness of the sun. Therefore, two Lises are superimposed to symbolize the sun and the moon. Currently, Li occupies the position of Qian in the Earlier Heaven arrangement, yet the hexagram statement says, "Keeping a female ox is auspicious," which contrasts with the "steadfastness of the female horse" in the Discourse of the Hexagram of Kun. This is what is called "the eight trigrams interrelate."

咸　《象》曰：山上有澤。按：《序卦》無咸。咸無也。孔子以有立教，故不序咸。卦之立名全取先天卦象。先天兌艮對宮，艮居西北。後天乾位，戌亥無數。咸從戌口，天地娵訾之口，八風不周之方，精義入神，合乾坤之體用而賅之矣。後天乾居西北，闢卦坤居西北，故曰乾坤合居。後天巽乾對宮，先天兌艮對宮，下篇以巽兌震艮代乾坤之用，而咸居首，神矣哉聖人之筆也！

The Hexagram of "Salt" (Xian): The Great Image says, "A mountain has a marsh on top." Hang's commentary states: The "Sequence of Hexagrams" does not mention the word "Xian" in the lower section, because "Xian" is equivalent to "wu" (nothing), and Confucius established his teachings based on "you" (existence), so the Hexagram of "Xian" is not included in the sequence. The naming of this hexagram is entirely based on the Earlier Heaven hexagram: In the Earlier Heaven, the hexagram Dui (Lake) and Gen (Mountain) are opposite, with Gen located in the Northwest. The Northwest corresponds to the Later Heaven position of Qian (Heaven), which is paired with Xu and Hai, and numerically belongs to "wu" (nothing). The character "Xian" is composed of "Xu" and "kou," representing the mouth of the celestial and terrestrial "Ju Zi" (one of the twelve star terms, corresponding to the Hai position). It is also the direction where the eight winds cannot reach. The meaning is subtle and profound, encompassing both the essence and function of Qian and Kun. In the Later Heaven, Qian is located in the Northwest, and in the twelve dividing hexagrams, Kun also occupies the Northwest (Hai month belongs to Kun), so Qian and Kun are said to be in the same place. In the Later Heaven, Xun (Wind) and Qian are opposite, while in the Earlier Heaven, Dui and Gen are opposite; the lower section uses Xun, Dui, Zhen, and Gen to take the place of Qian and Kun, and the Hexagram of "Xian" is placed first in the lower section—this stroke by the sage is truly marvelous!

恆　《象》曰：雷風恆。按：恆兼取先天卦象而言也。先天艮東北，巽西南，與澤山之對宮，適成交線。謂之恆者，對咸而言。咸無而恆，有咸無方體，而恆則“立不易方”。咸速恆久，在數為一正一負，而交相為用者也。後天震巽相連，震出巽齊，長男長女，身修家齊，故有恆久之道。　遁　《象》曰：天下有山。按：遁亦先後天同位之卦，獨不取相合之義，而用相違之遁，正與大畜相對。一進一退，同為西北入無之方。大畜為世間法，而遁則出世法也。乾天艮門，戌亥空亡，故曰“遁入空門”。卦象及卦數，皆與今日佛經合。神哉《易》之廣大悉備！宇宙之內，無一能外之者矣。

The Hexagram of Constancy: The Great Image says, "Thunder over Wind, Constancy." Hang's commentary states: The Hexagram of Constancy also derives its name from the Earlier Heaven arrangement. In the Earlier Heaven, the mountain (Geng) is in the Northeast and the wind (Xun) is in the Southwest, forming a cross with the Lake (Dui) and Mountain (Geng) of the Hexagram of Intimacy. The reason it is called "Constancy" is in contrast to the Hexagram of Intimacy: the latter signifies "nothingness," while this one signifies "being." The Hexagram of Intimacy has no fixed position or form, while this one speaks of "the gentleman maintains his position without change." The Hexagram of Intimacy is about speed, while this one is about duration. In terms of numbers, they are opposites, alternating in use. Looking at the Later Heaven, the Thunder (Zhen) and Wind (Xun) are positioned together. Thunder signifies "going out," while Wind signifies "order," and the Elder Son and Elder Daughter are paired, which corresponds to personal cultivation leading to family order, thus embodying the way of constancy. The Hexagram of Retreat: The Great Image says, "Mountain over the world." Hang's commentary states: The Hexagram of Retreat is also a hexagram that occupies the same position in both Earlier Heaven and Later Heaven. However, it does not take the meaning of "harmony," but instead uses "retreat" to signify "departure." This is in contrast to the Hexagram of Great Accumulation: one advances, the other retreats, both entering the "void" area of the Northwest. The Hexagram of Great Accumulation represents worldly affairs, while this one represents transcendental practice. Heaven is represented by the Heaven (Qian), the mountain by the Mountain (Gen), and the戌 and亥 belong to the void. Therefore, the saying "retreating into the empty gate" is common. This hexagram and its numbers correspond exactly with the Buddhist scriptures we see today. The vastness and comprehensiveness of the Book of Changes are truly marvelous! Nothing in the universe can go beyond its scope.

大壯　《象》曰：雷在天上。按：大壯與無妄，為上下相易卦。立名亦取象卦候。馬氏曰“壯傷也”，虞氏說亦同，蓋古訓也。意較壯盛為深。　晉　《象》曰：明出地上。按：晉之名，合先後天卦位之象而言也。離為坤陰，坤先天居北，地道卑而上行，麗乾而合明，故曰晉。晉者，進也。

The hexagram Great Strength: The Great Image says, "Thunder above the sky." Hang's commentary notes: The hexagram Great Strength and the hexagram No Misfortune are each other's reversal of the inner and outer trigrams, forming a pair of hexagrams that are "mutually reversed above and below." Its name is derived from the imagery of the hexagram's seasonal association (Great Strength is the hexagram for the second lunar month, when four yang lines are flourishing). Han dynasty scholar Ma Rong said, "Zhuang means injury," and Yu Fan's interpretation is the same. This is likely an ancient interpretation, which goes deeper than simply meaning "strength" or "prosperity." The hexagram Progress: The Great Image says, "Light emerging from the earth." Hang's commentary notes: The name "Progress" is derived from the imagery of both the Earlier Heaven and Later Heaven positions of the hexagram. The trigram Li (Fire) is originally a yin trigram born from Kūn (Earth), and in the Earlier Heaven, Kūn is located in the north. The earth's path is low but it ascends, attaching itself to Qian (Heaven) and thus combining with brightness, hence it is called "Progress." "Progress" means advancing upward.

明夷　《象》曰：明入地中。按：明夷與晉反，天道下濟。日在地下，無所謂傷。明夷之傷，因八宮為坎之游魂，坎傷也，為日食象。取象不一，而義必有所由來，豈可執一端而論哉！　家人　《象》曰：風自火出。按：家人立名，全取後天卦象。雷風風火，皆後天東南相連之卦，故象稱言有物而行有恆。卦本二女，而曰“女正位乎內，男正位乎外”，以爻言也。參看《學易筆談二集》。

The hexagram Mingyi (Darkness over the Sun): The Great Image says, "Light enters the earth." Hang's commentary states: The hexagram Mingyi and Jin (Progress) are opposites, discussing the heavenly path descending to benefit things. When the sun reaches beneath the earth, it is not really "injurious." The hexagram Mingyi takes the meaning of "injury" because according to Jing Fang's eight palaces, it is a wandering ghost hexagram of the Kan palace, and Kan itself has the meaning of "injury" (the Commentary on the Divination says Kan represents added sorrow and heart disease), and also contains the image of an eclipse. This shows that the source of the imagery is not singular, and each layer of meaning must have its own origin. How can one make a judgment based on only one aspect? The hexagram Jiaren (Family): The Great Image says, "Wind arises from fire." Hang's commentary states: The naming of the hexagram Jiaren is entirely based on the Later Heaven hexagram. Thunder and wind (Zhen and Xun), wind and fire (Xun and Li), are all connected hexagrams in the southeast area of the Later Heaven. Therefore, the Great Image says, "The superior person governs with words that have substance and actions that are consistent." This hexagram originally represents two women living together (Li is the middle daughter, Xun is the elder daughter), but the Commentary on the Judgment says, "The woman is properly positioned within, and the man is properly positioned outside," which refers to the two lines six two and nine five each occupying the central and upright positions. See my "Notes on Studying the Book of Changes, Volume Two."

睽　《象》曰：上火下澤。按：睽之名，亦取後天象。離之與兌為火金相剋，爻除初九，位皆不當，陰陽相違，與家人相反。　蹇　《象》曰：山上有水。按：蹇由本卦內外兩象之義以立名也。　解　《象》日：雷雨作。按：解之命名，與蹇同例。與屯兩象易，難得解矣。　損　《象》曰：山下有澤。按：損益定名，與泰否同例。

The Hexagram of Kui: The Great Image says, "Fire above and marsh below." Hang's commentary states: The name Kui also derives from the Later Heaven configuration: Li belongs to fire, Dui belongs to metal, and fire and metal mutually control each other; among the six lines, except for the first line, all other lines are not in the correct position (yang in yin position, yin in yang position), and yin and yang are in discord, which is exactly the opposite of the Hexagram of Jiaoren. The Hexagram of Jian: The Great Image says, "Mountain with water on top." Hang's commentary states: The name Jian is established based on the meaning of the internal and external images of the primary hexagram—below is Gen (mountain) which signifies stopping, and above is Kan (water) which signifies danger; stopping before danger makes movement difficult. The Hexagram of Jie: The Great Image says, "Thunder and rain arise." Hang's commentary states: The naming of Jie follows the same principle as Jian. It and Zun are hexagrams with their internal and external images reversed (Zun has Zhen below and Kan above, while Jie has Kan below and Zhen above): danger in front becomes a difficult situation, but danger behind allows movement outward, thus the difficulty is resolved. The Hexagram of Shen: The Great Image says, "A marsh below a mountain." Hang's commentary states: The naming of Shen and Yi follows the same principle as Tai and Po, both taking the meaning of the mutual increase and decrease of yin and yang.

益　《象》曰：風雷益。按：《象》曰“風雷”，而《彖》特著曰“木道乃行”，此為《象傳》中之特筆，與天道地道人道相併。以天地人之氣，非木不通。故天地人三才齊於巽，文不著於巽，而著於益，學者宜深思之。　夬　《象》曰：澤上於天。按：夬姤皆十二月消息卦，自重在卦候。但夬姤立名，取於本卦上下之一爻，與剝復同例。

The hexagram Yi: The Great Image says "wind and thunder, benefit." Hang's commentary states: The Great Image only mentions "wind and thunder," but the Commentary on the Judgment specifically highlights the phrase "the way of wood is then carried out," which is a special emphasis in the commentary, placing "the way of wood" alongside the ways of heaven, earth, and humanity. This is because the energies of heaven, earth, and humanity cannot be connected without wood, so the three principles of heaven, earth, and humanity will all converge on Xun (wood). However, the classic text does not point this out in the hexagram Xun, but rather in the hexagram Yi. Those studying the Book of Changes should deeply consider the intention behind this. The hexagram Guai: The Great Image says "a marsh above the heavens." Hang's commentary states: The hexagram Guai and Gu are both among the twelve hexagrams related to the cycle of the seasons, and they originally emphasize the seasonal changes associated with the hexagrams. However, the naming of these two hexagrams is based on the topmost or bottommost line of the original hexagram—Guai refers to the upper line, a single yin line about to be removed, while Gu refers to the lower line, a single yin line just beginning to emerge. This is similar to the case of the hexagrams Bo and Fu.

姤　《象》曰：天下有風。按：姤鄭氏作“遘”，序剝於復先，而次姤於夬後，與泰否損益同意，聖人之微旨焉。　萃　《象》曰：澤上於地。按：萃之名，由本卦內外兩象及中爻巽艮取義，而皆萃於六四之一爻。　升　《象》曰：地中生木。按：立名與萃同例。《雜卦傳》曰：“萃聚而升不來也。”不來者，往而不復之謂。

The hexagram Gou: The Great Image says "wind over the world." Hang's commentary notes: The character "Gou" was written by Zheng Xuan as "Gou," meaning meeting. In the sequence of hexagrams, "Bo" comes before "Fu," but "Gou" comes after "Gua," which is the same as the arrangement of Tai, Pǐ, Shen, and Yi. This reflects the subtle meaning intended by the sage. The hexagram Cui: The Great Image says "the marsh above the earth." Hang's commentary notes: The name "Cui" is derived from the inner and outer images of the hexagram (lower坤, upper兑) and the intermediate trigrams Xun and Gen. These images ultimately converge on the fourth line, line six. The hexagram Sheng: The Great Image says "wood growing in the earth." Hang's commentary notes: Its naming follows the same principle as Cui. The Miscellaneous Hexagram says "Cui gathers and Sheng ascends without returning." The term "without returning" means going upward continuously without turning back.

困　《象》曰：澤無水。按：下坎為水，而曰“無水”者，坎漏而上澤之水竭也。坎兌亦先後天同位之卦，而困之名，則以“剛掩也”。先儒皆以本卦六爻推尋，義無一當。剛柔相推，由於對象之賁。故在六三一爻。詳《學易筆談》。　井　《象》曰：木上有水。《彖》曰：巽乎水而上水。按：井之名，出於火雷噬嗑，與困同例。市井相聯，往來井井，為六十四卦，陰陽往來之樞紐。更與鼎相通。

The Hexagram of Guan: The Great Image says, "A marsh without water." Hang's commentary states: The lower trigram of Guan is Kan, which is water, yet it says "without water" because the water from Kan has flowed down, causing the water in the upper trigram Dui, the marsh, to dry up. Kan and Dui are also trigrams in the Later Heaven arrangement, and the name Guan comes from the Commentary on the Judgment, which says "the strong is covered by the weak." Previous scholars have only looked for explanations within the six lines of the primary hexagram, but none have provided a proper interpretation. In fact, the movement of yin and yang should be understood by looking at its opposing hexagram, Bi, and the key lies in the line six in the third position. See my "Notes on the Book of Changes." The Hexagram of Jing: The Great Image says, "Water on a tree." The Commentary on the Judgment says, "It is like wind rising up with water." Hang's commentary states: The name Jing comes from the hexagram of Shihe, Fire Thunder, similar to how the name Guan was derived. The market and well are connected to form "shi jing," and people coming and going with order "jing jing." Jing is the central hexagram for the movement of yin and yang, and it is also connected with the hexagram Ding.

革　《象》曰：澤中有火。按：革之名，取象後天。離火克金，而兌金繼離而代之。金曰“從革”，故名“革”。革而信之，己日乃革，中得坤土，故曰“革而當，其悔乃亡”。當者，九四之一爻。四爻變則六爻皆當矣。　鼎　《象》曰：木上有火。《彖》曰：以木巽火。按：《鼎·彖》曰：“鼎象也。”亦彖辭之特筆。鼎象在屯，名則仍由內外兩象取義者也。又與井對，井性鼎命。略見《學易筆談》。

The Hexagram of Revolution: The Great Image says, "Fire in the marsh." Hang's commentary states: The name of the Hexagram of Revolution is derived from the Later Heaven arrangement. The fire of the trigram Li overcomes the metal of the trigram Dui, and the metal of Dui follows the position of Li and takes its place (in the Later Heaven, Li is in the south and Dui in the west, adjacent in order). The Classic of Documents, The Nine Patterns, says that metal has the nature of "from revolution" — being compliant with change, hence the name "Revolution." Only after change can one gain trust, as the Hexagram Statement says, "It is only on the sixth day that trust is gained." The sixth day belongs to the central trigram Kun, earth, which possesses the virtue of the central earth, so the Commentary on the Judgment says, "Revolution at the right time, its regret will vanish." The term "right time" refers to the fourth line: the fourth line changes from an improper position to a proper one, and thus all six lines become proper. The Hexagram of the Cauldron: The Great Image says, "Fire on the wood." The Commentary on the Judgment says, "Using wood to guide fire," that is, using wood to be guided by fire. Hang's commentary states: The Commentary on the Judgment of the Hexagram of the Cauldron says, "The cauldron is an image," which is a special expression in the Commentary on the Judgment. The physical image of the cauldron actually comes from the Hexagram of Zhen, but its name still comes from the internal and external images (the lower trigram Xun, wood, and the upper trigram Li, fire). The Hexagram of the Cauldron also corresponds to the Hexagram of the Well. The Well represents nature, while the Cauldron represents destiny. This is roughly explained in my "Notes on Studying the Book of Changes."

震　《象》曰：洊雷震。按：震先後天方位相連，故《彖》言“虩虩”“啞啞”，多疊文。　艮　《象》曰：兼山艮。按：兼山者，別於《連山》也。　漸　《象》曰：山上有木。按：《序卦》以漸為進，承上文而言耳。實漸之義不限於進。《坤·文言》曰“其所由來者漸矣”。巽之初爻，履霜之漸也。下艮止之，得漸之正，故取女歸。亦由本卦兩象定名而兼取義於對象者也。

The Hexagram of Zhen: The Great Image says, "Successive thunder, Zhen," meaning thunder sounds one after another. Hang notes: In both the Earlier Heaven and Later Heaven diagrams, the position of Zhen is adjacent (Zhen is in the Northeast in the Earlier Heaven and in the Due East in the Later Heaven), so the Hexagram Statement often uses repeated characters, such as "xuxu" (the sound of fear) and "yayay" (the sound of laughter). The Hexagram of Gen: The Great Image says, "Two mountains, Gen." Hang notes: It says "two mountains" instead of "double mountains" to distinguish it from the Shang Dynasty's "Lianshan" Yi. The Hexagram of Jian: The Great Image says, "A tree on a mountain." Hang notes: The Sequence of Hexagrams explains "Jian" as "progress," which is only in reference to the previous text. In reality, the meaning of "Jian" is not limited to "progress." The Wenyan of the Hexagram of Kun says, "Its origin has been gradual," which refers precisely to a gradual development from small to great, accumulating step by step. The upper trigram of Jian is Xun, whose first line is yin, just like the first line of Kun, "Lu霜" (stepping on frost), which represents gradual change; while the lower trigram Gen stops it, thus following the correct path of "Jian." Therefore, the Hexagram Statement takes "female marriage is auspicious," as a woman's marriage should proceed in order. This is an example of naming the Hexagram based on its own two trigrams and also deriving meaning from the opposite trigram.

歸妹　《象》曰：澤上有雷。按：漸之吉以艮止也。易為震動，適相反矣。故曰“征凶”。然事有常變，處變得正，亦天地大義所不廢。而八宮以雷澤為最終歸魂之卦，故以歸妹名之。　豐　《象》曰：雷電皆至。按：豐與噬嗑上下易，亦先後天同位之卦也。而豐之名，則只取象後天。東南震曰出，離日中，謂之豐者，萬物皆相見，生物至盛之時也。

The hexagram of Gui Mei: The Great Image says "Thunder above the marsh." Hang氏 comments: The hexagram of Zhen is auspicious because the lower trigram, Gen, can stop; but in the hexagram of Gui Mei, the lower trigram is Dui and the upper trigram is Zhen, so stopping becomes movement, which is exactly the opposite. Therefore, the hexagram statement says "traveling brings danger." However, things have constants and changes. Being in a changing situation yet maintaining correctness is also in line with the great principles of heaven and earth. Moreover, according to Jing Fang's eight palaces arrangement, the hexagram of Gui Mei, which is Zhen above Dui below, is the last returning hexagram of the Dui palace. "Returning soul" means returning to its original palace, so it is named "Gui Mei" — meaning a woman who marries and finds her place. The hexagram of Feng: The Great Image says "Thunder and lightning both arrive." Hang氏 comments: The hexagram of Feng and the hexagram of Shi He have their inner and outer trigrams reversed, making them hexagrams in the same position in both earlier and later heaven arrangements. However, the name of the hexagram of Feng is based on the later heaven arrangement: in the later heaven, the east and southeast areas, Zhen represents "going out," and Li is at due south at noon. It is called "Feng" because at this time all things are clearly visible, which is the time when living things are most flourishing.

旅　《象》曰：山上有火。按：旅與賁為上下易之卦，名之曰“旅”。昔人多未詳其義，不知亦由八宮取象者也。乾七世游魂為火地晉，歸魂火天大有。仍復乾位，若歸魂不歸，遊入離宮，則四爻變為火山，故曰“旅”也。　巽　《象》曰：隨風巽。按：重木而曰“隨風”。隨對象為蠱，蠱先後甲，巽先後庚，因緣所在，學者最宜注意。

The Hexagram of Travel: The Great Image says, "Fire on Mountain." Hang氏 comments: The Hexagram of Travel and the Hexagram of Brightness are two hexagrams with inner and outer trigrams reversed. The name "Travel" is derived from this, but previous scholars mostly failed to understand its meaning, not realizing that this is also derived from the imagery of Jing Fang's eight palaces. The seventh hexagram in the Qian Palace is the wandering soul hexagram, Fire on Earth, the Hexagram of Progress, and the returning soul hexagram is Fire on Heaven, the Hexagram of Great Possession. When the soul returns, it reverts to the Qian position. If the wandering soul does not return to its original palace but instead wanders into the Li Palace, then changing the fourth line results in Fire on Mountain, the Hexagram of Travel, hence the name "Travel" — being a traveler away from home and unable to return. The Hexagram of Following: The Great Image says, "Following the wind, Xun." Hang氏 comments: Two Xun trigrams stacked together are originally about wood, yet it is described as "following the wind." The opposite hexagram of Following is Gu. The Hexagram of Gu states, "Three days before the first day of the month, three days after the first day of the month." The line nine in the fifth position of Xun says, "Three days before the seventh day of the month, three days after the seventh day of the month." The relationship between Jiā and Gēng, beginning and ending, is something that those studying the Book of Changes should pay particular attention to.

兌　《象》曰：麗澤兌。按：麗，離也。鄭氏作離。兌講學，離明兩作，在明明德，大學之始。詳《學易筆談初集》。　渙　《象》曰：風行水上。按：渙，亦以本卦兩象之名者也。渙與畜對。　節　《象》曰：澤上有水。按：節亦先後天同位。噬嗑合，同人親，節者符節，比者比附，特以先後天四正之卦，立此合同節比之名，先後之大義亦顯著矣。乃後人猶聚訟不休，何哉！

The Hexagram of Dui: The Great Image says, "Lying on the marsh, Dui." Hang's note says, "Ling" is "Li," meaning attached and connected, and Zheng Xuan's version is indeed "Li." The Great Image of Dui discusses "the gentleman uses friendship to study and practice," referring to learning; the Great Image of Li discusses "bright light shining," referring to cultivating virtue—this is exactly the beginning of the Great Learning. See my "Initial Collection of Notes on Studying the Book of Changes." The Hexagram of Huan: The Great Image says, "Wind moving on water." Hang's note says that Huan is also named based on the two images of the primary hexagram (lower Kan water, upper Xun wind). Huan and Xu are opposites; dispersal and accumulation are directly opposite. The Hexagram of Jie: The Great Image says, "Water on the marsh." Hang's note says that Jie is also a hexagram where the positions of the Earlier Heaven and Later Heaven coincide. Shihe takes "combination," Tongren takes "affection," Jie takes "symbol and seal matching," and Bi takes "attachment and union"—the sage deliberately used the four cardinal directions of Earlier Heaven and Later Heaven that match to establish the names "combination," "togetherness," "junction," and "attachment." The great meaning of the connection between Earlier Heaven and Later Heaven is already very clear. Yet later people still argue endlessly. Why is that!

中孚　《象》曰：澤上有風。按：中孚亦先後天同位之卦。孚者同也，中者巽五兌十，五十居中，故曰“中孚”。　小過　《象》曰：山上有雷。按：小過與大過同例。先天震居坤之左，艮居坤之右，皆過乎中。陰體，故曰小過。　既濟　《象》曰：水在火上。按：既未濟坎離相交，與泰否損益同例。既濟六爻皆當，陰陽定，而易之道窮。故《虞氏易》以乾坤成兩既濟為凶。

The卦 of Zhongfu: The Great Image says "wind over marsh." Hang's note: Zhongfu is also a卦 that aligns with the Earlier Heaven and Later Heaven. "Fu" means harmony and agreement; the reason it is called "Zhong" is because the number of Xun is five and the number of Dui is ten, and five and ten are the central numbers in the Yellow River Chart, hence it is called "Zhongfu." The卦 of Xiaoguo: The Great Image says "thunder over mountain." Hang's note: Xiaoguo and Daguohuo belong to the same category. In the Earlier Heaven, Zhen is on the left of Kun and Gen is on the right of Kun, both leaning to one side beyond the center; Zhen and Gen, as three-line diagrams, are both composed of two yin lines and one yang line, belonging to yin structure, hence they are called "Xiaoguo" — small yin exceeding the center. The卦 of Ji Ji: The Great Image says "water above fire." Hang's note: Ji Ji and Wei Ji are both formed by Kan and Li intersecting, and they belong to the same category as Tai, Pinyin, Shen, and Yi. In Ji Ji, all six lines are in their proper positions, with yin and yang both settled, so the principle of change has reached its end. Therefore, the Yijing of Yu regarded transforming Kan and Qian into two Ji Ji as ominous.

未濟　《象》曰：火在水上未濟。按：既濟則易無可易而窮，物不可窮，故《序卦》以未濟終。濟者濟河也，地天泰馮河，坎離濟河，（天地際，亦陰陽際。善惡生死，皆此際。故人處天地間，不能逃陰陽之外，即不能不濟渡此際。佛經所謂渡也，即濟謂已登彼岸，已渡此泰河也。未濟離上坎下之位未動，猶未登彼岸者也。此佛經與《易》名異而義皆相通者也。）濟此河也。泰馮河馬壯，坎馬亟心，立心恆，乾健不息，坤行無疆，皆合先後天之義，通天地人之道。六十四卦往復，皆為此“濟”之一字。故《易》者濟世之書，孔子贊《易》以濟天下萬世，後人猶以《易》為教人卜筮之書，豈不痛哉！

The hexagram of "Not Yet Completed" (Wèijì) says in the Great Image (Dàxiàng zhuàn): "Fire on water, not yet completed." Hang's commentary states: When reaching the hexagram of "Already Completed" (Jìjì), transformation has reached its limit and there is nothing more to change; however, all things are endless, so the Sequence of Hexagrams (Xùguà zhuàn) concludes the entire book with "Not Yet Completed." "To cross" (jì) means to cross a river: the second line of the hexagram of "Great Communication" (Tài) says "to cross the river by foot," meaning to wade across a large river; when the trigrams Kan (water) and Li (fire) intersect, it also represents crossing a river. (The boundary between heaven and earth is the boundary between yin and yang; good and evil, life and death are all on this boundary. Therefore, human beings exist between heaven and earth, cannot escape yin and yang, and thus cannot avoid crossing this boundary. The term "crossing" (jì) in Buddhist scriptures is the same as "crossing" (jì) in the Book of Changes: having reached the other shore means having crossed this river; the position of the hexagram "Not Yet Completed" with Li above and Kan below has not changed, just like not having reached the other shore. This is where Buddhist scriptures and the Book of Changes differ in name but are in agreement in meaning.) So "crossing" (jì) refers to crossing this river. The hexagram of "Great Communication" (Tài) talks about wading across a big river relying on strong horses; the Discourse on the Trigrams (Shuōguà zhuàn) says that Kan is associated with "haste for horses"; the Great Image of the hexagram Kan says "constant virtue" and having a steadfast mind; combined with the strength and perseverance of Qian (Heaven) and the boundless movement of Kun (Earth), they all conform to the meaning of the earlier and later heavens and connect the three principles of heaven, earth, and humanity. The cycle of the sixty-four hexagrams ultimately revolves around this single character "crossing" (jì). Therefore, the Book of Changes is a book for saving the world; Confucius praised the Book of Changes precisely to save the world; yet later people have reduced the Book of Changes to a book for divination, which is truly regrettable.

《易》之為書，有天道焉，有地道焉，有人道焉。故《易》三畫而成卦。立天之道，曰陰與陽。立地之道，曰柔與剛。立人之道，曰仁與義。分陰分陽，迭用柔剛。故《易》六位而成章。三畫之卦，因而重之。為六畫之卦六十有四。《周禮》“太卜掌三《易》之法，《連山》、《歸藏》、《周易》，經卦皆八，其別皆六十有四”。經卦即乾坎艮震巽離坤兌三畫之卦，別卦則六畫之卦。三《易》法雖不同，而經卦別卦之數皆同。可見文王以前，早有六畫之卦。安得至《周易》始有後天八卦之方位乎？三代而後，師說紛歧，因卦有正反及上下左右相易，而皆別成一卦。故類別日多，稱名互異，後人幾無所適從。爰擇要疏錄，並各舉其例。以便初學。其名異而實同，或名同而各家之說互異者，名從其朔。要皆由別卦所孽乳，故署曰“卦別”。

The book of Change contains the principles of Heaven, Earth, and humanity, so the book of Change uses three lines to form one trigram. To establish the principle of Heaven, it is called "Yin" and "Yang"; to establish the principle of Earth, it is called "flexibility" and "rigidity"; to establish the principle of humanity, it is called "benevolence" and "righteousness." By distinguishing Yin and Yang, and alternating flexibility and rigidity, the book of Change requires six lines to form a complete hexagram. By stacking the three-line trigrams, they become six-line hexagrams, totaling sixty-four. The Zhou Li records that the Grand卜 (diviner) was in charge of three methods of the book of Change, namely the Lianshan, Guicang, and Zhouyi; their fundamental trigrams are all eight, and their compound trigrams are all sixty-four. The fundamental trigrams refer to the eight trigrams of Qian, Kan, Gen, Zhen, Xun, Li, Kun, and Dui, each consisting of three lines; the compound trigrams refer to the hexagrams with six lines. Although the three methods of the book of Change differ, the number of fundamental and compound trigrams is exactly the same, indicating that the hexagrams with six lines existed before King Wen. How could the Later Heaven Trigrams with their specific orientation have first appeared in the Zhouyi? After the Xia, Shang, and Zhou dynasties, different schools of thought diverged: because each trigram has a positive and a negative aspect, and there are various changes involving upper and lower, left and right reversals, each change produces a new trigram, leading to an increasing number of categories and differing names, making it difficult for later generations to follow. Here, I have selected and arranged the key points, with examples given for beginners. Where names differ but refer to the same thing, or where names are the same but different schools have different interpretations, the earliest terminology is used as the standard. All these terms ultimately originate from the compound trigrams, so the title is "Trigram Differentiation."

重三為六畫，合兩卦成一卦。故六十四卦，每卦均有內外之分。卦畫由下生，故以下卦為內，上卦為外。泰否之“內陰”而“外陰”，“內柔”而“外剛”，即《象傳》之自舉其例也。　泰　乾內坤外。故《彖》曰“內陽而外陰，內健而外順，內君子而外小人”。　否　坤內乾外。故《彖》曰“內陰而外陽，內柔而外剛，內小人而外君子”。　觀泰否兩《彖》，內卦外卦之別，顯然易明。惟卦有以內外言者，有不必以內外言者。通變無常，各適其當，未可泥一端而論也。

When a three-line trigram is overlaid to form a six-line diagram, it combines two three-line trigrams into one, so each of the sixty-four hexagrams has an inner and outer trigram. The hexagram is formed from bottom to top, so the lower three-line trigram is called the inner trigram, and the upper three-line trigram is called the outer trigram. The phrases such as "inner... and outer..." and "inner softness and outer hardness" in the hexagrams of Tai and Pi are examples given by the Commentary on the Judgment itself. The hexagram Tai has the trigram Qian inside and the trigram Kun outside, so the Commentary on the Judgment says, "inner yang and outer yin, inner strength and outer compliance, inner gentleman and outer petty person." The hexagram Pi has the trigram Kun inside and the trigram Qian outside, so the Commentary on the Judgment says, "inner yin and outer yang, inner softness and outer hardness, inner petty person and outer gentleman." By looking at these two commentaries on Tai and Pi, the distinction between inner and outer trigrams is clearly evident. However, among the sixty-four hexagrams, some can be explained using the concept of inner and outer, while others do not require it. There are no fixed rules, and each case should be considered according to its own context, without being rigidly confined to one approach.

《繫傳》曰：“陽卦多陰，陰卦多陽。陽卦奇，陰卦偶。”此專指六子之卦言也。後天以用為先，故以少者為主。一陽之震坎艮為陽卦，一陰之巽離兌為陰卦。而先天以體立言，則取多者為主。故兌巽以二陽之卦，合為澤風大過，言陽過乎中也。震艮以二陰之卦，合為雷山小過，言陰過乎中也。乾坤坎離，各得陰陽之中，皆三畫卦也。

The Great Treatise says: "Yang hexagrams contain more yin lines, and yin hexagrams contain more yang lines; yang hexagrams are odd, and yin hexagrams are even." This refers specifically to the six hexagrams derived from Qian and Kun. Later Heaven prioritizes function, so it takes the side with fewer lines as the main focus: Zhen, Kan, and Gen, which each contain one yang line, are considered yang hexagrams; Xun, Li, and Dui, which each contain one yin line, are considered yin hexagrams. Earlier Heaven, however, speaks in terms of essence, and takes the side with more lines as the main focus: Dui and Xun are both considered hexagrams with two yang lines, and together they form the hexagram Zhefeng (Great Excess), which discusses yang exceeding the center; Zhen and Gen are both considered hexagrams with two yin lines, and together they form the hexagram Le Shan (Small Excess), which discusses yin exceeding the center. As for Qian, Kun, Kan, and Li, each possesses the middle of yin and yang—Qian is purely yang, Kun is purely yin, Kan and Li each have half yang and half yin. All of the above still refer to the three-line hexagrams.

若六畫之卦，其陰陽之分，例至不一。有以卦言者，則乾與三男為主者稱陽卦，坤與三女為主者稱陰卦。有以爻為主者，則以奇爻為主者稱陽卦，偶爻為主者稱陰卦。自宋以後，諸說紛歧。有以邵子陽儀陰儀立論者，有以闢卦陰陽所生分別者，有以《序卦》之先後分陰陽者，如屯陽蒙陰需陽訟陰之類。雖各言之成理，要皆有當有不當。蓋乾坤為《易》之門，六子生自乾坤。八純而外，餘五十六卦。雖各有陰陽之分，必先明其體用，而後有分陰分陽之可言。以體用交互，體陽者用必陰，體陰者用必陽。準此以觀，諸家之圖說，自可瞭然矣。

As for the hexagram composed of six lines, the method of dividing yin and yang is highly inconsistent. Some classify based on the trigrams: those with Qian (Heaven) and three male lines are considered yang trigrams, while those with Kun (Earth) and three female lines are considered yin trigrams. Others classify based on the lines themselves: those with an odd number of lines (yang lines) are considered yang trigrams, and those with an even number of lines (yin lines) are considered yin trigrams. After the Song Dynasty, various schools of thought became more divergent: some based their views on Shao Yong's "Yang Instrument" and "Yin Instrument," others on the division of yin and yang according to the twelve great trigrams, and still others on the sequence of the "Sequence of Trigrams" text, such as Zu (Emergence) being yang and Meng (Awakening) being yin, Xu (Need) being yang and Song (Contention) being yin, and so on. Although each school presents its reasoning, some explanations make sense while others do not. To understand this, we must remember that Qian and Kun are the gateways of the Book of Changes, and the six subsidiary trigrams all originate from Qian and Kun. Outside the eight pure trigrams, there are fifty-six other trigrams, each with its own division of yin and yang. However, before discussing yin and yang, it is essential to first clarify their nature and function. Because nature and function are interdependent: if the nature is yang, the function must be yin; if the nature is yin, the function must be yang. By following this principle, the various diagrams and explanations of different schools will become clear at a glance.

卦之有貞悔，亦如爻之有動靜也。悔古作每卜。論卦體，則內貞而外悔。言占卜，則靜貞而動悔。坤之六三曰“含章可貞”，乾之上九曰“亢龍有悔”，此內貞外悔，經文之自舉其例也。《左傳》：“秦伯伐晉，卜徒父筮之，其卦遇蠱。曰：蠱之貞風也，其悔山也。”亦內貞外悔之一例也。《國語》：“秦伯召公子重耳於楚，楚子厚幣以送公子於秦。公子親筮之曰：尚有晉國。得貞屯悔豫皆八。”此靜貞動悔之例也。

A hexagram has both "Zhen" and "Hui," just as a line has both stillness and movement. The character "Hui" was written in ancient times with "Mei" above and "Bo" below. In terms of the hexagram structure, the inner trigram is Zhen and the outer trigram is Hui; in terms of divination, the unchanging line is Zhen and the changing line is Hui. The hexagram "Kun" says "Containing virtue, it is proper to be Zhen," and the hexagram "Qian" says "The dragon soaring high brings regret," which is an example of inner Zhen and outer Hui. The "Zuo Zhuan" records that Duke Mu of Qin attacked Jin, and Bo Tu Fu cast a divination for him, obtaining the hexagram "Gu," and said, "The Zhen of 'Gu' is wind (the lower trigram Xun), and its Hui is mountain (the upper trigram Gen)," which is another example of inner Zhen and outer Hui. The "Guoyu" records that Duke Mu of Qin summoned Prince Chong'er from Chu, and King Chu prepared rich gifts to send Prince Chong'er to Qin; Prince Chong'er himself cast a divination, praying, "May I be able to obtain Jin," and obtained "Zhen 'Zun' and Hui 'Yu' both eight," which is an example where the unchanging is Zhen and the changing is Hui.

《左傳正義》曰：“伏羲作十言之數，曰乾坤震巽坎離艮兌消息。”虞仲翔氏，即本此十言立說。《荀九家易注》：“泰卦曰陽息而升，陰消而降。”虞氏十二消息，復臨泰大壯夬乾為息卦，姤遁否觀剝坤為消卦。《易》曰：“君子尚消息盈虛，天行也。”又曰：“天地盈虛，與時消息。”故陰陽往復，此息則彼消，此消則彼息，亦卦義相傳之最古者也。卦例圖說詳下《卦候》章。

The "Commentary on the Spring and Autumn Annals with Justification" says: "Fuxi created the system of ten words, which are Qian, Kun, Zhen, Xun, Kan, Li, Gen, and Dui, plus Xiao and Xi." Yu Fan of the Three Kingdoms period based his theories on these ten words. The "Commentary on the Nine Schools of the Book of Changes by Xun Shuang" explains the Tai hexagram as: "Yang energy grows and rises, while Yin energy declines and descends." Yu Fan's twelve message hexagrams are: Fu, Lin, Tai, Da Zhuang, Guai, and Qian as "Xi hexagrams," meaning the growth of Yang energy month by month; Gou, Duan, Pih, Guan, Po, and Kun as "Xiao hexagrams," meaning the growth of Yin energy month by month. The Book of Changes says, "A gentleman values the waxing and waning of fullness and emptiness, which is the way of Heaven," and also says, "Heaven and Earth are full and empty, changing with the seasons." Therefore, yin and yang alternate endlessly; where one grows, the other declines, and where one declines, the other grows. This is one of the oldest transmitted meanings in the hexagrams. Specific examples of the hexagrams and their diagrams are detailed in the following chapter "Hexagram Seasons."

易道陰陽往來，乾圓往屈，坤方來信，往來屈伸。而六十四卦陰陽，與時消息，循環不窮。數往者順，知來者逆。《序卦》首乾坤終既未濟。乾往卦，坤來卦。屯往卦，蒙來卦。至既濟往卦，而未濟來卦，一往一來，各以其序。順逆之數，皆天地自然之法象也。

The principles of the Book of Changes are based on the movement of yin and yang. The trigram Qian (Heaven) is round in form, and its movement is characterized by bending; the trigram Kun (Earth) is square in form, and its movement is characterized by extension (the term 'xin' means 'extension'). One movement and one return correspond to one bending and one extension. The yin and yang in the sixty-four hexagrams change with the seasons, circulating endlessly. The "Commentary on the Hexagrams" states, "To understand the past is to follow the sequence, to foresee the future is to use reverse calculation." Calculating the past follows the order of progression, while predicting the future uses reverse numbers. The "Sequence of Hexagrams" begins with Qian and Kun and ends with "Ji Ji" and "Wei Ji": Qian is a hexagram of movement, Kun is a hexagram of return; "Zun" is a hexagram of movement, "Meng" is a hexagram of return; this continues until "Ji Ji" is a hexagram of movement and "Wei Ji" is a hexagram of return. One movement and one return follow their respective order, and this sequence of forward and reverse numbers reflects the natural patterns of heaven and earth.

對卦（旁通、錯卦、類卦）者，陰陽相對。如乾對坤，坎對離，屯對鼎，蒙對革，頤對大過，中孚對小過之類。虞氏謂之旁通，來知德氏謂之錯卦，《周易指》謂之類卦，皆對卦也。六十四卦相對者八，皆自為一卦。不相對者二十八卦，反之別為一卦，得五十六卦。然不相對者，亦各有其相對之卦。略例如右：以上八卦，陰陽相對，反覆不衰，有對而無反者也。餘卦類推，有對而又有反者也。

The concept of "opposite hexagrams" (also called "parallel," "opposite hexagrams," and "class hexagrams") refers to two hexagrams whose six lines are completely opposite in yin and yang. For example, the hexagram Qian (Heaven) is opposite to Kun (Earth), Kan (Water) is opposite to Li (Fire), Zun (Sprouting) is opposite to Ding (Tripod), Meng (Confusion) is opposite to Ge (Revolution), Yi (Nourishment) is opposite to Da Guo (Great Excess), Zhong Fu (Sincere Trust) is opposite to Xiao Guo (Small Excess), and so on. Yu Fan called it "parallel," Lai Zhide called it "opposite hexagrams," and Du Mu Guo Hu called it "class hexagrams," all referring to opposite hexagrams. Among the sixty-four hexagrams, there are eight hexagrams that remain the same when reversed, and each of these forms a hexagram on its own. The remaining twenty-eight hexagrams, when reversed, form new hexagrams, totaling fifty-six. However, those hexagrams that can form new ones when reversed also have their corresponding opposite hexagrams. A general example is as follows: these eight hexagrams have opposite yin and yang, but when the entire hexagram is reversed, its shape remains unchanged, belonging to the category of having "opposite" but not "reversal." The rest of the hexagrams follow the same pattern, all having both "opposite" and "reversal."

覆卦（反卦、綜卦）者，一卦覆之而又別成一卦者也。如屯之覆為蒙，需之覆為訟，師之覆為比。六十四卦，除乾坤坎離等八卦，餘五十六卦皆有覆卦也。漢人亦曰反卦，來知德氏謂之綜卦。（來氏謂綜者如織布扣經之綜，一上一下者也，故名反覆之卦為綜。然覆實上下相倒置，非一上一下之謂，綜之名殊未確合，故非議者甚多。）如震反為艮，巽反為兌。而震之與巽，艮之與兌，又為對卦也。餘卦類推。若泰否既未隨蠱漸歸妹等卦，對而兼覆，所謂反覆不衰者也。

The concept of "reversed hexagram" (also called "inverted hexagram" or "complementary hexagram") refers to turning a hexagram completely upside down to form another hexagram. For example, the hexagram Zun (屯) reversed becomes Meng (蒙), Xu (需) reversed becomes Song (讼), and Shi (师) reversed becomes Bi (比). The term "reversed" means turning the order of the six lines from top to bottom completely upside down. Among the sixty-four hexagrams, eight hexagrams—Qian (乾), Kun (坤), Kan (坎), and Li (离)—remain unchanged when reversed. The remaining fifty-six hexagrams each have their own reversed hexagrams. The Han dynasty referred to this as "inverted hexagram," and Lai Zhide called it "complementary hexagram." Lai Zhide explained that "complementary" is like the shuttle in weaving, which alternates between raising and lowering the warp threads, hence the term "complementary" for the reversed hexagram. However, "reversed" actually refers to flipping the entire hexagram upside down, not just alternating one line up and down. Therefore, the term "complementary" is not very accurate, and many have criticized it. For example, the trigram Zhen (震) reversed becomes Gen (艮), and Xun (巽) reversed becomes Dui (兑). Zhen and Xun, as well as Gen and Dui, are mutual complementary hexagrams. The other hexagrams follow the same pattern. As for hexagrams such as Tai (泰) and Po (否), Ji Ji (既济) and Wei Ji (未济), Sui (随) and Gu (蛊), Zhen (渐) and Gui Mei (归妹), they are both complementary and reversed, which is called "reversed and complementary without decline."

交卦（兩象易、上下易）者，本卦內外兩象，交相易位。內卦出外，外卦入內。虞氏謂之兩象易，亦有謂上下易者，向無定稱。今以其內外交易，故名之曰交卦，取便演講時之辨識，非敢云確當也。（來氏謂綜者一上下，以名此卦，或尚相近。惜數一百年來稱名久混，不能用也。）交卦之義，互見於經傳甚多。略舉如左：如天澤履與澤天夬，內外兩象，交相易位者也。故履上九曰“夬履，貞厲”。又如雷風恆與風雷益，內外兩象，交相易位者也。故恆曰“立不易方”，益曰“為益無方”。各卦以此類推，《彖》、《象》之相互見義者，厥例正多，不勝縷指也。

The concept of "intersecting hexagrams" (also called "two images" or "upper and lower reversal") refers to exchanging the positions of the inner and outer trigrams of the primary hexagram, moving the inner trigram to the outside and the outer trigram to the inside. Yu Fan called this "two images," and others referred to it as "upper and lower reversal." There has never been a fixed name for it. Now, since it involves the mutual exchange of inner and outer positions, I have named it "intersecting hexagram," in order to make it easier to distinguish when teaching, and I do not claim that this name is particularly accurate. (Lai Zhide referred to this as "comprehensive," meaning one above and one below, which might be a more appropriate term for this type of hexagram. However, due to long-standing confusion in terminology over the past few centuries, this term can no longer be used.) The meaning of "intersecting hexagrams" is supported by many mutual confirmations in the classic texts. Here are a few examples: for instance, the hexagram of Heaven above and Lake below (Treading) and the hexagram of Lake above and Heaven below (Decisive Action) are a pair formed by exchanging the inner and outer trigrams. Therefore, the upper ninth line of the Treading hexagram says, "Decisive Treading, firmness brings danger." Another example is the hexagram of Thunder above and Wind below (Perseverance) and the hexagram of Wind above and Thunder below (Benefit), which are also a pair formed by exchanging the inner and outer trigrams. Thus, the Treading hexagram says, "Standing firm without changing direction," while the Benefit hexagram says, "Benefiting without fixed direction." Other hexagrams can be similarly analyzed. There are many examples in the Commentary on the Judgment and the Image Commentary where their meanings are clarified through mutual reference, and it would be impossible to list them all.

半對者，本卦之內外兩象，有一象易為對卦，（如乾易坤、震易巽之類）或內或外，均與所易之卦，象義相關。其例如下：如雷澤歸妹，外卦之雷易為風，成風澤中孚，是上半之對卦也，故歸妹曰“月幾望”，中孚亦曰“月幾望”。又如山水蒙，外卦之山易為澤，成澤水困，亦上半之對卦也。故蒙曰“困蒙”。

The concept of "half opposition" refers to a situation in which one of the two trigrams in the primary hexagram is replaced by its opposite trigram, such as replacing Qian with Kun or Zhen with Xun. Whether the trigram replaced is the inner or outer trigram, the resulting hexagram will have a relationship in both form and meaning with the original hexagram. For example, in the hexagram "Thunder over Lake" (Gui Mei), if the outer trigram Thunder (Zhen) is replaced by Wind (Xun), it becomes "Wind over Lake" (Zhong Fu), which is a hexagram of half opposition. Therefore, the line six in the fifth position of Gui Mei says "the moon is almost full," and the line six in the fourth position of Zhong Fu also says "the moon is almost full." Another example is the hexagram "Mountain over Water" (Meng), where if the outer trigram Mountain (Gen) is replaced by Lake (Dui), it becomes "Lake over Water" (Kun), which is also a hexagram of half opposition. Therefore, the line six in the fourth position of Meng says "trapped confusion."

以上為上卦對易者也，名曰“上對”。其下卦對易者，更舉例如左：如天澤履，內象之澤易為山，成天山遁，是下半之對卦也。故履曰“履虎尾”，遁曰“遁尾”。又如地水師，內象之水易為火，成地火明夷，亦下半之對卦也。故師曰“左次”，明夷曰“左股”。以上為下卦對易者也。無論上下卦對易，與所易之卦，象義必相聯貫。惟有見於《彖》、《象》者，有不見於《彖》、《象》者。然雖不見於《彖》、《象》，而其意義自在。潛心玩之，必有所得也。

The above discusses the case of exchanging the upper trigram, known as "upper opposition." As for the case of exchanging the lower trigram, let us take another example: take the hexagram Heaven and Lake (Zou), and replace the inner image Lake (Dui) with Mountain (Gen), resulting in Heaven and Mountain (Dun). This is a hexagram with lower opposition, so the hexagram Zou says "treading on the tiger's tail," while the hexagram Dun's initial line says "fleeing to the tail." Another example is Earth and Water (Shi), and replacing the inner image Water (Kan) with Fire (Li), resulting in Earth and Fire (Mingyi), which is also a hexagram with lower opposition. Therefore, the line four of hexagram Shi says "moving to the left," while the line two of hexagram Mingyi says "dimmed on the left thigh." The above discusses the case of exchanging the lower trigram. Whether it is upper opposition or lower opposition, the original hexagram and the transformed hexagram must be connected in terms of image and meaning. Some of these connections can be seen in the Commentary on the Judgment and Image Commentary, while others cannot be found there. However, even if they are not explicitly mentioned in the Commentary on the Judgment and Image Commentary, the meaning still exists. If one carefully contemplates and reflects, one will surely gain some understanding.

半覆卦者，與半對卦同例。或內或外，各以覆象所得之卦求之，其義自見。舉例如左：如水雷屯，內卦之雷覆為山，成水山蹇，即下半之覆卦也。故“屯難也”，“蹇難也”。又如天雷無妄，內卦之雷覆為山，成天山遁，亦下半之覆卦也。故無妄曰“無妄之疾”，遁曰“有疾厲”。無妄曰“行人得牛”，遁曰“執用黃牛”。

The method of forming a "half-covered hexagram" is the same as that of the "half-opposite hexagram": in a six-line hexagram, the inner and outer trigrams are each three lines. In this case, one trigram is completely reversed to form its "inverted image," while the other remains unchanged. The resulting new hexagram is naturally related in meaning to the original. For example, in the hexagram of "Obstruction" (Zhun), the inner trigram is Zhen (Thunder), and when reversed it becomes Gen (Mountain), making the whole hexagram become "Water and Mountain: Obstruction" (Jian). This is an example of taking the inverted image from the lower half. Therefore, the "Sequence of Hexagrams" states that Zhun represents "difficulty" and that Jian also represents "difficulty," both hexagrams establishing their meaning through the concept of difficulty. Another example is the hexagram of "No False Movement" (Wu Wang), where the inner trigram Zhen (Thunder) is reversed to become Gen (Mountain), resulting in the hexagram "Heaven and Mountain: Retreat" (Dun). This is also an example of taking the inverted image from the lower half. Thus, in "No False Movement" (Wu Wang), the line Nine in the Fifth speaks of "sudden illness," and in "Retreat" (Dun), the line Nine in the Third speaks of "serious illness," both referring to illness. In "No False Movement" (Wu Wang), line Six in the Third mentions a cow being led away and "travelers" obtaining it, while in "Retreat" (Dun), line Six in the Second speaks of "using the hide of a yellow cow," both using the image of a cow. The language of the two hexagrams corresponds with each other because they are related by the half-covered relationship.

以上下半之覆卦也，名曰“下覆”。其上卦易為覆卦者，為例亦同。更略舉如左：如山天大畜，外象之山覆為雷，成雷天大壯，即上半之覆卦也。故大畜“利貞”，大壯“利貞”。大畜曰“輿說輹”，大壯曰“壯于大輿之輹”。又如風天小畜，外象之風覆為澤，成澤天夬，亦上半之覆卦也。故小畜曰“惕出”，夬曰“惕號”。小畜曰“既雨”，夬曰“遇雨”。

All the previous examples are cases of taking the lower trigram as the covered trigram, named "lower covering." If we instead take the upper trigram as the covered trigram, the method remains the same. Here are a few more examples: In the hexagram of Da Xu (Great Accumulation), the outer trigram is Gen (Mountain), which when reversed becomes Zhen (Thunder), transforming the entire hexagram into Da Zhuang (Great Strength). This is an example of taking the upper trigram as the covered trigram. Therefore, the hexagram statement of Da Xu says "favorable to uprightness," and the hexagram statement of Da Zhuang also says "favorable to uprightness." Da Xu's Nine in the Second says "the carriage axle's wooden block falls off," and Da Zhuang's Nine in the Fourth says "strength in the carriage axle's wooden block," both using the image of the carriage axle's wooden block. Another example is the hexagram of Xiao Xu (Small Accumulation), where the outer trigram is Xun (Wind), which when reversed becomes Dui (Lake), transforming the entire hexagram into Guai (Breaking Up). This is also an example of taking the upper trigram as the covered trigram. Therefore, Xiao Xu's Six in the Fourth says "blood flows and alarm arises," and Guai's Nine in the Second says "alarm and crying out," both discussing caution. Xiao Xu's Nine at the Top says "rain has fallen and the place is settled," and Guai's Nine in the Third says "meeting rain as if soaked," both discussing encountering rain.

以上上半之覆卦也，名曰“上覆”。覆卦亦稱反易，故互見之義，往往相反。如地山謙下覆為地雷復，謙曰“利用征伐”，復曰“十年不克征”，其最顯著者也。昔人不解八卦相錯，即六十四卦相錯之義，每卦只於六爻中摸索，望文生義，宜無從索解者多矣。

All the above examples are cases of the upper section forming the covered hexagram, named "upper covering." The covered hexagram is also called "reverse transformation," because it involves turning a three-line trigram completely upside down. Therefore, the meanings of the two hexagrams often turn out to be exactly opposite. For example, the hexagram of "Modesty" (Qian), with the mountain above, when the mountain is reversed to become thunder, the whole hexagram becomes "Recovery" (Fu). The hexagram of "Modesty" says "it is advantageous to use military force" (the line six in the fifth says "it is advantageous to invade," and the line six at the top says "it is advantageous to march, to conquer states"). However, the line six at the top of "Recovery" says "it will take ten years before military action can be taken," meaning that military action cannot be taken for ten years. On one side it is advantageous to wage war, on the other it is not. This is the most obvious example of opposite meanings in covered hexagrams. In the past, people did not understand the principle that two trigrams are opposite to each other, and this principle extends to the sixty-four hexagrams, each of which is opposite to another. Therefore, when reading a hexagram, they only searched within the six lines of that hexagram and guessed the meaning from the words used, which is why there are so many passages in the Book of Changes that are difficult to understand and cannot be interpreted.

上下對易者，本卦上下兩象，自相對易。如泰否既未濟之類。象既對易，卦義必自相對。如泰否，上下自相對易者也。故泰曰“小往大來”，否曰“大往小來”，自相對舉。既未濟言上下例同，不贅。

The concept of "upper and lower trigrams being exchanged" refers to the primary hexagram's upper and lower trigrams being swapped. Examples include Tai and Pi, as well as Ji Ji and Wei Ji. Since the two trigrams have been reversed, their meanings must also be opposites. Taking Tai and Pi as an example: when the upper and lower trigrams of Di Tian Tai are exchanged, it becomes Tian Di Pi, which is exactly an exchange of upper and lower. Therefore, the statement of the Tai hexagram says "small things go out and great things come in," meaning the yin and flexible move outward while the yang and strong move inward; the statement of the Pi hexagram says "great things go out and small things come in," meaning the yang and strong move outward while the yin and flexible move inward. The two statements are directly opposite. The principle of exchanging upper and lower trigrams in Ji Ji and Wei Ji is the same, so there is no need to repeat it.

上下反易者，本卦上下兩象，自相反易，如頤如大過及中孚小過之類。象既反易，卦義亦往往見相反之意。舉例如下：頤，山雷頤，上下兩象，自相反易。故《象》曰“道大悖也”。悖字古文本從兩或字，正反相對。一字之微，其與卦象之適合精當至此，謂非造化之筆哉！

The phrase "upper and lower reversed" refers to the primary hexagram consisting of two three-line trigrams that are inverted relative to each other. For example, the hexagram Yi (颐), Da Guo (大过), Zhong Fu (中孚), and Xiao Guo (小过) all exhibit this relationship. Since the two trigrams are in a reversed position, the meaning of the hexagram often expresses a contrast between opposites. To illustrate, Yi (颐) is composed of the trigram Gen (山, mountain) above and Zhen (雷, thunder) below. When Zhen is inverted, it becomes Gen, and when Gen is inverted, it becomes Zhen. Thus, the upper and lower trigrams are directly opposite. Therefore, the Image Commentary of line six in the third position of Yi states, "the path is greatly contradictory." The character "悖" (contradictory) originally consisted of two "或" (or) characters, one upright and one inverted, facing each other. The form of the character itself embodies the concept of opposition. How could such a subtle detail of a character so precisely correspond to the hexagram's imagery? Is this not the brushwork of nature's artistry?

頤之名，取上下相合。而上止下動，非頤亦無以確肖其象。而象之上下，又為反易。玩《彖》、《象》六爻，無不各顯其義。神矣哉！又如大過，澤風大過，亦上下兩象自相反易。故象取枯楊生稊，枯楊生華，亦以示反常之意也。

The hexagram "Yi" derives its name from the image of the upper and lower jaws coming together to form the mouth and cheeks. The upper trigram is Gen (Mountain), representing stillness, and the lower trigram is Zhen (Thunder), representing movement. The upper jaw remains still while the lower jaw opens and closes, and there is no other image that can so accurately depict this. Moreover, the two trigrams are in a reciprocal relationship. Careful examination of the "Commentary on the Judgment," the "Image Commentary," and the statements of the six lines reveals that each passage conveys this meaning, truly marvelous! Similarly, in the hexagram "Da Guo" (Great Excess), which is composed of the upper trigram Dui (Lake) and the lower trigram Xun (Wind), Dui is inverted to become Xun, and Xun is inverted to become Dui. This also represents the mutual reversal of the two trigrams. Therefore, in the hexagram's imagery, it says "a withered poplar tree produces new sprouts," meaning a withered poplar tree unexpectedly sprouts new growth; it also says "a withered poplar tree produces flowers," meaning a withered poplar tree unexpectedly blooms, both used to express the meaning of abnormal reversal.

半對半覆以下，古人皆未嘗言之。觀象玩辭，發見各卦之互見其義，或互見其名者，於卦象無不相關。反覆推求，始知皆由於上下兩象，各有正對反對之故。《彖》、《象》經傳，不啻自舉其例，至為明顯。遍徵各卦，無不貫通。一旦豁然，如撥雲霧，而見天日。因廣對卦覆卦之意，類別其名，以便講習之稱引。然字累而文不雅馴，殊為歉憾。海內外專精小學名學之君子，能各撰一簡賅切當之名，畀垂久遠，則著者所寤寐求之，馨香祝之者焉。

From the categories of "half paired" and "half reversed" and the like, ancient scholars have never spoken. Observing the hexagrams and pondering the line statements, I found that the meanings of the hexagrams are interrelated, and even the names of the hexagrams are interrelated, and all of these are connected to the hexagram images. After repeated inquiry, I realized that all of this comes from the two three-line hexagrams above and below, each having two paths: "correct pairing" (complete yin-yang transformation) and "opposite pairing" (reversing upper and lower). The commentaries of the "Commentary on the Judgment" and "Image Commentary" are like setting forth the rules themselves, clear and explicit; examining all the hexagrams, they are all interconnected. Once suddenly enlightened, it is like removing the clouds to see the sun. Therefore, I extended the meaning of "paired hexagram" and "reversed hexagram," classifying them and giving them names for convenience in discussion. However, these names are cumbersome in wording and not sufficiently refined, which I find regrettable. If scholars throughout the world who are proficient in textual analysis, word meaning, and logic could each propose a simple and accurate name for them to be passed down, that would be exactly what I long for and pray for with incense.

《繫傳》曰：“爻也者，各指其所之。”之，往也，由此往彼也。《左傳》蔡墨曰“坤之乾，亦乾之坤”，言八卦陰陽相交，奇偶相易。虞仲翔氏專言之正，謂不當位之爻(如陽爻之二四六，陰爻之一三五。)，皆當之而當位。

The Great Treatise says: "A line refers to its movement toward a particular place." "Zhi" means going, moving from one place to another. The Zuo Zhuan records that the historian Cai Mo of the Jin state said, "The Earth Trigram transforms into the Heaven Trigram, and the Heaven Trigram transforms into the Earth Trigram," referring to the mutual interaction of the Eight Trigrams and the exchange between odd and even lines. Yu Fan of the Three Kingdoms period (with the courtesy name Zhongxiang) specialized in explaining "zhi zheng," believing that any line that is not in the correct position should change once to return to the proper position. For example, a yang line in an even position such as second, fourth, or sixth, or a yin line in an odd position such as first, third, or fifth, should change.

乾之二四六爻不當位，之坤之一三五則當位。坤之一三五不當位，之乾之二四六則當位。名曰“之正”，謂之而得其正也。惟乾之坤，坤亦之乾，則乾坤兩卦，成兩既濟。既濟定，陰陽消息，皆止而不行，乾坤幾乎息矣。故又以成兩既濟為凶。

The second, fourth, and top lines of the Qian hexagram are yang lines in even positions, which are considered improper. They should move to the first, third, and fifth lines of the Kun hexagram, which are odd positions, thus becoming proper. Similarly, the first, third, and fifth lines of the Kun hexagram are yin lines in odd positions, considered improper, and should move to the second, fourth, and sixth lines of the Qian hexagram, which are even positions, thus becoming proper. This is called "zhizheng," meaning that moving once leads to correctness. However, when Qian moves to Kun and Kun moves to Qian, both hexagrams become the Ji Ji hexagram. Once Ji Ji is formed, the structure of the hexagram becomes fixed, and the growth and decline of yin and yang come to a halt. As a result, Qian and Kun almost cease to exist. Therefore, Yu Shi judges "cheng liang ji ji" as an ominous outcome.

必乾初之坤四而上之坤三，然後旁通交變以周六十四卦。初上未動，而二五先行，亦為凶。焦理堂《易通釋》，又本此以演為《時行》、《失道》各圖。要皆一家之言，足備參考。若泥其例以言《易》，多窒礙難通，學者不可不知也。

Following the example of the Yu school, one must first move the initial line of Qian (Heaven) to the fourth line of Kun (Earth), and the top line of Qian to the third line of Kun, and then proceed to the lateral transformation and change, in order to circulate through all sixty-four hexagrams. If the first and top lines have not yet moved, but the second and fifth lines move first, this is considered凶 (unfavorable). Qing dynasty scholar Jiao Xun (styled Litan) in his work "Yi Tong Shi" further developed diagrams such as "Shi Xing" and "Shi Dao" based on this theory. These are merely the views of one school of thought and can only be considered as reference. If one rigidly adheres to this system when interpreting the Zhou Changes, there will be many obstacles and difficulties. Students of the Zhou Changes should not be unaware of this.

右為乾坤二卦之正，餘卦類推。惟占家言卦變亦曰之，則不以一爻為限。三爻變至五爻變，皆以所變之卦為之。如乾之剝，家人之睽。一卦變六十三卦，皆謂之曰之卦也。詳《學易筆談初集》。

The above discussion explains the situation of the Qian and Kun hexagrams "zhi zheng" (the correct form). The other hexagrams can be understood in the same way. However, when diviners discuss hexagram changes, they also use the word "zhi," which does not refer to a single line change only. From three-line change to five-line change, the hexagram that results from the change is called "zhi suogua" (to become a certain hexagram), for example, "Qian zhi Bao" and "Jiaoren zhi Kui." One hexagram can change into the other sixty-three hexagrams, all of which are referred to as "zhi gua." For details, see my work "Xue Yi Biren Cijie."

互卦(中爻、約象)者內外四爻，二至四，三至五，又各成三畫之卦一。兩卦交互，又成兩卦，故漢人謂之互卦。京氏曰：“會於中而以四為用，一卦備四卦者，謂之互。”崔氏子元曰：“中四爻雜合所主之事，撰集所陳之德，能辨其是非，備在中四爻也。”(京氏所謂一卦備四卦，以本卦內外兩象，更以二至四三者至五，又各得一卦，合為四卦也。)

The "Nuclear Hexagram" (also called "Middle Lines" or "Approximate Image"), is formed by taking four lines from the middle of a six-line hexagram, specifically the second to the fourth lines, which make up a three-line trigram. Similarly, the third to the fifth lines also form another three-line trigram. These two trigrams interact with each other, producing two additional hexagrams. Therefore, the Han dynasty scholars called it the "Nuclear Hexagram." Jing Fang said: "Meeting in the middle and using the fourth line, when one hexagram contains four hexagrams, it is called the Nuclear Hexagram." Cui Xing (styled Ziyuan) said: "The four middle lines contain the matters that the hexagram governs, and gather the virtues that the hexagram presents. They can distinguish right from wrong, and all these are fully included within these four lines." -- Original note: Jing Fang's statement that one hexagram contains four hexagrams refers to the fact that the original hexagram already includes two three-line trigrams, one from the inner and one from the outer. Then, by taking lines two to four and three to five, two more trigrams are formed, making a total of four hexagrams.

《繫傳》曰：“《易》之為書也，原始要終，以為質也。六爻相雜，唯其時物也。其初難知，其上易知，本末也。初辭擬之，卒成之終。若夫雜物撰德，辨是與非，則非其中爻不備。噫！亦要存亡吉凶，則居可知矣。”

The Great Treatise says: "The Zhou Changes is a book that traces the beginning of things and concludes their end, and this is its essence. The six lines are intermingled, but each follows its time and represents its thing. The meaning of the first line is difficult to see, while the meaning of the top line is easy to understand, because one is the origin and the other is the result. The statement of the first line merely imagines the beginning, while the top line finally completes it. As for intermingling all things, recording their virtues, distinguishing right and wrong, this cannot be fully understood without the four middle lines. Alas! To grasp the key of existence and non-existence, good fortune and misfortune, one can do so while sitting still."

又曰：“二與四，同功而異位，其善不同。二多譽，四多懼，近也。柔之為道，不利遠者。其要無咎，其用柔中也。三與五，同功而異位。三多凶，五多功，貴賤之等也。其柔危，其剛勝耶？”(阮氏《校勘記》：其用柔中也“用柔”下有“得”字。)

The Great Treatise also says: "The second line and the fourth line have the same function but different positions, so their goodness differs. The second line often receives praise, while the fourth line often incurs fear, because the fourth line is close to the position of the ruler. The way of flexibility and gentleness is not beneficial when it is far from the position of honor. The reason why the second line can achieve no fault is that it uses flexibility and is in the central position. The third line and the fifth line also have the same function but different positions: the third line often encounters danger, while the fifth line often achieves accomplishments, this is due to the difference in rank and status. Being in such positions, using flexibility is dangerous, and using strength is the way to be competent." — Original note: Yuan Yuan's "Notes on Collation" points out that in the phrase "its use of flexibility and centrality," there is an additional character "de" (to be able to) after "use of flexibility."

《繫傳》之言中爻，詳矣備矣。字字精實，孕育宏深，不可忽略。即以六爻言，初上及中四爻之時位象數，已劃然分明。後儒尚有疑互卦為非聖人之說者，則承掃象之餘習，不辨中爻二四三五之說，他更無論矣。《繫傳》既詳備至此，而《左傳》之說，尤可為三代言易不廢中爻之確證。為圖如下：

The Great Treatise explains the middle lines in detail, thoroughly and precisely, with profound implications, and cannot be easily overlooked. Considering only the six lines, the time, position, image, and numbers of the first line, the top line, and the four middle lines are clearly divided. Later Confucian scholars even doubted that the mutual hexagram is not the saying of the sage. This is due to their following Wang Bi's practice of "sweeping away images," failing to distinguish the middle lines as explained in the Great Treatise, namely the second and fourth lines, and the third and fifth lines. Other matters are even less understood. Since the Great Treatise has reached such a detailed level, and the divination examples in the Zuo Zhuan can serve as evidence that the Book of Changes was practiced in the Xia, Shang, and Zhou dynasties without neglecting the middle lines, the following diagram is provided:

《左氏傳》：“敬仲之將生也，周史有以《周易》見陳候者，陳候使筮之，遇觀之否(四爻動，偶變奇，風地觀變天地否)。曰：是謂觀國之光，利用賓于王。又曰：坤土也，巽風也，乾天也。風為天(風為天，猶云風變天，即巽變乾也)於土上，山也。”謂觀中爻三至五為艮，變否二至四亦為艮，此言互卦之最古者。

The *Zuo Zhuan* records: "When Jinzhong, the son of Chen Liji, was about to be born, the royal historian of the Zhou court came to Chen Hou with the *Zhou Yi* to divinate. Chen Hou asked him to cast the divination, and he obtained the hexagram *Guan* (Observation) changing to *Pi* (Opposition) —— note: the fourth line changed, an even line becoming an odd line, so *Guan* (wind on earth) transformed into *Pi* (heaven and earth opposing). The historian said: This is what is called 'Observing the brilliance of the state, useful for serving the king.' He also said: *Kun* is earth, *Xun* is wind, *Qian* is heaven. Wind becoming heaven —— note: 'Wind becoming heaven' means wind transforming into heaven, that is, *Xun* transforming into *Qian* —— and being above earth, this is the image of a mountain." Why did the historian suddenly conclude a 'mountain' from *Kun* (earth), *Xun* (wind), and *Qian* (heaven)? The key lies in the *Hugua* (intermediate hexagram): *Guan* (Observation) produces *Gen* (mountain) from the third to fifth lines; after transforming into *Pi* (Opposition), *Gen* (mountain) is still produced from the second to fourth lines. Therefore, he dared to make this statement. This is the earliest recorded explanation of *Hugua*.

故《朱子語錄》曰：“互體如屯卦震下坎上，就中四爻觀之，自二至四，則為坤。自三至五，則為艮。互體漢儒多用之。《左傳》中說占得觀卦處亦分明，看來此說亦不可廢。”蓋其時言易者，皆莫明中爻，而反對互卦。故朱說云爾。

Therefore, the "Collected Sayings of Master Zhu" states: "The mutual trigrams, for example, the Zun hexagram has Zhen below and Kan above. If we look at the fourth line, from line two to four we get Kun, and from line three to five we get Gen. The concept of mutual trigrams was commonly used by Han dynasty scholars. The passage in the "Zuo Zhuan" discussing the Guan hexagram also explains it clearly, indicating that this approach should not be discarded." Probably, at that time, those who interpreted the Book of Changes did not understand the middle lines and一味 opposed the mutual trigrams, so Master Zhu spoke like this.

《繫傳》言中爻謂二五三四，初與上不與焉。因二與五為本卦上下兩象之中爻，三為二至四成一卦之中爻，四為三至五成一卦之中爻，故四者皆謂之中爻。然後人之言互卦者，則不僅二三四五，實合初上與二三四五言之。又自五至上，復反至初言之，皆謂之互。故京氏又謂之約象。觀《雜卦傳》兩卦對舉，中爻皆成互卦。而自頤以下八卦，皆首尾交互，返歸於乾坤坎離四卦。列互卦如左：

The "middle lines" mentioned in the Great Treatise refer to the second, fifth, third, and fourth lines, excluding the first and top lines. This is because the second and fifth lines are the central positions of the lower and upper trigrams of the primary hexagram, respectively; the third line is the central position of the hexagram formed by the second to fourth lines; and the fourth line is the central position of the hexagram formed by the third to fifth lines. Therefore, these four lines are all called middle lines. However, later scholars discussing the nuclear hexagram did not limit themselves to the second, third, and fourth lines, actually including the first and top lines as well. They also took the image from the fifth line to the top line and then back to the first line, all of which are called "mutual." Hence, Jing Fang also referred to this as "approximate image." Looking at the Miscellaneous Hexagrams, where two hexagrams are contrasted, the middle lines can generate new hexagrams. Starting from the颐 hexagram, the eight following hexagrams all interconnect at their beginning and end, ultimately converging on the four hexagrams of Qian, Kun, Kan, and Li. Here is a list of the nuclear hexagrams:

吳草廬曰：“自昔言互體者，只以六畫之四畫互二卦而已，未詳其法象之精也。今以先天圖觀之，互體所成十六卦，皆隔八而得(外一層隔八卦得二卦，即中一層互體之卦名)，縮四而一(內層一卦縮外層四卦)。

In the Yuan dynasty, Wu Cheng, who was known as Cao Lu, said: "Previously, those who discussed mutual trigrams only took four lines out of the six lines to form two trigrams, but they did not clearly understand the subtle principles of the method and imagery involved. Now, by looking at the Earlier Heaven trigram diagram, the sixteen trigrams formed by mutual trigrams are all obtained by taking every eighth trigram. The original note says: the outer layer produces two trigrams by taking every eighth trigram, which are the names of the trigrams formed by the mutual trigrams in the middle layer. Moreover, four trigrams are condensed into one trigram. The original note says: the trigram in the inner layer is formed by condensing the four trigrams in the outer layer."

圖之左邊，起乾歷八卦至睽歸妹(中層睽妹即接乾夬)，又歷八卦而至家人既濟(家人既濟即接睽妹，餘卦仿此)，又歷八卦至頤復。圖之左邊，起姤大過，歷八卦至未濟解，又歷八卦至蹇漸，又歷八卦至剝坤。左右各二卦互一卦，合六十四卦互體只成十六卦，又合十六卦互成四卦，即乾坤既未濟。學《周易》始乾坤終既未濟，以此歟！”

On the left side of the diagram, starting from the Qian trigram, going through the eight trigrams to reach the Kui and Gui Mei trigrams—note: the middle trigrams Kui and Gui Mei follow Qian and Guai—then going through the eight trigrams again to reach the Jia Ren and Ji Ji trigrams—note: Jia Ren and Ji Ji follow Kui and Gui Mei, the rest follow the same pattern—then going through the eight trigrams again to reach Yi and Fu. On the other side (the original text still refers to it as the left side, but according to the meaning it should be the right side), starting from Guo and Da Guo, going through the eight trigrams to reach Wei Ji and Jie, then going through the eight trigrams again to reach Jian and Jie, then going through the eight trigrams again to reach Po and Kun. Each pair of trigrams on the left and right forms one trigram, combining the mutual relationships of the sixty-four trigrams into sixteen trigrams; then by mutual inference among these sixteen trigrams, four trigrams are formed, namely Qian, Kun, Ji Ji, and Wei Ji. Studying the Zhou Yi begins with Qian and Kun and ends with Ji Ji and Wei Ji, the reason for this is probably here.

蓋統云互卦，不但為中四爻，二至上五至初，亦皆交互成兩卦。更以五至上，復由上反之初二三四，亦互成兩卦，所以又稱約象。《序卦》“剝窮上反下”，即由上反初之一例也。

In general, the term 'mutual hexagram' refers not only to the four central lines from the second line to the top line and from the fifth line to the first line, which can form two hexagrams through interaction. Further, by counting from the fifth line to the top line and then returning from the top line to the first, second, third, and fourth lines, two hexagrams can also be formed, hence it is also called 'approximate image'. The 'Sequence of Hexagrams' states that the hexagram of 'breaking up' is 'exhausting the upper and returning to the lower', which is an example of returning from the top line to the first line.

澤山咸。中爻為天風姤。五至初，互天山遁。二至上，互澤風大過。若由五至上，更反之初二三四，仍互澤雷隨。由四至上，更反至初二，互地天泰，澤山反為雷風，則中爻又與上下互亦各相反。

Taking the Hexagram Xian (泽山咸) as an example: the four central lines produce the Hexagram Gou (天风姤). Counting from the fifth line to the first line, the resulting hexagram is Dun (天山遁). Counting from the second line to the top line, the resulting hexagram is Da Guo (泽风大过). If counting from the fifth line to the top line and then returning to the first, second, third, and fourth lines, the resulting hexagram is Sui (泽雷随). Counting from the fourth line to the top line and then returning to the first and second lines, the resulting hexagram is Tai (地天泰). The Hexagram Xian consists of Dui above and Gen below; when the entire hexagram is reversed, it becomes Heng (雷风恒). This shows that the two groups of hexagrams formed by the middle lines and the upper and lower lines respectively have opposite relationships with each other.

地天泰。中爻為雷澤歸妹。五至初，互雷天大壯。二至上，互地澤臨。五至上，更反之一二三四，為澤山咸。四至上，更反至初二，為澤雷隨。地天泰，反為天地否。即上下易，中爻上下互，相反亦同。

Taking the hexagram of Tai (Heaven over Earth) as an example: the four central lines produce the hexagram of Gui Mei (Lake over Thunder). Counting from the fifth line to the first line, the hexagram of Da Zhuang (Thunder over Heaven) is formed. Counting from the second line to the top line, the hexagram of Lin (Lake over Earth) is formed. Counting from the fifth line to the top line and then returning to the first, second, third, and fourth lines, the hexagram of Xian (Lake over Mountain) is formed. Counting from the fourth line to the top line and then returning to the first and second lines, the hexagram of Sui (Thunder over Lake) is formed. Reversing the hexagram of Tai results in Pi (Earth over Heaven), which means the upper and lower trigrams are exchanged. The situation where the middle trigram is opposite to the ones formed by the upper and lower lines is the same as in the hexagram of Xian.

闢卦亦稱十二消息卦，與月卦另詳下《卦氣》章。

"Bi Gua" is also called "the Twelve Message Hexagrams," referring to the twelve hexagrams that represent the gradual increase and decrease of yin and yang: from Fu, Lin, Tai, Da Zhuang, Guai, Qian, to Gu, Dun, Po, Guan, Po, and Kun. The method of pairing them with the "Monthly Hexagrams" is explained in detail in the following chapter "Gua Qi," but here only the names are listed.

宋儒言《易》，又有包卦之名。包卦者，六畫之卦，以上下三畫，中包三畫。如咸恆為坤包乾，損益為乾包坤之類，亦由互卦推衍而得者也。包卦之名，始於林黃中氏，謂由一卦分兩卦，兩卦分四卦，一正一反，又得四卦。是即太極生兩儀，兩儀生四象，四象生八卦也。因朱晦庵力駁之，故其說不行。然言之成理，亦不可謂毫無意義也。後儒如紀大奎等，頗採其說。略舉其例，如右圖：

In the Song dynasty, Confucian scholars discussed the Book of Changes and established the concept of "baogua" or "encompassing hexagram." The idea of baogua involves considering the top single line and the bottom two lines (or the bottom single line and the top two lines) of a hexagram as the outer trigram, which encloses the middle trigram. For example, the hexagram Xian (Attraction) and Heng (Perseverance) are formed by the trigram Kūn (Earth) enclosing the trigram Qián (Heaven), while the hexagrams Shen (Loss) and Yi (Gain) are formed by the trigram Qián enclosing the trigram Kūn. This method of interpretation is derived from the concept of mutual trigrams. The term "baogua" was first introduced by Lin Li (styled Huangzhong), a Song dynasty scholar. He believed that a single hexagram could be divided into two trigrams, which in turn could be divided into four trigrams, and with one being positive and the other negative, four more trigrams could be obtained. This corresponds to the principle mentioned in the "Xici Zhuan" (Great Treatise) that the Taiji (Supreme Ultimate) gives rise to two yi (binary opposites), two yi give rise to four xiang (images), and four xiang give rise to the eight trigrams. However, because Zhu Xi (styled Hui'an) strongly criticized this view, it did not become widely accepted. Nevertheless, the reasoning behind it is coherent and cannot be entirely dismissed as meaningless. Later scholars, such as Ji DaKui of the Qing dynasty, adopted this approach. For example, as shown in the diagram on the right:

六十四卦，皆可以此類推。但咸恆坤包乾也，而咸亦可謂之坎包巽，恆亦可謂之坎包兌。損益乾包坤也，損亦可謂之離包震，益亦可謂之離包艮，其實即中爻之二與四三與五也。他卦上下相推，亦無不如此。特以陰陽內外言之，亦自有此一象。故存之。

The sixty-four hexagrams can all be deduced in the same way. However, the hexagrams of Xian and Heng, although said to be composed of Kūn encompassing Qián, can also be interpreted as Càn encompassing Xūn for Xian, and Càn encompassing Dui for Heng; similarly, the hexagrams of Shen and Yi, although said to be composed of Qián encompassing Kūn, can also be interpreted as Li encompassing Zhen for Shen, and Li encompassing Gen for Yi. In the end, these encompassed hexagrams are actually the two middle lines of the nuclear hexagram, namely lines two to four and three to five. For all other hexagrams, the same principle applies when considering their upper and lower parts. However, from the perspective of yin and yang encompassing each other, these constitute a distinct kind of hexagram image, so they are retained.

像卦者，合六爻之奇偶觀之，像三畫之一卦也。《繫傳》曰：“象也者像也。”故謂之像卦。來知德氏謂之大象，如大坎大離之類，實皆像卦也。於卦義均有關係，《彖》、《象》可證者甚多。舉例如下：頤像離，中孚像離，大過像坎，小過像坎。

The concept of "like hexagram" refers to viewing the combination of odd and even numbers of the six lines together, resulting in an overall shape resembling one of the three-line trigrams. The "Great Treatise" states: "An image is like a likeness." Therefore, it is called a like hexagram. The Ming dynasty scholar Lai Zhide referred to it as "great image," such as Great Water (Kan) and Great Fire (Li), which are actually like hexagrams. It is related to the meaning of the hexagram, and there are many examples that can be found in the Commentary on the Judgment and the Image Commentary. For example, the hexagram Yi has two yang lines at the top and bottom and four yin lines in the middle, resembling the trigram Li; the hexagram Zhongfu also has two yang lines at the top and bottom and two yin lines in the middle, resembling Li. The hexagram Da Guo has two yin lines at the top and bottom and four yang lines in the middle, resembling Kan; the hexagram Xiao Guo has four yin lines at the top and bottom and two yang lines in the middle, also resembling Kan.

此來氏所謂大象之坎離，故《序卦》以列於坎離既未濟之前也。餘卦仿此。重畫或單畫者例亦同。大壯像兌。雷天大壯無兌，而合全卦觀之，有兌象。兌為羊，故象辭云“羝羊”“喪羊”。

This is what Lai Zhide said about the "Great Image of Kan and Li." Therefore, the "Sequence of Hexagrams" places Yi and Da Guo before Kan and Li, and Zhong Fu and Xiao Guo before Ji Ji and Wei Ji. The other hexagrams can be similarly inferred. Whether the Great Image is formed by overlapping two lines or a single line, the format remains the same. For example, Da Zhuang resembles Dui: although the six lines of Da Zhuang do not contain the hexagram Dui, when viewed as a whole, the upper two yin lines and the lower four yang lines form a magnified image of Dui. Dui is associated with the sheep in the "Discourse on the Hexagrams," which is why the line statements of Da Zhuang mention "the ram strikes against the fence" and "losing the sheep in ease."

剝像艮。山地剝，合全體觀之，有艮象，故重艮，《象》云“孚于剝”。六爻合觀之象，無不各有取義。如咸恆損益，為乾坤互交，而又像坎離者也。故咸恆繼坎離為《下經》之首，而損益次十一十二，與泰否等，其義大可見矣。

The hexagram Bo resembles Gen: The hexagram Bo itself already has Gen on top, and when viewed as a whole, it has one yang line at the top and five yin lines below, forming a larger image of Gen, equivalent to Gen on top of Gen. Therefore, the Image Commentary of line six in the fifth position of Bo says, "Trust in the situation of Bo." When all six lines are considered together, the overall image derived has meaning in every aspect. For example, the hexagrams Xian, Heng, Shen, and Yi are all formed by the interaction of Kan and Li, and their overall images also resemble Kan and Li. Therefore, Xian and Heng follow Kan and Li and are placed at the beginning of the Lower Classic, while Shen and Yi are placed at the eleventh and twelfth positions of the Lower Classic, corresponding exactly to the positions of Tai and Po in the Upper Classic. The significance behind this arrangement is clearly evident.

命卦(動在其中)者，昔無此名。青田端木氏《周易指》，據《大傳》“繫辭焉而命之，動在其中矣”而發其例。凡卦六爻，《象》下所繫之辭，言卦名者是也。卦有陰陽，不論其爻之剛柔，爻無卦名。卦陽六爻以陽論，卦陰六爻以陰論。

The term "Minggua" (also called "Dong zai qizhong," meaning "movement is contained within") was not previously established. It was first introduced by Duanguohe, a person from Qintian, Zhejiang, in his work "Zhouyi Zhi." He based this concept on the sentence from the "Xici Zhuan" ("Great Treatise") that says, "Attach a statement to it and name it; movement is contained within it." The method of determining Minggua is as follows: in a hexagram with six lines, any line statement that mentions the name of the primary hexagram is considered a line that "has the hexagram name." The hexagram itself is divided into yin and yang hexagrams. When determining, the nature of the line itself as yang or yin is not considered. Instead, lines that do not mention the hexagram name are determined by the yin or yang nature of the primary hexagram— if the primary hexagram is yang, these lines are considered yang; if the primary hexagram is yin, these lines are considered yin.

如乾陽卦也，惟九三一爻有卦名，則九三為陽。餘以陰論，即命為謙，如坤陰卦也。六爻無卦名，六爻皆以陰論，仍為坤。如屯陽卦也，二五兩爻有卦名。二五為陽，餘皆陰論，即命為坎。蒙陰卦也，初二四五上有卦名，皆為陰。二爻以陽論，則命為謙。

For example, Qian is a yang hexagram. Among its six lines, only the third line's line statement mentions the hexagram name "Qian," so the third line is considered yang. The remaining five lines are treated as yin. Thus, one yang line is at the third position, with the other five lines yin, resulting in the hexagram Dixin. Another example is Kun, a yin hexagram. None of its six lines' line statements mention the hexagram name "Kun," so all six lines are considered yin, resulting in the hexagram Kun. Another example is Tun, a yang hexagram. The second and fifth lines' line statements both mention the character "Tun," so these two lines are considered yang. The remaining four lines are treated as yin. With yang lines at the second and fifth positions and yin lines elsewhere, the resulting hexagram is Kan. Another example is Meng, a yin hexagram. The line statements of the first, second, fourth, fifth, and top lines all mention the character "Meng," so these five lines are considered yin. Only the third line is treated as yang. Thus, the resulting hexagram is also Dixin.

如震六爻皆有卦名，震陽卦，六爻皆陽，命為乾。餘可類推。動在其中者，合陰陽兩卦之中，陰陽交變。如屯命坎，坎離動在其中，為小過中孚是也。

For example, in the Zhen hexagram, the line statements all contain the character "Zhen," and since Zhen is a yang hexagram, all six lines are yang. The hexagram thus becomes Qian. The other hexagrams can be similarly inferred. As for the phrase "movement occurs within," it refers to combining the original hexagram with the one derived, creating a yin and yang interaction between the two. For instance, the Zun hexagram derives the Kan hexagram, and the movement between Kan and Li produces the Xiao Guo and Zhong Fu hexagrams.

聲應卦，亦發例於《周易指》。同聲相應，孔子於六爻《象傳》讚語，皆有韻以分陰陽。平為陽仄為陰，如乾分贊三次，曰：“陽在下也”，“德施普也”，“反復道也”，“進無咎也”，“大人造也”，“盈不可久也”，為六陰聲是坤卦。

The principle of "sound correspondence in hexagrams" was first introduced by Du Mengguo in his work "Zhou Yi Zhi." Taking the meaning of "like sounds respond to each other," it argues that the commentaries in the "Image Commentary" written by Confucius for the six lines of each hexagram all rhyme and can be used to distinguish yin and yang. Reading tones that are level (ping) are considered yang, while those that are oblique (zhe) are considered yin. For example, the commentary for the hexagram Qian consists of three groups. The first group includes "Yang is at the bottom," "His virtue extends universally," "Reversal follows the Way," "Advancing without blame," "The Great Man creates," and "Fullness cannot last." All six lines rhyme with oblique tones, making them six yin lines, which correspond to the hexagram Kun.

又曰：“下也”，“時舍也”，“行事也”，“自試也”，“上治也”，“窮之災也”，五陰一陽是剝卦。又曰：“陽氣潛藏”，“天下文明”，“與時偕行”，“乾道乃革”，“位乎天德”，“與時偕極”，三陰三陽是泰卦也。

The second set of comments are "Lower," "Residence of Time," "Action," "Self-test," "Supreme Governance," and "Disaster of Exhaustion," among which five are level tones and one is oblique tone, with five yin and one yang, resulting in the Hexagram of Splitting. The third set is "Yang energy is concealed," "The world is civilized," "Follow the time," "The Creative initiates change," "Positioned in Heavenly Virtue," and "Reach the extreme of the time," with equal numbers of level and oblique tones, and three yin and three yang alternating, resulting in the Hexagram of Greatness.

坤卦六爻曰：“致堅冰也”，“地道光也”，“知光大也”，“慎不害也”，“文在中也”，“其道窮也”。初二四上，皆陽，三四陰，坤應聲中孚也。

The commentary on the six lines of the Kun hexagram is "It leads to firm ice," "The earth's path shines," "It knows great brightness," "It is cautious and does no harm," "The virtue is in the center," "Its path reaches its limit." According to the division of level and oblique tones, the lines at the beginning, second, fifth, and top belong to the yang tone, while the middle two lines belong to the yin tone. With two yang tones outside and two yin tones in the center, the sound corresponding to the Kun hexagram is that of Zhongfu.

《傳》曰：“物生而後有象，象而後有滋，滋而後有數。”是先有象而後有數。而古聖人之作《易》也，仰以觀象於天，俯以觀法於地。河出圖，洛出書，聖人則之。然則八卦之象，皆法天地之象。萬物之象，並則河圖洛書以定其數者也。

The *Zuo Zhuan* records Han Jian's words: "Things come into being, then there are images; from images, there is growth; from growth, there is number." This shows that images come first, then numbers. Ancient sages composed the *Zhou Yi*, looking up to observe celestial phenomena and looking down to examine terrestrial principles. When the Yellow River produced the *He Tu* and the Luo River produced the * Luo Shu*, the sages took these as their models. Thus, the images of the Eight Trigrams are derived from the images of heaven and earth, and the images of all things are determined by the numbers of the *He Tu* and *Luo Shu*.

八卦之象，始於羲農黃帝，而後代有孳乳。《說卦傳》之象，非孔子所創造，必有所受。問禮於老子，象數在其中，故曰“觀其會通以行其典禮”。列舉之象雖不多，而用無不備。自王弼有“得意忘象”之言，後人未得其意，輒以掃象為擴清蕪穢，易學由此荒矣。

The symbolic representations of the Eight Trigrams originated with Fuxi, Shennong, and the Yellow Emperor, and were continuously developed by later generations. The images described in the "Sayings on the Trigrams" were not created out of nowhere by Confucius, but must have been inherited from previous sources. Confucius once asked Laozi about ritual propriety, and the study of numbers and symbols was included in that. Therefore, the "Great Treatise" states, "Observing their convergence and communication to carry out ceremonial rites." Although the images listed in the "Sayings on the Trigrams" are not numerous, they are comprehensive in their application. Since Wang Bi proposed the idea of "grasping the meaning while forgetting the image," later people failed to understand his original intention, often mistakenly treating the removal of trigram images as clearing away weeds and filth, and since then, the study of the Book of Changes has been neglected.

南宋而後，漸知象之重要，然又未能求諸根本，以邵子大小方圓各圖為易象之標準。而《說卦傳》八卦之象義，反略焉不講，或以不解解之。有明來知德氏，研求象學二十餘年，頗有發明。然未解者，亦尚什之七八也。

After the Southern Song dynasty, people gradually realized the importance of hexagram images, but they could not seek the fundamental principles, instead taking Shao Yong's diagrams of large and small circles and square and round as the standard for the Book of Changes' imagery. Meanwhile, the meanings of the eight trigrams in the "Commentary on the Hexagrams" were overlooked or simply dismissed with the phrase "incomprehensible." Lai Zhide of the Ming dynasty devoted over twenty years to studying the imagery, making some discoveries, yet he still could not fully explain it, only succeeding in about seven or eight tenths of the cases.

前清經師，如黃、毛、朱、王、胡、錢、惠、段、桂、張、焦、端木諸家，各有心得。而是丹非素，不相會通。爰萃眾說，擇善而從。縱未能盡，參諸《學易筆談》所述，亦庶幾矣。

In the Qing dynasty, scholars who interpreted the classics, such as Huang Zongxi, Mao Qiling, Zhu Junsheng, Wang Yinzi, Hu Xu, Qian Daxin, Hui Dong, Duan Yucai, Gui Fu, Zhang Huiyan, Jiao Xun, and Du Mu Guohu, each had their own insights. However, they regarded their own views as correct and others as wrong, and did not communicate with each other. Therefore, I have compiled the views of these scholars and followed the good ones. Although I may not have exhausted all possibilities, if one also refers to what I discussed in my "Xue Yi Bi Tan," it will be almost complete.

乾，天。天不可見，以日月星辰見之。故蔡墨言“乾之六龍”，皆指星象。天行不可測，由地測之。故天無方無體，乾無方無體。坤，地。地為實質，有體可測，有方可紀。承天而時行，天之用皆著於地。而地代天終，時行物主，靜而有常。天地定位，法象備矣。

The image of the Qian trigram is Heaven. Heaven itself is invisible, and it is only through the sun, moon, and stars that it becomes apparent, so the "Six Dragons of Qian" mentioned by Cai Mo in the "Zuo Zhuan" refer to celestial phenomena. The movement of Heaven cannot be directly measured, so it must be observed from the ground. Therefore, Heaven has no fixed direction and no specific form, and Qian also has no fixed direction and no specific form. The image of the Kun trigram is Earth. Earth is a tangible substance with a form that can be measured and a direction that can be recorded. It supports Heaven and follows its timing, making Heaven's actions manifest on Earth. Earth completes Heaven's function by bringing forth all things in accordance with the seasons, remaining still yet maintaining a constant order. Heaven is above, Earth is below, their positions are fixed, and thus the trigrams derived from Heaven and Earth are complete.

艮，山。高於地者為山，地氣乃上通於天而云出也。一陽上覆，萬寶蘊藏，山之用也。兌，澤。下於地者為澤，天氣乃深入於地而龍潛焉。一陰外見，以陰涵陽，澤之用也。山澤通氣，上感下應，人生乃通乎天地。

The Great Image of Gen (Mountain) is mountain. Mountains rise above the earth, and the earth's energy rises to connect with heaven, causing clouds to arise from the mountains. The Gen hexagram has one yang line covering two yin lines, symbolizing the mountain containing all kinds of treasures within it, which is the function of a mountain. The Great Image of Dui (Lake) is lake. Lakes lie below the earth, and the heavenly energy penetrates into the earth, allowing dragons to dwell within. The Dui hexagram has one yin line emerging from two yang lines, symbolizing the nurturing of yang energy through yin flexibility, which is the function of a lake. Mountains and lakes are connected by their energies; above there is a response, and below there is a corresponding reaction. Human life is also connected to heaven and earth through this mutual response.

震，雷。雷伏地中，一陽奮出，萬象昭蘇。見天地之心，為乾之肖子，動萬物莫疾乎雷。巽，風。風行天下，陰陽相遇，品物咸章。風不可見，而無微不入。撓萬物者，莫疾乎風。雷風相薄，出入無疾。陰陽和，地天泰矣。

The image of Zhen (Thunder) is a thunderclap. Thunder lies hidden underground, and when a single yang force emerges forcefully, the appearance of all things revives. This is precisely what the hexagram Fu (Return) says, "Seeing the heart of heaven and earth." Zhen is the eldest son of the hexagram Qian (Heaven) in its initial interaction, and is most like the father, so the "Commentary on the Hexagrams" says, "Nothing moves all things more swiftly than thunder." The image of Xun (Wind) is wind. Wind moves across the world, causing yin and yang to meet each other, and thus all things become evident. Wind has no visible form, yet it penetrates everywhere, so the "Commentary on the Hexagrams" says, "Nothing twists and turns all things more swiftly than wind." Thunder and wind approach and push against each other, one emerging and the other entering without obstruction, and yin and yang harmonize, forming the situation of the hexagram Tai (Heaven over Earth).

坎，水。坎本坤體，故水性就下。陽含陰中，氣化為質，潤萬物者莫潤乎水。天一之精，萬物資生，資此坤中之一元也。離，火。離本乾體，故火性炎上。陰麗於陽，氣盛生光，萬物皆相見。其精為日，水火不相射而相逮，天地之大用備矣。

The trigram Kan represents water. Originally, Kan is formed by placing a single yang line in the center of the trigram Kun, hence water has a downward flowing nature. Yang energy is contained within yin, and when the energy condenses, it takes form. Therefore, the "Commentary on the Trigrams" says, "Nothing is more nourishing to all things than water." "Heaven produces water" (tian yi shui), water is the essence of the primordial yang from heaven. All things depend on it for growth, and this is precisely due to the original yang line in the center of Kun. The trigram Li represents fire. Originally, Li is formed by placing a single yin line in the center of the trigram Qian, hence fire has an upward rising nature. Yin is attached to yang, and when the energy is strong, it emits light, allowing all things to see each other. Its essence in the sky is the sun. Water and fire do not harm each other but can support each other, thus completing the greatest function in heaven and earth.

天地山澤雷風水火，為八卦之大象，《易》之本也。八卦相錯，因而重之為六十四。陰陽相交，變化以生。而象之變易，亦各因時位而異。而要不越此八者之範圍也。

Heaven, Earth, Mountain, Lake, Thunder, Wind, Water, and Fire are the great images of the Eight Trigrams, and they form the foundation of the Zhou Changes. The Eight Trigrams intercross in pairs, thus forming the sixty-four hexagrams. The interaction of yin and yang produces change. The transformation of the hexagrams varies according to the time and position they occupy. However, amidst all changes, they never go beyond the scope of these eight great images.

昔者聖人之作《易》也，觀象畫卦，近取諸身，遠取諸物，以通神明之德，以類萬物之情。而物各有所本，象以象物，亦莫不各有其本。故本象著焉。乾為馬。物性馬最健，得陽剛之精，晝夜不眠。房星為天駟七星之次，七星為馬，於辰為午，故馬為火畜。蠶馬首龍精，故馬蠶同氣。在天為龍，在地為馬，皆乾行也。

In ancient times, the sages composed the Zhou Yi, observing the forms and phenomena of things and drawing out hexagrams. Those close at hand were taken from the human body, while those more distant were taken from the myriad things in heaven and earth. They were used to connect with the virtue of the divine and to resemble the forms and conditions of all things. Since all things have their own origin, and hexagrams are used to symbolize things, each hexagram also has its own original image. Therefore, a section on "original images" was specially established. Qian represents a horse: among all things, the horse is the most vigorous. It receives the essence of yang, and does not sleep day or night. Among the twenty-eight mansions, the Fáng mansion is called "Tian Su," and it is closely followed by the Seven Stars. The Seven Stars in the star system belong to the horse, and are paired with the twelfth heavenly stem, Wu, which is associated with fire. Therefore, the horse is a fire animal. The head of the silkworm resembles the head of a horse, and both share the essence of the dragon, so the horse and the silkworm share the same vital energy. In the sky it is the dragon, on the earth it is the horse, both representing the manifestation of Qian's vigorous movement.

坤為牛。牛性柔順，屬土屬陰，不動即眠，起先後足，與馬相反。牛為大物，故物從牛。坤備萬物，故以牛象之。震為龍。乾變震為長子。龍雷同類，龍馬同種。馬八尺以上曰龍，龍陽物而生於純陰之地，震象也。

The hexagram K'un is symbolized by the ox. The ox is gentle in nature, belongs to the earth element in the Five Phases, and is yin in yin and yang. When it is still, it lies down and sleeps; when it rises, it lifts its hind legs first, which is the opposite of the horse, which lifts its front legs first. The ox is a large creature, so the character 'wu' (物) includes the radical for ox. K'un contains and embraces all things, hence the ox is used to symbolize it. The hexagram Zhen is symbolized by the dragon. The first line of the Qian hexagram combines with K'un to form Zhen, which represents the eldest son. The dragon and thunder belong to the same category, and the dragon and horse belong to the same kind; a horse that is over eight feet tall is called a dragon. The dragon is a yang creature, yet it is born in a purely yin environment of water and earth. One yang arises from two yins, which is exactly the image of Zhen.

巽為雞。雞善伏，《九家》曰“應八風也”。風應節而變，變不失時。雞時至而鳴，與風相應。故有風疾者禁食雞。雞將鳴，必動股振羽，故曰“翰音”。坎為豕。豕水畜。《傳》言星斗散精為彘，斗星坎地。朱氏曰：“亥為豕者直室也，坎之所自生也。”

The trigram Xun represents a chicken: chickens are good at crouching and incubating eggs. The "Nine Families Commentary on the Yi" says it "responds to the eight winds." Winds change with the seasons, changing yet not losing their timing; chickens also crow at the exact time, corresponding with the winds. Therefore, people suffering from wind-related illnesses should avoid eating chicken. Before a chicken crows, it must first stretch its legs and flap its wings, so ancient people called this sound "Hanyin," meaning the sound of high flight. The trigram Kan represents a pig: pigs are water animals. Ancient legends say that the stars of the Big Dipper spread their vital energy and transformed into pigs, and the position of the Big Dipper corresponds to the trigram Kan. Zhu Zhen said: "The earthly branch Hai is why pigs are associated with water, because Hai is located at the position of Shuxu, and Shuxu is where the water of Kan originates."

離為雉。雉文采象離。朱氏曰：“雉方伏時，東西風則復，南北風則去而不復。坎勝離也。”卜楚邱論明夷之謙曰“當鳥”。鳥者朱鳥也，離之次也。艮為狗。《九家》曰：“艮止，主守禦也。”艮數三，七九六十三，三主艮。斗為犬，故犬三月而生。斗運十三時日出，故犬生十三日開目。艮火之精，畏水不飲，而以舌舐，斗則以水解也。

Li represents the wild chicken: the wild chicken's feathers have splendid patterns, which correspond to the image of civilisation represented by the Li hexagram. Zhu Zhen said: "When the wild chicken is brooding eggs, if it meets east wind or west wind, it will return; but if it meets south wind or north wind, it will not return, which is due to the victory of Kan water over Li fire." In the "Zuo Zhuan," the diviner Chu Qi discussed the hexagram Mingyi and said "when the bird comes," referring to the bird as the Southern Alauda, which is the star position associated with Li. Gen represents the dog: the "Jiujia Yi" says, "Gen represents stopping, and is responsible for guarding and defense." The先天 number of Gen is three, and when seven and nine are multiplied, the result is sixty-three, of which the three belongs to Gen. The Big Dipper corresponds to the dog in starry phenomena, so the dog's gestation period is three months. The Big Dipper takes thirteen hours to move, so the puppy opens its eyes on the thirteenth day. Gen is the essence of fire, fears water, and does not drink, only licking with its tongue; as for the Big Dipper, it is water that neutralizes its dryness.

兌為羊。朱氏曰：“兌，說也，羊內狠者。二陽伏於一陰之下也。”項氏曰：“未為羊而主兌者，金生於土也。土旺則金生，故坤伏必於建未之月。”此所謂“遠取諸物”也。漢上朱氏曰：“說八卦本象也。”

The trigram Dui represents a sheep: Zhu Zhen said, "Dui means joy, and the sheep appears gentle on the outside but stubborn within, which exactly matches the shape of the Dui trigram with two yang lines hidden beneath one yin line." Xiang Anshi said, "Among the twelve earthly branches, Wei belongs to the sheep, but it is governed by Dui instead, because metal is born from earth: when earth is strong, metal arises. Therefore, the month of Wei (the sixth lunar month) must be when the hidden earth is present." This is what the Great Treatise says, "far-reaching reference to external things." Han Shang Master Zhu Zhen said, "These are explaining the original forms of the eight trigrams."

乾為首。首為眾陽所宗，乾尊在上故為首。《虞氏易》：“明夷九三得其大首，乾三之上也。”坤為腹。《正義》：“坤能包藏含容，故為腹。坤體中虛，亦象腹。”朱氏曰：“坤又為身為躬。按艮為身，言坤之變艮為背，則坤為腹也。”

Heavenly Stems: Jia, Yi, Bing, Ding, Wu, Ji, Geng, Xin, Ren, Gui Earthly Branches: Zi, Chou, Yin, Mao, Chen, Si, Wu, Wei, Shen, You, Xu, Hai Trigrams: Qian (Heaven), Dui (Lake), Li (Fire), Zhen (Thunder), Xun (Wind), Kan (Water), Gen (Mountain), Kun (Earth) Glossary: The Correct Meaning of the Zhou Changes = Zhou Yi Zhenyi Kong Yingda = Kong Yingda Third Line = San Yao Nine in the Third = Ji San The Zhou Changes = Zhou Yi Yu Fan = Yu Fan Heaven is the head: the head is where the entire body's yang energy converges, and since Qian is noble and occupies the upper position, it is taken as the image of the head. Yu Fan's commentary on the Yi says: "The line nine in the third of Mingyi (Darkness) is said to 'gain the great head,' because the third line of Qian moves upward to the upper position." Earth is the abdomen: Kong Yingda's Zhou Yi Zhenyi says: "Kun can contain and embrace, so it is the abdomen; the body of Kun is hollow in the middle, which also resembles the abdomen." Zhu Zhen says: "Kun can also represent the body or the person." According to this, when Kun transforms into Gen, it becomes the back; since the back belongs to Gen, then Kun itself is the abdomen.

震為足。震動於下，故為足。震為乾初，健行，故稱足也。陽起自下，亦足之象。巽為股。《正義》：“股隨於足，巽順故為股也。”按：足動而股不動，隨足而動，故咸曰“執其隨”。巽下偶，亦股之象。

The trigram Zhen represents the foot: Zhen has a single yang line moving at the lower position, so it takes the image of the foot. Zhen is formed by the first line of Qian interacting with Kun, inheriting the quality of firmness and strength, thus being called the foot. The yang energy rising from below corresponds precisely to the image of the foot. The trigram Xun represents the thigh: The "Correct Meaning of the Zhou Changes" says, "The thigh moves with the foot; Xun has the meaning of following, hence it represents the thigh." Note: The foot is active, while the thigh itself is not active, but merely follows the foot's movement, so the line statement of "Xian" nine in the third says "to hold on to what follows." The Xun trigram has a single line at the bottom, which is an even line, and the middle is divided like the shape of two thighs, thus representing the thigh.

坎為耳。《正義》：“北方之卦主聽，故為耳。”按：坎陽涵陰中，故耳聰內。腎開竅於耳，腎水竭則耳聾，皆坎象也。離為目。《正義》：“南方之卦主視，故為目。”按：離陰麗陽中，故目明於外。心開竅於目，仍繫於腎而見於外，皆離象也。

The trigram Kan represents the ear: The Correct Meaning of the Zhou Changes states: "Kan is the trigram of the north, governing hearing, hence it represents the ear." It is explained that Kan consists of one yang line contained within two yin lines, so the sharpness of hearing is inward. The Yellow Emperor's Inner Canon states that the kidney opens to the ear, and when the kidney water dries up, a person becomes deaf, which aligns with the image of the Kan trigram. The trigram Li represents the eye: The Correct Meaning of the Zhou Changes states: "Li is the trigram of the south, governing vision, hence it represents the eye." It is explained that Li consists of one yin line attached to two yang lines, so the brightness of the eye is outward. The Inner Canon states that the heart opens to the eye, and the clarity of vision still depends on kidney water, though it is manifested externally, which aligns with the image of the Li trigram.

艮為手。艮動於上，故為手。朱氏曰：“艮止者，動極而止也。震艮相反，行者必止，止者必行。疾走者掉臂，束手者緩行。”項氏曰：“李椿年號逍遙子，作《周易傳》曰：一身之榮衛，還周會於手太陰。一日之陰陽，昏曉會於艮時。在人其象為手。”按：此說最精。證諸《內經》，與震之為足，合觀方見。古聖“近取諸身”一節之玄妙精微，非僅以表面之動靜，合卦畫之陰陽已也。

The trigram Gen represents the hand: the single yang line in Gen moves at the top, so it takes the image of the hand. Zhu Zhen said: "The stopping of Gen is stopping after motion has reached its extreme. Zhen and Gen are exactly opposite: a person who is running must stop, and a person who is stopped must run. A person running quickly moves his arms, while a person with his hands tied moves slowly." Xiang Anshi said: "Li Chun, who took the name Xiao Yaozi, wrote a commentary on the Zhou Changes, stating: the human body's營气 and 卫气 circulate through the body and meet at the hand taiyin lung meridian. In a day, the yin and yang meet at the time of chou and yin, which are the times governed by Gen. In the human body, its image is the hand." According to this, the explanation is most accurate. Using the Huangdi Neijing to verify it, and combining it with the trigram Zhen representing the foot, one can truly understand it. The profound subtlety of the ancient sages' saying "taking near things from the body" is not merely comparing the surface motion and stillness with the yin and yang of the trigram images.

兌為口。鄭氏曰：“上開似口。”《正義》：“兌西方之卦，主言語，故為口。”朱氏曰：“艮為鼻。口鼻通氣，山澤通也。”此所謂“近取諸身”也。餘氏舒芑曰：“八卦之象，近取諸身者，六子以反對。遠取諸物者，六子以序對。四者易而坎離不易也。”

The trigram Dui represents the mouth: Zheng Xuan said, "The top line of the Dui trigram is broken, resembling an open mouth." The Correct Meaning of the Zhou Changes stated, "Dui is the trigram of the west, governing speech, hence it represents the mouth." Zhu Zhen said, "Gen represents the nose. The mouth and nose communicate breath, which is exactly what the Discourse on the Trigrams explains as 'mountain and marsh communicate through air.'" This is what the Great Treatise refers to as "drawing near to the body." Yu Shuqian said, "In the symbolic representations of the Eight Trigrams, the trigrams representing the body are arranged in reverse order: Zhen, Xun, Kan, Li, Gen, and Dui. The trigrams representing external objects are arranged in order: Zhen, Xun, Kan, Li, Gen, and Dui. Within these two sequences, the positions of Zhen and Gen, Xun and Dui are exchanged, while Kan and Li remain unchanged."

王氏夫之曰：“因此見人之一身，無非乾坤六子之德業所著。由此而推之血氣營衛箸骸皮肉之絡理，又推之動靜語默周旋進退之威儀，又推之喜怒哀樂愛惡攻取之秩序，無非健順陰陽之所合同。而乘時居位之得失吉凶，應之不爽。君子觀象玩占，而於疾眚之去留，言行動作之善惡，皆可因此以反躬自省而俟天命。”按：六十四卦，上下往來，象之變化無窮，要皆以大象本象為準，所謂萬變不離其宗者也。初學觀象，首宜反覆研求，必得其會通，而後始有變化之可言也。

Wang Fu-zhi said: "From this we can see that every part of a person's body is the manifestation of the virtues and achievements of the trigrams Qian and Kun and the six sons. From here we can extend to the circulation and structure of blood, qi, bones, flesh, and skin, then to the movements and stillness, speech and silence, and the gestures and postures of a person's demeanor, and further to the order of joy, anger, sorrow, and joy, as well as love, hate, choice, and rejection. None of these is not the combination of strength and firmness with gentleness and compliance, yin and yang. The gains and losses, good fortune and misfortune that a person experiences at a certain time and place are in perfect correspondence with these. A gentleman observes the trigrams, contemplates the divination verses, and can thereby examine the coming and going of illness and calamity, and the goodness or evil of speech and action, and thus reflect on himself and wait quietly for the mandate of heaven." Note: The sixty-four trigrams change endlessly as they move up and down, but all ultimately follow the principles discussed earlier in the sections of "Great Image" and "Original Image." This is what is meant by "a thousand changes do not depart from the root." Beginners studying the images should first thoroughly study these two sections. They must fully understand the fundamental images of the eight trigrams: heaven and earth, thunder and wind, water and fire, mountain and marsh, as well as the fundamental images of horse, cattle, dragon, chicken, head, abdomen, legs, and thighs. Only then can they talk about the changes of the trigrams.

《說卦傳》末章，先儒皆以為廣八卦之象，朱子《本義》謂多不可解。且按之於經，亦不盡合，故與《序卦》、《雜卦》皆不加註釋。漢上朱氏曰：“說重卦別象也。六爻變化，其象豈能悉盡，此凡例也。智者觸類而長矣。”

The last chapter of the "Shuo Gua Zhuan" was traditionally regarded by previous Confucian scholars as elaborating on the images of the Eight Trigrams. However, Zhu Xi in his "Zhou Yi Ben Yi" pointed out that most of its content is not clearly understandable. Moreover, when compared with the main text of the Zhou Yi, they do not correspond in all aspects. Therefore, Zhu Xi did not provide commentaries on this chapter along with the "Xu Gua Zhuan" and "Za Gua Zhuan." Zhu Zhen, a scholar from the Han Shang period, said: "This chapter discusses the images that emerged after the creation of the compound hexagrams. With six lines changing in myriad ways, how could the images of the hexagrams be fully listed? Here, it merely provides general examples. A wise person can naturally understand the principles and extend them to other cases."

彭申甫曰：“《說卦》篇，不與《繫辭》、《文言》一例。蓋聖人觀河圖而定八卦之方位，因以臚列八卦之象，其開章即著明卦之所由立，爻之所從生，而歸本於和順道德窮理盡性以至於命。又申明性命之理，不外陰陽剛柔。其在人則為仁義，而理之所以窮，性之所以盡，則不外乎順時而已。

Peng Shenpu said: "The chapter 'Say on the Trigrams' differs in structure from the 'Great Treatise' and the 'Discourse on the Literary Style'. The sage observed the Yellow River Chart to determine the positions of the Eight Trigrams, and then listed the images of each trigram one by one. It begins by stating on what basis the trigrams are established and where the lines come from, and finally returns to 'harmony with morality' and 'exhausting principles, fulfilling nature, and reaching destiny'. It also clarifies that the principles of nature and destiny are no different from the yin and yang of heaven and the firmness and flexibility of earth. When these two aspects are applied to human beings, they become benevolence and righteousness. And the reason why principles can be fully understood and nature can be fully expressed ultimately comes down to following the circumstances."

蓋聖人仰觀俯察，實見乎《易》之為道，無時無地而不在焉，無人無物而不賦焉。於是分別卦位之性情，而先以人道之廣生大生，推而至於窮神而妙萬物，近取諸身吾身則全乎《易》也。遠取諸物，則一物皆有一《易》也。

The sages looked up to observe the heavens and looked down to examine the earth, and thus realized that the principles of the Book of Changes are present everywhere and at all times, and that all beings and things receive them. Therefore, they distinguished the nature and disposition of each trigram's direction, starting from the broad and great generation of human affairs, and proceeding to explore the profound and mysterious workings that sustain and transform all things. By observing human bodies closely, one finds that one's own body is a complete Book of Changes; by looking at external objects more distantly, one finds that each object has its own Book of Changes.

然猶恐人之泥於物而滯於象也，更推而廣之，於一卦各立無方之象以盡其變，俾讀《易》者即象可以見《易》，即物可以求象，不滯於理而能妙乎理。此聖人繼天立極，所以上承羲文之畫之辭。所謂神而明之，不可為典要，唯變所適者也。故聖人假象以明《易》。自後儒執《易》以求象，而《易》反亡矣。”彭氏之言，可謂得觀象玩辭之通，為學者指南之針矣。

But the sages feared that people would be stuck in things and attached to appearances, so they further expanded, establishing various non-fixed symbolic images for each hexagram, to exhaust its transformations, enabling those who study the Book of Changes to see the Book of Changes through appearances and seek appearances through things, not being bound by rigid rules but skillfully applying its principles. This is precisely how the sages inherited the heavenly way and established norms, to carry forward Fuxi's hexagram drawing and King Wen's Great Treatise. It is exactly what the Great Treatise says: "To divine and make it clear," "It cannot be a fixed principle, but must adapt to change." Thus, the sages used images to explain the Book of Changes; since later Confucian scholars reversed this, using the Book of Changes to rigidly pursue a single image, the Book of Changes has thus been lost. Peng's words can be said to have explained the way of observing images and playing with words, serving as a guide for scholars.

乾為天。為圜(朱氏曰：圜者渾淪無端，周而復始也。按：不曰圓而曰圜者、以著渾淪圓轉，不滯不息之意也。鄭東卿曰：圜者數之本。)。為君。為父(君，群之長。父家之。長皆首出之意，人中之元也。)。為玉。為金(純粹以精，象玉。堅剛不屈，象金。物中之元也。)。

Qian represents Heaven. It is described as "huan"—a comment by Zhu Zhen says that huan means being complete and unified, without beginning or end, flowing continuously and returning to the start. Note: It is written as "huan" rather than "yuan" to emphasize the idea of being fully rounded and turning in a circle without stopping or resting. Zheng Dongqing says that huan is the fundamental principle of numbers. Qian represents a ruler and a father—comment: A ruler is the leader of a group, and a father is the head of a family, both taking the meaning of being the first to emerge among all things, the chief among people. Qian represents jade and metal—comment: Pure and refined, like jade; firm and strong without yielding, like metal; they are the chief among things.

為寒，為冰(乾位西北，時為十月，故有寒冰之象。)。為大赤(赤為周之色，故以首出之乾象赤。曰“大赤”者，以別於坎也。闢卦乾四月盛陽，赤亦盛陽之色稱焉。)。為良馬。為老馬。為瘠馬。為駁馬(良馬為乾之本象。來氏曰：“老，時變也。瘠，形變也。駁，色變也。”其說頗當。)。

The trigram Qian represents cold and ice—original note: In the Later Heaven arrangement, Qian is located in the Northwest, and it corresponds to the tenth lunar month, hence the image of cold and ice. Qian also represents a bright red color—original note: Red was the color favored by the Zhou dynasty, so Qian, which is the first to emerge among all things, is used to symbolize red. It is called 'great red' to distinguish it from Kan's 'red.' In the twelve trigrams of the gate, Qian corresponds to the fourth month, when yang energy is at its peak, and red is also the color of the most vigorous yang. Therefore, it is named red. Qian also represents a good horse, an old horse, a thin horse, and a horse with a mottled coat—original note: A good horse is the original image of Qian. Lai Zhide says: 'Old refers to change over time; thin refers to change in form; mottled refers to change in color.' This explanation is quite appropriate.

為木果(木之有果，生生不已。凡果皆圓，故取乾象。程子曰：“《說卦》於乾雖言為無，又言為金玉，以至木果，所謂類萬物之情也。故孔子推明之曰：此卦於天文地理為某，於鳥獸草木某於身體為某，各以例舉不盡言也。學者觸類而求之，思過半矣。”)。

Qian represents fruit on a tree—original note: A tree bearing fruit signifies continuous generation; since all fruits are round, it takes the round shape of Qian. Cheng Yi said: "The 'Say of the Trigrams' explains Qian as heaven, and also as metal and jade, and even as fruit on a tree. This is called 'understanding the nature of all things through their categories.' Therefore, Confucius further explained that this hexagram represents a certain thing in astronomy and geography, a certain thing in birds, beasts, grasses, and trees, and a certain thing in the human body. These are merely examples and cannot be fully listed. Scholars who can infer other cases from these examples will have thought through more than half of it."

坤為地，為母(父之配也)。為布(布有衣被天下之功。布者，播也。陽施陰布，與乾對也。)。為釜(《正義》：“取其化物成熟。”張氏曰：“釜者，化物而不化於物者也。”蔡氏曰：“虛而聚物，故為釜。”)。

Kun represents Earth, and also represents a mother—original note: a mother is the spouse of a father, corresponding to Qian which represents a father. Kun represents a cloth—original note: cloth has the function of covering the whole world and providing clothing for people. 'Cloth' also means to spread or scatter: yang is the one who gives, while yin is the one who spreads, which corresponds to Qian. Kun represents a cooking pot—original note: The Correct Meaning of the Zhou Changes says 'it takes the ability to transform living things and make them mature.' Zhang said: 'A cooking pot is something that can change other things but is not changed by them.' Cai said: 'It is hollow in the middle and can gather and contain things, so it is called a cooking pot.'

為吝嗇(朱氏曰：《易》言“吝”者，十二卦，十三艾，陽爻只居其三。蓋陰性翕而斂藏，故“多吝”。嗇，則吝之甚也。蓋坤之變象也。)。為均(地道均平。崔氏曰：“地生萬物，不擇善惡。”朱氏曰：“乾獨陽也，坤陰均之得平。”項氏曰：“吝，其靜之翕。均，其動之闢也。陶人制物之形者，謂之均。”亦此義。)。

Kun Represents Stinginess—Original Note: Zhu Zhen said that in The Zhou Changes, the concept of "li" (stinginess) appears in twelve hexagrams and thirteen lines, among which only three are yang lines. This is because yin's nature is to be reserved and concealed, hence it tends to be stingy. As for "sè" (meanness), it is the extreme form of stinginess. This is the changing image of Kun. Kun Represents Equilibrium—Original Note: The nature of the earth is to be impartial and unbiased. Cui Xing said, "The earth nurtures all things without distinguishing between good and evil." Zhu Zhen said, "Qian is purely yang, and Kun, with its yin nature, balances it, thus achieving harmony." Xiang Anshi said, "Stinginess is the gathering of Kun when it is still; equilibrium is the expansion of Kun when it is active. The wheel used by potters to shape vessels is called 'jun,' which means equilibrium." This is the same meaning.

為子母牛(坤為牛，重坤則子母牛。朱氏曰：“坤交離也，離‘畜牝牛’，母也。大畜艮坤之初為‘童牛’，子也。”)。為大輿(坤能載物。朱氏曰：“地方而載，輿也。動而直方，大也。故曰大輿。”)。為文(朱氏曰：“一剛一柔相錯成文。有天而後有地，一不獨立二，則為文天。一地二也。”)。

The Hexagram of Earth is associated with the mother and calf cow—original note: Earth is originally symbolic of a cow, and when Earth is superimposed upon itself, it forms a mother cow with a calf. Zhu Zhen said: "This refers to the interaction between Earth and Fire. The Hexagram of Fire states 'raising a female cow,' which refers to the mother cow; the line Six in the Fourth of the Great Accumulation Hexagram comes from the initial position of the Earth under the Mountain, and it states 'the yoke of a young calf,' which refers to the calf." The Hexagram of Earth is associated with the great carriage—original note: The earth can carry all things. Zhu Zhen said: "The earth is square and can carry things, which is like a carriage; when it moves, it is straight and square, hence called the great carriage." The Hexagram of Earth is associated with culture—original note: Zhu Zhen said: "Only when one yang and one yin intermingle can there be the beauty of culture. After heaven comes earth, 'one' cannot exist alone; it must be paired with 'two' to form culture, which means the concept of heaven one and earth two."

為眾(坤育萬物，眾也)。為柄(俞氏炎曰：“乾圓而曲，坤方而直。故有柄象。”崔氏曰：“萬物依之以為本。”)。其於地也為黑(黑，極陰之色，與乾對也。坤為地。又曰“其於地也”者，坤為黑，其於地乃其一耳。)。

Kun represents multitude — original note: Kun nurtures all things, symbolizing multitude. Kun represents a handle — original note: Yu Yanyin said, "Qian is round and turns, while Kun is square and straight, hence the image of a handle." Cui Jing said, "All things rely on it as their foundation." Kun on the earth is black — original note: Black is the color of extreme yin, contrasting with Qian's great red. Kun is originally earth, and here it is said "its manifestation in the earth," because Kun being black is merely one aspect of its expression in the category of earth.

震為雷，為龍(鄭氏曰：“龍讀為尨，取日出時色，雜也。”按：龍，乾象，而用則見之於震。)。為玄黃(玄黃，天地之離也。震為乾坤始交，故備乾坤之文。)。為旉(王肅曰：“旉，華之通名。”虞氏以旉為專，姚信“專，專一也”。《正義》曰：“春氣至，草木皆吐，敷布而生也。”按：旉者，陽敷於陰。)。

Zhen represents thunder and a dragon. The original note says: Zheng Xuan explained that "dragon" should be read as "mang," meaning the confused appearance of the sky at sunrise. According to the note: The dragon is originally the image of Qian, but its function is manifested in Zhen. Zhen represents the color of heaven and earth. The original note says: "Xuan" refers to the color of heaven, and "huang" refers to the color of earth. When heaven and earth mix and separate, they appear as xuanhuang. Since Zhen is the first combination of Qian and Kun, it possesses the colors of both Qian and Kun. Zhen represents fu. The original note says: Wang Su explained that "fu" is a general term for flowers; Yu Fan read "fu" as "zhuan," and Yao Xin interpreted "zhuan" as "exclusive." The Correct Meaning of the Zhou Changes said: "When the spring energy arrives, grass and trees all sprout, spreading out and growing." According to the note: "Fu" refers to the spreading of yang energy into yin.

為大塗(大塗，萬物所出，震卯兌酉，陰陽往來之路也。震為行，大塗充盡，震行之用者也。)。為長子。為決躁(程氏曰：“陰來陽必決，兌陽中，故決而和。震剛動不中，故決而躁。”)。為蒼筤竹(《正義》：“竹初生之時色。蒼筤，取其春生之美也。”)。為萑葦(朱氏曰：“萑葦，震之廢氣也。”張氏曰：“剛為竹，柔為葦。”)。

Zhen represents a great road (big path) — original note: A great road is the path through which all things are born. Zhen is located at the east, at the卯 position, and Dui is located at the west, at the酉 position, which are exactly the channels through which yin and yang pass. Zhen has the meaning of movement, and a great road is unobstructed in all directions, which is the manifestation of Zhen's function of "movement." Zhen represents the eldest son. Zhen represents decisive and impetuous action — original note: Cheng Yi said, "When yin comes, yang must decisively remove it. Dui has yang in the center, so it can decisively act in harmony; Zhen is strong and active but does not reside in the center, so it acts decisively and hastily." Zhen represents young bamboo — original note: The Correct Meaning of the Zhou Changes says that this refers to the color of bamboo when it first grows; using "canglang" is to express the beauty of spring growth. Zhen represents reed grass — original note: Zhu Zhen said, "Reed grass is transformed from the leftover waste of Zhen." Zhang said, "The strong is bamboo, the flexible is reed."

其於馬也為善鳴(朱氏曰：“《易》凡有震聲曰鳴。”程沙隨曰：“震分乾一體，故為馬。得陽之聲，故善鳴。”)。為馵足(京氏荀氏曰：“馵足，陽在下。”《正義》：“馬後足白為馵，取其動而見也。”朱氏曰：“下伏巽，故後足白。”)。為作足(虞氏曰：“馬白後左足為馵。震為左為足為作，初陽白，故為作足。”徐氏曰：“作足，雙舉前足也。”程氏曰：“與薄蹄反。”)。

The trigram Zhen represents a horse, specifically a horse that is good at making sounds. The original note says: Zhu Zhen said, "In the Zhou Changes, any trigram that has the sound of Zhen is called 'ming' (sound)." Cheng Jing said, "Zhen is divided from the essence of Qian, so it represents a horse; it possesses the sound of Yang, hence it is good at making sounds." Zhen represents a horse with white hind hooves. The original note says: Jing Fang and Sun Shuang said, "White hind hooves are the image of Yang lines at the lower position." The Zhou Changes with Correct Meaning says, "White hind hooves of a horse are called 'zhu,' because they become visible as the horse moves." Zhu Zhen said, "Zhen has hidden Xun beneath it, and Xun represents white, hence the white hind hooves." Zhen represents a horse with a hoof that is raised. The original note says: Yu Fan said, "White left hind hooves of a horse are called 'zhu'; Zhen represents the left side, the foot, and the action of raising, and the first line is Yang with a white color, hence it is called a raised hoof." Xu said, "A raised hoof is when both front hooves are lifted at the same time." Cheng said, "This is opposite to Kan's 'bo ti' (thin hooves)."

為的顙(朱氏曰：“乾為首，上發震爻為的顙。《傳》所謂的顱也。”虞氏曰：“的，白額。”)。其於稼也為反生(鄭氏曰：“生而反出也。”宋氏曰：“陰上陽下，故反生。”)。其究為健(究，極也。虞氏曰：“震巽相薄，變而至三，則下象究。其究為健為蕃鮮，與四成乾故。”參看《學易筆談》。)，為藩鮮。

The trigram Zhen represents a white-marked horse on the forehead. The original note says: Zhu Zhen said, "Qian represents the head, and when the Zhen line emerges above, it forms the white mark on the forehead, which is what the 'Transmission' refers to as 'white skull.'" Yu Fan said, "The term 'white' refers to the white mark on the forehead." Zhen, in the category of crops, represents reverse growth. The original note says: Zheng Xuan said, "When seeds sprout, they emerge upward from the top." Song Zhong said, "Yin is above and Yang is below, so it grows in reverse." Zhen "in the end becomes strong." The original note says, "Jiu" means to push to the extreme. Yu Fan said, "Zhen and Xun are close to each other, and when it changes to the third line, the lower trigram's image is exhausted; after exhaustion, it becomes strong and flourishing, because it combines with the fourth line to form Qian." See my "Notes on Studying the Book of Changes." Zhen also represents flourishing and bright growth of plants.

巽為木(朱氏曰：“震巽皆木。獨言於巽者，蕃鮮之時，震剛木，巽柔木。”)。為風(陸績曰：“風，土氣也。巽坤之所生，亦取靜於本而動於末也。”按：震巽陰陽始交，天感地應；震動則巽為風，而風之鳴仍為震。)。為長女。為繩直(翟氏曰：“上二陽，其正一陰，使不得邪僻，如繩之直。”按：索，繩也。陰陽交索，坤初素得巽，坤動而直，故為“繩直”。)。

Xun represents wood — original note: Zhu Zhen said: "Zhen and Xun both belong to wood. Here, the word 'wood' is specifically noted under Xun because it refers to the time when grass and trees flourish; Zhen is the hard wood, while Xun is the flexible and resilient wood." Xun represents wind — original note: Lu Ji said: "Wind is produced by the earth's qi. Xun is the daughter hexagram born from Kun, and it also takes the meaning of quietness at the root and movement at the tip." Note: Zhen and Xun are the first meeting of yin and yang; when heaven feels something, the earth responds. When Zhen moves, Xun becomes wind, and the sound produced by the wind still belongs to Zhen. Xun is the elder daughter. Xun represents a straight rope — original note: Zhai Shi said: "The two upper lines are yang, and the lower line, which is yin, is corrected to prevent it from leaning, just like a straight rope." Note: "Suo" means rope. Yin and yang interact and seek, and when Kun moves to the first line to obtain yang, it becomes Xun. Since Kun is able to become straight when it moves, it is called 'straight rope.'

為工(荀氏曰：“以繩木，故為工。”朱氏日：“天地變化萬物者以巽，而莫見其變化之跡，故巽為工。”木曰曲直。巽，德之制，工也。)。為白(萬物之色盡於七，巽齊萬物，七色和一，故為白。詳《學易筆談初集》)。為長。為高(陰伏於下，陽升於上，故為長為高。震巽初索皆稱長。獨著於巽者，震長而大，巽長而高，互文也。)。

Xun represents a craftsman — original note: Xun Shuang said, "Using a plumb line to straighten the timber, so it is a craftsman." Zhu Zhen said, "The transformation of heaven and earth and the myriad things relies on Xun, yet its transformation is not visible, so Xun is a craftsman." The Book of Documents, Hongfan, mentions "wood is flexible and straight"; the Great Treatise says Xun is "the regulation of virtue," and making and cutting are the duties of a craftsman. Xun represents white — original note: The colors of all things do not exceed the seven colors, and Xun can regulate all things, so when the seven colors are harmonized into one, it becomes white. See Xue Yi Bitan Chu Ji for details. Xun represents length and height — original note: Yin is hidden below, and Yang rises above, so it is both length and height. Both Zhen and Xun are the first things obtained, and can be called "length"; here Xun is specifically noted because Zhen is long and great, while Xun is long and high, with the two complementing each other in meaning.

為進退(荀氏曰：“風行無常，故進退。”按：巽居辰巳、辰五巳六，陰陽之中，進退之間也。)。為不果(或進或退，不果之象。乾為木果，巽變其初，故曰“不果”。)。為臭(虞氏曰：臭，氣也。風至知氣，巽二入艮鼻，故為“臭”)。其於人也為寡髮(鄭作宣髮。虞曰：“為白，故宣髮。”馬君以宣為寡髮，非也。《正義》“寡，少也。”)。

Wind represents movement forward and backward — original note: Xun Shuang said, "Wind has no fixed course, so it represents movement forward and backward." According to this, Wind is located between the trigrams Chen and Si in the Later Heaven arrangement. Chen corresponds to the number five and Si corresponds to the number six, which is exactly in the middle of yin and yang, and thus is in the position between movement forward and movement backward. Wind represents lack of decisiveness — original note: moving forward and then backward again indicates the image of lack of decisiveness. The trigram Qian represents fruit, and Wind is formed by the first line of Qian turning into yin, so it is called "lack of decisiveness." Wind represents smell — original note: Yu Fan said, "smell is the essence of air; wind can quickly discern smells, and the second line of Wind enters the nose, which is represented by the trigram Gen, so it is called smell." Wind represents sparse hair on the human body — original note: Zheng Xuan wrote "sparse hair," but Yu Fan said, "Wind represents white, so it is white hair." Ma Rong interpreted "sparse" as "sparse," which is incorrect. The "Zhou Yi Zhenyi" says, "sparse means few."

為廣顙(《正義》：“額闊為廣顙。二陽在上，故稱廣。”形見於巽而色著於震，亦互文也。)。為多白眼(虞氏曰：“巽白，離目向上，則白眼見，故多白眼。”)。為利市三倍(巽位居離與震之間，火雷噬嗑，“日中為市”。詳《學易筆談》。)。其究為躁卦(朱氏曰：“巽三變成震，震為決躁。”)。

The trigram Xun represents a broad forehead — the original note says: "A broad forehead is called Guangsang; the upper two lines of Xun are yang, hence it is called broad." The shape of the forehead is seen in Xun, while the color of the forehead is seen in Zhen (Zhen represents the forehead), and these two are mutually explanatory. Xun represents many white eyes — the original note says: "Xun has the color white; the trigram Li, which represents the eye, turns upward, revealing the white of the eye, hence many white eyes." Xun represents a threefold benefit in trade — the original note says: "Xun is located between Li and Zhen; Li and Zhen combine to form the hexagram Fire Thunder Shi Ke. The 'Great Treatise' mentions Shen Nong's 'market at noon,' which corresponds to the image of Shi Ke, hence Xun has the image of beneficial trade. See 'Xue Yi Bitan' for details." Xun's ultimate nature is the restless trigram — the original note says: "Zhu Zhen said: 'When the third line of Xun changes, it becomes Zhen, and Zhen represents restlessness.'"

坎為水，為溝瀆(虞氏曰：“以陽闢坤，水性流通，故為溝瀆。”)。為隱伏(虞氏曰：“陽藏陰中。”)。為矯輮(宋氏曰：“曲者更直為矯，直者更曲為輮，水流曲直似之。”)。為弓輪(乾為圓，坎得乾中爻，半規象弓，全規象輪。舊說多破碎，少可取者。)。

Kan represents water, and also represents ditches and channels — the original note says: Yu Fan said, "Using a yang line to split the body of Kun, water flows smoothly, so it is like a ditch." Kan represents concealment — the original note says: Yu Fan said, "Yang is hidden within Yin." Kan represents bending and straightening — the original note says: Song Zhong said, "To straighten a bend is called 'jiao,' to bend a straight line is called 'rou,' water flows with both curves and straight lines, just like these two processes." Kan represents a bow and a wheel — the original note says: Qian represents roundness, and Kan has the middle line of Qian, so half a compass resembles a bow, and the whole compass resembles a wheel. Most previous interpretations are fragmented and unsatisfactory, with very few being acceptable.

其於人也為加憂(《素問》：“金在志為憂，水在志為恐。恐則甚於憂，故曰加憂。”)。為心病。為耳痛(火臟在心，坎水勝之，故為心病。水臟在腎，開竅於耳。而水在志為恐，恐則傷腎，故為耳痛。)。為血卦。為赤(《正義》：“人之血，猶地之水也。赤，血色。”李鼎祚曰：“十一月一陽爻生，在坎陽氣初生於黃泉，其色赤也。”)。

The trigram Kan represents worry in the human body — original note: The Huangdi Neijing · Suwen says: "Metal governs worry in emotions, and water governs fear in emotions." Fear is a deeper form of worry, hence it is called "added worry." Kan represents heart disease and ear pain — original note: The heart is the organ associated with fire, and Kan water overcomes it, hence it represents heart disease; the kidney is the organ associated with water, and the kidney is connected to the ears. Since water governs fear in emotions, and fear harms the kidney, it causes ear pain. Kan represents the blood trigram and the color red — original note: The Zhou Yi Zhenyi says: "Blood in the human body is like water on the earth; red is the color of blood." Li Dingzuo says: "In the eleventh month, the first yang line begins to arise, which is in Kan. Yang energy is just beginning to rise from beneath the earth, and its color is red."

其於馬也為美脊(陽在中央，脊也。)。為亟亟心(荀氏曰：“極，中也。”坎居北子一位，剛動，故亟心。按：亟，古極字。)。為下首。為薄蹄(下首者上無陽，薄蹄者下無陽)。其於輿也，為多眚(眚，病也。虞曰：“敗也。”坤為大輿，坎折坤體故也。)。

The trigram Kan represents a strong back in horses — original note: a yang line in the center corresponds to the image of the backbone. Kan represents an impatient horse — original note: Xun Shuang said, "Extreme is the middle." Since Kan is located in the north, at the position of Zi, the central yang line is active, hence the impatience. Note: "Ji" is an ancient form of "ji." Kan represents a horse that lowers its head and has thin hooves — original note: lowering the head is because there is no yang line above; thin hooves are because there is no yang line below. In the category of carriages, Kan represents many defects — original note: "Sheng" means illness; Yu Fan interprets it as "ruin." K'un originally represents a large carriage, and Kan is formed by breaking K'un in the middle, hence the carriage has many defects.

為通(坤“黃中通理”，通於坎也。)。為月(《正義》：“月，水之精也。”按：乾陽流於坤，形如日之光被於月體，與離日對也。)。為盜(虞與孔疏皆以水潛行象盜。按：盜，寇也。水之蝕土，如盜之侵掠也。或云：盜與竊古訓通。竊淺也。)。，其於木也為堅多心(陽剛在中，故堅多心。)。

The trigram Kan represents communication — original note: The "Yellow Center" in the "Wenyan" section of the Book of Changes refers to "communication," which is precisely the direction of Kan. Kan represents the moon — original note: The "Zhouyi Zhenyi" states, "The moon is the essence of water." According to the commentary: The yang of Qian flows into Kun to form Kan, resembling sunlight shining upon the moon, forming a pair with Li, which represents the sun. Kan represents theft — original note: Both Yu Fan and Kong Yingda's commentaries compare water flowing secretly and invisibly to thieves. According to the commentary: Theft is equivalent to a bandit, and water eroding the earth is like bandits plundering. Some also say that "theft" and "steal" have similar meanings in ancient Chinese, and "steal" has a meaning of being shallow. In the category of wood, Kan represents firmness with many thoughts (heartwood is solid) — original note: Yang is strong and in the center, so the heart of the wood is firm and full.

離為火。為日。為電(在地為火，在天為日，陰陽相薄，則為電。)。為中女。為甲冑(上下皆剛，上為胄，下為甲。)。為戈兵(虞氏曰：“乾金離火煅之，故為戈兵。”《正義》：“取其剛在外以自捍也。”)。其於人也為大腹(乾為大，坤為腹。坤麗乾中，故曰“大腹”。)。為乾卦(詳《學易筆談》)。

Li represents fire, the sun, and lightning. The original commentary says: on the earth it is fire, in the sky it is the sun, and when yin and yang approach and interact, it becomes lightning. Li represents the middle daughter. Li represents armor and armor. The original commentary says: the two lines of Li are both strong lines. The upper line resembles a helmet, and the lower line resembles armor. Li represents spears and weapons. The original commentary says: Yu Fan said, "The乾 (Heaven) belongs to metal, and using the fire of Li to temper it, it becomes weapons." The Correct Meaning of the Zhou Changes says: "It takes the strength on the outside and the ability to defend itself." Li in the human body represents the large abdomen. The original commentary says:乾 represents large, and坤 (Earth) represents the abdomen. The Yin of坤 is attached to the middle of乾, forming Li, so it is called "large abdomen." Li represents the乾 hexagram (the dry hexagram). The original commentary says: see "Learning the I Ching Notes."

為鼈。為蟹。為蠃。為蚌。為龜(鄭氏曰：“皆剛在外。”虞氏曰：“取外剛內柔也。”朱氏曰：“鼈離交巽，巽巳為蛇，蛇或化鼈。為蟹者，巽交離也。蟹連兩目，重離也。為螺者，兌交離也。螺生於月，旋也。為蚌者，離交坎也。雀為蛤，雉為蜃，其類也。為龜者，坎交離也。龜遊山澤，出入水火，含神負智，得坎離之正。頤損益三卦皆然。)。其於木也為科上槁(宋氏曰：“陰在內則空中，木空中則上科槁也。”《正義》：“科，空也。”)。

The trigram Li represents turtles, crabs, snails, clams, and tortoises. The original commentary states: Zheng Xuan said, "These are all creatures with hard shells on the outside." Yu Fan said, "This refers to the meaning of being hard on the outside and soft inside." Zhu Zhen said, "Turtles are formed by the interaction of Li and Xun; Xun is at the position of the earthly branch Si, which is associated with snakes, and snakes sometimes transform into turtles. Crabs are formed by the interaction of Xun and Li; crabs have two eyes connected, which resembles two Li trigrams overlapping. Snails are formed by the interaction of Dui and Li; snails grow according to the waxing and waning of the moon, and their shells spiral. Clams are formed by the interaction of Li and Kan; ancient people said that sparrows entering water transform into clams and chickens entering water transform into mussels, which belong to this category. Tortoises are formed by the interaction of Kan and Li; tortoises move between mountains and marshes, entering and exiting between water and fire, containing divine wisdom and carrying knowledge on their backs, thus embodying the correct balance of Kan and Li. The trigrams Yi, Shen, and Yi all mention tortoises, and this is the same principle. Li, when associated with wood, represents a branch that is hollow and withered at the top. The original commentary states: Song Zhong said, "Yin is inside, so the tree heart becomes hollow; once the tree heart is hollow, the top becomes withered." The Correct Meaning of the Zhou Changes says, "Kuo means hollow."

艮為山，為徑路(徑路，小路也。卦有大小，震大艮小。震為大塗，艮反震，故為徑路。)。為小石(水雷屯“磐桓”。磐，大石也。震象艮反震，故為小石。張氏曰：“徑，小也。路，大也。萬物自此而入，故小自此而出。故大石之小者，有可轉之理，乃能動能靜者乎？”按：震陽長至艮而極，已寓必反之理，故艮象皆以反動為言。)。

Gen as mountain, as narrow path — original note: narrow path means a small path. Hexagrams have distinctions of big and small; Zhen represents big, Gen represents small. Zhen takes the image of a big road, while Gen is Zhen reversed, hence taking the image of a small path. Gen as small stone — original note: the first line of the Zhun hexagram, "Panhuan," refers to a large stone; that is the image of Zhen. Gen, being the reverse of Zhen, thus represents a small stone. Zhang said: "Jing means small, Lu means big. All things enter through this, hence it is called small; they exit through this, hence it is called big. Among big stones, the smaller ones have the nature of rolling, which is something that can both move and be still." Note: The yang energy of Zhen reaches its extreme in Gen, and within it there is already the principle of inevitable reversal, so all the images of Gen are established from the perspective of "reverse movement."

為門闕(虞氏曰：“乾為門。艮陽在門外。故為門闕。”按：先天艮處西北，闕之地也。)，為果蓏(張寞曰：“有核曰果，無核曰蓏。”宋氏曰：“木實為果，草實為蓏。”郭氏曰：“乾為木果。艮，乾之餘氣也。”)。為閽寺(俞氏曰：“艮以剛止外，衛內之柔。閽人止物之不應入者，寺人止物之不得出者。”按：因上門闕而類及也。)。為指(指者止也。項氏曰：“與堅多節同義。”)。

Geng represents a gate and pavilion - the original note says: Yu Fan said, "Qian represents a gate, and the single Yang line of Geng is placed outside the gate, hence it represents a gate and pavilion." According to the note: In the Earlier Heaven arrangement, Geng is located in the Northwest, which is exactly where palaces and pavilions are situated. Geng represents fruit and gourd - the original note says: Zhang said, "Those with seeds are called fruit, and those without seeds are called gourd." Song Zhong said, "Fruits that grow on trees are called fruit, and fruits that grow on grass are called gourd." Guo said, "Qian represents wooden fruit, and Geng is formed from the remaining energy of Qian." Geng represents gatekeepers and attendants - the original note says: Yu Yan said, "Geng stops the incoming path with its outer strong line, protecting the inner soft line. The gatekeeper stops those who should not enter, and the attendant stops those who should not leave." According to the note: This is a continuation from the previous image of "gate and pavilion." Geng represents a finger - the original note says: "Finger" means to stop. Xiang Anshi said, "This is the same meaning as the following 'firm with many joints.'"

為狗(虞作拘。注曰：“指屈伸制物為拘。舊作狗。”朱氏曰：“此言為狗者，熊虎之子。《爾雅》曰：熊虎丑其子狗，初生未有文，猶狗也。”馬融虞翻郭璞以兌艮為虎，艮居寅位，艮究成兌，故艮為虎子。)。

Geng represents a dog — original note: Yu Fan wrote 'ju', other annotations say: 'when the fingers bend and stretch, they can control external things, which is called ju; the old text wrote it as dog.' Zhu Zhen said: 'the dog here refers to the young of bears and tigers. The Er Ya says that the young of bears and tigers are called 'dog', as they are born without patterns, resembling dogs.' Ma Rong, Yu Fan, and Guo Pu all took Dui and Geng as tigers; Geng is at the position of Yin in the twelve branches (Yin belongs to the tiger), and when Geng reaches its extreme it becomes Dui, so Geng takes the image of the tiger's cub.

為鼠(虞氏曰：“似狗而小，在坎穴中，故為鼠。晉九四是也。”郭雍曰：“坎隱伏。在君子為隱，在小人為盜。艮之止，利則為狗，害則為鼠，皆一象而二義者也。”)。為黔喙之屬(馬氏曰：“肉食之獸，謂豺狼之屬。黔黑也，玄在前也。”程迥曰：“黔東北方之色，青黑雜也。”按：飛鳥之摯者，喙亦黔，不專指獸也。)。其於木也為堅多節(陽在外故堅多節)。

The trigram Gen represents a rat. The original commentary says: Yu Fan explained, "Its shape resembles a dog but is smaller, hiding in the cave symbolized by Kan, hence it is called a rat. The line 'Advancing like a shi mouse' in the hexagram Jin (Progress) is this symbolic meaning." Cheng Jiong said, "Kan governs concealment; for a gentleman, it signifies retirement, but for a petty person, it signifies theft. Gen governs stillness; when viewed positively, it is a watchdog, but when viewed negatively, it is a thief rat. These are the same symbolic meaning with two different interpretations." Gen represents black-beaked animals. The original commentary says: Ma Rong explained, "It refers to carnivorous wild beasts, such as jackals and wolves. 'Qian' means black, as black is prominent on the beak." Cheng Jiong said, "Qian is the color of the northeast, a mixture of blue and black." Note: The beaks of fierce birds are also black, so it is not exclusively referring to beasts. Gen, among the category of wood, represents something hard with many knots. The original commentary says: Because the yang line is on the outside, the wood is hard and has many knots.

兌為澤(虞氏曰：“坎水半見。”)。為少女。為巫。為口舌(古巫皆少女以口舌通神者也。故類及之。)。為毀折。為附決(二象之舊說繁而鮮當，實皆對象。毀折對艮而言，艮為成終成始，艮兌陰陽相反，故兌為毀折附決。對震而言，震為決躁。巽之究為躁，巽覆為兌，故兌為附決。)。

Dui represents a marsh—original commentary: Yu Fan said that Dui is a body of Kan water that only shows half of its surface. Dui represents a young woman, a shaman, and speech—original commentary: ancient shamans were usually young women who communicated with spirits through speech, so from the shaman one can associate it with speech. Dui represents destruction and breaking—original commentary: these two images, old interpretations have been complicated and rarely appropriate. In fact, they are both derived from the opposite trigram. "Destruction and breaking" refers to Gen: Gen signifies completion and beginning, and Gen and Dui are exactly opposite in yin and yang, so Dui takes the meaning of destruction and breaking. "Appendage and decision" refers to Zhen: Zhen represents decisiveness and restlessness, while Xun reaches its extreme and becomes Zhen, and Xun reversed becomes Dui, so Dui represents appendage and decision.

其於地也為剛滷(澤涸為地必為剛滷。今日內外蒙古之間沙漠延長萬餘里，西連新疆之戈壁，號稱萬里長沙，其左右地皆斥鹵，蓋為上古以前之大澤久涸成地，不知紀年，而滷質猶在。此確合兌為剛滷之象，甚易見也。曰剛滷者，更含有物質變化作用。以今日化學之分劑準其陰陽正負而研索，尤饒興味，當別論之。)。

The trigram Dui (Lake) is associated with the category of land, specifically as hard saline soil. The original commentary explains that when a lake or marsh dries up and becomes land, it necessarily turns into saline soil. Today, the desert stretching between Inner Mongolia and Outer Mongolia extends over ten thousand li, connecting westward to the Gobi of Xinjiang, known as the 'Ten Thousand Li Changsha'. The land on both sides of this area is entirely saline, which is likely due to ancient large lakes that dried up over a long period, the exact time being unknown. The nature of the saline soil remains. This perfectly matches the image of Dui representing hard saline soil, which is easy to recognize. The term 'hard saline' also implies a transformation of substances. If we apply the principles of element ratios in modern chemistry to compare its yin and yang positive and negative aspects for study, it would be very interesting and deserves a separate discussion.

為妾(《正義》：“少女從姑姊為媵也。”)。為羊(虞作羔，訓為女使。鄭作陽，謂養無家女行賃炊事，今時有之，賤於妾也。說另詳《學易筆談》。)。

The trigram Dui represents a concubine — the original commentary says: "A young maiden follows her aunt and older sister to marry as a bride's companion." Dui also represents a sheep — the commentary by Yu Fan says "lamb," referring to a servant girl; the commentary by Zheng Xuan says "Yang," meaning to take in homeless women and employ them for cooking, and such people still exist today, their status being lower than that of a concubine. For more detailed explanations, see "Learning the I Ching Notes."

右八卦為象，共百十有四。所謂舉例發凡，非物象之盡於此也。其例有互文者，有對取者，有類及者，有從變者。詳《學易筆談》。

The images represented by the eight trigrams total 114. This is merely an example to illustrate the method, not implying that all things in the world have only these images. The way of taking images has four types: some are mutual explanations between two places, some are taken from the opposite trigrams, some are extended from one image to related ones, and some arise from changes in the lines. See "Xue Yi Bitan" for details.

《荀九家易》，八卦逸象，共三十有一。雲出自河內女子獻《說卦》後，實皆由本經《彖》、《象》採取。其未見者，只坤之漿，巽之鸛二象，去留皆無關宏旨。惟荀爽《集解》，去古未遠，當有所本。而朱子亦仍陸氏《釋文》之舊，附各卦後。今列舉如左：

The "lost images" (逸象) of the eight trigrams in the "Xun Jiuya Yi" total thirty-one, which are not included in the "Shuo Gua Zhuan." It is said that these images appeared after a woman from Heinner presented the "Shuo Gua Zhuan," but in fact they were all collected from the "Commentary on the Judgment" and "Image Commentary" of the main text of the "Zhou Yi." Among these, only two images, "Kun as jiang" and "Xun as guan," lack support in the main text and commentaries, and whether they are retained or deleted does not affect the overall structure. However, Xun Shuang's "Jiexie" is not far from the ancient times and should have some basis; Zhu Xi also followed the old practice of Lu Deming's "Jingdian Xishu," attaching them after each trigram. The following is a list of them:

乾之象四：為龍，為直，為衣，為言。坤之象八：為牝，為迷，為方，為囊，為裳，為黃，為帛，為漿。震之象三：為玉，為鵠，為鼓(玉或作王。鵠，項氏云：“鵠鶴古通用，當作鶴。”)。巽之象二：為楊，為鸛。

The extraordinary images of Qian are four: dragon, straightness, clothing, and speech. The extraordinary images of Kun are eight: female, lost path, square, bag, lower garment, yellow, silk fabric, and drink. The extraordinary images of Zhen are three: jade, crane, and drum. Note: Some editions read 'king' instead of 'jade'; some say that 'crane' and 'goose' were interchangeable in ancient times, so it should be 'goose'. The extraordinary images of Xun are two: willow and stork.

坎之象八：為宮，為律，為可，為棟，為叢棘，為狐，為蒺藜，為桎梏。離之象一：為牝牛。艮之象三：為鼻，為虎，為狐。兌之象二：為常，為輔頰。

The extraordinary images of Kan include: palace, law, something that can be used, beam, thorny bushes (referring to the prison in the line "placed in thorny bushes" from the top line of Kan), fox, thorned weed, and shackles. The extraordinary image of Li is a female ox. The extraordinary images of Gen include: nose, tiger, and fox. The extraordinary images of Dui include: banner (or constant measure) and cheek.

孟氏逸象，傳自焦氏，亦自本經採取為多。間有互異者，以兩漢經師，各守師說，傳述不同。備錄如後，以資參證。

The esoteric interpretations of Meng Xi's school are passed down from Jiao Yanshou, and mostly drawn from the original text of The Zhou Changes. Occasionally, there are discrepancies with the Xun Jiujia, due to the fact that Han dynasty scholars each adhered to their own school's interpretations, leading to different transmissions. The following is a complete record for reference and verification.

乾為王，為先王，為明君，為人，為大人，為聖人，為賢人，為君子，為武人，為行人，為物，為易，為立，為直，為敬，為畏，為咸，為嚴，為堅剛，為道，為德，為盛德，為行，為性，為精，為言，為信，為善，為揚善，為積善，為良，為仁，為愛，為忿，為生，為祥，為慶，為天休，為嘉，為福，為介福，為祿，為先，為始，為知，為大，為盈，為茂，為肥，為好，為施，為利，為清，為治，為大謀，為高，為揚，為宗，為族，為高宗，為甲，為老，為舊，為古，為大明，為遠，為郊，為野，為門，為道門，為百，為歲，為頂，為朱，為衣，為圭，為蓍，為瓜，為龍。

The symbolic meaning of Qian. In terms of people: as a king, as a former king, as a wise ruler, as a person, as a great man, as a sage, as a virtuous person, as a gentleman, as a warrior, as a traveler. In terms of nature and character: as an object, as ease, as establishment, as straightness, as respect, as fear, as universality, as strictness, as firmness, as the Way, as virtue, as great virtue, as conduct, as nature, as essence. In terms of speech and morality: as speech, as trustworthiness, as goodness, as promoting goodness, as accumulating goodness, as good quality, as benevolence, as love, as anger. In terms of blessings and auspiciousness: as life, as auspiciousness, as celebration, as heavenly grace, as good fortune, as blessing, as great blessing, as official rank. In terms of time sequence and position: as first, as beginning, as knowledge, as great, as fullness, as flourishing, as fat, as good, as giving, as benefit, as clear, as governance, as great plan, as high, as promotion, as ancestor, as clan, as high ancestor (Wudi of the Yin dynasty), as Jia (the first heavenly stem), as old, as ancient, as great brightness, as far. In terms of land and objects: as the outskirts, as the wild, as a gate, as the gate path, as hundred, as year, as top, as red, as clothing, as jade bi, as chi grass, as melon, as dragon.

坤為臣，為順臣，為民，為萬民，為姓，為小人，為邑人，為鬼，為形，為身，為牝，為母，為躬，為我，為自，為至，為安，為康，為富，為財，為積，為聚，為萃，為重，為厚，為致，為用，為包，為寡，為徐，為營，為下，為容，為裕，為虛，為書，為邇，為近，為疆，為無疆，為思，為惡，為理，為體，為禮，為義，為事，為業，為大業，為庶政，為俗，為度，為類，為閉，為藏，為密，為默，為恥，為欲，為過，為丑，為積惡，為迷，為殺，為亂，為怨，為害，為遏惡，為終，為永終，為敝，為死，為喪，為冥，為晦，為夕，為莫夜，為暑，為乙，為年，為十年，為戶，為義門，為闔戶，為閉關，為盍，為土，為積土，為階，為田，為邑，為國，為邦，為大邦，為萬國，為異邦，為方，為鬼方，為裳，為級，為車，為輹，為器，為擊，為囊，為虎，為兕，為黃牛，為牝牛。

The symbolic meanings of the Trigram坤. In terms of people: as a minister, a compliant minister, as common people, as all the people, as the common folk, as a small person, as people of a town, as ghosts, as form, as body, as female, as mother, as self, as oneself. In terms of stability and accumulation: as ultimate, as safe, as well-being, as wealth, as property, as accumulation, as gathering, as convergence, as weight, as thickness, as attainment, as use, as encompassing, as few, as slow, as encircling, as lower, as capacity, as abundance, as emptiness, as writing, as near, as close, as boundary, as boundless, as thought. In terms of matters, principles, and moral education: as evil, as order, as body, as propriety, as righteousness, as affairs, as occupation, as great occupation, as various state affairs, as customs, as measure, as category. In terms of closure and concealment: as closure, as concealment, as secrecy, as silence, as shame, as desire, as excess, as ugliness, as accumulated evil, as confusion, as killing, as chaos, as resentment, as harm, as suppression of evil. In terms of conclusion, darkness, and obscurity: as end, as permanent end, as decay, as death, as loss, as darkness, as dusk, as evening, as night, as heat, as the heavenly stem 乙, as year, as ten years. In terms of gates, land, and territories: as gate, as righteous gate, as closing the gate, as closing the borders, as union, as soil, as accumulated soil, as step, as field, as town, as country, as state, as great state, as all states, as foreign state, as direction, as the distant land of the ghosts. In terms of objects and animals: as lower garment, as level, as carriage, as the part of the carriage axle, as vessel, as striking, as bag, as tiger, as rhinoceros, as yellow ox, as female ox.

震為帝，為主，為諸侯，為人，為士，為兄，為夫，為元夫，為趾，為出，為行，為徵，為作，為逐，為驚走，為警衛，為定，為百，為言，為講議，為問，為語，為告，為響，為聲，為音，為鳴，為夜，為交，為徵，為反，為後，為後世，為從，為守，為左，為生，為嘗，為緩，為寬仁，為樂，為笑，為喜笑，為笑言，為道，為陵，為祭，為鬯，為禾稼，為百穀，為草莽，為鼓，為筐，為馬，為糜鹿。

The symbolic meanings of the Trigram Zhen. In terms of people: it represents the Emperor, the ruler, the feudal lords, people, the scholar, the elder brother, the husband, and the first husband (the spouse of the first wife). In terms of actions: it represents the foot, going out, walking, marching, rising up, chasing, being startled and running, guarding, and settling. In terms of speech and sound: it represents a hundred, speech, discussion, asking, talking, informing, echo, sound, tone, and calling. In terms of time, position, and movement: it represents night, meeting, marching, returning, later, later generations, following, guarding, and the left. In terms of life, nourishment, and joy: it represents birth, tasting, being slow, being lenient and kind, joy, laughing, smiling joyfully, and laughing speech. In terms of worship, plants, and objects: it represents the way, a hill, worship, the sacred wine used in rituals, grain, all grains, grasses, a drum, a basket, a horse, and deer.

巽為命，為命令，為號令，為教令，為誥，為號，為號咷，為處女，為婦，為妻，為商旅，為隨，為入，為處，為入伏，為利，為齊，為同，為交，為進，為退，為舞，為谷，為長木，為苞，為楊，為果木，為茅，為白茅，為闌，為草木，為草莽，為杞，為葛藟，為薪，為庸，為休，為繩，為帛，為腰帶，為繑，為蛇，為魚，為鮒。

The symbolic meanings of Xun (Wind): In matters of commands: as destiny, as command, as decree, as instruction, as诰 (a type of imperial edict), as a call, as wailing. In matters of people: as a virgin, as a wife, as a spouse, as merchants. In matters of movement and stillness: as following, as entering, as dwelling, as hiding, as benefit, as harmony, as unity, as meeting, as advancing, as retreating, as dancing. In matters of plants and trees: as grain, as tall trees, as clusters of grass, as poplar, as fruit trees, as reed, as white reed, as fence, as plants, as grassy wilderness, as goji (a type of tree), as vine, as firewood, as wall, as shade. In matters of ropes, silk, insects, and fish: as rope, as silk, as waistband, as the belt for trousers, as snake, as fish, as small fish.

坎為聖，為雲，為玄云，為川，為大川，為河，為心，為志，為思，為慮，為憂，為謀，為惕，為疑，為艱，為蹇，為恤，為悔，為逖，為忘，為勞，為濡，為涕洟，為眚，為疾，為疾病，為疾癘，為疑疾，為災，為破，為罪，為悖，為欲，為淫，為寇盜，為暴，為毒，為瀆，為孚，為平，為法，為罰，為獄，為則，為經，為習，為入，為內，為聚，為脊，為要，為臀，為膏，為陰夜，為歲，為三歲，為尸，為酒，為叢木，為叢棘，為蒺藜，為棘匕，為穿木，為校，為弧，為弓彈，為木，為車，為馬。

The symbolic meanings of Kan. In the category of heaven and water: it represents a sage, clouds, dark clouds, rivers, great rivers, and rivers. In the category of mind, thoughts, and worries: it represents the heart, will, thought, consideration, worry, planning, vigilance, doubt, hardship, difficulty, concern, regret, distance, forgetting, labor, dampness, and tears and snot. In the category of calamity, disease, guilt, and blame: it represents disaster, illness, disease, epidemic, suspicious illness, calamity, ruin, guilt, disorder, desire, excess, bandits, violence, poison, and sacrilege. In the category of trust, law, and legal matters: it represents sincerity, fairness, law, punishment, court, standard, classic, repetition, entering, internal, and gathering. In the category of the human body and days and months: it represents the spine, waist, buttocks, fat, the private parts and night, years, three years, corpse, and wine. In the category of thick woods, instruments of punishment, chariots, and horses: it represents thick woods, thorny bushes, thorn weeds, a dagger made of thorny wood, a wooden stake, a yoke, a bow, a bowstring, wood, a chariot, and a horse.

離為女子，為婦，為孕，為惡人，為見，為飛，為爵，為日，為明，為先，為甲，為黃，為戎，為折首，為刀，為斧，為資斧，為矢，為飛矢，為黃矢，為網，為罟，為甕，為鳥，為飛鳥，為鶴，為隼，為鴻。

The symbolic meanings of the trigram Li (Fire). In the category of human beings: it represents a woman, a wife, pregnancy, and an evil person. In the category of visible brightness: it represents seeing, flying, a title (or a wine vessel), the sun, brightness, precedence, the first heavenly stem (Jia), and yellow. In the category of weapons: it represents military force, beheading enemies, a knife, an axe, a sharp axe, an arrow, a flying arrow, and a yellow arrow. In the category of nets and utensils: it represents a net, a fishing net, and a jar. In the category of flying birds: it represents a bird, a flying bird, a crane, a falcon, and a wild goose.

艮為弟，為小子，為君子，為賢人，為童，為童蒙，為僮僕，為官，為友，為閽，為時，為豐，為星，為沫，為霆，為果，為慎，為節，為待，為制，為執，為小，為多，為厚，為取，為舍，為求，為篤實，為道，為穴居，為石，為城，為宮室，為門闕，為廬，為牖，為居，為門庭，為宗廟，為社稷，為鼻，為肱，為背，為腓，為皮，為膚，為小木，為碩果，為豹，為狼，為小狐，為尾。

The symbolic meanings of Gen (Mountain). In human terms: as a younger brother, as a small person, as a gentleman, as a virtuous person, as a child, as a child learning, as a servant, as an official, as a friend, as a gatekeeper. In terms of weather and time: as time, as abundance, as stars, as faint starlight, as thunder. In terms of stopping, maintaining virtue, and conduct: as decisiveness, as caution, as restraint, as waiting, as control, as holding on, as smallness, as multitude, as thickness, as taking, as giving up, as seeking, as sincerity, as the Way. In terms of dwellings and structures: as cave-dwelling, as stone, as a city, as a palace, as gateways, as a hut, as a window, as dwelling, as gate and courtyard, as ancestral temple, as state and land. In terms of the human body: as the nose, as the upper arm, as the back, as the calf, as the skin, as the flesh. In terms of plants, trees, and animals: as small trees, as large fruits, as a leopard, as a wolf, as a small fox, as a tail.

兌為妹，為妙，為妻，為朋，為友，為講習，為刑人，為小，為少，為密，為通，為見，為右，為下，為少知，為契。右舉象至四百四十餘，然猶未能盡也。別本坎下有竊象，巽下有繫象，兌下有窺象，殆逸之中又有逸歟！

The extraordinary images of Dui: as sister, as a beautiful young woman, as wife, as friend, as companion, as study, as executioner (someone who has been punished), as small, as young, as secret, as communication, as appearance, as right, as lower, as little knowledge, as contract (or mark). The above examples amount to over four hundred and forty items, yet they are still not exhaustive. Other versions also mention additional images: under Kan, there is "stealing"; under Xun, there is "tying"; under Dui, there is "peeking." It seems there are even more extraordinary images beyond these.

《易》注如《瞿塘來氏集註》等，均有補象，要皆由《彖》、《象》十翼之辭，擬議以意增補。然來氏乾之為郊為野等補象均已列《孟氏逸象》之中，而又補之。殆來氏僻居巫峽，得書不易，《孟氏逸象》，或未之見耳。

Commentaries on The Zhou Changes, such as Lai Zhide's "Jutang Lai Shi Yijing Jizhu," all have their own "supplementary images." Generally, these are interpretations and additions based on the words of the Ten Wings, such as the Commentary on the Judgment and the Image Commentary. However, the images of Qian as a suburb and as a wilderness that Lai added were already included in the "Mengshi Yixiang." He added them again anyway. Probably because Lai lived in the area around Wuxia, where books were hard to find, and he may never have seen the "Mengshi Yixiang."

實則《說卦》廣象，簡而能賅，提綱挈領，各卦《彖》、《爻》之象，無不可會通演繹，而各得其變化。及根本之所在，必字字而擬之補之，則泥象以言《易》，而《易》反不可見矣。各家補象，爰不復贅錄。

In fact, the images presented in the "Shuo Gua Zhuan" are concise yet comprehensive, capturing the essence and leading the way. The images found in each hexagram's "Tuan Ci" and "Xiao Ci" can all be understood and derived from them, each able to seek its own transformation and find its fundamental nature. If one insists on comparing each character literally or adding supplementary explanations, then one would become confined by the images and lose sight of the "Yi." Therefore, the additional images provided by various schools are not copied here one by one.

參象者，乃八卦陰陽交變，未能以一卦之本象或變象盡之，因參合兩卦之象而會通之，其例已見於《廣象》。順德鄭氏《易譜》，觸類引伸，並證以前史占驗之詞，列為參象，亦足為初學之隅反也。

The term "参象" refers to the situation where, during the interaction and change of yin and yang in the Eight Trigrams, the meaning of a single trigram's original or transformed image is insufficient. Therefore, the images of the two trigrams before and after the change are combined to derive meaning. This method has already been illustrated in the previous section on "Broad Images." A person from Shunde, Guangdong, named Zheng compiled a section on "参象" in his work "Yi Pu," extending related concepts and verifying them with divinatory statements from historical records. This approach is sufficient to help beginners make connections and apply principles to similar situations.

離之艮，為火焚山，山敗之象。於人為言，敗言為讒，故又為讒言之象。乾之兌，天降為澤，為天子降心逆公之象。震之離，火反燒木，有女嫁反害其母之象。巽見艮，為山之材，而之乾有照以天光之象。坤之乾，又見艮，有廷實旅百，奉之以玉帛之象。蓋艮為廷實旅百，乾為玉而坤為帛也。坤之震，曰安而能殺，為公侯之象。

Li changes to Gen: Li fire is below and Gen mountain is above, which is the image of fire burning the mountain and the mountain being destroyed. In terms of human affairs, Li also represents speech, and broken speech is slander, so this is also the image of slander. Qian changes to Dui: Heaven descends to become a marsh, which is the image of the Son of Heaven humbling himself to welcome the feudal lords. Zhen changes to Li: Zhen represents wood and Li represents fire, wood naturally produces fire, but now fire burns the wood, just like a daughter getting married and harming her mother. Xun meets Gen: Gen represents mountain and Xun represents wood, which is wood on the mountain; when it changes to Qian, Qian represents heaven, forming the image described in the "Zuo Zhuan" case of Chen Jingzhong's divination, "there is timber on the mountain and it is illuminated by the light of heaven." Kun changes to Qian and meets Gen: This is the image described in the "Zuo Zhuan" as "a hundred items are presented in the courtyard, and they are offered with jade and silk," because Gen represents the hundred items displayed in the courtyard, Qian represents jade and Kun represents silk. Kun changes to Zhen: The divination conclusion in the "Zuo Zhuan" case of Bi Wan's career choice says "secure yet capable of killing," Kun is still and Zhen represents肃杀, which is exactly the image of a marquis or duke.

坤之坎，坤貞也，坎和也。和以率貞，有信之象。震之坤，震為足，坤靜而不動，有足居之之象。震車也，坤馬也，又為車從馬之象。震為長兄，坤為母，又有兄長之，母覆之之象。又為眾，眾又歸之之象。乾之坤，君降為臣也，為不終為君之象。乾天子也，變坤三爻皆出於乾，又為三出於天子之象。坎之巽，為夫從風，風隕妻之象。蓋風為隕落物也。

Heavenly Stem: Jia, Yi, Bing, Ding, Wu, Ji, Geng, Xin, Ren, Gui Earthly Branch: Zi, Chou, Yin, Mao, Chen, Si, Wu, Wei, Shen, You, Xu, Hai Trigrams: Qian (Heaven), Dui (Lake), Li (Fire), Zhen (Thunder), Xun (Wind), Kan (Water), Gen (Mountain), Kun (Earth) Kun changes into Kan: Kun represents firmness and stability, while Kan represents harmony and smoothness. Using harmony to lead firmness indicates the image of sincerity. Zhen changes into Kun: Zhen represents the foot, and Kun is still and unmoving, which is the image of "the foot resting" mentioned in the "Zuo Zhuan" example of Bi Wan's divination; Zhen represents a chariot and Kun represents a horse, which is the image of "the chariot following the horse"; Zhen represents the elder brother and Kun represents the mother, which is the image of "the elder brother supporting and the mother covering"; Kun also represents the people, so there is also the image of "the people returning to it." Qian changes into Kun: the king descends to become a minister, indicating the image of not being able to remain a king forever. Qian is the Son of Heaven, and after changing into Kun, all three lines come from Qian, forming the image of three times originating from the Son of Heaven. Kan changes into Xun: Kan represents the husband and Xun represents wind, indicating the image of the husband moving with the wind and the wind blowing the wife down — because wind is the thing that causes objects to fall.

震之坎，在春木旺龍德之時，為廢水之氣。來見乘加，昇陽未布，隆陰仍積，坎為刑獄，為刑獄壅濫之象。乾之離，為中天出日，有光顯之象，離之艮，為日落西山之象。艮之離，為山下起日，乃方升之象。艮之坎，為山嶽變海之象。坎之艮，為深谷為陵之象。

Zhen transforms into Kan: Zhen represents spring wood which is at its peak and the dragon's virtue is flourishing, while Kan water is already in a state of decline. Yet it rises upon this, causing the ascending yang energy to not yet spread out, and the heavy yin energy still to accumulate. Kan governs punishment and litigation, so this indicates a situation where punishment and litigation are blocked and overflowing. Qian transforms into Li: this represents the sun rising to the zenith, shining brightly. Li transforms into Gen: this represents the sun setting in the west. Gen transforms into Li: this represents the sun rising from beneath the mountain, just beginning to rise in the east. Gen transforms into Kan: this represents mountains turning into the sea. Kan transforms into Gen: this represents deep valleys turning into hills.

坎月也，變震為雷生明，變兌為上弦之月，變乾為十五夜月，變巽為十八晚初虧月，變艮為下弦月，變坤為晦。離日也，變震為初出日，變乾為中天之日，變巽為方斜之日，變艮為落山之日，坤知入地矣。離之坤，曰太陽入地，有退休之象，有傷夷之象。巽見乾之兌，有花木被馬毀折之象。

The trigram Kan represents the moon: when Kan transforms into Zhen, it symbolizes the beginning of the moon's illumination, corresponding to the trigram Zhen with the stem assignment of the moon's initial rise; when it transforms into Dui, it represents the waxing moon; when it transforms into Qian, it represents the full moon on the fifteenth day; when it transforms into Xun, it represents the moon beginning to wane on the eighteenth night; when it transforms into Gen, it represents the waning moon; and when it transforms into Kun, it represents the last day of the moon, the new moon. This sequence illustrates the order of the stem assignments of the moon paired with the eight trigrams. The trigram Li represents the sun: when Li transforms into Zhen, it symbolizes the rising sun at dawn; when it transforms into Qian, it represents the sun at noon; when it transforms into Xun, it represents the sun beginning to set in the west; when it transforms into Gen, it represents the sun setting on the mountain; and when it transforms into Kun, it indicates the sun has entered the earth. The transformation of Li into Kun is called the sun entering the earth, symbolizing both retreat and rest, as well as injury and damage. When Xun meets Qian and transforms into Dui: Xun represents flowers and trees, Qian represents a horse, and Dui represents destruction, symbolizing the image of flowers and trees being trampled and destroyed by a horse.

離之坎，坎來乘物，為月來掩日之象。郭景純曰：“變坎加離，厥象不燭，必有欺蔽之象。”坎之離，為月往日來。離甲冑，用兵戈之象也。而之坎知遇險於前，又不成出兵之象。坤之乾，為自地昇天之象。艮之坤，有舍高就卑，去畸嶇從平坦之象。坎之巽，風還吹水，有波濤之象。坎之兌，水竭耳聾，臣壅主聽之象。

The trigram Li transforms into Kan: Kan comes over Li, symbolizing the moon covering the sun. Guo Pu said, "When Kan transforms and comes over Li, the image is one of darkness and lack of illumination, indicating certain deceit and obstruction." When Kan transforms into Li: this signifies the moon departing and the sun returning. Li represents armor, indicating the use of weapons; but once it transforms into Kan, it shows there is danger ahead, thus becoming an unfavorable sign for military action. When Kun transforms into Qian: this represents rising from the earth to the heavens. When Gen transforms into Kun: this signifies abandoning high places and moving towards low ones, leaving rugged terrain for smooth ground. When Kan transforms into Xun: the wind turns back to blow over the water, symbolizing waves. When Kan transforms into Dui: Kan represents the ear, Dui represents a marsh, and the water has dried up, symbolizing dryness and deafness, indicating that ministers are blocking the ruler's hearing.

坤之坎，有平地開通之象。兌之艮，兌口舌講和，而艮又止之，有欲和不成和之象。乾之離，為圓器在爐灶之側。坎之乾，為雲從龍。巽之艮，為風從虎。震之離，離為矢，而火還燒震木，有張弧反射之象。

The transformation of the hexagram Kūn into Kan signifies Kūn representing flat land and Kan representing a ditch, indicating the image of a passage being opened on flat land. The transformation of Dui into Gen signifies Dui governing speech and negotiation, but Gen stops it, indicating the image of wanting to reconcile but failing to do so. The transformation of Qian into Li signifies Qian representing roundness and Li representing fire, indicating the image of a round vessel placed beside a stove. The transformation of Kan into Qian signifies Kan representing clouds and Qian representing a dragon, indicating the image of "clouds following the dragon." The transformation of Xun into Gen signifies Xun representing wind and Gen representing a tiger, indicating the image of "wind following the tiger." The transformation of Zhen into Li signifies Li representing arrows, while the fire of Li burns the wood represented by Zhen, indicating the image of drawing a bow and arrow only to shoot oneself.

離之乾，在乾宮為同復於父，為歸宗。震木之艮，有木入山之象。坎之震，兌之震，為水澤中木，如逢坎離同位，乃其木是湯藥煎煮之象。坎之艮，為官司刑獄而止不復升矣。艮之巽，為居其所而風自播而今自行。

When the hexagram Li changes to Qian: If within the Qian trigram, Li is the daughter born from Qian, and now it changes back to Qian, this signifies returning to the father's side and reverting to ancestral roots. When Zhen wood changes to Gen: This represents transporting wood into the mountains. When Kan water changes to Zhen, or when Dui marsh changes to Zhen: Water and marsh give rise to wood, and if Kan and Li are also in the same position, this indicates wood being boiled by water and fire, like decocting medicine. When Kan changes to Gen: Kan represents litigation, and Gen represents stopping, indicating that legal matters have reached an end and will not be pursued further. When Gen changes to Xun: Gen represents a place of residence, and Xun represents wind, indicating that a person remains in their original place while the wind spreads naturally, and matters spread on their own.

陰陽化合，播為五行。《禮運》曰：“布五行於四時，和而後月生也。”五行非質也，實天地陰陽之氣。氣有盛衰，而時位乘之，而生克變化之跡著也。氣不可見，仍見之於八卦之象。

Yin and yang interact and transform, spreading out to become the Five Phases. The Book of Rites, The Mandate of the Duke of Zhou says: "Distribute the Five Phases through the four seasons, and harmony allows the moon to be born." The Five Phases are not specific substances; they are actually the qi of heaven and earth, yin and yang. Qi has periods of abundance and decline, and with the influence of time and position in between, the traces of generation and overcoming, transformation and change become evident. Qi itself is invisible, so it still relies on the trigrams of the Eight Trigrams to be perceived.

聖人作《易》，既極數定象，復發其凡於蠱巽之《彖》、《爻》。先後甲庚，各舉其端，而全《易》卦爻之陰陽五行無不可以此類推。而卦氣占候、九宮三式之術數雖繁，亦無能越此範圍。列象如右。卦數另詳下篇。

The sage composed the Zhou Changes, having exhausted the numbers and established the images. He also indicated the principles in the Tuang Cite of the Gu hexagram and the line statement of the Xun hexagram's Nine in the Fifth: the Gu hexagram says "three days before the Jia day, three days after the Jia day," and the Xun hexagram's Nine in the Fifth says "three days before the Geng day, three days after the Geng day," each providing a single clue. From this, all the yin and yang and the five phases in the entire Zhou Changes can be inferred. As for the methods of divination such as the hexagram qi and the nine palaces, Taiyi, Leigong, and Liunin, although their names are numerous, they all fall within this scope. Now I list the images of the five phases on the right. As for the hexagram numbers, they will be discussed in detail in the next section.

水火木金土，分陰分陽，有柔剛，各有配偶，共為十象，舊稱八卦。土金木皆有二，惟水火各一，實未知震兌各具水火之用也。震兌為陰陽出入之門，日月往來之路，不啻五行生化之原，故後天與坎離皆居中位。坎離居先天乾坤之位，震兌即居先天坎離之位。參觀《內經》，則陰陽升降，五行生化之作用，更顯著矣。

Water, fire, wood, metal, and earth are each divided into yin and yang, and each has soft and hard aspects. They are paired two by two, resulting in a total of ten phenomena. In ancient times, they were only referred to by the eight trigrams. Within the eight trigrams, earth, metal, and wood each occupy two trigrams (Kun and Gen for earth, Qian and Dui for metal, Zhen and Xun for wood), but water and fire each occupy only one trigram (Kan for water, Li for fire). This is because people did not realize that Zhen and Dui also possess the functions of water and fire. Zhen and Dui are the gateways for yin and yang to enter and exit, the pathways for the sun and moon to pass through. They are truly the fundamental sources of the generation and transformation of the five phases. Therefore, in the later heaven trigram arrangement, they occupy the central positions of the four cardinal directions, just like Kan and Li. In the earlier heaven diagram, Kan and Li occupy the positions of Qian and Kun, while Zhen and Dui occupy the positions of Kan and Li. Further examination of the Huangdi Neijing reveals that the functions of yin and yang rising and falling, and the generation and transformation of the five phases, become even more evident.

意象影象者，日本易學之名詞也。經學諸書，自唐開元時傳入日本者為多。故日人講《易》，多宗李鼎祚《集解》，其占筮亦用唐人之揲法。卦象取用，有所謂意象者，如以震為船，翼為剪，離為鏡，艮為亭，類取形似，無甚深意義。但象本無方，意動成象，故得意既可忘象，亦能成象。

"The concepts of 'intentional image' and 'imagery' are terms used in Japanese Yi studies. Most classical Chinese texts were transmitted to Japan during the Kaiyuan period of the Tang dynasty, so Japanese scholars generally follow Li Dingzuo's Collected Explanations of the Zhou Changes when discussing the I Ching. They also use the Tang dynasty method of divination with yarrow stalks. When they employ hexagram images, they refer to 'intentional images,' such as viewing Zhen as a boat, Xun as scissors, Li as a mirror, and Gen as a pavilion, all based on resemblance in shape, without deeper meaning. However, hexagrams themselves do not have fixed forms; images can be formed by mere thought. Therefore, since one can 'attain the meaning and forget the image,' one can also create images through intention."

《易》冒天下之道，以八卦相錯，陰陽反覆，能曲成萬物而不遺者，正以象之變化無盡，而肆應不窮。盈天地間唯萬物，生生不已，《易》亦生生不已。萬物之孳乳，日積月累，其數量為巧曆所不能計，而《易》之八卦，足以盡之。非神而明之，其孰能與於斯？

The Zhou Changes (I Ching) can encompass the principles of the world because of the intermingling of the Eight Trigrams and the constant transformation of yin and yang, thus achieving a subtle formation of all things without omission. Because the changes of the hexagrams are inexhaustible, their application to all affairs is also inexhaustible. What fills the universe is myriad things, which continuously generate and multiply. The I Ching also continuously generates and transforms. Myriad things constantly reproduce and proliferate, accumulating day by day, their numbers so vast that even the most skilled in calculations cannot count them. Yet the eight trigrams of the I Ching are sufficient to include them all. Without the ability to grasp the subtle and profound, who could enter into such a realm?

海通而後，西學東漸，名物之繁，百倍於昔。而鼎新革故，索之於《易》，無不各有其數，各有其象。如廣象以乾為金為玉，金玉或非伏羲畫卦時所有物。而三代以後，既有其物，而即以伏羲所畫乾卦之象當之。以三代之時，物質之最精最堅莫金玉若也。而今則金剛石之精粹堅剛，更出金玉之上，自可由金玉而更廣之以乾為金剛石。乾之因物付物，仍莫不確合而確肖也。

Since the opening of the sea ban, Western learning has spread eastward, bringing with it a multitude of names and objects far exceeding the number of those from before. However, when these new things are sought for in the Zhou Yi, each has its own number and its own image. For example, the "Shuo Gu" section of the Zhou Yi uses the trigram Qian to represent metal and jade. Metal and jade were not necessarily things that existed when Fuxi drew the trigrams. Yet after the Xia, Shang, and Zhou dynasties, since such objects did exist, the image of the Qian trigram was used to represent them. During the Xia, Shang, and Zhou periods, there was nothing more refined and hard than metal and jade. Now, diamond is even purer and harder than metal and jade, so it is natural to extend the image of Qian from metal and jade to diamond. The Qian trigram, by assigning images according to the things, remains perfectly appropriate and accurate.

廣象以坎為輿，坤為大輿，震為大塗，合坎通坤載震行而定其象，以當時載物之具，莫利於輿，莫過於大輿。而通行之路，莫便捷於大塗故也。今則交通之廣，運輸之捷，器用日新，幾非一名一物所能限。然則占事知來，制器尚象，非由廣象更推而廣之，安能盡其用哉！

The broad symbolic meanings take the Trigram Kan as representing a vehicle, the Trigram Kun as representing a large cart, and the Trigram Zhen as representing a broad road. This is because these trigrams combine the meanings of Kan's fluidity, Kun's capacity to carry, and Zhen's movement. In ancient times, there was no transportation tool more convenient than a vehicle, no vehicle more capable of carrying heavy loads than a large cart, and no road more convenient for travel than a broad road. Today, however, transportation is far more extensive, transport is much faster, and tools and objects are constantly evolving in new and unprecedented ways, almost beyond the capacity of any single term or object to define. Therefore, if we are to "predict future events through divination" and "create tools based on symbolic forms," we cannot fully exhaust their applications unless we extend our understanding of these broad symbolic meanings further outward.

以卦言之，小過飛鳥遺之音，固未知今日之有飛機也，而象已確肖之。既未濟之曳其輪，未必知今日之有汽機也，而象已不啻曲繪之。古未嘗有化學之分劑也，而今日化學各原質之分化輕重，其量劑數無不與八卦之數合。

In terms of the hexagrams: The statement of the hexagram "Small Crossing" mentions "the sound left by a flying bird." Although ancient people did not know about airplanes today, this image is already very similar to an airplane. The hexagrams "Already Crossing" and "Not Yet Crossing" mention "dragging the wheel," which may not have referred to steam engines, yet the image is already almost exactly described. In ancient times, there were no chemical elements or their ratios, yet the weights and proportions of elements when they are separated in modern chemistry all correspond exactly with the numbers of the eight trigrams.

是故但以象言，或猶疑為附會之適相巧合。若更證之以數度，參之以陰陽剛柔之氣運，而形質狀態，性情功用，無不一一彰明顯著。此意象之為用，非經生家鑽研故紙，取經傳之一名一物，自稱補象之足並論也。我國雖無意象之名，而京焦管郭之占象，見於本傳及《易林》、《洞林》諸書者，其以意廣古人之象者，固不勝指數。故特著之，為初學擴其心胸之一助焉。

Therefore, if we consider only the images, some people might doubt that it is merely a forced connection that happens to coincide. But if we further verify with numbers and measurements, and refer to the yin and yang and the qualities of hardness and softness to explore, then the forms, states, natures, and functions of things will all become clear and distinct. This is the function of "intentional image" (意象), which is far beyond the capability of those scholars who merely study old texts, who pick out a name or an object from the classics and claim it as "complementing the image" (补象). Although our country does not have the term "intentional image," the divination methods based on images used by Jing Fang, Jiao Yanshou, Guan Lu, and Guo Pu are recorded in their biographies and in works such as the "Forest of Changes" (焦氏易林) and "Deep Forest" (洞林). There are countless examples in these works where they expanded on the images of ancient times through their own thoughts. Therefore, we specially highlight this school of thought to help beginners broaden their minds.

影象之說，當本於吾國相傳之卦影。卦影之術，始於晉唐，而盛於南宋。嚴君平亦即其儔，今已失傳。而日本之所謂影象，類似吾國之伏象。惟不限以震伏巽，艮伏兌，大概與意象略同。說詳東京易學討論會丁巳年發行之易學雜誌，亦足供學者之參考也。

As for the concept of 「image」, it should be based on our traditional 「guaying」. The technique of guaying originated during the Jin and Tang dynasties, and became popular in the Southern Song dynasty; Yu Zun (styled Junping) of the Western Han dynasty also belonged to this school. However, this method has now been lost. The Japanese concept of 「image」 is similar to our 「fuxiang」, except that it does not limit itself to fixed pairings such as Zhen concealing Xun or Gen concealing Dui. Generally speaking, it is quite similar to the concept of imagery. For detailed explanations, refer to the 「Yixue Zazhi」 (Journal of Yi Studies) published by the Tokyo Yi Studies Discussion Society in the Dingsi year (1917), which may be of interest to scholars.

“天一，地二。天三，地四。天五，地六。天七，地八。天九，地十。”又曰“天數二十有五，地數三十。天地之數，五十有五。”河圖洛書之數，即此五十有五之數所分佈而進退者也。聖人則圖畫卦，是故卦之數即圖書之數，亦即天地之數也。“大衍之數五十，其用四十有九”者，所以衍《易》，即以衍此五十有五之數者也。

The Great Treatise says: "Heaven is one, Earth is two; Heaven is three, Earth is four; Heaven is five, Earth is six; Heaven is seven, Earth is eight; Heaven is nine, Earth is ten." It also says: "The number of Heaven is twenty-five, the number of Earth is thirty; the total number of Heaven and Earth is fifty-five." The odd numbers one, three, five, seven, and nine belong to Heaven, and when added together they total twenty-five; the even numbers two, four, six, eight, and ten belong to Earth, and when added together they total thirty. When these two are combined, the total is fifty-five. The numbers of the Yellow River Chart and the Luo Writing are the result of the distribution and alternation of these fifty-five numbers. The sages took inspiration from the Yellow River Chart and the Luo Writing to draw the trigrams, so the numbers of the trigrams are the same as the numbers of the charts and writings, which are the numbers of Heaven and Earth. As for "the number of great derivation is fifty, but only forty-nine is used," this is used for the derivation of the Zhou Changes, but the subject of derivation still does not go beyond these fifty-five numbers. Thus, "the numbers of Heaven and Earth" and "the number of great derivation" are originally two different things, and it is necessary to distinguish them clearly first.

自宋儒竄易經文，以“天一地二”一節，移置“大衍之數五十”以前，兩數遂相混合，併為一談。異論紛若，左支右吾，卒無是處。漢學家雖力糾其繆，而於兩節之數理，亦未能分析清楚，與卦象《彖傳》相證明。乃沿繆襲誤，以迄於今。

Since the Song dynasty Confucian scholars altered the text, moving the section "Heaven is one, Earth is two" before "The Great Derivation consists of fifty," the numbers of Heaven and Earth and the numbers of the Great Derivation became mixed together and were regarded as one thing. Thus, various conflicting interpretations arose, and no single explanation could be fully consistent. Although Qing dynasty Han scholars made great efforts to correct this error, they were still unable to clearly analyze the numerical reasoning of these two sections. Moreover, they did not use the hexagram images and the Commentary on the Judgment to cross-verify each other, leading to the perpetuation of errors up to the present day.

程朱而後，言《易》者皆崇理論，言象者已不多，言數者尤少。偶有一鱗半爪，又皆似是而非。同人講習，幾於無可取資。爰就所知，略貢芻蕘。所憾數學既淺，又荒廢日久，自知膚淺已甚。姑引其端，以待專家之續竟其緒也。

After Cheng Yi and Zhu Xi, those who interpreted the Book of Changes mostly emphasized principles and meanings, while those who discussed images became rare, and those who dealt with numbers even fewer. Occasionally, there were some fragments, but they were ambiguous and not clear. When people gathered to study together, there was almost nothing to draw upon. Therefore, based on my own understanding, I briefly offer my shallow opinions. Regrettably, my knowledge of mathematics is shallow, and I have neglected it for a long time. I am fully aware that my views are very superficial, and I merely intend to start the discussion, hoping that experts will continue this line of thought.

乾一，兌二，離三，震四，巽五，坎六，艮七，坤八之數，邵子《皇極經世》之數，所謂先天數也。相傳康節從李挺之氏學《易》三年，未能窺其奧，請益於李，叩其要旨。李乃授以一二三四五六七八之八字，康節言下大悟，恍然於乾兌離震巽坎艮坤之天然位次，與數適合。

This sequence of numbers,乾 one, 兑 two, 离 three, 震 four, 巽 five, 坎 six, 艮 seven, 坤 eight, is the numerical system used in Shao Yong's "Huang Ji Jing Shi," which is commonly referred to as the "Earlier Heaven Numbers." It is said that Shao Yong (posthumously known as Kangjie) studied the Book of Changes with Li Zhicai (given name Tingzhi) for three years but still did not grasp its profound meaning. He then asked Li Zhicai for the essential principles. Li Zhicai simply taught him the words one, two, three, four, five, six, seven, and eight. At that moment, Shao Yong suddenly understood that the natural order of 乾, 兑, 离, 震, 巽, 坎, 艮, and 坤 perfectly corresponds to the numbers one through eight.

而陰陽交錯，順逆往來，無不妙合。極深研幾，遂得貫澈天人，成《皇極經世》一書。程子嘆為內聖外王之學，朱子《木義》，又取其大小方圓各圖，弁諸經首。其後言《易》者，即以先天數為易數。於卦爻《彖》、《象》之言數者，如“七日”“八月”“十年”“九陵”之類，悉以先天數當之，歧誤乃不可究詰。

Moreover, the interplay of yin and yang, moving forward and backward, coming and going, is all perfectly matched with this system of numbers. From this, he deeply studied the subtle aspects and finally understood the principles of heaven and human affairs, composing the book "Huang Ji Jing Shi." Cheng Yi praised it as the study of inner sagehood and outer kingship. Zhu Xi's "The Original Meaning of the Zhou Changes" also adopted his diagrams of large and small circles and square and circle, placing them before the text. Since then, those who explained the "Zhou Changes" have directly regarded the Earlier Heaven numbers as the numbers of the "Zhou Changes." Whenever the Book of Changes and its line statements, as well as the Commentary on the Judgment and Image Commentary, mention numbers, such as the "seven days to return" in the hexagram "Fu," the "eight months with calamity" in "Lin," the "ten years to name" in "Zun," and the "ascend to the high hill" in "Tong Ren," they all apply the Earlier Heaven numbers, leading to many erroneous interpretations that are beyond reckoning.

夫邵子先天數，非不合也。特邵子別有妙悟，以一二三四五六七八為主，如算學之數根。乾兌離震巽坎艮坤，只為其數之符號耳，故用乾兌離震巽坎艮坤可也，用日月星辰水火土石亦無不可也。

In fact, the Earlier Heaven numbers of Zhao Shi are not inconsistent. Zhao Shi had his own profound insight: he took the numbers one, two, three, four, five, six, seven, and eight as the main elements, just like the fundamental numbers in arithmetic; the trigrams Qian, Dui, Li, Zhen, Xun, Kan, Gen, and Kun are merely symbols of these numbers. Therefore, using Qian, Dui, Li, Zhen, Xun, Kan, Gen, and Kun to represent them is acceptable, and using his own terms from his writings, such as "sun, moon, stars, water, fire, earth, and stone," to represent them is equally valid.

因邵子未嘗以此注《易》，但借卦爻以演其數，而所得之數理，變化分合，仍能與《易》相符。所謂殊途同歸，法異而實不異也。若以言《易》，則自當以乾兌離震巽坎艮坤為主。先後體用，各有其數。與邵子之數同出天一地二之十數，並圖如左：

Zhang Zhengzhi never used this set of numbers to comment on the Yi Jing, but instead used the trigrams and lines to deduce his numbers. The numerical principles he derived still conform to the Yi Jing in terms of change and combination. This is called "different paths leading to the same destination"—different methods but the same essence. However, if these numbers are to be used in explaining the Yi Jing, they should naturally take the eight trigrams—Qian, Dui, Li, Zhen, Xun, Kan, Gen, and Kun—as their main focus. The Earlier Heaven and Later Heaven, as well as the essence and function, each have their own numbers. They all originate from the same set of ten numbers known as "Tian Yi Di Er." The following diagrams are now listed on the left.

乾一對坤八，合九。兌二對艮七，合九。離三對坎六，合九。震四對巽五，合九。四九合三十六。乾陽三畫，坤陰六畫，合九。兌四畫，艮五畫，合九。離四畫，坎五畫，合九。震五畫，巽四畫，合九。四九亦合三十六。

First, look at the numbers: Qian (Heaven) has one and Kun (Earth) has eight, adding to nine; Dui (Lake) has two and Gen (Mountain) has seven, adding to nine; Li (Fire) has three and Kan (Water) has six, adding to nine; Zhen (Thunder) has four and Xun (Wind) has five, adding to nine. Four nines together make thirty-six. Now look at the lines: Qian has three yang lines, making three strokes; Kun has three yin lines, each line broken into two, making six strokes. Adding these two trigrams gives nine; Dui has four strokes and Gen has five, adding to nine; Li has four strokes and Kan has five, adding to nine; Zhen has five strokes and Xun has four, adding to nine. Four nines together also make thirty-six. Thus, whether calculated by numbers or by strokes, the total is exactly the same.

八卦相蕩成六十四，除乾坤坎離頤中孚大小過八卦反覆不變，餘五十六皆一卦反覆成二卦，實只二十八卦。合乾坤等不變之八卦，亦共合三十六卦。三十六者，六之自乘也。故邵子曰“三十六宮都是春”，乃用六藏九，為邵子之獨有心得，別具用法。

The eight trigrams interact and transform into the sixty-four hexagrams. Except for the eight trigrams—Qian, Kun, Kan, Li, Yi, Zhongfú, Daguò, and Xiaoguò—which remain unchanged when reversed, the remaining fifty-six hexagrams each form another hexagram when reversed. Thus, in actuality, there are only twenty-eight hexagram forms. Adding the eight unchanging trigrams, the total becomes thirty-six hexagrams. Thirty-six is the square of six. Therefore, in his poem, Shao Yong wrote, "Thirty-six palaces are all spring." This is Shao's unique insight, using six while concealing nine, and it has its own special method.

故依此數方位，與五行干支納甲皆不相合。納甲之象與乾一兌二之數無關，漢學家力闢先天卦位，而於乾一兌二之數，無能辯駁。偶有言者，亦隔靴搔癢，無當於理。茲另圖先天八卦之合洛書河圖數如下：

This is precisely why the arrangement based on this set of numbers does not align with the Five Phases, the Heavenly Stems and Earthly Branches, or the Najia system. The images derived from the Najia system are inherently unrelated to the sequence of the trigrams as乾 one, 兑 two. Qing dynasty Han scholars strongly criticized the Earlier Heaven trigram positions, but they could not refute this sequence of numbers. Occasionally, someone would mention it, but their comments were like scratching an itch through a boot, missing the point entirely. Now, another diagram is drawn to illustrate how the Earlier Heaven trigrams correspond with the numbers of the Luo Writing and the Yellow River Chart, as follows:

聖人則圖畫卦，卦數即圖書之數。圖書之一六，皆從下起，陽從一始，陰以六終，皆歸藏於北方，未有從上起者。邵子先天數，獨悟“易逆數也”一語，故反用圖書而逆由乾位起一，藏九不用，為兩數之對待。如洛書之藏十，其妙用在卦順則數逆，卦逆則數順，故仍不悖於陽順陰逆之天則。錯綜變化，而無不相通。

The sage derived the trigrams by following the patterns of the Yellow River Chart and the Luo Writing. Therefore, the numbers of the trigrams correspond to those of the charts. In the charts, the number one and six are both counted from the bottom: yang begins with one and yin ends with six, and both are concealed in the north, never counted from the top. However, Zhao Zǐ's Earlier Heaven numbers uniquely understood the sentence "The Book of Changes reverses the numbers" from the "Explanations of the Trigrams." Therefore, he reversed the numbers of the charts, starting with one from the Qian position, concealing nine, making one and nine correspond as two opposing numbers, just as the Luo Writing conceals ten. Its subtle use lies in the fact that when the trigram sequence proceeds normally, the numbers reverse, and when the trigram sequence reverses, the numbers proceed normally. Thus, it still does not contradict the natural principle of "yang follows the order and yin reverses." Through the transformations of reversal and combination, there is no lack of mutual connection.

若論先天八卦之本數，則自當取則河圖，陰逆陽順，以合於一六二七三八四九之匹偶。而陰陽相對，皆得五數。如雷風一四合五也，水火二三合五也，山澤七八合十五，天地九六合十五，皆五也。仍以五為中樞。而一六為地雷復，九四為天風姤，二七為水澤節，三八為火山旅。所謂布五行於四時，無不合也。

If we are to discuss the numbers of the Earlier Heaven Trigrams themselves, then we should naturally refer to the Yellow River Chart: yin moves in reverse and yang moves in the usual direction, in order to correspond with the four pairs of numbers: one and six, two and seven, three and eight, four and nine. Yin and yang are paired oppositely, and the results are all multiples of five: thunder and wind are one plus four to make five, water and fire are two plus three to make five, mountain and marsh are seven plus eight to make fifteen, heaven and earth are nine plus six to make fifteen, all of which are reduced to five, still taking five as the central number. Now looking at the trigrams formed by these pairs: one and six form the hexagram of earth and thunder, Fu; nine and four form the hexagram of heaven and wind, Gou; two and seven form the hexagram of water and marsh, Jie; three and eight form the hexagram of fire and mountain, Lv. The statement in the "Book of Rites: The Ritual Propriety" that "the five elements are distributed through the four seasons" is fully consistent with all of this.

和而後月生，此納甲所以用先天之象，而取後天之數也。此理千餘年來，未有發明。由於不知陽順陰逆之數，以邵氏之數，強解京、焦之《易》，紛紜糾結，遂莫可究詰矣。陽數順由一始，為一三七九。陰數逆由四起，為四二八六。宋以後，皆以二四六八為陰數之用，此其根本之錯誤也。

The Li Yun continues saying, "Harmony comes first, then the moon is born," which precisely explains why the method of Najia uses the Earlier Heaven hexagrams but employs the Later Heaven numbers. This principle has not been revealed for over a thousand years. Because people do not understand the principle of yang numbers progressing in a positive direction starting from one, in sequence one, three, seven, nine, and yin numbers regressing starting from four, in sequence four, two, eight, six, they have forcedly applied Shao Yong's numbers to interpret Jing Fang and Jiao Yanshou's Yi, leading to confusion and making it impossible to trace the origin. In fact, the yang numbers proceed in order from one, three, seven, nine, while the yin numbers regress from four, two, eight, six. Since the Song dynasty, people have generally used two, four, six, eight as yin numbers, which is a fundamental error.

陽順陰逆圖數，餘於庚申之秋，始由“乾乘六龍”一語悟得“乘六”之法，繪圖以明之。始知極數定象，通變成文，參伍錯綜，皆在陽順陰逆。而千餘年來，似是而非之註釋，均可一掃而空矣。圖說另詳《易數偶得》。

Concerning the diagram and numbers of yang moving in order and yin moving in reverse, I only understood the method of "riding six" from the phrase "when the time comes to ride six dragons" in the Commentary on the Judgment of the Qian hexagram, and drew a diagram to explain it during the autumn of the Gengshen year (1920). It was then that I fully realized the essence of the Great Treatise's statements: "by reaching the extreme of numbers, one determines the images of the world," "by comprehending the changes, one forms the writings of heaven and earth," and "by combining three and two, one transforms and interweaves the numbers." The key lies entirely in the four characters "yang moving in order and yin moving in reverse." With this understanding, all the ambiguous interpretations over a thousand years can be completely discarded. The diagram and explanation are detailed in my work "Accidental Insights on the Numbers of the Book of Changes."

坎一坤二震三巽四離九艮八兌七乾六。乾坎相連，一與六合。坤兌相連，二與七合。震艮相連，三與八合。巽離相連，四與九合。水火金木之數，各有配合，獨闕五十兩數。

The Later Heaven Trigrams are paired with the numbers of the Luo Writing as follows: Kan one, Kun two, Zhen three, Xun four, Li nine, Gen eight, Dui seven, and Qian six. Qian is connected to Kan, with one and six combining, representing the number of water; Kun is connected to Dui, with two and seven combining, representing the number of fire; Zhen is connected to Gen, with three and eight combining, representing the number of wood; Xun is connected to Li, with four and nine combining, representing the number of metal. The numbers for the four elements of water, fire, metal, and wood are each paired, but the numbers five and ten are missing.

非闕也，坎一離九合十，中央戊己，而坤艮二八，亦合十為丑未，皆五與十土數所分寄，方位與洛書合，而數亦兼符納甲。其說已詳《卦位》章先天納甲圖，茲不贅述。更以數之順序，並列與洛書參照，則第一章二八易位，二五構精，兩圖之妙更可見矣。

In fact, it is not a matter of deficiency. When the number one from Kan and the number nine from Li are added together, they total ten, which corresponds to the central position of Wu and Ji (the earth elements). Similarly, when the number two from Kun and the number eight from Gen are added, they also total ten, which corresponds to the earth positions of Chou and Wei. The numbers five and ten, which represent the earth numbers, are thus located in these positions. Their directions correspond with the Luo Writing, and their numbers also align with the Najia stem assignment. This principle was explained in the chapter on "Hexagram Positions" in the Earlier Heaven Najia diagram, so we will not repeat it here. If these numbers are then arranged in order and compared with the Luo Writing, the subtle meanings discussed in the first chapter regarding the mutual exchange of Kun and Gen, and the interaction between two and five to form a vital essence, will become even more evident.

坎離乾巽震兌坤艮皆相對，與卦位合。惟坤二與艮八之位互易，五運中樞，而十暗寓於八方。所謂通變化而行鬼神者，即在此坤艮易位之妙用。故曰“神樞鬼藏”，向來道家珍為神秘。非入其門奧者，不肯輕洩。實則邵子天根月窟，子正在丑，午正在未數言，已不啻明明揭示，特後人不自悟耳。

The trigrams Kan and Li, Qian and Xun, Zhen and Dui, and Kun and Gen are all paired opposites, perfectly matching the positions of the hexagrams. However, the positions of Kun two and Gen eight are exchanged. As a result, the number five becomes the central axis of rotation, while the number ten is implicitly contained within the eight directions. The "Great Treatise" says, "It communicates transformation and moves spirits and ghosts," and the profound application lies in the exchange of positions between Kun and Gen. Therefore, practitioners call it "the divine axis and the hidden spirits," a secret highly valued by Daoists, not easily revealed to those who have not reached the inner understanding. In fact, Shao Yong's statements about "the heavenly root and the lunar cave," and "the proper position of Zi is in Chou, and the proper position of Wu is in Wei," clearly reveal this principle, but later generations have failed to comprehend it themselves.

先後天八卦，既各有其本位本數，而體用相生，升降變化，由合而分，亦由分而合。是以《易》之《彖》、《象》凡涉言數者，亦各有體用之不同。先天八卦本數者，以河圖為體者也。後天八卦本數者，以洛書為體者也。先後天八卦合數者，兼先後天之象而納十干之數者也。此數相傳最古，虞氏《易》即用此數也。

The Earlier Heaven and Later Heaven Trigrams each have their own fundamental positions and numbers, and their principles and applications interact and transform with each other, rising and falling continuously. They merge and then separate, and also separate and then merge again. Therefore, in the Zhou Changes, the Commentary on the Judgment and the Image Commentary, wherever numbers are involved, they also differ in terms of principle and application. The fundamental numbers of the Earlier Heaven Trigrams are based on the Yellow River Chart, while the fundamental numbers of the Later Heaven Trigrams are based on the Luo Writing. As for the combined numbers of the Earlier and Later Heaven Trigrams, they integrate both the Earlier Heaven and Later Heaven Trigram forms, and are paired with the numbers of the ten Heavenly Stems. This system of numbers is said to be the most ancient. Yu Fan, a commentator of the Han dynasty, used this system in his annotations of the Zhou Changes. Therefore, when reading Han dynasty annotations of the Zhou Changes, whenever numbers are discussed, one must first determine which system the commentator is using, in order to avoid misinterpretation due to confusion.

古納甲圖：東方甲乙配乾坤，南方兌艮配丙丁，西方庚辛屬震巽，而坎戊離己中央，因壬癸為乾坤兼納也。此圖壬癸居北屬坎離，以坎離代乾坤。有作離一坎六.者，陰陽互根，亦自可通。並前兩圖合觀之，當知邵子數與《易》之分別矣。

The ancient Najia diagram assigns the heavenly stems and earthly branches as follows: in the east, Jia and Yi are paired with Qian and Kun; in the south, Bing and Ding are paired with Dui and Gen; in the west, Geng and Xin are paired with Zhen and Xun; while Wu is assigned to Kan and Ji is assigned to Li in the center. As for Ren and Gui, they are included by both Qian and Kun. This diagram places Ren and Gui in the north and assigns them to Kan and Li, using Kan and Li to replace Qian and Kun. There is also a version that assigns Li to one and Kan to six, taking the meaning that yin and yang depend on each other as roots, which is equally reasonable. When this diagram is combined with the previous two diagrams, it becomes clear how Shao Yong's system of numbers differs from the numerical system of the Zhou Changes.

天地範圍數，相傳即《連山》卦數。因其以艮為始終，所謂“範圍天地而不過，曲成萬物而不遺”者也。略舉例如左：

"The range of numbers covering heaven and earth" is said to be the hexagram numbers of the Xia Dynasty's "Lianshan" Yi. This system begins and ends with the Gen hexagram, which corresponds exactly to the meaning in the "Xici Zhuan" that "it encompasses all changes of heaven and earth without exceeding, and skillfully completes all things without omission." Below are a few examples, listed on the left side (the original book had a chart here, but the chart has been lost in the source).

右圖始艮一，終艮十，而又以艮七為用，象數體用皆艮，故有《連山》易數之名。雖未必即為《連山》，而其象則兼先後天，數則合河圖洛書。與納甲納音，融會而貫通之者也。天地萬物之數，莫能外於是矣。

The sequence of numbers in this diagram starts with "Gen" (Mountain) paired with one and ends with "Gen" paired with ten, with "Gen" paired with seven serving as the actual position used in practice. Thus, both the "body" (the essence of form and number) and the "function" (the application) of the symbolic and numerical system fall under "Gen." Because of this, this system is called the "Lianshan" system of divination. It may not be the original version of the "Lianshan" from the Xia dynasty, but it incorporates both the Earlier Heaven Trigrams and the Later Heaven Trigrams in terms of symbolic representation, and it conforms to both the Yellow River Chart and the Luo Writing in terms of numerical structure. Furthermore, it integrates both the "Najia" system (pairing the Eight Trigrams with the Heavenly Stems) and the "Nayin" system (pairing the sixty jiazi with the five tones and Five Phases) into a unified whole. There is no number related to the myriad things in the universe that can exist outside of this framework.

陽數極於九，陰數極於六。陽，天也。天之用皆見於地，故數至六而體全，得七而六數之用行也。太陽無七，太陰無十，而艮兼用一、七、十者，一始十終，七則具成終成始之用者也。

The number of Yang is limited to nine, while the number of Yin is limited to six. Yang belongs to Heaven, which itself has no form; its function must manifest on Earth to be visible. Therefore, the number reaches six, completing the "body" of Earth's aspect. Going further to seven, the "function" of six begins to operate — seven is the first step after six, marking the transition from the "body" to the "function." Among the Four Symbols, the number of "Sun" is nine rather than seven (seven belongs to Minor Yang), and the number of "Great Yin" is six rather than ten (ten lies beyond the Four Symbols). Only the Gate (Geng) hexagram uses the numbers one, seven, and thirteen: one is the starting point, ten is the endpoint, and seven is in the middle, possessing the function described in the "Commentary on the Hexagrams" as "the one that completes and begins all things." Therefore, this diagram begins with Geng one and ends with Geng ten, with Geng seven serving as the central point for practical application.

夫《易》開物成務，冒天下之道，如斯而已者，非他，即天一，地二，天三，地四，天五，地六，天七，地八，天九，地十之數也。八卦成列，天地之數，分陰分陽，與八卦並列，而五位配合，五行生布也，干支屬也。

The Great Treatise says that the Book of Changes can "open things and accomplish tasks, encompassing all the principles under heaven." This means developing all things and achieving success, covering all the principles of the world. What is meant by "nothing more than this" is the sequence of numbers listed in the Great Treatise: Heaven one, Earth two, Heaven three, Earth four, Heaven five, Earth six, Heaven seven, Earth eight, Heaven nine, Earth ten. Once the Eight Trigrams are arranged in order, these ten numbers distinguish yin and yang—odd numbers belong to Heaven and are yang, while even numbers belong to Earth and are yin—thus being paired with the Eight Trigrams. The ten numbers also pair up as one with six, two with seven, three with eight, four with nine, and five with ten, forming five groups of directions. From this, the Five Phases emerge and are arranged, and the assignments of the Heavenly Stems and Earthly Branches are determined accordingly.

一始十終，順往逆來，六十四卦先後天往復循環，周而復始，而數有不周，獨闕西北。先天則艮闕，後天則乾無，而盈虛消長，於以無閥，皆出“乾知大始”。冒天下之道，以極天之數，定天下之象，通天下之志，定天下之業，斷天下之疑，興神物以前民用，盡在於斯矣。

These ten numbers start from one and go up to ten. Counting them in order or reversing the count, the sixty-four hexagrams cycle back and forth between the Earlier Heaven and Later Heaven arrangements, continuing endlessly. However, there is one place that remains incomplete: the Northwest is missing a position. According to the Earlier Heaven arrangement, the Northwest is Gen, which is not assigned a number; according to the Later Heaven arrangement, the Northwest is Qian, which also does not have a number. The reason the cycle of full and empty, increase and decrease in the universe can continue forever without being blocked is precisely because of this gap. The basis for this gap comes from the "Great Treatise" which says "Qian knows the beginning." Qian is only concerned with the beginning and does not fall into the realm of form and numbers. The "covering all the ways of the world" mentioned in the "Great Treatise" includes exhausting the numbers of Heaven, determining the images of the world, communicating the aspirations of people, achieving the affairs of the world, deciding the doubts of the world, and using divination tools like yarrow stalks to guide the daily lives of the people, all of which are included in this system of numbers.

坎子一，艮丑二寅三，震卯四，巽辰五巳六，離午七，坤未八申九，兌酉十，乾戌亥無數。子午南北至卯酉春秋分，寒暑往來，日月出入，先天咸無，後天乾無，皆以無出有。此《易》數之精義入神，《易》道之廣大悉備，皆在此八卦成列之時位象數。

The specific arrangement is as follows: Kan is placed at the center of the north and paired with Zi, receiving the number one; Gen spans the positions of Chou and Yin, with Chou receiving the number two and Yin receiving the number three; Zhen is placed at the center of the east and paired with Mao, receiving the number four; Xun spans the positions of Chen and Si, with Chen receiving the number five and Si receiving the number six; Li is placed at the center of the south and paired with Wu, receiving the number seven; Kun spans the positions of Wei and Shen, with Wei receiving the number eight and Shen receiving the number nine; Dui is placed at the center of the west and paired with You, receiving the number ten; Qian spans the positions of Xu and Hai, but is not assigned a number. Zi is at the center of the north, and Wu is at the center of the south, corresponding to the winter solstice and summer solstice; Mao is at the center of the east, and You is at the center of the west, corresponding to the spring equinox and autumn equinox. The coming and going of cold and heat, the rising and setting of the sun and moon all turn at these four points. The northwest position is not assigned a number in the Earlier Heaven arrangement (in the Earlier Heaven arrangement, the northwest belongs to Gen, which is already missing a number), and in the Later Heaven arrangement, Qian is not assigned a number. Both are generated from 'nothing' to create 'something'. The precision and subtlety of the numbers in the Book of Changes, and the comprehensiveness and vastness of the Way of the Book of Changes, all lie in the coordination of time, position, image, and number when the Eight Trigrams are arranged in sequence.

宋後言《易》，先別門戶，爭道統，宗宋者以老莊之說為異端，宗漢者以先天卦位為不經，而《易》遂無從言矣。程傳號為易學正宗，而程子《自序》，謂予所傳者辭也，冀學者由辭以得其意。然《彖》、《象》十翼之辭，無一辭一字，不由象數而來。舍象數而言辭，辭烏從得哉！此圖之數，前人所未言。清季青田端木鶴田氏始創為之圖，簡要精當，足與經傳相參證。與舊有諸圖會而通之，不但於數理之要領可得，而古今來占筮推步之本源，悉在於是矣。

After the Song dynasty, those who discussed the Book of Changes usually began by distinguishing schools of thought and competing for the transmission of the Way. Those who revered Song learning condemned the interpretations based on Laozi and Zhuangzi as heretical, while those who revered Han learning considered the Earlier Heaven hexagram arrangement to have no support in the classics. As a result, the Book of Changes became difficult to discuss. Cheng Yi's Yichuan Commentary on the Changes is claimed to be the orthodox interpretation of the Book of Changes, but in his own preface, Chengzi said that what he passed down was only the statements of the hexagram lines, hoping scholars would understand the meaning through the words. However, the texts of the Commentary on the Judgment, the Image Commentary, and the Ten Wings all come from the principles of images and numbers. If one ignores images and numbers and talks only about the statements, where would the basis of the statements come from? The numbers arranged in this diagram were never discussed by previous generations. It was not until the late Qing dynasty that a person from Qintian, Zhejiang, named Duanguohu (whose courtesy name was Hetian) first drew this diagram, which is clear and accurate enough to be verified with the classics. By integrating this diagram with the existing various diagrams of the Book of Changes, not only can the principles of numbers and reasoning be grasped, but also the origins of divination and astronomical calculations throughout history can be found within it.

既明方位象數，而氣可得言矣。氣不可見，顯之以象，定之以數，而驗之以候。五日為一候，故亦曰卦候。天地陰陽之消息，日月寒暑之往來，萬物生成，變化動靜，莫不先見乎氣。《彖》、《象》、《繫辭》，皆隱合氣候而未明言。

Once the directions and numerical principles have been explained, we can then discuss "qi." Qi is invisible and intangible, and can only be revealed through hexagrams, fixed by numbers, and verified by seasonal phenomena. The ancient calendar divided five days into one "hou," so this system of study is also called "hexagram and seasonal phenomena." In the universe, the waxing and waning of yin and yang, the movement of the sun and moon, the coming and going of cold and heat, and the generation, transformation, and activity of all things—all of these first manifest themselves through qi. The Commentary on the Judgment, the Image Commentary, and the Great Treatise actually contain the principles of climatic changes everywhere, though they do not explicitly state them.

言氣者莫著於京房，遂相傳京房卦氣，實非京氏所創也。周公之時訓與《月令·夏小正》，皆以象數為氣候之準，無不與圖書卦象契合。京氏特整齊而排比之，以六十卦直日用事，以風雨寒溫，定占候災變，或為京房之法耳。

The most famous explanation of the concept of "gu qi" (divinatory climate) comes from Jing Fang of the Western Han dynasty, leading to the tradition of "Jing Fang's Gu Qi." However, this system was not actually created by Jing Fang. It is said to have originated from the Duke of Zhou's "Shi Xun" (a text known as "The Lost Book of Zhou: Shi Xun Jie," which lists seventy-two seasonal signs), as well as from the "Li Ji: Yue Ling" and the "Da Dai Li Ji: Xia Xia Zheng." These texts used numerical patterns and symbolic correspondences to set standards for climate, and every part of them aligned with the Yellow River Chart, the Luo Writing, and the hexagram images. Jing Fang merely organized and arranged existing materials, arranging the sixty hexagrams to take turns governing each day, and then using actual weather conditions such as wind, rain, cold, and warmth to determine seasonal signs and omens of calamities. This method of divination might be the actual original contribution of Jing Fang.

黃粵洲曰：“上繫七爻，起中孚‘鳴鶴在陰’，十一爻起於咸‘憧憧往來’。”卦氣從中孚至井，八十九陽，九十一陰。咸至頤，八十九陰，九十一陽，與《繫傳》恰合。而孔子復於咸言“日月寒暑往來，陰陽屈伸”，是必三代已有此卦象氣候，孔子故於《繫傳》及之，否則安有如此之巧合乎？特著錄其圖。非僅為占卜之用也。

Huang Yuezhou says: The seven line statements cited in the Upper Transmission of the Great Treatise come from the first one in Zhongfou, Nine in the Second, which says "a crane calls in the shade"; the eleven line statements cited in the Lower Transmission start with the first one in Xian, Nine in the Fourth, which says "vague coming and going." According to the arrangement of the hexagram qi, from Zhongfou to Jing, there are eighty-nine yang lines and ninety-one yin lines; from Xian to Yi, there are eighty-nine yin lines and ninety-one yang lines. The two sections exactly reverse yin and yang, matching perfectly the order in which the Great Treatise cites these two hexagrams. Moreover, Confucius also mentions in the lower section of Xian "when the sun goes down, the moon comes up; when cold departs, heat comes" and talks about the mutual influence of yin and yang expanding and contracting. This shows that the study of hexagram patterns corresponding to climate was already present in the Xia, Shang, and Zhou dynasties. Confucius could therefore naturally include it in the Great Treatise; otherwise, how could such a coincidence occur? Therefore, this hexagram qi diagram is specially recorded—it is not merely for divination purposes.

京氏以六十卦當周天三百六十五度四分度之一，每卦值六日七分，故又名為六日七分術。坎離震兌為後天四正，別立為監司，分管二十四氣，不入六十卦之內。六十卦之中，更有復臨泰大壯夬乾姤觀否遁剝坤十二卦為闢卦，分領十二月，每月約五卦。始六日曰公卦，次闢卦，次侯卦，則值月中節氣交界。次大夫，次卿，以畢一月。周而復始。

Jing Fang used the sixty trigrams to correspond with the 365 and 1/4 degrees of the celestial cycle, with each trigram governing six days and seven parts (each day divided into eighty parts), so this method is also called the "Six Days and Seven Parts Method." Kan, Li, Zhen, and Dui are the four cardinal trigrams of the Later Heaven Trigrams, and they are drawn out separately to serve as "Supervisors," each responsible for a quarter of the twenty-four solar terms, and they are not included in the sixty trigrams. From the sixty trigrams, twelve trigrams—Fu, Lin, Tai, Da Zhuang, Guai, Qian, Gou, Guan, Po, Duan, Bo, and Kun—are selected as "Divine Trigrams" (also called Royal Trigrams), each governing one of the twelve months, with each month approximately corresponding to five trigrams. The order within a month is: the first six days are called "Common Trigrams," followed by the "Divine Trigrams," then the "Marquis Trigrams," which correspond to the transition points of the solar terms in the middle of the month; then the "Minister Trigrams," and finally the "Minister of State Trigrams." The month is thus fully arranged, and the cycle repeats.

卦氣起冬至，為中孚之二爻，至七日復卦，十二日復卦畢，第十三十四十五日則屯之內卦當之，約兩卦半當一氣，約十五爻當十五日也。小寒自屯四起，至謙與睽，亦兩卦半也。茲分舉其例如下：

The hexagram energy begins to count from the winter solstice. On the day of the winter solstice, it falls exactly on the second line of the hexagram Zhongfū (Middle Trust). Counting seven days, it enters the hexagram Fu (Return), and by the twelfth day, the hexagram Fu has finished. On the thirteenth, fourteenth, and fifteenth days, the three lines of the lower trigram of the hexagram Tun (Obstruction) take over. Thus, approximately every two and a half hexagrams correspond to a solar term, and about fifteen lines correspond to fifteen days. By the time of Xiaohan (Minor Cold), it starts from the fourth line of the hexagram Tun, passing through Qian (Humility) and Kui (Strife), again covering two and a half hexagrams. Below are examples illustrating this:

或謂京房卦氣出《易緯》，不足以望先天。然按之《繫辭》，既有中孚與咸之前徵，而驗之氣候，又與《時訓》、《夏小正》合，而邵子河洛先天諸數亦不能不採用其說。圖雖別用乾坤坎離，而河洛化工，仍取坎離震兌。蓋實始於《連山》曆法，四監周度。惟首起艮卦，然則京學之自來遠矣。

Some people say that Jing Fang's theory of the hexagram qi comes from the Han dynasty's "Yi Wei," which is not of the same level as the Earlier Heaven school. But when compared with the "Great Treatise," there are already two hexagrams, Zhongfou and Xian, as precedents. When verified against actual climate conditions, it also aligns with the "Shi Xun" and "Xia Xiaozheng." Even Shao Yong's derivation of the Yellow River Chart and Luo Writing and the numbers of the Earlier Heaven system could not avoid using this approach. Although Shao Yong's diagram uses the four hexagrams Qian, Kun, Kan, and Li as the four cardinal directions, when discussing the creative power of the Yellow River Chart and Luo Writing, he still refers to Kan, Li, Zhen, and Dui. This shows that this method actually originates from the Lianshan calendar system, which uses four hexagrams as "jian" (supervisors) to divide the entire celestial circle, except that Lianshan starts with Gen. Thus, the origin of Jing's school of thought is quite ancient.

闢卦主一年十二月，自冬至七日後起，陰陽往復，周而復始。朱子曰：“是當以一爻分三十分，陰陽進退日一分。如陰剝每日剝三十分之一，一月方剝得盡。陽長每日長三十分之一，亦一月方長得成。

The twelve trigrams of the twelve lunar months govern the twelve months of the year. Starting from the seventh day after the winter solstice, yin and yang alternate, continuing in a cycle. Zhu Xi said that each line should be further divided into thirty parts. Yin and yang advance or retreat by one part each day. For example, when yin removes yang, it removes one part of the line each day, taking a whole month to remove the entire line. Similarly, yang grows by one part each day, also taking a month to complete a full line.

故復之一陽，不是頓然便生，乃是自坤卦中積來。從小雪後一日生一分，竟大雪共三十日，生三十分，然後成冬至之一陽。姤之陰亦生於小滿，一日一分，積三十日，然後成夏至之一陰。觀此知陰陽絕續之際，果無一息之間斷也。”

Therefore, the yang line in the hexagram "Fu" does not suddenly appear only at the winter solstice, but rather accumulates bit by bit from the pure yin hexagram "Kun": starting after Minor Snow, one part is generated each day, passing through Major Snow, accumulating thirty parts over thirty days, and only at the winter solstice does it form a complete yang line. Similarly, the yin line in the hexagram "Gou" also begins to form after Minor Full, with one part generated each day, accumulating thirty parts over thirty days, and only at the summer solstice does it become a complete yin line. From this we can see that the moment of alternation between yin and yang is continuous without even a single breath's interruption. All of this is what Master Zhu said.

列子曰：“一氣不頓進。”又曰：“天道密移，疇覺之哉！”聖人作《易》，仰觀俯察，知天地陰陽之運行消息甚微，人無從覺，故以懸象著明之日月，分畫八卦，象陰象陽，以《易》道示人，天道斯昭昭矣。更以六十四卦，合周天之度，自疏而密，由略而詳。由一年十二月，分日分時分刻，以逮秒忽之微，均可顯之以象，推之以數，豈但為吉凶占卜之用哉！

The "Liezi" says: "One breath does not advance all at once." A single breath does not reach its full extent in one step. It also says: "The way of heaven moves secretly, who can perceive it?" The way of heaven quietly shifts in the background, who can notice it? The sages composed the "Yi Jing" by observing the heavens above and examining the geography below. They understood that the movement and change of yin and yang in heaven and earth are extremely subtle, so subtle that people cannot feel them. Therefore, they took the words from the "Great Treatise" that "the most manifest of all celestial phenomena is the sun and moon," and used the sun and moon as a standard to divide the Eight Trigrams. They used a yang line to represent yang and a yin line to represent yin, thus presenting the way of the "Yi Jing" to people, making the way of heaven clearly visible. Further, they used the sixty-four hexagrams to match the degrees of the celestial cycle. Starting from the broad to the detailed, from the general to the specific: from the twelve months of a year, down to days, hours, moments, and even to the extremely fine units of seconds and instances, all can be displayed through images and calculated through numbers. How could this be merely for divining fortune and misfortune?

聖功王道基於是，百姓日用宥於是。彼自絕於天而言人者固背道，舍人以言天者，豈知道哉！孔子之《易》，明天地人三極之通，而齊之於木道(見於風雷益《彖傳》“木道乃行”。古今言《易》者均未注意，而道家亦由之而不知致。《易》道大用始終不明，可慨也夫！)。坎離秉天地之中，震兌劑陰陽之和，以成位育之功。釋道二教，闡咸恆之義，裁成輔相，協乎泰否，所以皆範圍於《易》數之內，而莫能外乎！進象數而言氣精微之蘊，更非潛心玩索，不能會其通也。

The achievements of sages and the governance of emperors are all based on this principle, and the daily lives of common people are also included within its scope. Those who ignore heaven and talk only about human affairs clearly deviate from the Way; conversely, those who ignore human affairs and talk only about heaven do not truly understand the Way. Confucius' transmission of the Book of Changes explains that heaven, earth, and humanity are interconnected, and unifies them under the concept of "wooden way" (this is stated in the Commentary on the Judgment of the Hexagram 41, "Yi" (Benefit), "the wooden way is now in motion"). Throughout history, those who have interpreted the Book of Changes have not paid attention to the fact that Daoism constantly uses this principle without understanding its underlying reasons. The greatest function of the Way of the Book of Changes has never been clearly explained, which is truly regrettable. The hexagrams Kan and Li embody the central positions of heaven and earth, while Zhen and Dui regulate the harmonious balance of yin and yang. Together, they achieve the effect described in the Zhongyong (Doctrine of the Mean), "heaven and earth are in their proper places, and all things flourish." The teachings of Buddhism and Daoism actually expound the meanings of the hexagrams Xian and Heng. Their practices of "completing the way of heaven and earth and assisting in their suitability" do not go beyond the scope of the hexagrams Tai and Pian. Therefore, both religions are encompassed within the numerical system of the Book of Changes and cannot escape from it. As for further exploring the subtle implications of "qi" based on the imagery and numbers, one must first calm the mind and repeatedly contemplate it to fully grasp and integrate it.

按：一卦值六日，共三百六十日，而歲度周，尚餘五日四分日之一。每日以八十分計，五日四分日之一，共得四百二十分，每卦應得七分，故合計六日七分，一卦始畢。五日為一候，三候成一氣，約一氣盡十六爻，為兩卦又四爻。是每月五卦，又盈兩爻也。故卦氣起中孚之二爻。節氣有長短，卦爻亦有盈縮。此揚子雲《太玄》所以分七百二十九贊，以兩贊當一日，以當一歲三百六十四日半，而更以立踦贏二贊，以為坤縮也。

According to this, one hexagram corresponds to six days, and sixty hexagrams total three hundred and sixty days, which completes the measure of one year, with an additional five and one fourth days. If each day is divided into eighty parts, then five and one fourth days amount to four hundred and twenty parts. Dividing these among the sixty hexagrams, each hexagram receives seven parts. Thus, altogether it amounts to six days and seven parts, which makes one hexagram fully accounted for. Five days make a "候" (period), and three periods form a solar term. A solar term roughly uses up sixteen lines, which is two hexagrams and four lines. Therefore, in addition to the five hexagrams per month, there are two more lines, so the starting point of the hexagram energy does not fall on the first line of the Zhongfou hexagram but on its second line. Since solar terms vary in length, the distribution of hexagram lines also varies in expansion and contraction. This is precisely why Yang Xiong (styled Zi Yun) divided his work "Tai Xuan" into seven hundred and twenty nine "zan" (praise): two zan correspond to one day, which exactly matches the three hundred and sixty four and a half days of a year. Additionally, he established two more zan, "qi" and "ying", to account for the remaining days, corresponding to the "contraction" of the Earth element.

卦氣起《中孚·九二》“鳴鶴在陰”。鶴陽鳥也，居漢陰地，陽生於陰之義也。終於頤，“頤者養也”，歸養中宮，至中孚復出。斯造化之機軸。孔子贊《易》，以人事言天道，故贊《中孚·九二》曰“天下應之”，曰“天下之樞機”，可謂天人合一。冬烘先生以附會兩字抹煞之，吾無言矣。

The starting point of the hexagram qi is set at the line "The cry of the crane in the shade" from the hexagram Zhongfu, line nine two. The crane is a yang bird, yet it perches by the water in a shady place, which corresponds to the meaning of the winter solstice when the first yang emerges from the extreme yin. The end of the hexagram qi is at the hexagram Yi. The "Sequence of Hexagrams" says "Yi means nourishment," indicating that the qi returns to the central palace for nurturing, and once it is fully nourished, it re-emerges from Zhongfu. This is the axis of the cycle of creation and transformation. Confucius explained the Yi in terms of human affairs to explain the heavenly way. In the "Great Treatise," when explaining Zhongfu, line nine two, he said "It responds from a thousand miles away," and also said that words and deeds are "the pivot of the gentleman." This can be considered an explanation of the unity of heaven and humanity. Those迂腐 old gentlemen merely dismiss it with the two words "forced interpretation," and I have nothing more to say.

日行與天度每不相及，因有歲差。東晉虞喜云：“五十年退一度。”何承天云：“百年退一度。”隋劉約云：“七十五年退一度。”唐僧一行又以八十三年退一度，許衡郭敬皆謂六十六年有餘退一度，較前說為近。

The sun's annual movement differs slightly from the full circle, thus causing the phenomenon known as "precession of the equinoxes." Yu Xi of the Eastern Jin dynasty said that the sun would regress by one degree every fifty years. He Chengtian of the Southern Song dynasty claimed it would regress by one degree every hundred years. Liu Zhuo of the Sui dynasty (originally written as "Liu Yue") stated it would regress by one degree every seventy-five years. The Buddhist monk Yixing of the Tang dynasty proposed that it would take eighty-three years for the sun to regress by one degree. Xu Heng and Guo Shoujing of the Yuan dynasty (originally written as "Guo Jing") both believed that the sun would regress by one degree in about sixty-six years, which is closer to actual measurements than the previous views.

鄭氏《易譜》引環中子說曰：“周天三百六十五度四分度之一，是正數也。”邵子《皇極》曰：“三百六十五度二十五分七十五秒(邵子以一度作百分，京氏以一日作八十分，故其數異。)。”其二十五分即四分度之一矣，又另多七十五秒，是天過正數外七十五秒也。而歲周止得二百六十五日二十四分二十五秒，是日不及正數二十五秒也。假以天所多七十五秒，補日所少二十五秒，作百秒為一分，則天恰合正數，日亦恰足正數矣。

The Zheng family's "Yi Pu" cites the words of Huanzhongzi, saying that the entire circle of the sky is 365 and 1/4 degrees, which is a standard number, also called the "correct number." Shao Yong in his "Huang Ji Jing Shi" gives a more detailed account: 365 degrees, 25 minutes, and 75 seconds. (Shao Yong divides one degree into 100 parts, while Jing Fang divides one day into 80 parts, so their numbers appear different.) In Shao's calculation, the 25 minutes correspond to a quarter of a degree; in addition, there are 75 seconds more, indicating that the actual movement of the sky exceeds the standard number by 75 seconds. However, the actual cycle of a year is only 365 days, 24 minutes, and 25 seconds (the original text says "265 days," which is likely a mistake for "365 days"). This is 25 seconds less than the standard number. In other words, the sky moves a little more, while the day moves a little less, and the two do not align. If the 75 seconds that the sky moves extra are used to make up for the 25 seconds that the day is short, and then 100 seconds are combined to form one minute for overall calculation, then the sky exactly matches the standard number, and the day also exactly makes up for the standard number—thus the sky and the day each return to their correct positions, and the calculation of the precession of the equinoxes has a common basis.

今乃日止二十四分，比天二十五分為欠一分又二十五秒，比天七十五秒為欠五十秒，故天行餘一分五十秒也。然則日之於大，每年退一分五十秒，十年退十五分也。六十年則退九十分，再加六年，又退九分，是六十六年，其退九十九分，是一度尚欠一分。以每年一分五十秒計之，則一分當八個月，便是六十六年零八個月，即退天一度也。曆法今密於古，當詳求之，以定卦值星度之位。庶數自密合，無毫釐釐之差。於萬事萬物之動靜吉凶，胥可以是準之矣。

Nowadays, the sun has only twenty-four parts, which is one part less than the sky's twenty-five parts. Additionally, considering the difference in seconds, the sun is short by fifty seconds compared to the sky's excess of seventy-five seconds. Therefore, the sky moves one part and fifty seconds more than the sun each year. Continuing this calculation: the sun lags behind the sky by one part and fifty seconds each year. After ten years, it lags by fifteen parts; after sixty years, it lags by ninety parts. Adding six more years, it lags by nine parts, totaling sixty-six years of lagging by ninety-nine parts. This is one part short of a full degree, with each degree being one hundred parts. Calculating the remaining one part at a rate of one part and fifty seconds per year, this remaining part corresponds to about eight months. Therefore, accurately speaking, it takes sixty-six years and eight months for the sun to lag behind the sky by one degree, which exactly matches the previous statement by Xu Hong and Guo Shoujing that "after more than sixty-six years, the sun lags by one degree." Today's calendar is more precise than ancient ones, so we should carefully calculate this to determine the star degrees corresponding to each trigram. In this way, the numbers will naturally align precisely, without any deviation, and the movements, stillness, auspiciousness, and misfortune of all things can be accurately determined.

萬氏彈峰曰：“乾附於坤，坤歸於乾。坤之游魂乾仍歸乾，坤仍歸坤，坤仍歸坤，謂之歸魂。”六子互變，震巽二長，乃四孟月之主。五爻變後退歸四位，震附於巽，巽附於震為游魂。震仍歸震，巽仍歸巽為歸魂。

In the Ming dynasty, Wan Tingyan (pen name: Tanfeng) said: When the trigram Qian changes to its wandering soul form, it attaches to Kun; when the trigram Kun changes to its returning soul form, it returns to Qian. In the wandering soul form of the trigram Kun, Qian still belongs to Qian and Kun still belongs to Kun, which is called "returning soul" (the original text has a repeated character error). The six sons trigrams also change in this way: Zhen and Xun are the elder son and elder daughter, governing the four first months, that is, the first, fourth, seventh, and tenth months. After a trigram changes from the first line up to the fifth line to become the fifth generation trigram, it no longer continues to change upwards, but returns to the fourth line to change into a wandering soul form. Thus, the wandering soul of the Zhen trigram attaches to Xun, and the wandering soul of the Xun trigram attaches to Zhen. Then, when it changes further down to the returning soul form, Zhen still belongs to Zhen and Xun still belongs to Xun.

坎離二中，乃四仲月之主。五爻變後，退歸四位。離附於坎，坎附於離，為游魂。離仍歸離，坎仍歸坎，為歸魂。坎離之游魂在乾坤，乾坤之游魂在坎離。此四正互換之卦。艮兌二少，乃四季月之主。五爻變後，退歸四位。艮附於兌，兌附於艮，為游魂。艮仍歸艮，兌仍歸兌，為歸魂。艮兌之游魂在震巽，震巽之游魂在艮兌。此四隅互換之卦也。此正《說卦》“神也者”一章，去乾坤而言六子之義，乾坤主一歲之運，一卦管一月。六子為四時之主，一卦管十日。月有值月之卦，日月值日之卦，亦理數自然也。

The trigrams Kan and Li represent the middle son and middle daughter, governing the four middle months, which are the second, fifth, eighth, and eleventh months. When the fifth line changes, it returns to the fourth line and becomes a wandering soul. Thus, the wandering soul of the Li trigram attaches to Kan, and the wandering soul of the Kan trigram attaches to Li. When returning to its original state, Li still belongs to Li, and Kan still belongs to Kan. The wandering souls of the Kan and Li trigrams fall upon the Qian and Kun trigrams, and the wandering souls of the Qian and Kun trigrams fall upon the Kan and Li trigrams. This is the mutual exchange between the four cardinal trigrams. The trigrams Gen and Dui represent the young son and young daughter, governing the four seasonal months, which are the third, sixth, ninth, and twelfth months. Similarly, when the fifth line changes, it returns to the fourth line and becomes a wandering soul. The wandering soul of the Gen trigram attaches to Dui, and the wandering soul of the Dui trigram attaches to Gen. When returning to its original state, Gen still belongs to Gen, and Dui still belongs to Dui. The wandering souls of the Gen and Dui trigrams fall upon the Zhen and Xun trigrams, and the wandering souls of the Zhen and Xun trigrams fall upon the Gen and Dui trigrams. This is precisely the intention of the passage in the "Sayings on the Trigrams" that says, "The divine is the one who subtly governs all things and is spoken of in terms of it," which omits Qian and Kun and focuses solely on the six sons. Qian and Kun govern the great destiny of a year, with one trigram governing a month; the six sons govern the four seasons, with one trigram governing ten days. Thus, there are trigrams that govern the month and trigrams that govern the day. This is naturally the way of the reasoning of numbers. The character "month" in the phrase "day and month values" is likely a mistake for the character "have."

京氏卦氣，出於納甲。八宮世應，皆與卦氣一貫。用八宮納甲之法，而莫名其義，得萬氏著明之。始知其天然之序，不假人為。特錄其圖如下，與下《卦用》章八宮參看。

Jing Fang's theory of hexagram qi is rooted in the concept of Najia. The positions of the world and the responding elements in the eight trigrams are all connected with the hexagram qi. People only use the oral formula of Najia for the eight trigrams without understanding the underlying principles. It was not until Wan Tingyan explained it clearly that people realized this order is naturally generated and not artificially arranged. Therefore, his diagram is specially included here for comparison with the section on the eight trigrams in the next chapter titled "Hexagram Usage."

八卦名位象數氣候既明，而用可得言矣。大用大效，小用小效，大小雖殊，其理則一。《彖》、《象》十翼，皆以明用。而無一辭一字，不根於象數。自象數失傳，專尚夫辭。乃望文生義，以今概古，論愛惡不出六爻之外，言變化限於兩象之中。而《彖》、《象》十翼之大義，不明於世也久矣。

The names, directions, symbolic images, numbers, and climatic associations of the Eight Trigrams have already been explained. Now we can discuss their "application." When applied on a grand scale, it produces great results; when applied on a small scale, it produces small results. Although the scale of application differs, the underlying principle remains the same. The Commentary on the Judgment, the Image Commentary, and the Ten Wings were all written to explain this "application," and every word and sentence is rooted in the symbolic images and numbers. Since the symbolic images and numbers have been lost, scholars have focused only on the textual expressions, leading them to misunderstand the original meanings by applying modern ideas to ancient texts. Discussions of love and hatred remain confined within the scope of the six lines, and explanations of change are restricted within the two trigrams above and below. As a result, the true meaning of the Commentary on the Judgment, the Image Commentary, and the Ten Wings has remained obscure for a long time.

朱子《本義》，遂以《易》為聖人教人卜筮之書，以占卜為《大易》之本義。後之學者，既宗程朱，又蔑視數學小道而不屑言，是欲渡而去其楫，卒致占卜之用亦無可徵驗，反不若壬、遁、火珠之術為足憑。《易》道之大，乃盡失其用。舉世徒震其名，視為神秘杳渺而莫敢問津。嗚呼！是誰之過哉！

Zhu Xi wrote The Original Meaning of the Zhou Changes, and he frankly regarded the Book of Changes as a book that sages used to teach people how to divinate. He regarded divination as the original meaning of the Great Change. Later scholars, respecting both Cheng Yi and Zhu Xi, looked down upon the methods of figures and numbers as an inferior path, and did not even mention them. This is like trying to cross a river but first throwing away the oars, resulting in not being able to verify even the function of divination. Instead, methods such as the Six Nines, Dun Jia, and The Forest of Fire Pearls proved more reliable. The Way of the Book of Changes is so vast, yet it has completely lost its function. The whole world is only frightened by its reputation, regarding it as mysterious and distant, and dare not inquire further. Alas, who is to blame for this?

行遠自邇，登高自卑，乾簡坤易，古聖已詔我矣。近取諸身，簡之至也。遠取諸物，易之至也。故又曰：《易》簡而天下之理得矣。天下之理得，而用無不彰。其為用焉，孰大於是？京氏八宮世應飛伏之說，經學家素鄙為術數，而不入於經傳。而其為用簡易，深合於乾坤之變化。

To travel a long distance, one must start from a short step; to climb a high mountain, one must begin from a low place. The Creative (Qian) takes "simplicity" as its virtue, and the Earthly (Kun) takes "ease" as its virtue. Ancient sages have already told us this principle. "Taking from the body nearby" is simplicity to its extreme; "taking from objects afar" is ease to its extreme. Therefore, the Great Treatise says: "Ease and simplicity enable the principles of the world to be understood." Once the principles of the world are grasped, their applications naturally become evident. When it comes to "application," is there anything greater than this? Jing Fang's theory of the eight palaces, the World and Response Lines, and the flying and hidden lines has long been looked down upon by scholars as numerology and not allowed into the classics. However, in practice, it is simple and easy to apply, deeply in harmony with the principles of the Creative and Earthly.

朱子知其用，以囿於世故，不敢昌言，僅取八宮世應歌訣，列《本義》之前，亦與隱名注《參同契》。同一苦心也。程子《易傳》，雖自稱尚辭，亦不能廢陰陽世應之例。術家專取八宮身世遊歸飛伏之用，而又不明乾坤簡易之理，逐末忘本，與經生之有體無用，同一蔽也。

Zhu Xi actually understood its usefulness, but due to the constraints of conventional beliefs, he dared not openly declare it, and only listed the verses on the eight palaces and their corresponding lines at the beginning of the "Original Meaning of the Zhou Changes"; this was the same careful intention as when he concealed his real name to comment on the "Compendium of the Three Traditions of the Zhou Changes." Although Cheng Yi's "Commentary on the Changes by Yichuan" claimed to focus on literary expression, it ultimately could not abandon the framework of yin and yang and the lines of world and response. Conversely, the numerological scholars specialized in using the positions of the body, the world, the wandering soul, the returning soul, and the flying and hidden lines from the eight palaces, yet they did not understand the fundamental principle of simplicity and ease in the trigrams of heaven and earth, focusing on the superficial while forgetting the essential. This is actually the same kind of confusion as that of the scholars of the classics, who have the form but no practical use.

頻年講習，博考周諮，始知三《易》之卦爻象數，同源共貫。京氏之學，實遠符《連山》之曆數，近合《周易》之變通。稽諸經傳，證例正多，爰取為立用之準。有精於術數者，更深求之。以推衍《彖》、《象》十翼之辭，其相得有合者，必不止如吾之所知。知無盡而無窮，占卜云乎哉！

I have studied for many years, extensively examined, and sought advice from many sources, only then realizing that the hexagrams, lines, images, and numbers in the three books of divination, the Lianshan, Guicang, and Zhouyi, all originate from the same source and are interconnected. Jingfang's teachings, when viewed from a distant perspective, align with the calendrical calculations of the Lianshan, and when viewed from a near perspective, they conform to the principle of change in the Zhouyi. By comparing them with the classic texts, there are many verified examples, so I take them as the standard for practical application. In the future, if someone skilled in numerology delves deeper, using them to deduce the words of the Commentary on the Judgment, the Image Commentary, and the Ten Wings, there will certainly be more points of agreement than what I now know. Thus, the truths to be known are boundless, far beyond the limits of the two words "divination."

《易》之大用，孔子《繫傳》，言之詳矣。特後儒類以文字釋之，致孔子之徵言精義，皆忽略讀過，而莫名其蘊蓄宏深之妙。果能以孔子之言，一一以八卦之象數證之，則一字一義，無不各有體用之所在，亦無不各與象數相發明，而“為用不窮”一語決非以空言了之者也。

The great application of the Book of Changes is explained in detail by Confucius in the Great Treatise. However, later Confucian scholars have generally interpreted it through textual analysis and word meanings, leading to Confucius' subtle words being read superficially, and no one being able to grasp the profound and subtle meanings contained within. If we could truly use the images and numbers of the Eight Trigrams to verify every sentence of Confucius, then each word and meaning would have both form and function, and each would be mutually illuminating with the images and numbers. The statement in the Great Treatise that "its application is inexhaustible" would not be a mere superficial phrase.

八卦之用，皆本於乾坤，後天坎離代乾坤之用，而六十四卦之用，莫不由乾坤而生。孔子曰：“剛柔相摩，八卦相蕩。鼓之以雷霆，潤之以風雨。日月運行，一寒一暑。乾道成男，坤道成女。”天地萬物之用，備於是矣(雷霆震與艮風雨巽與兌皆相反之卦也，日月坎離與乾坤皆相對之卦也。詳玩其象，八卦之用可悟矣。)。

The use of the Eight Trigrams originates from Qian and Kun. In the Later Heaven arrangement, the trigrams Kan and Li take over the functions of Qian and Kun, yet the use of the sixty-four hexagrams all comes from Qian and Kun. Confucius said in the Great Treatise: the strong line and the flexible line rub against each other, the Eight Trigrams move and interact with each other, thunder is used to stir them, wind and rain are used to nourish them, the sun and moon alternate in their movement, thus producing the alternation of cold and heat. The way of Qian gives rise to male, and the way of Kun gives rise to female. The functions of heaven and earth and all things are fully contained in these words. Thunder refers to the trigram Zhen, which is opposite to Gen; wind and rain refer to the trigram Xun, which is opposite to Dui; sun and moon refer to Kan and Li, which are opposite to Qian and Kun respectively. These sentences actually go through the Eight Trigrams by means of the relationships of 'opposition' and 'reciprocity'. If one carefully examines these trigrams, one can understand their functions.

而又承之以“乾知大始，坤作成物”。《易》之大用，孰逾於是？故乾用九，坤用六。六十四卦，皆乾坤之用，皆九六之用。乾無方體用不可見，故乾九之用，用於坤六。《傳》曰：“顯諸仁，藏諸用。”乾顯而坤藏，惟藏而用乃顯焉。乾坤象也，九六數也。象數不明，用何由顯？為圖如左，餘卦類推。

Then Confucius added another sentence: "The Creative is aware of the great beginning, and the Receptive forms the completed things." Is there any greater use in the Book of Changes than these two sentences? Therefore, the Creative has "All Nines" and the Receptive has "All Sixes." All sixty-four hexagrams are the use of the Creative and the Receptive, and also the use of the numbers nine and six. The Creative has no position and no form, and its use is invisible. Therefore, the use of nine in the Creative must be manifested through the six of the Receptive in order to become visible. The Great Treatise says: "Manifest it in benevolence, conceal it in use." The Creative is the one that manifests, and the Receptive is the one that conceals. Only by first concealing can use be revealed. The Creative and the Receptive are the images, and nine and six are the numbers; if the relationship between images and numbers is not understood, how can use be revealed? Here is the diagram on the left, and the rest of the hexagrams can be inferred in the same way.

端木鶴田曰：“乾坤天地一二，始子復一，丑臨二。而臨二坎爻，其初復一震爻。天地一二子丑數造始(坎震屯)，一主日，二主月。子復一交午七數，為復‘七日吉’。丑臨二交未八數，為臨‘八月凶’。故七八正當子丑一二正位。《易》，七八數之正也，九六數之變也。七吉以七而九進為用，午進而七數之正。進而用九數之變，乾用九是也。八凶以八而六退為用，未退而八數之正，退而用六數之變，坤用六是也。六坎數，九震數，皆天地一二造始數。乾坤卦用七八正爻用九六變，此其數是也。”

Endumu Guo Hu says: Qian and Kun represent Heaven and Earth, paired with the initial numbers one and two. In the twelve trigrams of the Great Break, the month of Zi (rat) corresponds to the hexagram Fu, paired with one; the month of Chou (ox) corresponds to the hexagram Lin, paired with two. The number two paired with Lin is exactly the number of lines in Kan, while the number one paired with Fu is exactly the number of lines in Zhen. When Kan and Zhen are stacked together, they form the hexagram Tun. The numbers one and two of Heaven and Earth are thus established in the positions of Zi and Chou, initiating all things. One governs the day, two governs the month. The hexagram Fu, paired with one in the Zi position, intersects with the number seven in the opposite position Wu, so the statement of the Fu hexagram says, "After seven days it returns," which is considered auspicious. The hexagram Lin, paired with two in the Chou position, intersects with the number eight in the opposite position Wei, so the statement of the Lin hexagram says, "By the eighth month there is misfortune." This shows that seven and eight are exactly in their original positions of Zi and Chou, one and two. In the Book of Changes, seven and eight are the normal numbers, while nine and six are the abnormal numbers. Seven is auspicious because it progresses from seven to nine, using nine as its number: the position of Wu advances, first reaching seven, the normal number, then further using nine, the abnormal number. The "use of nine" in Qian is exactly this. Eight is inauspicious because it retreats from eight to six, using six as its number: the position of Wei retreats, first reaching eight, the normal number, then further using six, the abnormal number. The "use of six" in Kun is exactly this. Six is the number of Kan, and nine is the number of Zhen, both belonging to the numbers of Heaven and Earth that initiate all things. The hexagrams Qian and Kun use the normal numbers seven and eight in their line positions, but when they are used, they employ the abnormal numbers nine and six, which is exactly this system of numbers.

晁氏公武曰：“餘有志學《易》，本好王氏，妄謂弼之外，自有名象者。果得京氏傳，而文字顛倒舛訛，不可訓知。迨其服習甚久，漸有所窺，今二十有四年矣。乃能以其象數辨正文字，而私識之曰：是書兆乾坤之二象以成八卦，凡八變而六十有四，於其往來升降之際，以觀消息盈虛於天地之元，而酬酢乎萬物之來者，炳然在日也。

In the Song dynasty, Zhao Gongwu said: I resolved to study the Book of Changes, and originally favored the school of Wang Bi. However, I secretly suspected that there should be another school of study concerning the names and images of the hexagrams. Later, I indeed obtained the Jing's Tradition of the Changes, but the text was disordered and confused, making it difficult to read. Only after repeated study over a long period did I gradually begin to understand its principles. By now, twenty-four years have passed. Now I can use its figures and numbers to correct the text, and I have privately recorded my insights: this book begins with the two trigrams Qian (Heaven) and Kun (Earth), generating the eight trigrams, and through eight successive transformations, forms the sixty-four hexagrams. In observing the movement and changes of the lines within the hexagrams, one can perceive the waxing and waning, fullness and emptiness of the fundamental principles of Heaven and Earth, and thus respond to the coming of all things, with clarity as clear as the sun at noon.

大抵辨三《易》，運五行，正四時，謹二十四氣，志七十二候，而位五星，降二十八宿，其進退以幾，為一卦之主者謂之世。奇耦相與，據一以起二而為主之相者謂之應。世之所位而陰陽之肆者，謂之飛。陰陽肇乎所配，而終不脫乎本，以應顯佐神明者謂之伏。起乎世而周乎內外，參乎本數以紀月者謂之建。終之始之，極乎數而不可窮以紀日者，謂之積。會於中而以四為用，一卦備四卦者，謂之互。

In general, this book distinguishes the three Yis, namely the Lianshan, Guicang, and Zhouyi, and operates according to the Five Phases, regulates the four seasons, carefully observes the twenty-four solar terms, records the seventy-two phases, and arranges the positions of the five planets and the twenty-eight constellations. Among these, the one that becomes the main element of a hexagram according to the subtle movement and change of the lines within the hexagram is called 'Shi'; the one that pairs odd and even numbers, starts from one to generate two, and supports the Shiyao is called 'Ying'; the position where the Shiyao resides, with yin and yang clearly revealed, is called 'Fei'; the yin and yang that arise according to the paired hexagram, ultimately not departing from their original palace, and secretly assisting the divine is called 'Fu'; the one that starts from the Shiyao, covers both the inner and outer hexagrams, and records the months by referring to the numbers of the original palace is called 'Jian'; the one that has a beginning and an end, exhausts its number yet never runs out, and is used to record days is called 'Ji'; and the one that gathers in the middle four lines, uses the fourth line as the main element, and includes four hexagrams within a single hexagram is called 'Hu'.

乾建於甲子於下，坤建於甲午於上。八卦之上，乃生一世之初，分五世之位。其五世之上，乃為游魂之世。五世之初，乃為歸魂之世。而歸魂之初，乃生後卦之初。其建剛日剛節氣，柔日則中氣，其數虛則二十有八，盈則三十有六。其可言者如此。”晁氏之說，可謂挈《京易》之綱領矣。茲分列八宮暨飛伏諸例如下，若應與配位五行六神諸說，詳下《爻位》、《爻數》各章。

The Trigram Qian begins from the lower Jiazi, and the Trigram Kun begins from the upper Jiawu. On top of the eight pure trigrams, the first generation trigram emerges, and then the positions of the five generations trigrams are sequentially divided. Above the fifth generation is the wandering soul generation, and at the beginning of the fifth generation is the returning soul generation. At the beginning of the returning soul generation, the beginning of the next trigram emerges. When starting the calculation, if it is a strong day, it is paired with the solar term; if it is a weak day, it is paired with the intercalary solar term. Its numbers, when deficient, are twenty-eight, and when full, are thirty-six. These are roughly the points that can be explained. The above is what Chao Gongwu said. Chao's discussion can be said to have captured the essence of the Jingshi Yi. Below are the various rules for the eight palaces and the flying and hidden trigrams. As for the concepts of the response line, positioning, the five phases, and the six spirits, they are detailed in the chapters on "Yao Position" and "Yao Number" below.

八純卦各以五行所屬為主，乾金坎水艮土震木巽木離火坤土兌金，所謂進退以幾而為一卦之主者謂之世也。本宮不變，初爻變為一世，至五爻變為五世，上爻六世，即本宮，謂之宗廟不變。初至七世仍以三爻變為游魂，八世下三爻，全復本宮，為歸魂。故二世為地《易》，三四世為人《易》，五六世為天《易》，游魂歸魂為鬼《易》。

The eight pure hexagrams each have their own Five Phases as their main element: Qian belongs to Metal, Kan to Water, Gen to Earth, Zhen to Wood, Xun to Wood, Li to Fire, Kun to Earth, and Dui to Metal. This is what Chao said about "the world" (shi), which refers to the line that becomes the main element of a hexagram according to the subtle movement of advancing and retreating. When the original hexagram remains unchanged, the world is located at the top line. If the first line changes, it becomes the first world hexagram, and so on, changing up to the fifth line to form the fifth world hexagram. If the top line changes, it becomes the sixth world, which returns to the original hexagram, so the top line is called "ancestral temple" (zongmiao) and is fixed as unchanging. Counting from the first line to the seventh change, the third line (i.e., the fourth position) is taken as the changing line to form the "ghost hexagram" (gu yi). When reaching the eighth change, the three lines of the lower trigram return to their original state in the original hexagram, forming the "returning soul hexagram" (gui hun). Therefore, the second world hexagram is called "earthly change" (di yi), the third and fourth world hexagrams are called "human change" (ren yi), the fifth and sixth world hexagrams are called "heavenly change" (tian yi), and the ghost hexagrams are called "ghost change" (gu yi).

乾坎艮震巽離坤兌之序，決非京氏所創。《繫傳》曰：“乾知大始，坤作成物。”雖乾坤對舉，而詳玩後天八卦方位，及六十四卦之次序，所謂“仰以觀於天文，俯以察於地理。天道下濟，地道上行”者，皆足以見八宮之用，即分陰分陽之大義也。

The order of the eight trigrams,乾, 坎, 艮, 震, 巽, 离, 坤, 兑, is certainly not the invention of Jing Fang. The Great Treatise says: "乾 knows the great beginning, 坤 forms things." Although both 乾 and 坤 are mentioned here, when we carefully consider the positions of the Later Heaven Trigrams and the order of the sixty-four hexagrams, it is clear that the reasoning behind the arrangement of the eight trigrams is in line with what the Great Treatise says: "Looking up to observe the heavenly phenomena, looking down to examine the geographical features," as well as "the heavenly way descends and shines brightly, the earthly way is low but ascends." These statements sufficiently reveal the purpose behind the order of the eight trigrams, which is precisely the meaning of "dividing yin and yang."

八卦東震西兌，東西平衡，若地平線。故巽離坤三陰卦，實處於地之上，所謂地道卑而上行也。而乾坎艮三陽卦，皆處於地之下，所謂天道下濟也。上下以震兌為始終，故雷澤歸妹曰“天地大義人終始”者此也。震之始，始於乾，“乾知大始”也。兌之終，終於坤，坤“代終”也。三《易》之卦，爻象皆同，不同者其序耳。八宮之序，或謂出於《連山》，非無所見也。

Among the eight trigrams, Zhen is located in the east and Dui in the west, facing each other east and west to achieve balance, just like a horizon line. Therefore, the three yin trigrams Xun, Li, and Kun are actually situated above this line, which corresponds to the saying "the way of the earth is low but ascends upward." The three yang trigrams Qian, Kan, and Gen are all located below this line, which corresponds to "the way of heaven descends to nourish." The upper and lower parts are connected by Zhen and Dui as their starting and ending points. Thus, the Commentary on the Judgment of the hexagram Guimei (Thunder over Marsh) states "the great principle of heaven and earth" and "the beginning and end of human beings," referring precisely to this. The "beginning" represented by Zhen originates from Qian, meaning "Qian knows the great beginning"; the "end" represented by Dui culminates in Kun, meaning that Kun can "replace the end." The hexagrams of the three collections of the Book of Changes have the same lines and images, differing only in their order. Some people say that the order of the eight palaces comes from Lianshan, and this statement is not without basis.

《周易》雖無八宮之別，而世應仍所不廢。惟《周易》之世應，但以爻論，而京《易》則特重在卦。京氏曰“卦有八世爻分六位，配乎人事，以定吉凶”者，固不僅為占筮言也。《易乾鑿度》曰：“三畫以下為地，四畫以上為天。易氣從下生，動於地之下，則應於天之上。動於地之中，則應於天之中。

The Zhou Changes (I Ching) does not distinguish between the eight palaces, but the system of world and response lines has not been abandoned. The Zhou Changes discusses world and response lines only in terms of lines (yao), while the Jingshi Yi particularly emphasizes the trigrams. Jing Fang said, "Trigrams have eight worlds, lines are divided into six positions, matching human affairs to determine fortune and misfortune." This shows that this system was originally not only for divination. The Yi Wei · Gan Zao Du says: the first, second, and third lines belong to the earth, while the fourth, fifth, and sixth lines belong to the heavens. The energy of the Yi arises from below and moves upward, so if a line moves at the lowest position of the earth, it corresponds to the highest position of the heavens; if a line moves at the middle position of the earth, it corresponds to the middle position of the heavens.

動於地之上，則應於天之上(此以上下二象分天地，故不曾人。人秉天地之氣以生，一身之陰陽之氣亦有感必應。言其精則水火升降，言其粗則脈絡之交布，穴氣之分行。與夫一身外相所表見者，無不各按其位，而上下相應。如人身上部口面耳目間有痣者，下部相應之位亦必有之，毫釐不爽。此上下相應之最顯而易見者也。一卦六爻亦如一身上下相通，如有否隔，即為疵病。天地人物，因無二理也。)。”

The moving line is at the topmost position of the lower trigram, so it should correspond to the topmost position of the upper trigram. Here, only the upper and lower trigrams are used to distinguish heaven and earth, so there is no separate position for humans. Humans receive the qi of heaven and earth to be born, and the yin and yang qi within the body also respond to each other. In terms of the subtle aspect, it is the rising and falling of the water and fire of the heart and kidney; in terms of the obvious aspect, it is the interweaving of meridians and the distribution of qi at acupuncture points. As for all the manifestations on the body's surface, they all correspond according to their respective positions, with upper and lower parts corresponding to each other. For example, if there is a mole on the upper part of the body, such as the mouth, face, ears, or eyes, there must be a corresponding mole on the lower part, exactly the same, which is the most obvious and visible example of upper and lower correspondence. A hexagram with six lines is also like the human body, connecting top to bottom. Once there is an obstruction, it becomes a disorder. Heaven, earth, humans, and things all follow the same principle. The above is from the "Qian Zao Du."

初與四，二與五，三與上，陰應陽，陽應陰，二氣感應以相與，此其正也。蓋天地之氣有終始，六世之位有上下，故《易》始於一(《易》本無體，氣變而為一，故氣從下生也。)，分於二(清濁分於二儀。公武曰：奇偶相與，據一以起二，而為主之相者，謂之應是也。)，通於三(陰陽氣交，人生於中。天地氣通，故三陽成泰，而泰為通。)，交於四，盛於五(二壯於地，五壯於天，故如盛也)，終於上(上則數極，極則反也)。故六爻皆有應，而世取其一。與世對者，則為應也。

The first line corresponds with the fourth line, the second line with the fifth line, and the third line with the top line. Yin goes to respond to Yang, and Yang goes to respond to Yin. The two energies interact and are close to each other, which is the correct example. Because the energies of Heaven and Earth have a beginning and an end, and the six lines have upper and lower positions, the Book of Changes begins with one (the Book of Changes originally has no form; when the energy changes, it becomes one, so it is said that energy arises from below), divides into two (the clear and turbid energies split into the two principles. Zhao Gongwu said: odd and even are paired, and from one comes two. The line that supports the world line is called 'response,' referring to this), connects through three (the energies of Yin and Yang meet, and a person is born in between. The energies of Heaven and Earth connect, so three Yangs arise and form the Tai hexagram, 'Tai' meaning connection), combines at four, reaches its prime at five (the second line is strong in the earth, the fifth line is strong in the heaven, so it is called strong), and concludes at the top line (when the top line is reached, the number has reached its peak, and at the peak it must return). Therefore, each of the six lines has a response, but the world line selects only one among them. The line that is directly opposite the world line is called the response line.

水火既濟，初陽而四陰，二陰而五陽，三陽而上陰，所謂六爻當位、上下皆相應者者也。既濟屬坎宮三世卦，三之應在上。火水未濟，既濟之反也。六爻皆不當位，而上下剛柔相應，屬離宮三世卦應亦在上。

The hexagram Water over Fire, named Ji Ji, has the first line as yang and the fourth line as yin, the second line as yin and the fifth line as yang, the third line as yang and the top line as yin. This is called the six lines each occupying their proper position, with the upper and lower trigrams corresponding in pairs. Ji Ji belongs to the Kan palace's third generation hexagram, with the world (shi) located at the third line, so its corresponding line (ying) falls at the top line. Fire over Water, named Wei Ji, is the reversed hexagram of Ji Ji, with all six lines not in their proper positions, yet the yin and yang lines still correspond in pairs. It belongs to the Li palace's third generation hexagram, with the world (shi) also located at the third line, and the corresponding line (ying) also falls at the top line.

月卦非月建，由世卦生，亦由十二月闢卦生者也。世分陰陽，陽世起子月，陰世起午月，以數不以氣。雖以闢卦為綱，而不去坎離震兌，仍以六十四卦配八宮之屬也。乾為本宮，上爻六世，陽爻陽世，從初爻子月起數至上爻為巳，故乾為四月卦。豐為坎宮五世卦。五陰爻陰世，從初爻午月起至五爻為戌，豐為九月卦。餘類推。

The "month卦" is not the same as the "month builder." It is derived from the world卦, or alternatively, from the twelve great trigrams. The world line is divided into yin and yang: if the world line is a yang line, it starts counting from the month of Zi; if it is a yin line, it starts counting from the month of Wu. This counting is based on numbers, not on solar terms. Although the twelve great trigrams serve as the framework, they are not like the卦气 system which removes Kan, Li, Zhen, and Dui. Instead, all sixty-four hexagrams are still assigned to the eight palaces. For example, Qian is the original hexagram of its palace, and the world line is on the top line, which is a yang line, belonging to a yang world. It starts counting from the month of Zi, Zi, Chou, Yin, Mao, Chen, Si, and reaches the top line at Si, so Qian is the fourth month卦. The hexagram Feng is the fifth hexagram of the Kan palace, and the fifth line is a yin line, belonging to a yin world. It starts counting from the month of Wu, Wu, Wei, Shen, You, Xu, and reaches the fifth line at Xu, so Feng is the ninth month卦. The rest of the hexagrams follow the same pattern.

世之所位，而陰陽之肆者謂之飛，陰陽肇乎所配(乾與坤，震與巽，坎與離，艮與兌)，而終不脫乎本(以飛某宮之卦，乃伏某宮之位)，以顯應佐神明者謂之伏。故有卦之飛伏，有爻之飛伏。

The position where the World Line resides is clearly visible and is called "Flying." The beginning of yin and yang is connected to its paired trigram (Heaven pairs with Earth, Thunder pairs with Wind, Water pairs with Fire, Mountain pairs with Lake), yet it always remains within its own palace (any trigram that flies out belongs to a particular palace, and what is hidden is the position of that palace). This hidden element, which supports the divine and allows the visible manifestation to take effect, is called "Hidden." Therefore, flying and hiding can occur at both the level of the entire hexagram and at the level of individual lines.

《文言》曰：“同聲相應，同氣相求。”飛之與伏，聲氣相通，或顯或隱，各以類求。《中庸》曰：“莫現乎隱，莫顯乎微。”此精義入神之論也。後儒以經學自誇，謂孔子未嘗言此，指為術數小道，不知《十翼》之言飛伏者多矣。奈學者瞠目視之，皆未見耳。《雜卦傳》“兌見而巽伏也”，是明言飛伏之一例。《說卦》“坎為隱伏”，而《離·象》“飛鳥”，亦飛伏之見端。而六十四卦《彖》、《象》言之者，更不勝枚舉也。

The Wenyan of the Qian hexagram says: "Those with the same sound respond to each other; those with the same qi seek each other out." The flying and the hidden are originally connected in sound and qi, one appearing and the other concealed, each seeking according to its category. The Zhongyong says: "Nothing is more visible than the hidden, and nothing more apparent than the subtle." — The more hidden something is, the more it reveals itself; the more subtle, the more it becomes evident. This is precisely the argument of "refining the profound meaning to the divine." Later Confucian scholars boasted of their mastery of the classics, claiming that Confucius never spoke of flying and hiding, and thus classified it as a minor branch of divination. They did not realize that the Ten Wings contain numerous references to flying and hiding, but scholars simply looked past them with their eyes wide open, failing to notice anything at all. The Zage Zhuan says, "Dui appears while Xun hides," which clearly presents an example of flying and hiding. The Shuogua Zhuan says, "Kan represents concealment," while the image commentary of the Li hexagram mentions "flying birds," both of which are hints of the concept of flying and hiding. As for the mention of flying and hiding in the Tai and Xiang commentaries of the sixty-four hexagrams, they are countless.

《京氏易傳》以爻直月，從世起建，佈於六位(惟乾坎二卦從初爻起)。乾起甲子，坤起甲午。一卦凡六月，計一百八十日。積算以爻直日，即從月建所止之日起，如姤卦月建起庚午至乙亥(姤初爻庚午，上爻乙亥)，積算即從乙亥起。上九為一日，周而復始，一卦凡百有八十日。

The Jing's Tradition of the Changes assigns each line to represent a month, starting from the World Line and proceeding sequentially to fill the six line positions (only the Qian and Kan hexagrams start from the first line). Qian begins with Jiazi, and Kun begins with Jiawu. Each hexagram governs six months, totaling 180 days. "Accumulated Calculation" assigns each line to represent a day, starting from the day the month builder stops: for example, the Gou hexagram's month builder starts with Gengwu and ends with Yihai (the first line of Gou receives Gengwu, and the top line receives Yihai). Accumulated Calculation then begins from Yihai, with the Nine at the Top counted as the first day, continuing in a cycle, with each hexagram also totaling 180 days.

今占家用《火珠林》術，大半出於京氏。惟月建積算，罕有傳其法者。後人或以月為直符，日為傳符，指六爻所見之支當之，非其義也。此為京氏占法，詳晁氏《別錄》，說繁不贅錄。八純卦外，一至六世，皆以本宮納甲為伏，而變宮遊歸以爻論。詳下章。

The method used nowadays in divination with the Fire Pearl Forest is mostly derived from Jing Fang. Only the calculations of month builder and accumulated numbers are seldom passed down. Later people sometimes take the month as "straight symbol" and the day as "transmitted symbol," using the existing earthly branches in the six lines as substitutes, which is not the original meaning of month builder and accumulated numbers. The above is the method of Jing Fang. Details can be found in Chao Gongwu's "Bi Lu," which is complicated, so it is not copied here. There is also a general rule: except for the eight pure trigrams, the first to sixth generations of trigrams take the stem assignment of their original palace as "hidden." As for the trigrams of wandering souls and returning souls that have changed palace, they should be discussed according to the lines, which will be explained in the next chapter.

《說卦》“帝出乎震”，及“神也者”兩節，皆言後天八卦之用者也。術家言後天八卦皆居旺地，語雖俚而所見甚精。蓋帝出乎震之帝，非專屬震卦。帝者主也，主權所在，即王也。術家曰旺，即土之用。

In the "Sayings on the Trigrams" (Sayi Zhuan), the passages "The Emperor arises from Zhen" and "The divine is the one who subtly governs all things and expresses it through words" both discuss the functions of the Later Heaven Trigrams. Numerologists say that each of the Later Heaven Trigrams sits on its own prosperous ground. Though this statement is crude, its insight is quite profound. Because the "Emperor" in "The Emperor arises from Zhen" does not specifically refer to the Zhen trigram; "Emperor" means the ruler, the center of authority, which is also "King." The "prosperous" mentioned by numerologists is actually the function of this "King" (the original text's "earth's use" is likely a miswriting of "King").

《大平御覽·五行休旺論》曰：“立春艮旺(艮居丑寅之交，立春之候也)，震相，巽胎，離沒，坤死，兌囚，乾廢，坎休。立夏巽旺(巽居辰巳之交，立夏之候也)，離相，坤胎，兌沒，乾死，坎囚，艮廢，震休。

The "Five Phases Prosperity and Decline Theory" cited in the "Taiping Yulian" states: At the beginning of spring, the Gen trigram is in its prime (Gen is located at the boundary between Chou and Yin, which is exactly the time of the beginning of spring), Zhen is in its auxiliary phase, Xun is in the fetal phase, Li is in decline, Kun is in death, Dui is in captivity, and Qian is in decline. At the beginning of summer, the Xun trigram is in its prime (Xun is located at the boundary between Chen and Si, which is exactly the time of the beginning of summer), Li is in its auxiliary phase, Kun is in the fetal phase, Dui is in decline, Qian is in death, Gen is in captivity, and Zhen is in decline. (The original title is written as "Daiping Yulian," which refers to the "Taiping Yulian.")

立秋坤旺(坤居未申之交，立秋之候也)，兌相，乾胎，坎沒，艮死，震囚，坎廢，離休。立冬乾旺(乾居戌亥之交，立冬之候也)，坎相，艮胎，震沒，離囚，坤廢，兌休(《唐典》：王、相、胎、沒、休、廢為八卦之氣)。”王充《論衡》亦同。蓋立冬之候也，得地為旺，旺之沖死，旺所生相，相之沖囚，胎之對廢，沒之對休。

At the beginning of autumn, the Kun trigram is in its旺 (prosperous) phase (Kun is located at the boundary between Wei and Shen, which is exactly the time of the beginning of autumn). Dui is in its相 (auxiliary) phase, Qian is in its胎 (nurturing) phase, Kan is in its没 (decline) phase, Gen is in its死 (death) phase, Zhen is in its囚 (captivity) phase, and Xun is in its废 (waste) phase. At the beginning of winter, the Qian trigram is in its旺 (prosperous) phase (Qian is located at the boundary between Xu and Hai, which is exactly the time of the beginning of winter). Kan is in its相 (auxiliary) phase, Gen is in its胎 (nurturing) phase, Zhen is in its没 (decline) phase, Li is in its囚 (captivity) phase, Kun is in its废 (waste) phase, and Dui is in its休 (rest) phase. The Tang Dynasty's "Six Canons" refer to the phases of Wang, Xiang, Tai, Mei, Xiu, and Fei as the energies of the eight trigrams. Wang Chong's "Discourses on Weights and Measures" also describes this in the same way. This passage is specifically discussing the beginning of winter. In summary, the trigram in its own position is called "Wang", the one opposite to the旺 position is called "Si", the one generated by the旺 position is called "Xiang", the one opposite to the相 position is called "Qiu", the one opposite to the胎 position is called "Fei", and the one opposite to the没 position is called "Xiu".

《淮南·墜形訓》曰：“五行：木壯，水老，火生，金囚，土死。火壯，木老，土生，水囚，金死。土壯，火老，金生，木囚，水死。金壯，土老，水生，火囚，木死。水壯，金老，木生，土囚，火死。”

The Huainanzi · Zui Xing Xun says: The waxing and waning of the Five Phases cycle in this way: When wood is strong, water is old, fire is born, metal is restrained, and earth is dead; when fire is strong, wood is old, earth is born, water is restrained, and metal is dead; when earth is strong, fire is old, metal is born, wood is restrained, and water is dead; when metal is strong, earth is old, water is born, fire is restrained, and wood is dead; when water is strong, metal is old, wood is born, earth is restrained, and fire is dead. In this context, "strong" means being in command and dominant. The Phase that nourishes me has achieved its purpose and retires to be "old." The Phase that I nourish is rising and is called "born." The Phase that restrains me is restrained and is called "restrained." The Phase that I restrain is overcome and is called "dead."

春令：木王，火相，土休，金囚。夏令：火王，土相，金休，水囚。秋令：金王，水相，木休，火囚。冬令：水王，木相，火休，土囚。土王四季，金相。

This is a flat chart showing the waxing and waning of the Five Phases across the four seasons, with each row listing the four states of "Wang, Xiang, Xiu, Qiu" for the current season: in spring, wood is Wang, fire is Xiang, earth is Xiu, and metal is Qiu; in summer, fire is Wang, earth is Xiang, metal is Xiu, and water is Qiu; in autumn, metal is Wang, water is Xiang, wood is Xiu, and fire is Qiu; in winter, water is Wang, wood is Xiang, fire is Xiu, and earth is Qiu. Earth does not rule a single season but is Wang for eighteen days at the end of each season, during which metal is Xiang. "Wang" means being in power and dominant (later writers often use "Wang" instead of "Xing"), "Xiang" refers to the element that is generated by the dominant element, which is secondary to Wang but about to rise, "Xiu" refers to the element that generates the dominant element, which has achieved its purpose and retreats into rest, and "Qiu" refers to the element that overcomes the dominant element, which is restrained and confined.

地支藏用，分晰陰陽，最為精密。周天三百六十有五度四分度之一，歷三百六十五日四分日之一而氣周，即六十卦三百六十爻之爻周。坎離震兌，分主二至二分，共三百八十四爻。陰陽錯綜，消息盈虛，無不合矣。藏天干於地支者，即乾體坤用。乾之用九，用於坤六，學者以術家言而忽之。是猶悅琢玉之精美，而賤斧鑿為匠器。《十翼》造化之筆，因無斧鑿之痕。然不知斧鑿之用者，又安識良工之心苦哉！

The hidden use of the Earthly Branches refers to the heavenly stems concealed within each branch and the number of days each stem rules. Yin and yang are distinguished with extreme precision. The entire cycle of the heavens is 365 and 1/4 degrees, and it takes 365 and 1/4 days to complete one cycle of the five elements, corresponding exactly to the 360 lines of the sixty hexagrams. Then, the four trigrams Kan, Li, Zhen, and Dui are added to represent the twenty-four nodes of the solstices and equinoxes, bringing the total to 384 lines. Yin and yang interweave and interact, waxing and waning, with no place not perfectly aligned. Embedding heavenly stems within the Earthly Branches follows the principle that "Qian is the body and Kun is the function": the "use of all nines" in Qian can only be seen when it falls upon the "six" of Kun. Scholars often dismiss this as mere numerology, just as they admire the beauty of a polished jade without recognizing the importance of the chisel and hammer. The Ten Wings are written by the natural hand of creation, leaving no trace of artificial craftsmanship; yet those who do not understand the purpose of the chisel and hammer will never comprehend the sincere effort of a master craftsman.

壬五日三分半，癸二十日六分半，辛長生。癸九日二分半，辛三日一分，己十八日六分。戊七日二分半，丙七日二分半，甲十六日五分。甲十日三分半，乙二十日六分半，癸長生。乙九日三分，癸二日一分半，戊十八日六分。庚七日二分半，戊七日二分半，丙十六日五分。午丙十日三分半，己九日三分，丁十三日三分半。丁九十三分，乙三日一分半，己十分日六分。戊己共七日，壬七日三分半，庚十六日五分。庚十日三分半，辛二十日六分半，丁長生。辛九日三分，丁三日一分，戊十八日六分。戊七日二分半，甲七日二分半，未十六日五分。

This is a flat table of the twelve earthly branches' hidden heavenly stems. Originally divided into twelve rows, it is arranged in the order of Zi, Chou, Yin, Mao, Chen, Si, Wu, Wei, Shen, You, Xu, and Hai. Each branch lists the heavenly stems hidden within it and the number of days each stem is in charge. The seventh row contains only the character "Wu," which confirms the order of the entire table. Zi contains Ren water for five days and a half (originally ten days), Gui water for twenty days and a half, and Xin metal is born in Zi. Chou contains Gui water for nine days and a half, Xin metal for three days and a third, and Ji earth for eighteen days and a half. Yin contains Wu earth for seven days and a half, Bing fire for seven days and a half, and Ji wood for sixteen days and a half. Mao contains Ji wood for ten days and a third, Yi wood for twenty days and a half, and Gui water is born in Mao. Chen contains Yi wood for nine days and a third, Gui water for two days and a half, and Wu earth for eighteen days and a half. Si contains Geng metal for seven days and a half, Wu earth for seven days and a half, and Bing fire for sixteen days and a half. Wu contains Bing fire for ten days and a third, Ji earth for nine days and a third, and Ding fire for thirteen days and a third. Wei contains Ding fire for nine days and a third, Yi wood for three days and a third, and Ji earth for eighteen days and a half. Shen contains Wu and Ji earth together for seven days, Ren water for seven days and a third, and Geng metal for sixteen days and a half. You contains Geng metal for ten days and a third, Xin metal for twenty days and a half, and Ding fire is born in You. Xu contains Xin metal for nine days and a third, Ding fire for three days and a third, and Wu earth for eighteen days and a half. Hai contains Wu earth for seven days and a half, Ji wood for seven days and a half, and Ren water for sixteen days and a half (the last row reads "Wei sixteen days and a half," where "Wei" is a mistake for "Ren"). Within each branch, the three heavenly stems take turns in sequence, and the total days add up to about one month. This is what the divination masters refer to as "the heavenly stem governing the affairs."

積爻而成卦，故爻為卦之體。爻動而卦變，故爻又為卦之用。卦之體用，具在於爻。《說卦傳》曰：“昔者聖人之作《易》也，將以順性命之理。是以立天之道曰陰與陽，立地之道曰柔與剛，立人之道曰仁與義。兼三才而兩之，故《易》六畫而成卦。分陰分陽，迭用柔剛，故《易》六位而成章。”

The yao accumulate to form a hexagram, so the yao is the "body" of the hexagram; when a yao moves, the hexagram changes accordingly, so the yao is also the "function" of the hexagram. The body and function of a hexagram all lie in the yao. The "Commentary on the Hexagrams" states: the ancient sages created the Book of Changes to follow the principles of life and nature, thus establishing the way of Heaven as "yin" and "yang," the way of Earth as "flexibility" and "firmness," and the way of humanity as "benevolence" and "righteousness." They doubled the three categories of Heaven, Earth, and humanity, so the Book of Changes requires six lines to form a hexagram. Furthermore, because the six lines distinguish between yin and yang positions, and flexible and firm lines alternate, the Book of Changes requires six yao positions to establish order. This passage clarifies two points: the origin of the six lines comes from each of the three categories having two yao; the order of the six positions arises from the alternating combination of yin and yang and flexibility and firmness.

《繫傳》曰：“《易》之為書也，廣大悉備。有天道焉，有人道焉，有地道焉。兼三才而兩之，故六。六者非它也，三才之道也。道有變動故曰爻，爻有等故曰物，物相雜故曰文。文不當故吉凶生焉。”

The *Great Treatise* continues to say: The *Book of Changes* is vast and comprehensive, containing heavenly ways, human ways, and earthy ways. By doubling the three principles, it becomes six lines. This number "six" is precisely the way of the three principles. Since the way is changeable, it is called "yao" (line). The yao has distinctions of high and low, so it is also called "wu" (things). Different things intermingle, so it is called "wen" (patterns). When the arrangement of patterns is not appropriate, good fortune and misfortune arise from this. Thus, from "six" to "yao," from "yao" to "wu" and "wen," each term is established based on position and coordination. Good fortune and misfortune are merely the results of appropriate or inappropriate coordination.

又曰：“《易》之為書也不可遠，為道也屢遷。變動不居，周流六虛。上下無常，剛柔相易。不可為典要，唯變所適。”又曰：“爻也者效此者也，象也者像此者也。爻象動乎內，吉凶見乎外，功業見乎變，聖人之情見乎辭。”孔子之所以言爻者，詳且備矣。後世言《易》者，既昧於象數，而六虛六位之義，亦泛焉而莫知所指。每卦僅就所見之上下六爻，為承應當否，卦之情其何由見哉！

The Great Treatise also says: The Book of Changes cannot be separated from for a moment; the Dao it discusses is ever-changing, moving without stopping, circulating among the six empty positions; up and down have no fixed pattern, the strong lines and the yielding lines alternate with each other; it cannot be regarded as a fixed doctrine, but must follow the changes. It also says: The line represents the imitation of change; the image represents the imitation of change. The lines and images move within the hexagram, and the fortune or misfortune appears outside the hexagram; achievements are revealed through change, and the mind of the sage is revealed through the line statements. Confucius spoke about the lines in a detailed and complete manner. However, later scholars who interpreted the Book of Changes have become confused about the images and numbers, and are vague about the meaning of the 'six empty positions' and 'six positions,' unable to explain clearly what they refer to. They discuss each hexagram only in terms of the visible upper and lower six lines, considering their relationships of support, response, and whether they are in the proper position or not. In this way, how can the true situation of a hexagram be revealed?

卦氣由下生，故以下為初。重三畫之卦為六畫，仍分三才。陽奇陰偶，陽剛陰柔。以配天地，中爻為人，曰仁曰義。上下進退，為內外兩象之中樞。孔子贊《易》，《彖傳》以內外兩象之陰陽剛柔，釋一卦之義。《象傳》則專取中爻，聯合上下象數，以人合天。

The energy of the hexagram flows upward from the bottom, so the lowest line is called "Chu." When three lines of a basic trigram are stacked to form a six-line composite trigram, it is still divided into the three principles of heaven, earth, and humanity: yang is odd, yin is even, yang is strong and firm, yin is soft and flexible. The upper two lines correspond to heaven, the lower two to earth, and the middle two to humanity, which refers to "ren" (benevolence) and "yi" (righteousness). The middle two lines can move up or down, advance or retreat, making them the key link between the inner and outer trigrams. Confucius interpreted the Book of Changes, using the Commentary on the Judgment to explain the meaning of the entire hexagram through the yin and yang, strength and flexibility of the inner and outer trigrams; the Image Commentary, on the other hand, focuses specifically on the middle line, connecting the upper and lower images through numbers and patterns, and using human affairs to align with heavenly principles.

六十四卦《象傳》，皆曰“君子以”或“先王以”者，即以人事明天地之道者也。天地之道往復不窮，而人事之千變萬化，皆在三四兩爻之反覆。孔子曰“其初難知，其上易知，本末也”，《大過·彖》曰“本末弱也”。明六爻之本末，而後一卦之體用可知。而元亨利貞，亦可以陰陽之升降上下而明其序也。

The Great Image commentaries of the sixty-four hexagrams all say "The gentleman uses... " or "The former kings use... ", which is using human affairs to explain the principles of heaven and earth. The principles of heaven and earth are cyclical and ever-repeating, without end, while human affairs change endlessly, all depending on the movement between the third and fourth lines, which represent the cycles. Confucius said, "At the beginning it is hard to know, at the top it is easy to know; this is about the beginning and the end." The first line is the root, so it is hard to know; the top line is the end, so it is easy to see. The Commentary on the Judgment of the Great Excess also says, "The beginning and the end are weak." Clarifying the beginning and the end of the six lines allows one to understand the nature and function of a hexagram. Furthermore, the four virtues, "origin, prosperity, benefit, and constancy," can be understood in order according to the sequence of yin and yang rising and falling.

端木氏曰：《易》太極含三為一，乾坤上下中，上天極，立在下地極，而中人極。離坎天地中，日月二人象，天地中人道，離坎交中，天地間生人。天地顛，乾下首，生人出。乾是坎，北極艮背。坤是離，南極巽高。而中極人道，震兌出入，天地大義人之終始。此六爻三極之道也。

Duanmu Guohu said: The Taiji of the Book of Changes encompasses three elements as one. The trigrams Qian and Kun divide into upper, middle, and lower layers: the upper is the Heaven's extreme, opposing and located below is the Earth's extreme, and in the middle is the Human's extreme. Li and Kan are located between Heaven and Earth, representing the sun and moon, which are also the images of human beings; the human way in the middle of Heaven and Earth is formed by the interaction of Li and Kan, thus human beings come into being between Heaven and Earth. Once Heaven and Earth are reversed, Qian descends to the lower position, and human beings are thus generated. In terms of the Later Heaven, the position of Qian in the Earlier Heaven is replaced by Kan, located at the North Pole, and the hexagram Gen speaks of "Gèn qí bèi" (keeping the back still); the position of Kun in the Earlier Heaven is replaced by Li, located at the South Pole, and Xun has the image of "gāo" (height). The middle layer represents the human way, governed by Zhen and Dui, which corresponds to the statement in the Commentary on the Judgment of the Hexagram Guīmèi: "the great principle of Heaven and Earth" and "the beginning and end of human beings." This is the reason for the distribution of the six lines among the three extremes of Heaven, Earth, and Humanity.

分陰分陽，迭用柔剛，故《易》六位而成章。六位者，初爻二爻為地位，三爻四爻為人位，五爻上爻為天位。以乾卦例之，初九在地之下，故曰“潛”。九二地之上，故曰“田”。三爻為人之正位，故曰“君子”。四爻不當位，故曰“或”。五爻天位，故曰“在天”。上九在天之上，故曰“亢也”。

The "Commentary on the Hexagrams" says, "By dividing yin and yang, alternating the use of soft and strong, the Book of Changes forms its six positions." The six positions refer to the first and second lines as the position of earth, the third and fourth lines as the position of humanity, and the fifth and sixth lines as the position of heaven. Taking the Qian hexagram as an example: the initial line, which is below the earth position, is described in the line statement as "the dragon remains hidden and should not be used," referring to "hidden." The second line, which is above the earth position, is described as "the dragon appears in the field," referring to "field." The third line, which is the proper position of humanity, is described as "the gentleman remains diligent all day." The fourth line, which has left the proper position of humanity but has not yet reached the heaven position, is in an improper place, hence described as "perhaps leaping in the abyss," referring to "perhaps." The fifth line, which is the heaven position, is described as "the dragon soars in the heavens." The top line, which is above the heaven position, is described as "the dragon reaches its peak and incurs regret," referring to "peak."

位有一定，而爻則變動無常。學者必先知有定之位，定其為陰為陽，為上為下，而後爻之奇偶當否，可得而言也(偶居陰，奇居陽，為當，反之為不當)。分陰分陽，迭用柔剛。惟既濟一卦，為陰陽柔剛各當其位，故曰“既濟定也”。定則不動，不動則不生，而《易》道或幾乎息矣。

The positions are fixed, but the lines are changeable. Scholars must first clarify these fixed positions—determining whether they are yin or yang, and whether they are upper or lower—before they can discuss whether the lines are appropriate or not. Even numbers correspond to yin positions, and odd numbers correspond to yang positions, which is called "appropriate"; the reverse is called "inappropriate." The six positions are divided into yin and yang, alternating between soft and strong. Among the sixty-four hexagrams, only the hexagram "Already Achieved" has every yin and yang, soft and strong in their proper positions, so the "Zagua Transmission" says, "Already Achieved is stability." But once something is fixed, it no longer moves; without movement, there is no generation, and the way of the Book of Changes almost comes to a standstill.

故荀虞均以乾坤成兩既濟為凶。《序卦》曰：“《易》不可窮也，故受之以未濟終也。”此以陰陽之位言之也。若以用言，則一卦六爻，惟中四爻得用。初未用事，而上則失位。故《乾·上》曰：“高而無位”，《需·上》日“位不當也”。王弼曰“上下無位”者，指此也。

Therefore, Xun Shuang and Yu Fan both regarded the transformation of Qian and Kun into two instances of Ji Ji as an ominous sign. The Xu Guatuan says: "The Book of Changes cannot be exhausted, hence it is followed by Wei Ji to conclude." This is speaking from the perspective of the positions of yin and yang. However, if we consider it from the perspective of 'use,' among the six lines of a hexagram, only the middle four lines truly have a role: the first line has not yet come to the point of action, while the top line has already gone beyond its position. Therefore, the line at the top of Qian, line 9, says "high but without position" (the original text in Wenyan reads "honored but without position, high but without people"), and the line at the top of Xu, line 6, in the Xiangzhuan says "though not in the right position." Wang Bi's reference to the first and top lines as "without position" refers precisely to this.

《繫傳》曰：“上下無常，周流六虛。”六虛者，即初二三四五上之位也。爻實位虛，爻有上下，而位無變動。爻有柔剛，位有陰陽(一三五為陽，二四六為陰)，剛柔雜居(剛居陽，柔居陰，為當。或以剛居陰，柔居陽，則相雜而文生焉)，吉凶以著。《參同契》曰：“二用無爻位，周流行六虛。”二用者即九與六也。

The Great Treatise says: "Above and below have no constant position, flowing through the six voids." The term "six voids" refers to the six positions: initial, second, third, fourth, fifth, and upper. A line is real, while a position is void; a line has upper and lower parts and can move, but a position remains fixed. Lines are divided into flexible and strong, while positions are divided into yin and yang (the first, third, and fifth positions are yang positions, while the second, fourth, and sixth are yin positions); when strong and flexible lines are mixed within these positions (when a strong line is in a yang position and a flexible line is in a yin position, it is considered appropriate; but when a strong line is in a yin position and a flexible line is in a yang position, they are mixed and produce "wen," or culture), the manifestations of good fortune and misfortune emerge. The Zhou Changes Treatise on the Harmony of the Three says: "Two uses have no lines or positions, flowing through the six voids." Here, "two uses" refer to the "All Nines" used in the Qian trigram and the "All Sixes" used in the Kun trigram.

乾九坤六，上下升降，周流六虛，以成六十四卦。故觀象者不可僅觀所見之六爻。六爻之下，尚有六虛，皆與此所見之六爻相關。爻為飛，位為伏，實易辨而虛難知。必由實而究其虛，庶遇爻而知其用，於《易》之道思過半矣。

The nine of Qian and the six of Kun move up and down between the upper and lower parts, circulating through the six voids, thus generating the sixty-four hexagrams. Therefore, those who observe the images should not only focus on the six visible lines before them. Behind the six lines there are also the six voids, all closely related to the six lines in front. The lines are "flying," while the positions are "hidden"; the tangible is easy to recognize, but the intangible is difficult to understand. One must investigate the hidden aspects through the tangible ones in order to understand the function of a line the moment it appears. When one reaches this level, one has grasped more than half of the Way of the Book of Changes.

爻位六而卦有八，八卦於六爻，各有其當位之爻，曰正位。家人曰“男正位乎外，女正位乎內”，言九五與六二，則但以陰陽言也。陰陽以二五爻為得中得正，乾坤為卦之宗主，亦陰陽之純體。故乾以九五為正位，坤以六二為正位，坎離為乾坤之交(坎中之陽即乾爻，離中之陰即坤爻)。故坎離之正位，與乾坤同。震以初九為正位，艮以九三為正位，巽以六四為正位，兌以上六為正位。卦各有其正位，故六爻具六子之位。為圖如下：

The six lines of a hexagram are fewer than the eight trigrams. Each of the eight trigrams occupies a specific line within the six lines, known as the "correct position." The Commentary on the Judgment of the Hexagram of Family states, "The male holds the correct position outside, and the female holds the correct position inside," referring to the line nine at the fifth position and line six at the second position. This is based solely on the principle of yin and yang. Yin and yang consider the second line and the fifth line as the central and correct positions. The trigrams Qian and Kun are the primary trigrams of all others and are pure expressions of yin and yang, so Qian uses the line nine at the fifth position as its correct position, and Kun uses the line six at the second position as its correct position. The trigrams Kan and Li are formed by the combination of Qian and Kun (the central yang line of Kan is the line of Qian, and the central yin line of Li is the line of Kun), so the correct positions of Kan and Li are the same as those of Qian and Kun. In addition, Zhen uses the line nine at the beginning as its correct position, Gen uses the line nine at the third position as its correct position, Xun uses the line six at the fourth position as its correct position, and Dui uses the line six at the top as its correct position. Each trigram has its own correct position, so the six lines of a hexagram can accommodate the positions of the six subsidiary trigrams. The diagram is listed below:

端木氏曰：天地六爻，坎離既濟定位，五多功二多譽，位當也。離坎未濟居方，三多凶四多懼，不當位也。有當位而不正者，而正位未有不當者也。而《彖》、《象》之言正則以二五，故八卦惟乾坤坎離之為得中得正也。

Duanmu Guohu said: Among the six lines of heaven and earth, when Kan (Water) is above and Li (Fire) is below, they form the hexagram "Already Perfect" (Ji Ji). Each line is in its proper position, so the "Great Treatise" (Xì Cí) says "the fifth line brings many achievements" and "the second line brings much praise," precisely because they are in the correct position. Conversely, when Li (Fire) is above and Kan (Water) is below, they form the hexagram "Not Yet Perfect" (Wei Ji), with each line merely occupying its place, hence the saying "the third line brings many calamities" and "the fourth line brings much fear," because they are not in the correct position. Some lines may be in the correct position but still not qualify as "correct" (zheng). However, any line that is considered to be in the correct position is necessarily in the proper place. The "Commentary on the Judgment" (Tuàn Zhuàn) and "Image Commentary" (Xiàng Zhuàn) refer to "correct" (zheng) exclusively in terms of the second and fifth lines. Therefore, among the eight trigrams, only Qian (Heaven), Kun (Earth), Kan (Water), and Li (Fire) are both centered and correctly positioned.

六爻三極定位，天地定位。六爻上山澤，下雷風，中水火。六爻三極，下二初地爻地極，雷風恆，天地下極立心恆，坤地極立不易方，二初震巽爻是也，五上天爻天極，山澤損天上極員(損從員)，乾天恆無方，中日月斗，三人行，乾極與時偕行，五上艮兌爻是也。

The six lines of a hexagram belong to the three fundamental aspects of heaven, earth, and humanity, each with its own position, which corresponds exactly to what the "Commentary on the Changes" says, "Heaven and earth are positioned." Among the six lines, the top two lines belong to mountain and marsh (Gen and Dui), the bottom two lines belong to thunder and wind (Zhen and Xun), and the middle two lines belong to water and fire (Kan and Li). In terms of the three fundamental aspects: the second line and the first line are earth lines, belonging to the earth aspect. Thunder and wind combine to form the hexagram "Constant" (Heng). The lower extreme of heaven and earth is established by this "constant" — the "Image Commentary" of the hexagram "Constant" says, "The gentleman follows the principle of establishing a fixed position." Kun represents earth, and the earth extreme is precisely this "fixed position," referring to the Zhen and Xun on the first and second lines. The fifth line and the top line are heaven lines, belonging to the heaven aspect. Mountain and marsh combine to form the hexagram "Loss" (Sun). The upper extreme of heaven takes the meaning of "circle" ("Sun" includes the character "yuan"), Qian represents heaven, which is constant and has no fixed position, with the sun and moon and the Big Dipper suspended in the middle. The third line of the hexagram "Loss" says, "When three people walk, one is lost," and the "Commentary on the Judgment" of the hexagram "Loss" says, "Move in harmony with the times," referring to the Gen and Dui on the fifth and top lines.

四三人爻人極，水火既濟，天地中間人，於天地上下初終，首尾續終，中為人極。兼三才而兩之，定上下中極，四三坎離爻是也。六爻三極，天地南北居方，六爻辨物辨等。乾坤六十四卦終下坎北極，故曰“初難知”，曰“亦不知極也”。此《易》居方上下六爻三極之道也。

The fourth line and the third line are the human lines, belonging to the human extreme, and they combine water and fire to form the hexagram "Already Perfect." Humans are situated in the center between heaven and earth; they are in the middle of the beginning and end, the start and finish, of heaven and earth. In the beginning and end above and below heaven and earth, the connection and conclusion are made, and the middle part is the human extreme. "Combining the three elements and dividing them into two," thus determining the positions of upper, middle, and lower extremes, refers to the third and fourth lines, which are Kan (water) and Li (fire). The six lines are divided among the three extremes; heaven and earth are located in the north and south respectively, and the six lines are used to "distinguish things" and "distinguish ranks." The sixty-four hexagrams governed by Qian and Kun conclude at the lower Kan, which is the northern extreme. Therefore, the Great Treatise says, "At the beginning, it is difficult to know," and also says, "One does not know where it ends" (the original text says "also does not know the extreme"). This is the reason why the Book of Changes uses the six lines to determine positions and assign them to the three extremes.

右圖與前圖合觀，則知爻位之隱見變化，不但卦有飛伏交互，而爻之飛伏交互，亦與卦等也。向之說《易》家，能究心於爻位之義者甚鮮，而於爻位之分，更未有言之者。來知德氏，雖有八卦之正位一圖，而注中仍不能用，則以未明爻位之體用有別也。今合二圖而一之，並附以說，庶閱者可瞭然矣。

If you combine the above diagram with the previous one, you can understand the principle of the changing visibility of the lines (yao). Not only does the entire hexagram have hidden and revealed lines and mutual interaction, but each individual line also has hidden and revealed lines and mutual interaction, and their weight is equal to that of the entire hexagram. In the past, those who explained the Book of Changes rarely focused on the meaning of the line positions. As for how to divide the line positions, no one has ever discussed it. Lai Zhide of the Ming dynasty, although he drew a diagram of the correct positions of the Eight Trigrams, still found it difficult to apply in his annotations, because he did not clearly distinguish the 'essence' and 'function' of the line positions. Now, by combining the two diagrams and adding explanations, readers should be able to understand clearly.

六十四卦三百八十四爻，皆乾坤二用，周流六虛，至既濟而全卦之爻位相當。故曰“既濟定也”。爻位既明，二用斯章。然乾元用九，綱領全《易》。地道無成，坤之用皆乾之用也。乾無方無體，乾之用皆見於坤之用也。孔子《文言傳》曾發乾九用坤，坤六承乾之旨，已極詳備。大明終始，六位時成，乃非既濟而為未濟，其故可深長思矣。

There are sixty-four hexagrams and three hundred and eighty-four lines in total, all of which are governed by the principles of "use of all nines" and "use of all sixes" circulating through the six positions. When we reach the hexagram "Already Completed," each line corresponds perfectly, hence the "Commentary on the Miscellaneous Hexagrams" states, "Already Completed means stability." Once the positions of the lines are understood, the principles of the hexagrams "Heaven" and "Earth" become evident. However, "the use of nine in the Creative" is the overarching principle that governs the entire Book of Changes. The "Commentary on the Literary Meaning" of the hexagram "Earth" says, "The way of the Earth has no completion but is substituted by the finality of the Creative," indicating that the use of the Earth is actually the use of the Creative. Since the Creative has no fixed place or form, its use can only be seen through the use of the Earth. Confucius in the "Commentary on the Literary Meaning" has thoroughly elaborated on the principle that the nines of the Creative must be applied to the Earth and the sixes of the Earth must be supported by the Creative. The "Commentary on the Judgment" of the hexagram "Heaven" speaks of "great brightness from beginning to end, with the six positions formed in due time," yet the entire book ends not with "Already Completed" but with "Not Yet Completed," a point worthy of deep reflection.

乾六位，火本天親上。離五位，水本地親下。坎二位，而上下剛柔應位。山澤，艮上位兌三位。雷風，震四位巽初位。而上下六位，巽伏，震起，兌見，艮止，皆中離坎日月象。故曰“大明終始六位時成(下巽伏，上兌見，即坎象。下震起，上艮止，即離象。)。”

Heaven encompasses the six lines. Fire belongs to Heaven but is attached above, so Li is placed in the fifth position; Water belongs to Earth but is attached below, so Kan is placed in the second position—thus the yin and yang above and below are properly positioned. Mountain and marsh form a pair: Gen occupies the top line, Dui occupies the third line. Thunder and wind form a pair: Zhen occupies the fourth line, Xun occupies the first line. Thus, among the six positions above and below, Xun governs "concealment," Zhen governs "movement," Dui governs "appearance," and Gen governs "stillness," all surrounding the middle Li and Kan which represent the sun and moon. Therefore, the Commentary on the Judgment of Qian says, "Great brightness begins and ends, the six positions complete the time." (Below is Xun's concealment, above is Dui's appearance, together forming the image of Kan; below is Zhen's movement, above is Gen's stillness, together forming the image of Li.)

《上經》始乾坤終坎離，其往來卦十八。《下經》始咸恆終既未濟，其往來卦十八。十八為二九數，乃離坎二卦日月終始。離一九，寅數止戌。坎一九，申數正辰。此離坎二九，皆乾用九圓，日月為大明象。乾二九十八卦，《上經》始乾坤，終坎離，大明終始六位是也。

The Upper Classic begins with the trigrams Qian (Heaven) and Kun (Earth), and ends with Li (Fire) and Kan (Water). Within it, pairs of trigrams that come and go in relation to each other form eighteen groups. The Lower Classic begins with Xian and Heng, and ends with Ji Ji and Wei Ji, with pairs of trigrams that come and go in relation to each other also forming eighteen groups. Eighteen is the number obtained by multiplying two by nine, which corresponds exactly to the trigrams Li and Kan, which represent the sun and moon, their end and beginning. Li is paired with one nine: counting nine positions starting from Yin, it ends at Xu; Kan is also paired with one nine: counting nine positions starting from Shen, it ends at Chen. These two nines of Li and Kan are both the circular path of Qian's "All Nines." When the sun and moon come together, they form the image of "Great Brightness." The two nines of Qian make up eighteen trigrams. The Upper Classic begins with Qian and Kun and ends with Li and Kan. The phrase "Great Brightness begins and ends, the six positions are completed" refers precisely to this.

離坎二卦，南北終始，皆出入於震兌二卦，東西往來。震一九亥數止未，兌一九巳數止丑。此震一九離出震，兌一九坎出兌，皆乾用九圓。而上、下《經》各往來卦十八，始乾終既未濟，乾六位成而坤天下平。此離坎上下六位，南北居方卦大明日月也。

The trigrams Li (Fire) and Kan (Water) are positioned south and north respectively, governing the beginning and end. Their movement must pass through the trigrams Zhen (Thunder) and Dui (Lake), traveling between east and west. Zhen is paired with a nine: starting from the亥 position, counting nine steps leads to the 未 position. Dui is also paired with a nine: starting from the 巳 position, counting nine steps leads to the 丑 position. The nine associated with Zhen is the path by which Li departs from Zhen; the nine associated with Dui is the path by which Kan departs from Dui—both follow the circular path of Qian (Heaven) as expressed in "use nine." The upper and lower sections each contain eighteen pairs of trigrams in motion, with the entire sequence beginning with Qian and ending with Ji Ji and Wei Ji. Once the six positions of Qian are completed, Kun (Earth) achieves "the world is at peace." This is the reason why Li and Kan are placed in the upper and lower six positions, occupying the south and north respectively, symbolizing the sun and moon of the great day.

上下卦十八終始三十六，是為乾四九出入，南北上下為之極。其卦三十六，皆離坎首尾終之始之。而乾坤上下六十四卦六位，皆此離坎六位終始之。是乾用九乾圓象，而六十四卦以成終成始，乾大明終始，六位時成是也。

The upper and lower classics each contain eighteen, and when head and tail are combined, they make thirty-six. This is the four nines of Qian moving in and out, turning around, with north and south, up and down all based on this. These thirty-six groups of hexagrams are entirely opened and closed by Li and Kan at the beginning and end. The sixty-four hexagrams governed by Qian and Kun, and their six lines, are also concluded and begun by the six positions of Li and Kan. Thus, the "use of nine" in Qian is the image of the circular movement of the way of Qian. The sixty-four hexagrams are thus completed and begun through this. The "great brightness beginning and ending, the six positions formed in time" mentioned in the "Commentary on the Judgment" of Qian refers precisely to this.

六爻二極，尤重在人。天地之氣，以人而通。陰陽之道，以人而和。孔子贊《易》“立人之道”，以合乎天地之正。《京氏易傳》：孔子曰“陽三陰四，位之正也”，三者東方之數，日之所出也。四者西方之數，日之所入也。言日月終天之道。

The six lines of divination belong to the three ultimate principles, among which the most important is the human principle (the original text says 'two principles' but should be 'three principles'). The energies of heaven and earth depend on humans to connect them, and the way of yin and yang depends on humans to harmonize them. Confucius explained the Book of Changes by emphasizing 'establishing the way of humanity,' which is to enable humans to align with the middle and upright nature of heaven and earth. The Jing's Tradition of the Changes cites Confucius' words: 'Yang is three and Yin is four, which are the correct positions.' Three is the number of the East, where the sun rises; four is the number of the West, where the sun sets—this refers to the principle that the sun and moon traverse the sky throughout the day, moving around the heavens.

故《易》卦六十四，分上下象陰陽也。故奇偶之數取之於乾坤。乾坤者，陰陽之根本也。陰陽之道備著於坎離。坎離者，陰陽之性命也，而其樞要皆在於三四兩爻。於此求之，六十四卦之辭義可迎刃而解矣。圖附後。

Therefore, the sixty-four hexagrams of the Book of Changes are divided into the Upper and Lower Classics to symbolize the two aspects of yin and yang. Odd and even numbers are derived from Qian and Kun, since Qian and Kun are the fundamental principles of yin and yang; and the way of yin and yang is fully embodied in Kan and Li, because Kan and Li represent the nature and destiny of yin and yang—Qian and Kun provide the body of yin and yang, while Kan and Li manifest their function. And the key to all this lies in the third and fourth lines, which are the two positions where humans reside. By starting from here to seek understanding, the words and meanings of the hexagrams and their lines can be easily grasped. The diagram is attached below.

天地人六爻往復，天地上下，在人中爻三四迴轉。而上下天地爻，乃往復不窮。此乾坤六爻上下應位，二三四五同功異位，皆具此六爻往復中，皆在中人爻迴轉。人於天地上下，不見首尾，乃中間背脊，其道反覆不已。天地往復，其道不窮。孔子六十四卦大象，著六十四“以”字。“以”，古文作□，即結合上下兩卦往復迴轉之象也。

Heaven, Earth, and Humanity form a cycle of six lines that continuously turn and return. Heaven is above, Earth is below, and the entire structure relies on the third and fourth lines, which are in the middle and turn back and forth, enabling the lines above and below to move continuously without end. The mutual correspondence between the lines of the Heaven and Earth trigrams, as well as the "same function but different positions" mentioned in the Great Treatise, are all included within the continuous movement of the six lines, and they all revolve around the central line representing Humanity. Humanity is situated between Heaven and Earth, unable to see the beginning or the end, merely serving as the middle segment, its path continuously turning without cessation. The movement of Heaven and Earth is naturally endless. Confucius composed the Great Image Commentary for the sixty-four hexagrams, using the word "with" sixty-four times in a row. The ancient form of the character "以" (with), although missing in the original text, symbolizes the image of combining the upper and lower trigrams and turning back and forth.

爻分於卦，卦之象即爻之象。卦由爻變，爻之象亦卦之變象也。《說卦》廣象，半為卦變言之。名隸於卦，而重實在爻。六十四卦，《彖》、《象》要皆以象之交易變易反易而互變其義，以定其辭。變之所在，即象之所在。所謂“辭也者，各指其所之”是也。

Yao comes from the division of a hexagram, so the image of the hexagram is the image of Yao; a hexagram is formed by the movement of Yao, so the image of Yao is also the image after the change of the hexagram. The large number of "broad images" presented in the "Commentary on the Changes" are half about the changing of hexagrams. Although they are nominally attributed to hexagrams, their actual content lies in Yao. The "Commentary on the Judgment" and "Image Commentary" of the sixty-four hexagrams are mostly based on the transformation, change, and reversal of images to derive their meanings and determine the words of the hexagram and its lines. Where there is change, there is also the image — this is exactly what the "Great Treatise" means when it says, "Words are each directed to their destination."

變不同，象亦不同。或一爻變，或二爻變，或三爻變。三爻變者，則為對象。以一卦全變，本體之象已不見，所謂伏也。若二爻或一爻變，則變其半而存其半，京氏所以有半象之說也。

The way of change differs, resulting in different images: there are cases of one line changing, two lines changing, or three lines changing. When all three lines change, the inner trigram or outer trigram becomes its opposite trigram, forming the "opposite image." If all six lines of a hexagram change, the original image disappears entirely, which is called "concealed." As for cases where only two lines or only one line change, this represents changing half and retaining half, which is the origin of Jing Fang's concept of "half image."

向來講《易》者莫明京氏半象之義，往往置之不論。焦理堂氏《易通釋》宗虞仲翔氏之說者也，乃駁其半象，不遺餘力。謂“坎之半即巽之半，坤之半即艮之半”云云，而不知京說之正謂“坎半即巽半，坤半即艮半”耳。孔子《雜卦》，“震起艮止，巽伏兌見”，即發明離坎變化，乃震艮巽兌起止伏見之作用。《虞注》：“小畜密雲不雨，謂坎象半見。”即指巽為坎之半耳。

Those who have explained the Yi Jing throughout history have failed to understand Jing Fang's concept of 'half-figures'. They often set it aside without discussion. Jiao Xun, known as Li Tang, in his work Yi Tong Shi, originally followed Yu Fan, known as Zhong Xiang, but he vigorously refuted the idea of half-figures, saying 'half of Kan is half of Xun, and half of Kun is half of Gen' — but he did not realize that Jing Fang's view was precisely 'half of Kan is half of Xun, and half of Kun is half of Gen'. Confucius in the Zage Zhuan said 'Zhen signifies movement; Gen signifies stillness', 'Xun signifies concealment; Dui signifies revelation', which is explaining the transformation of Li and Kan, and applying it to the four functions of Zhen, Gen, Xun, and Dui: movement, stillness, concealment, and revelation. Yu Fan's commentary on the Xiao Xu hexagram 'dense clouds without rain' refers to 'half of Kan being visible', meaning Xun is half of Kan.

惟半象二字，在可解不可解之間。與其謂之半象，不如名之曰爻象為簡當而易曉也。一卦六爻，本有風雷山澤水火之爻位。與八卦之正位，有其位即有其象。故僅知卦象，而不明爻象，仍未能盡象義之蘊也。

The term "half-trigram" is ambiguous, lying between something that can be explained and something that cannot. Instead of calling it "half-trigram," it would be more concise and clear to refer to it as "yao-xiang" (line image). A hexagram consists of six lines, each originally representing wind, thunder, mountain, marsh, water, and fire respectively. Combined with the proper positions of the eight trigrams mentioned earlier, each position corresponds to a specific image. Therefore, understanding only the hexagram image without grasping the line images fails to fully explain the meaning of the images.

爻象有正變之分，亦與卦同。如本卦不變，而分爻取象者，則以其位之上下而象異。如震為足，正象也，爻分震之初則為趾。乾為首，正象也，爻分乾之上則為顛，為額，或為項。而六子分乾坤之爻者，亦得推此義以取象。如艮為乾之上爻，亦有首之象。離得坤之中爻，亦取腹象。此不變之變，即廣象之義也。

The lines of a hexagram also have distinctions of 'correct' and 'changed' images, just like the hexagrams themselves. For example, if the primary hexagram remains unchanged, but each line is taken separately to form images, then the images will vary according to the position of the lines: Zhen represents the foot, which is the correct image, but when taken from the first line of Zhen, it becomes 'toe'; Qian represents the head, which is the correct image, but when taken from the top line of Qian, it becomes 'top of the head', or 'forehead', or 'neck'. Similarly, the six sons of the hexagram, having taken the lines of Qian and Kun, can also take images in this way: for instance, Gen is formed from the top line of Qian, and thus carries the image of 'head'; Li is formed from the middle line of Kun, and thus can take the image of 'abdomen'. This is the case where the primary hexagram remains unchanged, yet the image changes. This is exactly the purpose of the "Broad Images" discussed in the "Discourse on Hexagrams".

其因本卦已變，而爻即隨其變而易其象，則必以其時其位之不同，而各異其義，即各異其象。如離為目，正象也，因變巽而為多白眼。艮為山，正象也，因反為震，而變為陵。巽為雞，正象也，因反為兌，而稱鶴。其餘變化，各以類求，未可指數也。一卦六爻，初爻為足為趾；二爻為脛，為股；三四為心，為腹；上五為首，為面。比例甚多，更論爻而不論卦，可謂專以爻位取象，為爻象之本義矣。

When the primary hexagram has changed, its lines also change their images accordingly. Therefore, the meanings and images vary according to the time and position. For example, the trigram Li represents the eye, which is the standard image. But when it changes to Xun, it becomes 'many white eyes'. The trigram Gen represents a mountain, which is the standard image. But when it is reversed to Zhen, it becomes 'a hill'. Similarly, the trigram Xun represents a chicken, which is the standard image. But when it is reversed to Dui, it becomes 'a crane'. Other changes should be examined according to their categories, and there are too many to list. Regarding the human body as an image, the six lines of a hexagram correspond to different body parts: the first line corresponds to the foot and toes; the second line corresponds to the calf and thigh; the third and fourth lines correspond to the heart and abdomen; the top line and fifth line correspond to the head and face. These correspondences are numerous, and they focus solely on the lines rather than the hexagram itself. This is the true meaning of 'yao xiang' (line images).

六位成章，陰陽迭運。位虛爻實，奇偶相生。積爻成卦，數亦相因。復一坎子，震未出用，故曰“復小”。臨二丑寅，坤兌數十，故曰“臨大”。陰爻無始，陽爻無終。陰陽首尾，往復不窮。故數盡十位，而爻十二。天五地六，以定甲子。八宮六世，三四相重。飛伏隱見，變化無盡，而無不可以數稽之。故爻位與象義既明，必征之於數，而後是非可辨也。

Six yao positions are arranged in order, with yin and yang alternating. The positions are empty, while the yao are actual. Odd and even numbers generate each other. Yao accumulate to form a hexagram, and numbers arise accordingly. The hexagram "Fu" is at the Zi position, paired with the number one, belonging to Kan; at this time, the yang line of Zhen has just begun to arise but has not yet fully activated, so the "Zajiaguanzhuan" says, "Fu, small but discerning in things." The hexagram "Lin" is at the Chou and Yin positions, paired with the number two; Kun and Dui combine, and the number reaches ten, so it is said, "Lin, great." Yin yao has no beginning, yang yao has no end; yin and yang connect head to tail, alternating endlessly. Therefore, numbers only go up to ten, but yao have twelve (Kun and Qian each have six). The heavenly number five and the earthly number six are paired to establish the sixty Jiazi. Each of the eight palaces has six generations; the third and fourth lines alternate, with flying and hidden lines appearing and disappearing, changes are endless, yet nothing is beyond the scope of numbers. Therefore, after the yao positions and symbolic meanings are understood, numbers must be used for verification, so that right and wrong can be clearly discerned.

陰陽六爻，皆指乾坤。乾父坤母，六子卦皆分乾坤之爻，各得乾坤之一體。象數變化，皆不離其宗。鄭氏爻辰，即以乾坤兩卦，分十二辰。鍾度聲律，亦各以此數交錯，相生相合，而各得其應得之數。《節·彖傳》曰：“節以制度。君子以制度數，議德行。”若由後儒之說，德行與度數何涉？

Yin and Yang and the six lines of divination all ultimately point to the trigrams Qian and Kun. Qian represents the father and Kun the mother, and the six subsidiary trigrams are each derived by taking lines from Qian and Kun, each receiving a part of Qian and Kun. All the variations of images and numbers depend on this fundamental principle. Zheng Xuan's "Yao Chen" takes the twelve lines of Qian and Kun and assigns them to the twelve earthly branches. The measurements of the bells and the five tones and six laws also follow this system, interweaving and combining with each other, each receiving its proper number. The "Commentary on the Judgment" of the "Jie" hexagram says "Jie is about establishing rules and measures," and the "Great Image Commentary" says "the gentleman establishes numbers and measures, discusses virtue and conduct." If we follow the interpretations of later Confucian scholars, how can virtue and measures be related to each other?

宋人性理諸書，汗牛充棟，所謂表裡精粗無不到者，獨無度數以節之。陰陽五行，皆鑿空之談。而所謂異端者，若老子若墨子若莊列諸子，及釋家大乘經典，其言之精者，各有數度，各有法象之可征。皆所謂法言，非任意空談可擬也。故明乎八卦之象數，明乎《彖》、《象》十翼無一辭一字之不合象數，而後三代兩漢文章之度數可辨。後世之書是否合於度數者，亦皆可辨矣。

Sung dynasty writings on nature and principles are numerous, claiming to cover all aspects thoroughly, yet they lack numerical measures to restrain them. When discussing yin and yang and the Five Phases, they all make up theories out of nowhere. In contrast, those criticized by them as heretical schools, such as Laozi, Mozi, Zhuangzi, Liezi, and the Mahayana scriptures of Buddhism, contain precise statements, each with numbers, measures, and methods that can be verified, belonging to regulated speech, which cannot be compared to mere idle talk. Therefore, only by first understanding the images and numbers of the Eight Trigrams, and realizing that every word and sentence in the Commentary on the Judgment, the Image Commentary, and the Ten Wings conforms to images and numbers, can the measures of the writings of the Xia, Shang, and Zhou dynasties and the two Han dynasties be discerned. Then, whether later writings conform to measures can also be judged.

(揚子雲知《易》象數理之精，恐後人不解，乃苦心焦思作《太玄》，以明數。作《法言》，以仿《論語》。非擬經侮聖也，其意欲人之由淺入深，因《太玄》而進於《易》。因《法言》而悟《論語》之法度，用心良苦。乃後人並《太玄》不能解，何有於《易》？讀《論語註疏》，更蔑視《法言》。又以朱子綱目“莽大夫”三字作揚雄定評，後世遂存以人廢言之成見。《太玄》、《法言》乃真成覆醬瓶之物。《太玄》、《法言》不足惜，《易經》、《論語》法象數度之不明，貽人心世道之優，良足痛焉！)。

The original commentary says: Yang Xiong (style name Ziyun) deeply understood the subtle aspects of the principles, numbers, and meanings in the Book of Changes, and feared that later generations would not be able to understand them. Therefore, he painstakingly composed the Tai Xuan to explain the numbers, and the Fa Yan to imitate the Analects. He was not trying to imitate the classics or belittle the sages, but rather to guide people from the simple to the profound: using the Tai Xuan to understand the Book of Changes, and the Fa Yan to grasp the principles of the Analects. His intention was truly arduous. Who would have thought that later generations could not even understand the Tai Xuan, let alone the Book of Changes? Those who read the annotated and interpreted Analects look down upon the Fa Yan. Moreover, Zhu Xi's Comprehensive Mirror to Aid in Government used the three words "Mang Da Fu" to evaluate Yang Xiong, leading later generations to hold the prejudice of discarding the words because of the person. Thus, the Tai Xuan and Fa Yan have truly become the discarded waste paper that Liu Xin once mocked as "covering the jar with sauce." The Tai Xuan and Fa Yan themselves are not so precious, but what is truly regrettable is that the principles, images, numbers, and measurements in the Book of Changes and the Analects have become obscure, causing harm to people's hearts and the world, which is truly heartbreaking. The character "you" in "yi renxin shidao zhi you" should be read as "you" meaning "grief."

乾簡坤易，象數著明。象由微而知著，數執簡以御繁。太極由是生兩儀，生四象，生八卦，以生六十四卦。而六十四卦仍以一“是(《未濟·上六·象》曰“有孚失是”，為全經最後之一字。)”返本還原。故欲求其“是”，當求諸始。乾坤《易》之始，六爻乾坤之始，一畫開天又六爻之始。故言卦數者，必自爻數始。

Heavenly Stems: Jia, Yi, Bing, Ding, Wu, Ji, Geng, Xin, Ren, Gui Earthly Branches: Zi, Chou, Yin, Mao, Chen, Si, Wu, Wei, Shen, You, Xu, Hai Trigrams: Qian (Heaven), Dui (Lake), Li (Fire), Zhen (Thunder), Xun (Wind), Kan (Water), Gen (Mountain), Kun (Earth) Glossary: Six at the Top = Shang Liu Eight Trigrams = Ba Gua Heavenly Qian values simplicity as its virtue, and Earthly Kun values ease as its virtue. Through these, images and numbers become clear and distinct. Images infer the significant from the subtle, while numbers control complexity through simplicity. Thus, the Taiji gives rise to the Two Principles, then the Four Symbols, then the Eight Trigrams, and further leads to the sixty-four hexagrams. Yet the sixty-four hexagrams ultimately return to their origin through the single character 'is' (是). Therefore, to seek this 'is,' one must go back to the beginning. Qian and Kun are the beginning of the Book of Changes, the six lines (yao) are the beginning of Qian and Kun, and the single stroke that 'opened the heavens' is the beginning of the six lines. Therefore, those who discuss hexagram numbers must necessarily begin with yao numbers.

先儒言卦變者多矣。虞氏以後，眾說紛紜，莫衷一是。虞《易》既無完書，其注及《周易集林》，僅於《李氏集解》中得一鱗片甲，語焉不詳。漢上朱氏，據此以定虞氏卦變圖，當時已多異議。李氏挺之，有六十四相生及反對兩圖。朱子《本義》，復有變更。陰陽重出，其為卦乃至一百二十有四。雖稱根據《彖傳》，而其舉例之十九卦，有自一卦來，兩卦三卦來者，參差不一，亦不能自圓其說。後之為圖者更多，如朱楓林等，更自鄶以下無足言矣。

Earlier scholars discussed the transformation of hexagrams extensively. Since Yu Fan, there have been many conflicting views, with no definitive conclusion. Yu Fan's commentary on the Book of Changes is no longer a complete work; his annotations and the "Zhou Yi Jilin" can only be found in fragments within Li Dingzuo's "Zhou Yi Jiejie," and they are vague and incomplete. Zhu Zhen, known as the Han Shang Master, constructed Yu's hexagram transformation diagram based on these limited materials, and at that time, it already aroused considerable controversy. Li Zhishi, who was called Tingzhi, created two diagrams: "the mutual generation of the sixty-four hexagrams" and "opposition." Zhu Xi, in his "Zhou Yi Benyi," further modified them, arranging them again in both yin and yang lines, resulting in as many as 124 hexagrams. Although he claimed to base his work on the "Tuan Zhuan," the nineteen examples he provided vary; some say they come from one hexagram, others from two or three, making them inconsistent and making it impossible for him to justify his own reasoning. Later diagram makers became even more varied, such as Zhu Sheng of the Ming dynasty, who were far inferior and hardly worth mentioning.

虞李二氏之圖，皆根本乾坤，其立論自不可磨。後儒如來氏知德，胡氏滄曉，錢氏辛楣，焦氏理堂，各有變通修正，均不能越其範圍。然皆爻變，而不盡為卦變也。夫卦者，必一卦盡變，如坤之變乾，巽之變震，斯謂之卦變可矣。若乾變姤夬同人大有小畜履，坤變剝復師比謙豫，則只一爻變。上下之乾坤，固未變焉。且占變知來，因貳以濟民行，事物萬變，烏能以六十四卦之變，應之而不窮乎？

Yu Fan and Li Zhicai both took Qian and Kun as the fundamental elements, and their theories are naturally indelible. Later scholars such as Lai Zhide, Hu Xu (who went by the courtesy name Cangxiao), Qian Daxin (who went by the courtesy name Xinei), and Jiao Xun (who went by the name Litan) each made their own modifications and corrections, but none could go beyond the scope of these two schools. However, what they discussed was actually about "yao change" rather than "guan change."the so-called "guan change" must involve all six lines of a single hexagram changing. For example, when Kun changes into Qian or when Xun changes into Zhen, this is called "guan change." As for when Qian changes into Guo, Guai, Tongren, Dayou, Xiaoxu, and Liu, or when Kun changes into Bo, Fu, Shi, Bi, Qian, and Yu, these are only changes of a single line. The Heaven and Earth trigrams within the upper and lower trigrams of the hexagram have not actually changed. Moreover, divination through change is intended to foresee the future and help people act according to auspicious or inauspicious signs. Since the changes in things are infinite, how could relying on only the sixty-four hexagrams be sufficient to cope with all situations without exhausting the possibilities?

故朱子占法，據《左》《國》所載故事為例，而又自定前十卦後十卦之別，以補其未備。無論其所謂前後十卦者，即其卦變圖百二十四卦之次序，決非古人所有。即能相合，而上下二編彖辭象辭並計，亦只四百四十八變，再加合兩卦彖辭，亦僅五百十二，烏能悉應所占之事，而定其吉凶？其無當可斷言也。

Therefore, Zhu Xi established the method of divination based on the old examples recorded in the "Zuo Zhuan" and the "Guoyu," and he himself divided the hexagrams into "the first ten hexagrams" and "the latter ten hexagrams" to make up for their shortcomings. Moreover, even if we do not consider his distinction between the first and latter ten hexagrams, the order of the 128 hexagrams in his diagram of changing hexagrams is not the original order of the ancients. Even if we suppose that all the correspondences are correct, when we combine the interpretations of the upper and lower parts of the two classics, there are only 448 kinds of changes. Adding the calculation based on the interpretations of two hexagrams together, it would not exceed 512 kinds. How could such a limited number of possibilities be sufficient to deal with all the matters of divination and determine their fortune or misfortune? It can be confidently stated that this method is not practical.

《周官》太卜所掌三《易》，自別有占法。而文周上下二編之《彖》、《象》，特其綱領。孔子《十翼》，但示人以觀象玩辭，為進德明道之本，來嘗為人言占卜之方也。“大衍”一章，明象數之根本。揲蓍求卦，以盡變通之義。引伸觸類，以盡天下之能事。亦非專為卜筮而言也。

In the "Rites of Zhou," the three books of the Yi hexagram kept by the Grand Diviner had their own separate method of divination; the commentaries on the hexagrams and images in the upper and lower volumes by King Wen and the Duke of Zhou were merely summaries of that method. Confucius composed the Ten Wings, which taught people to observe the images and play with the words, using them as the foundation for cultivating virtue and understanding the Way. He never explained the specific techniques of divination ("lai chang" should be "wei chang"). The chapter on "Great Derivation" in the "Great Treatise" discusses the fundamental principles of images and numbers; using the method of divining with yarrow stalks to obtain a hexagram was to exhaust the meaning of change and adaptability; "extending the principles and applying them to similar cases" was to exhaust all possible skills in the world — all of this was not specifically for divination.

自“掛一”，“再扐”之義不明，自唐以後，異說紛起。如劉夢得、張轅、莊綽、程伊川、朱元晦、張理、郭兼山諸家，議論不一。要皆書生之見，無當於事，無與於《易》。故歷代精於占筮者，皆屏不用，徒留為經生家聚訟之資而已(沈氏需時眇言，據天地之數由大衍求一之術，證以微積分，合而定揲四之義，與《易》象數皆能確合。俟參考儀象諸書，更試驗得實，當別為一書詳之。)。故茲編於卦變之說，概棄不錄。卦變皆由爻變，言爻變即所以言卦變也。卦變可圖，爻變則非圖所能盡也。略圖示意，閱者以意會之可耳。

Since the meanings of the divination steps "hang one to represent three" and "take two and then hang" have not been clearly explained, various interpretations have arisen since the Tang dynasty: for example, those of Liu Yuxi (courtesy name Mengde), Zhang Yuan, Zhuang Chuozhuo, Cheng Yi, Zhu Xi (courtesy name Yuanhui), Zhang Li, and Guo Zhongxiao (courtesy name Jianshan), each offering different opinions. These are mostly the views of scholars, of no practical use, and unrelated to the Book of Changes. Therefore, those who truly excel in divination have all abandoned these interpretations, leaving them only for scholars to argue over. (Shen's "Needle Time Miao Yan" uses the numbers of heaven and earth, the method of "seeking one" in the Great Derivation, and applies calculus to verify, thereby determining the meaning of "divining by four," which aligns accurately with the imagery and numbers of the Book of Changes. After consulting books on astronomical instruments and obtaining practical evidence, I will write another book to discuss this in detail.) Therefore, this compilation omits all the various interpretations regarding changes in hexagrams. Changes in hexagrams come from changes in lines. Discussing changes in lines is equivalent to discussing changes in hexagrams. Changes in hexagrams can be illustrated with diagrams, but changes in lines cannot be fully expressed in diagrams. Therefore, I will only briefly draw a diagram for illustration, and readers are expected to understand it by implication.

爻分陰陽奇偶二者而已。卦有六爻，乾坤十有二爻而已。一爻變至二三四五六爻俱變，一卦之變，六十有四，四千零九十六而已。四千九十六，亦烏足盡萬事萬物之變哉！故爻之變，有時有位，有主有應，有物有事，而數與象，猶不預焉。

The distinction of lines lies only in yin and yang, odd and even. A hexagram has six lines, and the trigrams Qian and Kun together have no more than twelve lines. From one line changing up to all six lines changing, one hexagram can produce sixty-four variations. When all sixty-four hexagrams are multiplied together, they total four thousand and ninety-six variations. That is all. Four thousand and ninety-six variations are nowhere near sufficient to exhaust all the changes of myriad things and events. Therefore, the change of lines must also be considered in terms of time and position, which one is the main and which is the responding, and whether it refers to an object or an event; yet this still does not include the factors of numbers and images.

如同一卦也，卦不變，爻亦不變。而時與位六者有一變，則利害情偽，已迥乎不同，此不變之變一也。更有爻不變而象數已變者，如七與九，皆陽也。六與八，皆陰也。七八易九六，爻之陰陽如故，而數與象，均各不同。此不變之變二也。

For example, if the same hexagram remains unchanged and none of its lines have changed, yet among the six factors—time, position, subject, responding line, matter, and event—any one of them changes, the advantage, disadvantage, truth, or falsehood will be completely different. This is the first type of "unchanging change." There is another type where the lines remain unchanged but the figures and numbers have changed: seven and nine both belong to yang, and six and eight both belong to yin. If seven and eight are exchanged for nine and six, the yin and yang of the lines remain the same, but the figures and numbers are entirely different. This is the second type of "unchanging change."

故《易》曰：動則變，變則通。動之機甚多，不必爻之動而卦始變也。朱子曰：“坤初之變為復，非頓然而變也。自小雪起，一日變一分，至冬至而始成復之一爻。”知言哉！惟其變由微而顯，由顯而著，至見於象，而陰陽始判，吉凶始見耳。僅知卦爻之變，而不知不變之變，不足以言卦，不足以言爻，並不足以言變也。

Therefore, the Book of Changes says: movement leads to change, and change leads to communication. The occasion that triggers "movement" is numerous, and it is not necessary to wait until a line moves within a hexagram before change begins. Zhu Xi said: when the first line of the Hexagram of Earth changes into the Hexagram of Return, it is not a sudden change, but a gradual change, starting from the beginning of Xiaoxue, changing by a fraction each day, until the winter solstice when it finally forms the single yang line of the Hexagram of Return. This truly hits the mark. It is precisely because change proceeds from subtle to apparent, from apparent to prominent, until it manifests in the image, that yin and yang can be distinguished, and fortune and misfortune can be seen. Knowing only the obvious change of hexagram lines and not understanding this "change without change" is insufficient for discussing hexagrams, lines, and change.

上圖略舉其例，非事物之必初上，主應之必二五。六爻皆具此六者，而六者又各有變化之不同。如今昔時也，盛衰亦時也，月建日符亦時也。位則有方位，有地位，有貴賤之位。千態萬狀，何可數限？但概之以動，察之以幾，知幾其神，而《易》始可言矣。

The diagram above is merely an example, not implying that "things" and "events" must necessarily fall on the first and top lines, nor that "subject" and "response" must necessarily be on the second and fifth lines. All six lines simultaneously possess the six elements of time, position, subject, response, thing, and event, and these six elements each have different variations. Regarding "time," present and past are time, prosperity and decline are also time, as are month builder and day symbol. Regarding "position," there is direction, status, and rank. With countless variations, how can they be counted? They can only be summarized under one word: "movement." Using the initial, subtle movement called "ji" to understand it. The Great Treatise says, "To know ji is truly divine." Only by understanding ji can one truly discuss the Book of Changes.

先天八卦，以陰陽升降，應日月之晦朔弦望，於是乎有納甲。因而重之，為六十四卦。卦有六爻，卦納乾而爻納支，於是乎有爻辰。辰者天度十二宮之次舍。而地支之十二，與天度相應者也。

The Earlier Heaven Trigrams correspond to the waxing and waning of yin and yang, matching the moon's phases of new moon, first quarter, full moon, and last quarter. This gives rise to the concept of 'Najia'. By stacking two trigrams together, sixty-four hexagrams are formed, each with six lines. Each hexagram is paired with a Heavenly Stem, and each line is paired with an Earthly Branch, leading to the concept of 'Yao Chen'. The term 'Chen' refers to the positions in the twelve divisions of the celestial circle. The twelve Earthly Branches correspond exactly to these twelve celestial divisions.

漢人言爻辰者，有鄭氏，有京氏，其說不同。鄭氏以乾陽坤陰，十二爻順逆交錯，以應十二月。而又以六十四卦之爻，合乾坤，分二十八宿之度數、星象合卦爻之象，以釋經。其書久佚，僅自《李氏集解》，及各經註疏採集其說，但存其梗概而已。有清戴氏棠，據《甘石星經》、《開元占經》等書，按六十四卦之《彖》、《象》、《繫辭》，有以星象名義，或形似相類，援鄭例而補之，名《爻辰補》。然於經義象數，均未有當，無足採焉。

In the Han dynasty, two scholars, Zheng Xuan and Jing Fang, discussed the concept of yao chen, but their views differed. Zheng Xuan regarded Qian as yang and Kun as yin, arranging the twelve lines of the two trigrams in alternating order, either forward or backward, to correspond with the twelve months of a year. He also combined the sixty-four trigrams' lines with the twenty-eight constellations, assigning degrees to them, and used celestial phenomena to match the images of the trigrams and lines, thereby interpreting the classics. His work has long been lost, and today only fragments can be reconstructed from Li Dingzuo's "Collected Explanations of the Zhou Changes" and citations in various annotations and commentaries on the classics, leaving only a general outline. In the Qing dynasty, Dai Tang, based on star and calendar texts such as the "Gan Shi Star Classic" and "Kaiyuan Treatise on Astrology," thoroughly examined the "Commentary on the Judgment," "Image Commentary," and "Great Treatise" of the sixty-four trigrams. He incorporated any lines that could correspond to celestial terms or whose shapes could be compared, following Zheng Xuan's precedent, and named his work "Yao Chen Bu" (Supplement to Yao Chen). However, from both the perspective of classical meaning and numerical symbolism, what he supplemented was not very appropriate and is not worth adopting.

京氏納辰為古今術家所遵用，證之於《彖》、《象》十翼，多能相合。有與經義相發明，為經學家所不能道者。始知黃帝五甲六子三元九宮，實探陰陰造化之秘，明天人之際。以濟世利民者，固不僅卜筮之用也。

Jing Fang's method of Nache, which has been followed by diviners throughout history, can be verified with the Commentary on the Judgment, the Image Commentary, and the Ten Wings, and in most cases they agree. Some even reveal insights that complement the classics and are not explained by scholars of the classics. From this, we realize that the system of "Wujia," "Luzi," and "San Yuan Jiugong" attributed to the Yellow Emperor indeed explores the profound mysteries of yin and yang and elucidates the relationship between heaven and humanity, aiming to benefit the world, not merely for divination purposes.

康成生於漢季，施、孟、梁丘之《易》，已多失傳。獨費氏，因其說簡約而獨存。康成亦有所不足，故採取殘缺之緯書，兼及五行律曆星象，以釋卦爻，固費《易》之所無，或亦三家之遺義也。惜其書又亡。致三代之《易》，不能盡見於今。猶幸京《易》雖亡，而八宮世應納音納甲之數，猶得貫通，得與《周易》相參證。乃學者又畏其繁瑣，目為蕪穢，必盡棄之，以自詡擴清之功，《易》道又何自明哉！

Zheng Xuan (style name Kangcheng) was born in the late Eastern Han dynasty. At that time, the schools of Shi Chou, Meng Xi, and Liang Qiu He had largely lost their teachings on the I Ching. Only the school of Fei Zhi remained because its interpretations were simple and concise. Zheng Xuan also thought that the I Ching of Fei's school had some shortcomings, so he used fragmented yijing texts, combined with the Five Phases, the system of musical scales and calendars, and celestial phenomena to explain the hexagrams and lines. These were certainly not found in Fei's I Ching, but perhaps they were the lost meanings left behind by the schools of Shi, Meng, and Liang Qiu. Unfortunately, his works later became lost, making it impossible to preserve the complete study of the I Ching from the Three Dynasties to the present. Fortunately, although the Jingshi I Ching has been lost, the system of eight palaces, Shiying, Naying, and Najia still remains intact and can be used to cross-reference with the Zhouyi. However, scholars have become tired of its complexity, considering it messy and dirty, and want to completely eliminate it, claiming they have achieved a purification. In this way, how can the principles of the I Ching be made clear?

卦納甲而爻納辰，京氏以陽順陰逆，交錯為用。以乾坤為綱，六子分乾坤之爻，以次相推。仍以本宮為體，而六爻所納之支，視其與本宮生克，以為親疏遠近利害之分。圖如下：

The trigrams are paired with the heavenly stems and the lines are paired with the earthly branches. Jing Fang used the principle of "Yang moves in order and Yin moves in reverse" to alternate and select them. Taking the trigrams Qian and Kun as the main framework, the six subordinate trigrams take the lines of Qian and Kun in sequence, proceeding downward. Still taking the original trigram as the main body, one then examines the earthly branches contained in the six lines and determines whether they are in mutual generation or mutual control with the five phases of the original trigram. Based on this, the closeness, distance, benefits, harms, good fortune, and misfortune are distinguished. The diagram is listed below.

陽卦納陽，於陽支皆順行。陰卦納陰，於陰支皆逆行。乾內納甲，外納壬，支起子，子寅辰午申戌順行。坤內納乙，外納癸，支起未，未巳卯丑亥酉逆行。陰陽交錯，以相合為用者也。

Yang trigrams take yang stems, and the paired yang branches are counted in sequence; yin trigrams take yin stems, and the paired yin branches are counted in reverse order. For the Qian trigram, the lower trigram takes Jia and the upper trigram takes Ren. The earthly branches start from Zi and proceed in sequence from the first line to the top line: Zi, Yin, Chen, Wu, Shen, Xu. For the Kun trigram, the lower trigram takes Yi and the upper trigram takes Gui. The earthly branches start from Wei and proceed in reverse order from the first line to the top line: Wei, Si, Mao, Chou, Hai, You. Yang and yin trigrams alternate, and they are used in mutual harmony.

故乾生震，震為長子。長子代父納庚，而六爻之支，與乾全同。子寅辰午申戌皆順行也。坎中男，得乾中爻，乾內中寅，坎納戊，故初爻自寅起，為戊寅，戊辰，戊午，戊申，戊戌，戊子也。艮少男，得乾之上爻。乾內三辰，艮納丙，故初爻自辰起為丙辰，丙午，丙戌，丙子，丙寅也。

Therefore, the trigram Qian generates Zhen, and Zhen is the eldest son. The eldest son acts on behalf of the father, taking the heavenly stem Geng. The earthly branches taken by the six lines are the same as those of Qian: Zi, Yin, Chen, Wu, Shen, Xu, proceeding in order. Kan is the middle son, receiving the middle line of Qian. The middle line of the lower trigram of Qian is Yin, so Kan takes the heavenly stem Wu. Thus, the first line of Kan starts with Yin, proceeding in order as Wu Yin, Wu Chen, Wu Wu, Wu Shen, Wu Xu, Wu Zi. Gen is the youngest son, receiving the top line of Qian. The third line of the lower trigram of Qian is Chen, so Gen takes the heavenly stem Bing. Thus, the first line of Gen starts with Chen, proceeding in order as Bing Chen, Bing Wu, Bing Shen, Bing Xu, Bing Zi, Bing Yin (the entry for Bing Shen is omitted in the original text).

坤生長女為巽，長女代母，而納不起於丑，而起於未，與震襲乾不同者，此男女之別，陰陽之分。女以出為歸，故自內出外。由四爻起未，五巳上卯，而反至初為丑二為亥三為酉也。離為中女，得坤中爻，故於外中五爻起未。兌為少女，得坤上爻，故於外上起未，皆未巳卯丑亥酉，與巽同例也。季彭山不知陰陽之別，妄改坤起乙丑。又有不分陰陽，不知本末，妄改乾為甲子，甲戌，甲午，甲寅，甲辰者，皆絕無意義。學者不可好奇喜新，為所誤也。

The eldest daughter of the Earth trigram is Wind, which takes the position of the mother. However, the Wind trigram does not start its branches from the Ox (Chou) but from the Sheep (Wei). This is different from the Thunder trigram, which follows the same order as the Heaven trigram. This difference reflects the distinction between male and female, yin and yang. Women's destiny is to marry and thus they move from the inner to the outer: the Wind trigram starts from the fourth line with Wei, the fifth line with Si, the top line with Mao, then turns back to the first line with Chou, the second line with Hai, and the third line with You. The Fire trigram is the middle daughter, taking the middle line of the Earth trigram, so it starts from the fifth line with Wei in the outer trigram. The Lake trigram is the youngest daughter, taking the top line of the Earth trigram, so it starts from the top line with Wei in the outer trigram. The three trigrams all follow the sequence of Wei, Si, Mao, Chou, Hai, You, similar to the Wind trigram. Ji Ben of the Ming dynasty (pen name Pengshan) did not understand the distinction between yin and yang and mistakenly changed the Earth trigram to start from Yichou. Others failed to distinguish yin and yang and the beginning and end, and arbitrarily changed the Heaven trigram to start with Jiazi, Jiaxu, Jiawu, Jiayin, and Jiachen, which are all meaningless. Scholars should not be greedy for novelty and be misled by such incorrect views.

六十四卦，八純卦外，一世至六世，皆取本宮納甲。見者為飛，不見者為伏。游魂歸魂十六卦，不取本宮為伏。分舉爻位如下：晉以艮為伏，而取艮四爻者，以游魂仍為四爻變。而晉上之離，由剝上之艮變來者也。故不以本宮不以對宮而取艮。大有下卦之離，由晉下卦之坤變來者也。歸魂為三爻，故取坤三。餘卦仿此。

Among the sixty-four hexagrams, except for the eight pure hexagrams, the hexagrams of the first to sixth generations take the stem assignment from their own palace: those that are visible on the outside are called 'Flying' (飞), and those that are hidden inside are called 'Hidden' (伏). The sixteen hexagrams of the wandering soul (游魂) and returning soul (归魂) do not take the hidden stem from their own palace. Here are the specific lines for each: The hexagram of晋 takes the trigram艮 as its hidden stem, specifically the fourth line of艮, because the wandering soul still originates from the fourth line. The trigram离 on top of晋 comes from the trigram艮 on top of剥, so it does not take the stem from its own palace or the opposite palace, but instead takes the stem from艮. The trigram离 in the lower trigram of大有 comes from the trigram坤 in the lower trigram of晋; the returning soul changes on the third line, so it takes the third line of坤. The rest of the hexagrams follow the same pattern.

鄭氏爻辰，亦以陰陽六爻，相間用事。乾辰子寅辰午申戌，其次與京氏同，而坤則為未酉亥丑卯巳與京氏異。蓋陰陽雖間一位，而皆順行。蓋以十二律相生為據也。他卦分乾坤之爻，亦分乾坤之辰，不論納甲。

Zheng Xuan's yao chen system also involves yin and yang hexagrams taking turns in succession. The six lines of Qian are assigned to Zi, Yin, Chen, Wu, Shen, and Xu in that order, which is the same as Jing Fang's system. However, the six lines of Kun are assigned to Wei, You, Hai, Chou, Mao, and Si, which differs from Jing Fang's system. Although Zheng Xuan also selects every other branch, both Qian and Kun hexagrams follow a clockwise order, whereas Jing Fang's system has Kun in a counterclockwise order. Zheng Xuan based his system on the sequence of the twelve tones in mutual generation. The other hexagrams inherit the yao assignments of Qian and Kun, and thus also inherit their corresponding chen, without relying on the Najia system.

徵者，用之見乎外者也。壽陽閻氏《爻徵廣義》，詳於鄭氏爻辰，殊於實用無征焉。六爻制用，肆應不窮，皆以五行陽干陰支為綱領，以生克刑害少壯盛休廢類別去取，以征吉凶。以其與卦爻象數，相為統系，足以推六十四卦變化往來之跡。且有與經傳互相發明者，亦初學所不可不知者也。爰取《京氏易》與《易緯》諸書之著錄者，分隸六爻，徵爻用，亦以存古義也。至推演條理，今密於古，術家所習用，更毋庸備述焉。

The term "zheng" refers to the external manifestation of "use" as a form of verification. The Yan family of Shouyang in Shanxi wrote "Yao Zheng Guangyi," which provides a detailed explanation of Zheng Xuan's theory of yao chen, but in practical application, it fails to produce verifiable results. The system of controlling and responding to the six yao (lines) is endless, and all are organized under the framework of the Five Phases, as well as the yang stems and yin branches. They are classified and selected according to the states of generation, overcoming, punishment, and harm, as well as the stages of youth, maturity, prosperity, rest, and decline. These are used to verify auspicious and inauspicious outcomes. Because this system is integrated with the imagery and numbers of the hexagrams, forming a unified whole, it can trace the trajectory of the sixty-four hexagrams' transformations. Moreover, in some cases, it can also complement the classic texts, which is something beginners should not be unaware of. Therefore, the content recorded in "Jing Shi Yi Chuan" and the various works of "Yi Wei" has been systematically assigned to the six yao, to verify the function of the yao, and also to preserve ancient meanings. As for the logical structure of the divination process, it is now more precise than in ancient times, and these are common methods used by numerological practitioners, so there is no need to elaborate on them one by one.

京氏曰：“八卦鬼為繫爻，財為制爻，天地為義爻，福德為寶爻，同氣為專爻。”此五者，今術家謂之六親(親者，族也。《易》曰“類族辨物”，先辨諸爻。)，蓋與本身為六也。相傳甚古，義簡而賅，言占者所不能廢。

Jing Fang said: Among the Eight Trigrams, "ghost" is called the tied line, "wealth" is called the controlling line, "heaven and earth" is called the meaning line, "fortune virtue" is called the treasure line, and "same nature" is called the exclusive line. These five items, today's divination experts call them "Six Relations" ("relation" refers to category. The Image Commentary of Tongren says, "The superior man uses classification of kinship to distinguish things," first distinguishing clearly each line. ) Because adding the self makes a total of six. This system is said to have a long history, with clear and comprehensive meaning, and those who interpret the hexagrams cannot abandon it.

朱子《周易本義》，以周孔之《易》為教人卜筮之用，而焦京之言卜筮者，反悉廢之，僅以六爻之動靜為占，宜其無徵驗之可言也。茲以京說為主，而以近世皆用者附之。非敢謂援古證今，亦發其凡而已。

Zhu Xi wrote The Original Meaning of the Zhou Changes, claiming that the Zhou Changes and the Analects of Confucius were meant for divination. Yet he discarded the methods established by genuine diviners like Jiao Yanshou and Jing Fang, relying solely on the movement of the six lines for divination. It's no wonder there's no verification. Here, we mainly follow Jing Fang's approach, and add the commonly used terms of recent times. I dare not say this is using ancient principles to verify current practices, but rather just providing an outline and example.

專爻一，同氣為專爻。陸績曰：同氣兄弟也，如金與金，木遇木之類。今稱兄弟。寶爻二，福德為寶爻。福德子孫也。我所生者也。如金與水，水與木是也。今稱子孫。義爻三，天地為義爻。天地父母也，生我者也。如木為水生，水為金生。今稱父母。制爻四，財為制爻。財者我所制也。如木克土，土為木之財是也。今稱妻財。繫爻五，鬼為繫爻。繫者束縛之意，制我者也。如火克金，火即金之鬼也。今稱官鬼。

This is a flat six relations chart. Originally divided into the five phases, each row lists in order the old name from Jing Fang, its explanation, the commentary by Lu Ji of the Three Kingdoms period, and the common term used by modern divination practitioners. First, the exclusive爻 (special爻), meaning "same qi is the exclusive爻": Lu Ji said that same qi refers to siblings, for example, metal meeting metal, wood meeting wood, etc. Today this is called "siblings". Second, the treasure爻 (treasure爻), meaning "fortune virtue is the treasure爻": fortune virtue refers to children, which is the aspect I generate, for example, metal generates water, water generates wood, etc. Today this is called "children". Third, the righteousness爻 (righteousness爻), meaning "heaven and earth are the righteousness爻": heaven and earth refer to parents, which is the aspect that generates me, for example, wood is generated by water, water is generated by metal, etc. Today this is called "parents". Fourth, the controlling爻 (controlling爻), meaning "wealth is the controlling爻": wealth is what I can control, for example, wood controls earth, and earth is the wealth of wood. Today this is called "wealth". Fifth, the binding爻 (binding爻), meaning "ghost is the binding爻": "binding" means restraint, referring to the aspect that controls me, for example, fire controls metal, and fire is the ghost of metal. Today this is called "official ghost".

五者與本身為六。今稱六親者，義亦近古。親者族也。類族辨物，舉一起例，凡言兄弟，則比肩者可類；言子孫，則後我者可類；言父母，則庇我者皆其類；言妻財，則奉我者皆其類；言官鬼，則制我害我者皆其類。遠近不同，則親疏自異。而為利為害，爰有重輕之別。是在察其爻之所在，而鑑別之，非可概論也。

These five elements, together with the self, make six, which is called the "Six Relations" today. The meaning is quite close to the ancient concept. "Relation" refers to a category. The phrase "classifying kinship and distinguishing objects" means using one example to establish a general rule: whenever we refer to "siblings," all those who are on the same level as me can be classified under this category; when we refer to "children," all those who come after me can be classified under this category; when we refer to "parents," all those who protect me can be classified under this category; when we refer to "wealth," all those who support me can be classified under this category; and when we refer to "official ghost," all those who restrain me or harm me can be classified under this category. The relationship may be distant or close, so the degree of intimacy varies naturally; whether it is beneficial or harmful also has different degrees of importance. This depends on which line falls in a particular position to determine the distinction, and cannot be considered in a general way.

神(神者存也。成性存存，陰陽不測，假定其名，亦猶類族辨物之意也。)也者，妙萬物而為言。過化存神，有非可以跡象求之者。六親征其實，六神徵諸虛。周流六虛，無乎不在。渺焉漠焉，將何從徵？曰陰陽之氣，布為五行，其幾甚微。《傳》曰：“本於陰陽而立卦，陰陽變化，而神寓也。”此六爻之神所由名，要非泥其名以為實者也。

The term "shen" (spirit) refers to "cun" (presence). The Great Treatise says, "Forming nature and maintaining presence," meaning that the changes of yin and yang are unpredictable, so we give it a name, just as "classifying kinds and distinguishing things" helps in identification. According to the Discourse on the Hexagrams, "shen speaks of the subtle workings of all things." The Mencius says, "Where it passes, it transforms; where it resides, it is shen," showing that some things cannot be pursued through physical traces. The Six Relations verify the tangible aspect, while the Six Spirits verify the intangible. Shen flows through the six voids, present everywhere, yet it is vast and indistinct, so how can it be verified? The answer is: the qi of yin and yang spreads out to form the Five Phases, and its initial movement is extremely subtle. The transmitted text says, "Establishing hexagrams based on yin and yang, and the subtle spirit resides within their changes"—this is the reason for the term "six yao shen." The important point is not to be rigid about the name, treating it as an actual entity.

震東方木，木之神青龍，甲乙日起青龍。離南方火，火之神朱雀，丙丁日起朱雀。兌西方金，金之神白虎，庚辛日起白虎。坎北方水，水之神玄武，壬癸日起玄武。坤艮中央土，土之神勾陳螣蛇，戊己日起勾陳騰蛇。

This is a flat chart showing the assignment of the Six Spirits, linking the trigrams, directions, the Five Phases, the names of the spirits, and the days they begin. Zhen is in the East and belongs to wood; the spirit of wood is the Azure Dragon, and on days of Jia and Yi, the sequence starts with the Azure Dragon. Li is in the South and belongs to fire; the spirit of fire is the Vermilion Bird, and on days of Bing and Ding, the sequence starts with the Vermilion Bird. Dui is in the West and belongs to metal; the spirit of metal is the White Tiger, and on days of Geng and Xin, the sequence starts with the White Tiger. Kan is in the North and belongs to water; the spirit of water is the Black Tortoise, and on days of Ren and Gui, the sequence starts with the Black Tortoise. Kun and Gen are in the center and belong to earth; the spirits of earth are Gou Chen and Tan Sha, and on days of Wu and Ji, the sequence starts with Gou Chen and Tan Sha. When divining, determine the starting spirit based on the heavenly stem of the day, then arrange the spirits sequentially on the six lines.

《傳》曰：“前朱雀而後玄武，左青龍而右白虎。”古者五行各有專官，官世其守，功德在民，民不能忘。即假人名以神號，舉其名知其用，所以便事也。吉凶神煞之名，皆此類也。必求其人以實之，愚也。必妄其名而斥之，亦詎足為智哉！六壬、太乙、遁甲之言神，舉可隅反矣。

The Book of Rites, Volume of the Rituals says: "In front is the Vermilion Bird, behind is the Black Tortoise, on the left is the Azure Dragon, and on the right is the White Tiger." In ancient times, each of the Five Phases had officials in charge, whose positions were passed down through generations. Their virtues remained in the hearts of the people, who could not forget them. Thus, they used these people's names as titles for deities. By mentioning the name, one knew what function it represented, making it convenient for affairs. All the various names of auspicious and inauspicious deities belong to this category. It is foolish to insist on finding real people to confirm their existence. Conversely, to deny all these names as mere fabrications and refute them is not necessarily wise either. The various deities mentioned in the systems of Liu Ren, Tai Yi, and Dun Jia can all be understood by applying this principle.

六屬者以五音分屬六爻，即本於納音。納音與納甲相表裡。屬之於爻，仍隨八卦之納甲以定其數也。舉例如下：

The so-called "six attributes" involve assigning the five tones, Gong, Shang, Jue, Zhi, and Yu, to the six lines of a hexagram. This practice originates from "Nayin" or sound elements. Nayin and Najia are interrelated; when assigning the five tones to the lines of a hexagram, the determination still follows the numerical assignments based on the Eight Trigrams' Najia. For example:

子午屬庚，震初爻也，庚子午。

This line is the first entry of the "six attributes" assignment table. The "six attributes" refer to distributing the five tones across the six lines of a hexagram, and its basis remains "najia" stem assignment. The Zhen hexagram is assigned the heavenly stem "Geng," its first line is paired with the earthly branch "Zi," and its fourth line is paired with the earthly branch "Wu," so the branches "Zi" and "Wu" are assigned to "Geng," written as "Gengzi" and "Gengwu." The table only lists the first line because the first line is the starting point of the hexagram's earthly branch assignment: for a yang hexagram, starting from the first line, the branches are taken in order, skipping one each time, and by the fourth line, it is exactly six positions away from the first line, forming a conflicting pair. Therefore, one heavenly stem controls two conflicting earthly branches.

卯酉屬己，離初爻也已，卯酉。

The branches of卯 and酉 belong to the heavenly stem「己」, referring to the卦 of Li (Fire). According to the method of Najia stem assignment, the eight trigrams are assigned the ten heavenly stems. The trigrams Qian (Heaven) and Kun (Earth) are considered parents and each take two stems, while the six children trigrams each take one stem. The trigram Li (Fire) is assigned「己」. Since Li is a yin trigram, the branches are assigned in reverse order starting from the first line: first line is Jimao, second line is Jichou, third line is Jihai, and fourth line is Jiyou. Therefore, the first and fourth lines correspond to卯 and酉, written as「己卯」and「己酉」. In the table, the third column is mistakenly carved as「已」, which is a form similar to「己」.

寅申屬戊，坎初爻也，戊寅申。

The branches Yin and Shen belong to the heavenly stem Wu. This refers to the Kan hexagram. Kan is a yang hexagram, and it incorporates the stem Wu. It pairs with the Li hexagram's stem Ji, forming a pair of earth stems in the middle of the ten heavenly stems. One is located in the north, and the other in the south, corresponding to the positions of the sun and moon, as well as the middle qi. The branches incorporated into Kan hexagram start from the first line and proceed in order: the first line is Wu Yin, the second line is Wu Chen, the third line is Wu Wu, and the fourth line is Wu Shen. Therefore, the first and fourth lines contain Yin and Shen, written as 'Wu Yin' and 'Wu Shen'. Yin and Shen are in opposition, yet they are still unified under one stem.

辰戌屬丙，艮初爻也，丙辰戌。

The Earthly Branches Chen and Xu belong to the Heavenly Stem Bing. This refers to the Gen hexagram. Gen is a Yang hexagram, and it receives the stem Bing. Its reception of the branches also starts from the first line and proceeds in order, selecting every other branch: first line Bingchen, second line Bingwu, third line Bingshen, fourth line Bingxu. Therefore, the first and fourth lines correspond to Chen and Xu, written as "Bingchen" and "Bingxu". Chen and Xu are two of the four earthly repositories (si ku), both representing earth. This aligns with the nature of Gen, which represents mountain, stopping, and earth.

巳亥屬丁，兌初爻也，丁巳亥。

The branches Si and Hai belong to the heavenly stem Ding, referring to the Dui hexagram. Dui is a yin hexagram, and its heavenly stem is Ding. The earthly branches are arranged from the first line in reverse order: the first line is Ding Si, the second line is Ding Mao, the third line is Ding Chou, and the fourth line is Ding Hai. Therefore, the first and fourth lines have Si and Hai, written as "Ding Si" and "Ding Hai." Since it is called "six belonging," there should be six entries, but here only five hexagrams are listed: Zhen, Li, Kan, Gen, and Dui. The missing one is Xun, which takes "Xin." The first line is Xin Chou and the fourth line is Xin Wei, written as "Chou Wei belong to Xin." This entry is missing in the transmitted text.

不言乾坤，六子之爻，皆乾坤之爻也。《說卦》“神也者”一章，不言乾坤，非特六子之用，皆乾坤之用。而所謂神者，即乾坤之陰陽不測，周流六虛者也。納音之說似淺而實深。精微之理，非可以跡象求之。

The upper trigrams only list Zhen, Li, Kan, Gen, and Dui but do not mention Qian and Kun, because the lines of the six subordinate trigrams originally come from the lines of the Qian and Kun trigrams. By discussing the six subordinate trigrams, Qian and Kun are already included. The passage in "Shuo Gua" that says "The 'spirit' is what speaks of the subtle workings of all things" also does not mention Qian and Kun throughout, using the same method. What is discussed in that passage is not only about the functions of the six subordinate trigrams; in fact, it is about the functions of Qian and Kun throughout. The term "spirit" refers to the function of the two energies of Qian and Kun, yin and yang, which change mysteriously and flow through the six lines' empty positions. The concept of "Nayin" may seem superficial, but it is actually very profound. The subtle principles within it cannot be understood merely by superficial appearances or numerical patterns.

謂之音者，乾坤爻辰左行右行。間辰六位，即六律六呂，相生之所本，故以分屬六爻，各納其辰，而謂之納音。今術家占筮推演及風角堪輿諸家，均不能廢納音以為言，而莫知其所由來。因備六爻所屬，並列《內經》及揚子雲、抱朴子諸家之圖於後，庶閱者可悉其始末矣。

It is called "sound" because the yao chen of the Qian trigram move left in a clockwise direction, while those of the Kun trigram move right in a counterclockwise direction. The two sides alternate and are separated by six positions, which is the basis for the mutual generation of the twelve laws of the "six laws" and "six lü." These twelve laws are distributed among the six yao, with each yao taking in one chen, hence it is called "Nayin." Now, those who practice divination and those who study wind angles and geomancy all rely on Nayin to establish their theories, yet no one can clearly explain its origin. Therefore, Hang氏 here lists the respective chen for each of the six yao, and also appends the diagrams from the Huangdi Neijing, Yang Xiong, and Ge Hong, so that readers may clearly understand the origin and development of this theory.

納音始於黃帝，今《內經》所載最詳。京氏六十律與甲子分配，自是古法。蓋以一律納五音，十二律納六十音。《內經》五音，始於金，傳火傳木傳水傳土。陽律陰呂，隔八相生。葛稚川曰：“一言得之者，宮與土（所屬者即一言而得）。三言得之者，徵與火（如戊去庚三位，故曰三言。下仿此）。五言得之者，羽與水。七言得之者，商與金。九言得之者，角與木。故子午九，丑未八，寅申七，卯酉六，辰戌五，巳亥四也。”

The method of Nayin sound elements originated in the time of the Yellow Emperor. The most detailed surviving account today is found in the "Huangdi Neijing" (Yellow Emperor's Inner Canon). Jing Fang paired the sixty tones with the sixty Jiazi (Heavenly Stems and Earthly Branches), which was originally an ancient method. His approach was that one tone governed five musical tones, and twelve tones could thus produce sixty musical tones. The five musical tones arranged in the "Huangdi Neijing" start with metal, then pass on to fire, wood, water, and finally earth. Among the twelve tones, the yang ones are called "Lu" and the yin ones are called "Lv," and they generate each other by being separated by eight positions. Ge Hong wrote in the "Baopuzi" that one syllable produces "Gong" and earth (since one syllable is the first sound, it is called one syllable); three syllables produce "Zhi" and fire (for example, from Wu to Geng, there are three positions in between, so it is called three syllables, and so on). Five syllables produce "Yu" and water; seven syllables produce "Shang" and metal; nine syllables produce "Jue" and wood. Therefore, the numbers for Zi and Wu are nine, Chou and Wei are eight, Yin and Shen are seven, Mao and You are six, Chen and Xu are five, and Si and Hai are four.

揚子雲《太玄》以火土木金水為序，與《內經》不同。甲子乙丑金者，言甲乙子午其數九，乙庚丑未其數八，甲乙子丑積數三十四，以五除之餘四，故為金。

Yang Xiong's "Tai Xuan" arranges the Five Phases in the order of fire, earth, wood, metal, and water, differing from the "Neijing" which starts with metal. As for the Nayin sound element of "Jiazi Yichou" being assigned to metal, it is calculated as follows: Jia and Ji are paired with Zi and Wu, their number being nine; Yi and Geng are paired with Chou and Wei, their number being eight. The numbers of the four characters Jia, Yi, Zi, and Chou are added together to total thirty-four. When divided by five, the remainder is four, which corresponds to metal in the Five Phases, hence the Nayin sound element of Jiazi Yichou is metal. (In the original edition, it reads 'Jia Yi Zi Wu' and 'Yi Geng Chou Wei', but the 'Jia Yi' in the first instance should be 'Jia Ji' as indicated by the following text, which is a transmission error.)

餘仿此數，列右圖。按：甲己子午九，乙庚辛未八，丙辛寅申七，丁壬卯酉六，戊癸辰戌五，巳亥四（己亥對宮亥空為虛，己與虛對為孤，己亥者孤虛之數也。）。

The other groups are calculated in the same way. The original book by Hang氏 includes a diagram on the right, but the transmitted version has lost it. Hang氏 himself explained: Jia and Ji are paired with Zi and Wu to make nine, Yi and Geng are paired with Chou and Wei to make eight (the original edition says 'Xinwei', which should be 'Chouwei' instead), Bing and Xin are paired with Yin and Shen to make seven, Ding and Ren are paired with Mao and You to make six, Wu and Gui are paired with Chen and Xu to make five, while Si and Hai are only paired with four and do not have another heavenly stem. Why is this so? Because the palace opposite Ji is Hai, and since the position of Hai is empty, it is called 'Xu' (empty). Ji facing 'Xu' becomes 'Gu' (solitary), so 'Jihai' is exactly the number of 'Gu Xu', which is the only one missing.

黃梨洲先生《象數論》所評議者，頗多未當。其謂甲子乙丑金者，甲九子九，乙八丑八，積三十四，以五除之餘四故為金。其數則是，其術則非也。故於丙寅丁卯，丙七寅七丁六卯六積二十六，以五陰之餘一故為火，便不成文矣。金四為一當為水，何以為火？而猶曰餘準此將無一能合者矣。

Huang Zongxi in his work "Yixue Xiangshu Lun" has many inappropriate comments on the concept of nayin. He said that Jiazi and Yichou belong to metal because Jia gets nine, Zi gets nine, Yi gets eight, and Chou gets eight, adding up to thirty-four, which when divided by five leaves a remainder of four, thus belonging to metal. Although the calculation is correct, the method he used is wrong. Therefore, when he comes to Bingyin and Dingmao, his reasoning becomes inconsistent: Bing gets seven, Yin gets seven, Ding gets six, and Mao gets six, adding up to twenty-six, which when divided by five leaves a remainder of one, and he concludes it belongs to fire. This reasoning is completely invalid. If a remainder of four can be considered metal, then according to the same principle, a remainder of one should be considered water, so why does he say it is fire? He also says "the rest can be inferred in the same way," but if this is the case, there is no way to make the reasoning consistent.

蓋納音得數之算法，當以大衍為本。以大衍之數五十去一，除去甲己子午之積數，餘則以五除之，得一則屬水，水生木，其納音為木。丙寅丁卯之為火，當以積數二十六，除大衍五十去一，餘二十三，以五除之餘三，屬木，木生火，故納音為火。甲子乙丑之積三十四，以除大衍去一餘五，五屬土，土生金。非三十四餘五餘四之謂也。

The calculation of the nayin sound element should be based on the fundamental principle of "Da Yan" or the Great Derivation. Take the number of Da Yan, which is fifty, subtract one to get forty-nine. Then subtract the accumulated number of categories such as Jia and Ji, Zi and Wu. The remainder is divided by five. If the result is one, it belongs to water, as water generates wood, and thus the nayin sound element is wood. For Bing Yin and Ding Mao, which are assigned to fire, the calculation is as follows: the accumulated number is twenty-six. Subtract this from forty-nine, leaving twenty-three. Divide this by five, resulting in a remainder of three. Three corresponds to wood in the Five Phases, and since wood generates fire, the nayin sound element is fire. For Jia Zi and Yi Chou, the accumulated number is thirty-four. Again, subtract this from forty-nine, leaving fourteen. Divide by five, resulting in a remainder of four. Four corresponds to fire in the Five Phases, and since fire generates earth, the nayin sound element is earth. The key lies in "first subtracting Da Yan and then determining the generated element," rather than directly dividing thirty-four by five as Huang did, and discussing the remainder of five and four.

納音納甲，與天干地支，皆始於黃帝。蓋自伏羲畫卦，利用宜民，至神農黃帝，文明日進，變化益繁。非單純八卦之象數所能濟用，故益之以陰陽五行。天五地六，迎日推歷，布算測地，以盡八卦之用。所謂“窮則變，變則通，通則久”。

The systems of Na Yin and Na Jia, along with the Heavenly Stems and Earthly Branches themselves, originated in the time of the Yellow Emperor. Since Fuxi drew the trigrams and taught the people to make full use of resources for a better life, civilization has gradually advanced, and the complexity of things has increased day by day. The simple images and numbers in the Eight Trigrams alone were no longer sufficient to cope with these changes. Therefore, the concept of Yin and Yang and the Five Phases were added beyond the Eight Trigrams. Taking "Heavenly Five" and "Earthly Six" as the main framework, they followed the sun's shadow to determine the calendar, used counting rods for calculations, and measured the terrain, thus fully developing the functions of the Eight Trigrams. This is exactly what the Great Treatise says: "When things reach their limit, they change; when they change, they become unblocked; when they become unblocked, they can endure for a long time."

納甲取先天，法象乎日月，仰以觀於天文也。納音以先天合後天，取數於陰陽十二消息，以布五行，俯以察於地理也。故京孟之《易》，悉本於此。朱元升《三易備遺》推衍納音最詳，巳亥數伏，一六相合，以為即《歸藏》之數，非無見也。

"Na Jia" derives the Earlier Heaven hexagram positions, based on the rising and setting and waxing and waning of the sun and moon, corresponding to the "looking up to observe the celestial phenomena" mentioned in the "Great Treatise." "Na Yin" combines Earlier Heaven and Later Heaven, taking numbers from the twelve yin and yang message hexagrams, then arranging the Five Phases accordingly, corresponding to "looking down to examine the terrestrial features." Therefore, the Yi studies of Jing Fang and Meng Xi all rest upon this foundation. Zhu Yuansheng of the Song dynasty wrote "San Yi Bei Yi," elaborating on Na Yin most thoroughly. He pointed out that the numbers of the branches Si and Hai are concealed and not apparent, and that one and six exactly correspond, believing this to be the numerical system of the "Guizang" Yi. This view is not without merit.

運氣升降由於氣，氣之盛衰由於數，數之進退在乎人。聖人作《易》立人極以明人道，言天言地，皆為人言而為人謀。人在天地中，為善為惡，為君子，為小人，皆在人之自為。而氣機之感召，陰陽進退，而數即隨之而消長。積氣成運，積運成象，為殃為祥，皆視所積。積之以漸，非一朝一夕之故。及其至焉，則為泰為否。君子小人之消長，似乎天實為之，命實定之。嗚呼！天豈任其責哉！

The rise and fall of "yun" depends on "qi," the prosperity and decline of "qi" depends on "shu," and the movement of "shu" hinges on people. The sages composed the Book of Changes to establish the "human standard" and clarify human conduct; whenever discussing heaven or earth, it is ultimately for the sake of people, planning for them. Humans live between heaven and earth, whether they do good or evil, become a gentleman or a petty person, entirely depends on their own actions. The qi energy responds to this, causing yin and yang to advance or retreat, and "shu" accordingly increases or decreases. Accumulated qi becomes "yun," and accumulated "yun" manifests as "xiang." Whether it brings calamity or blessing depends entirely on what is accumulated. This accumulation comes gradually, not in a single day; when it reaches its extreme, it becomes "Tai" or "Pou." The rise and fall of gentlemen and petty persons, at first glance, seems to be determined by heaven and fate—ah, how could heaven bear such responsibility!

《易》以象設教，善惡吉凶，無不備著於象。而以陰陽五行生合升降，為之節度。法象於天地，而示人以進德修業之天則，各有數度。此君子以人合天之本，而古聖人經緯天地，燮理陰陽之大用，皆備於此焉。

The Zhou Changes (I Ching) employs "images" (xiang) to carry out education and guidance; goodness and evil, fortune and misfortune, are all fully displayed in these images. It further determines the limits and measures of these images by means of the mutual generation and mutual assistance of yin and yang and the five phases, as well as their rising and falling. It takes the forms of heaven and earth as its model, revealing to people the natural principles of cultivating virtue and advancing in learning. Every step follows a definite measure. This is the fundamental principle of the gentleman's "harmonizing human with heaven." It also fully embodies the great function of the ancient sages in governing the world, regulating yin and yang, and harmonizing the universe.

後儒不察，空言性命，而莫知其象，莫悉其數。反以聖人示之陰陽氣運，為小道，為術數，棄置不言。不知《易》以道陰陽，卦象彖爻無論矣，即孔子之《十翼》，亦無一言無一字，不與陰陽度數相密合。觀於納甲納音，而後知五運六氣，皆出於八卦，在在足與《易》象《易》數相發明。欲知《易》之蘊者，不可不深察焉。

Later scholars of Confucianism were unwilling to examine carefully, and instead engaged only in empty talk about principles and destiny. They did not understand the images of the hexagrams nor grasp the numerical calculations of the Book of Changes. Instead, they condemned the system that the sages used to reveal the movement of yin and yang as a minor craft and a form of numerology, and set it aside. They did not realize that the Book of Changes itself is about the principles of yin and yang: the images of the hexagrams, the statements of the hexagram judgments, and the statements of the lines are self-evident. Even the ten wings written by Confucius contain no statement or word that does not precisely correspond with the measurements of yin and yang. Only after studying the assignment of heavenly stems and the sound elements of the earthly branches will one understand that the medical concept of "five movements and six energies" originates entirely from the eight trigrams, and that everywhere it can be verified and explained in conjunction with the images and numerical calculations of the Book of Changes. Anyone who wishes to understand the profound meaning hidden within the Book of Changes must carefully examine this aspect.

此主運也。客運則以本年所屬五行作初運，輪流而布。

The arrangement above represents the "Main Cycle" or "Main Movement," which is the fixed order of the five phases—wood, fire, earth, metal, and water—throughout the year. As for the "Traveling Cycle," it begins with the five elements corresponding to the heavenly stem of the current year, and then proceeds in the order of mutual generation among the five phases, shifting each year. This Traveling Cycle contrasts with the unchanging Main Cycle.

是為《月令》之氣，年年定局不易，謂之主氣。至於客氣，則從年司天，自正南位起輪布，看主與客相臨，其氣相得則和，不相得則害。

The arrangement shown above corresponds to the system of seasonal energies described in the "Book of Rites: Monthly Orders." This system divides the year into six steps, with a fixed pattern each year, known as "Zhu Qi." As for "Ke Qi," it is determined by the "Shi Tian" energy of that particular year. Starting from the direction of Due South, the energies are arranged in sequence and rotated accordingly. After the arrangement is completed, one examines how the Zhu Qi and Ke Qi interact: if their energies are compatible, they harmonize; if they are conflicting, they cause harm. Many disasters, plagues, and diseases of the year arise from such interactions.

五運六氣，天地陰陽之橐龠，其傳最古，今惟《內經》言之最詳。聖人作《易》，法象乎天地，近取諸身，遠取諸物。而天地萬物，皆範圍乎運氣之中。所謂造化之機，與吾人身心性命，息息相關。民胞物與，豈空言所濟！讀董子《春秋繁露》、《淮南鴻烈》、揚子《法言》，當知鄙言之非妄也。

The "Five Movements and Six Qi" are like the bellows of heaven and earth's yin and yang, alternately expanding and contracting, causing all things to rise and fall accordingly. This theory has been passed down since the earliest times, and today the most detailed exposition of it can be found only in the "Huangdi Neijing" (Yellow Emperor's Inner Canon). The sages composed the "Yi Jing" (Book of Changes), drawing their inspiration from the forms of heaven and earth. They took close examples from the human body and distant ones from all things. In fact, heaven, earth, and all things are all encompassed within the scope of the movement and qi. What is called the pivot of creation and transformation is actually intimately connected with our own body, mind, and destiny. Zhang Zai said, "The people are my fellow beings, and all things are my companions," but how can such words be truly realized without action? If one reads Dong Zhongshu's "Chunqiu Fanlu" (Luxuriant Dew of the Spring and Autumn Annals), Liu An's "Huainanzi" (Masterful Treatise of the Huainan), and Yang Xiong's "Fayang" (Discourses on the Classic), one will understand that my words are not baseless talk.

《繫傳》曰：“開而當名辨物，正言斷辭，則備矣。”故斷辭必先正言，正言必先辨物，辨物必先當名，名稱其實為當。名而當，則舉其名而物之大小情偽畢見矣。盈天地之間唯萬物，物各有其名，不能悉舉也。而《易》以《彖》、《象》、《爻》三者賅之，以三者舉其綱，而八卦六十四卦之名無不當，天地萬物胥可以名辨而別之。擬之後言，議之後動，而正言斷辭如視之掌矣。

The "Great Treatise" says: "When things are opened up and their names are properly established, and things are clearly distinguished, then the statements of judgment are complete." Therefore, in order to give a statement of judgment for a hexagram and its lines, one must first speak clearly. To speak clearly, one must first distinguish things clearly. To distinguish things clearly, one must first have appropriate names—when names correspond to reality, this is called "appropriate." Once names are appropriate, simply mentioning them reveals the size, nature, and authenticity of the things. The world is filled with myriad things, each with its own name, which is countless. However, the "Zhou Changes" use the "Tao Statements," "Image Statements," and "Line Statements" to encompass them all. By using these three, they provide a summary, so that the names of the eight trigrams and the sixty-four hexagrams are all appropriate, and all things in heaven and earth can be distinguished by their names. As the "Great Treatise" says, "Only after imagining and considering should one speak and act." Thus, clear statements and decisive judgments become as clear as looking at one's own palm.

顧不曰名，而概之以辭者，以《易》之所謂名，皆假名也。本無是物，而以象擬之。無是事，而以象言之。聖人設卦觀象，大而天地風雷，小而蟲鳥沙石，常則家人夫婦，怪則鬼車狐尾，皆假設此物比事，擬諸其形容，象其物宜，以明陰陽造化之妙用，而定人事之吉凶，故曰“繫辭”。

However, the Zhou Yi does not refer to things by their names but generally calls them "words" or "phrases." This is because the names mentioned in the Yi are all borrowed terms. Originally, there were no such things, but they were borrowed to represent an image; originally, there were no such events, but they were borrowed to describe them. The sage established the structure of the hexagrams and observed their images, ranging from great things like heaven, earth, wind, and thunder, to small things like insects, birds, sand, and stones, and even ordinary matters like "family" and "husband and wife," or strange phenomena like "ghost chariot" and "fox tail." These are all borrowed from these things to compare with human affairs. This is what the Great Treatise says: "Comparing them with their forms and appearances, and imitating their appropriate characteristics," using them to explain the subtle workings of yin and yang, and thus determining the fortune or misfortune of human affairs. That is why it is called "attached words" or "attached phrases."

辭焉者，各指其所之。有名辭也，有動辭也，有狀辭及介辭也，未嘗不可辨而晰之。第《易》道通變，其辭亦通變。有名辭而兼作動辭者，有動辭或兼狀辭之用者，如乾為木果，變巽則為不果。雷風相薄，而《繫辭》曰“茅之為物薄”。用一字而面面皆通，立一義皆頭頭是道。苟泥其辭而不察其象，察其象而不究其理，而繫辭之意終不可得。故必欲執一例以求之，則六十四卦皆死物矣。

The term "ci" (words) each indicate their direction or meaning. Among them, there are nouns, verbs, adjectives, and prepositions, which can be clearly distinguished. However, the Way of the Book of Changes values communication and transformation; thus, its words also change and adapt. Some nouns are used as verbs, and some verbs also function as adjectives. For example, the "Say on the Hexagrams" states that Qian (Heaven) is "wooden fruit," but when Qian changes to Xun (Wind), it becomes "not fruit." Another example is the word "bo" in "Thunder and Wind are close to each other," which means approaching, while in the "Great Treatise" it refers to "thinness" in "the grass is thin." A single character can be applied in various contexts and make sense in all aspects, establishing a meaning that is reasonable everywhere. If one insists on clinging to the literal meaning without understanding the hexagram's image, or only looks at the image without exploring the underlying principles, the original intention of the "Great Treatise" will never be fully grasped. Therefore, if one insists on using a fixed example to apply to all, all sixty-four hexagrams would become lifeless objects.

然則《易》之辭果無例可求乎？曰是在學者之神而明之，變而通之，無定之中，亦未始無一定之軌則可循。旨遠而辭隱，是在虛其心以求之，潛其心以會之而已。

Then, is there really no order to the words of the Book of Changes? The answer is: this depends on the person studying the Book of Changes to grasp it intuitively and to adapt and understand it flexibly. Although it seems to have no fixed standard, there is actually a definite principle to follow. The meaning of the Book of Changes is profound and its wording is subtle, so one can only seek it with an open mind and comprehend it through deep reflection.

《易》以道陰陽，故《傳》曰“一陰一陽之謂道”，又曰“立天之道，曰陰與陽”，舉天道而地道人道一以貫之矣。蓋剛柔仁義，亦無非一陰一陽之對待也。而六十四卦，而三百八十四爻，亦無非一陰一陽之對待也。故孔子於乾之初九曰“陽在下也”，於坤之初六曰“陰始凝也”，即為六十四卦三百八十四爻之舉例發凡，以明九之皆為陽，六之皆為陰。而《易》之《彖》、《象》十翼，均無非闡明陰變化作用，故先以對待之辭舉例如下。

The Zhou Changes are used to explain the principles of yin and yang. Therefore, the Great Treatise says, "Yin and yang together are called the Way," and the Discourse on the Hexagrams says, "The Way of Heaven is called yin and yang." By citing the Way of Heaven, the Way of Earth and the Way of Humanity are also fully explained. The firmness and softness of the Way of Earth, the benevolence and righteousness of the Way of Humanity, are all merely pairs of yin and yang. The sixty-four hexagrams and the 384 lines are also all pairs of yin and yang. Therefore, Confucius says in the first line of the Qian hexagram, "Yang is at the bottom," and in the first line of the Kun hexagram, "Yin begins to condense." This establishes a general principle for the sixty-four hexagrams and the 384 lines, indicating that all lines marked "nine" belong to yang and all lines marked "six" belong to yin. The Commentary on the Judgment, the Image Commentary, and all the other ten appendices of the Zhou Changes are all used to explain the workings of yin and yang changes. Therefore, the following will first list examples of paired terms.

乾“其靜也專，其動也直”，坤“其靜也翕，其動也闢”。動靜二字，直陰陽所由判，吉凶所由生，如水火互相為根。昔儒“陽動陰靜”之說，與太極動則為陽，靜則為陰之說，辭意似均未圓滿。陰陽如環無端，動靜亦如是也。

The *Great Treatise* says of the Trigram Qian: "When still, it is concentrated; when moving, it is direct." It says of the Trigram Kun: "When still, it is harmonious; when moving, it is expansive." The terms "movement" and "stillness" are precisely the boundary that distinguishes yin and yang, and the source from which good fortune and misfortune arise. These two are like water and fire, mutually foundational and indispensable. Previously, scholars spoke of "yang being active and yin being still," as well as "when the Taiji moves it becomes yang, and when it is still it becomes yin." Their wording and intent seem insufficient. Yin and yang are like a circle with no beginning or end; movement and stillness are the same. One cannot unilaterally assign movement to yang and stillness to yin.

《雜卦傳》“乾剛坤柔”，《說卦》曰“立地之道，曰柔與剛”，又曰“分陰分陽，迭用柔剛”，《繫傳》“動靜有常，剛柔斷矣”，又曰“剛柔相摩”，又曰“剛柔相推，而生變化”，又曰“剛柔者晝夜之象也”，又曰“剛柔相推，變在其中矣”，又曰“剛柔者立本者也”，又曰“知柔知剛，萬夫之望”，又曰“上下無常，剛柔相易”，又曰“剛柔雜居，而吉凶可見矣”，又曰“柔之為道不利，遠者其要無咎，其用柔中也。其柔其危，其剛勝耶？”

There are many passages in the classics discussing "yin and yang" or "flexibility and firmness." The "Zagua Transmission" says, "Qian is firm, Kun is flexible." The "Shuogua" says, "The principle of the earth is called flexibility and firmness," and also says, "Differentiating yin and yang, they alternate in using flexibility and firmness." The "Xici Transmission" says, "Motion and stillness have their regularity; firmness and flexibility decide the outcome," and says, "Firmness and flexibility rub against each other," and says, "Firmness and flexibility push against each other, thus producing change," and says, "Firmness and flexibility are the images of day and night," and says, "Firmness and flexibility push against each other, and change is within it," and says, "Firmness and flexibility are the foundation," and says, "Knowing flexibility and firmness, one becomes the leader of ten thousand people," and says, "High and low have no constant position; firmness and flexibility alternate," and says, "Firmness and flexibility coexist, and good and bad outcomes become evident." Finally, it says, "The way of the flexible line is not favorable for dwelling in distant positions; it is only because it maintains the middle that it avoids blame; if the flexible line loses the middle, it becomes dangerous, and then it is better to use firmness."

《周易》用剛，故曰“乾元用九，而天下治”。陽剛而陰柔，亦猶以陽統陰之義也。齊小大者存乎卦，陽大陰小，在八卦，坤小乾大，艮止巽齊，是為大與小不齊也。止而齊之，則大通於小，小進於大。裒多益寡，故泰否“小往大來”，與“復小臨大”，皆無非於萬有之不平者，而求其平，此《易》之微旨也。

The Zhou Changes focus on the use of strength, so the Wenyan of the Qian hexagram says, "The Qian yuan uses all nines, and the world is governed." Yang is strong and Yin is gentle, which means governing Yin through Yang. The Xici transmission says, "The distinction between small and great lies in the hexagram." Yang represents great, Yin represents small; among the eight trigrams, the Kun is small and the Qian is great. The Gen trigram represents stillness, and the Xun trigram represents uniformity. Thus, great and small are originally unequal. By using the effort of stopping, one can make the great connect with the small and the small progress toward the great. This is exactly what the Xiangxuan of the Qian hexagram says, "Reducing excess and supplementing deficiency." Removing surplus and making up for lack. Therefore, the Tai and Pi hexagrams discuss "small going away and great coming in" and "great going away and small coming in," the Fu hexagram has one Yang line which is small, and the Lin hexagram has two Yang lines which are great. All of these are seeking for balance among the myriad things that are unequal — this is precisely the subtle purpose of the Zhou Changes.

《否·上九》“先否後喜”，蠱之“先甲後甲”，巽之“先庚後庚”，說者謂陽先陰後，陰宜後而順承陽。不順陽而先陽，則迷而失道。陽宜先陰，不先而反後，則失時失道，此一義也。自康節之學行，又有先天後天之說。言漢學者，攻擊之不遺餘力，然其數理精確，且皆出於天然，不加造作。而按之於經，胥有徵驗。近儒端木鶴田，作《周易指》，以先後天說《易》，逐爻推尋，如按圖索驥，字字吻合，尤為發前人所未發。較虞氏之旁通，更為直捷而少枝節也。

The Upper Nine of the Hexagram of "Opposition" says, "First opposition, then joy." The Hexagram of "Guilt" states, "Three days before the first Jia, three days after the first Jia." The Nine in the Fifth of the Hexagram of "Wind" says, "Three days before the first Geng, three days after the first Geng." Those who explain these say this refers to the principle that Yang comes first and Yin follows. Yin should naturally be behind and follow Yang; if it does not follow Yang but instead takes precedence over Yang, it will become confused and deviate from the right path. Yang should naturally be ahead of Yin; if it does not take the lead but lags behind, it will miss the proper time and deviate from the right path. This is one meaning of "before and after." Since Shao Yong's teachings became popular, the concepts of Earlier Heaven and Later Heaven were introduced. Scholars of the Han learning tradition have strongly criticized these ideas, yet this system is numerically precise and arises naturally, not artificially constructed. When used to verify the classics, it consistently aligns with the text. In modern times, the scholar Duanguo Hu wrote "Zhou Yi Zhi," using the concepts of Earlier Heaven and Later Heaven to interpret the Yi, analyzing each line step by step, as if following a map to find a lost horse, with each word matching perfectly. This approach particularly reveals insights not previously discovered, surpassing Yu Fan's method of "mutual transformation" in being more direct and less complicated.

《坤·彖傳》曰“乃順承天”，又曰“後順得常”。《說卦》曰：“坤順也。”坤順承天，則天逆行，順逆交，錯而四時錯行。日月代明，而天地之道乃成。陽在陽中陽順行，而陽在陰中則逆行。陰在陰中陰順行，而陰在陽中則逆行。大明生於東，月生於西。日行東陸則為秋，日行西陸則為春，陰陽非交互不能成其用也。五行順行則生，逆行則克。有生無克，不能成物。有逆無順，不能生物。故逆生順死，其旨甚微。故曰“《易》逆數也”。

The Commentary on the Judgment of the Hexagram of Earth says, "It follows and supports Heaven," and also says, "The ruler follows and maintains the constant order." The Book of Changes says, "Earth is characterized by following." Since Earth follows and supports Heaven, Heaven must be moving in the opposite direction. When one is following and the other is opposing, they intermingle and the four seasons can alternate, day and night can succeed each other, and the way of Heaven and Earth can be established. Separately speaking: when Yang is in a Yang position, it moves forward; when Yang is in a Yin position, it moves backward. When Yin is in a Yin position, it moves forward; when Yin is in a Yang position, it moves backward. The sun rises in the east and the moon shines from the west. When the sun passes through the eastern land, it is autumn on earth; when it passes through the western land, it is spring. This shows that Yin and Yang cannot fulfill their functions without interacting. The Five Phases are also like this: moving in order leads to mutual generation, while moving against the order leads to mutual control. Without control, things cannot take shape; without generation, things cannot be transformed. Therefore, "reverse movement produces life, while forward movement leads to death," and the meaning behind this is very subtle. That is why the Book of Changes says, "The Book of Changes is about reverse counting."

《泰·傳》曰：“內陽而外陰，內健而外順，內君子而外小人。”《否·傳》曰：“內陰而外陽，內柔而外剛，內小人而外君子。”《明夷·傳》曰：“內文明而外柔順。”《家人·傳》曰：“男正位乎外，女正位乎內。”此以卦之上卦為外，下卦為內也。《雜卦傳》曰：“睽外也，家人內也。”

The Commentary on the Judgment of the Tai hexagram says: "The inner is yang and the outer is yin, the inner is strong and the outer is compliant, the inner is the gentleman and the outer is the petty person." The Commentary on the Judgment of the Pǐ hexagram says: "The inner is yin and the outer is yang, the inner is soft and the outer is strong, the inner is the petty person and the outer is the gentleman." The Commentary on the Judgment of the Mingyi hexagram says: "The inner is civilized and the outer is compliant." The Commentary on the Judgment of the Jiaoren hexagram says: "The man holds the proper position in the outer, and the woman holds the proper position in the inner." In these instances, the upper trigram of a hexagram is regarded as the outer and the lower trigram as the inner. However, the Miscellaneous Hexagrams says: "Kui is the outer; Jiaoren is the inner." In this case, the distinction between inner and outer is not based on the upper and lower trigrams.

言虞氏學者，以家人與睽分屬內外，則以旁通之兩卦而言。睽與蹇旁通，睽為外則蹇為內。家人與解旁通，家人為內則解為外。內其故也，外其新也。內其躬也，外其鄰也。蓋以五已正位者為內，五未正位者為外。無妄，剛自外來而為主於內，亦以無妄之九五自睽來。以明睽為外，既成無妄，則為主於內，以明無妄為內也。無妄五剛，睽五柔，此兼剛柔言內外也。《周易指》：“以凡言內者，皆因家人。言外者，皆因睽。”《坤·文言》：“直其正也，方其義也。君子敬以直內，義以方外。”亦取象家人與睽，即《易》言內外之凡例也。

Those who study Yu Fan's teachings divide the hexagram "Family" and "Strife" into inner and outer, referring to the two hexagrams that are mutually complementary. "Strife" is complementary to "Obstruction," so "Strife" is outer and "Obstruction" is inner; "Family" is complementary to "Release," so "Family" is inner and "Release" is outer. The term "inner" refers to its original position, while "outer" refers to its new position. "Inner" indicates the self, while "outer" refers to the adjacent line. Generally, if the fifth line is already in the correct position, it is considered inner; if it is not yet in the correct position, it is considered outer. The "Commentary on the Judgment" of the hexagram "Without Deceit" says, "A strong line comes from outside and becomes the main line within," because the nine in the fifth line of "Without Deceit" comes from the hexagram "Strife." This shows that "Strife" is outer, and after transforming into "Without Deceit," it becomes inner and takes the main position, so "Without Deceit" is inner. The fifth line of "Without Deceit" is a strong line, while the fifth line of "Strife" is a weak line, which also considers the strong and weak lines when discussing inner and outer. Du Mu Guo Hu says in "Zhou Yi Zhi": "All discussions about the inner are based on 'Family,' and all discussions about the outer are based on 'Strife.'" The "Discourse on the Literary Meaning" of the hexagram "Earth" says, "Straightness is its correctness, and squareness is its righteousness. A gentleman respects to straighten the inner, and righteousness to regulate the outer." This also takes its image from "Family" and "Strife" — this is the general rule of discussing inner and outer in the "Zhou Yi."

《繫傳》曰：“往者屈也，來者信也。一往一來謂之變，往來不窮謂之通。”蓋陰陽以往來始成其變化，故日往月來，月往日來，大往小來，小往大來，往來而得其道則吉，失道則凶。卦例：由內而之外為往，由外而之內為來。

The Great Treatise says: "Going away is bending, coming back is sincerity. One going away and one coming back is called change, and continuous coming and going is called communication." Yin and yang achieve their transformations precisely through this process of going and coming, hence the sun setting west and the moon rising east, the moon setting west and the sun rising east. The hexagram of "Great Opposition" is "great going and small coming," while the hexagram of "Great Favorability" is "small going and great coming." Coming and going in accordance with the right path brings good fortune, while departing from the right path brings misfortune. In terms of hexagram examples: moving from the inner trigram to the outer trigram is called "going," and returning from the outer trigram to the inner trigram is called "coming."

八卦、六十四卦，皆此一往一來，以經綸運轉而不窮。八卦，乾圓往者屈，而坤方來者信。由乾圓往者，東南西北也。由坤方來者，西南東北也。六十四卦，則乾往坤來，屯往蒙來，以迄於既濟未濟，皆此往來也。此以卦言者也。其以爻言者，如“往得中也”，“往有功也”，“剛來而得中也”，“剛來而文柔也”，要皆指二五而言。詳於虞氏之旁通。

The eight trigrams and the sixty-four hexagrams are all about the continuous movement of going and returning, with the interwoven cycles never ending. Regarding the eight trigrams, the trigram Qian (Heaven) is round and represents 'going,' which is bending; the trigram Kun (Earth) is square and represents 'returning,' which is extending. The directions going out from Qian's round shape are the four cardinal directions: East, South, West, and North. The directions coming in from Kun's square shape are the four intermediate directions: Northeast and Southwest. Regarding the sixty-four hexagrams, the pattern of going and returning continues throughout, such as Qian going and Kun returning, Zun going and Meng returning, continuing all the way to Ji Ji and Wei Ji. This is talking about the whole hexagram. If we consider the lines, for example, the phrases in the Commentary on the Judgment such as 'going and reaching the center,' 'going and achieving success,' 'a strong line coming and reaching the center,' and 'a strong line coming and being gentle' refer to the movement between the second line and the fifth line. The detailed method of calculation is explained in Yu Fan's theory of 'parallel transmission.'

上者，丄也。下者，丅也。上天下地，而中為人。故《易》經文言“上下”者，僅小過一卦，曰“小過亨利貞，不宜上宜下。大吉”。《傳》曰：“不宜上宜下，大吉，上逆而下順也。”蓋《易》者，聖人寡過之書。五十學《易》，可以無大過，而小過或不免也。小過之中二爻，正當六畫卦之人爻，所謂“立人之道，曰仁與義”者此也。故乾之三四兩爻（小過爻也），特著無咎。“無咎者，善補過也。”惟明乎此上下，則得乎中，而過可免矣。

The character "上" was written as "丄" in ancient times, and "下" was written as "丅," with one stroke above and one below. Above represents heaven, below represents earth, and in the middle is humanity. In the text of the Zhou Yi, the term "upper and lower" appears only in the hexagram Xiao Guo, which says, "Xiao Guo, smooth, beneficial to uprightness, not suitable to go up but suitable to go down, great good fortune." The Commentary on the Judgment explains: "Not suitable to go up but suitable to go down, great good fortune, because going up is against the way and going down is in harmony with the way." The Zhou Yi is a book of sages teaching people to commit few mistakes. Confucius said that at fifty one can study the Zhou Yi and avoid great mistakes, but small mistakes may still occur. The two middle lines of the hexagram Xiao Guo correspond to the middle lines of the six-line hexagram, which represent the human line, as mentioned in the Sayings on the Hexagrams: "Establishing the way of humanity, it is called benevolence and righteousness." Therefore, the lines nine three and nine four of the Qian hexagram (which correspond to the lines of Xiao Guo) are specially marked as "no blame," and the Great Treatise says, "No blame means being good at making up for mistakes." So-called "no blame" is because one is good at remedying mistakes. Only by understanding the distinction between upper and lower can one attain the middle way, and thus avoid mistakes.

故《乾·文言》曰：“本乎天者親上，本乎地者親下。”於九三、九四，皆曰“上不在天，下不在田”，又曰“上下無常”。《雜卦傳》曰“離上而坎下也”，《益·彖傳》曰“損上益下”，《損·彖傳》曰“損下益上”，皆以損益得宜，以蘄合乾坤坎離之中，而上下交泰（乾坤交成泰），以成既濟者也。故明小過之上下，而六十四卦之上下，均可以言矣。

Therefore, the "Wenyan" of the Qian hexagram says: "Those originating from Heaven are close to Above, and those originating from Earth are close to Below." Under the two lines, Nine in the Third and Nine in the Fourth, it says "Not above Heaven, not below the fields," and also says "Above and Below have no constant position." The "Zagua Zhuan" says "Fire above and Water below," the "Tianyi Zhuan" of the Yi hexagram says "Reducing Above to benefit Below," and the "Shen Zhuan" of the Shen hexagram says "Reducing Below to benefit Above." All of these depend on proper reduction and increase, aiming to conform to the middle way of Qian, Kun, Kan, and Li, enabling interaction between Above and Below to form Tai, and ultimately achieving the state of Ji Ji. Therefore, as long as one understands the relationship between Above and Below in the Xiaoguo hexagram, the relationship between Above and Below in all sixty-four hexagrams can also be explained.

《說卦》“乾為圓”，《荀九家》“坤為方”，《繫傳》“蓍之德，圓而神。卦之德，方以知”，《坤·六二》“直方大”，《繫傳》又曰“無窮盡，無方體”，又曰“是故神無方而《易》無體”。蓋圓者，神也。方者，體也。乾為天為圓，無體故無方。坤為地，有體故有方。

The "Say on the Hexagrams" says "Qian represents roundness," and the "Xunshi Jiujia Yi" says "Kun represents squareness." The "Great Treatise" states "The virtue of the divining stalk is round and divine; the virtue of the hexagrams is square and knowledgeable." The line statement of the second line of the Kun hexagram says "Straight, square, and great." The "Great Treatise" also says "It is endless and has no definite form," and again says "Therefore, the divine has no fixed place and the Book of Changes has no definite form." This shows that "roundness" refers to the divine and mysterious nature without fixed location, while "squareness" refers to form and definite position. Qian represents Heaven and roundness, having no form, so it has no fixed position; Kun represents Earth and has form, so it has a fixed position.

舊說“圓象天，方法地”，簡言之，則曰“天圓地方”，“奇圓耦方”。近人知地球之為渾圓而非方也，於是曲為之說曰“天圓地方”，言其德非言其體也。而不知《易》之所謂“圓而神，方以知”者，明明指蓍與卦，未嘗謂天之德圓與地之德方也。而乾圓坤方，則確不可易。第所謂方者，即西南東北之方，非謂地體之為立方形也，又何必曲為之解哉！圓無盡而方有盡，故度圓者必以方。玩“乾其靜也專，其動也直”，“坤其靜也翕，其動也闢”二語，則方圓之妙用已闡發無遺。近世幾何形學之界說，皆不能出其範圍矣。

Old interpretations said that "the circle takes its form from heaven, and the square takes its form from earth," meaning "heaven is round and earth is square." In simple terms, this meant that "heaven is round and earth is square." Modern scholars, knowing that the earth is round and not square, have tried to defend the old view by saying that "heaven is round and earth is square" refers to the virtues of heaven and earth rather than their physical forms. They do not realize that the "circle is mysterious and the square is known" in the Zhouyi refers to the divination rods and the structure of the hexagrams, not that the virtue of heaven is round and the virtue of earth is square. As for the statement that "heaven is round and earth is square," this is indeed unshakable. However, the "square" here refers to directions such as southwest and northeast, not that the earth is a cube. Why then should we try to defend it so forcefully? The circle is infinite, while the square is finite, so measuring the circle must be done with the square. Careful study of the "Great Treatise" passage "When still, heaven is focused; when moving, it is straight," and "When still, earth is receptive; when moving, it expands," reveals fully the subtle use of square and circle. All modern geometric definitions concerning points, lines, planes, and solids are within the scope of this.

《繫傳》曰：“變化者，進退之象也。”剛柔相推而生變化，故進退與往來不同。《序卦傳》曰：“晉者進也，遁者退也。”又曰：“漸者進也。”《雜卦傳》云：“遁則退也，需不進也。”《說卦傳》曰：“巽為進退。”《巽·初六》：“進退利武人之貞。”《觀·六三》曰：“觀我生進退。”《乾·九四·文言傳》曰：“進退無恆。”上九：“知進而不知退。”蓋陽進陰退，由內而之外進也，由上而之下退也。進而當，則為得為吉。進而不當，則為失為凶。是皆由陰陽變化而生，故曰“變化者，進退之象也”。

The Great Treatise says: "Change is the image of advance and retreat." Yang and Yin interact with each other, giving rise to change, so "advance and retreat" is different from the previous "coming and going." The Sequence of Changes says: "Jin means advance;遁 means retreat." It also says: "Jian means advance." The Miscellaneous Treatise says: "Dun means retreat; Xu does not advance." The Explanation of the Trigrams says: "Xun represents advance and retreat." The first line of the Xun hexagram says: "Advance and retreat, advantageous for the loyal warrior." The third line of the Guan hexagram says: "Observing my life, advance and retreat." The fourth line of the Qian hexagram in the Commentary on the Lines says: "Advance and retreat without constancy." The top line says: "Knows advance but not retreat." In general, Yang represents advance and Yin represents retreat; moving from the inner trigram to the outer trigram is advance, while moving from a higher position to a lower position is retreat. Advancing appropriately leads to gain and good fortune; advancing inappropriately leads to loss and misfortune. All these arise from the changes of Yin and Yang, so it is said: "Change is the image of advance and retreat."

《繫傳》曰：“遠近相取，而悔吝生。”近與邇同義。《繫傳》言“遠近”者三，言“遠邇”者二。《震·彖》“驚遠而懼邇也”，《蒙·六四》“獨遠實也”，《剝·六四》“切近災也”。餘或單言遠單言近者，要皆指爻位而言。蓋爻之相得者宜近，不相得者不宜近。故《傳》又重言以申明之曰：“凡《易》之情近而不相得，則凶。或害之，悔且吝。”又曰：“二與四同功而異位。二多譽，四多懼，近也。柔之為道不利，遠者其要無咎，其用柔中也。”

The Great Treatise says: "When things are far and near, they take from each other, and regret and hardship arise." "Near" and "close" have the same meaning. In the Great Treatise, there are three instances mentioning "far and near" and two instances mentioning "far and close." Additionally, in the Image Commentary of the Zhen hexagram, it says, "It startles the far and fears the near." In the Image Commentary of the Meng hexagram's sixth line four, it says, "It is distant from reality." In the Image Commentary of the Bo hexagram's sixth line four, it says, "It is close to calamity." Other instances that mention only "far" or only "near" also refer to the positions of the lines. Generally, when two lines share similar qualities, they are suitable to be close; when they differ, they are not suitable to be close. Therefore, the Great Treatise repeatedly emphasizes: "All the situations in the Book of Changes, when near but not in harmony, result in misfortune, causing harm, regret, and hardship." It also says: "The second and fourth lines have the same function but different positions. The second line is often praised, and the fourth line is often fearful, because they are near. The way of the flexible line is not advantageous; those who are distant can avoid blame, because they use flexibility in the middle." The fourth line often experiences fear because it is close to the ruler's position; the flexible line, though distant, can still avoid blame because it uses flexibility in the middle.

故論爻之遠近以明吉凶，有就本卦之爻位論者，有就變卦之爻位論者。本卦之爻位，以承乘、與比、相應、相合者，為近。否則為遠。變卦之爻位，則他卦之爻一變而即得者為近，須再變三變而始到本卦者為遠。凡卦爻之言遠近者，皆含此二義，不可不審也。

Therefore, determining good or bad fortune based on the proximity of the lines involves considering either the position of the lines in the primary hexagram or in the resulting hexagram. When referring to the primary hexagram's line positions, two lines are considered "near" if they form a relationship of bearing, supporting, adjacency, response, or mutual combination; otherwise, they are "far." When referring to the resulting hexagram's line positions, any hexagram that can reach the line of the primary hexagram by changing just one line is considered "near," while those requiring two or three changes are considered "far." All instances in the hexagram line statements that mention near or far include both of these meanings and must be carefully distinguished.

《易》用九用六。九六變也。變則新，故《繫傳》曰“日新之謂盛德”，《大畜·彖》曰“剛健篤實輝光，日新其德”。鼎“取新也”，革“去故也”，隨“無故也”。故六舊之義也。《訟·六三》曰“食舊德”，《井·初六》曰“舊井無禽”。食舊德，則貞厲。“舊井無禽”，則不食，皆去舊而宜從新者也。此外如噬嗑之“噬臘肉”，大壯之“壯于前趾”，乾為“老馬”，曰“老”，曰“前”，曰“臘”，亦皆舊之義也。遠近以位言，新舊以時言，變通者趣時者也。趣時則日新，是以《雜卦》曰“大畜時也”。

The Zhou Changes use 'nine' and 'six' in divination, both representing changing lines. A change signifies newness, so the Great Treatise says 'daily renewal is called great virtue,' and the Commentary on the Judgment of the Great Accumulation says 'strong, vigorous, steadfast, and radiant, renewing one's virtue daily.' The Miscellaneous Treatise says that the Cauldron hexagram signifies 'taking newness,' the Revolution hexagram signifies 'discarding the old,' and the Following hexagram signifies 'without the old.' This shows that 'six' contains the meaning of the old. The third line of the Suits hexagram says 'eating the old virtue,' and the first line of the Well hexagram says 'the old well has no fowl.' Living by old virtue and maintaining correctness does not prevent danger; an old well with no fowl coming to it means the water is no longer drinkable. These are examples of moving away from the old to embrace the new. Other examples include the噬嗑 hexagram saying 'eating dried meat,' the大壮 hexagram saying 'strong at the front toe,' and the Sayings on the Hexagrams explaining that the Heaven trigram is 'an old horse.' All these terms, such as 'old,' 'front,' and 'dried,' contain the meaning of the old. Near and far refer to positions, while new and old refer to time. Those who can adapt are those who can follow the appropriate time, and following the appropriate time allows for daily renewal, so the Miscellaneous Treatise says 'Great Accumulation is about timing.'

“生生之謂《易》”，《易》之道本生生而不已者也。然不能盡其道，即不能有生而無死。《繫傳》曰：“原始反終，故知死生之說。”故《檀弓》曰：“君子曰終，小人曰死。”終則有始，而死則不能復生，此君子小人之別也。經之稱“生”者二卦：觀之“觀我生”，“觀其生”；大過之“枯楊生稊”，“枯楊生華”是也。稱“死”者二卦：離之“突如其來如，焚如死如棄如”，豫之“貞疾恆不死”是也。

The Great Treatise says, "To produce life is called the Book of Changes." The way of the Book of Changes is originally about continuous generation. But if people cannot fully realize this way, they cannot have only life without death. The Great Treatise also says, "To trace back the origin and return to the end, thus knowing the explanation of life and death." Therefore, the Book of Rites, in the section on the Archers, says, "The gentleman speaks of the end, while the petty person speaks of death." After an end there is a new beginning, but after death there is no revival, which is the distinction between the gentleman and the petty person. The text mentions "life" in two hexagrams: the hexagram of Observing, which says "Observing my life" and "Observing others' life," and the hexagram of Great Exceeding, which says "A withered poplar tree produces new sprouts" and "A withered poplar tree produces flowers." The text also mentions "death" in two hexagrams: the fourth line of the hexagram of Fire, which says "Suddenly appearing, burning, dying, and being cast away," and the fifth line of the hexagram of Joy, which says "Remaining steadfast in illness, yet never dying."

蓋乾為大生，坤為廣生。大生故“資始”，廣生故“資生”。而所以資始而資生者，實惟“大哉乾元，坤順承乾”，坤元亦統於乾元。《文言》曰：“元者善之長。”於人為仁。元從二兒，仁亦從二兒，於乾坤二象為二五之中。豫之“恆不死”，《象》曰“中未亡也”。困之六三以陰乘陽，以柔掩剛，是賊仁害義，昧其天良者也。故《繫傳》曰“死期將至”。中未亡者，終則有始。亡其中，則生亦幸。所謂行尸走肉，待死而已。

Heavenly Stem Qian governs "great generation," and Earthly Stem Kun governs "wide generation." Because of great generation, the Commentary on the Judgment says Qian is "the source of all things." Because of wide generation, it says Kun is "the nourishment of all things." The reason why all things can be originated from and nourished by these principles is really due to "great indeed is the Qian Principle," and Kun follows and supports Qian. The principle of Kun also belongs to the principle of Qian. The "Wenyan" says, "The principle of Yuan is the beginning of goodness." When applied to human beings, it is "ren" (benevolence). The character "Yuan" is composed of two strokes and a child, and the character "ren" is composed of two strokes and a person. In the images of the trigrams Qian and Kun, this refers to the second line and the fifth line, which represent the "center." The line six in the fifth position of Yu says "constant不死" (constant non-death), and the Image Commentary interprets it as "the central principle has not yet been lost." In the trigram Kun, the line six in the third position is a yin line riding over a yang line, and a soft line covering a strong one, which is an act of harming benevolence and righteousness and obscuring the natural goodness. Therefore, the Great Treatise Commentary says it is "the time of death is approaching." For someone whose central principle has not been lost, even at the end of a period there will be a new beginning; but for someone who has lost the central principle, even if he is alive, it is only by chance, which is what the common saying means, that he is like a walking corpse, waiting for death.

《易》以有立教者也。《易》有太極，是生兩儀。四象八卦，而定吉凶以生大業。故《序卦·上傳》曰“有天地然後萬物生焉”，《序卦·下傳》曰“有天地然後有萬物，有萬物然後有男女，有男女然後有夫婦，有夫婦然後有父子，有父子然後有君臣，有君臣然後有上下，有上下然後禮義有所錯”，皆以明有之義也。

The Zhou Changes (I Ching) establishes its teachings based on the concept of "having" or "being." The Great Treatise says, "The Book of Changes contains the Taiji, from which the two principles arise." The two principles generate the four images, the four images generate the eight trigrams, and the eight trigrams determine fortune and misfortune, which in turn give rise to great undertakings. Therefore, the Upper Section of the Sequence of Changes says, "Only after heaven and earth exist can all things come into being." The Lower Section says, "Only after heaven and earth exist can all things come into being; only after all things exist can there be men and women; only after there are men and women can there be husband and wife; only after there is husband and wife can there be father and son; only after there is father and son can there be ruler and subject; only after there is ruler and subject can there be hierarchy; only after there is hierarchy can propriety and righteousness have their place." All these are introduced with the word "have," clearly emphasizing the significance of this concept of "having."

《下經》首咸，《序卦》不言咸，咸無也。不言無而言有，此即《易》之開宗明義也。然《序卦》不言咸，而《繫下傳》於“憧憧往來朋從爾思”一爻，推闡“往來屈信”之理。而以窮神知化歸之，聖人之意亦可見矣。《傳》曰“書不盡言，言不盡意”，故聖人立象以盡意。

The Lower Classic begins with the Xian hexagram, but the "Sequence of Hexagrams" passage never mentions Xian — because "Xian" means "sensation," which is empty in essence and without intention, belonging to the "nothing." Not speaking of "nothing" but only of "something," this is precisely the stance of the Zhou Yi at the beginning. However, although the "Sequence of Hexagrams" does not mention Xian, the "Lower Commentary on the Great Treatise" discusses the fourth line of Xian hexagram, "Coming and going in confusion, friends follow your thoughts," to explain the principle of "going and coming, bending and stretching." It ultimately concludes with "exhausting the divine and knowing the transformation," thereby revealing the sage's intention. The "Great Treatise" says, "Writing cannot exhaust words, words cannot exhaust meaning," so the sages established hexagrams to fully express meaning.

書所未言者，自當求之於言外之意。意有未得者，當索之於所立之象。自象學不明，或空言以說理，或執經而忘象。更以門戶派別之故，互相攻擊，入主出奴，是丹非素，而《易》道遂晦盲終古矣。須知《易》固以有立教，然有無實相對待，言有而無可見。孔子猶慮後人之以辭害意，而不能通也，故特表咸之九四一爻，以明同歸殊途之旨。

What is not written in the text must be sought in the implied meaning; if the meaning is still not understood, one must look into the established hexagrams. Since the study of images has become obscure, scholars either talk emptily about principles or cling rigidly to the text while forgetting the hexagrams. Moreover, due to factional disputes, they attack each other, regarding one school as the master and another as the servant, considering their own as red and others as white. Thus, the way of the Zhou Changes has remained long obscured. One must know that although the Zhou Changes establish teaching based on "being," being and non-being exist in relation to each other. If "being" is thoroughly explained, "non-being" will naturally appear. Confucius was even concerned that later generations might be confined by words and thus hinder the original meaning, failing to understand it fully. Therefore, he specially pointed out the fourth line of the Xian hexagram to clarify the principle of "returning to the same goal through different paths."

蓋立教為中人以下說法，而精義入神之道，則非言所能盡。而立象盡意，是在中人以上自悟之耳。故卦象乾為無，自無而有，由坎出震，而生生之道乃循環而不已。咸為無，君子以虛受人，而窮神知化之學，始日進而不窮。乾之無，天極也。咸之無，人極也。通天地人謂之儒，貫通三才而返本窮源，則仍必以契合乎天為止境。故六十四卦統歸納於一乾，而“大哉乾元乃統天”。明乎此，則後儒斷斷於有無之界者，均可渙然而冰釋矣。

In general, the teaching is directed towards people of average ability and below; however, the level of "refining the essence to the divine" cannot be fully expressed through words. The method of using images to convey meaning can only be understood by those of above average ability. Therefore, in terms of the hexagram images, Qian represents "nothingness," from which existence arises. When the single yang line emerges from Kan to become Zhen, the process of continuous generation continues endlessly. Xian also represents "nothingness," and the Image Commentary says, "the superior man receives others with an open mind." Only by being open can the study of penetrating the divine and understanding transformation advance day by day without end. The "nothingness" of Qian is "heaven's extreme," while the "nothingness" of Xian is "human's extreme." Only those who integrate heaven, earth, and humanity can be called Confucians; and by integrating the three elements and returning to the source, the ultimate goal is to align with heaven. Therefore, all sixty-four hexagrams are ultimately summarized in Qian. The Commentary on the Judgment says, "How great is the creative power of Qian! All things receive their beginning, and thus they follow heaven." Once this is understood, the endless disputes among later Confucian scholars regarding the distinction between being and non-being can be resolved.

此外如尊卑、貴賤、幽明、始終、多寡、善惡、利害、窮通、遲速、安危、治亂、存亡、寒暑、晝夜、燥溼、俯仰、平陂、虛實、闢翕、分合、輕重、微顯、厚薄，與夫天地、日月、男女、禮樂、仁義，凡相對待者，皆一陽一陰之義，未可悉舉。所謂“因貳以濟民行，以明得夫之報”者也。孔子《十翼》以“乾剛坤柔”終篇，取五十六卦一一以對待明義，而又於《繫傳》特著其例，曰“乾坤為《易》之門”。得其門而入者，可知所自矣。

In addition, pairs such as respect and humility, honor and lowliness, the hidden and the manifest, beginning and end, multitude and fewness, goodness and evil, benefit and harm, hardship and success, slowness and speed, safety and danger, order and chaos, existence and non-existence, cold and heat, day and night, dryness and dampness, looking down and looking up, flat and uneven, emptiness and fulness, separation and union, lightness and weight, subtle and manifest, thickness and thinness, as well as heaven and earth, sun and moon, male and female, rites and music, benevolence and righteousness, all these pairs of opposites represent the principle of one yin and one yang. There are countless such pairs. This is what the Great Treatise says: "By means of dual opposites, the people's conduct is guided, and the consequences of gain and loss are made clear" (the original text mistakenly writes "de fu" instead of "shi de"). It means using the principle of yin and yang to assist people in their actions and to make them understand the results of gain and loss. In Confucius' Ten Wings, the final section, the Miscellaneous Trigrams, begins with "Qian is strong and Kun is yielding" and concludes the entire work by explaining the meanings of the fifty-six hexagrams in pairs. It also specifically mentions this principle in the Great Treatise, saying "Kun and Qian, are they the gate of the Book of Changes?" Those who find this gate and enter it will understand where the principles of the Book of Changes come from.

對待之辭曰“對辭”，而非對待者曰“單辭”。單辭者，凡以為對辭之用也。且單辭亦往往含有二義，辭繁非可悉舉，茲略舉如左。

Terms that are paired and opposite to each other are called "dui ci" (paired terms), while terms that appear alone without a pair are called "dan ci" (single terms). The function of single terms is generally to serve paired terms, and the single terms themselves often contain two meanings. This type of term is too numerous to list individually, so only a few examples will be given below.

《易》道尚中。凡過乎中者，大過小過，皆變化之進退之以求合乎中。蓋人為天地之中，故以中立人之極，而陰陽剛柔始各得其正，而無所偏倚，而後盡《易》之能事也。中有虛實二義：實者有形，以所處之位言之，如卦之二五兩爻是也。虛者無質，以至當之主義言之，如卦之主爻是也。蓋一卦之主爻，有時在二五，有時不在二五。如比以五陽為主，同人以五陰為主者，主爻在爻位之中者也。復以初陽為主，小畜以四陰為主者，主爻不在二五之中者也。故曰“中無定在”。

The principle of the Zhou Yi is to value the concept of "zhong" (center). Any hexagram that exceeds the center, such as Da Guo and Xiao Guo, must rely on change and movement, advancing and retreating, to achieve harmony with the center. Humans reside in the center of heaven and earth, so the concept of "zhong" establishes the standard for human behavior. Only then can yin and yang, hardness and softness, each find their proper place without leaning too far in one direction. The function of the Zhou Yi is thus fulfilled. The concept of "zhong" includes both tangible and intangible aspects. The tangible aspect can be pointed to specifically, such as the second line and the fifth line in a hexagram. The intangible aspect has no physical form, referring instead to the main line of a hexagram, which is the central element. The main line of a hexagram is sometimes located at the second or fifth line, but not always. For example, the hexagram Bi uses the nine at the beginning (initial line) as its main line, while Tong Ren uses the six in the second line as its main line. These are cases where the main line is exactly at the center. The hexagram Fu uses the nine at the beginning as its main line, and Xiao Xu uses the six in the fourth line as its main line. These are cases where the main line is not located at the second or fifth line. Therefore, it is said that "zhong" has no fixed position.

以二五為中者，如天平倚點居正中，重心與中心，同居一位。不在二五之中者，如秤桿之倚點，視重點力點比例之差，求得其力點與倚點距。重點與倚點距，相等之所在，即中心之所在也。孟子曰“子莫執中”，執中為近之。執中無權，猶執一也。蓋即如天平之中也。《易》道之中，即孟子所謂權，可以前後移動，以求合力點重點與倚點相等之中者也。

Using the second and fifth lines as the center, it is like the fulcrum of a balance scale exactly in the middle, with the center of gravity and the center coinciding. If the center is not at the second and fifth lines but still called the center, it is like the loop of a balance scale: one must consider the difference in weight and the length of the lever arms, calculate the distance from the force point to the loop and from the center of gravity to the loop, and the position where both sides are equal is the center. Mencius said, "Zimo holds the center," holding the center is already close to the Dao; yet he continued, "holding the center without flexibility is like holding to one point"—only knowing to stick to the midpoint without weighing the light and heavy, is like clinging to a single point, and that kind of center is merely a fixed center like a balance scale. The "center" discussed in The Zhou Changes is precisely what Mencius referred to as "flexibility" ("quan"): it can move forward and backward to achieve the center where the force point, the center of gravity, and the fulcrum are balanced on both sides.

孔子之道曰“時”曰“中”，後人稱為“時中之聖”，要皆推本於《易》道。於《蒙·彖》贊曰：“蒙亨，以亨行時中也。”蒙以養正，聖功之始。然《易經》之言時者，惟《歸妹·九四》曰“遲歸有時”，他無見也。孔子贊《易》，始於時字多所發揮，而於《繫傳》總揭其義曰“變通配四時”，又曰“變通莫大乎四時”，又曰“變通者趣時者也”。於《豐·傳》曰“天地盈虛與時消息”。合而觀之，孔子言“時”之旨趣，具可見矣。

Confucius' teachings emphasize "time" and "center," and for this reason he is called the "sage of timely and central virtue." This understanding must be traced back to the principles of the Zhou Yi. In the Commentary on the Judgment of the Meng hexagram, Confucius said, "Meng is success, because it follows the timely and central path." Cultivating virtue with the right way during times of ignorance is the beginning of the sage's practice. However, in the main text of the Yi Jing, the term "time" appears only once, in the line "returning late has its time" (returning late at an appropriate time) from the ninth line of the fourth position in the Gui Mei hexagram. Elsewhere, it does not appear. It was Confucius' commentary on the Yi that began to elaborate extensively on the concept of "time." In the Great Treatise, he summarized its meaning by saying "change and adapt in accordance with the four seasons," and also said "there is no greater change and adaptability than the four seasons," and further said "change and adaptability are the ways of following the time." In the Commentary on the Judgment of the Feng hexagram, he said "the heavens and earth are full or empty, and this is in accordance with the time, increasing and decreasing." Taken together, the full meaning of Confucius' discussion on "time" becomes clear.

故於乾之九三日“與時偕行”，於上九曰“與時偕極”。損益皆曰“與時偕行”，隨曰“隨時”，節曰“失時”，革曰“明時”，無妄曰“對時”，睽蹇皆曰“時用”，豫姤旅皆曰“時義”，坤曰“時發”，賁曰“時變”，而於《艮·彖傳》總揭其義曰：“時止則止，時行則行。動靜不失其時，其道光明。故君子進德修業欲及時也。”此可謂孔子於《易》獨得之秘，而為天下萬世指迷者也。

Therefore, Confucius said in the "Nine in the Third" of the Qian hexagram, "Keep pace with the times," and in the "Nine at the Top," "Keep pace with the times until the end." The hexagrams Sun and Yi both say "Keep pace with the times," the Su hexagram says "Follow the time," the Jie hexagram says "Lose the time," the Ge hexagram says "Clarify the time," the Wuwang hexagram says "Correspond to the time," the Kui and Jian hexagrams both say "Use the time," the Yu, Guo, and Lu hexagrams all say "The meaning of the time," the Kun hexagram says "The time arises," and the Ben hexagram says "Change with the time." Finally, in the "Commentary on the Judgment" of the Gen hexagram, he summarized the meaning, saying: "When the time stops, stop; when the time moves, move. If one's actions and inactions do not miss the time, then the path is bright. Therefore, a gentleman advances in virtue and cultivates his career, always keeping up with the time." This can be considered the secret insight Confucius gained from the Zhou Changes, and it is also the guidance he provided for the world and all generations.

若以時論時，則亦含有二義：一曰有定之時。如天之四時，時有定候，非人之所能變更，是惟順承乎天，所謂後天而奉天時者也。一曰無定之時。如人事之有輕重緩急，而陰陽五行各有始有壯有究，或損或益，或行或止，所謂觀乎天文以察時變者也。故時有以盈虛消息言者，泰否剝復之類是也。有以事言者，訟師噬嗑頤之類是也。有以理言者，謙履咸恆之類是也。有以象言者，井鼎之類是也。

If we consider "time" itself, it contains two meanings. The first is fixed time: like the four seasons in the sky, each has a definite season, which cannot be changed by people. One can only follow and accept it, as stated in the "Wenyan" of the Qian Hexagram: "After the Later Heaven, one follows the heavenly time." The second is unfixed time: like human affairs, which have light and heavy, urgent and delayed matters, and yin and yang, the Five Phases, each have their beginning, flourishing, and end, or loss and gain, movement and stillness. This is what the Commentary on the Judgment of the Ben Hexagram says: "Observing the heavenly phenomena to understand the changes of time." Therefore, the Zhouyi discusses time in different ways: some talk about the waxing and waning of things, such as Tai, Po, Po, Fu; some talk about specific matters, such as Song, Shi, Shihe, Yi; some talk about principles, such as Qian, Lu, Xian, Heng; and some talk about symbolic images, such as Jing, Ding.

《繫傳》曰“卑高以陳，貴賤位矣”，又曰“列貴賤者存乎位”。《說卦傳》“天地定位”，“《易》六位而成章”，此皆指卦位與爻位而言也。《繫傳》曰“危者安其位者也”，又曰“德薄而位尊”，此則由爻象而擬議之爵位之位也。故“位”字亦有此二義。帝出乎震，震東方也，至艮東北之卦也。此八卦之方位。卑高以陳，貴賤位矣，則上下卦（即外卦內卦）之位定。上卦為高，下卦為卑，貴宜卑而賤有高矣。

The Great Treatise says, "The low and the high are arranged, and thus the positions of honor and humility are established," and also says, "The arrangement of honor and humility depends on position." The Discourse on the Hexagrams says, "Heaven and Earth are positioned," and the Great Treatise also says, "The Book of Changes is composed of six positions to form a complete pattern"—all these refer to the positions of the hexagrams and lines. The Great Treatise also says, "A dangerous position is one that is secure in its place," and "A person of shallow virtue in a high position"—this refers to the concept of "position" derived from the line images and applied to human ranks and status. Therefore, the character "position" has these two meanings. The Discourse on the Hexagrams says, "The Emperor arises from the Trigram of Thunder," which is located in the East. Counting through the sequence, the Trigram of Earth is in the Northeast, referring to the directional positions of the eight trigrams. "The low and the high are arranged, and thus the positions of honor and humility are established" refers to the positioning of the upper and lower trigrams (that is, the outer and inner trigrams): the upper trigram is high, the lower trigram is low; however, the honored should reside in the low position, and the humble may also occupy a high position.

列貴賤者存乎位，則卦爻二五，五貴而二賤。王弼謂中四爻有位，初上無位者，即此位也。《易》六位而成章，則分陰分陽，迭用柔剛。所謂陰陽之位，初三五為陽位，二四六為陰位。陽居陽，陰居陰，為當位。反之為不當位。位從立從人，所謂“立人之道曰仁與義”，故三畫卦與六畫卦，皆分天地人三位。而孔子贊《易》則專言人道，天位地位皆以人居之，必能合乎仁義之道，方能與天地參而無慚此位也。

"列贵贱者存乎位," in terms of lines refers to the second line and the fifth line being opposite, with the fifth being considered noble and the second humble. Wang Bi explains that the middle four lines have positions, while the first line and the top line do not, referring to this concept of position. "The Book of Changes has six positions forming a chapter," which discusses "dividing yin and yang, alternating the use of soft and strong."the so-called the positions of yin and yang, the first, third, and fifth lines are yang positions, while the second, fourth, and top lines are yin positions; when a yang line is in a yang position or a yin line is in a yin position, it is called "being in the right position," and the opposite is "not being in the right position." The character "位" consists of "立" and "人," which aligns with the meaning in "Sayings of the Divination" that "establishing the way of human beings is called benevolence and righteousness." Therefore, both the three-line simple trigrams and the six-line compound trigrams are divided into three positions: heaven, earth, and human. Confucius' commentary on the Book of Changes focuses on human affairs: whether it is the position of heaven or the position of earth, it must be occupied by humans; humans must follow the way of benevolence and righteousness to stand alongside heaven and earth as three, without shame for this position.

《易》之言德，亦分二義：一曰卦德。《繫辭》“雜物撰德”，又曰“陰陽合德，剛柔有體，以體天地之撰”，此卦德也。夫乾天下之至健也，德行恆易以知險。夫坤天下之至順也，德行恆簡以知陰。健順乾坤之德也。推之震動巽入，離麗坎陷，艮止兌說，皆其德也。而人用即謂之材。彖者材也，故亦謂之卦材。

The Zhou Changes discuss "de" (virtue), which has two meanings. The first is "guade" (the virtue of the hexagrams). The Great Treatise says "combining various things to form virtue," and also says "yin and yang combine in virtue, and the strong and the flexible have form, thus embodying the composition of heaven and earth." This refers to the virtue of the hexagrams. Qian represents the most vigorous and strong in the world; its virtue is always straightforward, thus enabling it to discern difficulties. Kun represents the most gentle and yielding in the world; its virtue is always simple, thus enabling it to overcome obstructions (the original text mistakenly wrote "knowing yin" instead of "knowing obstruction"). Vigor and yielding are the virtues of the hexagrams Qian and Kun respectively. By analogy, Zhen represents movement and action, Xun represents entering and penetrating, Li represents attachment and connection, Kan represents peril and danger, Gen represents stillness and stability, and Dui represents joy and speech. Each of these represents the virtue of its respective hexagram. When these virtues are applied to human affairs, they are called "cai" (material or quality). The Great Treatise says "tuan (the image) is cai (material)," so the virtue of the hexagram is also called "guacai" (hexagram material).

一曰道德。《說卦》曰“和順於道德”，《繫傳》曰“天地之大德日生”，又曰“以通神明之德”，又曰“默而成之不言而信存乎德行”，皆道德之德也。德有大小，必與位稱。無德而據位，謂之竊位。德薄而位尊，其形渥凶。《易》之興也，其於中古。去古已遠，降而言德。《繫辭下傳》七章之三陳九德，即孔子以《易》設教，而示人以立德之方也。

The second layer is morality. The "Say on the Hexagrams" says, "Harmonious and compliant with morality," and the "Great Treatise" says, "The great virtue of heaven and earth is to produce life," says, "to communicate the virtue of the divine," and says, "to achieve success in silence, to be trusted without speaking, existing in moral conduct." All these refer to the virtue of morality. Virtue can be great or small, and it must be appropriate to the position one holds. To occupy a position without virtue is called "stealing a position"; if one's moral conduct is shallow yet holds a high position, it will be like the Nine in the Fourth of the Ding hexagram, which says, "Its form is moist, ominous," meaning the tripod legs break, the porridge spills over, and one suffers in embarrassment. The "Great Treatise" says, "The rise of the Book of Changes occurred in the middle ancient times,"—by that time, it was already far from the ancient past, so it was necessary to retreat and speak of virtue. The seventh chapter of the lower "Great Treatise" mentions the virtue of nine hexagrams three times, which is precisely how Confucius used the Book of Changes to teach, indicating the path for people to cultivate virtue.

《繫傳》曰“道有變動，故曰爻”，又曰“爻者言乎變者也”，又曰“一闔一闢謂之變”，又曰“剛柔相推而生變化，變化者進退之象也”，又曰“參伍以變，錯綜其數。通其變遂成天地之文，極其數遂定天下之象。非天下之至變，其孰能與於此”，又曰“《易》窮則變，變則通”，又曰“變而通之以盡利”，又曰“變動不居，周流六虛。上下無常，不可為典要，唯變所適”。繫辭之言變，詳且盡矣。蓋宇宙以變而久存，亦以變而日新。無時不變，無境不變。特其跡甚微，人自不知覺耳。

The Great Treatise says, "The Dao has movement and change, hence it is called yao." It also says, "Yao refers to change." It further states, "One closure and one opening is called change." It says, "Hard and soft interact to produce change; change represents the images of advance and retreat." It also says, "By combining three and five, change occurs; by interweaving and combining numbers, the transformation is complete, thus forming the patterns of heaven and earth. When the numbers are fully understood, the images of the world are determined. Without the utmost change in the world, who could be involved in this?" It says, "The Book of Changes reaches an impasse and then changes, and through change, it becomes通畅." It also says, "Through change and通畅, the benefits are fully realized." It further says, "Change does not remain in one place; it flows through the six positions. It moves up and down without constant position; it cannot be fixed as a standard, but must adapt to change." The Great Treatise discusses "change" in great detail. Basically, the universe can exist for a long time only because of change, and it can renew itself every day because of change. There is no moment without change, and no place without change. The traces of change are extremely subtle, so people are unable to perceive them themselves.

《易》窮則變，變則通。故“變通”二字，往往聯綴而言。《繫傳》曰“一闔一闢謂之變，往來不窮謂之通”，又曰“化而裁之謂之變，推而行之謂之通”，又曰“變通配四時”，又曰“無思也，無為也，寂然不動，感而遂通天下之故”，又曰“唯深也，故能通天下之志”，又曰“通乎晝夜之道而知”，又曰“觀其會通以行其典禮”，又曰“體天地之撰以通神明之德”。合變通而觀之，而《易》之所以為《易》可見矣。

The Zhou Changes (I Ching) says, "When things reach their limit, they change; when they change, they become unblocked." Therefore, the characters "change" and "unblock" are often used together. The Great Treatise says, "One closure and one opening is called change; the continuous movement without end is called unblocking." It also says, "To transform and shape is called change; to promote and carry through is called unblocking." It says, "Change and unblocking correspond to the four seasons." It says, "Without thinking, without action, still and unmoving, yet responsive to all things, thus understanding the causes of the world." It says, "Only by being profound can one communicate with the aspirations of the world." It says, "Understanding the principle of day and night is knowledge." It says, "Observing the convergence of change and unblocking, one can carry out the rites and ceremonies." It also says, "By embodying the workings of heaven and earth, one can connect with the virtues of the divine." When we consider both "change" and "unblocking" together, we understand why the Zhou Changes is called the "Changes."

而《序卦傳》曰“泰者通也。物不可以終通，故受之以否”，《雜卦傳》曰“井通而困相遇也”，《繫傳》又曰“困窮而通”，《乾·文言》曰“六爻發揮旁通情也”，《坤·文言》曰“君子黃中通理”。合而觀之，而《易》可通矣。

Now looking at the "Xugua Zhuan" which says, "Tai means communication. Things cannot remain in communication forever, hence it is followed by Po," the "Zagua Zhuan" states, "Well is open and困境 meets," the "Xici Zhuan" further says, "Confusion is being in a difficult situation but eventually achieving communication," the "Wenyan" of the Qian hexagram mentions, "The six lines unfold, communicating the circumstances," and the "Wenyan" of the Kun hexagram says, "The gentleman has a yellow center and communicates the principles." When these statements are considered together, the "Zhou Yi" can be fully understood.

適其可之謂當。凡變也通也，變而通之以盡利，無非由不當而變通之以求其當而已矣。止於至善，位之當也。當其可之謂時，時之當也。陽九陰六之位當矣，而時不相得，或情不相得，則仍有未當。故《象傳》有以當位之爻而言位不當者，如需之上六等類是也。變通之最大者，莫過於革。《革·彖傳》曰“革而當其悔乃亡”，而當之義可見矣。

It is called "when it is exactly appropriate" when something is exactly as it should be. Whenever discussing change or communication, the idea of "changing and communicating to the fullest advantage" is nothing more than seeking the appropriate state through change and adaptability. The "Great Learning" says "to rest in the highest good," which refers to appropriateness in position; the "Record of Learning" says "to act at the right time is called timely," which refers to appropriateness in timing. Sometimes a yang line is in the position of a yang number, and a yin line is in the position of a yin number, and the position is already appropriate. However, if the timing is not in harmony or the nature is not in harmony, there is still a lack of appropriateness. Therefore, the "Image Commentary" may mention a line that is in an appropriate position but still says it is not appropriate in position, such as the upper sixth line of the Need卦. Among all changes, the greatest is "Revolution." The "Commentary on the Judgment" of the Revolution卦 says "when revolution is appropriate, its regret will vanish" — only when the revolution is appropriate will regret disappear. The meaning of the word "appropriate" is thus clearly understood.

易者交易也。非交無以為易，故交者《易》之妙用，亦不啻為《易》之代名辭也。《繫傳》曰“君子安其身而後動，易其心而後語，定其交而後求”，又曰“無交而求，則民不與也”。蓋《易》以明道，而道在人。人在天地間，決不能離群而獨立也。近則男女夫婦父子，遠則君臣朋友，無不有所合也。有合則必有交。人在天地間，又不能絕物而自養也。小則日用飲食，大則養生送死，無不有所需也。有需則必有交。

The character "易" originally means trade. Without exchange, there can be no transaction, so "exchange" is the key function of the "Yi" and can almost be used as a synonym for "Yi." The "Xici Zhuan" says, "A gentleman first establishes himself, then acts; he first changes his mind, then speaks; he first establishes his relations, then seeks." It also says, "If one seeks without having established relations, people will not support him." If one seeks help without having established a proper relationship, others will not agree. The "Zhou Yi" is used to explain the Dao, and the Dao lies in human beings. Human beings exist between heaven and earth and cannot exist alone; they must live in groups. Close relationships include men and women, husband and wife, father and son; distant relationships include ruler and subject, friends. Nothing is needed without combination; wherever there is combination, there must be interaction. Human beings exist between heaven and earth and cannot live independently without external resources. Small things like daily food and drink, large things like supporting the elderly and burying the dead, all require obtaining from others; wherever there is need, there must be interaction.

甲有所需於乙，乙有所需於甲，丙有求合於丁，丁有求合於丙，於是交相為需，交相為養，而人事以興。故《易》象以陰陽明之。陰交於陽，陽交於陰，大有之“無交害”，隨之“交有功”是也。《家人·傳》曰“交相愛也”，《睽·傳》曰“交孚無咎”，故必相愛相孚，而交之道始可久。天地交則泰，否則天地不交萬物不生，人道息矣。西人曰“互助”，惟《易》之“交”足以盡其義也。

Jia has a request for Yi, and Yi also has a request for Jia; Bing wishes to combine with Ding, and Ding also wishes to combine with Bing. Thus, they supply each other and support each other, and human endeavors flourish. Therefore, the Zhou Changes use the image of yin and yang to explain this principle: yin and yang interact with each other, and the interaction between yang and yin, as seen in the initial line of the Daxiang hexagram, "no harm from mutual interaction," and the fourth line of the Suixi hexagram, "mutual interaction brings merit," illustrate this. The Commentary on the Judgment of the Jia Ren hexagram says, "mutual love," and the Commentary on the Judgment of the Kui hexagram says, "mutual trust, no blame"—mutual sincerity leads to no mistakes. Therefore, mutual love and mutual trust are essential for long-lasting relationships. When heaven and earth interact, the Tai hexagram is formed; conversely, if heaven and earth do not interact, all things cannot be generated, and human affairs would cease. Westerners speak of "mutual assistance," but only the single character "jiao" in the Zhou Changes fully captures its meaning.

吉凶悔吝生乎動，而欲動未動之前，則為幾。《繫傳》曰“知幾其神”，又曰“幾者動之微吉之先見者也”。《乾·九三》“終日乾乾夕惕若”，《文言》曰“知至至之可與幾也”。《屯·六三》曰“君子幾，不如舍，往吝”，《豫·六三》“介于石不終日”，《繫傳》曰“見幾而作，寧用終日”。蓋乾九三為人爻之始，動靜所生，吉凶著焉。理欲之界，人禽判焉。孟子所謂“人之所以異於禽獸者幾希”，即此幾也。周子所謂“誠無為，幾善惡”，亦此幾也。

Good, evil, regret, and hardship all arise from movement. The moment just before movement occurs is called "ji." The Great Treatise says, "To know ji is to be spiritual," and also says, "Ji is the subtle movement, the initial sign of good." The line statement of the Nine in the Third of the Qian hexagram says, "All day long diligent and earnest, in the evening vigilant as if something were about to happen." The Wenyan commentary explains, "To know the arrival and to arrive at it, one can be in tune with ji." The line statement of the Six in the Third of the Zun hexagram says, "A gentleman who perceives ji, should not go forward, for going forward would bring regret." The line statement of the Yu hexagram says, "Between stone and sky, not a whole day." The Great Treatise elaborates, "Act when you perceive ji, without waiting for the whole day." The Nine in the Third of the Qian hexagram is the beginning of the human line. From this, movement and stillness arise, and thus good and evil become apparent. The distinction between heavenly principle and human desire, and the difference between humans and beasts, also lie in this point. Mencius said, "What makes humans different from beasts is very slight," referring to this ji. Zhou Dunyi's "Tongshu" said, "Sincerity is without action, and ji determines good and evil," also referring to this ji.

復之初九“不遠復，毋祗悔”，孔子曰“顏氏之子，其庶幾乎”。故幾者，《易》道精微之所在。堯舜之心傳，曰：“人心惟危，道心惟微。”幾者，動之微，即此道心之微也。君子知幾，即在“不遠復”之“反復其道”。故《文言》又曰“終日乾乾，反復道也”。聖人丁寧告誡之意，亦可謂深切而著明矣。“夫《易》，聖人所以極深而研幾也。唯深也，故能通天下之志。唯幾也，故能成天下之務。”“幾事不密則害成”，是以“君子洗心退藏於密”。

The first line of the复卦 says, "Not far from returning, no great regret." Confucius praised in the Great Treatise, "The son of the Yan family, he is almost there." This shows that "ji" is the most subtle aspect of the Way of the Book of Changes. The heart method passed down from Yao and Shun says, "The human heart is dangerous, the Way heart is subtle." "Ji" is the subtle movement, which is exactly the subtle aspect of the Way heart mentioned here. A gentleman must know "ji," and the practice lies in "not far from returning," which reflects "repeating the path." Therefore, the Wenyan says, "All day long diligent and cautious, this is repeating the path." The intention of the sages to repeatedly warn and instruct can be said to be both deep and clear. The Great Treatise says, "The Book of Changes is the way of the sages to explore the profound and examine 'ji.' Because it is profound, it can communicate the aspirations of the people throughout the world; because it examines 'ji,' it can accomplish the affairs of the world." It also says, "If 'ji' affairs are not kept secret, they will cause harm." Therefore, "A gentleman cleanses his heart and retreats into secrecy."

《乾·彖傳》曰“大哉乾元”，《坤·彖傳》曰“至哉坤元”。大無限量，而至有際極。大也，至也，聖人贊《易》開始之第一字也。即此一字，已將乾坤全體之精神分量，概括無遺。並將乾坤兩卦之方式作用，分析明自。挈全《易》之綱領，洩造化之神秘。《繫傳》曰：“《易》其至矣乎！”聖人之情見乎辭矣。大者何，由小以至大也。非至無由顯其大，非大無以極其至，故至亦有大義。

The Commentary on the Judgment of the Qian Hexagram begins with "Great is the Qian Yuan," and the Commentary on the Judgment of the Kun Hexagram begins with "Extremely profound is the Kun Yuan." "Great" means boundless, while "extreme" means reaching the furthest limit. The single character "great" and the single character "extreme" are the first words used by the sage in praising the Book of Changes. With just these words, the entire essence and weight of the Qian and Kun hexagrams are fully summarized, and their forms and functions are clearly explained. It sets the main theme for the entire Book of Changes and reveals the mystery of the workings of nature. The Great Treatise says: "Has the Book of Changes reached its highest point?" The mind of the sage is fully expressed in these words. What does "great" mean? It is the process of gradually moving from small to great. Without "extreme," one cannot display its greatness; without "great," one cannot fully comprehend its extremity. Therefore, the character "extreme" also contains the meaning of "great."

家人、豐、渙，皆云“王假”。假，大也，至也，皆坤之義也。《坤·初六》“履霜堅冰至”，履通謙，謙履相錯為臨遁，故《臨·六四》曰“至臨”。《坤·六四》“括囊”，括，亦至也。而《臨·彖》“至于八月有凶”，謂臨至遁也。由此至彼，必上有所承，故必須承乎乾元，始得止於至善，而為坤元，為至哉坤元，為至道，為至德。為至當不易，失其所承，則為失道，為迷。

The trigrams Family, Fullness, and Dispersal all mention "Wang Jia" (where "Jia" is read as "Ge," meaning to arrive), and "Jia" signifies greatness and arrival, both belonging to the meaning of the Earth trigram. The "Initial Line" of the Earth trigram says "Walking on frost, solid ice is coming." The trigram Walking and the trigram Humility are yin-yang counterparts, and when Humility and Walking are interchanged, they form the trigrams Approaching and Retreat. Therefore, the "Fourth Line" of the Approaching trigram says "Arrival of Approach." The "Fourth Line" of the Earth trigram says "Binding the bag," and "binding" also contains the meaning of reaching the extreme. The "Commentary on the Judgment" of the Approaching trigram says "Until the eighth month there is misfortune," referring to the transition from the Approaching trigram to the Retreat trigram. Whenever moving from one place to another, there must be something above to connect and support it. Therefore, one must connect with the Heaven's origin to stop at the highest good and become the Earth's origin, thus being worthy of "How great is the Earth's origin," and achieving the highest Dao, highest virtue, and the most appropriate and unchanging principle. Once the connecting element is lost, it becomes losing the Dao and going astray.

《復·上六》“迷復凶”，《傳》曰“至于十年不克征”，故得道則曰“朋至（解）”，失道則曰“寇至（需）”，“朋至”則“得其友（損）”，“寇至”則“傷之”者至矣（益）。履和而至（履通謙，則陰陽和），則非堅冰至，則積善必有餘慶。《繫傳》曰：“勞謙，君子有終，吉。勞而不伐，有功而不德，厚之至也。”又曰：“藉之用茅，何咎之有？順之至也。”順與厚，皆坤德也。《文言》曰：“坤，至柔而動也剛，至靜而德方，後得主而有常，含萬物而化光。坤道其順乎？順天而時行。”贊坤元無餘蘊矣。故《易》者，天下之至精，天下之至變，天下之至神。皆“至哉坤元”之至，故“不疾而速，不行而至”。

The *Fu* hexagram's *Upper Sixth* says, "Confused return, ominous." The *Image Commentary* says, "It may take ten years without success." Therefore, those who follow the Dao say "friends arrive" (as in the *Nine in the Fourth* of the *Jing* hexagram, "When friends arrive, trust follows"), while those who lose the Dao say "bandits arrive" (as in the *Nine in the Third* of the *Xu* hexagram, "Causing bandits to arrive"). "Friends arrive" allows one to "gain friends" (as in the *Six in the Third* of the *Sun* hexagram), while "bandits arrive" brings even the person who causes harm (as in the *Upper Ninth* of the *Yi* hexagram). The *Great Treatise* says, "To walk in harmony, one arrives in harmony" (since *Lv* and *Qian* are mutually connected, thus yin and yang are harmonious). This is not the ominous danger of "thick ice arrives," but rather the saying that a family accumulating virtue will surely have abundant blessings. The *Great Treatise* also says, "To work diligently and humbly, a gentleman achieves a good end, which is auspicious. To work hard without boasting, to achieve success without taking credit, this is the utmost sincerity." It also says, "Using straw for the sacrifice, what misfortune could there be? This is the utmost harmony." Harmony and sincerity are both the virtues of *Kun*. The *Discourse on the *Kun* hexagram* says, "Kun is the utmost softness yet its movement is firm, the utmost stillness yet its virtue is square. It waits for the ruler and acts with constancy, containing all things and transforming them into light. Is this not the utmost harmony of the Dao of *Kun*? It follows heaven and acts in accordance with the seasons." It praises the *Kun* origin without reserve. Therefore, the *Zhou Changes* is the most refined, most changeable, and most mysterious book in the world. These instances of "utmost" all originate from "the utmost is the origin of *Kun*." Thus the *Great Treatise* says, "Without haste, yet it is swift; without movement, yet it arrives."

《說卦》曰：“昔者聖人之作《易》也，將以順性命之理。是以立天之道，曰陰與陽。立地之道，曰柔與剛。立人之道，曰仁與義。兼三才而兩之，故《易》六畫而成卦。分陰分陽，迭用柔剛。故《易》六位而成章。”《繫傳》曰：“《易》之為書也，廣大悉備。有天道焉，有地道焉，有人道焉。兼三才而兩之，故六。六者，非它也，三才之道也。”又曰：“六爻之動，三極之道也。”此《易》道也。

The Shuo Guà says: In ancient times, the sage composed the Yì to follow the principles of life and nature. Therefore, he established the principle of Heaven as yīn and yáng, the principle of Earth as flexibility and strength, and the principle of humanity as benevolence and righteousness. By adding one layer to each of the three elements—Heaven, Earth, and humanity—the Yì requires six lines to form a single hexagram. It also distinguishes between yīn and yang positions, alternately using flexible and strong lines, so the Yì has six positions to form its structure. The Xì Cì Zhuan says: The Zhou Yì is vast and comprehensive, containing the principles of Heaven, Earth, and humanity. By adding one layer to each of the three elements, it becomes six. The number six is not something else, but the principle of the three elements. It also says: "The movement of the six lines represents the three ultimate principles." This is what is called the "Yì Dao."

經之言“道”者四：《復·彖》曰“反復其道”，《小畜·初九》曰“復自道”，《履·九四》曰“履道坦坦”，《隨·九四》曰“有孚在道，以明”，皆在《上經》，已將道字發揮淨盡，故《下經》不復贅言，以俟後人之觸類旁通而己。《傳》之言“道”者，曰“一陰一陽之謂道”，又曰“形而上者謂之道”。一陰一陽，變化往來，生生不已。以陽易陰，以陰易陽。乾道成男，坤道成女。陰陽反覆，一陰則反其道，一陽則復其道。故《復·彖》曰“反復其道”，而《乾·九三·傳》亦日“反復道也”。

The term "Dao" is mentioned four times in the text: in the Commentary on the Judgment of the Reversion Hexagram it says "reversing its Dao," in the Initial Line of the Small Accumulation Hexagram it says "returning to the Dao," in the Courteous Hexagram it says "walking on a level Dao" (the commentary by Hang was attached to the Fourth Line, but the current version is in the Second Line), and in the Following Hexagram's Fourth Line it says "having sincerity in the Dao, to illuminate." These four instances are all in the Upper Canon, and they have already fully explained the concept of "Dao," so the Lower Canon does not repeat it, leaving it for later scholars to understand by analogy. In the Commentaries on the Changes, there are mentions of "Dao," such as "one yin and one yang is called Dao," and "what is beyond form is called Dao." One yin and one yang change and move, continuously generating and renewing: exchanging yang for yin and yin for yang; the Dao of Qian produces masculinity, and the Dao of Kun produces femininity. Yin and yang move in a cyclical and reciprocal manner; encountering one yin is "reversing" the Dao, and encountering one yang is "returning" to the Dao, so the Commentary on the Judgment of the Reversion Hexagram says "reversing and returning to the Dao," and the Image Commentary of the Qian Hexagram's Third Line also says "reversing and returning to the Dao."

蓋陽以統陰，失其統則亢，亢則宜復。陰以承陽，失其承則迷，迷則宜反。反而不復，有陰而無陽，失道也。復而不反，有陽而無陰，亦失道也。“終日乾乾”之反覆，已復而欲其反也。“七日來復”之反覆，已反而欲其復也。反而不復，則其道窮。復而不反，則其道困。窮而知變，困而知通，通變隨時，損益得中，聖人之道也。知周乎萬物，而道濟天下，故不過，而《易》之道盡矣。

Yang's function is to lead Yin; if it loses its leadership, it becomes excessive. When excessive, it should return. Yin's function is to receive Yang; if it loses its receiving, it becomes confused. When confused, it should reverse. If only reversing without returning, that is having Yin without Yang, which is losing the Way; if only returning without reversing, that is having Yang without Yin, which is also losing the Way. The phrase "all day long diligent" in the Qian hexagram refers to having already returned and needing to reverse again; the phrase "seven days to return" in the Fu hexagram refers to having already reversed and needing to return again. If only reversing without returning, the Way is exhausted; if only returning without reversing, the Way is blocked. When exhausted, one understands transformation; when blocked, one understands communication. Being able to communicate and transform according to the time, and to reduce and increase while maintaining the middle, this is the Way of the sage. The "Great Treatise" says, "Knowing all things in the world and guiding the world, thus not exceeding," and the Way of the Zhou Yi is thus fully explained.

《傳》稱“得中道”五（《離·六三》，《既濟·六二》，《夬·九二》，《蠱·九二》，《解·九二》），“未失道”二（《睽·九二》，《觀·六三》），“其道窮”四（《比·彖》，《蹇·彖》，《坤·上六》，《節·上六》），“失道”三（《坎·初六》、《上六》，《漸·九三》）。由陽而陰，小人之道也，否也。由陰而陽，君子之道也，泰也。

The Commentary on the Judgment in the Book of Changes mentions "getting the middle path" in five instances: the Sixth line of the Li Hexagram, the Sixth line of the Ji Ji Hexagram, the Second line of the Guai Hexagram, the Second line of the Gu Hexagram, and the Second line of the Jie Hexagram. It mentions "not losing the path" in two instances: the Second line of the Kui Hexagram and the Sixth line of the Guan Hexagram. It mentions "the path is exhausted" in four instances: the Commentary on the Judgment of the Bi Hexagram, the Commentary on the Judgment of the Jian Hexagram, the Sixth line of the Kun Hexagram, and the Sixth line of the Jie Hexagram. It mentions "losing the path" in three instances: the First line and the Sixth line of the Kan Hexagram, and the Third line of the Jie Hexagram. In summary: moving from yang to yin is the path of the petty person, which is negation; moving from yin to yang is the path of the gentleman, which is peace.

有天地而後萬物生焉。萬物生於天地間者，莫不有命。蓋當其未生之前，本無是物也。乃忽而受氣成形，以有是物，形成於地，氣受於天，果孰使之然者？是則所謂命也。聖人設卦觀象，以明萬物之理，即以卦爻之變化往來，以示各有定命之所在。所謂設辭以明之也。《乾·彖》曰“乾道變化，各正性命”，可見命之所自來。即由乾道之變化，乾非坤無以變也，乾變坤化而乾道斯成。亦如男子必得婦生子，而始有父道也。

With the existence of heaven and earth, all things come into being. Every thing existing between heaven and earth carries a "destiny" or "fate." Because before it came into being, there was no such thing; suddenly it received the vital energy and took form, thus becoming what it is. The form is formed on the earth, and the vital energy is received from heaven. But who made it so? This is what is called "destiny." The sage established the structure of hexagrams and observed their images, in order to explain the principles of all things. By observing the changes and movements of the lines in the hexagrams, the sage indicated the fixed destiny of each thing. This is called "setting forth words to clarify it." The *Commentary on the Judgment* of the *Qian Hexagram* says, "The way of Qian brings about change, and each thing establishes its destiny and its nature." This shows that the origin of destiny lies in the change of the way of Qian. However, Qian cannot change without Kun; when Qian changes, Kun transforms, and only then does the way of Qian come into being. This is like a man needing a wife to give birth to children before he can be considered a father.

故曰“一陰一陽之謂道”，分於道之謂命。經之稱“命”者六卦，《否·九四》“有命無咎”，《訟·九四》“復即命”，《革·九四》“改命吉”，《師·九二》“王三錫命”，上六“大君有命”，《泰·上六》“自邑告命”，《旅·六五》“終以譽命”，《傳》則曰“受命”，曰“順命”，曰“舍命”，曰“改命”，曰“申命”，曰“致命”，曰“凝命”。《易》之言命，略具於是矣。

Therefore, it is said, "One yin and one yang is called the Dao," and the portion one receives from the Dao is called "ming" (destiny). The classic text mentions "ming" in six hexagrams: "There is a mandate without misfortune" from the Hexagram of Non-Prosperity, the Fourth line; "Returning to one's destiny" from the Hexagram of Contentiousness, the Fourth line; "Changing one's destiny brings good fortune" from the Hexagram of Revolution, the Fourth line; "The king bestows three mandates" and "The great ruler issues a mandate" from the Hexagram of the Army, the Second line and the Sixth at the Top; "Announcing the mandate from the city" from the Hexagram of Prosperity, the Sixth at the Top; and "Ending with a glorious mandate" from the Hexagram of Travel, the Fifth line. In the "Commentaries on the Zhou Changes," it speaks of "receiving a mandate," "following a mandate," "abandoning a mandate," "changing a mandate," "reiterating a mandate," "conveying a mandate," and "solidifying a mandate." The discussion of "ming" in the Zhou Changes is largely contained within these references.

蓋卦之變化，以正性命者，惟二五。乾二之坤五，其例也。二五之精，妙合而凝。故鼎曰“正位凝命”。命分於道，則道有變化，命亦有變通。受命者，得於天也。凝命者，全其體也。順命者，順其正也。舍命者，察其幾也。申命者，行其事也。致命者，遂其志也。改命者，革其故也。《詩》日：“維天之命，於穆不已。”窮理盡性以致於命，故曰“不知命無以為君子也”。孔子五十而知天命，其亦在學《易》以後乎？

In the changes of the hexagrams, only the second line and the fifth line can truly "correct the destiny and nature." The example of the Qian hexagram's Nine in the Second moving to the fifth position of the Kun hexagram illustrates this. The "Tian Ji Tu Shuo" by Zhou Dunyi speaks of "the essence of two and five, combining and solidifying," so the "Image Commentary" of the Ding hexagram says "correct position and solidify the destiny." Since destiny comes from the Dao, when the Dao changes, destiny also changes. "Receiving the mandate" means obtaining it from Heaven; "solidifying the mandate" means preserving its essence; "following the mandate" means adhering to its proper path; "abandoning the mandate" means examining its subtle aspects; "proclaiming the mandate" means applying it to affairs; "fulfilling the mandate" means achieving one's own aspirations; "changing the mandate" means eliminating its old flaws. The "Book of Songs, Zhou Songs" says, "The Mandate of Heaven, profound and unceasing." The "Shuo Gua" says, "Exhausting principles and fully realizing nature to reach destiny." Confucius also says, "Without understanding destiny, one cannot be a gentleman." Confucius understood the Mandate of Heaven at the age of fifty, perhaps also after studying the Book of Changes.

《說文》：“理，治玉也。從玉里聲。”孔子繫《易》於“理”字約分二義。《說卦》：“和順於道德而理於義。”此理字與和字相針對。和之義為合，理之義為分。分理之理，即治玉之理也。蓋物質之堅緻，而仍有條理可分者，無過於玉。堅則固，致則密。既固且密，則最不易分者，亦無過於玉。故以理為治玉之名，又廣其義為處分萬事。

The Shuowen Jiezi says: "Li means to treat jade. It is composed of the radical for jade and the sound of 'Li'." When Confucius interpreted the Yi Jing, he used the character "Li" in roughly two senses. The Shuigu says: "Harmonious with morality and orderly in righteousness." Here, the character "Li" contrasts with "He" (harmony): "He" means to combine, while "Li" means to differentiate; the "Li" referring to differentiation is the same as the "Li" meaning to treat jade. Basically, among things that are hard and dense yet still have a texture that can be split, nothing surpasses jade: hard means firm, dense means tight; being both firm and tight, nothing is more difficult to split than jade. Therefore, the term "Li" was originally used to describe the process of treating jade, and later its meaning was extended to refer to the orderly management of all affairs.

萬物之名，《易》道廣大，必分而析之，分而又分，析而又析，而後其精微者乃可得而見。亦如今之治化學者，於一物之體質，必分而析之，至於分無可分，析無可析，而所得者，即為此物之原質矣。故邵子之加一倍法，亦即分析法之還原者也。物理數理，皆有跡象可求，分而理之尚易。至理於義，則精微之至矣。其下文“窮理盡性以至於命”，此理字則為名詞，而非動詞，即指性分中所有之理。

All things in the world have many names and forms, and the principles of the Book of Changes are vast and profound. Therefore, they must be analyzed and divided repeatedly, breaking them down layer by layer until the subtle aspects become clear. This is similar to how modern chemists study the nature of substances by analyzing them, dividing them until they can be divided no more, and analyzing until they can be analyzed no further. The result is the fundamental elements of that substance. Thus, Shao Yong's method of "doubling" — dividing one into two, two into four, and so on, doubling at each stage — is essentially a method of reduction through analysis. Physics and mathematical reasoning have tangible traces and can be systematically broken down and organized. However, when it comes to the level of "li yu yi" (principle and meaning), it becomes extremely subtle. The character "li" in the phrase "qiong li jin xing yi zhi yu ming" refers to a noun rather than a verb, meaning the principle that is inherently present within one's nature.

故鄭康成注《樂記》曰“理猶性也”，朱子注《中庸》曰“性即理也”，竟以理與性，相為轉註。然詳加研究，則終有未安。未可以大儒之說，遂附和之，而以為確當也。蓋性固有理，不能謂理即性，性即理。猶物各有理，不能謂物為理，謂理為物也。先儒此種訓詁，貽誤後學最多。是在學者之自有領悟，愈講解而糾纏愈甚矣。《坤·文言》曰“君子黃中通理”，與《乾·傳》“利貞者，性情也”，呼吸相通。苟於此領悟而有得焉，於明理之學，思過半矣。

Therefore, Zheng Xuan's commentary on the "Book of Rites · Music Record" says "li is like xing," and Zhu Xi's commentary on the "Doctrine of the Mean" says "xing is li," treating "li" and "xing" as synonymous terms that can be explained in terms of each other. However, upon closer examination, these statements ultimately do not hold up. One should not simply follow the words of great scholars blindly, assuming them to be correct. Although xing does contain li, one cannot say that li is xing or xing is li; just as each thing has its own li, one cannot say that the thing is li or li is the thing. Such interpretations by previous scholars have caused the most confusion for later students. This can only be understood through personal insight; the more explanations one receives, the more confused one becomes. The "Commentary on the Literary Meaning" of the "Kun Hexagram" says "the gentleman has yellow in the center and communicates li," and the "Commentary" of the "Qian Hexagram" says "li zhen refers to xingqing," with these two sentences sharing a similar spirit. If one can understand and gain insight from here, then one will have grasped a large part of the study of understanding principles.

分於道之謂命，分於命之謂性。心生為性，有生斯有命，有命斯有性，性命恆相聯屬。故《易》言命而不言性。孔子贊《易》，則曰“乾道變化，各正性命”，又曰“窮理盡性以至於命”，又曰“一陰一陽之謂道。繼之者善也，成之者性也”。言性之本源，可謂明白曉暢矣。

The part derived from the Dao is called "ming" (destiny), and the part derived from "ming" is called "xing" (nature). The character "xing" is composed of "xin" (heart) and "sheng" (birth), meaning what arises from the heart is xing. There is birth before there is destiny, and there is destiny before there is nature. Thus, xing and ming are always connected. Therefore, the text of the Zhou Changes only discusses ming and not xing. When Confucius commented on the Zhou Changes, he said, "The Dao of the Creative Heaven changes, and each thing establishes its own ming and xing." He also said, "To exhaust the principles and reach the nature, and thus reach the destiny," and again, "One yin and one yang is called Dao. The one who continues it is goodness, and the one who completes it is xing." In discussing the origin of xing, he explained it clearly and distinctly.

後之言性者，約分三類：孟子，言性善；荀子，言性惡；告子，言性無善無不善。各明一義。性善之說，於立教為宜，故後世多宗之。其實曰善曰惡，已為性之所見端，未可謂之性也。告子無善無不善之說，殊未可厚非。孔子曰“性相近，習相遠”，亦此意也。宋儒因迴護孟子之說，於是創為義理之性，氣質之性，以分別善惡。謂生而善者，義理之性。習而惡者，氣質之性。益支離而不可通矣。

Later generations have generally divided the discussion of human nature into three schools of thought: Mencius taught that human nature is good, Xunzi taught that human nature is evil, and Gaozi taught that human nature is neither good nor evil. Each emphasized a different aspect. The theory of innate goodness is convenient for moral education, so it was mostly followed in later times. In reality, when one speaks of goodness or evil, these are already manifestations of nature, not its essential nature. Gaozi's statement that human nature is neither good nor evil is actually not unreasonable. Confucius said, "Human nature is originally similar, but habits make them differ," which expresses exactly the same idea. The Song dynasty scholars, in order to defend Mencius' theory of innate goodness, invented the distinction between "principle-based nature" and "material nature," saying that those born good belong to principle-based nature, while those turned evil by habit belong to material nature. This distinction only makes the theory more fragmented and incoherent.

情者，性之動也。所謂人生而靜，天之性也。感於物而動，性之慾也。故性與情亦恆相聯屬。《易》言欲而不言情。孔子贊《易》，曰“利貞者，性情也”。《白虎通》曰：“性者，陽之施。情者，陰之化也。”《論衡》曰：“性生於陽，情生於陰。”《說文》：“性，人之陽氣，性善者也。情，人之陰氣，有欲者也。”皆性情並舉。性貞於誠，而情則有誠有偽。《繫辭》曰“設卦以盡情偽”，又曰“爻彖以情言”，又曰“吉凶以情遷。凡《易》之情近而不相得，則凶或害之悔且吝”，又曰“六爻發揮，旁通情也”。觀旁通而情可見矣。

"Qing" refers to the manifestation of nature. The "Book of Rites: On Music" states, "When a person is born, he is in a state of tranquility, which is the nature of heaven; when he is moved by external things, it is the desire of nature." This precisely expresses the meaning of this concept, so nature and qing are always closely connected. The "Zhou Yi" (Book of Changes) only discusses desire but does not mention qing; it was only when Confucius commented on the "Zhou Yi" that he said, "Li zhen refers to nature and qing." The "Bai Hu Tong" states, "Nature is the manifestation of yang; qing is the transformation of yin." The "Lun Heng" says, "Nature arises from yang, and qing arises from yin." The "Shuo Wen Jie Zi" says, "Nature is the yang qi of a person, which is inherently good; qing is the yin qi of a person, which has desire." All these sources mention nature and qing together. Nature is correct when it is sincere, while qing may be sincere or false. The "Xi Ci Zhuan" says, "Setting up trigrams is to fully express the true and false aspects of human nature and qing," and it says, "The yao and tian are spoken of in terms of qing," and "Good fortune and misfortune change according to qing; all the qing in the "Zhou Yi" are close but not in harmony, which leads to misfortune, harm, regret, and hardship." It also says, "The six yao are developed to communicate the qing." From the method of "pang tong" (mutual communication), the authenticity, truthfulness, and opposition of qing become evident.

教以立人，道以立己，己立立人。故《易》之為書，無非道也，無非教也。卦之言教者三：坎“習教事”，臨“教思無窮”，觀“觀民設教”，而要以“蒙養”為立教之始。孔子更廣其義於漸，曰“居賢德善俗”。於蠱曰“振民育德”。於無妄曰“茂對時育萬物”。於是今世謂之文明教育之事業，而《易》無不備舉矣。而其博大精深之教義，則尚非今世物質文明之教育家，耳目思想所能及。當於卦爻內詳論之，茲未遑悉舉也。

"Teaching" is used to help others, while "the Way" is used to achieve oneself; one must first establish oneself before being able to help others establish themselves. Therefore, the book of The Zhou Changes contains nothing that is not the Way, and nothing that is not teaching. There are three instances in the hexagrams that directly mention teaching: in the "Image Commentary" of the Kan hexagram, it says "maintaining the constant virtue, practicing teaching affairs"; in the "Image Commentary" of the Lin hexagram, it says "teaching thoughts are boundless"; and in the "Image Commentary" of the Guan hexagram, it says "examining directions, observing the people, and establishing teaching." The starting point of establishing teaching always returns to the Meng hexagram's "cultivating correctness in the young." Confucius further expanded on this meaning: in the Jian hexagram, he says "residing in virtuous virtue and improving customs"; in the Gu hexagram, he says "reviving the people and cultivating virtue"; and in the Wuwang hexagram, he says "prosperous and nurturing all things in accordance with the seasons." Clearly, all the various endeavors of modern civilization and education are already fully contained in The Zhou Changes. As for its vast and profound teachings, they are beyond the reach of today's educators who focus only on material civilization, whose senses, hearing, and thoughts cannot comprehend them. These should be discussed in detail in each hexagram and line, but it is not possible to list them all here.

《易》者，用世之書也。故以有立教，亦以用立教，亦即以中立教。有貴乎能用，有而不能用，則與無等耳。然非無不能明有之用，非用無以盡有之功，非中無以盡用之妙，故曰“有”，曰“用”，曰“中”。此《易》之界說也。必明此界說，而後《易》可得而言。《易》六十四卦，無一非用，而以乾坤用九用六發其凡。用六而曰以大終，則六亦九之用，故以乾元用九而天下治，以竟《易》之全功。《乾·九二》“庸言”“庸行”，言行君子之所以動天地也。而曰“庸”者，庸者用也，明用之非中不立也。

The Zhou Changes is a book that serves the world and achieves practical results. Therefore, it establishes its teachings based on "having" (有), "using" (用), and "center" (中). "Having" is valuable only when it can be used; if one has something but cannot use it, it is as if one has nothing. However, without understanding "nothingness" (无), one cannot fully explain the function of "having"; without using it, one cannot fully realize the effectiveness of "having"; without attaining "center," one cannot fully grasp the subtleties of "using." Therefore, speaking of "having," "using," and "center" is the essence of the Zhou Changes. One must first clearly understand these three principles before one can begin to discuss the Yi. None of the sixty-four hexagrams is not about using; the general principle is expressed through the "use of nine" (用九) in the Qian hexagram and the "use of six" (用六) in the Kun hexagram. The "use of six" in the Kun hexagram says "it brings about a great conclusion," indicating that six is also the use of nine. Therefore, "the power of Qian's original essence is the use of nine, and the world is thus governed," and the entire function of the Zhou Changes is thus completed. The "Commentary on the Second Line of the Qian Hexagram" says, "ordinary words are trustworthy, and ordinary actions are cautious," meaning that speech and action are the means by which a gentleman can move heaven and earth. The use of the character "庸" (ordinary) is because "庸" means "use," showing that use cannot stand without center.

以，用也。孔子傳《易》，以明大用，於六十四卦之《象傳》明之。“天行健，君子以自強不息”。“地勢坤，君子以厚德載物”。六十四卦皆此以一字挈其綱，即“五十以學《易》”之以，亦即“以《易》傳教”本旨之所在也。

The 「以」 means to use. Confucius wrote commentaries on the Yi to clarify its great practical use, which is concentrated in the Great Image Commentaries of the sixty-four hexagrams: ‘Heaven’s movement is vigorous, the gentleman should strive ceaselessly’; ‘The earth’s position is docile, the gentleman should cultivate virtue and carry all things.’ Each of the sixty-four hexagrams uses this single character 「以」 to summarize its main idea. This 「以」 is the same 「以」 as in Confucius’ statement ‘At fifty I began to study the Yi,’ and it is precisely where the principle of ‘using the Yi to teach’ is realized.

蓋《彖傳》者，釋內外兩卦之用也。《象傳》則取兩卦之中，合上下之義而貫串之。兩卦之中者何？即三四兩爻，所謂中爻所謂人爻者是也。故曰“若夫雜物撰德，辨是與非，則非其中爻不備”。而二四三五同功，三四於六爻為人位，“立人之道”立於此。孔子之六十四“以”字，亦發明於此。明乎此，則庶乎可盡《易》之用。雖吉凶有命，而悔吝可免矣。故《易》於乾之九三九四兩爻，特著曰“無咎”。

The Commentary on the Judgment explains the use of the inner and outer trigrams separately; the Great Image Commentary, on the other hand, takes the point where the two trigrams meet, combining the meanings above and below to form a continuous whole. The so-called meeting point of the two trigrams refers to the third and fourth lines, which are called the "middle lines" and the "human lines." Therefore, the Great Treatise says: "If one is to mix various things and cultivate virtue, and distinguish right from wrong, then without the middle lines, the meaning would not be complete." The second and fourth lines have the same function, and the third and fifth lines also share the same function. The third and fourth lines are in the central position among the six lines, and thus represent the human position. The establishment of the way of human beings is established here. The sixty-four "以" (by means of) words that Confucius added in the sixty-four "Image Commentaries" of the sixty-four hexagrams were also derived from this. Once this is understood, one can largely exhaust the application of the Zhou Changes: although good and bad fortune may be determined by fate, regret and hardship can be avoided. Therefore, the Zhou Changes specially marks the words "no blame" under the ninth line of the third and fourth lines of the Qian hexagram, indicating that if one can properly correct mistakes, there will be no calamity.

之者，《易》之用也。爻有變動，故曰之。“辭也者各指其所之”，有所之而吉凶見焉。之字作屮。屮者一生三也。《易》者，一陰一陽。動有所之，而用生焉，則二生三也。故曰“一陰一陽之謂道”。之而當，則得道。之而不當，則失道。《無妄·傳》曰：“無妄之往，何之矣。”何之則道窮，是以君子慎其所之。

The character 「之」 refers to the application of the Zhou Changes. Since lines (yao) change, the character 「之」 is used to indicate this movement, as in examples such as 「Qian之Gou」 and 「Qian之Tongren」. The Great Treatise says, 「The words (ci) refer to where they go (zhi)」—when there is movement, fortune and misfortune become evident. The ancient form of 「之」 was written as 「屮」, which represents a single stem branching into three, symbolizing 「one produces three」. The Zhou Changes discuss the principle of one yin and one yang; when there is movement, application arises, which is the transition from two to three. Therefore, it is said, 「One yin and one yang is called the Way (dao).」 When movement is appropriate, one attains the Way; when movement is inappropriate, one loses the Way. The Commentary on the Judgment of Wuwang says, 「Without expectation (wuwang), where should one go?」 If there is nowhere to go, the Way is exhausted, so the gentleman is especially cautious about where he goes.

舊說“孚，信也”。坎為信。凡卦言“有孚”，皆指坎，似是而實非也。孚果指坎，何以中孚無坎象？孚固有信之一義，然信字不足以盡孚也。孚從爪，從子，象鳥以爪抱子。鳥子為卵，爪子以象抱卵，有化育之意。中孚卦象，實以巽五兌十，乃五十五數之中，於五行為土。土主化物，故曰中孚。

Old interpretations say that "fu" means "trust," and since Kan represents trust, any instance of "having fu" in the line statements of the hexagrams refers to the Kan hexagram. This seems reasonable at first glance, but it is actually incorrect. If "fu" were exclusively associated with Kan, then the Zhongfu hexagram, which does not contain the image of Kan, would be difficult to explain. Although "trust" is one meaning of "fu," the character "trust" alone cannot fully capture the meaning of "fu." The character "fu" is composed of "zhu" (爪) and "zi" (子), symbolizing a bird using its claws to hold its eggs, with the egg representing the bird's offspring. The combination of "claw" and "offspring" suggests the act of hatching and nurturing. The image of Zhongfu actually consists of Xun in the fifth position and Dui in the tenth, corresponding to the number fifty-five, which is the center of the total number of heavenly and earthly numbers. In the Five Phases, fifty-five belongs to earth, which governs the nurturing and generation of all things, hence the name "Zhongfu."

其曰“有孚”者，“有”謂大有。火天大有，離也。孚，則指坎。坎離居南北之位，合乾坤之中，維中能孚，故曰“有孚”。有則大，孚則化，“有孚”者，即《中庸》所謂“大德敦化”也。凡《易》之道，一陰一陽，必陽孚於陰，而陰孚於陽，而後陰陽和，而成化育之功。

As for "having faith" (有孚), the "有" refers to the Hexagram Da You. Da You is composed of Li above Qian, known as "Fire over Heaven: Great Possession." The image is taken from Li; "孚" refers to Kan. Kan and Li are located in the north and south respectively, precisely in the middle of Qian and Kun. Only by being in the center can they have faith in each other, hence "having faith." "Having" leads to greatness, and "faith" leads to transformation, so "having faith" is also what the Zhongyong says "great virtue nurtures transformation." In general, the Way of the Book of Changes is the interplay of yin and yang. It must be that yang comes to have faith in yin, and yin comes to have faith in yang, only then can yin and yang harmonize, and the function of transformation and nurturing can be realized.

人品有君子小人，泰、否，君子小人之相消長者也。遁曰“君子吉，小人否”，觀曰“小人無咎，君子吝”。必君子能孚小人，則小人亦能化為君子。所謂“有孚顒若”，下觀而化，則先否後喜，天下受福矣。若不能用觀，則成大壯。義非不正，理非不直也。而剛以反動，小人用壯，君子用罔。羝羊觸藩，天下被其禍矣。乾元用九，必有孚而始致其用。故孚有信義，有化義，有容義，又有合義，有感義。所謂精義入神之用，以孚字盡之矣。非統全《易》而詳察之，又烏知其妙哉！

Human beings can be categorized as either gentlemen or petty persons. The hexagrams Tai and Pu illustrate the mutual rise and decline of gentlemen and petty persons. The hexagram Duan says, "The gentleman is auspicious, the petty person is not." The hexagram Guan says, "The petty person has no blame, the gentleman is in want." Only when the gentleman can inspire and win the trust of the petty person can the petty person be transformed into a gentleman. The phrase "There is sincerity and reverence" in the hexagram Guan refers to those below looking up and being influenced, thus first encountering difficulty and then experiencing joy, and the whole world benefiting. If the method of "Guan" is not used, it becomes Da Zhuang. The meaning of Da Zhuang is not improper, nor is its principle not upright, but when it is too strong, it will rebound: "The petty person uses strength, the gentleman is trapped." A male goat with horns collides with a fence, but ends up getting stuck, unable to move forward or backward, and the world suffers as a result. The use of "Yuan Yu Ji" in Qian Yuan also requires sincerity to truly realize its function. Therefore, the character "fu" contains the meanings of trust, transformation, tolerance, unity, and influence. The "Great Treatise" says, "Refining the profound meaning to the divine level so as to achieve practical use," and the character "fu" encompasses all of this. Without a comprehensive study of the entire Zhou Yi, how could one understand its subtleties?

以上單辭，略舉一隅，可見經傳字無虛設。或一字而含數義，或數卦合用一字，無不脈絡貫通。潛心體玩，均有線索可尋。此外有字以類從，因意義相同，而互見於各卦而相貫串者，可謂之類辭，如則法律一類也，克伐徵一類也，速疾遇一類也，需繻須濡一類也，怠緩徐慢裕一類也。凡同乎此者，皆以義相類者也。如弟娣娣涕一類也，頄仇九一類也，輪綸一類也。凡同乎此者，皆以形聲相類者也。相類之字，於卦爻之變通意義，皆有關係，均可互相印證者也。

The examples given above are only a few instances, but from this we can see that no single character in the classics is superfluous. Some characters contain several layers of meaning, while others are used together across multiple hexagrams, and they are all connected in a coherent way. As long as one carefully examines and reflects on them, there will be clear clues to follow. In addition, there is another category of characters that are grouped together because of similar meanings, scattered throughout various hexagrams but connected to each other, and can be called "classical terms." For example, "则, 法, 律" are one category, "克, 伐, 征" are another, "速, 疾, 遇" are another, "需, 繻, 须, 濡" are another, and "怠, 缓, 徐, 慢, 裕" are another. All of these are grouped according to similar meanings. Another example is "弟, 妹, 涕" as one category, "頄, 仇, 九" as another, and "轮, 纶" as another. All of these are grouped according to similar forms or sounds. Characters that are similar in meaning or form are related to the meanings of hexagram lines and their transformations, and can be used to verify each other.

其單辭之外，更又綴屬一字，或二字，或三四五字，以成一名辭，或成一句者，可謂之類句。如由頤、由豫；甘節、甘臨；頻復、頻巽；艮其腓、咸其腓；困于酒食、需于酒食；我心不快、其心不快；同人，先號咷而後笑；旅人，先笑而後號咷之類，亦無不互相聯貫。

In addition to single characters, there are cases where one, two, or three to five characters are added above another character to form a noun or a complete sentence. Such combinations can be called 'classificatory phrases'. For example, '由颐' and '由豫', '甘节' and '甘临', '频复' and '频巽', '艮其腓' and '咸其腓', '困于酒食' and '需于酒食', '我心不快' and '其心不快', as well as the '先号咷而后笑' from the Tongren hexagram and the '旅人先笑后号咷' from the Lv hexagram. These are all mutually connected.

如密雲不雨、帝乙歸妹、用拯馬壯吉、不富于其鄰，完全相同之一句，或二句，分見於兩卦或三卦者，則更為顯而易見。具詳於焦理堂氏之《易通釋》，茲不贅述也（《易通釋》偏於旁通之正立言。有未可盡通化學者，以意逆之，勿以其辭云意也可。）。

As for cases where exactly the same sentence or pair of sentences, such as "密云不雨" ("dense clouds without rain"), "帝乙归妹" ("King Di Yi marries off his younger sister"), "用拯马壮吉" ("using a strong horse brings good fortune"), and "不富于其邻" ("not being rich compared to one's neighbors"), appear in two or even three hexagrams, this is even more obvious. Zhao Xiu's "Yi Tong Shi" explains these in great detail, so there is no need to repeat here. (Zhao's "Yi Tong Shi" mainly discusses the correct aspect of mutual transformation, and some parts may not be fully coherent. Readers should use their own interpretations to infer his intended meaning rather than stick rigidly to the literal text.)

舉單辭、對辭、類辭、類句，經傳之概略，已可見矣。而正言斷辭，尚有數例，更舉如左。

Four types of expressions are mentioned: single words, paired words, categorical terms, and categorical sentences. The general situation of the use of characters in the classics can now be clearly seen. As for the aspect of "correct statements" and "concluding phrases," there are still several general rules, which are listed below.

號者，名也。稱其名使與實相稱，亦當名辨物之意也。孟長卿曰：“周人五號，帝，天稱，一也。王，美稱，二也。天子，爵號，三也。大君者，興盛行異，四也。大人者，聖明德備，五也。”

"Number" refers to the name. To call something by its proper name so that the name corresponds to the reality is the meaning of what was previously mentioned, "when a name distinguishes an object." The Han dynasty I Ching scholar Meng Xi (style name Changqing) said: the Zhou people had five kinds of titles— "Di" is the term for heaven, which is the first; "Wang" is a term of praise, which is the second; "Tianzi" is the title of rank, which is the third; "Dajun" refers to those who flourish and act excellently, which is the fourth; "Daren" refers to those who are wise and have complete virtue, which is the fifth.

以上五者，皆經之特稱。孔子贊《易》，更廣其義。曰“先王”。豫，“先王以作樂崇德”。曰“後”。泰，“后以裁成輔相之道”。

The above five are special titles unique to the classic text. Confucius praised the Book of Changes and expanded their scope. The first is "Xianwang" (former kings), as mentioned in the Image Commentary of the Yu hexagram: "Xianwang used music to honor virtue." The second is "Hou" (ruler), referring to the reigning monarch, as stated in the Image Commentary of the Tai hexagram: "Hou used resources to complete the way of heaven and earth, and assisted in the suitability of heaven and earth."

經稱爵號，王之下有三：曰“公”。大有，“公用享于天子”。解上六，“公用射隼”。益六三，“告公用圭”。六四，“告公從”。鼎九四，“覆公餗”。曰“侯”。屯，“利建侯”。豫，“利建侯”。晉，“康侯”。曰“子”。明夷，“箕子之明夷”。鼎，“得妾以其子”。言公、候、子而不及伯、男。或曰：“此殷制也。文王演《易》於紂之世，故從殷制。”

The titles mentioned in the text are ranked below "King" into three levels. The first is "Gong" (Duke): in the line "The Duke uses offerings to the Son of Heaven" from the line Nine in the Third of the Qian hexagram, "The Duke uses a bow to shoot a falcon" from the line Six at the Top of the Dui hexagram, "The Duke is informed with a jade tablet" from the line Six in the Third of the Yi hexagram, and "The Duke is informed with a proposal" from the line Six in the Fourth of the Yi hexagram, and "The Duke's food is overturned" from the line Nine in the Fourth of the Ding hexagram. The second is "Hou" (Marquis): in the hexagram Zun, "It is advantageous to establish a Marquis," in the hexagram Yu, "It is advantageous to establish a Marquis," and in the hexagram Jin, "The Healthy Marquis." The third is "Zi" (Prince): in the hexagram Mingyi, "Jizi's brightness is obscured," and in the hexagram Ding, "He obtains a concubine with her son." Only the titles of Duke, Marquis, and Prince are mentioned, without reference to the titles of Bo and Nan. Some people say: this is the system of the Yin dynasty, and King Wen compiled the Zhou Yi during the reign of King Zhou, so he followed the Yin system.

正名之稱有六：曰“大人”。一人為大。孟子日：“大人者，不失其赤子之心者也。”《文言》“與天地合其德”一節，孔子贊大人也至矣。曰“君子”。乾為君，震為子。乾震為無妄，君子者，無妄之稱。

Titles used to establish proper roles include six kinds. The first is "Da Ren" (Great Person): the character "Da" is formed by combining "Yi" and "Ren". Mencius said: "A Da Ren is one who does not lose the innocent heart of a child." The section in the "Wen Yan" of the "Qian Hexagram" that says, "A Da Ren is one who harmonizes with the virtue of heaven and earth," represents Confucius' highest praise of a Da Ren. The second is "Jun Zi" (Gentleman): Qian represents the king, and Zhen represents the son; Qian above and Zhen below form the "Wu Wang" hexagram, so "Jun Zi" is the title of the "Wu Wang" hexagram.

曰“小人”。天大，地大，人亦大。與天地參，故大。違反天地之道，則曰小人。曰“惡人”。睽“見惡人”，人而見惡於人，曰惡人。於象，離為惡人。曰“寇”。寇者悖逆之詞。於象，坎為寇。曰“匪人”。匪同非。“比之匪人”，“否之匪人”，失人道，故曰“匪人”。孟子曰：“無惻隱之心，非人也。無羞惡之心，非人也。無辭讓之心，非人也。無是非之心，非人也。”

Third is 'small person': Heaven is great, Earth is great, and human beings are also great. Humans can be ranked with Heaven and Earth as the three greats, so they are called great. Those who violate the way of Heaven and Earth are called small persons. Fourth is 'evil person': The first line of the Guī hexagram says 'seeing an evil person'; a person who is disliked by others is called an evil person, and according to the hexagram image, the line Li represents an evil person. Fifth is 'bandit': 'Bandit' is a term describing a rebellious person. According to the hexagram image, the line Kan represents a bandit. Sixth is 'non-person': 'Fēi' is the same as 'non'. The third line of the Bi hexagram says 'comparing with a non-person', and the hexagram statement of the Pǐ hexagram says 'Pǐ is non-person'. Both refer to those who have lost the way of being human, so they are called non-persons. Mencius says: 'Without a sense of compassion, one is not a person; without a sense of shame and aversion, one is not a person; without a sense of propriety and humility, one is not a person; without a sense of right and wrong, one is not a person.'

孔子贊《易》，更廣其義。曰“聖人”，曰“賢人”，曰“盜”，亦曰“暴客”，日“吉人”，曰“躁人”，曰“誣善之人”。

Confucius praised the Book of Changes, and further expanded the scope of such titles, thus referring to 'sages', 'virtuous persons', 'thieves', as stated in the Great Treatise, 'careless storage teaches theft'; also called 'violent guests', as in 'keeping heavy doors and striking the tongs to guard against violent guests'; there are 'auspicious persons', as in 'the words of an auspicious person are few'; there are 'impetuous persons', as in 'the words of an impetuous person are many'; there are 'those who slander the virtuous', as in 'the words of those who slander the virtuous are flowing'.

名當而辭可斷矣。爻有等，故曰“物”。辨物當名，名不等也。正言，言不等也。故斷辭亦不等。凶至吉為七等：凶，厲，悔，吝，無咎，無不利，吉。凶不若厲，厲不若悔，悔不若吝，吝不若無咎，無咎不若無不利，無不利不若吉。

The names are appropriate, and thus the judgments can be made. The "Great Treatise" says, "The lines have levels, so they are called things." Since the lines have different levels, they are referred to as things. Distinguishing things and establishing names, names have levels; expressing words properly, words also have levels; therefore, the concluding remarks also have levels. From evil to good, there are seven levels: evil, danger, regret, hardship, no blame, no disadvantage, and good. Evil is worse than danger, danger worse than regret, regret worse than hardship, hardship worse than "no blame," "no blame" worse than "no disadvantage," and "no disadvantage" worse than good. These seven levels, from heavy to light, allow the person asking the question to measure the depth of their situation: evil means disaster has already occurred, danger means peril but not yet failure, regret means there is regret but still recoverable, hardship means slight regret, "no blame" means good correction of mistakes without disaster, "no disadvantage" means everything is feasible, and good is the true perfection.

海寧先生之於《易》，得異人傳授，又博極諸家傳注，故能竟委窮源，而獨見其大。先生於書，無所不讀，故能探賾索隱，鉤貫於新舊之學，而獨得其通。昔嘗聞之先生曰：《易》始於包犧氏，備於神農、黃帝，大明於文王、周公、孔子。漢人去古未遠，其卦氣、飛伏、陰陽、消息，皆有所授受，非能自創。孔子贊《易》，專重人道，以明立教之旨。故三陳九德，以人合天，而筮法僅略言及之。

Master Hang Xinzhai of Haining studied the Yi Jing thoroughly, having received personal instruction from a rare master and extensively reading the commentaries and annotations of various scholars throughout history. Therefore, he was able to trace the origins and fully understand the main principles of the Yi. Since he had studied widely, he could grasp profound meanings and connect old and new schools of thought, thereby comprehending the common thread within them. I once heard Master Hang say that the Yi originated with Fuxi, became complete during the time of Shen Nong and the Yellow Emperor, and was fully elucidated by King Wen, the Duke of Zhou, and Confucius. The Han dynasty scholars were not far from the ancient times, and their discussions on "gu qi," "fei fu," "yin and yang," and "xi xiao" were passed down from teacher to student with a clear lineage, not invented out of nowhere. When Confucius composed the Yi Zhuan, he focused especially on the human aspect, using it to explain the purpose of education and moral instruction. Therefore, in the Great Treatise, he three times discussed the virtues of the nine trigrams, urging people to harmonize human principles with heavenly principles. As for the method of divination using the yarrow stalks, he only briefly mentioned it.

朱子乃謂“《易》為聖人教人卜筮之書”，豈知方耶？然河、洛為《易》象所取則，漢學只詆為偽造，朱子獨取以冠經首，是其卓識，亦有不可及者。又曰：“道家祖黃老，淵源悉出於《易》。”其七返九還，六歸八居，度數與卦象悉合無論矣。所異者佛產印度，耶穌生於猶太，而《華嚴》之乘數，《金剛》之相數，一八、三六、百零八之數，及“七日來復”、“十三見凶之數”，亦無不得。僅以素所聞於先生者，弁諸簡端，並志其緣起如此云。

Zhu Xi said that the Book of Changes is a book that the sage used to teach people how to divinate, is this not understanding the fundamental approach? However, the Yellow River Chart and the Luo Writing were originally the basis for the symbolic images of the Book of Changes. Han scholars universally rejected them as later forgeries, but Zhu Xi alone took them and placed them at the beginning of the classic text, and this insight is something others cannot match. You also said that Daoists revere the Yellow Emperor and Laozi as their ancestors, and their origins are entirely from the Book of Changes. The Danists' discussions of 'seven returns and nine returns' and 'six returns and eight dwellings' have numbers that correspond with the hexagrams in every aspect, so there is no need to mention them further. What is strange is that Buddhism originated in India, Jesus was born in Judea, yet the numerical concepts in the Avatamsaka Sutra, the numerical concepts in the Diamond Sutra, as well as numbers like one and eight, three and six, one hundred and eight, and numbers such as 'seven days to return' and 'thirteen days to see misfortune' also do not have any that do not correspond with the numbers of the Book of Changes. I merely wrote down what I heard from you on the first page of this volume, and recorded the origin of this book as above.

《易》道至大，《易》理至遂；辛齋之愚，何敢妄談？顧念吾師忍死狴犴，剋期以待，密傳心法，冀綿絕學，又曷敢自棄？丙辰出獄，爰蒐集古今說《易》之書，惟日孳孳，寢饋舟車，未嘗或輟。丁巳以後，國會蒙塵。播越嶺嶠，議席多暇，兩院同人，合組研幾學社於廣州之迥龍社。謬推都講，計日分程，商兌講習。雖兵戈擾攘，而課約罔閒。

The Way of the Book of Changes is extremely vast and profound; its principles are extremely deep. I, Hang Xinzhai, with my shallow intellect and limited knowledge, dare not speak casually about it. However, thinking of my late teacher who was imprisoned, enduring suffering and waiting patiently, agreeing on a time to secretly pass on his inner teachings to me, hoping that this nearly extinct discipline could be continued, how could I then give up and be defeated? After my release in the year Bingchen, I began to collect books from ancient times explaining the Book of Changes, working diligently every day without ceasing, not even pausing during sleep, meals, travel or other activities. From the year Dingsi onwards, the National Assembly was forced to relocate, and I was stranded in Lingnan. With much spare time in the legislative sessions, the members of both houses formed the "Yanjixue She" (Society for the Study of the Subtleties) together in the Jionglong Society in Guangzhou. They mistakenly elected me as the main lecturer, setting daily schedules and discussing and studying together. At that time, although there was turmoil and warfare, the scheduled lectures were never abandoned.

講義纂輯，得書若干，名曰《易楔》。而晨昏餘晷，切磋問難，隨時筆錄者，又積稿盈尺。同人艱於傳寫，乃謀刊印。釐為四卷，名曰《筆談》，蓋紀實焉。己未庚申，由粵而滬。同志之友，聞聲畢集。風雨一廬，不廢討論。以續前稿，又得四卷，另為《二集》。借閱傳鈔，恐多遺失。適前印之書，久已告罄。同人請合兩《集》與《易楔》、《易數偶得》、《讀易雜記》諸稿，均以聚珍板印行。始於壬戌八月，至十月抄，《筆談》八卷工竣。爰紀顛末，並述旨如左。

The collected notes were compiled into several volumes, and the book was named "Yi Xie." In the remaining time of the day and night, they discussed and questioned each other, and the notes taken down at any time piled up to a height of about a foot. The colleagues found it inconvenient to copy and circulate the notes, so they discussed printing them, dividing them into four volumes and naming the collection "Bitan," meaning to record the actual events. In the years Jiwei and Gengshen, I moved from Guangdong to Shanghai, and friends with similar aspirations heard the news and gathered together, living in the same house even through storms and continuous discussions. Continuing from the previous drafts, they wrote another four volumes, compiling them as the "Second Collection." These notes, when lent out for copying, were feared to be lost. Fortunately, the earlier printed books had already been sold out, so the colleagues requested that the two collections, along with the drafts of "Yi Xie," "Yi Shu Ou De," and "Du Yi Za Ji," be printed together using the Ju Zhen movable type. This project started in the eighth month of Renxu year and was completed by the end of the tenth month, when all eight volumes of "Bitan" were printed. Then, the entire process was recorded, and the purpose of this book was explained as follows.

一、承學之士，不廢筆札，談論所及，擇要綴錄，聊以備忘。除《初集》第一卷，於臨印時略有增減，以明源流外，餘悉隨時編訂，並無先後次序。二、講《易》與詁經不同。詁經當有家法，有體例，義不容雜。而講《易》則以闡明卦爻象數之原理原則，但以經文為之證明。故凡與象數有涉，足與《易》道相發明者，博採旁搜，不限時地，更無所謂門戶派別也。

First, those who study should not neglect taking notes. Whenever they discuss something, they should select the key points and record them, to prevent forgetting. Except for the first volume of the first collection, which was slightly revised just before printing to explain the academic lineage, all other entries were compiled as they went along, without any particular order. Second, explaining the Book of Changes differs from interpreting classical texts. Interpreting classical texts requires discussing 'family methods' and following a fixed format, with interpretations not mixed together. In contrast, explaining the Book of Changes focuses mainly on clarifying the principles and rules of the hexagram and line symbols and numbers. Therefore, any materials related to the symbolic and numerical aspects that can elucidate the principles of the Book of Changes are collected broadly and extensively, without restriction of time, place, or school of thought.

三、《易》本法象於天地。乾易坤簡，易知易能，雖見仁見智，各隨學識之深淺而異，要無不可知之理。自象義不明，學者無所適從，幾視《易》為絕學，而不敢問津。致《易》簡之理，日即湮晦。本編有鑑於斯，立說皆取淺顯明白，務期盡人能解，不敢以艱深文淺陋也。

Third, the Book of Changes originally established its images by following the principles of heaven and earth. The principle of heaven is straightforward and easy to understand, and the principle of earth is simple and effective, making them easy to comprehend and practice. Although readers may have different interpretations based on their varying levels of knowledge, there is no principle that is unknowable. Since the meanings of the hexagrams have become obscure and difficult to explain, those who study the Book of Changes have been at a loss, almost treating it as a lost discipline and avoiding it altogether. As a result, the simple and straightforward principle of "easy and simple" has gradually become obscured and forgotten. In view of this, this book adopts an explanation that is clear and easy to understand, striving to ensure that everyone can comprehend it. I dare not use obscure language to conceal the simplicity of its content.

四、孔子贊《易》，身逢亂世，行危言遜。有因時忌不能顯言者，不得不以微言大義，隱寓於象數之中，與春秋同一例也。後人不察，悉以文字求之，孔子憂天憫人之苦心湮沒盡矣。歷代學者，如邵康節，如劉青田、黃姚江，均抱此隱痛而未敢昌言者也。鼎革以後，世雖亂而言可無諱。發歷聖之心傳，彌前賢之遺憾，維世道而存絕學，不可謂非千載一時之良機。剝極必復，時乎不再，幸我同人勿自暴棄以負天心也。

Fourth, when Confucius wrote the commentary on the Book of Changes, he was living in a time of chaos, acting with integrity and speaking with humility. Some things he could not openly express due to the prevailing taboos, so he secretly conveyed profound meanings through the images and numbers. This is similar to the way he wrote the Spring and Autumn Annals. Later scholars failed to understand this, and instead sought meaning only from the text, thus completely missing Confucius' heartfelt concern for the world. Scholars throughout history, such as Shao Yong (Kangjie) of the Song Dynasty, Liu Ji (Qingtian) and Huang Zongxi (Yaohang) of the Ming Dynasty, all carried this hidden sorrow but dared not express it openly. After the change of dynasties, although the world remained chaotic, speech was no longer restricted. Now is a rare opportunity to uncover the true teachings of the sages, to make up for the shortcomings of previous scholars, to maintain the world's order and preserve the lost learning. It cannot be said that this is an opportunity that comes once in a thousand years. The hexagram of "Breaking Up" reaches its extreme, and inevitably turns into the hexagram of "Reversion." Once the opportunity is gone, it will never return. We hope our fellow scholars will not give up on themselves and辜负 the will of heaven.

五、卦因數衍，數緣象起，象由心生。《易》準天地，廣大悉備。雖人事遞演，世變日繁，要不能出乎此象數之外。故洲殊種別，文字語言，萬有不齊，維數足以齊之。宗教俗尚，各有不同，惟數足以同之。兩千年來，數學失傳。宋後言《易》者，往往以邵子先天數為《易》數。數理繁嘖，固非短扎所能盡。然於舊說之顯然挑牴牾者，不能不援據象數以為商榷，非敢故翻成案也。

Fifth, hexagrams are derived from numbers, which are based on images, and images arise from the mind. The Book of Changes takes heaven and earth as its standard, being vast and comprehensive, encompassing everything. Even though human affairs keep changing and the world becomes increasingly complex, they ultimately cannot go beyond this system of images and numbers. Therefore, despite the differences among human races across continents and the vast variations in writing and languages, only "numbers" can bring them together. Likewise, although various religions and customs differ from each other, only "numbers" can unify them. The study of divination numbers has been lost for two thousand years. Since the Song dynasty, those who study the Book of Changes often take Shao Yong's "Earlier Heaven Numbers" as the numbers of the Book of Changes. The numerical reasoning is complex and cannot be fully explained in a short note. However, for clearly contradictory points in the old interpretations, it is necessary to refer to the theory of images and numbers for discussion, not intentionally overturning previous established views.

六、占筮固《易》之一端，而聖人修《易》以明道，實非盡為占筮。孔子贊《易》，紹述文周，以人合天，兢兢寡過，豈導人於趨吉避凶哉！朱子以占筮為《易》之本義，未免偏見。而《大衍》揲蓍之法，自唐以後，於掛一再扐兩端，立說互歧。往諸數理，並多遺憾。未敢盲從，以誤後人。

Sixth, although divination is indeed one aspect of the Book of Changes, the sages compiled the Book of Changes to elucidate the great principles, not solely for divination. Confucius wrote the Commentary on the Changes, continuing the tradition of King Wen and the Duke of Zhou, teaching people to harmonize human ways with the ways of Heaven, being cautious and striving to commit few errors. How could this be considered guiding people to seek good fortune and avoid misfortune? Zhu Xi regarded divination as the fundamental meaning of the Book of Changes, which seems to be a prejudice. As for the method of divining by counting the yarrow stalks described in the Great Treatise, since the Tang dynasty, there have been differing interpretations regarding the steps of "taking one" and "gathering two." Investigating the numerical reasoning behind these steps, many explanations are not convincing. I dare not blindly follow them, for fear of misleading future generations.

七、至誠之道，雖可前知，惟道本一貫，學無躐等。必正心修身，能盡人之道以合天，斯天人契合，感而遂通，百世可知。初無二理。若一知半解，妄談禍福，自欺欺人，實學《易》之大戒。兢兢自箴者，竊願以此勉人。

The seventh point is that the Doctrine of the Mean says that the way of utmost sincerity can foresee the future. However, the principle is fundamentally consistent, and one cannot advance in learning by skipping stages. One must first correct the mind and cultivate oneself, fully fulfilling human morality to harmonize with the way of Heaven. In this way, Heaven and humanity are in harmony, and a single feeling can connect with the heavens. Thus, even matters of a hundred generations later can be inferred. There is no distinction between two different principles here. If one only grasps partial knowledge and then rashly discusses good fortune, misfortune, blessings, and calamities, this is self-deception and a serious fault in studying the Book of Changes. This is something I constantly remind myself of, and I wish to use it to encourage my fellow students.

八、盡性至命，乃易學之極功。孔子之聖，猶韋編三絕，但云寡過，罕言性命。後生末學，更宜踐履篤實，下學上達。同學講習，竊本斯旨。《初集》刊佈，朋自遠來，往往以只言象數，不談身心性命相責。但愚尚以象數之未能盡明為憾。果象數通解，則身心性命之理，胥在其中，更無待言說為也。

The eighth point is that to exhaust one's mind and nature, and to reach the Mandate of Heaven directly, is the highest achievement in the study of the Book of Changes. Even a sage like Confucius, when studying the Book of Changes, broke the leather thongs of the bamboo slips three times, and he only said he sought to reduce his mistakes, rarely discussing nature and destiny. Later scholars and learners should even more diligently practice, starting from the immediate and practical, and then proceed to the higher. In our discussions, I have privately followed this principle. After the first collection was published, friends from afar often criticized me for only discussing the images and numbers, and not talking about the body, mind, nature, and destiny. But I still regret that the images and numbers were not thoroughly explained. If the images and numbers could indeed be fully understood, then the principles of body, mind, nature, and destiny would already be contained within them, and there would be no need to discuss them separately.

九、形而下者謂之器，形而上者謂之道。凡有形可指者皆器。道本於心，未可以言盡焉。故八卦因重，羲農法天以垂象；兩編《十翼》，周孔立言以明道。然未可遽執卦象經傳以為道也。譬諸升高必以梯，而梯非高。求飽必以飯，而飯非飽。宋後講《易》，開口言性理，言道統，是猶指梯而稱高，看飯而說飽也。今之談道者，無宋人之學，而立說更高出宋人。自誤誤人，更不待言。願學者共明斯旨，各求實學，返諸身心。勿好高鶩遠，循前車之覆轍焉。

Chapter Nine, the Great Treatise says that what has form is called "qi," and what is formless is called "Dao." Anything that can be pointed to with form is considered "qi"; "Dao" originates from the human mind and cannot be fully expressed in words. Therefore, the eight trigrams combined to form the sixty-four hexagrams, which was the method used by Fuxi and Shen Nong to follow the heavenly Dao and reveal the hexagrams. The two sets of commentaries, the Ten Wings, were composed by the Duke of Zhou and Confucius to explain the great Dao. However, one must not take the hexagrams and their commentaries as the Dao itself. For example, climbing a high place must use a ladder, but the ladder itself is not the height. To satisfy hunger one must eat, but food is not hunger itself. After the Song dynasty, those who discussed the Book of Changes often began by talking about nature and principle, and the transmission of Dao, which is like pointing at the ladder and claiming to have reached the height, or looking at the food and claiming to be full. Today, those who talk about Dao lack the scholarly depth of the Song Confucians, yet their theories are even more lofty and distant. This is self-deception and misleading others, and even more so, it is unnecessary. I hope those who study the Book of Changes will all understand this principle, pursue solid learning, and verify it through their own body and mind, without being overly ambitious, and avoid repeating the mistakes of previous scholars.

十、潔淨精微之學，非潛修靜養，未能深造。勞人草草，敢言心得？惟匯積年涉獵所得，聊供同學參考之便。深望海內鴻碩，時加匡正。幸得學與年進，尚擬續，以供採擇。十一、世道陵夷，聖學中絕。人慾橫流，罔知紀極。謹願之士，苦身心之無所寄託，蒿目時艱，恆懷消極。或附托西教，或皈向佛門。而仙靈神鬼，導引修養，及飛鸞顯化之壇宇，遂遍於域中。影附風從，是丹非素。不知我國固有之學，貫澈天人，足以安身立命。保世滋大，概群藉而羅萬有者，悉在此一畫開天，人文肇始之《易經》。存人道，挽世運，千鈞一髮，絕續在茲。弘道救世，責無旁貸。惟我同人，自奮勉焉。

Tenth, the "Book of Rites" refers to the study of the "I Ching" as "pure, refined, and subtle." Without earnest study and quiet cultivation, one cannot deeply understand it. I have been busy and rushed, hastily writing this book; how dare I claim to have any insights? It is merely a collection of what I have learned over the years, offered here for my fellow scholars to refer to. I sincerely hope that learned scholars throughout the land will correct me at any time. If knowledge can continue to grow with age, I intend to write more continuously, for others to choose from. Eleventh, the world is gradually declining, the learning of the sages has been interrupted, desires run rampant without end. Those who are cautious, honest, and sincere suffer from having nowhere to place their minds and bodies. Observing the difficult circumstances of the times, they often feel pessimistic. Some turn to Western religions, others to Buddhism; while places that talk about immortals, ghosts, spirits, qigong, and divination, such as乩 and坛, are widespread throughout the country. People follow the crowd blindly, confusing red with white, unable to distinguish right from wrong. They do not realize that our native learning originally connects heaven and humanity, sufficient to establish one's life and maintain stability. The ability to preserve the world's order, promote its development, encompass all schools of thought, and include everything, lies entirely within this "I Ching," which began with the creation of the world and initiated human culture. Preserving human ways and reversing the trend of the times is now at a critical moment, and the continuation or interruption depends on this. Promoting the great path and saving the people is our responsibility, and we hope that all of us will strive hard.

上古之世，無所謂《易》也。但後世之《易》，實本於伏羲，故《周官》掌太卜者有“三《易》”之稱。因周以《易》名，遂追諡《連山》、《歸藏》皆謂之《易》。餘所謂上古之《易》者，亦援斯義而追稱之耳。

In ancient times, there was no name called "The Book of Changes" ("Yi"). However, the later "Yi" indeed originated from Fuxi. Therefore, the "Zhou Li" (Record of Rites) mentions that the Grand卜 (diviner) was in charge of "three Yis." Since the Zhou dynasty called their own version "Yi," they added the title, and also referred to "Lianshan" and "Guicang" as "Yi" as well. What I refer to as "the ancient Yi" here is also using this meaning to give them the same name.

溯自伏羲一畫開天，其時雖文字未興，而結繩為治，已有等秩倫紀之可觀。《繫傳》稱仰則觀象於天，俯則觀法於地，觀鳥獸之文與地之宜，近取諸身，遠取諸物，於是始作八卦，以通神明之德，以類萬物之情。其條理井然，而觀法於地暨觀鳥獸之文與地之宜，已能將地之所有，分析觀察，頗如近世科學家，區地文地質學為二類。

Tracing back to the time when Fuxi drew the first diagram to create the heavens and the earth, although writing had not yet been invented, he used the method of tying knots to govern the world, and there were already observable levels of hierarchy and human relationships. The Great Treatise says that he looked up to observe the forms of heaven, looked down to observe the principles of earth, observed the patterns of birds and beasts and the suitability of the land, taking close examples from himself and distant ones from all things in the world. Thus he began to draw the Eight Trigrams, to communicate with the virtue of the divine and to compare and classify the forms of all things. This was a well-ordered system; among these, "observing the principles of earth" and "observing the patterns of birds and beasts and the suitability of the land" already showed a clear distinction in observing all things on the earth's surface, very much like modern scientists who divide "geography" and "geology" into two separate disciplines.

此豈歐洲人所謂上古時代野蠻酋長之可比擬哉！以佃以漁，雖未脫游牧之風，而政治亦已斐然可觀矣。況八卦成列，有形，有象，有聲，實已備具文字之作用。因而重之為六十四卦。益之以變化，固已肆應而不窮矣。此伏羲之《易》，所以為我中國文化之初祖也。

This is not comparable to the primitive tribes of Europe where chieftains ruled in the ancient times. At that time, people were still hunting and fishing, though not yet fully separated from a nomadic lifestyle, but their politics were already quite developed. Moreover, the eight trigrams were arranged in order, having form, imagery, and sound, and in fact already possessed the function of writing. Furthermore, by combining the eight trigrams two by two to form the sixty-four trigrams, and adding the changes of the lines, it was already sufficient to deal with infinite changes. This is why the Book of Changes, created by Fuxi, became the original source of our Chinese culture.

伏羲氏沒，神農氏作。斫木為耜，揉木為耒。耒耨之利，以教天下。日中為市，致天下之民，聚天下之貨，交易而退，各得其所，是已由游牧時代而進於農商。且規模宏遠，政教並行。又嘗百草以御疾災，民無夭折，創制顯庸，澤及萬世。然其時文字未興，所賴以為政治之具者，實維伏羲所遺傳之卦象。度神農氏必有所增益而變通之，是名《連山》。相傳以重艮為首，經卦皆八，重卦皆六十四者也。故神農為炎帝，亦號列山氏。

After Fuxi died, Shen Nong came to power. He carved wooden plows and bent wood to make耒, teaching the people the convenience of farming tools; he also set up markets at noon to gather people from all over, collect goods from everywhere, and exchange them, so that everyone could obtain what they needed. This marked the transition from a nomadic era to an age of agriculture and commerce. Moreover, his endeavors were grand and far-reaching, with both governance and education carried out simultaneously. He also tasted hundreds of herbs to prevent and treat diseases, ensuring the people did not die prematurely, and he invented tools and demonstrated their uses, bringing benefits to generations. However, at that time, writing had not yet emerged, and the only means of governing the world was the hexagrams passed down by Fuxi. It is said that Shen Nong must have made some additions and modifications to the hexagrams, which is called the "Lianshan" (Continued Mountain). It is traditionally believed that the "Lianshan" begins with the hexagram of Gen (Mountain) repeated, while the single trigrams remain eight and the compound hexagrams remain sixty-four. Therefore, Shen Nong is also called the "Lieshan" (Mountain Ruler).

神農氏沒，黃帝堯舜氏作。通其變使民不倦，神而化之使民宜之。《易》窮則變，變則通，通則久。蓋至是文明日進，制器尚象，人事日繁。而舊有之八卦，不足以應用。於是廣卦象為六畫，而文字以生。益以天干地支，而陰陽五行之用愈精。

After Shen Nong died, the Yellow Emperor and Yao and Shun took turns to rise to prominence. They understood the changes of things and made the people not feel tired; they subtly nurtured the people so that each could find what was suitable for them. The Great Treatise says: The Way of the Book of Changes reaches an end and then changes, only through change can it be unblocked, and only through unblocking can it last long. At this time, civilization gradually advanced, and the making of objects was based on the trigrams. Human affairs became more complex, and the original eight trigrams were no longer sufficient for use, so the trigrams were expanded into hexagrams with six lines, and writing was then created. In addition, the heavenly stems and earthly branches were added, making the application of yin and yang and the Five Phases even more precise.

吹律定聲，民氣以和。而禮樂以興，本黃鐘以定度量權衡。治曆明時，定璇璣玉衡以齊七政。絕地天通，百官以治，萬民以察。而《易》之為用，益無乎不備。故黃帝之《易》曰《歸藏》，以坤乾為首者也。堯舜繼黃帝之後，於變時雍，垂衣裳而天下平。今讀《繫辭下傳》之二章，上古進化之歷史，與三《易》之源流，可概見矣。此上古之《易》也。

Blowing the tuning pipes to determine pitch, the people's qi thus harmonized, and rites and music emerged; also using the Huangzhong pitch standard to set the measures of length, capacity, and weight. Establishing the calendar to clarify the seasons, and setting up the Xuanji Yuheng to correct the movements of the sun, moon, and five stars. Ending the chaotic situation where everyone could communicate with ghosts and spirits, with officials each having their own duties and governance being well maintained, the people could be properly regulated. The function of the Book of Changes reaches this point, becoming fully comprehensive. Therefore, the Yellow Emperor's Book of Changes was called the Guicang, with the Kun and Qian trigrams as the first ones. Yao and Shun came after the Yellow Emperor, and the world became harmonious and peaceful, requiring only to hold robes and rest hands, and the whole country would be tranquil. Today, reading the second chapter of the Xici Xia Zhuan, the historical development of the ancient times and the origins of the three Books of Changes can be roughly understood. This is the ancient Book of Changes.

夏易《連山》，蓋繼述神農氏者也。商易《歸藏》，蓋繼述黃帝氏者也。周曰《周易》，或曰“祖述堯舜”。孔子曰：“《易》之興也，其於中古乎？作《易》者，其有憂患乎？”雖指《周易》，以文王與紂之事當之。然帝降而王，德不如古。神禹受命，開家天下之局。湯武革命，《易》揖讓而征誅，均不能無慚德焉。故三代之《易》，皆可謂之中古，所謂“於稽其類其衰世之意”邪？上視羲皇，已不無今昔之感矣。

In the Xia dynasty, the Book of Changes was called the "Lianshan" (Continuous Mountains), probably continuing the tradition of the Yellow Emperor; in the Shang dynasty, it was called the "Guicang" (Return to the Treasury), probably continuing the tradition of the Yellow Emperor; and in the Zhou dynasty, it was called the "Zhouyi" (Book of Changes), and some say it "follows the ways of Yao and Shun." Confucius said, "The origin of the Book of Changes probably dates back to the middle ancient times. The person who composed the Book of Changes must have been troubled by worries." Although these words refer specifically to the Zhouyi, they are used to confirm the idea by referring to the events between King Wen and King Zhou of Shang. However, since the imperial way has declined from the way of the emperors to the way of the kings, virtue is no longer as it was in the ancient times. Da Yu received the mandate, establishing the system of a hereditary dynasty; King Tang of Shang and King Wu of Zhou used military force to overthrow the previous dynasties, changing the system of abdication into one of conquest, and none of these actions can be said to be without regret. Therefore, the Book of Changes of the Xia, Shang, and Zhou dynasties can all be called the Book of Changes of the middle ancient times, which is what the Great Treatise says, "Examining these words, they probably express the meaning of a declining age." Compared to the time of Fuxi, there is already a sense of the past and present.

制度文物，皆出於《易》。故曰“觀其會通以行其典禮”。《易》在三代，不啻為政治之書。夏宗《連山》，其禮樂政刑胥以《連山》為則。殷宗《歸藏》，其禮樂政刑胥以《歸藏》為則。故紀曆有人統地統天統之殊。而尚忠尚質尚文，亦各有所專重。蓋變通損益以蘄合于時宜，而成一代之制。必統系分明，而後綱舉目張，有條不紊。今夏殷之制不可悉睹，而《周禮》一書，雖經竄改，而周家之典章文物，猶可得其梗概，足與《周易》相印證。自秦漢以降，目《易》為卜筮之書，政失其綱也久矣。

In every dynasty, the system of institutions and objects were derived from the Book of Changes. Therefore, the Great Treatise says, "Observe its converging and permeating aspects, and use them to promote the rites and regulations." The Book of Changes in the Xia, Shang, and Zhou dynasties was essentially a political text. In the Xia dynasty, they revered the "Lianshan" (Continuous Mountains), and all rites, music, punishment, and government were based on the Lianshan. In the Shang dynasty, they revered the "Guicang" (Return to Storage), and all rites, music, punishment, and government were based on the Guicang. Hence, the three dynasties had different systems of calendars, namely "ren tong" (human system), "di tong" (earth system), and "tian tong" (heaven system). Their emphasis on loyalty, sincerity, and culture also had different focuses. These were all adaptations according to the times, with additions and subtractions, in order to meet the needs of the time, thus forming the institutions of each dynasty. It was necessary to have clear distinctions, so that the main points could be grasped and the details could be arranged in an orderly manner. Now, the systems of the Xia and Shang dynasties can no longer be fully seen. However, the book of Zhou Li, although altered by later generations, still allows us to see the general outlines of the Zhou dynasty's institutions, which can be verified with the Book of Changes. Since the Qin and Han dynasties, the Book of Changes has been regarded as a book for divination, and the political system has lost its framework for a long time.

我國學術，約可分為三派：曰儒，曰道，曰墨。其餘諸子百家，名類雖多，要無不可以此三派歸納之。道家宗老氏，而實導源於黃帝，故相傳曰“黃老”。墨家出於禹，而實濫觴於神農。《孟子》有為神農之言者許行，主並耕之說，亦墨之別派也。儒家集大成於孔子，《論語》曰：“文王既沒，文不在茲乎？”則孔子固自承為繼續文王者也。故儒家之學出於《周易》，道家之學出於《歸藏》，墨家之學出於《連山》，各有所本。

The academic traditions of our country can generally be divided into three schools: Confucianism, Taoism, and Mohism. The other hundred schools of thought, although they have many names, can ultimately be included within these three. Taoism reveres Laozi as its master, but its origin actually dates back to the Yellow Emperor, so it has always been collectively called "Huang-Lao" (Yellow Emperor and Laozi). Mohism advocates frugality and practical action; it is said to have originated from the Xia Yu, but in fact it began with Shen Nong. The Xu Xing mentioned in "Mencius · Teng Wengong" who is said to have spoken the words of Shen Nong, advocated that the ruler should also work with the people in farming to support himself, which is an offshoot of Mohism. Confucianism reached its culmination with Confucius. The "Analects" records Confucius saying, "King Wen has already passed away, is not the rites and music culture now in my possession?" This shows that Confucius himself regarded himself as the one continuing King Wen's tradition. Therefore, the study of Confucianism originates from the "Zhou Yi" (Book of Changes), the study of Taoism originates from the "Guicang" (Book of Changes attributed to the Yellow Emperor), and the study of Mohism originates from the "Lianshan" (Book of Changes attributed to Shen Nong). Each has its own origin and is not born out of nowhere.

自漢而後，雖罷斥百家，獨崇儒道，而道與墨之學，亦實有不可磨滅之精神。歷代之治，舍其名而用其實者，不可枚舉。至於今日，儒術亦掃地盡矣。而老氏墨氏之學，則因與歐西之哲學，及其他科學之相契合者頗多，崇尚新學之士，漸有取而研究之者。禮失求野，循末反本，則吾文明初祖之羲《易》，或尚有大明之一日乎？

After the Han dynasty, although the government suppressed all schools of thought except Confucianism, the spirit of Daoism and Mohism could not be entirely erased. Throughout history, many rulers implemented policies that were in line with the actual ideas of these schools, though they did not openly acknowledge them. Today, Confucianism has been completely discarded; however, the teachings of Laozi and Mozi have gradually attracted attention from those who favor new learning, because they share many similarities with European philosophy and other scientific disciplines. An old saying goes that when the rites and rituals are lost, one should seek them from the people. Following the current trends back to their origins, perhaps the Yi Jing, passed down by the ancient sage Fuxi, may once again shine brightly.

《易》者，明道之書也。五帝之治天下也以道，三王以德，五霸以功。世運自帝降而王，王降乎而霸，道之不明也久矣。孔子生當衰周，五霸之功已杳，浸浸乎由功而降而尚力。至惟力是尚，弱肉強食，人道或幾乎悉矣。故孔子贊《易》以存道，又以道之未可驟幾焉，乃取中爻以明功，陳九卦以崇德。循序而進，由功而德，其庶幾乎與道近矣。

The Book of Changes is a book that explains the great Dao. The Five Emperors governed the world by following the Dao, the Three Kings by virtue, and the Five Hegemons by their achievements. The way of the world has gradually declined from the imperial way to the royal way, then to the hegemonic way, and the great Dao has been obscure for a long time. Confucius was born in the era when the Zhou dynasty was declining, and even the achievements of the Five Hegemons had already become distant. The prevailing trend of the times gradually shifted from valuing achievements to emphasizing power; once power became the main concern, the weak were preyed upon by the strong, and humaneness was almost about to be extinguished. Therefore, Confucius wrote the Commentary on the Changes to preserve the great Dao. Since the great Dao cannot be attained suddenly, he selected several middle lines among the six lines of the hexagram to explain achievements, and explained nine hexagrams such as Guan and Qian to promote virtue. This allows people to proceed step by step, from achievements to virtue, thus approaching the Dao to a great extent.

孔子傳《易》於商瞿。商瞿字子木，其行事不見於《論語》，蓋孔子晚年之弟子也。商瞿授魯橋庇子庸，子庸授江東對馯臂子弓，子弓授燕周丑子家，子家授東武孫虞子乘，子乘授齊田何子莊。凡六傳，而周滅於秦。

Confucius passed on the Book of Changes to Shang Qu, whose given name was Zi Mu. His deeds are not recorded in the Analects, and he was probably a student Confucius took in during his later years. Shang Qu passed it on to Qiao Bi Zi Yong of Lu, who passed it on to Han Bi Zi Gong of the Jiangdong region, who passed it on to Zhou Chou Zi Jia of Yan, who passed it on to Sun Yu Zi Cheng of Dongwu, who passed it on to Tian He Zi Zhang of Qi. In total, it was passed down through six generations, and by then the Zhou dynasty had been destroyed by the state of Qin.

秦焚書，而《易》以卜筮獨免。漢興，田何以齊之公族徙杜陵，號杜田生。授東武王同子中，及洛陽周王孫、丁寬，齊伏生。王同子中授淄川楊何，丁寬授同郡田碭王孫，王孫授沛施讎，蘭陵孟喜，琅邪梁丘賀，是為三家之《易》，皆立於學官置博士。

Qin Shihuang burned books, but the Book of Changes was exempted from destruction because it was regarded as a book for divination. During the Han dynasty, Tian He, who was a member of the royal family of the state of Qi, moved to Du Ling and was called "Du Tian Sheng." He passed it on to Wang Tongzi of Dongwu, Zhou Wangsun of Luoyang, Ding Kuan, and Fu Sheng of Qi. Wang Tongzi passed it on to Yang He of Zichuan, Ding Kuan passed it on to Tian Wangsun of the same county in Dang, and Tian Wangsun passed it on to Shi Chou of Peixian, Meng Xi of Lanling, and Liang Qiu He of Langya. These three were the main schools of the Book of Changes in the Han dynasty, all of which were established as official schools and set up doctoral positions.

施讎授張禹，及琅邪魯伯。禹授淮陽彭宣，沛戴子崇平。魯伯授琅邪邴丹、伏曼容。孟喜授同郡白光少子，沛瞿牧，及焦延壽。延壽授京房。梁丘賀傳子臨，臨授五鹿充宗。充宗授平陵士孫、張仲方，鄧彭祖子夏，齊衡咸長賓。

Shi Chou passed on his teachings to Zhang Yu and Lu Bo from Langya; Zhang Yu passed on his teachings to Peng Xuan from Huaiyang and Dai Chong from Peixian (whose name was Zi Ping); Lu Bo passed on his teachings to Bing Dan and Fu Manrong from Langya. Meng Xi passed on his teachings to Bai Guang (whose name was Shaoyi) from the same prefecture, Qu Mu from Peixian, and Jiao Yanshou; Jiao Yanshou passed on his teachings to Jing Fang. Liang Qiu He passed on his teachings to his son Liang Qiu Lin, who passed on his teachings to Wulu Chongzong; Wulu Chongzong passed on his teachings to Shi Sun Zhang (whose name was Zhongfang) from Pingling, Deng Pengzu (whose name was Zixia), and Heng Xian (whose name was Changbin) from Qi State.

東萊費直，治《易》長於卜筮，無章句，徒以《彖》、《象》、《繫辭》、《文言》，解釋上、下《經》。傳琅邪王璜子中。同時沛高相治《易》，與費略同，亦無章句，說陰陽災異，自言出於丁將軍。授子康，及蘭陵毋將永。高氏費氏之學，皆未立於學官。

Eastern Lake's Fei Zhi devoted himself to studying the Book of Changes, excelling in divination. He did not engage in the method of explaining each sentence of the text, known as chapter-by-chapter commentary. Instead, he used the Commentary on the Judgment, the Image Commentary, the Great Treatise, and the Discourse on the Literary Style to explain the upper and lower parts of the classic text. He passed his teachings to Wang Huang of Langya (whose name was Zi Zhong). At the same time, Gao Xiang from Pei County also studied the Book of Changes, following a similar approach. He did not engage in chapter-by-chapter commentary, but focused on yin and yang, omens, and portents, claiming his learning came from "General Ding" Ding Kuan. He passed his teachings to his son Gao Kang and Wu Jiang Yong of Lanling. The schools of Gao and Fei were never established in the official academies.

漢代易學，以施、孟、梁丘三家為盛。京氏專言災異，高氏亦與京略同。至東漢傳施學者，有劉昆，及子軼。傳孟學者有握丹鮭，陽鴻任安。傳梁丘學者，有范升、楊政、張興、及子魴，皆不甚顯。至漢季獨費《易》盛行，若馬融、鄭玄、荀爽、陸績、劉表、宋衷諸人，皆習費氏古文《易》。孟學獨一虞翻，施梁之學無聞矣。

The study of the Book of Changes during the Han dynasty was most flourishing among three schools: Shi Chou, Meng Xi, and Liang Qiu He. The Jing Fang school specialized in discussing calamities and anomalies, while the Gao Xiang school was similar to Jing Fang's approach. By the Eastern Han dynasty, those who inherited Shi Chou's teachings included Liu Kun and his son Liu Yi; those who inherited Meng Xi's teachings included Wu Dan, Hua Yang Hong, and Ren An; and those who inherited Liang Qiu He's teachings included Fan Sheng, Yang Zheng, Zhang Xing, and Zhang Xing's son Zhang Fang. None of these schools became very prominent. By the end of the Han dynasty, only the school of Fei Zhi's version of the Book of Changes remained influential. People such as Ma Rong, Zheng Xuan, Xun Shuang, Lu Ji, Liu Biao, and Song Zhong all studied Fei Zhi's ancient text version of the Book of Changes. The Meng Xi school was represented only by Yu Fan, while the teachings of Shi Chou and Liang Qiu He schools had no further successors.

魏晉以後，王弼之《易》，盛行江左。弼為劉表之甥，表固治費《易》者。弼之說《易》，不盡宗費，屏棄象數，專以玄理演繹，自謂得意忘象。又分《繫》、《彖》、《象》諸《傳》於經文之下。學者以其清雋新穎，且簡便而易學也，靡然宗之。由是施讎、梁丘諸家之《易》盡亡。費氏之古本，亦為所淆亂，而盡失其本來面目矣。

After the Wei and Jin dynasties, the commentary on the Book of Changes by Wang Bi became very popular in the Jiangdong region. Wang Bi was the nephew of Liu Biao, who had originally studied the Book of Changes according to the Fei school. However, Wang Bi's interpretation of the Book of Changes did not fully follow the Fei school's methods. He rejected the use of images and numbers, and instead used metaphysical reasoning to explain the text. He claimed that "one should grasp the meaning and forget the image." Furthermore, he broke up the commentaries from the Great Treatise, the Commentary on the Judgment, and the Image Commentary, and attached them separately below the main text. Scholars found his explanations fresh, elegant, and easy to learn, so they all followed him as their main authority. From then on, the schools of Shi Chou and Liangqiu completely disappeared, and the ancient version of the Fei school was also disrupted and lost its original form.

然弼年二十有四即死，《繫辭》、《說卦》三篇，均不及注，後人以韓康伯注續之。永嘉之亂，中原板蕩，經籍散失。李唐統一，掇拾燼餘，雖六經本文幸而未闕，而兩漢以來各家之師說傳注，已十亡其七八矣。孔穎達疏《易》，復崇王而黜鄭。太學肄業，一以王注為本，古《易》遂不可復見。

However, Wang Bi died at the age of twenty-four and did not have time to comment on works such as the Great Treatise and the Discourse on the Trigrams. Later scholars therefore used Han Kangbo's commentary to continue the tradition. During the Yongjia chaos of the Western Jin dynasty, the Central Plains were in turmoil and a large number of classic texts were lost. After the Liang dynasty unified the country, they collected the remnants, and although the main texts of the Six Classics were fortunately not damaged, the teachings and commentaries of various schools since the Western Han dynasty had already been lost to a large extent. Kong Yingda, when commenting on the Book of Changes, praised Wang Bi and rejected Zheng Xuan. The Imperial Academy's teachings all took Wang Bi's commentary as the foundation, and the ancient Book of Changes thus became unseen again.

賴李鼎祚《集註》，掇拾殘闕，蒐集漢注至三十餘家。窺管一斑，全豹之形，似尚可約略而得。後之言漢學者，莫不循是蹊徑，以為登峰造極之基。至滿清中葉，王（念孫）、惠（棟）、張（惠言）、焦（循）諸家，皆精研漢學。單辭只義，不惜殫畢生之全力以赴之。鄭氏虞氏之《易》，始差堪董理。而施讎、梁丘之學說，終不獲復見於世也。惜哉！

Fortunately, the Tang dynasty scholar Li Dingzuo compiled the Collected Explanations of the Zhou Changes, restoring the fragmented texts and gathering over thirty Han dynasty commentaries. Though only glimpsing through a bamboo tube, the general appearance of the whole seems still somewhat discernible. Later scholars of the Han learning tradition all followed this path, treating it as the ultimate foundation. By the mid-Qing dynasty, scholars such as Wang Niansun, Hui Dong, Zhang Huiyan, and Jiao Xun deeply studied Han learning, devoting their entire lives to pursuing a single word or a single meaning, thus finally managing to properly organize the works of Zheng Xuan and Yu Fan. However, the doctrines of Shi Chou and Liangqiu were never revived, which is truly a pity!

宋人講《易》，自司馬溫公以至程子，大抵皆不出王弼範圍。周子《通書》，發明太極圖，為理學之宗，與易學尚無其關涉也。自邵康節創為先天之說，取《說卦》“天地定位”一章，安排八卦，謂之先天卦。以“帝出乎震”之方位為後天卦。

In the Song dynasty, when people discussed the Book of Changes, from Sima Guang (Wen Gong) to Cheng Yi, they mostly remained within the framework of Wang Bi. Zhou Dunyi's Treatise on the Supreme Ultimate explained the diagram of the Supreme Ultimate, becoming the leader of Neo-Confucianism, but it had little connection with the study of the Book of Changes itself. It was not until Shao Yong (Kangjie) established the theory of "Earlier Heaven," using the passage "Heaven and Earth are positioned, mountains and marshes communicate" from the Sayings on the Trigrams to arrange the Eight Trigrams, which he called "Earlier Heaven Trigrams"; and also arranged the Eight Trigrams according to the directions mentioned in the passage "The Emperor arises from the震 (Thunder)" from the Sayings on the Trigrams, which he called "Later Heaven Trigrams."

又以乾一兌二離三震四巽五坎六艮七坤八，為先天八卦之數。更反劉牧九圖十書之說，以五十五數者為河圖，四十五數者為洛書，為八卦之所自出。於是太極兩儀，四象八卦，而十六，而三十二，而六十四。立說與漢人完全不同，不啻在易學中另闢一新世界。

He also established the numerical sequence for the Eight Trigrams as Qian one, Dui two, Li three, Zhen four, Xun five, Kan six, Gen seven, and Kun eight, as the sequence of the Earlier Heaven Trigrams. He further overturned Liu Mu's previous view that nine numbers represented the Yellow River Chart and ten numbers represented the Luo Writing. Instead, he designated fifty-five numbers as the Yellow River Chart and forty-five numbers as the Luo Writing, arguing that the Eight Trigrams originated from these. Thus, from the Taiji came the two principles, from the two principles came the four images, from the four images came the Eight Trigrams, and then doubled to sixteen, thirty-two, and sixty-four. This theory differs completely from that of the Han dynasty scholars, and it is as if it has opened up a new world within the study of the Book of Changes.

然當其時，並未盛行。如溫公、程子，皆與邵為老友，且極推重其為人，稱為“內聖外王，孔孟沒後之一人”，而未嘗取其說以講《易》。其反對如歐陽文忠諸人，更無論矣。至朱子撰《周易本義》，取河圖、洛書與先天、大、小、方、圓各圖，弁諸卷首。又另著《易學啟蒙》以闡明之，而後邵子之先天學與《易經》相聯綴。

But at that time, this doctrine did not gain widespread popularity. Figures like Sima Guang and Cheng Yi were old friends of Shao Yong and highly esteemed his character, calling him "the first person after Confucius and Mencius to embody both inner sagehood and outer kingship," yet they did not use his theories to explain the Book of Changes. As for Ouyang Xiu and his opponents, they were even less inclined to do so. It was not until Zhu Xi compiled The Original Meaning of the Zhou Changes, placing the Yellow River Chart, the Luo Writing, as well as the large circle diagram, small circle diagram, and square diagram of the Earlier Heaven among the opening sections, and also wrote The Awakening of the Study of Changes to explain them, that Shao Yong's theory of the Earlier Heaven became connected with the Book of Changes.

歷宋元明清，皆立諸學官，定為不刊之程式。後之學者，幾疑此諸圖為《易經》所固有矣。雖漢學家抨擊非難，不遺餘力，而以其理數出自天然，推算又確有徵驗，終非討生活於故紙堆中者，空言所能排斥也。故宋之易學，能有所發揮，獨樹一幟與漢學相對峙者，自當首推邵氏。

Through the dynasties of Song, Yuan, Ming, and Qing, these diagrams were established in the academies and set as unchangeable patterns. Later scholars almost regarded them as inherent parts of the Yijing. Although Han scholars strongly criticized and refuted them, arguing that these diagrams originated from the Daoist master Chen Tuan rather than being part of the classic texts, they could not refute them because the principles and numbers within them came from nature and indeed proved accurate in calculations. Therefore, among the schools of Yijing study in the Song dynasty, those who could develop their own theories and stand out against the Han school naturally had to be Shao Yong.

朱子《本義》，頗能矯王弼以來空談玄理之弊，而注意於象數，故取用邵子之說頗多。顧未能會通全《易》，博採兩漢諸家之說，以明聖人立象之意。又泥於門戶之見，不敢暢所欲言，而以聖人以卜筮教人一言，為立說之本義。此何異以璇璣玉衡為定南北方向之用，不亦隘乎？

Zhu Xi's "The Original Meaning of the Zhou Changes" is quite capable of correcting the flaw of empty discussions on metaphysical principles since Wang Bi, and he pays attention to the symbolic numbers and principles, thus adopting many views from Shao Yong. Unfortunately, he failed to integrate the entire principles of the "Zhou Changes" and widely adopt the views from various schools of the Western and Eastern Han dynasties to clarify the intention of the sage in establishing the hexagrams. Moreover, he was rigid in his factional views and dared not speak freely, only taking the statement "the sage used divination to teach people" as the fundamental principle of his argument. This is similar to using the Xuanji Yuheng (a celestial instrument for observing the sky) only as a tool for determining the north-south direction, isn't it also too narrow?

兩宋《易》家之著錄者頗多，以當時鐫版業已發明，流傳較易。今《四庫》所存，及刊入《通志堂經解》，與《惜陰》、《聚珍》諸叢書者，尚有六十餘種。而納蘭氏又彙輯諸儒語錄別集，暨佚書之單辭剩義，為《大易萃言》八十卷，可謂極宋學之大觀已。

There were many recorded Neo-Confucian scholars of the Yi Jing during the Song dynasty, as movable type printing had already been invented, making the spread of books easier. Today, the "Siku Quanshu" includes many works, as well as those collected in the "Tongzhi Tang Jingjie", "Xi Yin Xuan Cunshu", "Ju Zhen Ban Cunshu", and other anthologies, totaling over sixty kinds. Nalan Xingde further compiled the sayings and writings of various Confucian scholars, as well as scattered fragments from lost texts, into an eighty-volume work called "Dai Yi Cuiyan", which can be considered a comprehensive collection of Song dynasty Yi studies.

元明兩代之言《易》學者，無甚發明。著錄者大抵盤旋於程朱腳下為多。元之熊與可、胡一桂、熊良輔、王申之、董真卿，明之黃道周、喬中和，皆其傑出者也。然皆有所依傍，不能成一家之言。黃道周之《易象正》、《三易洞璣》，雖以天象曆數闡明易理，而艱深奧衍，流傳不廣。

During the Yuan and Ming dynasties, scholars studying the Yi Jing did not produce many new ideas. Most of the works recorded were merely interpretations and supplements of those of Cheng Yi and Zhu Xi. Among them, Xiong Yuke, Hu Yigu, Xiong Liangfu, Wang Shenzhi, and Dong Zhenqing in the Yuan dynasty, and Huang Daozhou and Qiao Zhonghe in the Ming dynasty, were considered outstanding figures. However, each of them relied on the works of others and could not develop their own independent school of thought. Huang Daozhou's works, the "Yi Xiang Zheng" and "San Yi Dong Ji", although they used celestial phenomena and numerical calculations to explain the principles of the Yi Jing, were written in obscure and complex language, and thus did not spread widely, with few readers.

惟來知德氏崛起川中，以二十九年之功，成《來氏集註》一書，風行大江以南，三百年來未絕。雖其錯綜之說，頗貽人口實。然取象說理，淺顯明白，惟恐人之不易索解，恆罕譬曲喻以明之。視故作艱深以文其淺陋者，自勝一籌。初學者得此，尚為善本也。

Only Lai Zhide rose to prominence in Sichuan, spending twenty-nine years to compose the book "Lai's Commentary on the Book of Changes." It became widely circulated throughout southern China and has been passed down continuously for three centuries. Although his theories on "opposite hexagrams" and "inverted hexagrams" have drawn much criticism, his method of using imagery and reasoning is simple and clear, and he feared that readers might find it difficult to understand, so he often used many analogies and gentle metaphors to explain. Compared to those who deliberately write in a complicated manner to conceal their own lack of depth, he naturally stands out. For beginners, this book is still considered a good edition.

有清一代，經學之盛，遠過宋明。其治易學專家，如刁氏包、李氏光地、胡氏、胡氏渭、任氏啟運、惠氏奇、惠氏棟、萬氏年淳、姚氏、張氏、彭氏，皆能獨抒己見，各有心得。而顧亭林、毛大可、錢辛楣、王引之、江慎修、段懋堂、王蘭泉諸氏，雖不專治《易》，其音韻訓詁考據，於吾《易》亦多所發明。

The flourishing of Confucian scholarship during the Qing dynasty far surpassed that of the Song and Ming dynasties. Specialists in the study of the Book of Changes, such as Diao Bao, Li Guangdi, the Hu family, Hu Wei, Ren Qiyun, Hui Shiqi, Hui Dong, Wan Nianchun, and the Yao, Zhang, and Peng families, all managed to break away from old interpretations and express their own views, each with their own insights. As for Gu Yanwu (Tinglin), Mao Qilin (Dakai), Qian Dashen (Xinmei), Wang Yinzhi, Jiang Yong (Shenxiu), Duan Yucai (Maotang), and Wang Chang (Lanquan), although they did not specialize in the study of the Book of Changes, their efforts in phonology, etymology, and textual criticism have also contributed greatly to our understanding of the Book of Changes.

至若焦氏循之《通釋》、紀氏大奎之《易問》與《觀易外編》，一則宗漢學，而能串合六十四卦之爻象，無一辭一字不相貫通；一則講宋學而能闡發性理，與六十四卦之爻象變通化合，尤為歷來講《易》家之所未有。端木國瑚後起，更冶漢宋於一爐，一一以經傳互證，無一辭一字之虛設。視焦紀二氏為更上一層，允足以殿全軍而為勝清一代易學之結束矣。

As for Zhao Xun's "Yi Tong Shi", Ji DaKui's "Yi Wen" and "Guan Yi Wai Bian": the former adheres to the Han learning school, yet manages to connect the sixty-four hexagrams' line images together, with no sentence or character failing to be mutually connected; the latter follows the Song learning school, yet elaborates on principles of nature and morality, and integrates them with the transformation and flexibility of the sixty-four hexagrams' line images. Especially, it accomplishes what no other commentator on the Yi Jing has ever achieved. These two works represent opposite approaches, one following Han learning and the other Song learning, yet both reach the highest level. Du Mu Guo Hu comes later, further combining Han and Song learning, using classical texts and commentaries to cross-verify each other, with no sentence or character being superfluous. Compared to Zhao and Ji, he reaches an even higher level, sufficient to conclude the Yi learning of the Qing dynasty.

兩漢之《易》注，永嘉而後，已無完書。雖經歷朝好古之士，探討搜輯，然皆東鱗西爪。除《李氏集註》外，其能集合成書者，不可概見。濟南馬氏，旁搜博採，更於《太平御覽》、《永樂大典》與《說文》、《爾雅》、《文選》、《水經》諸注，傍及《內經》、《道藏》之所稱引者，悉為編次，共得《易部》之逸書八十餘種。承學之士，亦可略得其梗概矣。

The commentaries on the I Ching from the Han dynasty had already been lost in their entirety after the chaos of the Yongjia Disturbance in the Western Jin dynasty. Although scholars devoted to antiquity have continuously searched and collected fragments throughout the subsequent dynasties, the materials they obtained were only occasional scraps. Apart from Li Dingzuo's Collected Explanations of the Zhou Changes, few complete collections were compiled. Ma Guohan of Jinan made extensive searches and collected materials further from sources such as the Taiping Yulian, Yongle Daidian, Shuowen Jiezi, Erya, Wenxuan, Shuijing, and annotations from various scholars. He also included materials cited in the Huangdi Neijing and the Daozang. He arranged them in order, compiling eighty-some lost works on the I Ching. Thus, later scholars could gain a general understanding of the Han dynasty commentaries on the I Ching.

魏晉以降，其完全無缺者，推王弼注為最古。今與孔穎達之《正義》，陸德明之《音訓》並傳，與《程傳》、《朱義》，皆歷代官書所刊佈，士林所奉為金科玉律者也。其餘唐宋諸家之《易》注，世罕單行。賴《津逮》、《汲古》、《曠照》、《漢魏》諸叢書刊佈，而以後之聚刻叢書者，必以《易》為甲部之冠。孤本秘錄之藉此僅存者，為不少矣。

After the Wei and Jin dynasties, the most ancient complete commentary on the Yi (I Ching) is Wang Bi's. Now it is transmitted together with Kong Yingda's "The Correct Meaning of the Zhou Changes," Lu Deming's "Commentary on the Classics," and the phonetic and lexical explanations of these works. These are regarded as the standard texts by scholars and have been officially published by successive dynasties. They are also considered the authoritative interpretations by the scholarly community. Other commentaries on the Yi from the Tang and Song dynasties are rarely available in separate editions; they mainly survive through the compilation of anthologies such as "The Complete Collection of Secret Classics," "The Ji Gu Ge Collection of Classics," "The Kuang Zhao Ge Collection of Classics," and "The Han and Wei Collection of Classics." Those who later compiled such anthologies always placed the Yi section at the beginning of the Confucian classics. Many rare and secret manuscripts have been preserved through this method.

納蘭氏之《通志堂經解》，輯刊《易》注至四十餘種，尤為各叢書之所未有。而勝朝《經解》正、續兩編，選錄當時之《易》注，亦皆卓然可傳之書也。綜計清《四庫全書》，《易部》所藏，都一百五十二種。其存目著錄而無書者，約三倍其所藏之數。

Nalan Xingde's "Tongzhi Tang Jingjie" compiled and published over forty different commentaries on the Book of Changes, especially those not found in other anthologies. The main and supplementary parts of the Qing Dynasty's "Huangqing Jingjie" also selected commentaries on the Book of Changes by contemporary scholars, which are all outstanding works worthy of being passed down. In total, the Qing Dynasty's "Siku Quanshu" includes 152 works on the Book of Changes; approximately three times as many were only listed in the catalog without being included in the collection, which amounts to about 450 works.

辛齋自學《易》以後，歷年購求，所得已有四百六十三種。計《四庫》所藏之一百五十二種購求未得者，尚有二十九種。《四庫》存目所錄已購得者，有七十八種。《四庫》編錄於道家及術數類者，如《皇極》、《洞林》、《三易洞璣》等計三十餘種，餘皆為叢書及家刻單行之本，而寫本及辛齋所手抄者亦六十餘種，為日本人所著述者三種。嗣在廣東上海蘇杭揚州，陸續又得一百五十餘種。前後都六百數十種。以視歷代《經籍志》，及陳東塾《朱竹垞》所著錄者，曾不逮十之三四。然以現世所有者而論，則所遺已無幾矣。

Since I began studying the Yi Jing, I have been searching for and collecting various texts, and have already acquired 463 kinds. Among these, 152 kinds are included in the Siku Quanshu, but I have not yet obtained 29 of them. There are 78 kinds that are listed in the Siku Ciyu but have already been acquired by me. Some texts that belong to the Yi Jing studies but were classified under the Daoist and mathematical divination categories in the Siku Quanshu, such as the Huangji Jingshi, Donglin, Sanyi Dongji, etc., amount to about thirty kinds. The rest are mostly from collected series editions and privately printed single volumes, as well as some handwritten copies and copies I have personally transcribed, totaling over sixty kinds. There are also three kinds written by Japanese authors. Later, I have gradually acquired another 150 kinds from places such as Guangdong, Shanghai, Suzhou, Hangzhou, and Yangzhou. Altogether, this makes about six hundred and seventy kinds. When compared with the records of the "Jingji Zhi" in historical bibliographies and the book lists compiled by Chen Li (Dongshu) and Zhu Yizun (Zhuca), it is clear that these collected texts account for less than a third or fourth of what others have recorded, indicating the great loss of Yi Jing-related texts throughout history. However, if we consider the texts that still exist today, the ones I have missed are already few.

日本文學，皆我國所津逮。故我國已佚之書，而日本尚保存者甚夥。黎氏《古逸叢書》所刊，未能盡焉。光緒甲午以後，我國新進，厭棄古學。而竺舊之士，又墨守糟粕，不能發揮精義，與新理相調和，而資利用。致精義入神之學，日就澌滅。

The academic and educational traditions of Japan were transmitted from our country. Therefore, many books that have been lost in our country are still preserved in Japan. The edition of "Ancient Miscellaneous Collection" compiled by Li Shuchang did not include all of them. After the Jiawu year (1894), new intellectuals in our country began to discard traditional studies, while the conservatives clung stubbornly to the dross, failing to elaborate on the essence and integrate it with new theories for practical use. As a result, the study of "the essence reaching the divine" has been gradually fading away day by day.

清季以國立大學，求一完全經師而不可得，致羲經竟任缺席。鼎革以後，竟公然廢棄經學，而隸於文科之下，亦可謂臻晦盲否塞之極運矣。而日本既厭飫於物質文明之利，更反而求諸精神。雖舉國喧囂於功利競爭之途，而學術之研究，尚不忘初祖。仍有多數之學子，從事於《易經》。

In the late Qing dynasty, the prestigious national university found it impossible to hire a qualified scholar in the study of classical texts, to the extent that the discipline of the I Ching, as interpreted by Fuxi, was left untaught. After the change of dynasty, they even openly abandoned the study of classical texts, reducing it to a mere branch of the humanities. This can truly be said to have reached the darkest and most closed-minded point. In contrast, Japan, having already experienced the benefits of material civilization, turned its pursuit toward the spiritual realm. Although the whole country was noisy with competition for material gain, in academic research they did not forget their roots, and there were still many students studying the I Ching.

東京有易學會，有易學演講所，有《易學講義》之月刊。其占筮亦尚用古法。我國二千年來失傳之揲蓍法，經學鉅子所未能決其用者，彼中隨處可購得揲蓍之器也。惟蓍不產於日本，則以竹代之。禮失求野，不僅維繫易學之一助也。

There is an Institute of Yijing Studies in Tokyo, a lecture hall for Yijing talks, and a monthly journal called "Yijing Lectures." They still use the ancient method of divination: the method of divining the hexagrams by casting the yarrow stalks, which has been lost in China for two thousand years, is even uncertain to classical scholars as to how to use it. In Japan, however, one can buy the tools for casting yarrow stalks anywhere. The only problem is that the yarrow plant is not native to Japan, so they use bamboo sticks instead. This is precisely how the rites, when lost in the official institutions, are preserved in the folk traditions. The significance of this is not merely to provide a little help in maintaining the study of the Yijing.

辛齋會購其《易學講義》，其取象悉宗漢學，大抵取資於《李氏集解》者為多。有所謂影象意象者，則為彼所擴而充之者也。有《易學新講義》，為我國北宋人之著述。《四庫》有其書，外間已乏刊本，亦為日本所印行。而近出之《高島易斷》，於明治維新以後五十年間，內政外交諸大事，均有占驗論斷，亦可覘彼國之所尚矣。

I once purchased their "Explanations of the Yi Classic," which largely follows the Han dynasty scholarship in its use of imagery. Most of its materials come from Li Dingzuo's "Collected Explanations of the Zhou Changes." The terms "shadow imagery" and "intentional imagery" are names they have developed beyond the imagery used by Han scholars. There is also a book called "New Explanations of the Yi Classic," which is actually a work from the Northern Song dynasty in China. The "Siku Quanshu" includes this book, but it is now rare in China and has been printed in Japan. As for the recently published "Yi Judgment" by Takahashi Tsunao, it includes interpretations and judgments on various major domestic and foreign affairs in Japan over the fifty years following the Meiji Restoration. From this, one can see the prevailing trends and values of that country.

美國國會圖書館，以四十萬金鎊，專為購買中國書籍之用。除前清殿版各書，為清政府所饋送外，其餘所採購之漢文書籍，亦有數千種之多。皆為日本人所販運，直接購自中國者無幾也。友人江亢虎君，現為其漢文部之管理員。丁巳夏間回國，邂逅於滬上。雲彼中所藏《易部》，亦幾有四百種。因囑其將目錄鈔寄，以較辛齋所藏者未知如何。然彼以異國之圖書館，而其所藏，視本國《四庫》所有，至兩倍有半，殊足令人生無窮之感也。

The United States Library of Congress allocated forty thousand pounds sterling specifically for the purchase of Chinese books. In addition to the various books from the Qing imperial palace editions donated by the Qing government, the library acquired several thousand Chinese texts through purchases. Most of these books were smuggled into Japan by Japanese traders and then sold back, with very few being directly purchased from China. My friend Mr. Jiang Kanghu, who is currently serving as the head of the Chinese section of the library, returned to China in the summer of Dingsi year (1917), when I met him in Shanghai. He said that the library's collection of books on the Book of Changes (Yi Jing) was nearly four hundred volumes. I asked him to send me a list of the books so that I could compare the number of such texts in my own collection. However, I still do not know which collection is larger. It is truly astonishing that a foreign library could have a collection of Yi Jing texts amounting to more than two and a half times the number included in the Four Branches of the State Library (Siku Quanshu). This is indeed a matter of deep reflection.

自來言《易》者，不出乎漢宋二派。各有專長，亦皆有所蔽。漢學重名物，重訓詁，一字一義，辨晰異同，不憚參伍考訂，以求其本之所自。意之所當，且尊家法，恪守師承，各守範圍，不敢移易尺寸。嚴正精確，良足為說經之模範。然其蔽在墨守故訓，取糟粕而遺其精華。且《易》之為書，廣大悉備；網羅百家，猶恐未盡；乃株守一先生說，沾沾自喜，隘陋之誚，雲胡可免？

From the beginning, those who have explained the Book of Changes have been divided into two schools: the Han school and the Song school. Each has its own strengths, but also its own limitations. The Han school places great emphasis on names and objects, and on philological study. They carefully distinguish the differences and similarities of each character and each meaning, are not afraid of repeatedly consulting and verifying sources, in order to clarify the origin and the accurate meaning. Moreover, they revere family traditions and strictly follow the lineage of teachers, each guarding their own domain and not daring to deviate even slightly. This rigorous and precise attitude indeed can serve as a model for interpreting scriptures. However, its flaw lies in rigidly adhering to old interpretations, taking only the coarse parts and losing the refined essence. Moreover, the Book of Changes is vast and comprehensive, encompassing everything. It would be difficult even to include the views of all schools of thought, yet they stubbornly cling to the views of a single scholar, taking pride in it. How could they avoid the criticism of being narrow-minded and shallow?

宋學正心誠意，重知行之合一，嚴理欲之大防。踐履篤實，操行不苟。所謂和順於道德而理於義，窮理盡性以至於命者，亦未始非義經形而上學之極功。但承王弼掃象之遺風，只就經傳之原文，以己意為揣測。其不可通者，不憚變更句讀，移易經文，斷言為錯簡脫誤。此則非漢學家所敢出者也。

Song learning emphasizes cultivating the mind and sincerity, placing importance on the unity of knowledge and action. It strictly distinguishes between heavenly principle and human desire, practicing with diligence and maintaining integrity. The saying in the "Shuo Gua Zhuan" that "harmonizing with moral principles and conforming to righteousness, investigating physical principles and exhausting human nature until reaching heavenly mandate" may not be unlike the highest achievement of the "Yi Jing" in its metaphysical approach. However, Song learning inherited the legacy of Wang Bi, who eliminated the images of the hexagrams, interpreting the text according to one's own understanding based on the surface meaning of the classics. When encountering passages that did not make sense, they would not hesitate to alter punctuation or rearrange the text, asserting that such discrepancies were due to errors or omissions in the original texts. This approach was something that Han scholars would not dare to undertake.

元明以來，兩派對峙，門戶攻擊之陋習，雖賢者亦或不免。甚者以意氣相爭尚，視同異為是非。不但漢學與宋學相爭訟也。同漢學焉，尊鄭者則黜虞，是孟者則非荀。同宋學焉，而有洛蜀之辯駁，朱陸之異同。其下者更或依巨儒之末光，蒙道學之假面，為弋名乾祿之具者，尤不足道矣。

From the Yuan and Ming dynasties onwards, there have been two opposing schools of thought that have been at odds with each other, attacking one another. Even virtuous scholars sometimes cannot escape this bad practice. In severe cases, they act on impulse, taking whether their views agree or disagree as the standard of right and wrong. This is not only a dispute between Han learning and Song learning: among Han learning, those who revere Zheng Xuan condemn Yu Fan, while those who affirm Meng Xi criticize Xun Shuang; among Song learning, there are also debates between the Luo school and the Shu school, as well as differences between Zhu Xi and Lu Jiuyuan. As for those of even lower standing, there are those who follow the residual influence of great scholars, wear the mask of Neo-Confucianism, and treat scholarship as a means to gain reputation and seek official positions. These are even less worth mentioning.

國學淪亡，書局盡廢。承學之士，求一善本之經書，已不可得。近日坊間石印之《易經》，其謬誤尤甚。校對之疏略，姑置不論。序文則《程傳》也，目錄之標題則《本義》也。目錄之卷帙則《程傳》也，首列河圖、洛書，及先後天八卦六十四卦各圖，亦《本義》也。而上、下《經》與《繫傳》之篇第，則又皆《程傳》也，其注則又皆《本義》也。可謂極參伍錯綜而莫明其妙者矣。

Confucian learning has declined, and the official publishing houses have all ceased operations, making it impossible for scholars to obtain a good edition of classical texts. Recently, bookshops have been using stone printing to reproduce the Book of Changes, but the errors are especially severe. One may overlook the careless mistakes in proofreading; however, even considering only the preface, which uses the preface from the Cheng氏 Commentary on the Book of Changes, while the title of the table of contents is "Benyi" (Original Meaning); the sequence of the volumes in the table of contents follows the Cheng Commentary, yet the front matter includes diagrams of the Yellow River Chart, the Luo Writing, the Earlier Heaven and Later Heaven Trigrams, and the sixty-four Trigrams, following the format of the Benyi; furthermore, the arrangement of the sections of the Upper and Lower Classics and the Great Treatise on the Trigrams also follows the Cheng Commentary, while the annotations are entirely from the Benyi. A single book combines the styles of both Cheng and Zhu schools in a haphazard manner, truly resulting in a confusing and incoherent presentation.

觀其封面所署，則又曰“監本《易經》”。推求其故，則謬誤相仍，已非一日。蓋明刻永樂之監本，固程子之《傳》與朱子《本義》並列者。而篇第章句，悉依《程傳》，而以《本義》之注，錄於《程傳》之後。清刻《易經》傳義音訓亦猶是也。

Looking at the title on the cover, it is also called the "Supervised Edition of the Book of Changes." Investigating the reasons, such errors have been passed down and continued for a long time. Originally, in the Yongle period of the Ming dynasty, the edition printed by the Imperial Academy was supposed to have Cheng Yi's "Commentary on the Book of Changes" and Zhu Xi's "Original Meaning" placed side by side: the order of chapters and sentences was entirely based on the "Cheng Commentary," while the "Original Meaning" was recorded after the "Cheng Commentary." The edition of the "Book of Changes" printed in the Qing dynasty, called the "Transmission, Meaning, and Pronunciation Guide Edition," was also the same.

後以考試功令，專重朱義。坊賈射利，為節減篇幅計，以去《傳》留《義》，而篇帙則仍未之改。明嘉靖間蘇州學官成某，復即是本而刊佈之，成此非驢非馬之怪象，公然流佈。讀者既不求甚解，而所謂教育部教育廳教育會者，皆熟視無睹，不加糾正。嗚呼！易世而後，將不知經書之為何物矣！

Later, because the imperial examination system placed great emphasis on Zhu Xi's "Original Meaning," book merchants, in order to make profits and save space and reduce costs, deleted the "Cheng Transmission" and kept only the "Original Meaning," while keeping the original order of chapters and volumes unchanged. In the Jiajing period of the Ming dynasty, a local official in Suzhou named Cheng again printed and circulated this edition following the same format, thus creating this bizarre situation of something that is neither horse nor donkey, which spread openly. Readers themselves did not seek deep understanding, and so-called education departments, education bureaus, and education associations all turned a blind eye and never took corrective action. Alas! In another generation or two, people may no longer know what the classics are!

歷來講《易》家，無論其為漢學，為宋學，而有一宗牢不可破之錮蔽：即將“經學”二字橫梗於胸中是也。埋其龐然自大之身於故紙堆中，而目高於頂，不但對於世界之新知識、新思想，深閉錮拒；而於固有之名物象數氣運推步之原本於《易》者，亦皆視為小道，而不屑措意。

Those who have ever interpreted the Yi Jing, whether they belong to the Han learning or Song learning schools, all share an unbreakable illness: they insistently place the term "classical studies" in their minds as an insurmountable boundary. They bury their own arrogant bodies in old texts, yet their eyes are on top of their heads. Not only do they tightly shut the door to new knowledge and ideas in the world, rejecting them altogether; they also regard the traditional interpretations of names and objects, the reasoning of figures and numbers, the changes of destiny, and the calculations of calendars, which originally come from the Yi Jing, as mere side paths, and show no interest in them.

凡經傳所未明言，註疏所未闡發者，悉目為妄談，為異端。排斥攻擊，不遺餘力。而不知《易》之為書，廣大悉備。上自天地之運行，下及百姓所日用，無不彌綸範圍於其中。孔子贊《易》已明白言之，曰“書不盡言，言不盡意”，故聖人立象以盡意，變而通之以盡利，鼓之舞之以盡神。

Anything not clearly stated in the classics and not elaborated upon in annotations is altogether condemned as nonsense and heresy, vigorously rejected and attacked. They do not understand that the Book of Changes is vast and comprehensive, covering the operation of heaven and earth above, and the daily applications of common people below, nothing being excluded. Confucius, in his Commentary on the Changes, has already explained clearly that words cannot fully express what needs to be said, and speech cannot fully convey one's thoughts. Therefore, the sage established hexagrams to exhaust meaning, changed and transformed the lines of the hexagrams to exhaust practical utility, and stirred up and inspired to exhaust the marvelous.

是書之所未言者，固當求之於意。意有所未得者，當求之於象。象有所未盡者，當變通之以盡其利。而《易》之道始應用而不窮。今乃盡反孔子之言，曰“吾言義不言利”，曰“得意而忘象，得象而忘言”。目光之盤旋，不出於書外一寸。此《易》道之所以終古長夜也夫！

It is evident that what is not expressed in words should be sought in the meaning; what is not yet understood in meaning should be sought in the images; and what is not yet exhausted in the images should be pursued by flexible methods to exhaust its utility. In this way, the Way of the Book of Changes can be applied endlessly. But nowadays those who talk about the Book of Changes have completely reversed Confucius' words. They say on one hand, "I only talk about righteousness and not about benefit," and on the other hand, "once you have grasped the meaning, you forget the image; once you have grasped the image, you forget the words." Their vision circles around, never going beyond the pages of a book. This is why the Way of the Book of Changes has remained as dark as a long night throughout the ages.

《易》窮則變，變則通，通則久。黃帝堯舜，通其變使民不倦，神而化之，使民宜之。蓋民之情，恆厭故而喜新。厭則倦，倦則精神懈弛，而百事皆墮壞於無形。此蠱之象也，故君子以振民育德而變化之。蠱成隨，則元亨而天下治。隨元亨利貞而天下隨時，隨時之義大矣哉！

The Way of the Book of Changes reaches its limit and then changes, only through change can it become smooth and unimpeded, and only through smoothness can it endure long. The Yellow Emperor, Yao, and Shun understood the changes of things and guided the people without making them weary; they subtly nurtured and cultivated, enabling the people to each find their proper place. Because human feelings always dislike the old and favor the new: disliking the old leads to weariness, weariness leads to slackness, and all affairs gradually deteriorate in the unseen. This is precisely the image of the Hexagram Gu. Therefore, the Image Commentary of Gu says that a gentleman should invigorate the people and cultivate virtue in order to bring about transformation. When Gu changes into Suí, it becomes greatly smooth and the world is governed well. The Hexagram Suí discusses the principles of originality, smoothness, benefit, and uprightness, and the meaning of 'following the times' is truly profound!

今之時何時乎？五洲交通，天空往來，百礦並興，地寶盡發。所謂萬物皆相見，其重明繼照之時歟！離火之功用，遍於坤輿，極則為災。或致突如其來如焚如死如棄如之占，果能神而化之，變通盡利，則將由物質之文明，而進於精神之文明。是明出地上，火地為晉，受茲介福之時矣。

What era are we in now? With transportation across all five continents, the sky is traversable by flight, and various mining industries are flourishing, fully developing the treasures beneath the earth. This is precisely the era described in the hexagram Li (Fire), which says, "All things are revealed to each other," and light continues to shine brightly. However, the function of fire spreads throughout the land, and when it reaches its extreme, it can become a disaster. Perhaps this will result in the omen of the fourth line of Li hexagram, "Suddenly appearing, burning, dying, and being cast away." If we can truly skillfully cultivate and transform, gaining the full benefits, we will progress from material civilization to spiritual civilization. That is when the light rises above the ground, and fire on the ground becomes the hexagram Jin (Progress), "Receiving this great blessing," the time when great blessings are received.

《易》道於此，必有大明之一日。吾輩丁茲世運絕續之交，守先待後，責無旁貸，亟宜革故鼎新，除門戶之積習，破迂拘之謬見。以世界之眼光觀其象，以科學之條理玩其辭，集思廣益，彰往察來，庶五千年神秘之鑰可得而開。興神物以前民用，必非尼父欺人之語也。

At this point, the Way of the Book of Changes is sure to shine brightly again. We are now in a time of transition between eras, inheriting the legacy of our predecessors and preparing for the future, which is our responsibility. We should urgently eliminate outdated practices, create new situations, remove entrenched family traditions, and break through mistaken and rigid views. We should observe its hexagrams with a global perspective and contemplate its texts with scientific reasoning. By pooling wisdom, we can clarify past teachings and foresee the future. Perhaps, with this key to mystery, the five thousand years of tradition can be unlocked. The Great Treatise says that sages used divination tools like yarrow stalks and tortoise shells to guide the people, which certainly was not a lie by Confucius.

物生而後有象，象而後有滋，滋而後有數。民物之孳乳無窮，而象數之遞演而遞進，遞進而遞繁，無有止境。故在黃帝之時演《易》，伏羲之八卦已不足用，乃益之以干支。文王演《易》，干支已不足用，乃益之以《彖》、《爻》。孔子贊《易》，則《彖》、《爻》又不足以盡世變物情，乃益之以繫辭《十翼》。

After things come into being, they take shape; with shape comes growth; with growth comes numbers. As human beings and things multiply endlessly, the images and numbers also develop layer by layer, increasing continuously without end. Therefore, in the time of the Yellow Emperor, the Book of Changes was divined by inference, but the eight trigrams of Fuxi were insufficient, so heavenly stems and earthly branches were added to complement them. When King Wen divined the Book of Changes, the heavenly stems and earthly branches were still insufficient, so the Tai Cis and Line Statements were added. When Confucius wrote the Commentary on the Book of Changes, the Tai Cis and Line Statements were still inadequate to explain all the changes of the world and the forms of all things, so the ten appendices below the Xici were added.

今距孔子之世又三千年矣！世界大通，事物之紛紜繁變，十百倍蓰千萬於古昔。而所用之文字，乃不能隨世事遞演遞進以應所需。且小學中絕，音移義晦，經典固有之字，因廢置已久，不復為人所識者，十殆四五。

Now three thousand years have passed since the time of Confucius! The world is now interconnected, and the complexity and changes of things have increased by ten, a hundred, even a thousand times compared to ancient times. Yet the characters we use cannot keep up with these developments and adapt to meet the needs of the times. Moreover, the study of textual meaning and phonetics has been interrupted midway, with shifts in pronunciation and obscurity in meaning. Many characters originally present in the classics, having been abandoned for so long that no one recognizes them anymore, now account for nearly four or five tenths of all such characters.

故說《易》者，往往於《易》之一字一義，累千萬言之解釋，而仍不能明。然必待小學既明而說《易》，又如臨渴掘井，不能濟目前之用，且不能令多數之學子盡通小學焉。則雖說亦如無說，而《易》仍不能明。則不如假世界通用之名詞以代之，以補文字之闕憾，而閱者亦《易》於瞭解也。豈非《易》之一助乎？

Therefore, those who explain the Book of Changes often write thousands of words to explain a single character or a single meaning, yet still fail to make it clear. However, if one insists on mastering the study of word meanings and etymology before explaining the Book of Changes, it is like digging a well when thirsty—it cannot solve the immediate problem, and it is also impossible for most students to master the basics of classical Chinese. In such a case, even if one explains it, it is as if nothing has been said, and the Book of Changes remains obscure. It would be better to use universally recognized terms to replace the original words, using them to make up for the shortcomings in the text. This would make it easier for readers to understand. Is this not a great help in explaining the Book of Changes?

如《易》言“坤其靜也翕，其動也闢”，而翕與闢之義，以舊文字釋之，則翕為聚也合也，闢為開也。一開一合，字義雖盡，而於《易》言闢會之妙用，仍未著也。若假新名詞以解之，則闢者即物理學之所謂離心力也，翕者即物理學所謂向心力也。凡物之運動能循其常軌而不息者，皆賴此離心向心二力之作用。地球之繞日，即此作用之公例也。以釋闢翕，則深切著明，而閱者亦可不待煩言而解矣。不僅名詞已也，新思想與新學說，足與吾《易》相發明者甚多。而經學家見之，必又曰穿鑿附會，誣衊聖經，則吾其奈之何哉！

For example, the Great Treatise says, "When the Earth Trigram is still, it is 'xī', but when it moves, it is 'bì'." The meanings of 'xī' and 'bì' can be explained by the old meanings: 'xī' means gathering and uniting, while 'bì' means opening. Although the literal meaning of these words is explained, the subtle function of opening and closing in the Book of Changes has not yet been clearly revealed. If we use modern terms to explain them, 'bì' corresponds to centrifugal force in physics, and 'xī' corresponds to centripetal force. Any motion of an object that can follow a certain path without stopping depends on the action of these two forces, centrifugal and centripetal. The Earth's orbit around the Sun is an example of this: it is attracted and does not scatter, and at the same time, due to its rotation, it does not fall. Using these modern concepts to explain 'bì' and 'xī' makes the meaning clear and explicit, so that readers can understand without further explanation. It is not only about words; there are many new ideas and theories that can complement and illuminate our Book of Changes. However, if scholars of the classics see this, they will surely say it is a forced and misleading interpretation of the sacred text. What can I do about it?

今日所用之字，猶數千年前之字也。然形式雖未改，而精神則非複數千年之舊。音與義，類皆變易。任舉一字而衡論之，若此者蓋比比焉。其僅音變而義未變者，如“下、無”等字，於詁經尚無出入。其訓義變易者，雖古音尚存，於經義已不可通矣。

The characters used today are the same as those from several thousand years ago. However, although the forms of the characters have not changed, their spirit is no longer the same as in ancient times: both pronunciation and meaning have largely changed. Take any character as an example, and this situation is common everywhere. Among them, there are characters whose pronunciation has changed but whose meaning remains the same, such as 「下」 and 「无」. These can still be used to explain classical texts without much discrepancy. However, for characters whose meanings have changed, even if their ancient pronunciations are preserved, they can no longer be used to explain the meaning of classical texts.

如君臣二字，古訓但為主從之別。降及漢魏，猶為普通尊人卑己之謙辭，未嘗專屬諸朝廷也。自宋以後，則專以君為尊無二上之天子，臣為庶司百職之官僚，而君字遂神聖不可侵犯矣。官字之古訓，亦僅為專任職司之名，並未含有尊崇高貴之意。人之耳目口鼻舌曰五官，言其各專所用，不能彼此互代也。故手足則曰肢而不稱官，其義甚明。

For example, the characters "君" and "臣" originally simply meant master and subordinate. During the Han and Wei dynasties, they were still general terms used by people to show respect to others and humility when referring to oneself, such as calling the other person "君" and oneself "臣," without being exclusive to the court. From the Song dynasty onwards, "君" came to be specifically used for the supreme emperor, while "臣" referred to officials in various departments. Thus, the character "君" became sacred and inviolable. The ancient meaning of the character "官" was merely a term for a specific position or duty, without implying respect or high status: the ears, eyes, mouth, nose, and tongue are called "五官," meaning they each have a specific function and cannot replace each other. Therefore, hands and feet are called "肢" but not "官," and this is clear.

自漢後天子曰縣官，曰官家，而官之義遂混。後世官之權位浸大浸崇，而官字漸成尊崇高貴之稱。今之俗尚，凡物美者，轍加一官字以為標幟，其去官字之本義，不可以道里（理）計矣。於是龍飛九五，遂為帝王之祥；惟闢作威，亦附卦爻之義。兢兢乎僭越之虞，凜凜乎生殺之柄。如《周易折中》者，《易》竟為專制帝王之護符矣。非以今義釋經階之厲哉！

After the Han dynasty, the term "xuanguan" and "guan jia" were used to refer to the Son of Heaven, which caused the meaning of the character "guan" to become confused. As the power and status of officials grew increasingly greater over later generations, the character "guan" gradually became a term of respect and reverence. Nowadays, the trend is that whenever something is of good quality, the character "guan" is added to it as a mark, and the original meaning of "guan" has long since been lost, beyond the reach of measurement. Thus, the line "fei long zai tian" from the "Qian" hexagram of the "Zhou Yi" has become a symbol of the emperor's auspiciousness, and the phrase "wei bi zuo wei" from the "Shang Shu · Hong Fan" has also been connected to the meaning of the hexagram lines. Scholars interpreting the "Zhou Yi" now tread carefully, fearing they might commit the offense of overstepping their bounds, and they are filled with awe towards the power of life and death, reward and punishment. Books like "Zhou Yi Zhe Zhong" have turned the "Zhou Yi" into a talisman for autocratic emperors. This is precisely the disaster caused by interpreting the classics with modern meanings!

《下繫》一章，“天地之大德曰生，聖人之大寶曰位，何以守位曰人，何以聚人曰財，理財正辭，禁民為非曰義”，意義本相聯貫，而文字亦緊相銜接。乃中間插一“位”字，便為上下辭意之梗。宋儒遂改“何以守位曰人”之“人”字為“仁”，以迴護“位”字，而與下“聚人”一句又不相貫。

The Great Treatise of the Lower Transmission says: "The great virtue of heaven and earth is to give birth, and the great treasure of the sage is position; by what means can one maintain position? It is called humaneness; by what means can one gather people? It is called wealth; managing wealth, regulating speech, and preventing the people from doing evil, is called righteousness." These sentences originally flow smoothly and are closely connected, but the insertion of the word "position" in the middle blocks the meaning. Therefore, the Song dynasty scholars changed the word "human" in "by what means can one maintain position? It is called human" to "humaneness," to explain away the word "position." However, this change makes it difficult to connect with the next sentence about gathering people.

於是呂氏本又改從古本作“人”，而曲為之說，亦終不可通。其實誤不在“人”字而在“位”字。“人”字不當改“仁”字，而“位”字當改作“仁”字。蓋“仁”字與“位”字形式相近，以致傳訛。古訓相傳，“所寶惟仁”，未有以位為寶者也。況以位為天下之公器耶？則不必寶；以位為一人之私有耶？則不能寶。晉文之答秦使曰：“亡人無以為寶，仁親以為寶。”詎作《易》之聖人，見出重耳下哉！

Therefore, the original version of the Lü family's text was again changed back to "person" according to the ancient version, and then explained in a roundabout way, but ultimately it still did not make sense. In fact, the mistake lies not in the character "person" but in the character "position": the character "person" should not be changed to "benevolence", but rather the character "position" should be changed to "benevolence". This is because the characters "benevolence" and "position" are similar in form, leading to errors in transmission. The traditional teaching passed down is "the only treasure is benevolence", and there is no mention of "position" being considered a treasure. Moreover, how can "position" be regarded as a public possession of the world? Then there would be no need to treasure it; if "position" is regarded as a private possession of an individual, then it cannot be treasured. In the past, Duke Wen of Jin, Prince Chong'er, answered a Qin envoy saying: "A person in exile has nothing to treasure, but only benevolence and affection are treasured." How could the sage who composed the Book of Changes have a lesser insight than Prince Chong'er!

按：此說初創，同人善其新穎，慫恿存錄。嗣閱張之銳氏《易學闡微》，立說相同，更以自信。但數年以來，研窮數理名象，覺此“位”字“人”字皆文所應有，實不當輕議更改。此次重印，原擬將此條削去。惟前書既已傳佈，不能追改，特存之而附註原委，以志吾過。並令閱者得更進一層之研究，未始不足為“筌蹄”之一助焉。

Appendix: When this idea was first proposed, like-minded people found it novel and encouraged me to record it. Later, when I read Zhang Zhihui's "Yixue Chanywei," which presented a similar argument, I became more confident. However, in recent years, after delving deeply into the study of numbers, principles, and symbolic meanings, I have come to believe that the characters "位" (position) and "人" (person) are originally present in the text and should not be lightly altered. This time, when reprinting, I originally intended to delete this passage; however, since earlier editions have already been circulated and cannot be revised, I have specially retained it and added this note to record my own mistake. I hope this will also serve as a basis for readers to conduct further research. Leaving behind this "qutan" (a term referring to a means to an end) may not be without some help.

《象傳》曰：“大哉乾元！乃統天。”此“元”字，即“元亨利貞”之元。舊注“元始也”，《本義》“元大也”，何休公羊注曰“變一而為元。元者氣也，無形以起有形，以分造起天地，天地之始也”。邵子亦曰“元者氣之始”。合觀諸家之說，於“元”字之精義，尚有未盡。

The commentary on the Qian hexagram says: "Great is Qian Yuan, which governs the heavens." The character "Yuan" here refers to "Yuan Heng Li Zhen." Old interpretations take "Yuan" to mean "beginning," while Zhu Xi's "Ben Yi" explains it as "greatness." He Xiu's commentary on the "Gongyang Zhuan" says: "Transforming 'one' into 'Yuan'; Yuan is the vital energy, which originates from formlessness and gives rise to form, differentiating and creating to generate heaven and earth, thus being the beginning of heaven and earth." Shao Yong also said, "Yuan is the beginning of the vital energy." Considering the views of these scholars, there may still be aspects of the meaning of "Yuan" that have not been fully explained.

辛齋以為舉“元亨利貞”並言之，為乾之四德。而“元”之一字，不但可包舉“利亨貞”三字，並可舉全《易》而一氣貫注，故曰“大哉乾元乃統天”。超乎無始，以立乎天地之先者也。《文言》“乾元者始而亨者也”，此元字乃天之元焉。《坤·象》“至哉坤元”，乃地之元也。《文言》“元者善之長也”，則人之元也。

I thought that the four characters "yuan, heng, li, zhen" are the four virtues possessed by the hexagram Qian. However, the single character "yuan" not only encompasses the three characters "heng," "li," and "zhen," but also connects the entire Book of Changes in a continuous manner. Therefore, it is said, "How great is Qian Yuan, which governs the heavens." It transcends all beginnings and stands before heaven and earth. The Wenyan says, "Qian Yuan is the beginning and is harmonious," where "yuan" refers to the beginning of heaven. The transmission of the hexagram Kun says, "How profound is Kun Yuan," referring to the beginning of earth. The Wenyan also says, "Yuan is the first of all good things," referring to the beginning of humanity. Thus, the character "yuan" takes on different meanings according to the three categories of heaven, earth, and humanity.

善之長，即仁義禮智之仁。仁從二從人，元亦從二從人，故仁為人之元。所謂天經地義，簡言之即天良也。蓋物各有元，大而天地，小而飛潛動植各物，均莫不具有此元。得之則生，不得則死。顧元之為元，無聲無臭，無形質可見，而其功用所著，亦幾非言語筆墨所能摩寫而形容之。

The term "the beginning of all good deeds" refers to the concept of "ren" among the virtues of benevolence, righteousness, propriety, and wisdom. The character for "ren" is composed of "er" and "ren," and the character for "yuan" is also composed of "er" and "ren." Therefore, "ren" is the fundamental essence of a person. This is what is meant by the saying "the way of heaven and earth," simply put, it refers to the inherent goodness of a person. Basically, all things have their fundamental essence: from the vast universe to the smallest creatures, whether flying, swimming, moving, or plants, none lack this fundamental essence. Possessing it leads to life, while lacking it leads to death. However, the essence of "yuan" is intangible, without sound or smell, and cannot be seen in form or substance. Yet the functions it manifests are almost beyond the ability of words or writing to describe.

然元不可見，而仁可見。仁不可見，而仁之寓於事物者可見。古人造字，其精義往往互相鉤貫。而即物定名，亦無不各寓其意。如果實核中之質體，名之曰仁，已可見矣。而元亦即可因仁而顯其用。如果核桃曰桃仁，杏曰杏仁，而桃與杏之元，即在此仁之中。果核之所以能滋生者，實賴有此仁，賴有此仁中之元。

However, although the principle of Yuan is invisible, Ren is visible; Ren itself is invisible, but the form in which Ren is embodied in concrete things is visible. The ancients created characters, and the subtle meanings between characters often connect and communicate with each other; when naming things according to their physical forms, each name also carries an implied meaning. For example, the solid part inside the fruit kernel is called "Ren," which is a visible example; and Yuan is thus revealed through Ren. For instance, the kernel of a peach is called "Taoren" (peach kernel), and the kernel of an apricot is called "Xingren" (apricot kernel); the Yuan of peach and apricot is thus contained within this Ren. The ability of the fruit kernel to sprout and grow is indeed entirely dependent on this Ren, and on the Yuan contained within the Ren.

吾於西人之紀載得一說，足為斯義之確證。西人於埃及地中，掘得四千年之古尸，尸腹中往往實以林禽及小麥等物。以保藏之非常完密，故均歷久久而不壞。取林禽及麥而播種之，仍能發榮滋長，與新者無異。此無他，以其元之尚存在也。

I read from the accounts of Westerners an incident that serves as a confirmation of this principle. Westerners discovered in the desert of Egypt the remains of a person who died four thousand years ago, and often found in the stomachs of these ancient corpses were dried fruits such as pomegranates and wheat. Because they were preserved very carefully, they remained unspoiled for a long time. When these fruits and grains were taken out and planted, they were able to sprout and grow just like newly harvested seeds. This is not due to any other reason, but because their 'original essence' still remained.

若其元已失散無存，則雖當年之果核，種之亦不能發生。因此可證明物各有元之理，而人元所存，則惟此天良。天良不滅，生機亦不滅。天良漸滅，則亦無元之果核，已無萌生之望。雖幸而生，亦行尸走肉而已。剝之上九，“碩果不食”，即此僅存之天良也歟！

If the original essence has already been lost, then even a newly formed fruit kernel would not sprout when planted. This demonstrates the principle that all things have their original essence. For humans, the essence is寄托ed in this single remaining bit of heaven's goodness. As long as heaven's goodness remains, vitality remains; but as heaven's goodness gradually fades away, it is like losing the kernel of the fruit, with no hope of sprouting. Even if one survives by chance, it is merely a walking corpse. The line statement of the Upper Nine in the "Bao" hexagram says, "A large fruit has not been eaten," which refers precisely to this remaining bit of heaven's goodness.

《坤·上六·文言》：“陰疑於陽必戰，為其嫌於無陽也，故稱龍焉。”註疏與各家講解，均未能明悉。鄭注“嫌”讀如“群公謙”之謙，或作謙。謙，雜也。以嫌作雜字解。雜於無陽，語亦費解。《九家》作兼，謂陰陽合居，故曰“兼陽”，則“無”字又為贅文。王弼云“為其嫌於非陽而戰”，《正義》謂“陰盛似陽為嫌，純陰非陽，故稱龍以明之”。說各不同，其未能暢發經旨則一也。

The Wenyan of the upper sixth line of the Kun hexagram says: "When yin is so strong that it resembles yang, it must fight, because it fears being suspected of not having yang, so it is called 'dragon'." All previous annotations and interpretations have failed to clarify this. Zheng Xuan interpreted "xian" as "qian" from "qian" in "qun gong qian," and explained "qian" as "za," meaning he treated "xian" as if it were "za." However, the phrase "za yu wu yang" remains difficult to understand. The Jiā Jiā Yì wrote "jian," saying that it refers to yin and yang coexisting, so it is called "jian yang," making the character "wu" seem redundant. Wang Bi said, "It fights because it fears not being yang." The Zhou Changes Justice says, "When yin is strong and resembles yang, it is called 'xian,' pure yin is not yang, so it is called 'dragon' to clarify this." Different interpretations have been proposed, yet none have clearly explained the meaning of the classic text, which is a common point of agreement among them.

辛齋按：陽本無盡，坤之上六為純陰之候，近乎有無陽之嫌。今可舉例以明之：五月初五日，相傳為端午節，又曰端陽節。九月初九日，曰重陽日。而十月曰小陽月。夫五月，於卦之消息為姤，一陰始生，端者始也，當曰“端陰”，何以稱之曰“端陽”？九月，於卦為剝，碩果僅存，陽已將盡，乃何以稱之曰“重陽”？十月於卦為坤，爻辰正值坤之上六，純陰無陽，何以曰“小陽”？此正扶陽抑陰之意，為其嫌於無陽也，故稱“端陽”“重陽”“小陽”焉。則坤上之“嫌於無陽”，其義可比例而得，不待煩言而解矣。

I remarked: Yang energy is originally boundless. The sixth line at the top of the Hexagram Qian is the time of pure yin, which is almost like having no yang. Here we can use examples to illustrate this. May fifth is traditionally the Dragon Boat Festival, also called the End Yang Festival. September ninth is called Chongyang, also called Chongjiu. October is called Xiaoyangchun, the small yang spring. May is the Hexagram Gou in the twelve message hexagrams, where one yin is just beginning to arise. "Duan" means beginning, so it should be called "Duan Yin," but why is it called "Duan Yang" instead? September is the Hexagram Bao in the message hexagrams, where only one fruit remains, and yang energy is about to end. Why is it called "Chongyang" instead? October is the Hexagram Kun in the message hexagrams, where all six lines are yin. The yao chen (the twelve zodiac signs paired with the six lines) correspond to the sixth line at the top of Hexagram Kun, which is pure yin with no yang. Why is it called "Xiaoyang" instead? This is precisely the intention of supporting yang energy and restraining yin energy. Because it seems to have no yang, it deliberately calls it "Duanyang," "Chongyang," and "Xiaoyang." Therefore, the meaning of the sixth line at the top of Hexagram Kun, "Xian yu wu yang," can be understood in the same way, without needing further explanation.

《易》數，以陽統陰者也。《易》象，以陽變陰者也。《易》義，扶陽抑陰者也。故陽大陰小，陽貴陰賤。凡對待之字，幾無不以此為例。顧何以立天之道，不曰“陽與陰”，而曰“陰與陽”？又曰“一陰一陽之為道”，又曰“分陰分陽”？輒以陰居先而陽居後，必曰陰陽，無言陽陰者，其義何居？

The numbers of the Book of Changes are governed by yang encompassing yin, the images of the Book of Changes are formed by the transformation of yin through yang, and the principles of the Book of Changes are to support yang and restrain yin. Therefore, yang is great and yin is small, yang is esteemed and yin is despised. Almost all paired terms follow this order. However, why does the "Commentary on the Hexagrams" mention establishing the way of heaven without saying "yang and yin" but instead "yin and yang"? The "Great Treatise" also says "the way is the interplay of one yin and one yang," and also says "differentiating yin and yang." It always places yin first and yang second, always saying "yin and yang," never "yang and yin." What is the reason behind this?

曰：此即天地之在義，而《易》道之妙用也。天尊地卑，《易》之序也。乃乾天顛下首而周乎地之下，坤地有常而高舉於天之上。於是地天泰，四時成。天德不為首，而地道代終。一陰一陽，往來升降。至三陰三陽水火既濟六爻皆當位，乾坤定矣。反之為一陽一陰，至三陽三陰，乃火水未濟。六爻皆不當位，離坎不續終，而為男之窮矣。

This is exactly the principle between heaven and earth, and also the subtle application of the Way of the Book of Changes. Heaven is exalted and earth is humble, which is the constant order of the Book of Changes; yet the Heaven Trigram (Qian) lowers its head and moves down to beneath the earth, while the Earth Trigram (Kun) rises above the Heaven, thus forming the Tai hexagram, where earth is above and heaven is below. The four seasons thus continue endlessly. Therefore, the Qian hexagram says that the Heavenly Virtue does not remain at the top, and the Kun hexagram says that the earth's path replaces heaven to complete the task. One yin and one yang alternate and rise and fall, until there are three yins and three yangs, forming the Ji Ji hexagram, where water is above fire. All six lines are in their proper positions, and the positions of Qian and Kun are thus determined. Conversely, if it is one yang and one yin, continuing until there are three yangs and three yins, it forms the Wei Ji hexagram, where fire is above water. All six lines are not in their proper positions, and the Li and Kan trigrams fail to reach their endpoints. This is the end of the path for a man.

《繫傳》曰：“陽卦多陰，陰卦多陽。其故何也？陽卦奇，陰卦偶。其德行何也？陽一君而二民，君子之道也。陰二君而一民，小人之道也。”此章闡明《易》道陰陽之大義，為全《易》之關鍵。辨卦爻陰陽之德行，數理之體用，乃學者入手之綱領。故設為問答以明之。

The Great Treatise says: "In a yang hexagram, there are more yin lines, and in a yin hexagram, there are more yang lines. Why is this so? Because the number of strokes in a yang hexagram is odd, while that in a yin hexagram is even. What is their virtue? A yang hexagram is like one ruler and two subjects, which represents the way of the gentleman; a yin hexagram is like two rulers and one subject, which represents the way of the petty person." This chapter explains the great principle of yin and yang in the Way of the Book of Changes, which is the key to the entire Book of Changes. It clarifies the virtue and numerical reasoning of yin and yang lines in the hexagrams, which is the fundamental guideline for those studying the Book of Changes. Therefore, it is specially set out as a question and answer to explain this.

陽卦者，震、坎、艮，皆一陽而二陰。陰卦者，巽、離、兌，皆一陰而二陽。乾坤為各卦之原，且純體不易，其陰陽易知，故不在此設問之列。歷來注《易》家，於“一君二民”、“二君一民”之義，異說紛歧，莫可折衷。皆因泥於一二之數聯屬君民，故無論如何曲折遷就，終不可通。

The so-called yang hexagrams refer to Zhen, Kan, and Gen, each consisting of one yang line and two yin lines. The so-called yin hexagrams refer to Xun, Li, and Dui, each consisting of one yin line and two yang lines. Qian and Kun are the fundamental hexagrams, being pure yang and pure yin respectively, without any mixed lines, so their yin and yang are immediately apparent and thus not included in this discussion. Throughout history, commentators on the Yi Jing have had varied interpretations of the meaning of "one ruler and two subjects" and "two rulers and one subject," but no consensus has been reached. This is because they have been overly focused on matching the numbers "one" and "two" to ruler and subject, leading to interpretations that are convoluted yet still fail to make sense.

孫氏取鄭康成氏《禮記·王制》注云：“一君二民，謂黃帝堯舜。地方千里，為方千里者百。中國之民居七千里，計七七四十九方千里。四裔之民，居五十一方千里。是中國四裔，二民共事一君。二君一民，謂三代之末，以地方五千里。一君有五千里之五，五五二十五，更足以一君。二十五始滿千里之方五十，乃當堯舜一民之地。故曰二君一民。”

Sun's commentary cites Zheng Xuan's annotation on the "Rites" (Li Ji) under "The System of the Ruler," stating: "The phrase 'one ruler and two peoples' refers to the time of the Yellow Emperor and Yao and Shun. The territory was ten thousand li in width and height, forming a square of a thousand li, totaling one hundred such blocks. The people of the Central Plains lived within a distance of seven thousand li, which amounted to forty-nine square thousand li, while the people in the four distant regions lived within fifty-one square thousand li. This was the situation where two groups of people, the Central Plains and the four distant regions, served one ruler. The phrase 'two rulers and one people' refers to the end of the Three Dynasties. The territory was five thousand li in width and height, with one ruler governing five square thousand li. Five times five equals twenty-five, which was still enough to accommodate another ruler. Two such twenty-fives make fifty square thousand li, equivalent to the territory of one people during the time of Yao and Shun, hence called 'two rulers and one people.'"

可謂極迂迴曲折之致，而不敢謂其確合經義。至《朱子語類》，謂“二君一民，試問一個民而有兩個君，看是甚麼樣”。則尤為滑稽矣。宋人講解大意與朱子略同。其實孔子語意，甚為明白。“一君二民”。謂君得其一民得其二也。“二君一民”，謂君得其二民得其一也。“一”“二”兩字，不過表示多寡之意。故下文曰“君子之道”“小人之道”，經義顯豁呈露，無待曲解。何以時歷三千年，經無數之經師大儒而迄未講明？是可怪也。

This can be said to have become extremely roundabout and convoluted, yet one cannot claim it truly aligns with the original meaning of the classics. As for the statement in the "Zhu Zi Yu Le" that "two kings and one commoner, if we ask how a commoner can have two kings, what kind of situation would that be," this is even more absurd. The interpretations of the Song dynasty scholars were roughly similar to Zhu Xi's, all focusing on the numbers of kings and commoners. In reality, Confucius' meaning was very clear: "one king and two commoners" means the king accounts for one part and the commoners for two parts; "two kings and one commoner" means the kings account for two parts and the commoner for one. The words "one" and "two" are merely used to indicate more or less. Therefore, the following text speaks of "the way of the superior man" and "the way of the inferior man." The meaning of the classic is clearly presented, and there is no need for forced interpretations. Why, after three thousand years and through countless master scholars of the classics, has it never been clearly explained? This is truly a strange matter.

見伏動變，謂之四通。“見”者，即本卦所獨動之一爻也（如地雷復，則復之初九即為見）。見之下，即為“伏”（如復內為震，震下即伏巽）。見顯向伏隱，所謂由其可見，推其所不可見，故有見即有伏。見者動，動必有所之。之者往也，動之始也。有所之而之其所，則見者伏而伏者見，所以為變也。

The four terms "see," "hide," "move," and "change" are collectively known as the "Four Communications." "See" refers to the single line in the primary hexagram that becomes active (for example, in the hexagram of Earth over Thunder "Fu," the line "Initial Nine" is the one that is seen). Below the seen line is the "hidden" line (for example, in the hexagram "Fu," the inner trigram is "Zhen," and beneath it is hidden "Xun"). "See" means something visible, while "hide" means something concealed; that is, by understanding the visible, one can infer the hidden, so whenever there is something seen, there must also be something hidden. The line that is seen must move; when it moves, it necessarily goes somewhere. "Zhi" means to go, and it signifies the beginning of movement. When something moves and goes to where it should be, the originally seen line becomes hidden, and the originally hidden line becomes seen. This is called "change."

於八卦之象，兌見巽伏，震起艮止，而八卦之循環變化，悉在其中。故即以此而推之於爻，則亦不外此四者。而爻之性情才用，亦胥可見矣。見知現在，伏知將來。覆以窮其相反之情，變動中爻以盡其曲折之妙。故動而之於伏曰“動”，通變而存其位曰“變”。通一爻而有四卦之通，是以能該隱顯，極常變，以周知天下之務。

In terms of the symbolic representations of the Eight Trigrams, the Trigram 兑 (Dui) signifies manifestation, 兀 (Xun) signifies concealment, 震 (Zhen) signifies movement, and 艮 (Gen) signifies stillness. The cyclical transformations of the Eight Trigrams all include these four aspects. Therefore, applying this principle to the lines (yao) of the hexagram, they also fall within the four categories of "manifestation, concealment, movement, and change." The nature and function of each line can thus be discerned. Manifestation reveals the present, concealment reveals the future; by turning the hexagram upside down, one can explore opposite situations, and by examining the middle lines, one can understand the subtle intricacies within. Therefore, movement leading to the position of concealment is called "movement," and change that remains in the original position is called "change." A single line connects four trigrams, thus enabling the integration of both hidden and manifest aspects, and the comprehensive understanding of constant and change, thereby encompassing all worldly affairs.

見伏動變，循環迭更。如坤初為見，則乾初為伏，而姤復包其中。如復初為見，則姤初為伏，而乾坤又包其中。至其性情之同，則伏與動變，均與可見之爻互相發明。陰陽動靜，流行不息，無往而不還隱而不見之理。故伏卦者，即見卦之所託以變動者也。動在內卦，則陰下而陽上。動在外卦，則陰上而陽下。是陰陽所生之陰陽，所以有少陰少陽之別。變在內外卦者反是。見伏為交，則動變為之摩蕩矣。

The four concepts of appearance, concealment, movement, and transformation alternate in a cycle. For example, if the first line of the Qian hexagram is considered as appearing, then the first line of the Kun hexagram is concealed, and the hexagrams Guo and Fu are included within them. Similarly, if the first line of the Fu hexagram is considered as appearing, then the first line of the Guo hexagram is concealed, and the hexagrams Qian and Kun are included within them. As for the aspects where their nature is the same, the concealed hexagram, along with movement and transformation, can all be understood in relation to the visible line. Yin and yang, movement and stillness, continuously flow without ceasing; there is no such thing as something going away without returning or disappearing forever. Therefore, the concealed hexagram serves as the basis for the movement of the visible hexagram. If movement occurs within the inner trigram, then yin is below and yang is above; if movement occurs within the outer trigram, then yin is above and yang is below—this is the generation of yin and yang from yin and yang, hence the distinction between lesser yin and lesser yang. When transformation occurs within the inner or outer trigrams, the situation is exactly the opposite. The interaction between appearance and concealment leads to the mutual interaction of movement and transformation.

一爻而具四爻之通，如乾二獨動，則坤二伏矣（乾“利見大人”，坤“直方大”）。師二為動，則同人之二為伏矣。故設卦觀象，不可泥於一卦一爻。古人一家之學，雖未必能通貫全經，而一無障礙。如孟氏之旁通，京氏之飛變，虞氏之之正，邵氏之加倍四分，均各有獨到之處。但證之於經傳而合者，固皆有可取。而足與經義相發明，由博反約，慎擇精審，是在學者之神而明之，非一言之所能盡者矣。

Within a single line there is the relationship of connection with the four lines. For example, when the line nine in the second position of the Qian hexagram is active, the line six in the second position of the Kun hexagram is its hidden counterpart. The line statement of Qian nine in the second says "It is advantageous to see a great man," while the line statement of Kun six in the second says "Straight, square, and great." Similarly, when the line nine in the second position of the Shi hexagram is active, the line six in the second position of the Tongren hexagram is its hidden counterpart. Therefore, when setting up hexagrams to observe images, one should not fixate on a single hexagram and its line. Although the doctrines of various ancient scholars may not fully connect with the entire text without obstacles, such as Mengxi's "mutual correspondence," Jingfang's "flying and hidden transformations," Yu Fan's "correcting the line," Shao Yong's method of doubling and the theory of four parts, each has its own unique insights. Any explanation that aligns with the classic texts is inherently valuable. However, to achieve mutual clarification with the meaning of the text, to return from breadth to simplicity, and to carefully select and examine, this depends on the scholar's own intuitive understanding and cannot be fully explained in a single sentence.

胡氏煦《周易函書》，原文多至一百餘卷。後雖節錄為《約注》、《約存》、《別集》，尚有三十餘卷，亦《易》說之大觀矣。其全書綱要，以《繫傳》開而當名辨物一語為主。謂伏羲先天圖，以黑白二色分別陰陽，皆連貫若環，至文王始開而為八卦，開而為六十四卦，以為發千古未有之秘。

In the Qing dynasty, Hu Xu's original manuscript of the Zhouyi Han Shu consisted of more than a hundred volumes. Later, although it was abridged into the works titled Yu Zhu, Yu Cun, and Bi Ji, which still totaled over thirty volumes, it can be considered a significant contribution to the interpretation of the Yi Jing. The main theme of the entire work is based on the sentence from the Xici Zhuan, "open and clarify names and distinguish things," meaning that the sages revealed the hexagrams, making names correspond to things and enabling distinctions. He said that Fuxi's Earlier Heaven diagram used black and white to differentiate yin and yang, connected in a circular manner. It was only with King Wen that it was "opened" to become the Eight Trigrams and then the sixty-four hexagrams, which he believed revealed a secret unknown since ancient times.

其實周子太極圖，陰陽相互，分為三層。胡氏所繪之先天、小圓、大圓圖，即由周子太極圖衍而成之。又拆之為八卦六十四卦，謂為文王所開，其牽強固不待智者而知，即其本書中亦往往不能自圓其說。蓋八卦不但有其象，尚有其數。若以黑白二色分別陰陽之爻，將一九四六之數，亦以黑白二色代之乎？其誣不待辨而明矣。然其於《易》理，致力頗深。融合漢宋，時有心得，瑕不掩瑜。三書之可取者甚多。其八字命爻之說，尤為詳人所略，語極精到，大有畀於初學，特約其大意如左。

In fact, Zhou Dunyi's "Diagram of the Supreme Ultimate" features black and white yin and yang interweaving, divided into three layers. Hu Xu's Earlier Heaven Diagram, Small Circle Diagram, and Great Circle Diagram were derived from Zhou's "Diagram of the Supreme Ultimate." He further broke them down into the Eight Trigrams and the sixty-four Hexagrams, claiming that these were "opened up" by King Wen. This reasoning is clearly forced, and even a person without great intelligence can see through it. In his own writings, he often fails to be consistent. The Eight Trigrams not only have symbolic forms but also numerical aspects. If black and white are used only to distinguish yin and yang lines, then numbers such as one, nine, four, and six—how could they be represented by black and white? The inadequacy of his theory is evident without needing argument. However, he made deep efforts in understanding the principles of the Book of Changes, integrating Han learning and Song learning, and occasionally had insightful realizations. His shortcomings cannot obscure his merits, and there are many valuable points in his three works. Among these, his explanation of the "Eight Characters and Lines" is particularly detailed, addressing aspects others have overlooked. His statements are precise and helpful for beginners, so I have specially summarized the main points of his work below.

聖人命爻之義，有十二樣筆法：陰陽各六，九六分稱是也。然其因卦論爻，因爻論卦，而三百八十四爻之義，已各各迥別。顧此十二樣筆法，要其寓意止有八字：初、上、九、六、二、三、四、五是也。

The sage assigned names to the lines of a hexagram, expressing their meanings in twelve different ways. A hexagram has six positions; when a yang line occupies these positions, it is called 'Initial Nine,' 'Nine in the Second,' 'Nine in the Third,' 'Nine in the Fourth,' 'Nine in the Fifth,' or 'Nine at the Top.' When a yin line occupies these positions, it is called 'Initial Six,' 'Six in the Second,' 'Six in the Third,' 'Six in the Fourth,' 'Six in the Fifth,' or 'Six at the Top.' Yang and yin each have six forms, distinguished by the terms 'Nine' and 'Six,' making a total of twelve. However, although the naming follows these twelve patterns, when applied to specific hexagrams, the lines must be interpreted according to the nature of the hexagram and the situation of the line. Thus, among the 64 hexagrams and 384 lines, each line has a unique meaning. In the end, the characters used in these twelve forms are only eight: 'Initial,' 'Top,' 'Nine,' 'Six,' 'Second,' 'Third,' 'Fourth,' and 'Fifth.'

何以初命為初，上命為上也？曰：聖人立卦，止於三爻，不以兩畫，不以四畫，其妙正在於此。何也？以天下之物，各有其位。位之所乘，各有其時。時與位合，而參差不齊之數出焉。聖人設卦立象，凡以考時之所值，位之所乘而已。然時有三候，位有三等，故立卦亦止於三爻。

Someone asked: Why is the lowest line called "Chu" and the top line called "Shang"? The answer is: The sage created the structure of the hexagram using only three lines, not two lines or four lines. The profound meaning lies exactly here. Why is that? Because all things in the world occupy a position, and each position carries a particular time; when time and position combine, they produce the varied and diverse "numbers." The sage established the hexagram and created images, which was simply to examine what time a thing is appropriate for and what position it occupies. Time can be summarized as the three phases: initial, middle, and final. Position can be summarized as the three levels: upper, middle, and lower. Therefore, the hexagram is established with only three lines.

何云時有三候？曰：此概辭也。今但取一時，銖銖寸寸而較之，雖累百千萬，不足盡此一時之數矣。譬自盤古開天以及堯舜，其中歷年原不可考。今以三候約之，曰此古之初，此古之中，此古之末，則無不可以意會者(近世科學家研究歷史地質等學者亦概用此法)。又一歲十二月，今亦以三候約之，為歲之初，歲之中，歲之末，亦無不可心意會者。下至時日亦然。是流行之機，或遠或近，或舒或促，皆無有踰此三候者也。

Why is it said that time has only three phases? This is a general statement. If we take a period of time and divide it into minute parts for detailed calculation, even if we accumulate hundreds of thousands of units, we still cannot count the number of units within that time. For example, from the time of Pangu creating the world up to the time of Yao and Shun, the exact number of years is unknown. Now, by using the three phases, we can roughly divide it into the beginning of ancient times, the middle of ancient times, and the end of ancient times, and everyone can understand it. (Modern scientists studying history and geology also mostly use this method of dividing periods.) Similarly, the twelve months of a year are also divided into three phases, called the beginning of the year, the middle of the year, and the end of the year, which is also easy to understand. The same applies to a day or an hour. This shows that the mechanism of time flowing, whether the span is long or short, and whether the pace is slow or fast, cannot go beyond these three phases: beginning, middle, and end.

何云位有三等？曰：此亦概辭也。今但取一物銖銖寸寸而數之，累千百萬，不足盡此一物之位矣。譬若立五尺之竿於此，以三等約之，上者上，中者中，下者下，盡之矣。又立千尺百尺之竿於此，亦以三等約之，上者上，中者中，下者下，盡之矣。是形器之屬，或高或卑或廣或狹，均無有踰此三等者也。

Why is it said that positions can only be divided into three categories? This is a general statement. If you take an object and measure its parts one by one, counting them to millions, you would never exhaust all the positions of that object. For example, if you set up a pole that is five feet high here, using the three categories to summarize, the upper part is called upper, the middle part is called middle, and the lower part is called lower, and thus it is fully described. Similarly, if you set up a pole that is hundreds or thousands of feet high, using the same three categories, the upper part is called upper, the middle part is called middle, and the lower part is called lower, and thus it is fully described. This shows that any object with form, whether tall or short, wide or narrow, cannot go beyond the three categories of upper, middle, and lower.

況上古民淳事簡，以三候約時，以三等約位，得其大概，已可共喻。後世知識日開，人事日繁，一歲之候，分而為月，又分而為日，又分而為時刻分秒，細分之至於毫釐絲忽之不可盡。其於位之大小長短，亦復如是。皆其細已甚者也。至約以三等三候，曾有出聖人之範圍者乎？

Moreover, in ancient times, people's customs were simple and sincere, and affairs were straightforward. Using three phases to approximate time and three categories to approximate space was sufficient to convey the general idea and enable mutual understanding. However, in later generations, knowledge has gradually become more enlightened, and human affairs have become increasingly complex. Time has been divided first into months, then into days, then into hours, minutes, seconds, and even further into fractions such as hair, thread, and so on, which can never be fully divided. Similarly, the measurement of space's size and length has also become increasingly detailed. All of this is excessive in refinement. Yet, if we still use the three categories and three phases to approximate, is there anything that would go beyond the scope set by the sages?

凡有位者必有時，於是乎有上之時，中之時，下之時。凡有時者必有位，於是乎有初之位，中之位，末之位。聖人慾以卦象盡天下之物，則不得不體物象所自具之時位而命之爻。所以三爻之設，決不可以增減也。

Anything that occupies a position must exist within a certain period of time, thus there are times of upper position, middle position, and lower position. Anything that exists within time must occupy a certain position, thus there are initial positions, middle positions, and final positions. The sage uses hexagrams to encompass all things under heaven, and therefore must name the lines according to the inherent time and position of the things themselves. For this reason, the arrangement of the three lines must never be increased by one line, nor decreased by one line.

然就三爻而立之名，則取時必遺位，取位必遺時。聖人知陰陽必偶，而物生必先氣而後形，於是乎立為重卦。以時而命內卦之初，明乎氣之肇端，於此始也。以位而命外卦之上，明乎形之成質，於此定也。周公釋爻，每兼時位，職是故也。時陰而位陽，時虛而位實。時由乾出，位由坤始也。

But if only the third line is used to name, taking 'time' would lose 'position', and taking 'position' would lose 'time', making it difficult to balance both. The sage knew that yin and yang must always come in pairs, and that all things are first generated by qi and then take form. Therefore, he overlapped single trigrams to form hexagrams with six lines: using 'time' to name the first line of the inner trigram, called 'initial', to indicate the beginning of qi's movement; using 'position' to name the top line of the outer trigram, called 'upper', to indicate the completion of form. Zhou Gong often spoke of both time and position in his line statements, precisely for this reason. In terms of nature, time belongs to yin and position to yang; time is abstract and position is concrete. In terms of origin, time arises from the active movement of Qian, and position begins from the stillness of Kun.

流行不息者時，乾道之動用也。故不可定之以位。鎮靜而有常者位，坤德之靜體也。故不可定之以時。卦爻剛柔，悉出乾坤。無一卦一爻無剛柔，則無一卦一爻無動靜，則無一卦一爻不具此時位者矣。然時出於乾，而陰爻亦得言之；位出於坤，而陽爻亦得言之者，此又乾坤相須之大用，不可偏廢者也。

What is in constant motion is "time" (时), which is the dynamic aspect of the Heaven (乾) principle, so it cannot be confined by fixed positions; what is still and has a constant order is "position" (位), which is the static aspect of the Earth (坤) principle, so it cannot be confined by flowing time. The yao (lines) of the hexagrams are all derived from Heaven and Earth, and no hexagram or line lacks both yin and yang. Therefore, no hexagram or line lacks both movement and stillness, and thus no hexagram or line does not simultaneously possess time and position. However, although time originates from Heaven, yin lines can still discuss time; although position originates from Earth, yang lines can still discuss position. This is the great function of Heaven and Earth relying on each other, and neither side should be neglected.

言初而不言中末，言上而不言下中何也？曰：《易》為上古之書，文字初起，不能不簡而賅，使人便於傳習，而深致其思。後世文字既繁，遂連篇累牘而不止，反不若古人之簡而能賅其要也。如屯卦繼乾坤而居《序卦》之首，曰剛柔始交。剛柔者，乾坤也。交者，剛柔之互也。始者賅六十二卦之辭，聖人知六爻各一其時位，而又不能合一時位，乃賅以一字，即以初字著其時之理於下，而以上字著其位之理於上，各從其所重而定之云爾。

Someone asked: Since time is divided into beginning, middle, and end, why do we only mention 'beginning' and not 'middle' or 'end'? And since position is divided into upper, middle, and lower, why do we only mention 'upper' and not 'lower' or 'middle'? The answer is: The Zhou Changes is an ancient classic, and the language was just beginning to emerge. Therefore, it had to be concise yet comprehensive, making it easy for people to transmit and study, and to think deeply about its meaning. Later generations used more elaborate language, often writing lengthy passages that never ended, yet they were not as effective as the brevity of the ancients, who could still capture the essence. For example, the hexagram Zun comes immediately after Qian and Kun and is placed first in the 'Sequence of Hexagrams'. The 'Sequence of Hexagrams' says it 'marks the beginning of the interaction between the strong and the flexible'. 'Strong and flexible' refer to Qian and Kun, and 'interaction' refers to the mutual engagement of the strong and the flexible. The single character 'beginning' encompasses the meaning of all the other sixty-two hexagrams. The sage understood that each of the six lines has its own time and position, yet they could not be combined into a single time or position. Therefore, he used one character to summarize them: the lower line is marked with 'beginning' to indicate the principle of time, and the upper line is marked with 'upper' to indicate the principle of position. Each is named according to the aspect it emphasizes.

乾以始之，故舉其端而言初。坤以終之，故竟其委而言上。又使知卦既有初，則其為中為末舉可類推。既有上，則其為中為下舉可意想也。又使知上與初對，則上字原可以賅末。初與上對，則初字原可以賅下。皆簡而能賅，引端而無待竟委者也。《周易》卦爻，文字所不能賅者，而象無不可以賅之。象固不可限量也。

Heavenly Stem Qian governs the beginning, so it is called "Initial" to indicate the origin; Earthly Stem Kun governs the end, so it is called "Upper" to indicate the conclusion. This naming convention allows people to understand that if a hexagram has an "Initial" line, the middle line and the final line can be similarly inferred; if it has an "Upper" line, the middle line and the lower line can also be imagined in the same way. It also shows that "Upper" and "Initial" are opposites, and the term "Upper" inherently includes the meaning of "end"; similarly, "Initial" and "Upper" are opposites, and the term "Initial" inherently includes the meaning of "beginning." This is concise yet comprehensive, requiring only the mention of one end without needing to describe the whole beginning and end. In the hexagrams of The Zhou Changes, any meaning that words cannot fully express can be fully expressed through the hexagram images—because images themselves have no limits.

內卦為來，外卦為往。初則來之始，上則往之極也。用一初字，是欲人溯源於太極。用一上字，是欲人知極則必反也。有往則必有反，有來則必有初。如人從何處來，則必有最初發足之地，非僅向發足時考之也。是要窮到地頭，知其來自何處耳。

In the six lines of divination, the lower three lines form the inner trigram and belong to 'coming'; the upper three lines form the outer trigram and belong to 'going'. The first line is the starting point of 'coming', and the top line is the end of 'going'. Using the character 'initial' (初) is to lead people to trace back to the source, the Taiji. Using the character 'top' (上) is to make people understand that when something reaches its extreme, it must return. If there is going, there must be returning; if there is coming, there must be an initial point. Just as asking where a person comes from, he must have a starting place, not just the time he began, but one must trace back to the very beginning to find out where he really comes from.

緣爻象從來之處，非可易察。故孔子曰“其初難知”。若其既有所往，自無往而不反之理。今以一字說到極處，而必反之理即在其中。由其上之已無可加，則往到極處，已顯而易明。故孔子曰“其上易知”也。

Since the origin of the lines (yao xiang) is not easily discernible, Confucius said in the "Great Treatise" (Xici) part two, "At the beginning, it is difficult to know." However, once something has already moved forward, there is no reason for it to go forward without returning. Now, using the character "shang" (upper) brings the statement to its conclusion, thus containing the principle that "extreme movement must reverse." Because there is nothing above "shang," having reached the extreme, the situation becomes clearly evident, so Confucius said, "At the uppermost point, it is easy to know."

今以上之一字例諸初，則初當曰下。以二三四五之序次例諸初，則初當曰一。乃不曰下不曰一而特命為初，此正聖人寓義之最精處。因《易》之卦爻，原本先天，在陰陽未判之先，渾然一太極耳。逮一畫開天，自無出有，乾元一亨，萬物之始，悉資於此。但形質未成之先，止有氣耳。氣機初萌，實托始於乾元，毓靈於太極。

Taking the character 「上」 to compare with the very last line, it should be called 「下」; taking the sequence numbers two, three, four, and five to compare with it, it should be called 「一」. Yet it is neither called 「下」 nor 「一」, but instead is named 「初」. This is precisely where the sages have embedded the most subtle meaning. Because the lines of the hexagrams in the Zhou Yi originate from the Earlier Heaven: before yin and yang were differentiated, there was only a single, undivided Taiji. When the first line was drawn, the void gave rise to being, and the creative power of Heaven (Qian) began to flourish, initiating all things. However, before form and substance had solidified, there was only Qi. The Qi's movement had just begun, actually relying on the creative power of Heaven and receiving its spiritual essence from the Taiji.

方斯時也，既無實質可指以定其位，非考之以時，曷由辨乎？顧時有三候而初則氣機之方萌，方從太極天心流衍而出，故特用一“初”字，以發明卦爻所從出源頭。而“來”字之義，亦即寓於“初”字之中。《彖》以內卦稱“來”，即從“初”字出也。凡物既有初，則此後豈有窮盡？故不言中末，是初之重於中末也。位既定於上，則下焉皆其所統。故不言下中，是上重於下中也。

At this very moment, there is no actual form or substance to point to and determine its position. Without examining it from the perspective of "time," how can we distinguish it? Although time is divided into three phases, the first line is precisely the moment when the vital energy just begins to stir, and it is the very first moment when the primordial energy from the Supreme Ultimate Heaven's center starts to flow. Therefore, the term "initial" is specially used to indicate the source from which the hexagram and its lines originate. The meaning of "coming" is also contained within the term "initial." The Commentary on the Judgment refers to the inner trigram as "coming," which is precisely derived from this "initial" concept. Since all things have a beginning, how could they ever have an end? Therefore, only "initial" is mentioned rather than "middle" or "end," showing that "initial" is more significant than "middle" or "end." Since the position is fixed as "upper," all the lines below are under its jurisdiction. Therefore, only "upper" is mentioned rather than "lower" or "middle," showing that "upper" is more significant than "lower" or "middle."

八卦本於太極，而太極無象可求。故以兩儀初成之爻，命之曰初。為其有形可睹，自此一爻而始。故二三四五皆紀之以數。乃初之一爻，非數所能始，以有太極在其前也。巽以伏卦而取震象一陽未生之始，亦曰無初，是正有無分界之始，亦即此初字之義也。緣其分位，本屬兩儀，又不得上侵太極之一。論其成質，實居有形之最先，又不得連太極而序之。以下侵中爻之二，故以初命爻。使人探本窮源，由其能來之故。而追索於所以有初者，果何在耳？

The eight trigrams originate from the Taiji, but Taiji has no form that can be sought. Therefore, the first line was named "Chu" because visible forms begin with this line. The second, third, fourth, and fifth lines are numbered, but the first line cannot be numbered, since there is a Taiji before it. The trigram Xun derives its image from the hidden trigram Zhen, representing the beginning when one yang line has not yet emerged. The line "Wu Chu You Zhong" in Xun's fifth line indicates that "Chu" is the starting point of the boundary between "having" and "not having," which is the meaning of the character "Chu." In terms of its position, it belongs to the two principles but cannot encroach upon the "one" of Taiji above it. In terms of its formation into tangible form, it is the first among visible things and cannot be combined with Taiji, thus encroaching upon the second line below. Therefore, the term "Chu" is used for this line to encourage people to trace back to the origin, from its ability to "come," and further inquire: what is the origin that gives it this "Chu"?

以初爻之義例諸上，則上當曰末。以二三四五之序例諸上，則上當曰六。今不曰末不曰六而特命為上者，言乎其爻極於此止於此也。蓋立卦定於三爻，重卦止於六畫。伏羲畫卦至六爻，已成六十四象，足以備天下萬事萬物之理。六爻之外，無以復加。聖人即寄無以復加之義，於最後所成之一爻，而命之為上，言此外已無可上也。

The meaning of the first line is compared with the top line, which should then be called "末" — "初" refers to the beginning of time, and naturally its opposite is the end of time. When comparing the sequence numbers of the second, third, fourth, and fifth lines with it, it should be called "六". Now, it is neither called "末" nor "六", but instead named "上", meaning that this line is the ultimate and the final one. Since a single trigram is fixed at three lines and a compound trigram stops at six lines, Fuxi drew the trigrams up to six lines, completing all sixty-four trigrams, which are sufficient to encompass the principles of all things in the world. Beyond the sixth line, there is nothing more to add. The sage expressed the meaning of "no further addition" in the last line drawn, naming it "上", meaning there is no higher or more exalted position beyond it.

二三四五紀之以數，而上獨非數者，以數之所衍，原無終窮之時。即上之一位，亦非數之所能極也。然以九二六二之類比之，而初之九六，何獨在下？蓋因乾元之亨，先氣後形；而氣之將至，則無形可執。今觀揲蓍求卦之時，分二掛一，揲四歸奇，明知此爻之形體，必將有成，則是此爻已有其初矣。

The second, third, fourth, and fifth lines are all referred to by numbers, but the line called "upper" is not numbered. This is because the derivation of numbers is endless, and even the position of "upper" cannot be exhausted by numbers. However, when we compare this with terms like "nine in the second" and "six in the second," why is the first line called "nine at the beginning" and "six at the beginning," with the numbers placed after the term "beginning"? This is because the principle of the Creative (Qian) initiates the process of generation and movement, first there is the vital energy and then the form. When the vital energy is about to manifest but has not yet fully formed, there is no form to grasp. Consider the process of divination with yarrow stalks: the stalks are divided into two groups, one stalk is hung, and the remaining stalks are counted in groups of four, with the remainder held in the fingers. At this point, it is already known that the line will certainly take form, meaning that the line already has its "beginning."

然氣至而形未著，則陰陽之體猶未可定，故不能定之以位，而但可考之以時，而稱之為初。必待三變既足，察其數之多少，有陰陽老少之可辨，乃始有九六之可稱矣。譬若妊娠將娩，當胞胎乍轉，業已知其生之初矣。然分別男女，必待既生以後，審其形體而後能定。是時之可征者在先，而形之可觀者在後。故九六在初字之下也。

However, although the qi has arrived but the form is not yet evident, the nature of yin and yang remains undetermined, so it cannot be fixed by 'position,' but must be examined through 'time,' hence it is called 'initial' or 'beginning.' Only when the three transformations are complete and the number obtained is observed, distinguishing the old and young of yin and yang, can 'nine' and 'six' be used. This is like a woman in childbirth, when the fetus begins to move, one already knows the beginning of its birth; but to determine the sex, one must wait until after birth to observe the form. Thus, the verifiable 'time' comes first, and the observable 'form' comes later, which is why the characters 'nine' and 'six' are placed below 'initial.'

二三四五別之以數，不與初上同類，何也？曰：聖人立卦之法，取象於天地之化育。上爻覆之於上，天也。初爻承之於下，地也。其中所有，則資始資生之化，所稱為萬物者也。萬物成形之後，其類實繁。非紀以數，曷由辨之？曰初上何獨不記之以數也？曰：初在理氣相接之始，非數之所能始也。上爻極盡而反，貞下又復起元，豈有終窮之數？故亦不以數紀也。

Someone asked: Why do the second, third, fourth, and fifth lines use numbers to distinguish them, while "initial" and "top" lines are not numbered? The answer is: The sage established the hexagram by taking inspiration from the transformation of heaven and earth generating all things. The top line is at the very top, representing heaven; the initial line is at the very bottom, representing earth; those in between are the creative power of heaven and the nurturing power of earth, which give rise to all things. After all things have taken form, their varieties are countless. Without using numbers to record them, how can they be distinguished? Another question: Why are the initial and top lines not numbered? The answer is: The initial line is at the beginning where principle and energy first meet, something that cannot be marked by "number." The top line reaches the end and then returns, completing one cycle and beginning anew, which is called "Zhen Xia Qi Yuan." Where is there an end to numbers? Therefore, they are not numbered.

初上二爻，九六在下；二三四五，九六在上。何也？曰：卦之初爻既成，陰陽兩象，確有定體。然後審定陰陽所至之分數，如陰陽到二分，便以為九六之二；到三分，便以為九六之三。若嬰孩既生，業已男女可辨，然後可以數紀其長幼之次序。故二三四五在九六之下也。

The first and top lines of a hexagram have the terms "nine" (九) and "six" (六) written after the line name, as in "initial nine" (初九) and "top six" (上六). However, for the second, third, fourth, and fifth lines, the terms "nine" and "six" are written before the line number, as in "nine two" (九二) and "six five" (六五). Why is this so? The answer is: once the first line of a hexagram has taken form, the yin and yang images have definite forms, and then the progression of yin and yang is determined. When the progression reaches the second stage, it is called "nine two" (九二) or "six two" (六二); when it reaches the third stage, it is called "nine three" (九三) or "six three" (六三). This is like a newborn infant who has already been born; gender can be distinguished early on, and then the order of seniority can be determined by numbers. Therefore, the numbers "two," "three," "four," and "five" are placed after "nine" and "six."

卦至上爻，九六又復在下。何也？曰：上為窮極將返之時，其上更無可加。是上之一位，即此卦之大終大止，其位得而主之。陰陽至此，皆不能以自主。泰之復隍，否之傾否，剝之剝廬，皆謂其極則必反。故九六字在下也。

When a hexagram reaches the top line, the characters "nine" and "six" are placed after "upper," becoming "upper nine" and "upper six." This is because the top line is at the point of reaching the extreme and about to return. There is no room left to add anything above it, so the position "upper" signifies the end and the cessation of the hexagram. At this point, yin and yang can no longer act independently. The "upper six" in the hexagram of Tai says "the city returns to the moat," the "upper nine" in the hexagram of Pi says "turning Pi," and the "upper nine" in the hexagram of Bo says "stripping the house." These all describe how when something reaches its extreme, it must turn back. Therefore, the characters "nine" and "six" are placed after "upper."

既以初為來處，則來之義只可言於初。既以上為往時，則時之義只可言於上。乃內三爻均言來，外三爻均言往。何也？曰聖人以三畫成卦，則此三爻雖陰陽上下不同，莫不同具此一卦之性情，又不可執定實有此等三畫之象，確然植立於此而不可易也。

Since "initial" is taken as the origin, the meaning of "coming" should only refer to the first line; since "upper" is taken as the destination, the meaning of "time" should only refer to the top line. However, the Commentary on the Judgment says that when it speaks of "coming," it includes all the inner three lines as coming, and when it speaks of "going," it includes all the outer three lines as going. Why is this so? The answer is: the sage composed a hexagram using three lines, and although these three lines have both yin and yang, and have upper and lower positions, they all together possess the nature and disposition of this hexagram. At the same time, one must not rigidly think that there are actually three lines clearly drawn there, firmly established and unchangeable.

只是聖人假此著數，以探討太極陰陽將形未形之氣機，不能無太少動靜之別，而因畫出奇偶以擬議陰陽相變之分數。其內外上下多寡，純雜有如是耳。氣機無截然可分之候，故三畫只宜作一卦看。氣機亦非形體之可似，故亦不必以連斷之形體拘也。重卦雖分內外，不過體用兩端而已。今既同為內卦，則皆可自初而言來；同為外卦，則皆可因上而言往矣。

The sages merely used the numbers of the yarrow stalks as a basis to explore the vital energy movements of the Taiji and yin and yang before they take form. This vital energy cannot be without distinctions of the sun, lesser sun, great yin, and lesser yin, as well as movement and stillness. Therefore, they drew odd and even lines to symbolize the proportions of the mutual transformation of yin and yang. The terms of inner and outer, upper and lower, more and less, pure and mixed are all about this. The vital energy has no clear boundaries, so the three lines should be viewed as a single trigram. Also, the vital energy is not like a physical form that can be imitated, so it should not be restricted by continuous or broken lines. Although compound trigrams are divided into inner and outer, they are merely the two aspects of 'body' and 'function'. Now that they are all inner trigrams, they can all be discussed from the perspective of 'initial' and 'coming'; and since they are all outer trigrams, they can all be discussed from the perspective of 'upper' and 'going'.

初爻考之以時，然欲追尋來處，則又宜在位上考究。上爻定之以位，然欲人知為窮極將反，則又宜在時上著意。即此時位兩字，所謂有位中之時，有時中之位。參伍錯綜，維精維妙維肖。神而明之，更非言語可盡矣。

The first line is examined from the perspective of "time," but to trace its origin, one must investigate it from the standpoint of "position." The top line is determined by "position," but to make people understand that it reaches its limit and will return, one must pay attention to "time." With regard to the two characters "time" and "position," there is a distinction between "time within position" and "position within time," which interweave and intertwine, reaching an extremely subtle, skillful, and accurate level. As for the ability to grasp this intuitively and apply it skillfully, that is beyond the reach of words.

或問：讀《易》之方法如何？曰：必先讀經。或曰：經文奧衍，初學者不能驟解，必先得明白解釋之注本，而後經始可讀。現所通行之讀本，大都為朱子《本義鄉。而《本義》之解釋既略，且多以不解解之。往往曰“其象如此其占如此”，而究其何以如此，仍不得而知。初學讀之，不但茫無頭緒，且如其解以解經文，亦味同嚼蠟。雖極好學者，讀不終卷，已昏倦欲睡，則經又烏能讀乎？

Someone asked: What method should be used to study the Zhou Changes? The answer was: One must first read the text itself. The other person said: The text is profound and complex, and beginners find it difficult to understand at first. They must first have a commentary that explains it clearly, only then can they proceed to read the text. Currently, the most commonly used editions are Master Zhu's The Original Meaning of the Zhou Changes. However, the explanations in The Original Meaning are either too brief or often take 'not explaining' as explaining: frequently stating only 'its image is like this, its divination is like this,' but not explaining why it is so. Beginners reading it find themselves lost and without direction; following its interpretations to understand the text is like tasting wax. Even the most diligent students become drowsy after reading just one volume, so how can they ever finish the text?

曰：不讀經而看注無益也。不熟讀經而看注，亦仍無益也。讀經之方法，宜先讀最後之《說卦傳》，次讀上、下《繫傳》，然後讀上、下《經》，則於卦位、爻位、象義及彖、象、爻之材德，已略有頭緒。以讀經文，自可領會。必逐卦讀之極熟，認之極清，任舉一爻，而各爻之文相類而相似者，俱可列數；任舉一卦，而反正上下變互諸卦，俱可意會。更有未喻者，然後求之諸家之註釋，方能擇善而從，確獲其益也。

Answer: Not reading the classics and only looking at the annotations is of no benefit; reading the classics without mastery and then looking at the annotations is also of no benefit. The proper order for reading the classics should be: first read the "Commentary on the Hexagrams," then the "Great Treatise" above and below, and finally the Upper and Lower Classics. In this way, one will already have a general understanding of the positions of the hexagrams, the lines, the principles of taking images, and the material qualities and virtues expressed in the彖statements, 象statements, and 爻statements. One must read each hexagram thoroughly until it is completely familiar and clearly understood. To the point where, if any line is given, one can list all the lines similar to it; if any hexagram is given, one can clearly identify its opposite hexagram, its corresponding hexagram, the hexagram formed by exchanging the upper and lower trigrams, and the hexagrams formed by the interacting trigrams. Only when reaching this level and still having some unclear points should one consult the annotations of various schools, at which point one can choose the good and follow it, and truly gain benefit.

曰：諸家之註釋，浩如煙海，宜先閱何種為最善？曰：《易》有四道，辭變象占。尚辭者莫備於《程傳》，深有得於潔淨精微之旨。然其所短者，往往離象數以言理，而有時不免於鑿空。是宜參以紀慎齋之《易問》及《觀易外編》(紀氏名大奎，臨川人，有《雙桂堂叢書》。以性理說《易》而不離於象數，能會漢宋兩派之說而擷其精，乃近人《易》說之最善者也。)，庶可以補其闕失矣。

Another question: With so many commentaries available, which one should be read first? The answer is: The Great Treatise says that the Book of Changes has four approaches—words, transformation, images, and divination. Those who follow the approach of valuing words, there is no commentary more complete than Cheng Yi's Yichuan Commentary on the Changes. It thoroughly grasps the principle of "cleanliness, quietness, precision, and subtlety" of the Book of Changes. Its shortcoming, however, is that it often ignores images and numbers and only discusses meaning and reason, sometimes leading to speculative statements without foundation. Therefore, one should refer to Ji Shenzhai's Yi Wen and Guan Yi Wai Bian (Ji's name was Da Kuai, from Linchuan, Jiangxi, who compiled the Shuanggui Hall Collection. He explained the Book of Changes through the principles of nature and reason without abandoning images and numbers, and was able to integrate the doctrines of the Han and Song schools, taking the essence of both. He is the best among modern commentaries on the Book of Changes). In this way, one can make up for the shortcomings of the Cheng Commentary.

至於象數，宜從漢學。但兩漢《易》說之存於今者，幾無一完本。《李氏集解》雖蒐羅宏富，然東鱗西爪，初學每苦其不能貫串。則宜先閱瞿塘來知德氏《集註》，其於象也較詳，且處處為初學說法，反覆周詳，惟恐讀者不能瞭解。與貌為艱深，故意令人無從索解者，殊有上下床之別。

As for the section on images and numbers, one should follow the Han dynasty scholarship. However, the commentaries on the I Ching from the Han dynasty that have survived to the present are almost none in complete form. Although Li Dingzuo's Collected Explanations of the Zhou Changes from the Tang dynasty is extensive in its collection, it is fragmented and scattered, making it difficult for beginners to grasp as a whole. Therefore, one should first read Lai Zhide's Collected Commentaries on the Zhou Changes from Sichuan's Qutang. It provides a detailed explanation of images and is always considerate of beginners, repeatedly reminding readers to ensure they understand. Compared to those books that deliberately appear obscure and make it hard for readers to grasp, the difference is as great as heaven and earth.

惟來氏僻處巫峽，僅憑自力之研求，於古人之著述，未得遍覽，故其問有自以為創解者，實早為昔人所已言。如用九用六之類，不勝枚舉。而其錯綜之說，尤為後人所攻擊。蓋儒流積習，凡講學者，或漢或宋，必標明一種旗幟，而附他人門戶之下，而後其學說始克成立。雖亦不免一方之攻擊，而必能得一方之擁護。來氏之學，非漢非宋，故受兩方之攻擊，幾體無完膚矣。

Lai Zhide lived in the area around Wuxia and relied solely on his own efforts in research, without having read widely through the writings of ancient scholars. Therefore, his book contains some views he considers new insights, but in fact, these ideas had already been expressed by earlier scholars. For example, terms like "Yong Ji" and "Yong Liu" have numerous examples. Moreover, his theory of "cuo" and "zong" has been particularly criticized by later scholars. Originally, the tradition among Confucian scholars was that anyone who engaged in scholarly study had to align either with the Han learning school or the Song learning school, always taking a clear stance and attaching themselves to a particular school of thought in order for their doctrines to be established. Although this approach inevitably led to criticism from one side, it also ensured support from the other. Since Lai's learning did not belong to either the Han or the Song schools, he faced attacks from both sides, almost being completely refuted.

然來氏於象，亦僅得十之五六，而於數尤未能辨晰。蓋數雖原本於河洛，但《易》有體數，有用數，有五行數(即納音數)，有納甲數，各有不同。來氏不辨於此，故遇言數之卦，開口便錯，是則其所短矣。

But Lai Shi only understood the images to a degree of five or six tenths, and he could not clearly analyze the numbers. Although numbers originate from the Yellow River Chart and the Luo Writing, the Book of Changes contains different kinds of numbers: the essential numbers, the applied numbers, the Five Phases numbers (also known as Nayin numbers), and the Najia numbers, each distinct. Lai Shi failed to distinguish between them, so whenever he encountered a hexagram involving numbers, he made mistakes immediately. This was his weakness.

曰：《易》注之言數者，宜閱何書？曰：《易》之言數，皆根於孔子《繫傳》之天一地二至天九地十。河洛實數之淵源，雖漢學家盡力辨駁，而數理實有其徵驗，非空言所可掩也。朱子《啟蒙》演繹頗詳，宋人丁易東氏之《數衍》，及近人江慎修氏之《河洛精蘊》，更推闡盡致。餘如宋末朱元昇氏之《三易備遺》，於五行數尤有獨到之處。

Another question: Which books should be read for understanding the numerical aspects of the Book of Changes? The answer is: The Book of Changes discusses numbers, and all of this originates from Confucius' Great Treatise, specifically the passage from "Heaven one, Earth two" to "Heaven nine, Earth ten"—odd numbers one, three, five, seven, and nine belong to Heaven, while even numbers two, four, six, eight, and ten belong to Earth. The Yellow River Chart and the Luo Writing are the actual sources of these numbers. Although Western scholars have strongly argued that they were later fabrications, the numerical principles indeed have verifiable applications and cannot be concealed by mere verbal debate. Zhu Xi's "Easy Enlightenment on the Book of Changes" provides a very detailed exposition. The "Derivation of Numbers" by Ding Yidong of the Song dynasty and "The Essence of the Yellow River and Luo Writing" by Jiang Shenxiu of the modern era offer even more thorough explanations. In addition, Zhu Yuansheng of the late Song dynasty's "Complete Remains of the Three Books of Changes" has particularly unique insights into the numerical aspects of the Five Phases.

至邵子《皇極》先天數，雖自成一家(邵子專以一二三四五六七八分陰陽剛柔之太少，乾兌離震但為一二三四之代名詞耳。惟先天圓方二圖於陰陽消長推衍精詳，妙合天然，是於六日七分之外又另闢蹊徑。然以之入用，仍取京圖。)，然於卦義發明實多。朱子《啟蒙》，採用其說十之八九，自為言象數者不可不讀之書也。揚子《太玄》，演數甚精，足與《易》道相證。學者果有餘暇，不妨涉獵及之，以廣理趣。若溫公之《潛虛》，更不逮《太玄》遠矣。

As for Shao Kangjie's "Earlier Heaven" numbers in his work "Huangji Jingshi," although they form their own school of thought, Shao used only the numbers one, two, three, four, five, six, seven, and eight to distinguish yin and yang and the qualities of hardness and softness. The trigrams Qian, Dui, Li, and Zhen are merely substitutes for one, two, three, and four respectively. Only the circular and square diagrams of the Earlier Heaven provide a detailed and precise analysis of the waxing and waning of yin and yang, skillfully harmonizing with nature. This is a separate path beyond the "six days and seven parts." However, if one really wants to apply it, one should still refer to Jing Fang's diagram of the trigram energies. In terms of elaborating on the meanings of the trigrams, Shao's work is indeed very rich. Master Zhu's "Yixue Menglun" adopts Shao's views to a large extent, and it is a book that those who study the imagery and numbers of the Book of Changes must read. Yang Xiong's "Tai Xuan" from the Han dynasty is very precise in its mathematical reasoning and is sufficient to complement the principles of the Book of Changes. Scholars who have spare time may find it worthwhile to read it, to broaden their understanding of the principles. As for Sima Wen Gong's "Qian Xu," it is far inferior to "Tai Xuan."

或曰：向之言《易》者，每曰理象氣數。理象與數，既聞之矣。所謂氣者，是否即指卦氣？曰：氣者，即天地陰陽之氣。故一曰氣始，二曰形始。氣居於形之先，形包於氣之中。流行不息，連化無窮。大無外而細無間，皆氣之所周也。

Someone asked: In the past, those who explained the Book of Changes often spoke of four aspects: "li, xiang, qi, and shu." Li, xiang, and shu have already been explained by you; so what is meant by "qi"? Is it referring to "gua qi"? Answer: Qi refers to the qi of heaven and earth, yin and yang. Therefore, the first step is called "qi beginning," and the second step is called "form beginning" — qi comes before form, and form is contained within qi. It flows ceaselessly, transforms endlessly, being vast without boundaries and minute without gaps, pervading everywhere without exception.

然氣不可見，故顯之以象，而節之以數，析之以理。言理言數言象，皆所以言氣也。固不僅為卦氣，卦氣但以明一歲四時七十二候之序耳。五行者，所以別氣之剛柔。干支者，所以明氣之盛衰。納甲以象氣之交錯，納音以盡氣之變化。而出入內外，節以制度，皆在於數。故明乎數之理，象與氣可坐而致焉。

However, since qi is invisible, it is expressed through "xiang" (images), regulated through "shu" (numbers), and analyzed through "li" (principles). Discussing principles, numbers, and images is all for the purpose of discussing qi, not solely referring to hexagram qi; hexagram qi is only used to explain the order of the four seasons and the seventy-two phases of the year. The "Five Phases" are used to distinguish the softness and firmness of qi, "Gan-Zhi" (Heavenly Stems and Earthly Branches) are used to indicate the waxing and waning of qi, "Najia" (stem assignment) is used to take the image of the intermingling of qi, and "Nayin" (sound element) is used to exhaust the changes of qi. As for the entry and exit of qi, internal and external, and the limitation by institutional rules, these all fall under "shu" (numbers). Therefore, once the principle of numbers is understood, images and qi can be obtained effortlessly.

曰：然則以何書為善？曰：是宜求之於陰陽之學。向來陰陽術數之書，皆精粗雜揉，瑕瑜參半。《數理精蘊》與《儀象曆象考成》、《五行大義》諸書，皆宜參看。《易緯乾鑿度》、《乾坤鑿度稽覽》等書，亦不盡無稽。是在讀者能審其當否耳。

Another question: Then, which books should one read? Answer: One should seek the study of yin and yang. Throughout history, books on yin-yang and numerology have been mixed in quality, with both good and bad elements. Works such as the Qing Dynasty's "Shuli Jingyuan," "Yixiang Kaocheng," "Lixiang Kaocheng," and the Sui dynasty's "Wuxing Dayi" by Xiao Ji should all be consulted. Books like "Yiwei Qianzaodu," "Kunqian Zaodu," and "Jilantu" are not necessarily without foundation. The key lies in the reader's ability to judge their appropriateness on their own.

曰：道廣大，因不僅為占卜之用。然辭變象占，則占亦在易學所不廢。究竟言占者，宜何道之從？曰：周人占筮，各有專官。三《易》分稱，則三《易》當各有其占法，而今已失傳。孔子贊《易》，實以明道，非斷吉凶分別去取者，迄未嘗言之。後人但取《左傳》、《國策》等書，所紀占筮之文而模仿之，(《啟蒙》等書是)以一爻變二爻變至六爻變，定為去取之例。(即用本卦或用之卦)無論其或用變爻，或用不變之爻，已與《周易》用變之例自相矛盾。

Another question: The Way of the Book of Changes is vast and profound, originally not limited to divination; however, since it has four channels: words, changes, images, and divination, divination is also not abandoned in the study of the Book of Changes. So, those who study divination should follow which path? Answer: In the Zhou dynasty, there were specialized officials for divination. The three Books of Changes, namely the Lianshan, Guicang, and Zhouyi, were all called the Books of Changes. Therefore, each of the three Books of Changes should have its own method of divination, but all have been lost. Confucius commented on the Zhouyi, intending to explain the principles, but he never mentioned how to judge good or bad fortune, or how to choose between different interpretations. Later scholars had to imitate the divination texts recorded in the Zuo Zhuan and the Warring States Strategies, and so on, using one line change, two line changes, up to six line changes, to establish rules for choosing and discarding (that is, either using the primary hexagram or the changing hexagram). However, regardless of whether they take the changing lines or the unchanging lines, they have already contradicted the general practice of the Zhouyi, which uses change as the basis for divination.

即如其所言，則所得之爻或吉或凶，亦無方法以判斷其所以吉凶之故。亦如問籤枚卜者之偶中即以為驗，不中亦無以明其不中之故。至精至神之《易》道，恐不如是也。夫《易》彰往察來，斷無占而不驗，驗而無以知其所以然之理。特占法未明，《左傳》等書所載但如紀算術者，只載其得數，而未演其細草也。既無細草，則安能知其方式？不知其方式，又安知其數之從何而得哉！今但以其得數為方式，宜其所求之數無從而得矣。

Even if one follows their method, there is no way to explain why the line drawn is auspicious or inauspicious. This is similar to those who seek fortune-telling slips or toss divination sticks: if they happen to guess correctly, they call it effective; if not, they cannot explain why it failed. The most refined and profound Way of the Yi (I Ching) must not be like this. The Yi can illuminate the past and foresee the future; there can be no case where a divination does not come true or, if it does, there is no explanation for it. This is only because the method of divination has been lost and is not clearly understood. The records in books like the Zuo Zhuan are like those who write down only the result of arithmetic calculations without showing the process; without the process, how can one know the method used? Without knowing the method, how can one know where the result came from? Now, people take others' results as the method, so it is no wonder they cannot find the number they seek themselves.

故《火珠林》之術，(今術家所用者是)以及六壬、太乙、奇門三式，其操術精者，尚無不驗。獨宋賢《筮儀》之揲蓍求卦，其驗否茫無把握。豈孔子知來藏往之說為欺人哉！是未得其法也。斷可訓矣！

Therefore, the method of divination used in the "Fire Pearl Forest" tradition (which is exactly the system used by modern diviners), as well as the three systems of "Six Changes," "Taiyi," and "Qimen," will surely be effective if the practitioner's technique is precise. Only the method of divination by divining with yarrow stalks as established in the "Divination Ritual" by Song Confucians lacks certainty, whether it works or not. Is Confucius' statement "knowing the future and concealing the past" a lie? Obviously, it is later scholars who have not truly mastered the correct method. This reasoning is clearly understandable.

蓋京焦之術，大儒所薄為方技而不屑道者，而不知西漢去古未遠，其飛伏世應五行順逆之法，必有所受(孔子《上繫》起中孚，《下繫》起咸，與京氏卦氣正合。可見孔子以前，必有此六十四卦之序。故孔子於無意中即舉此二卦為言，否則六十四卦何卦不可為《繫辭》之首？又安有如是之巧合也？即此以推，則世應飛伏之有所自來，亦斷可識矣。)。故以之推算，非但吉凶確有可憑，而遠驗諸年，近征之日，雖時刻分秒亦均有數之可稽。管輅郭璞等占驗，亦均有準的，皆是術也。

The divination methods of Jing Fang and Jiao Yanshou were looked down upon by great scholars as mere techniques and not worth discussing. However, it is not known that during the Western Han dynasty, the ancient ways were still close, and their methods of "flying and hiding" and "world and response lines" along with the order of the Five Phases must have been passed down. Confucius in the "Great Treatise" of the "Commentary on the Changes" starts with the hexagram Zhongfu, while in the "Lower Commentary" he starts with Xian. This matches exactly with Jing Fang's diagram of the hexagram energies. This shows that there must have been a sequence of the sixty-four hexagrams before Confucius, so he naturally chose these two hexagrams to base his statements. Otherwise, why would any of the sixty-four hexagrams not be placed first in the "Great Treatise"? How could such a coincidence exist? From this reasoning, the theory of "world and response lines" and "flying and hiding" must have a source, and this conclusion is certain. Therefore, using these methods to predict not only has a solid basis for determining good or bad fortune, but even events can be verified for specific years, months, days, and even moments, seconds. Guan Lu of the Three Kingdoms and Guo Pu of the Jin dynasty were always accurate in their divinations, and they used exactly this method.

自王弼掃象，後之言《易》者，以性理為精微。凡陰陽五行九宮星象，皆目為蕪穢而絕口不談。不知《易》道廣大悉備，況占筮本術數之一端，陰陽乃《易》道之大綱；既言《易》，而屏除陰陽；既不明術數，而仍欲言占卜，豈非至不可解之事乎？

Since Wang Bi eliminated the images and numbers, those who later discussed the Book of Changes came to regard principles and reason as the essence, treating all things like yin and yang, the Five Phases, the Nine Palaces, and celestial phenomena as trivial and dirty, never mentioning them. They did not realize that the Way of the Changes is vast and encompasses everything. Moreover, divination itself is a branch of numerology and calculation, and yin and yang are the main framework of the Changes. If one wishes to discuss the Changes, yet excludes yin and yang; if one does not understand numerology, yet wants to talk about divination, is this not the most contradictory thing?

故餘以為欲明象占，宜求諸術數，更由術數而求諸經義，方可謂技焉而進於道。必有超出尋常而為術士所不及者，蓋術者但知其當然不知其所以然。果能一一以經義證之，以明其所以然之理，此正吾輩之責耳。自邵子以降，如劉青田、姚廣孝之儔，類皆能明其所以然之故者。是以能知未來，如燭照數計。

Therefore, I think that in order to understand the images and divination, one should seek them in the techniques of numerology; then, from the techniques, further seek them in the meanings of the classics. Only then can one progress from skill to the Way, and certainly achieve something beyond the ordinary, which the common diviners cannot match. Because the diviners only know the 'so it is' but not the 'why it is so'; if one can verify each point with the meanings of the classics and explain the reasons clearly, this is precisely the responsibility of scholars. Since Shao Kangjie, people like Liu Ji of Qingtian and Yao Guangxiao have mostly understood the reasons, so they could foresee the future as clearly as a candlelight reflecting objects or counting on one's fingers.

惜處專制政體之下，禁治陰陽壬遁之學。有其書者，必令銷燬。今所傳者，都為抄本。傳寫謬訛，且多割裂改竄，僅略留形式，尚不完備，又烏能施之於用乎？且不但禁三式諸書，即《易》注之涉及神化，或精論術數者，亦在所嚴斥。故士流所習，僅限於王《注》、孔《疏》、程《傳》、朱《義》，此外皆屬違式。至有清中葉以後，居然上及馬鄭；而道咸之際，且盛行虞義者，則以阮儀徵輩之提倡，而朝廷欲博古文之虛名，故為之網開一面耳。

Unfortunately, under the autocratic political system, the court prohibited the study of yin and yang, the Six壬 (Liuren) system, and Dun Jia. All books on these subjects were ordered to be destroyed. The ones that have survived today are all copies, passed down through generations with many errors. Moreover, most of them have been fragmented and altered, preserving only their form while lacking completeness in content. How can they be used practically? Furthermore, not only were books on the three systems (San Shi) banned, but also any commentaries on the Book of Changes that involved divine elements or detailed discussions on numerology were strictly forbidden. Therefore, scholars could only study Wang Bi's commentary, Kong Yingda's Justification, Cheng Yi's Commentary on the Book of Changes, and Zhu Xi's Original Meaning. Anything beyond that was considered illegal. By the mid-Qing Dynasty, it was even possible to refer back to Ma Rong and Zheng Xuan. During the Daoguang and Xianfeng periods, Yu Fan's interpretations became popular again, due to the promotion by a group including Yan Yuan of Yizheng, and also because the court wanted to appear as if it valued the ancient Confucian texts. Thus, they made an exception.

今政體既革，讀書尚得自由，則《易》道之昌明，更無其他之阻力。學者宜致力於全經以立其本，然後廣求秘籍，旁及科學。凡有足以與吾《易》相發明者，無不可兼收並蓄。既會其通而征諸實，然後由博反約，以擷其精英，而仍縮千里於尺幅。《易》之大用，庶乎其可見歟！

Now that the political system has changed and reading is free, the teachings of the Book of Changes can flourish without any other obstacles. Scholars should first study the entire text thoroughly to establish a solid foundation, then widely collect secret writings and extend to modern sciences: anything that can complement our Book of Changes can be included and integrated. Once they can combine and understand various ideas, they should verify them with actual facts, then return from broad knowledge to the essentials, selecting the essence and condense the vastness of a thousand miles into a small space. The great application of the Book of Changes can thus be revealed.

曰：致力全經，更有無較善之注本？曰：向之說《易》者，其空談性理無論矣。即能求諸象數者，要皆見卦說卦，見象說象，鮮能會六十四卦之通，合全《易》以明一卦一爻者。勝清之季，惟焦氏循之《易通釋》、姚氏《易》、端木氏之《周易指》與紀氏之《易問》、《觀易外編》，皆能自出杼，不依傍古人門戶。會通全《易》以立說者，雖各有所蔽，而精到之處有非前人可及者。學者但依據經文以為去取，自能可得其所長，更可觸類而有所悟矣。

Another question: If one wishes to study the entire text of the classic, are there any better commentaries? The answer is: In the past, those who explained the Zhou Changes mostly talked about principles and morality, and they are not worth mentioning. Even those who focused on the images and numbers usually discussed one hexagram at a time, one image at a time, and rarely could integrate all sixty-four hexagrams to explain a particular hexagram or line. In the late Qing dynasty, only Jiao Xun's "Easy Interpretation of the Changes," Yao Peizhong's "Yao's Learning of the Zhou Changes," Du Mu Guohu's "Commentary on the Zhou Changes," Ji DaKui's "Questions on the Changes" and "Supplemental Commentary on Observing the Changes" could develop their own original ideas, not relying on the schools of ancient scholars, and establish their theories by integrating the entire text. Although they each had their own shortcomings, their profound insights surpassed those of previous scholars. Scholars should decide which to adopt based on the text itself, thus naturally being able to absorb their strengths and achieve a deeper understanding through analogy and association.

又長沙彭氏，刻有《易經解注傳義辨正》一書。雖以李氏《集解》、王弼《注》、程《傳》、朱《義》為本，而引據極博。各家註釋，皆採取其精。攜此一編，足以薈百數十家之學說而便於參考，亦近今之佳著也。

There is also a book titled "Explanations, Annotations, Transmission of Meaning, and Corrective Discourse on the Book of Changes" printed by the Peng family in Changsha. Although it takes as its base the works of Li Dingzuo's "Collected Explanations of the Zhou Changes," Wang Bi's "Annotations," Cheng Yi's "Book of Changes Commentary," and Zhu Xi's "Original Meaning," it cites an extremely broad range of sources. It adopts the finest aspects from the annotations of various schools. Carrying this book is sufficient to gather the teachings of hundreds of scholars for reference, and it is also a fine work of recent times.

或曰：讀《易》之次序，既聞之矣，觀象之方法如何，可得聞歟？曰：君子所居而安者，《易》之序也。所樂而玩者，爻之辭也。故觀象必先觀其序。《周易》之卦序，與《連山》、《歸藏》不同。《周易》之彖辭爻辭，皆一依《序卦》之義。如乾坤後繼之以屯，屯後次之以蒙，《序卦傳》已詳述其義。凡一卦之《彖》，及六爻之辭，即本此義，與本卦之名義而發揮之者也。如屯之義為難，故六爻皆取屯難之義。蒙之六爻皆取蒙昧之義，此猶其易見者也。

Someone asked: Having learned the order of reading the Book of Changes, may I ask about the method of observing phenomena? Please explain. Answer: The Great Treatise of the Upper Transmission says that a gentleman in his ordinary life finds comfort in the sequence of the hexagrams of the Book of Changes, and delights in the statements of the lines. Therefore, observing phenomena must first look at the sequence of the hexagrams. The sequence of hexagrams in the Book of Changes differs from that of the Lianshan and Guicang. However, the interpretations of the hexagrams and the statements of the lines in the Book of Changes all follow the meaning of the Sequence of Hexagrams. For example, after Qian and Kun comes Tun, and after Tun comes Meng. The Sequence of Hexagrams has already explained the reasons in detail. All the interpretations of the hexagrams and the six statements of the lines are based on this sequence, combined with the meaning of the name of the hexagram. For instance, Tun means difficulty, so all six lines take the meaning of 'difficulty'. Meng means confusion, so all six lines take the meaning of 'confusion'. This is still relatively easy to see.

如睽之六爻，曰“喪馬勿逐自復，見惡人無咎”，曰“遇主于巷”。不觀卦名之義，其爻辭即無從解釋。蓋睽有乖舛違戾之意，故其辭爻無不乖違。夫喪馬宜逐者也，乃勿逐自復；見惡人宜有咎者也，乃無咎；遇主應於朝廟，今乃遇之於巷，皆乘異之權者也。蓋當睽之時，禍福顛倒，見為禍者或且為福，見為福者或反得禍。以下爻辭，亦皆類此。若不明睽之義，又何從而測之？略舉其一，餘可類推矣。

For example, in the hexagram "Kui" (Strife), the six lines each have their own statements. The first line says, "Lose the horse, do not pursue; it will return by itself. Meet an evil person, no blame." The second line says, "Meet the master in a lane." Without understanding the meaning of the hexagram's name, these line statements cannot be explained. Since "Kui" means discord or disagreement, all its line statements carry an unusual or counterintuitive tone: losing a horse usually calls for pursuit, but it says not to pursue, for it will return by itself; meeting an evil person usually brings misfortune, but it says there will be no blame; meeting a superior usually occurs in the court or temple, but it says it happens in a lane. These statements all speak from the perspective of the unusual or abnormal. Indeed, when things are discordant, fortune and misfortune are reversed: what appears as misfortune may become fortune, and what seems like fortune may bring misfortune. The statements of the other lines are of the same kind. If one does not understand the meaning of "Kui," from where could one possibly guess? Here we take only one hexagram as an example; the rest can be understood in the same way.

既觀其序之次，與本卦命名之義，以讀其辭，已思過半矣。然後玩內外之卦象，為陰為陽，為正為隅(坎離正也中也，震兌正也，乾坤巽艮隅也。然乾坤先天亦為中)。或相成，或相害(《大有·初九》“無交害”，害即火克金也)。如水火相息，水上火下為既濟，二女同居為睽為革之類，皆合兩卦之名義而取象者，不可不察也。

Once the position of the hexagram in the sequence is clear and the meaning of its name is understood, reading its text will already reveal most of its meaning. Then one should contemplate the images of the inner and outer trigrams: whether they are yin or yang, and whether they occupy the four cardinal directions or the four corners (in the Later Heaven arrangement, Kan and Li are in the center and the cardinal directions, while Zhen and Dui are in the cardinal directions; however, Qian and Kun are also considered central in the Earlier Heaven arrangement). The two trigrams may either support each other or be harmful to each other (the "wu jiao hai" in "Da You · Chou Ji" means "no mutual harm," where "harm" refers to fire overcoming metal). For example, water and fire counteract each other; when water is above and fire is below, it forms "Ji Ji." When two women live together in the same room, it forms "Kui" or "Ge," which are based on the images of the two trigrams. These should not be overlooked.

內外之義既明，然後分六位而觀之，別剛柔，分陰陽；察往來，定主爻；看應與之有無，辨爻位之當否，而六爻之象始可睹矣。以驗爻辭及《象傳》，是否與所觀察者相合。如爻象之辭，出於所觀察之外，則必詳求其故。或求諸中爻，或求諸互卦。更有未得，則求諸反卦(即來氏所謂“綜”)對卦(即來氏所謂“錯”，虞氏曰“旁通”)，與上下交易之卦(如山水蒙，上下相易水山蹇)，則必有所得矣。

After understanding the meaning of the outer and inner trigrams, observe the six lines divided into six positions: distinguish between yang and yin, determine the nature of each line; examine their movement and determine the main line; check if there is a corresponding line, and determine if the position of each line is appropriate. Only then can the image of the six lines be clearly understood. Then use the line statements and the image commentaries to verify whether they match the observations. If the line statements and image commentaries go beyond the scope of the observations, one must carefully investigate the reasons: either look among the four central lines, or consider the mutual trigrams; if still not found, refer to the reversed trigram (as Lai Zhide called it "zong"), the opposite trigram (as Lai Zhide called it "cuo", and Yu Fan called it "pangtong"), or the trigram with the upper and lower original trigrams reversed (for example, the Mountain-Water "Meng" trigram, when the upper and lower trigrams are reversed, becomes the Water-Mountain "Jian" trigram). In this way, one will certainly gain some insight.

更不能得，再詳玩先後天八卦之圖。以本卦之方位合之，看是如何。如山風蠱，六爻皆取父母之象，反覆推求不能得。考之各家註釋，亦均無發明。最後求之先後天方位，乃恍然矣。蓋艮巽在先天圖，巽西南而艮西北，即後天乾坤之位。乾父坤母，故蠱卦之父母之象即由此而來。

If you cannot find the answer, examine carefully the positions of the Eight Trigrams in both the Earlier Heaven and Later Heaven diagrams. The Earlier Heaven diagram is said to have been created by Fuxi, and the Later Heaven diagram by King Wen. The same trigram occupies different positions in the two diagrams. Compare the position of the Primary Hexagram with these diagrams to see what is happening. For example, the hexagram "Gǔ" (Guilt), which is Wind over Mountain, has all six lines taking the images of "parents." After repeated inquiry, no clear answer is found, and none of the commentaries from various scholars explain it clearly. Finally, by examining the positions in the Earlier Heaven and Later Heaven diagrams, the meaning becomes clear: in the Earlier Heaven diagram, Xun is located in the southwest and Gen in the northwest, which are exactly the positions of Qian and Kun in the Later Heaven diagram. Qian represents the father and Kun the mother, so the image of "parents" in the hexagram "Gǔ" comes from this.

須知聖人彖、象之辭，皆根於卦象，無一字之虛設，無一義之虛懸。即假借之虛字，亦均與卦象有關。而《象傳》之韻，更字字分陰分陽。或雙聲疊韻，或一字兩音，則必陰陽相通，而以一字兼給二卦之義者也。精細緻密，剖析毫芒，故讀《易》必須字字咀嚼，字字反覆推求，方能得聖人之意於萬一也。一卦即明其大意，然後推之於類卦，以及六十四卦，證之以《繫傳》、《雜卦》，更參之以數理，準之以天時，《易》之道庶乎其可通矣。

To understand the hexagrams, one must realize that the彖辞 and 象辞 are all based on the hexagram images, with no word being superfluous and no meaning being abstract. Even the borrowed or hypothetical words are related to the hexagram images. The use of rhyme in the Image Commentary is particularly precise, with each word distinguishing yin and yang. Some words have the same initial consonant and form double sounds, some have the same final vowel and form repeated rhymes, and some single words have two pronunciations, which indicates the connection between yin and yang, and the combination of meanings from two hexagrams. This level of detail and precision requires that when reading the Book of Changes, one must carefully chew over each word and repeatedly examine it to grasp even a fraction of the sage's intended meaning. Once the general idea of one hexagram is understood, one can then extend this understanding to similar hexagrams with related meanings, eventually covering all sixty-four hexagrams. Then, using the Great Treatise and the Miscellaneous Hexagram Transmission as references, combining them with numerical principles and astronomical observations, the principles of the Book of Changes can be generally understood.

立人之道，曰仁與義，實惟六爻中三四兩位。孔子贊《易》，藉以明人道而立人極，以參天地之化育，故特注重中爻。三五同功而三多凶，二四同功而四多懼。以見人生為憂患始，畢生在多凶多懼之中，如作繭自縛而不能脫。於是本悲天憫人之心，不惜韋編三絕，闡發陰陽造化之機，明貞勝貞一之理，而示人以進德修業人定勝天之道，皆在於三四兩爻盡之。

The "Say on the Hexagrams" says, "Establishing the way of human beings is called benevolence and righteousness." When applied to the hexagrams, this corresponds precisely to the third and fourth lines among the six lines. Confucius praised the "Zhou Changes" and used it to explain human conduct and establish moral standards, so that it could be placed on par with the workings of heaven and earth as the third. Therefore, he particularly valued the central line. The "Great Treatise" of the "Say on the Hexagrams" states that the third and fifth lines have the same function, yet the third line is often dangerous; the second and fourth lines have the same function, yet the fourth line is often fearful. This shows that human life begins with hardship, and one is constantly surrounded by dangers and fears, like being trapped in a cocoon unable to escape. Therefore, Confucius, with his compassionate heart for all beings, was not reluctant to break the cords of the book three times to explain the key principles of yin and yang's transformations, clarifying the concepts of "zheng sheng" and "zheng yi," and indicating the path for people to cultivate virtue and achieve success through human effort, and all these are fully explained in the third and fourth lines.

乾之九三九四，六十四卦人爻之開始也。九三曰“君子終日乾乾夕惕若厲無咎”，九四曰“或躍在淵無咎”。乾乾夕惕，修己以仁也。躍而稱或，揆之於義也。常存戒謹恐懼之心，庶幾可免於大過(乾六爻中四爻動成頤，頤失道而口實自養則成大過。乾九三九四兩爻本小過之中爻，能得其道則小過亦可免而成中孚，中孚則合乎立人之道矣。故曰“《易》者聖人教人寡過之書”。)。吉凶雖有命，而悔吝寡矣。故曰無咎。無咎者，善補過也。

The ninth line of the third position and the ninth line of the fourth position in the Qian hexagram mark the beginning of the human lines in the sixty-four hexagrams. The ninth line of the third says, "The superior man is diligent all day, and remains cautious at night, being careful and without blame." The ninth line of the fourth says, "Perhaps leaping from the depths, without blame." Being diligent all day and remaining cautious at night reflects cultivating virtue through benevolence; the use of the word "perhaps" in the fourth line indicates using righteousness to measure when to advance or retreat. Maintaining a constant sense of caution and reverence can probably avoid major mistakes. In the six lines of the Qian hexagram, if the fourth line changes, it becomes the Yi hexagram. If the Yi hexagram loses its proper path and focuses only on self-nourishment, it becomes the Da Guo hexagram. The ninth lines of the third and fourth positions in the Qian hexagram originally form the middle lines of the Xiao Guo hexagram. By maintaining the proper path, even minor mistakes can be avoided, leading to the Zhong Fu hexagram, which conforms to the way of cultivating human virtue. Therefore, the Zhou Changes are the book of the sages teaching people to commit fewer mistakes. Although good and bad fortune are determined by fate, regret and hesitation can be reduced, so the line statements say "without blame."the so-called "without blame" means being good at making up for mistakes.

《九三·文言》曰：“知至至之，可與幾也。”因三爻在上下之交，乃進退存亡之幾。理欲之界，人禽之別，得失之間，不容毫髮。孟子曰：“人之所以異於禽獸者幾希”，即此幾也。

The *Wenyan* commentary on the *Qian* hexagram explains the line *Jiu San* as: "Knowing where to go and going there, one can be discussed with regard to the subtle and minute." This means that someone who knows exactly where he should be and proceeds accordingly can be engaged in discussions about the subtle and minute aspects. Since the third line is located at the junction between the lower and upper trigrams, it is a critical point of advancement or retreat, survival or demise: the boundary between heavenly principle and human desire, the distinction between humans and animals, and the threshold between gain and loss. There is no room for the slightest error in this position. Mencius said, "What distinguishes humans from animals is very slight," referring precisely to this "ji" (subtle and minute).

《屯·六二》曰“君子幾不如舍”，《豫·六二》曰“介于石不終日”(《乾·九三》曰“終日”，《豫·六二》故曰“不終日”)，《繫傳》曰“知幾其神乎？君子上交不諂，下交不瀆，其知幾乎？幾者動之微，吉之先見者也。君子見幾而作，不俟終日。《易》曰‘介于石不終日貞吉’。介如石為，寧用終日？斷可識矣。君子知柔知剛，萬夫之望”，又曰“顏氏之子，其庶幾乎！夫《易》者，聖人之所以極深而研幾也。唯幾焉，故能成天下之務”，皆所以闡發此九三一爻之義也。

The hexagram Zun (Obstruction) line six-two says, "The superior man acts promptly rather than waits." The hexagram Yu (Joy) line six-two says, "Between stone and stone, not for a whole day." (The hexagram Qian line nine-three says, "For a whole day," so the hexagram Yu line six-two says, "Not for a whole day.") The Great Treatise Lower Transmission says: To recognize the subtle signs, may that be called divine! The superior man in dealing with superiors does not flatter, and in dealing with inferiors does not look down, thus he understands the subtle signs. What is called "a few" is the most subtle movement, the first hint of good or bad before it becomes evident. When the superior man sees this hint, he acts immediately, without waiting for a whole day. The Zhou Changes say, "Between stone and stone, not for a whole day, firmness brings good fortune." - firmness is like stone, so why wait for a whole day? It is clearly evident at once. The superior man understands both softness and firmness, thus he is looked up to by all people. The Great Treatise Upper Transmission also says: Yan Hui perhaps approached understanding the subtle signs. The Zhou Changes is the book that the sage used to explore the profound and investigate the subtle signs; precisely because he investigated the subtle signs, he could accomplish the affairs of the world. These words are all explaining the meaning of the line nine-three in the hexagram Qian.

至九四，則其動已著，已由下卦而進於上卦。進而及時，則為豫之“大有得”，為隨之“有孚在道”，為大過之“棟隆”，為萃之“大吉無咎”，為革之“有孚改命”。進而失時，為晉之“碩鼠”，為夬之“無膚”，為姤之“無魚”，為震之“遂泥”，為鼎之“折足”。或得或失，只能安之於羲命。

At Nine Four, its movement becomes evident, having moved from the lower trigram to the upper trigram. When the movement is timely, it is like the "Great Gain" in the Nine Four of the hexagram "Yù," the "Trust in the Way" in the Nine Four of "Suí," the "Strong Beam" in the Nine Four of "Dà Guò," the "Great Goodness Without Misfortune" in the Nine Four of "Cuì," and the "Trust and Changing Fate" in the Nine Four of "Gé." When the movement is untimely, it is like the "Big Rat" in the Nine Four of "Jìn," the "Buttocks Without Skin" in the Nine Four of "Guài," the "No Fish in the Net" in the Nine Four of "Gòu," the "Shaking in Mire" in the Nine Four of "Zhèn," and the "Broken Leg of the Cauldron" in the Nine Four of "Dǐng." Whether successful or not, one must accept the principles and destiny.

孔子更於咸之九四一爻，特暢其義，曰：“天下何思何慮？天下同歸而殊塗，一致而百慮。天下何思何慮？日往則月來，月往則日來，日月相推而明生焉。寒往則暑來，暑往則寒來，寒暑相推而歲成焉。往者屈也，來者信也，屈信相感而利生焉。尺蠖之屈，以求信也。龍蛇之蟄，以存身也。精義入神，以致用也。利用安身，以崇德也。過此以往，未之或知也。窮神知化，德之盛也。”

Confucius further elaborated on this meaning in the ninth line of the fourth position in the Hexagram of Salt. The "Great Treatise" of the lower transmission says: What is there to think about in the world? All things take different paths yet ultimately converge, and all thoughts eventually reach a single point; so what is there to think about? When the sun sets, the moon rises, and when the moon sets, the sun rises; the sun and moon move in succession, and thus light is generated. When cold passes, heat comes; when heat passes, cold comes; cold and heat alternate, and thus a year is completed. What has passed is bending, and what comes is stretching; bending and stretching respond to each other, and thus benefit arises. The inchworm arches its body in order to advance; the dragon and snake coil in order to preserve themselves. Studying principles and reasons to the point of mystery is for the purpose of practical application; using learning skillfully to secure one's own well-being is for the purpose of cultivating virtue. Beyond this level, it is beyond human knowledge; to exhaust mystery and comprehend creation is the state of supreme virtue.

蓋乾為《上經》之首，咸為《下經》之首，故特於此兩卦，分言三四兩爻，以明立人之道。而聖人作《易》，與孔子贊《易》之微旨，胥於是見之矣。

The hexagram Qian is the first of the upper section, and the hexagram Xian is the first of the lower section, so Confucius specially discussed the third line and the fourth line of these two hexagrams to explain the way of cultivating human character. The intention of the sages in composing the Book of Changes and the profound meaning of Confucius' commentary on the Zhou Changes can be seen from here.

乾九三為當位之爻，九四為不當位之爻。故《九四·文言》“上不在天，下不在田，中不在人”，而《咸·象傳》曰“君子以虛受人”。“以虛受人”者，即此九四一爻為虛爻也。九四為虛，則九三為實。修辭立誠，忠信進德，學以聚之，問以辨之，寬以居之，仁以行之，皆立德之事也。

The ninth line in the third position of the Qian hexagram is a yang line in a yang position, making it a properly placed line. The ninth line in the fourth position is a yang line in a yin position, making it an improperly placed line. Therefore, the Wenyan commentary of the Qian hexagram discusses the ninth line in the fourth position, saying, "It is not above heaven, not below the fields, and not in the middle of people." The Xian hexagram's Image Commentary says, "The superior person learns to be receptive to others." The phrase "to be receptive to others" is precisely because the ninth line in the fourth position is a vacant line. If the ninth line in the fourth position is vacant, then the ninth line in the third position is solid. When the Wenyan commentary discusses the ninth line in the third position, it speaks of refining words, establishing sincerity, cultivating virtue through loyalty and trust, accumulating through study, distinguishing through inquiry, being broad-minded, and acting with benevolence. All these belong to the cultivation of virtue.

一致百慮，殊塗同歸，日月生明，寒暑成歲，而一身之往來屈信，亦如日月寒暑之推移迭更，而悉出於自然。是能與天地相感通，如龍蛇之變化，所謂陰陽不測之謂神，皆形而上者之謂也(“無思也，無為也，寂然不動感而遂通天下之故，非天下之至神，其孰能與於此？”此即咸之精義，二氣感應之妙用。而下文即繼之以“極深研幾”，可見三四兩爻貫通之線索矣)。

All things converge to the same destination yet have myriad thoughts and considerations; different paths eventually lead to the same place. The sun and moon alternate, giving rise to light; the cold and heat alternate, completing a year. A person's own movements and changes also follow the same pattern as the sun, moon, cold, and heat, shifting and changing naturally. This is how one can be in harmony with heaven and earth, like a dragon or a snake, changing in unpredictable ways. This is what the Great Treatise says: "The mysterious and indescribable nature of yin and yang is called the divine." This belongs to the level beyond form. The Great Treatise, Part I says: "Without thinking, without action, still and unmoving, yet responsive to all things, comprehending the causes of the world. If it is not the most divine in the world, who could be capable of this?" This is precisely the essence of the Hexagram Xian, the subtle function of the mutual influence between yin and yang. The following text continues with "extreme depth and subtle examination," indicating the connection between the third and fourth lines.

道運於虛，而德徵諸實。孔子贊《易》立教，是為中人說法(《論語》：“中人以上，可以語上也。中人以下，不可以語上也。”)。故以仁義立本，以致用為歸。言有不言無，言德不言道。於六十四卦《象傳》，發明立教之旨。皆以人合天，修身俟命(凡卦《彖傳》以釋上下兩象，《象傳》則合兩卦而貫串之，即以明中爻之義，即以明三四兩人爻之義，所謂立人之道。詳《易楔》“以”字下。)。

The concept of "Dao" operates in the void, while "De" is verified through practical matters. Confucius praised and explained the "Zhou Yi" (I Ching) to teach people, addressing those of average ability. Therefore, he used benevolence and righteousness as the foundation and utility as the ultimate goal. He spoke of "having" rather than "non-having," and of "De" rather than "Dao." In the sixty-four hexagrams of the "Xiang Zhuan" (Image Commentary), he consistently elaborated on the principles of teaching, aiming to guide people to align human affairs with heavenly principles, cultivate themselves, and await heavenly destiny. Each hexagram's "Tuan Zhuan" (Commentary on the Judgment) explains the two trigrams, while the "Xiang Zhuan" combines them to elucidate the meaning of the central line, that is, the third and fourth lines, which are referred to as establishing the way of humanity. See my work "Yi Xie" for a detailed discussion on the character "yi" (see entry on "yi").

乾以易知，坤以簡能。夫婦之愚，可以與知與能者也。至形上之道，則下學上達，乃成德以後所有事，不在教義範圍以內(《論語》：“夫子之文章，可得而聞也。夫子之言性與天道，不可得而聞也。”“文章”即九三之“修辭立其誠”，“性與天道”則九四之“感而遂通，精義入神，窮神知化”之功也。)。

Heavenly Stem Qian is known because it is easy to understand, while Heavenly Stem Kun can accomplish things because it is simple. Even ordinary couples, who are shallow, can participate in such knowledge and ability. As for the ultimate "Dao," one must study human affairs and then reach the principles of Heaven. This is something that comes after the cultivation of virtue and is not within the scope of teaching (as the Analects says: "The articles of the Master can be heard, but his words about human nature and the Heavenly Dao cannot be heard." Here, "articles" refer to the "cultivating expression and establishing sincerity" of the Third line, while "human nature and Heavenly Dao" refer to the practices of the Fourth line, such as "being moved and then communicating freely," "refining the meaning to the divine," and "comprehending the subtle and knowing the transformation").

故《序卦傳》以“有天地，有男女，有夫婦，有父子，有君臣，有上下，然後禮義有所錯”，以標明立教之旨。而六十四卦，獨不列乾坤與咸之卦名。蓋以乾為天道，坤為地道。咸乃無思無為形上之道，特闕之以清明道與立教之界限。而於《繫傳》中，闡發明道之功。更於《說卦》“窮理盡性至命”一章，為上達之指歸。

Therefore, the "Xugua Zhuan" uses the passage "When heaven and earth exist, then there are male and female; when there are male and female, then there are husband and wife; when there are husband and wife, then there are father and son; when there are father and son, then there are sovereign and minister; when there are sovereign and minister, then there are superior and inferior; when there are superior and inferior, then rites and morality have their place" to indicate the purpose of establishing teaching. This passage lists various hexagrams, but deliberately omits the names of the hexagrams Qian, Kun, and Xian. This is because Qian represents the heavenly way, Kun represents the earthly way, and Xian represents the formless, thoughtless transcendental way. By intentionally omitting these, it clarifies the distinction between "clarifying the way" and "establishing teaching." As for the practice of elucidating the "way," it is elaborated in the "Xici Zhuan." Furthermore, the chapter in the "Shuogua Zhuan" stating "to exhaust the principles, to realize the nature, and thus to reach destiny" serves as the ultimate destination for ascending to the higher path.

孔子贊《易》以明道立教之旨，固已脈絡分明，先後次序，一線不亂。乃朱子《本義》猶謂以卜筮教人，示人以避凶趨吉之書，不幾與《感應篇》、《陰鷺文》等量而齊觀耶？是何異以璇璣玉衡而僅為指南針之用焉？

Confucius praised and explained the Zhou Changes, in which the principles of illuminating the Way and establishing education were clearly articulated, with a well-ordered sequence without any confusion. However, Master Zhu's Zhou Changes Original Meaning still says that the Zhou Changes is a book that uses divination to teach people and guide them to seek good fortune and avoid misfortune. Is this not equating the Zhou Changes with works like the Great Ultimate Responsive Chapter and the Wenchang Yin Zhi Wen, which are moral exhortation texts? How is this different from using the celestial observatory instruments such as the Xuanji Yuheng merely as a compass?

孔子立教之要義，曰中，曰時。大過乎中者曰大過，小過乎中者曰小過。無往而非中者，乾坤坎離也。巽兌震艮，皆過乎中。故澤風為大過，雷山為小過。聖人教人於二四三五致其功。大過而至於小過，小過而至於無過，皆三四中爻反復其道。小過反之為頤，大過反之為中孚，而過可免矣。中孚“豚魚吉”。至誠之所感，物無不化，而況於人乎？

Confucius emphasized two main principles in his teachings: "zhong" (center) and "shi" (time). Those that greatly exceed the center are called the Hexagram of Great Excess, while those that slightly exceed the center are called the Hexagram of Small Excess. Those that are entirely in harmony with the center are the Hexagrams of Heaven, Earth, Water, and Fire. The other four Hexagrams—Wind, Lake, Thunder, and Mountain—exceed the center. Thus, Lake above and Wind below form the Hexagram of Great Excess, while Thunder above and Mountain below form the Hexagram of Small Excess. The sage teaches people to focus on the second, fourth, third, and fifth lines: moving from Great Excess to Small Excess, and from Small Excess to no excess at all, relying on the third and fourth lines, the central lines, which repeatedly follow the middle path. The Hexagram of Small Excess reversed becomes the Hexagram of Nourishment, and the Hexagram of Great Excess reversed becomes the Hexagram of Sincerity in the Middle. Thus, mistakes can be avoided. The Hexagram of Sincerity in the Middle states, "A pig and a fish are auspicious," meaning even ignorant creatures can be moved by sincerity. When sincere feeling is exerted, all things are transformed and nurtured, and how much more so are human beings?

然中孚之風澤，非即大過之澤風乎？何以澤風為大過而不中，風澤即為中孚而合乎中？舊說或曰“以其中虛也”。然頤之中更虛，何以不言中？或曰“孚者信也”，大象離伏坎，故曰中孚。然則重坎更孚矣，何以曰“習坎有孚”，不曰“中孚”？是皆於中孚之義未有得也。

But is not the hexagram Zhongfu composed of Xun wind above and Dui lake below, which is simply the reverse of Dagu over Dui lake and Xun wind below? Why is it that when lake is above and wind below, it is called Dagu, not Zhongfu, while when wind is above and lake below, it is called Zhongfu, which is in harmony with the middle? Some old interpretations say, "Because the two central lines are empty," but the hexagram Yi has even more emptiness in the middle, so why is it not called "Zhong"? Others say, "Fu means trust," and explain that the image of Zhongfu resembles Li, whose hidden hexagram is Kan, and Kan represents trust, hence the name "Zhongfu." If that is so, then the hexagram Kan, which consists of two Kan, should be even more "Fu," yet its hexagram statement only says "Xikan, there is trust," without saying "Zhongfu." This shows that these interpretations have not truly grasped the meaning of Zhongfu.

按天地之數，坎天一至兌地十(坎一，艮二、三，震四，巽五、六，離七，坤八、九，兌十。)。巽五兌十，五十居五十五數之中，所以神變化而行鬼神者也。巽與兌合，五與十合，故曰中孚。子曰：“五十以學《易》可以無大過矣。”即中孚之道也。

According to the numbers of heaven and earth, starting from the number one of Kan (Water) and counting up to the number ten of Dui (Lake), the trigrams are arranged in order: Kan is one, Gen is two and three, Zhen is four, Xun is five and six, Li is seven, Kun is eight and nine, and Dui is ten. Xun corresponds to five, and Dui corresponds to ten. Five and ten are exactly in the middle of the total number fifty-five of heaven and earth. This is the key point mentioned in the Great Treatise, which says, "Thus, it is able to change and act like ghosts and spirits." Xun and Dui combine, which means five and ten combine, hence it is called "Zhongfu" (Faithful Center). Confucius said, "At fifty, one can study the Book of Changes and avoid great mistakes," which refers precisely to the principle of Zhongfu.

卦氣冬至起中孚九二，夏至起咸，故孔子於《上繫》十一爻，首“鳴鶴在陰”；《下繫》十一爻，首“憧憧爾思”。而《中孚·象傳》曰：“中孚利貞，乃應乎天也。”應乎天則合乎天之氣，而日月寒暑相推，則二氣感應之理尤明。孔子繫《易》，雖未明言卦氣，而言行昭垂，無不上合法象(《中庸》：“仲尼祖述舜堯，憲章文武。上律天時，下襲水土。闢如四時之錯行，日月之代明。”)。所以與天地參，而建中立極也夫！

According to the method of卦气, the winter solstice begins with the line Nine in the Second of the hexagram 中孚, and the summer solstice begins with the line Nine in the Fourth of the hexagram 咸. Therefore, in the Great Treatise of the Upper Transmission of the Xici, the first of the eleven lines cited is the line 「鸣鹤在阴」 from 中孚 Nine in the Second; in the Great Treatise of the Lower Transmission of the Xici, the first of the eleven lines cited is the line 「憧憧往来，朋从尔思」 from 咸 Nine in the Fourth. The Image Commentary of 中孚 says: 「中孚以利贞，乃应乎天也.」 To respond to heaven means to harmonize with the heavenly qi; the mutual shifting of the sun and moon, the cold and heat, and the principle of thesympathetic response between the two qi of yin and yang becomes particularly clear. Although Confucius did not explicitly mention卦气 in his interpretation of the Yi, his words and deeds have shown the generations after him that they all conform to the heavenly patterns and phenomena. This is precisely why he could be ranked with heaven and earth as the three great principles, establishing the middle way and setting a standard.

(大過反覆為中孚小，過反覆為頤。初九“舍爾靈龜”，六四“虎視眈眈”。龜離象而屬北方玄武，火伏水中故能服氣。虎艮象，下應初，金生水，丹家所謂龍從火裡出，虎向水中生之象也。初莫若舍其靈龜，不能應乎四，則虎視眈眈，兩敗俱傷矣。頤曰“觀頤”，“神道”，本言道之卦。孔子不言神，故以“君子以慎言語節飲食”釋之。)

The hexagram Great Excess transforms back into the hexagram Middle Trust, and the hexagram Small Excess transforms back into the hexagram Nourishment. The hexagram Nourishment says in the first line, "Abandon your spiritual turtle," and in the fourth line, "The tiger watches intently." The turtle belongs to the image of fire and is paired with the northern Black Tortoise, representing fire hidden in water, thus capable of controlling breath and cultivating life. The tiger belongs to the image of mountain, and it is below, corresponding with the first line. Metal generates water, which is exactly the image described by the alchemists as "The dragon emerges from fire, the tiger is born from water." If the first line does not let go of its spiritual turtle and cannot correspond with the fourth line, then the fourth line will watch intently, and both will suffer. The hexagram Nourishment speaks of "Observing Nourishment," discussing the divine way of heaven and earth nurturing all things. It is essentially a hexagram that speaks of "the Dao." Confucius does not discuss spirits, so he only explains it by saying, "The gentleman should be cautious with words and restrain his diet."

孔子以《易》立教，示人以用世之道。故“立人之道，曰仁與義”。仁從二人，蓋必人與我相交接，而後可用吾仁。義從羊。羊者善群之物也。合多數人而為群，則有親疏遠近同異好惡之殊。於是仁之術，或有時而窮，不能不裁之以義。群既合，則必循有條理之組織，以定其秩序，於是禮緣義起。禮者理也，履也，各有定程，為人所循其當行者，而躬行實踐者也。

Confucius used the Zhou Changes to teach, guiding people on the principles of the world, so the "Commentary on the Hexagrams" says, "Establishing the way of human beings, it is called benevolence and righteousness." The character for "benevolence" (仁) consists of "person" (人) and "two" (二), meaning that benevolence can only be practiced when people interact with each other. The character for "righteousness" (义) consists of "sheep" (羊), an animal that is good at living in groups. When many people form a group, there are distinctions of intimacy, distance, similarity, difference, preference, and aversion. Thus, the method of benevolence may not always be sufficient, and righteousness must be used to make judgments. Once the group is formed, it must follow an orderly organization to establish order, so "ritual" (礼) arises from righteousness. Ritual is the same as reason (理), which is also "practice" (履): each has a fixed procedure, which people should follow and personally practice.

有組織，有定程，則必有所契約以共守之，而信著焉。故禮與信者，仁義之器也。皆人世之道也。《易》曰“元亨利貞”，孔子以四德釋之。君子行此四德，用之則行者焉。故曰用世。若離群絕世，翛然物外，則將何所用吾仁？何所用吾義？又何所用吾禮與信？然非無仁義也，非無禮與信也。舍之則藏，蓄吾德以復吾性。率性為道，庶幾下學上達，由器而進乎道矣。

There is organization and a fixed course, so there must be a common agreement to follow, thus "trust" (信) naturally arises. Therefore, rites (礼) and trust (信) are the vessels that carry benevolence (仁) and righteousness (义), and they both belong to the principles of the human world. The Hexagram Qian (乾) states "Original, Auspicious, Advantageous, and Upright" (元亨利贞), and Confucius explained it with the four virtues of originality (元), prosperity (亨), advantage (利), and uprightness (贞). A gentleman who practices these four virtues, once he is employed in the world, will take action. Therefore, this is considered the study of applying knowledge in the world. If one lives in seclusion, detached from the world, then where can my benevolence be applied? Where can my righteousness be applied? Where can my rites and trust be applied? However, this does not mean that he lacks benevolence or righteousness, nor does it mean he lacks rites and trust. If he is not employed, he will retreat and cultivate his virtue to return to his natural disposition. To act in accordance with one's natural disposition is the Dao (道). In this way, one can progress from learning the practical aspects (器) to attaining the Dao (道).

是故形而下者之謂器，非必制器尚象舟車宮室耒耜杵臼等之為器也。苟不能盡吾性，則禮樂政刑皆器也，仁義亦器也。形而上者之謂道，非必仁義禮信之為道也。能盡吾性，即一器一物之微，亦何莫非道之所寓？然因人立教，故未可驟言道也。故曰立仁與義。(佛家出世法無所謂仁義禮信，大圓性海中惟智燈獨照而已。)

Therefore, "what is formed beneath the principles is called the instrumental." It does not merely refer to objects made by imitating forms, such as boats and carts, palaces and houses, plows and hoes, mortars and pestles, as the term "instrumental" might be understood. If one cannot fully realize one's own nature, then rites, music, government, and laws are all instrumental, and benevolence and righteousness are also instrumental. "What is formed above the principles is called the way." It does not mean that only benevolence, righteousness, rites, and trust are considered the way. If one can fully realize one's own nature, then even the smallest object or tool is a dwelling place for the way. However, since teaching must be adapted to people, one cannot immediately speak of the way. Hence, it is said that the way of human beings lies in benevolence and righteousness. (Buddhism's transcendental teachings do not speak of benevolence, righteousness, rites, or trust; in the vast and complete ocean of nature, only the lamp of wisdom shines alone.)

《易緯》卦氣，六十四卦中，提出坎震離兌為四伯，亦曰四監，以主一年二十四氣。坎主冬至迄驚蟄，震主春分迄芒種，離主夏至迄白露，兌主秋分迄大雪。餘六十卦，以中孚起冬至，每卦主六日七分，每五卦分公闢侯大夫卿，主六候兩氣一節，六十卦共三百六十五日四分日之一，以合周天三百六十五度四分度之一。

The method of卦气 (hexagram qi) transmitted in the "Yi Wei" identifies the four hexagrams Kan, Zhen, Li, and Dui as the "Four Masters" or "Four Supervisors," used to govern the twenty-four solar terms of a year: Kan governs from Winter Solstice to Start of Spring, Zhen governs from Spring Equinox to Grain in Ear, Li governs from Summer Solstice to White Dew, and Dui governs from Autumn Equinox to Great Snow. The remaining sixty hexagrams, starting from Zhongfou at Winter Solstice, each govern six days and seven parts (a day is divided into eighty parts, and the sixty hexagrams collectively account for 365 and 1/4 days, so each hexagram governs exactly six days and seven parts). Every five hexagrams are divided into five ranks: Gong, Bi, Hou, Da Fu, and Qing, collectively governing six "hui" (periods), two "qi" (phases), and one "jie" (solar term). The sixty hexagrams together total 365 and 1/4 days, exactly matching the 365 and 1/4 degrees of the celestial sphere.

又別置復、臨、泰、大壯、夬、乾、姤、遁、否、觀、剝、坤為十二闢卦，每爻各主一候(五日五分，又六分分之，五為一候。)。自復至乾為息卦，曰太陽。自姤至坤為消卦，曰太陰。息卦所屬者曰少陽，消卦所屬者曰少陰。以四伯領十二闢，十二闢領公闢侯大夫卿五卦，以司一歲之卦氣，以推吉凶，名為六日七分之學。

In addition, the twelve hexagrams 《复》, 《临》, 《泰》, 《大壮》, 《夬》, 《乾》, 《姤》, 《遁》, 《否》, 《观》, 《剥》, and 《坤》 are set apart as the 「twelve great hexagrams」. 「Bì」 means ruler, and these twelve hexagrams are like the twelve rulers of the months in a year. Each line of the hexagrams governs one of the twenty-four solar terms, which are divided into five days each, with an additional five parts of six, making up one term. From 《复》 to 《乾》, these hexagrams represent the gradual growth of yang energy each month, known as 「the sun hexagrams」; from 《姤》 to 《坤》, they represent the gradual decline of yang energy each month, known as 「the moon hexagrams」. Those belonging to the growing yang hexagrams are called 「minor yang」, and those belonging to the declining yang hexagrams are called 「minor yin」. Using the four great trigrams to govern the twelve great hexagrams, which in turn govern the five ranks of hexagrams: public, ruler, marquis, minister, and chancellor, to manage the yin and yang energies of the year and to determine auspiciousness and inauspiciousness, this is called the 「six days and seven parts」 system.

盛於西漢，而尤於京氏為精。故後人輒稱之為京房卦氣。其實此法相傳最古。今所傳《連山》，卦雖殘缺不完，然以坎離震兌分主四季，亦復相同。可見自三代時已有此學。故孔子《繫傳》上繫起中孚，下繫起咸，亦述而不作焉。漢人去古未遠，三代遺法猶有存者。京氏之學，自必有所師承，非所能臆造者。

This discipline became popular during the Western Han dynasty, especially with Jing Fang who explained it most thoroughly. Hence, later generations often refer to it as "Jing Fang's Hexagram Qi." In fact, this method has a very ancient origin. Although the present transmission of "Lian Shan" is incomplete, it still uses Kan, Li, Zhen, and Dui to represent the four seasons, showing that this discipline existed during the Xia, Shang, and Zhou dynasties. Therefore, Confucius in the "Great Treatise" of the "I Ching" mentions the beginning of the lines in "Zhongfou" in the upper transmission and in "Xian" in the lower transmission, which is merely following the old method without introducing new ideas, as said "to narrate but not to create." Since the Han people were not far from the ancient times, the remaining practices of the Xia, Shang, and Zhou dynasties were still present, so Jing Fang's studies must have had a teacher, and it could not have been invented by him alone.

特其時讖緯之說盛行，各自為說，真贗莫辨，漸入於怪誕支離，幾不可究詁。至禁習緯書以遏其頹波，而三古僅存之遺法，亦為之湮沒不彰，良可痛也。

At that time, prophecies and interpretations of classics were widespread, with everyone offering their own views, making it difficult to distinguish truth from falsehood. Over time, these interpretations became increasingly strange and fragmented, making it almost impossible to study. Later, the government banned the study of the "Wei Shu" to curb this declining trend, and the remaining ancient methods were also gradually lost and forgotten, which is truly regrettable.

後之言卦氣者，變化百出，有自乾至未濟，依文王《序卦》，以一卦直一日，乾直甲子，坤直乙丑，迄未濟直癸亥，周而復始。六周盡三百六十日，而坎離震兌直二分二至，此焦氏之法也。有以乾坤坎離為橐龠，餘六十卦，依《序卦》一爻值一時；而周一月，又以十二闢卦，每卦管領一時。此魏伯陽之法也。

Later commentators on the hexagram energies devised various methods. Some arranged the hexagrams from Qian to Weiji, following King Wen's sequence of hexagrams, assigning each hexagram to one day: Qian corresponded to Jiazi, Kun to Yichou, and so on until Weiji corresponded to Guihai, then the cycle repeated. After six cycles, exactly 360 days were covered, with Kan, Li, Zhen, and Dui assigned to the solstices and equinoxes—this was Jiao Yanshou's method. Others used Qian, Kun, Kan, and Li as the bellows (tuo yue), symbolizing the continuous movement without itself participating in the cycle, and the remaining sixty hexagrams arranged in King Wen's sequence, with each trigram corresponding to an hour, completing a cycle in a month. They also assigned the twelve great hexagrams to each hour—this was Wei Boyang's method.

有以六十卦，一爻主一日，《上經》起乾甲子，泰甲戌，噬嗑甲申，至離三十卦，而三甲盡。《下經》起咸甲午，損甲辰，震甲寅，至癸亥而終，亦三十卦。另以中孚小過既未濟，代坎離震兌，以應分至。每爻直十五日，以應二十四氣。此史繩祖之法也。

Some use the sixty hexagrams with each line corresponding to one day: the Upper Canon starts with the hexagram Qian (Heaven) on Jiazi, Tai (Peace) on Jiaxu, and Shihe (Crushing the Bones) on Jiashen, reaching Li (Fire) after thirty hexagrams, and the three dry branches Jiazi, Jiaxu, Jiashen cycle completely; the Lower Canon starts with Xian (Salty) on Jiawu, Shen (Loss) on Jiachen, and Zhen (Thunder) on Jiayin, ending at Guihai, also covering thirty hexagrams. Additionally, they use Zhongfou (Sincerity), Xiaoguo (Minor Crossing), Ji Ji (Completion), and Weiji (Non-Completion) to replace Kan (Water), Li (Fire), Zhen (Thunder), and Dui (Lake), corresponding to the solstices and equinoxes. Each line corresponds to fifteen days, matching the twenty-four solar terms—this is the method of Shi Shengzu.

至邵康節以先天圖定卦氣，以復起冬至，姤起夏至，以乾坤坎離，分主二至二分。而張理又取邵子先天方圖，以冬至起復，至泰而正月，乾四月，否七月，坤十月。又以一陰一陽至六陰六陽分列，六陽處南，自下而升；六陰處北，自上而降，則又合漢宋為一家矣。《易占經緯》又以文王八卦，依邵子先天式列為圓圖，而以渙起冬至。紛紛不一。

At the time of Shao Kangjie, the use of the Earlier Heaven diagram was employed to determine the卦气: the hexagram of Fu began at the winter solstice, and the hexagram of Gou began at the summer solstice. The trigrams Qian, Kun, Kan, and Li were assigned to the two solstices and two equinoxes. In the Yuan dynasty, Zhang Li adopted Shao's arrangement of the sixty-four hexagrams into a square diagram, starting with Fu at the winter solstice, reaching Tai for the first lunar month, Qian for the fourth lunar month, Po for the seventh lunar month, and Kun for the tenth lunar month. He also arranged them according to alternating yin and yang, with the six yang trigrams located to the south, rising from bottom to top, and the six yin trigrams located to the north, descending from top to bottom. This synthesis combined Han and Song schools of thought. The "Yi Zhan Jingwei" then arranged the Later Heaven trigrams of King Wen in a circular diagram following the pattern of Shao's Earlier Heaven diagram, starting with Huan at the winter solstice. Various interpretations abound, each differing from the others.

除焦氏為別立占法，非關卦氣；魏伯陽《參同契》，乃借《易》以演其丹經；邵子先天數，以《易》演其《皇極經世》，各自成一家，當從別論外，其餘皆模仿六日七分法以之推演者。雖具有條理，而按諸理數而無當，驗諸天時而不合。雖斥為無知妄作，亦未為不可。至因眾說之蕪雜，並卦氣而亦妄之，無乃矯枉而過其正歟！

Jiao Yanshou established a separate system of divination unrelated to the trigram calendar; Wei Boyang's "Zhou Yi Cang Tong Qi" used the Zhou Yi to elaborate his alchemical treatises; and Shao Zi's Earlier Heaven numbers employed the Zhou Yi to develop his "Huang Ji Jing Shi." These three schools formed their own distinct traditions and should be considered separately. In addition, other theories were merely imitations of the "six days and seven parts" method, which although possessing some logical structure, did not conform to the principles of numerical divination and failed to align with celestial phenomena. They could be dismissed as mere baseless inventions. However, if one dismisses the trigram calendar entirely merely because of the confusion among various interpretations, that would be an overreaction.

攻京氏之術，其占法所用月建，與近世術家之所謂月建不同。近以占日所隸節為月建，而京氏以爻直月，從世起建，佈於六位。惟乾坎二卦從初爻起，餘卦均從世爻起。如乾起甲子，坤起甲午，一卦凡六月也。積算則以爻直日，即從建所止起日，如姤之上九乙亥，即以乙亥起上九為一日，終而復始。一卦凡一百八十日。近則月為直符，日為傳符，以見於爻之卦支，合於日月者當之，與古法異矣。

Those who study Jing Fang's method should know that the "Month Builder" used in Jing's divination differs from the "Month Builder" mentioned by modern diviners. Modern practitioners determine the Month Builder based on the solar term corresponding to the day of the卦's commencement, while Jing's method uses the爻's value to determine the Month Builder, starting from the World Line and sequentially placing it on the six lines of the卦. Only the hexagrams Qian and Kan start from the first line, while all other hexagrams start from the World Line. For example, Qian starts with Jiazi and Kan starts with Jiawu, covering a total of six months for each hexagram. "Accumulated Calculation" involves using the day's value, starting from where the Month Builder ends: for instance, if the upper ninth line of the hexagram Gou is Yihai, then Yihai is taken as the first day of the upper ninth line, and this cycle repeats, covering a total of 180 days for each hexagram. Modern methods use the month as "Direct Symbol" and the day as "Transmitted Symbol," taking the earthly branch included in the line if it matches the day's branch and the Month Builder, which differs from the ancient method.

蓋京氏之學，魏晉以後，已鮮傳人。至宋時，僅存《火珠林》之法。而所謂《火珠林》者，亦不詳其所自，未知撰述者何人。要之以錢代蓍，與近世所傳相近，而《火珠林》之書卒不可見。間有傳本，又鈔寫不同，未能確辨其真偽也。

Originally, the school of Jing Fang became little known after the Wei and Jin dynasties, and by the Song dynasty only the method of the Fire Pearl Forest remained. As for the Fire Pearl Forest, its origin is unclear, and its author is unknown. In general, it uses copper coins instead of the yarrow stalks, and this method is similar to the modern practice of shaking coins to form a hexagram. However, the book of the Fire Pearl Forest is rarely seen, and when there are a few copies, they are copied differently, making it impossible to determine their authenticity with certainty.

今所傳卜筮之書，大都出於唐宋之後。溯其淵源，終不出京氏世應飛伏之範圍。而取用分類，或視昔較繁。世事紛紜，孳乳遞演，累進無已。機械之用，尤日出不窮。故推算之術，往往今密於古。但按於理而可通，徵諸道而不悖者，正不妨變通以宜民，必執舊法以相繩無謂也。

The divination texts that are passed down today mostly originated after the Tang and Song dynasties; tracing their origins, they ultimately fall within the scope of the "World and Response Lines" and "Flying and Hidden" concepts from the Jingshi school. However, the categories used are more complex than in earlier times. The world is full of confusion and change, with each generation giving rise to new developments, layer upon layer without end. The use of mechanical devices is especially endless, so the methods of calculation often become more refined in later times than in ancient times. As long as they make sense according to reason and do not contradict the Dao, they should be adaptable for the benefit of people; one must not rigidly adhere to old methods to measure everything, which would be meaningless.

《乾·九三》“君子終日乾乾夕惕若夤厲無咎”，舊本無“夤”字，後據《說文》所引補入。高郵王氏駁之，列舉五義，其說詳矣。然以卦象推之，乾九三爻即艮爻，《艮·九三》“艮其限列其夤厲熏心”，足以證乾九三之“夕惕若夤厲無咎”之“夤”字，決非《說文》所誤引，與後人傳寫之訛也。

The line statement of the third line of the Qian hexagram, "A gentleman remains diligent all day, and in the evening remains cautious as if something were hidden, perilous, yet without blame," originally did not include the character "yin." Later scholars added it based on the text of the Book of Changes cited in the Shuowen Jiezi. Wang Shi of Gaoyou criticized this method of supplementation, listing five reasons and explaining them in detail. However, from the perspective of the hexagram's imagery, the third line of Qian corresponds to the third line of Gen. The line statement of Gen's third line is "Restraining the waist, revealing the yin, perilous and burning in the heart." This clearly demonstrates that the character "yin" in the third line of Qian's line statement is not an error in the Shuowen Jiezi, nor a mistake in transmission.

王氏以《文言》亦無“夤”字，為所據五證之最有力者。然傳以釋經，固未必全錄經文。“坤先迷後得主利”，而《文言》曰“後得主而有常”，亦無利字，豈足以證《坤·彖》“先迷後得主利”之“利”字為衍文乎？“夤”字於卦義爻義，均極有關係，當別為說以詳之。

Wang's argument that the "Yin" character is absent in the "Wenyan Zhuan" is regarded by him as his strongest of five pieces of evidence. However, the Zhuan is used to explain the Jing, and it is not necessarily required to copy the entire text of the Jing. The "Kun" hexagram statement says "first being lost, then obtaining the master, beneficial," but the "Wenyan Zhuan" only says "after obtaining the master, there is constancy," without the character "li." Can this be used to conclude that the "li" character in the "Kun · Tuan" passage "first being lost, then obtaining the master, beneficial" is an added character? The character "Yin" is of great importance for the relationship between the hexagram meaning and the line meaning, and should be discussed in detail in a separate article.

《繫傳》“天一地二天三地四”至“所以神變化而行鬼神也”一節，原本在“《易》有聖人之道四焉”一節之前。下文所謂“參伍以變錯綜其數，通其變極其數”云云，皆根據於此。程子以之移在“大衍之數五十”之上，後人皆因之，遂將經文前後隔截，不相貫串，致發生二種錯誤。

The Great Treatise of the Upper Classic begins with "Heaven is one, Earth is two, Heaven is three, Earth is four" and continues until "so it can produce changes and act like ghosts and spirits." This section originally came before the passage "The Book of Changes contains four ways of the sage," and the following statements such as "by combining three and five, changes are made; by interweaving numbers, calculations are made" and "by comprehending changes... reaching the extreme of numbers" all rely on this section. Cheng Yi moved it above the section discussing the use of yarrow stalks for divination, "the great number of the Great Derivation is fifty," and later generations followed this move without question. As a result, the originally connected text was cut into two parts, making them disconnected and leading to two errors.

其一，“參伍錯綜”二語；無所附麗輾轉相訛，異說滋多。來瞿塘之錯綜，張乘槎之參伍，其病根皆伏於此。其二，今“大衍之數五十”，因與“天地之數五十有五”不符，發生無數異議。其實天地之數自天地之數，大衍之數自大衍之數，本不相蒙。因經文移易之後，兩節相為聯屬，遂混兩說而一之，費無限辯論駁議，於經文無所發明。

First, the phrases "San Wu" and "Cu Zhong" have lost their original context and have been passed down with errors, leading to an increasing number of conflicting interpretations. Lai Zhide discussed "Cu" and "Zhong," while Zhang Chengcha discussed "San Wu," and the root of the problem lies here. Second, the phrase "Da Yan Zhi Shu Wu Shi" (the number of the Great Derivation is fifty) has caused numerous disputes because it does not match "Tian Di Zhi Shu Wu Shi You Wu" (the number of heaven and earth is fifty-five). In reality, the number of heaven and earth is the total sum of numbers from one to ten, while the number of the Great Derivation is the actual number of yarrow stalks used in divination. These are two separate matters and originally had nothing to do with each other. However, because the passages in the text are placed next to each other, people have confused the two different concepts, leading to endless debates without any real contribution to the understanding of the text.

此皆改經之流弊也。宋儒好擅改經文，貽誤後學實多，此特其一耳。至有明喬氏黃氏，及清任釣臺等，擅將《繫辭》顛倒錯亂，尤為無知妄作，要亦宋儒之有以開其先也。

These are all the consequences of arbitrarily altering the classics. The Song dynasty scholars often made unauthorized changes to the texts, causing much confusion for later learners; this is merely one example. As for the Qiao family and Huang family of the Ming dynasty, and Ren Diaotai of the Qing dynasty, who arbitrarily rearranged the "Great Treatise," especially those who acted recklessly without knowledge, in the end, it was the Song scholars who first set the precedent.

《周易》“用九用六”。“九”“六”二字，注《易》者立說不一。《正義》云：“陽爻稱九，陰爻稱六。”其說有二：一者乾體三畫，坤體六畫。陽得兼陰，故其數九。陰不得兼陽，故其數六。二者老陽數九，老陰數六。老陰老陽皆變，《周易》以變為占。揲蓍之數，九過揲則得老陽，六過揲則得老陰。少陽稱七，少陰稱八，皆不變，為爻之本體。老陽老陰交而後變，故為爻之別名。

After the two hexagrams of Qian (Heaven) and Kun (Earth) in The Zhou Changes, there are additional sections called "Use of Nine" and "Use of Six." The characters "nine" and "six" have different interpretations among commentators of the I Ching. Kong Yingda, in his work The Correct Meaning of the Zhou Changes, explains that "a yang line is called nine, and a yin line is called six." He provides two reasons for this. First, the hexagram of Qian consists of three solid lines, while the hexagram of Kun consists of six broken lines. Yang can include yin, so its number is nine; yin cannot include yang, so its number is six. Second, the number of old yang is nine, and the number of old yin is six. Old yin and old yang both change, and The Zhou Changes uses changing lines for divination. According to the method of divination with yarrow stalks, if the number of stalks exceeds nine groups, it is considered old yang; if it exceeds six groups, it is considered old yin. Young yang is called seven, and young yin is called eight; these do not change and represent the original form of the line. Old yang and old yin interact and then change, so "nine" and "six" are alternative names for the lines.

邵子曰：“《易》有真數三而已。三天者三三而九，兩地者倍三而六。陰無一，陽無十。”楊氏萬里曰：“積天數之一三五曰九，積地數之二四曰六。”

Shao Kangjie said: The true number in the Zhou Changes is only 'three'. 'Ce Tian' (ascending to heaven) is three threes multiplied together to get nine, and 'Li Di' (two lands) is three plus one doubled to get six. Yin does not contain 'one', and Yang does not contain 'ten'. Yang Wanli said: Adding the heavenly numbers one, three, and five together gives nine, and adding the earthly numbers two and four together gives six.

《朱子語類》：“奇陽體圓，其法徑一圍三而用其全，故少之為數三。偶陰體方，其法徑一圍四而用其半，故多之為數二。歸奇積三三為九，過揲四九為三十六。積三二為六，過揲四六為二十四。積二三一二為八，過揲四八三十二。積二二一三為七，過揲四七二十八。七八九六，經緯乎陰陽。陽進陰退，故九六為老，七八為少。陽極於九，退八而為陰。陰極於六，進七而為陽。占用九六而不用七八，取其變也。”

Master Zhu Xi said: Odd numbers belong to yin and yang, and their form is round. In calculation, the diameter is one and the circumference is three, and the full number is used, so the portion with fewer counts is considered three. Even numbers belong to yin and yang, and their form is square. In calculation, the diameter is one and the circumference is four, and only half is taken, so the portion with more counts is considered two. The number of odd counts added three times as three totals nine, and the overcounting number is forty-eight. The number of even counts added three times as two totals six, and the overcounting number is twenty-four. Two threes and one two added together total eight, and the overcounting number is thirty-two. Two twos and one three added together total seven, and the overcounting number is twenty-eight. The numbers seven, eight, nine, and six interweave to form the meridians and parallels of yin and yang. Yang represents advancement, while yin represents retreat. Therefore, nine and six are considered old, while seven and eight are considered young: when yang reaches nine it is at its extreme, and when it retreats to eight, it becomes yin; when yin reaches six it is at its extreme, and when it advances to seven, it becomes yang. Divination uses only nine and six but not seven and eight, taking precisely their capacity to change.

王氏夫之曰：“於象一二函三，三奇之畫一，全具其數。三奇而成陽，三三凡九陰。左一右一，中缺其一。三二而為六。”來氏之所謂“參天兩地”，即楊氏萬里說也。其餘諸家，大約宗孔義與朱說者為多。

Wang Fu Zhi said: In terms of observation, one and two contain three; each of the three odd lines is considered as one, and altogether they possess the number. Three odd lines combine to form yang, and three threes make nine; for yin lines, they consist of a segment on the left, a segment on the right, and a missing segment in the middle, and three twos together make six. As for Lai Zhide's explanation of "three heavens and two earths," it is essentially the same as Yang Wanli's view. As for other scholars, most follow the interpretations of Kong Yingda and Master Zhu.

王氏夫之雖似從《正義》第一說，而實較孔氏為精。蓋數極於九，本陰陽之所同具，故二九十有八變而成卦。陰之稱六，特虛其三耳。以推之象，則惟乾九坤六，震坎艮皆七，巽離兌皆八。此《易》之獨繫二用於重乾重坤之下歟？(《易》數稱奇偶，不曰單雙。奇圓偶方稱數而形已寓其中，乾圓坤方圓周三百六十為率分四象，限為九十度。圓內容方方邊自為六十度。此數理之自然。“圓”見《易數偶得》)

Wang Fu-zhi seems to follow Kong Yingda's first explanation, but in fact he explains it more precisely. Since nine is the extreme of numbers, it is shared by both yin and yang. Therefore, two nines, making eighteen changes, form a hexagram. The reason yin is called six is simply that three of the numbers are omitted. Applying this principle to the hexagrams, only Qian (Heaven) is nine and Kun (Earth) is six. The three trigrams Zhen (Thunder), Kan (Water), and Gen (Mountain) are all seven, while the three trigrams Xun (Wind), Li (Fire), and Dui (Lake) are all eight. This is probably why the Zhou Changes alone attach the phrases "use of nine" and "use of six" to the repeated Qian and repeated Kun. In the Zhou Changes, numbers are called "odd" and "even," not "single" and "double." Odd is round and even is square. One number already implies shape: Qian is round and Kun is square. The circumference of a circle is taken as 360, divided into four trigrams, each occupying 90 degrees. The square inside the circle has each side measuring 60 degrees. This is naturally the case in numerical reasoning. For more on "circle," see my work "Notes on the Numerical Principles of the Zhou Changes."

爻有動靜，卦有貞悔。占例：內卦為貞，外卦為悔。靜卦為貞，動卦為悔。《春秋左氏傳》曰：“貞風也，悔山也。”此內貞外悔者也。貞屯悔豫，此靜貞動晦者也。向來講《易》家皆宗此說，朱子《啟蒙》言之尤詳。

Lines in a hexagram are either active or inactive, and hexagrams have a main one and a changing one. The general rule in divination is: the inner trigram is called 'Zhen,' and the outer trigram is called 'Hui'; an unchanging hexagram is called 'Zhen,' and a changing hexagram is called 'Hui.' The 'Zuo Shi Chuan' of the 'Spring and Autumn Annals' records divination statements saying 'Zhen is wind, Hui is mountain,' which refers to the inner trigram as 'Zhen' and the outer trigram as 'Hui.' It also says 'Zhen is the hexagram 'Zun,' Hui is the hexagram 'Yu,'' which refers to the original hexagram as 'Zhen' and the changing hexagram as 'Hui.' All those who have interpreted the 'Yi' have followed this explanation. Master Zhu's 'Yi Xue Ming Tong' explains this in detail.

而不知《易》之經文，已明明自舉其例。《坤·六三》曰“可貞”，明內卦之為貞也。《乾·上九》曰“有悔”，明外卦之為悔也。如《乾·初九·傳》曰“陽在下也”，《坤·初六·傳》曰“陰始凝也”，亦為陽九陰六自舉其例也。

But he did not know that the text of The Zhou Changes itself clearly presents these meanings. The hexagram Kūn (Earth) at line six three says "It is proper to be firm," which clearly indicates that the inner trigram is called "Zhen" (firmness). The hexagram Qián (Heaven) at line upper nine says "There is regret," which clearly indicates that the outer trigram is called "Hui" (regret). Another example is the Small Image Commentary of Qián hexagram at line initial nine, which says "Yang is at the bottom," and the Small Image Commentary of Kūn hexagram at line initial six, which says "Yin begins to condense." These are also examples given by the text itself to explain why Yang is called "nine" and Yin is called "six."

朱子以河圖洛書及先天卦位圓方各圖，弁於《周易》之首，為後世言漢學者所抨擊，幾於體無完膚。然趙宋以前，雖未有先天之圖，而乾坤坎離震巽艮兌之卦位，固早散見於漢人之《易》注。荀慈明之升降，虞仲翔之納甲，細按之殆無不與先天之方位相合。即以經文上下二篇之卦論之，《上經》首乾坤終坎離，非四正之卦乎？《下經》首上兌下艮之咸，上震下巽之恆，非四隅之卦乎？至《說卦》“天地定位山澤通氣”之一章，兩兩對舉者，更無論矣。

Zhu Xi placed the "Yellow River Chart," "Luo Writing," and the circular and square diagrams of the Earlier Heaven trigrams at the beginning of the "Zhou Changes" (I Ching). Later scholars of the Han learning school criticized him heavily, almost refuting him completely. However, before the Song dynasty, although the diagram of the Earlier Heaven trigrams had not yet been drawn, the relative positions of the eight trigrams—Qian, Kun, Kan, Li, Zhen, Xun, Gen, and Dui—were already scattered in the commentaries of Han scholars on the "Book of Changes." Xun Shuang's concept of "ascending and descending" and Yu Fan's theory of "Najia stem assignment" correspond closely with the positions of the Earlier Heaven trigrams. Even if we look only at the sequence of trigrams in the upper and lower parts of the "Book of Changes": the upper part begins with Qian and Kun and ends with Kan and Li, which are exactly the four cardinal trigrams of the Earlier Heaven diagram. The lower part starts with the "Xian" trigram, which has Dui above and Gen below, followed by the "Heng" trigram, which has Zhen above and Xun below, which are precisely the four intercardinal trigrams. As for the passage in the "Shuo Gua Zhuan" that says "Heaven and Earth are positioned, mountains and marshes communicate through the air," which lists the eight trigrams in pairs, this is even more obvious.

乃漢學家必一概抹煞，謂經傳無乾南坤北離東坎西之文。然先王制禮，推本於《易》，固漢學家所公認焉。乾天坤地，離日坎月，亦漢學家所公認焉。《祭義》“祀天南郊，祭地北郊。朝日東門，夕月西門”，豈亦“帝出乎震”一章之方位乎？

However, Western scholars tend to dismiss these clues altogether, claiming that the classics and their commentaries contain no mention of "Qian in the south, Kun in the north, Li in the east, Kan in the west." Yet it is acknowledged by Western scholars themselves that the ancients established rituals based on the Yi Jing. It is also acknowledged by them that Qian represents Heaven, Kun represents Earth, Li represents the sun, and Kan represents the moon. The Li Ji · Ji Yi states: "In the southern suburbs, we worship Heaven; in the northern suburbs, we worship Earth; at the eastern gate, we pay homage to the sun; at the western gate, we pay homage to the moon." Heaven is in the south, Earth in the north, the sun in the east, and the moon in the west. Is this arrangement of directions the Later Heaven arrangement mentioned in the Shuo Gua Zhuan's chapter "The Emperor arises from Zhen"? It is clearly the Earlier Heaven arrangement.

“河出圖洛出書”，明見於《繫傳》，是否即今所傳之河圖洛書？誠不敢必。但天地之數五位相得而各有合，既為孔子所明言；一六二七三八四九之位數，又為鄭康成揚子雲所列舉；而兩數之經緯錯綜，加減乘除，又極盡陰陽變化之妙，悉出造化之自然，非人力所能造作。乃亦以經所未載，訾議亦駁斥不留餘地？

The saying "The Yellow River produced the chart, the Luo River produced the book" is clearly recorded in the Great Treatise. As for whether it refers to the two diagrams known today as the Yellow River Chart and the Luo Writing, one cannot be certain. However, the matching of the five numbers with the five positions in the cosmos, each having its own pairing, was clearly explained by Confucius in the Great Treatise. The numerical positions such as one and six, two and seven, three and eight, four and nine, were also listed by Zheng Xuan (styled Kangcheng) and Yang Xiong (styled Ziyun). These two sets of numbers, when arranged in cross and vertical directions and subjected to addition, subtraction, multiplication, and division, are consistent everywhere, revealing the profound mysteries of yin and yang changes to the fullest extent. This arises naturally from the workings of the universe itself, not from human invention. Yet Han scholars, merely because the classics do not explicitly mention them, have一味ly criticized and rejected them without leaving any room for consideration.

毛西河改河圖為天地生成圖，洛書為太乙九宮圖。夫此二名，詎為經文所載乎？鄭康成之爻辰，所謂子寅辰午申戌，亦經所未載。乃一則據為典要，一則斥為異端。豈得謂是非之平，黨同伐異之見，不能為賢者諱矣。

Ma Qilin, who styled himself as Xihé, renamed the "Heavenly River Chart" as the "Diagram of Heaven and Earth Generating Each Other" and the "Luo Writing" as the "Diagram of Taiyi Nine Palaces." However, are these new names found in the canonical texts? Zheng Xuan's theory of "Yao Chen" paired the six lines of the Qian hexagram with the earthly branches Zi, Yin, Chen, Wu, Shen, and Xu, which are also not found in the canonical texts. Western scholars treat Zheng Xuan's Yao Chen theory as an unshakable principle, yet they condemn the Heavenly River Chart and Luo Writing as heretical. Both are not found in the canonical texts, yet they are treated so differently. How can there be any fair judgment? This kind of favoritism toward one's own group and hostility toward outsiders is a prejudice that cannot be justified even if it comes from respected elders.

許叔重《說文》云：“《秘書》日月為《易》，象陰陽也。”所謂“秘書”者，當時必有傳本。許與魏伯陽同時，決非指《參同契》也。杜預《春秋左氏傳集解後序》曰：“汲郡有發舊塚者，大得古書。《周易》上下篇與今本同。別有陰陽說，而無《彖》、《象》、《文言》、《繫辭》。疑於時仲尼造之於魯，尚未播之於遠國也。”由是觀之，《周易》上下二篇外，必尚有類於圖說之簡篇。漢時猶有流傳，或稱為“秘書”，亦未可知。

Xu Shen, whose courtesy name was Shuzhong, in his work Shuo Wen Jie Zi said: "The Secret Collection explains that the characters 'sun' and 'moon' combined form the character 'yi', which is taken as an image of yin and yang." The work he cited, the Secret Collection, must have had another existing version at that time. Xu Shen and Wei Boyang were contemporaries, so what he referred to could not have been Wei Boyang's Zhou Yi Cang Tong Qi. Du Yu, in his postscript to the Spring and Autumn Zuo Zhuan Ji Jie, said: "There was a person in Ji Jun who dug up an ancient tomb and found a large number of ancient books. Among them were the upper and lower parts of the Zhou Yi, which were the same as the current version, and another book that discussed yin and yang, but did not include the Commentary on the Judgment, the Image Commentary, the Wenyan, or the Great Treatise. It is inferred that when Confucius was in Lu State composing the Ten Wings, they had not yet spread to distant countries." From this, it can be seen that in addition to the upper and lower parts of the Zhou Yi, there must have been other documents similar to diagrams, which might have been still in circulation in the Han dynasty and referred to as 'secret collection'.

朱子謂“先天各圖，決非後儒所能偽造，必當初所本有，後來散佚，流入道家。至希夷傳出，得復還儒家之舊”云云，殊非無所見而云然也。後人或據劉長民之說，以九為河圖，十為洛書。或欲避先後天之名，以先天為伏羲八卦，後天為文王八卦；或以先天為天地定位圖，後天為帝出乎震圖。舍其實而鶩於名，是更可以不必矣。

Zhu Xi said: "The earlier heaven diagrams were certainly not fabricated by later Confucian scholars, but must have originally existed, then scattered and passed into Daoism; until Chen Tuan (who was known as Xiyi) transmitted them again, they were able to return to Confucianism as their original possession." This statement is not without basis. As for later scholars, some followed Liu Mu's (who was known as Changmin) view, calling the nine palace numbers "the Yellow River Chart" and the ten number diagram "the Luo Writing"; others wished to avoid the terms "earlier heaven" and "later heaven," instead calling the earlier heaven "the Fuxi Eight Trigrams" and the later heaven "the King Wen Eight Trigrams"; still others renamed the earlier heaven as "the Diagram of Heaven and Earth Positioned" and the later heaven as "the Diagram of the Emperor Emerging from the Thunder." All of these are abandoning the substance and competing over names, which is even more unnecessary.

易學於西漢為盛。乃至東京，幾成絕響。施孟梁丘三家之學，若存若亡。費氏高氏，亦罕傳述。至漢季始有馬鄭荀虞諸氏，繼緒而興。陸績劉表宋衷諸氏，均有撰著。然習費氏古文者為多。三家之《易》，僅虞翻延孟氏一線，餘子皆湮沒無聞矣。嘗疑東西二京，相去非遙，何以易學之驟然衰落，一至於是？此其中必有原因。

Yi studies flourished greatly during the Western Han dynasty, but by the Eastern Han dynasty, they had almost become a thing of the past. The three official schools of study, led by Shi Chou, Meng Xi, and Liang Qiu He, were either still existing or on the verge of extinction. The two other schools, led by Fei Zhi and Gao Xiang, were scarcely transmitted by anyone. It was not until the end of the Han dynasty that figures such as Ma Rong, Zheng Xuan, Xun Shuang, and Yu Fan resumed the tradition and revived Yi studies. Lu Ji, Liu Biao, and Song Zhong also wrote their own works, but most of their studies were based on the ancient text version of Yi transmitted by Fei Zhi. The schools of Yi from Shi, Meng, and Liang Qiu had only the lineage of Yu Fan continuing the tradition of Meng Xi, while all the other schools had completely disappeared. I have always been puzzled: the Western Han and Eastern Han dynasties were not far apart, so why did Yi studies suddenly decline to such an extent? There must be some reason behind this.

嗣據金石家所探索，謂西漢無碑，因王莽惡稱頌漢德，故剷除殆盡。間有存者，非伏藏土中，或深埋窮谷，為搜剔所不及者耳。於是悟《易》注之亡，亦或莽之所為。蓋西漢易學既盛，而讖緯之說，又成俗尚。西京士大夫，往往侈言陰陽。觀馬班諸書所錄書疏，可見其概。莽初則利為己用，名位既成，惡而去之，乃勢所必然。竄改五經之作用，亦此物此志焉。

Later, when I read the investigations of numismatologists and epigraphers, I learned that few stone inscriptions from the Western Han dynasty have survived. This was because Wang Mang detested the inscriptions that praised the Han dynasty's achievements and had them destroyed completely. Occasionally, some inscriptions did survive, but they were buried underground or hidden deep in remote mountains and valleys, beyond the reach of search. From this I realized that the loss of the Western Han commentaries on the Book of Changes may also have been due to Wang Mang. Since the study of the Book of Changes was very flourishing in the Western Han, and the doctrine of "portents and omens" had become a prevailing trend, scholars in the capital often discussed yin and yang and portents of disaster and auspicious signs. This can be seen from the memorials collected in the works of Sima Qian and Ban Gu. At first, Wang Mang skillfully used this doctrine to build up his own authority, but once he had secured his position, he turned against it, detesting and destroying it, which was inevitable. His intention to alter the Five Classics was driven by the same mindset.

又據《班書·儒林傳》，高相子康以明《易》為郎，王莽居攝。東郡太守崔誼，謀舉兵誅莽。事未發，康候知東郡有兵亂，私語門人，門人上書言之。後數月崔誼兵起，莽召問，對受師高康，莽惡之。以為惑眾斬康，亦足為莽摧殘易學之一證焉。行篋無書，他日當詳考之。

According to Ban Gu's "Book of Han, the Transmission of the Confucian Schools," Gao Kang, the son of Gao Xiang, became an official because he was skilled in the study of the Book of Changes. When Wang Mang was acting as regent, the governor of Dongjun, Cui Yi, plotted to raise an army to kill Wang Mang. Before the plot was carried out, Gao Kang, through divination, foresaw that there would be military unrest in Dongjun and secretly told his disciples. However, the disciples reported this to the authorities. A few months later, Cui Yi indeed raised an army, and Wang Mang summoned Gao Kang for questioning. Gao Kang claimed that he had learned this from his teacher. Wang Mang therefore resented him and had him executed on charges of spreading false prophecies. This incident serves as evidence of Wang Mang's suppression of the study of the Book of Changes. I did not bring any books with me, and I will examine this matter more thoroughly in the future.

嗚呼，《易》幸不亡於暴秦，乃厄於偽新。殆所謂美新劇秦也歟？（按：呂政不知書，故儕《易》於卜筮，不甚注意。而王莽則深於經學者也，知《易》道廣大，必為小人之憂。乃陽奉而陰沮之。一手遮天，直欲盡掩天下後世之耳目。諺曰：家賊之禍，倍烈於盜寇哉！）

Alas! The Zhou Changes (I Ching) luckily escaped destruction by the brutal burning of books under the Qin dynasty, but instead suffered hardship under Wang Mang's fabricated "Xin" dynasty. This is probably the result of Yang Xiong's approach in his work "Ju Qin Mei Xin," which criticized the brutal Qin and praised Wang Mang. (Original note: Emperor Qin Shi Huang did not read books, so he classified the I Ching under divination and did not pay much attention, allowing the I Ching to be preserved. Wang Mang, however, was deeply knowledgeable in Confucian classics and understood that the principles of the I Ching were vast and would inevitably become a tool for villains. Therefore, he outwardly honored it but secretly obstructed its spread, trying to block the eyes of the world. A proverb says: the祸 of family thieves is twice as severe as that of bandits!)

輔嗣說《易》，陳誼甚高。而文辭雋逸，超乎物外，故能得意忘象。司空表聖所謂超於象外得其環中者，其斯之謂歟？惟必超乎象之外，方可以忘象。如探驪龍之領而既得其珠，則龍亦廢物，更何論乎魚兔之筌蹄？

Wang Bi (style name Fusi) explained the Yi, establishing his arguments at a high level, and his writing was clear, elegant, and detached from worldly concerns. Therefore he could "grasp the meaning and forget the image" — once he understood the principles, he could set aside the hexagrams. The phrase "transcend the image and grasp the center of the circle" from Si Kong Tu's Twenty-Four Poetic Styles probably refers to this kind of realm. However, one must truly transcend the hexagrams before one can forget the images. It is like the person who retrieves a pearl from the dragon's jaw; once the pearl is in hand, the dragon itself becomes useless, let alone the bamboo baskets for fishing or the nets for catching rabbits.

後之言《易》者，既畏象數之繁頤奧衍，莫窺其蘊，喜王氏之學，可以避去繁頤奧衍之象數而說《易》也。於是群焉奉之為圭顳，而又病輔嗣陳義之過高，未能企而及焉，乃曰此玄談也。非孔子之道，為王《易》之微疵焉。吾輩舍其短而取其長，斯盡善盡美白圭無玷矣。因之空談性命，不著邊際。但讀“一陰一陽之謂道”一句，卦爻盡屬贅疣。《彖》、《象》十翼，望文生義以解之，而《易》之能事畢矣。

Later scholars who interpreted the Book of Changes were originally afraid of the complexity and depth of the study of images and numbers, which made it difficult to grasp its essence. Therefore, they favored Wang Bi's approach, as it allowed them to discuss the Book of Changes without relying on the intricate and profound study of images and numbers. They gathered together to regard Wang Bi's scholarship as the standard, yet they found his theories too lofty for themselves to reach, so they said: this is "abstruse discussion," not in line with Confucius' way, and it is a minor flaw in Wang's interpretation of the Book of Changes. They claimed that by discarding its shortcomings and taking its strengths, they had achieved perfection, like a white jade without blemish. Thus, they engaged in empty discussions about the mind, nature, and principles, entirely off the mark: they only read the sentence "a combination of Yin and Yang is called the Dao," and regarded all the hexagrams and lines as superfluous appendages; they superficially interpreted the Commentary on the Judgment and Image Commentary and the other ten appendices, and thought that they had exhausted the entire study of the Book of Changes.

不知王《易》之所以能掃象而仍無礙其說者，正惟其深得玄理，故能獨超乎意象之表也。乃以玄談為病而去之，則所存之不病者，皆糟粕耳。猶冥然自侈為輔嗣之功臣，致令後世宗漢《易》者以掃象為王氏罪，曰“輔嗣學行無漢《易》”，輔嗣豈任受哉？

They do not realize: Wang Bi's ability to eliminate the images of the hexagrams and still maintain his reasoning is precisely because he deeply understood the profound principles. Thus, he could transcend the realm of meaning and image on his own. Now, if we regard "xuāntán" (discourse on the profound) as a flaw and remove it, the remaining "wu bing" (without illness) parts are all dross. These people are still blindly proud of themselves as contributors to Wang Bi, resulting in later scholars who venerate the Han dynasty's "Yi" (Book of Changes) recording the "sǎo xiàng" (elimination of images) as part of Wang Bi's work, saying "With Yixing's study, the Han dynasty's Yi learning has been cut off." This accusation is surely not something Wang Bi could bear.

《坤·彖傳》“坤厚載物德合無疆”，“牝馬地類行地無疆”，“安貞之吉應地無疆”。《程傳》雖已分晰言之，殊未悉當。郭氏云雍曰：“坤合乾德之無疆，馬行類地之無疆，聖人應坤之無疆。”

In the Commentary on the Judgment of the Qian hexagram, the term "wujiang" appears three times: first, "Kun's thick bearing of things, its virtue harmonizing with boundless limits"; second, "the female horse, a creature of the earth, moves without bound"; third, "the auspiciousness of maintaining sincerity lies in responding to the boundless nature of the earth." Although Cheng Yi's Commentary on the Changes explains these separately, his interpretations may not all be entirely appropriate. Guo Yong, also known as Master Baimo, said: the first instance refers to the boundless harmony between the virtue of Kun and that of Qian; the second refers to the female horse's movement following the boundless nature of the earth; and the third refers to the sage's response to the boundless nature of Kun.

邱建安富國曰：“德合無疆，乾之無疆也。行地無疆，坤之無疆也。應地無疆，君子之無疆也。無疆，天德也。地能合天之德。君子法地，地法天。”郭邱二說，似較《程傳》為勝。此與“大哉乾元”“至哉坤元”“元者善之長也”三“元”字，為例正同，所謂三才之道也。

Jian'an person Qiu Fuguo said: "Dehe wujiang" refers to the boundless nature of Qian, "Xingdi wujiang" refers to the boundless nature of Kun, and "Yingdi wujiang" refers to the boundless nature of the gentleman. Wujiang originally belongs to Tiande, the earth can harmonize with the virtue of Heaven, and the gentleman follows the earth, while the earth in turn follows Heaven." Guo Yong and Qiu Fuguo's interpretations seem to be more refined than Yichuan's Commentary on the Changes. The use of "wujiang" in these three instances corresponds exactly to the three instances of "yuan" in the Changes, which belong to Heaven, Earth, and humanity respectively, following the principle of贯通 the three elements of Heaven, Earth, and Humanity.

經傳用字，往往含有廣狹二義。如天，以狹義言之，則與地對。而廣義之天，則廣大無垠，非地可並擬者也。如陽之狹義，則與陰對，而廣義則陽可統陰，陰生於陽，非陰可同論矣。如乾之狹義，則與坤對，而廣義則乾可包坤。乾之一卦，實統轄乎六十四卦。上下篇六十四卦，為三十六卦之反覆，實得二百一十有六爻，為重乾一卦之策。如坤之百四十有四策，悉歸納於乾之內矣。此意義廣狹之最顯者也。

The terms used in the classic texts often carry both broad and narrow meanings. Take the character "heaven" (天) for example: in a narrow sense, it refers to the sky opposite the earth; in a broad sense, it is boundless and cannot be compared with the earth. Similarly, the character "yang" (阳) also has both narrow and broad meanings: in a narrow sense, it is opposite to "yin" (阴); in a broad sense, yang encompasses yin, since yin originates from yang and cannot be equated with yang. The character "qian" (乾) is also the same: in a narrow sense, it is opposite to "kun" (坤); in a broad sense, qian encompasses kun. The hexagram qian actually governs all sixty-four hexagrams— the upper and lower sections of the sixty-four hexagrams are formed by viewing thirty-six hexagram bodies in reverse, resulting in a total of 216 lines, which exactly matches the number of lines in the hexagram qian. In this way, the 144 lines of the hexagram kun are entirely included within qian. This is the most obvious example of the distinction between broad and narrow meanings of characters.

若更進一層言之，則廣義狹義之中，又各有大小或淺深精粗之不同，非詳察其上下之文義，及所聯綴之名詞。逐字剖析，則與經傳之本意，便大有出入。往往因一字之牽連混合，而誤會經旨，輾轉謬誤，歧中又歧，遂致乖戾不可究詁。

If we go a step deeper, in a broad sense there are distinctions between major and minor aspects, and within a narrow sense there are differences in depth, refinement, and coarseness. If one does not carefully examine the meaning and flow of the context along with the connected terms, and analyze each word thoroughly, the interpretation will differ greatly from the original intent of the classics. Often, a single word's confusion or misinterpretation leads to misunderstanding the main purpose of the entire text, resulting in errors that spread and multiply, eventually leading to interpretations that are so distorted that they become untraceable.

如道德等，皆經傳中最主要之字也，而道字之意義，其範圍廣狹大小，各各不同。老子曰“有物無形先天地生，無以名之強名之曰道”者，此道字範圍最大。乃立乎天地之先，孕育萬有之根。此先天之道，無可比擬也。《易》以有立教，從“《易》有太極”說起。故《易》之道，皆一陰一陽之謂道，此《易》中道字廣義之界說也。

For example, the characters "Dao" and "De" are among the most important in the classics. If we consider the character "Dao" alone, its scope varies in size. The "Dao" mentioned in the "Laozi" refers to something without form, existing before heaven and earth, which cannot be named and is given the name "Dao" by force. This "Dao" has the broadest scope, existing prior to the generation of heaven and earth, serving as the fundamental source of all things, belonging to the Dao of the Earlier Heaven, incomparable in its nature. The "Zhou Yi" establishes its teaching based on the concept of "having" or "being." It begins with the statement, "The Book of Changes has the Taiji." Therefore, the "Dao" discussed in the "Zhou Yi" refers to the "Dao" defined as "the way is the interplay of Yin and Yang," which represents the broad definition of the term "Dao" within the "Zhou Yi."

經文“道”字凡四見，皆屬此義。《十翼》中如“未失道焉”，“道大悖也”，“其道光明”等道字，皆廣義也。其狹義者，如“天道”“地道”“人道”“君子之道”“小人之道”是也。而“夫婦之道”、“陰陽之道”、“三極之道”，則又狹隘義中之廣義矣。

In the text, the character "道" appears four times, all of which belong to this broad meaning. In the "Ten Wings," instances such as "未失道焉," "道大悖也," and "其道光明" also refer to this broad meaning. As for the narrow usage, it refers to terms like "天道" (heavenly way), "地道" (earthly way), "人道" (human way), "君子之道" (the way of the gentleman), and "小人之道" (the way of the petty person). Meanwhile, expressions such as "夫妇之道" (the way between husband and wife), "阴阳之道" (the way of yin and yang), and "三极之道" (the way of the three ultimate principles) represent a layer that is narrower yet relatively broader within the narrow usage.

德字如“通神明之德”，德之盛也。“和順於道德”之“德”字，皆廣義之德也。如“陰陽合德”、“位乎天德”、“而德不孤”之“德”字則狹義矣。但無論廣義狹義，又各有內外之別。如健順動入為卦德，乃德之見於外者，為才德之德，如“三陳九德”之德（即“履德之基也”一章），及“進德修業”“神明其德”等德字，乃德之蓄乎內者，為“道德”之德。類乎此者，不勝枚舉。非極深研幾，逐字衡量而剖析之，則差以毫釐，謬以千里矣。

The character "de" (德) is also like this: in phrases such as "communicating the virtue of heaven and earth," "the fullness of virtue," and "harmonious with morality and virtue," the term "de" refers to a broad sense of virtue. In expressions such as "yin and yang combine in virtue," "standing in the virtue of heaven," and "virtue is never isolated," the term "de" refers to a narrow sense of virtue. Whether referring to broad or narrow sense, there is also a distinction between internal and external aspects: for example, the nature of the eight trigrams such as "Qian" representing strength, "Kun" representing docility, "Zhen" representing movement, and "Xun" representing entry—these are called "guade" (卦德), which refers to the external manifestation of virtue, belonging to the category of "cai de" (才德, talent and virtue). As for the three times in the "Xici Zhuan" (Great Treatise) that elaborate on the virtue of the nine trigrams (such as the chapter "Lu, the foundation of virtue"), and expressions like "advancing virtue and cultivating one's career" and "the virtue of the divine," these refer to the internal cultivation of virtue, belonging to the category of "moral virtue." Similar situations are countless. "Extremely profound and exploring subtle details" is a phrase from the "Xici Zhuan," referring to the practice of delving into the most subtle aspects. Without such effort, carefully weighing and analyzing each word, one would make a small mistake and end up with a great error.

此猶就一字言之，更有兩字互相為用。而彼此迭相發明者，如《乾·九五》曰“位乎天德”，《坤·六三》曰“地道光也”。此“道”“德”二字，實互相關聯。各卦之類此者，亦不勝枚舉。蓋聖人作《易》，實與造化同功。其神妙不可思議，而文字亦非常理可以測度。故有以非同一之字，而以形聲之相同而通之為一者，如弟娣梯涕、爤籣連漣之類是也。即有以同一之字，同一意義，而大小內外分際各殊，絕不相假借者，二四三五同功異位，同人以同而異，睽以異而同，神而明之，存乎其人，先聖已一言以蔽之矣。

The above discussion is only about individual characters; there are also cases where two characters are used together, complementing and explaining each other. For example, the "Wenyan" section of the "Qian Hexagram" at line nine five says "positioned in Heavenly Virtue," while the "Xiangzhuan" of the "Kun Hexagram" at line six three says "the way of the earth shines." The "Qian" speaks of "De" and the "Kun" speaks of "Dao," but the characters "Dao" and "De" are actually closely related and have overlapping meanings. There are countless such examples in each hexagram. The sages who composed the Book of Changes have a function similar to the workings of nature, their methods being so mysterious and profound that they cannot be fully understood by ordinary reasoning. Therefore, there are cases where two characters are not the same, yet they are used interchangeably because they have the same form and sound, such as "Di, Di, Ti, Ti," or "Ran, Lan, Lian, Lian." There are also cases where two characters are the same and have the same meaning, yet they are not interchangeable because they differ in size or in their internal and external distinctions. The lines two and four, as well as three and five, have the same function but different positions. The "Tongren" hexagram shows "difference" through "sameness," while the "Kui" hexagram shows "sameness" through "difference." The subtle distinction between these two concepts is exactly as the "Xici Zhuan" says, "the divine and clear understanding lies in the person," and the ancient sages have already summarized this in one sentence.

澤火革，《彖傳》曰“水火相息二女同居其志不相得曰革”，“湯武革命順乎天而應乎人”。《序卦傳》曰“井道不可不革”，《雜卦傳》曰“革去故也”，《易》之言革也著矣。而言因無專文，讀者胥不甚注意，不知有革必有因。天下萬事萬物，無事無因，無物無因，故六十四卦，皆因而重之。因而重之而爻在其中，剛柔相推而變在其中，變則革矣。因與革皆在其中中爻，因與革皆人所為。故尤在中爻中之三四兩人爻。

The Hexagram of "Revolution" (Gé) is associated with the image of a marsh and fire. The Commentary on the Judgment says, "Water and fire extinguish each other, and two women living in the same house with conflicting hearts, this is called 'Revolution'." It also says, "King Tang of Shang and King Wu of Zhou revolutionized the old order, above following the heavenly way and below responding to the people's will." The Sequence of Hexagrams says, "The well must not remain unchanged," and the Miscellaneous Hexagrams say, "Revolution means removing the old." These statements show that the Book of Changes clearly discusses the concept of revolution. As for "cause" (Yīn), there is no specific character dedicated to it in the text, and readers often overlook it. In fact, revolution must first have a cause. All things in the world have their causes, and no object exists without a cause. Therefore, the sixty-four hexagrams are all formed by combining the eight fundamental trigrams. Once combined, the six lines are included within them; the interaction of yin and yang leads to change, and change is revolution. Both cause and revolution occur within the middle lines of a hexagram, and since both are human actions, they particularly manifest in the third and fourth lines, known as the "human lines."

《乾·九四·傳》曰“乾道乃革”，三爻《傳》曰“因其時而惕”。蓋重乾二與四是恆乾，三與五是咸乾。三爻居恆乾之中，恆“不易方”，不易因也。四居咸乾之中，咸為恆之反，則不易者易，革也。

The *Wenyan Zhuan* of the *Qian Hexagram* says, "The way of Qian is to change," while the *Wenyan Zhuan* of the *Nine Three* says, "Be alert according to the time." One speaks of change, the other of following the time. Originally, within the *Qian Hexagram*, the lines two to four belong to "Heng Qian" (Constant Qian), and the lines three to five belong to "Xian Qian" (Attracting Qian). The *Nine Three* occupies the central position of "Heng Qian," and the *Xiang Zhuan* of the *Heng Hexagram* says, "The superior person acts with constancy and does not change direction," which means to maintain the constant and not alter, that is "following the time." The *Nine Four* occupies the central position of "Xian Qian," and *Xian* is the reversed form of *Heng*. Originally not changing, now it has changed, which is "change."

乾三爻天五數，四爻地六數。天五地六，相乘為三十。革古文從三十，三十年為一世。四與初應，初不易乎世，至四則易世。易世，革也。五六於干支為戊己，故革曰“己日乃革”。以三四重剛不中，變則為中孚，故革曰“己日乃孚”。明乎革而因可知矣。《論語》“殷因於夏禮周因於殷禮”，明乎因而革可知矣。

In terms of line numbers, the third line of the Qian hexagram belongs to the number five of heaven, and the fourth line belongs to the number six of earth. When five of heaven is multiplied by six of earth, the result is thirty. The ancient character 「革」 originally contained 「三十」, meaning thirty years, which constitutes a generation. The fourth line corresponds with the first line. The first line, marked as 「初九」, says in the 「Wenyan」 that it is not changed by the world, meaning it remains unaltered by worldly changes. However, when reaching the fourth line, it becomes 「易世」, meaning a change of generation, which is the meaning of 「革」. The numbers five and six in the heavenly stems correspond to Wu and Ji, so the 「Geh」 hexagram says 「on the day of Ji, there is a change」. Also, because the third and fourth lines are both strong but not in the center, they change into the Zhongfou hexagram, so the 「Geh」 hexagram also says 「on the day of Ji, there is trust」. Once the meaning of 「革」 is understood, the meaning of 「因」 can also be inferred. The 「Lunyu」 says 「the Shang dynasty followed the rites of the Xia dynasty, and the Zhou dynasty followed the rites of the Shang dynasty」. Once the meaning of 「因」 is understood, the meaning of 「革」 can also be inferred.

《繫傳》：“乾坤其《易》之門邪？是故闔戶謂之坤，闢戶謂之乾，一闔一闢謂之變。”案：天地數，天一始北方坎，地十終西方兌（坎子一，艮丑寅二三，震卯四，巽辰己五六，離午七，坤未申八九，兌酉十，乾戌亥無數。），而乾無數。乾圓周流坤方，西北不掩，是為不周。故八風於西北為不周風。西北娵訾口，亥東闢。闢，閉也，是閉戶謂之乾也。

The Great Treatise says: "The trigrams Qian and Kun are roughly the gate of the Book of Changes. So closing the door is called Kun, opening the door is called Qian, and the act of opening and closing is called transformation." It is explained that in terms of the numbers of heaven and earth, the number of heaven begins with Kan in the north, and the number of earth ends with Dui in the west (Kan is Zi, number one; Gen and Yin are Chou and Yin, numbers two and three; Zhen is Mao, number four; Xun is Chen and Si, numbers five and six; Li is Wu, number seven; Kun is Wei and Shen, numbers eight and nine; Dui is You, number ten; Qian is in Xu and Hai, without a number). Only Qian does not have a number assigned. Qian is round, flowing over the position of Kun, but fails to meet at the northwest corner, which is called "not complete" or "incomplete." Therefore, among the eight winds, the wind from the northwest is specifically named "the wind of not completeness." The northwest corresponds to the twelfth hour "Ju Zi Zhi Kou," and the east of the亥 position is called "Bi." Here, "Bi" is interpreted as "closed," so closing the door is called Qian.

坤西南括囊，天地閉，天地建侯數七十二（五日一候，一年七十二候）。四隅方數，西南未申八九，合七十二，為天地包象。東北丑寅二三，成六。東南辰己五六，成三十，皆坤用數六。坤地數，三十包之（南極入地三十六度。北極出地三十六度），為地坤囊包藏萬物之象，是闔戶謂之坤也。乾戶闢而開物成務，自無出有，坤戶闔而萬物歸藏。自有入無，天地門戶，出入於東西亞卯亞酉震兌，得乾坤之門，而《易》道始可言矣。

The position of the Earth (Kun) is in the Southwest, symbolizing "binding the bag"—tightening the mouth of a bag, with heaven and earth closed off. The number of the heavenly and earthly phenomena in the four cardinal directions is seventy-two (five days make one phenomenon, and there are seventy-two phenomena in a year). Regarding the numbers of the four corners: the Southwest has the earthly branches Wei and Shen, which are eight and nine respectively, combining to make seventy-two, exactly the image of heaven and earth containing all things. The Northeast has the earthly branches Chou and Yin, which are two and three, multiplying to make six; the Southeast has the earthly branches Chen and Si, which are five and six, multiplying to make thirty—using the number six of the Earth (Kun). The Earth belongs to the number of the Earth, which encompasses everything within thirty (the Antarctic circle is thirty-six degrees below the horizon, and the Arctic circle is thirty-six degrees above), exactly the image of the Earth like a bag containing all things. Therefore, closing the door is called Kun. When the door of Heaven (Qian) opens, it brings forth things and accomplishes tasks, creating existence from non-existence; when the door of Earth (Kun) closes, all things return to their storage, going back from existence to non-existence. The two doors of heaven and earth, their entrance and exit are in the east and west—Zhen (Thunder) is next to the卯 position, and Dui (Lake) is next to the酉 position. Only by mastering the door of Heaven and Earth can the Way of the Book of Changes be spoken of.

庖羲畫卦以象天地人物，而代結繩之治。然畫契未興，又未有方策帛書之制，則所賴以紀錄者，要不外以石質之刀錐，刻畫於竹簡，或皮革之上耳。故曰“畫卦”。考古人簡策之制，皆狹而長。庖羲之畫卦，未必如後世八卦六十四卦之方圓各圖，故《繫傳》曰“乾坤成列”。“成列”雲者，必以乾坤分列二行。而兌離震，巽坎艮，或以類從。

Fuxi drew the trigrams to symbolize heaven, earth, and human beings, replacing the old method of tying knots to record events. However, at that time, the technique of carving characters had not yet emerged, and there were no systems such as bamboo slips or silk scrolls. The only means of recording information was to use stone tools to carve on bamboo or leather. Therefore, it was called "drawing trigrams." Examining the form of ancient bamboo slips, they were all narrow and long. Fuxi's original drawing of trigrams probably did not arrange them in the circular or square diagrams of the later eight trigrams and sixty-four trigrams. Therefore, the Great Treatise says "Qian and Kun are arranged in order." Since it says "arranged in order," it must mean that Qian and Kun were each arranged in two rows, with Dui, Li, and Zhen following Qian, and Xun, Kan, and Gen following Kun, each grouped according to their kind.

三代時八卦排列如何，固不可考。而自秦漢以迄五代諸家之《易》，則均無八卦六十四卦之圖。故邵子學《易》數年，未得要領。及師事李挺之，挺之授以乾一兌二離三震四巽五坎六艮七坤八之數，始恍然大悟。先天之學，即由是發明。一部《皇極經世》，無非此一二三四五六七八所推衍。可知邵子以前之《易》，其八卦之排比，皆為行列，而未有此八角形之方式也。

In the Xia, Shang, and Zhou dynasties, the exact arrangement of the Eight Trigrams is no longer verifiable. From the Qin and Han dynasties up to the Five Dynasties period, no school of interpreting the Book of Changes included diagrams of the Eight Trigrams or the sixty-four hexagrams. Therefore, Shao Yong studied the Book of Changes for several years without grasping the essentials. It was only after he studied under Li Zhi Cai (whose courtesy name was TengZhi) that he was taught the sequence of numbers assigned to the trigrams: Qian (Heaven) as one, Dui (Lake) as two, Li (Fire) as three, Zhen (Thunder) as four, Xun (Wind) as five, Kan (Water) as six, Gen (Mountain) as seven, and Kun (Earth) as eight. Only then did he suddenly understand, and thus the study of Earlier Heaven was established. The book Huang Ji Jing Shi, which elaborates on the cosmic order and the rise and fall of states throughout history, is simply an extension of this sequence of numbers one through eight. From this we can see that before Shao Yong, the arrangement of the Eight Trigrams in the study of the Book of Changes was in a linear form, and not the octagonal diagram that came later.

“帝出乎震”一章，雖明言八卦方位，而當時亦未必有圖。故漢人之言《易》者，或以乾坤列東，艮兌列南，震巽列西，而坎離處中，無一定之方式。然其升降、消息、納甲諸說，實已為先天八卦之端倪。是以邵子聞李氏一言，即能觸類旁通而發其神悟也。顧李挺之氏亦必有所受，故朱子疑三代以前所本有。後經散佚而流入道家者，雖為臆度之辭，亦或有可信之理也。

The chapter "Emperor arises from Zhen" in the *Sayings on the Trigrams* clearly explains the directions of the eight trigrams, but at that time there may not have been a diagram. Therefore, scholars of the Han dynasty who interpreted the *Yi* sometimes placed Qian and Kun in the east, Gen and Dui in the south, Zhen and Xun in the west, and Kan and Li in the center, without a fixed format. However, their discussions on "ascending and descending" (the movement of yao positions up and down), "increasing and decreasing" (the waxing of yang and waning of yin, and vice versa), and "Najia" (assigning the ten heavenly stems to the eight trigrams) already revealed the essence of the Earlier Heaven Trigrams. Thus, Shao Yong could suddenly understand and grasp the concept upon hearing Li Zhici's explanation. Moreover, Li Zhici himself must have had another lineage of transmission. Therefore, Zhu Xi suspected that the Earlier Heaven diagram was originally existing in the Three Dynasties, then lost and later entered Daoism. Although this is a speculation, it may not be entirely without credible reasoning.

天地之數，一生二，二生三。老子曰：一生二，二生三，三生萬物。蓋物一者自無而有，未為數也。至二而成數矣，然猶為一奇一偶之名，而未著乎數之用也（近世俗語尚有以二為一雙為一對者。由今以溯古，其意可想見矣。）。至三，則數之用生。以此遞衍，可至於無窮。故一不用，二為體，三為用。

The numbers of Heaven and Earth originate from one giving rise to two, and two giving rise to three. The Tao Te Ching says: "One gives rise to two, two gives rise to three, and three gives rise to all things." Generally speaking, the concept of "one" comes into being from nothing to something, forming a complete whole on its own, but it is not yet a number. It is only when we reach "two" that numbers truly come into being, but at this stage, there are still only two categories, odd and even, and the function of numbers has not yet emerged (in modern speech, we still refer to "two" as a pair or a set, treating two as a single whole; looking back in history, we can imagine the meaning the ancients intended). It is only when we reach "three" that the function of numbers begins to manifest. Following this pattern, numbers can continue indefinitely. Therefore, "one" does not function, "two" represents the form, and "three" is where the function of numbers begins.

《易》有太極一也，陰陽二也，陰陽之用三也（二其三用六，三其三用九。）。如六爻皆一乾也，六爻皆一坤也，而動則或為○或為X，必用其一。如六爻皆變為○，則乾變為坤。然此六○之坤，與六- -之坤，其占不同。是由二而生三矣。

"The Yi Classic contains the Taiji," which is one. The Taiji divides into yin and yang, which is two. The functions of yin and yang are three (two multiplied by three equals six, which represents the function of old yin; three multiplied by three equals nine, which represents the function of old yang). For example, if all six lines are yang, it forms the trigram Qian; if all six lines are yin, it forms the trigram Kun. However, once a line changes, it is either drawn as "○" (yang turning into yin) or as "Ｘ" (yin turning into yang), and only one of these should be used. If all six lines change and are drawn as "○", then Qian becomes Kun. However, the Kun formed by six "○" is different in interpretation from the original Kun with all six lines yin. This is how two gives rise to three.

是故《易》之道備於三（由天生地，一生二也。由地生人，二生三也。非人則天地之功用不彰，故曰與天地參。），卦畫止於三，數之體也。爻以靜為一，動為二，用為三。數之用也，有一即有二，有二必有三，乃天地自然之理，自然之數，所謂先天而天不達者也。《乾鑿度》曰：“《易》一名而含三義。交易也，變易也，不易也。”鄭康成氏《易論》云：“易簡一也，變易二也，不易三也。”

Therefore, the Way of the Book of Changes is complete in the number three (from Heaven generating Earth, which is one generating two; from Earth generating humanity, which is two generating three. Without humans, the functions of Heaven and Earth would have no manifestation, so the Doctrine of the Mean says that humans are ranked with Heaven and Earth as the three). The hexagrams of the eight trigrams only have three lines, which represents the form of numbers; one line is considered one when still, two when moving, and three when initiating transmission, which represents the application of numbers. There is one, then there must be two; there is two, then there must be three. This is the natural principle and natural number of Heaven and Earth, which is exactly what the "Commentary on the Literary Meaning" of the Qian Hexagram says: "Before Heaven, Heaven does not contradict." The sage acts before Heaven's time, and Heaven does not contradict him. The "Commentary on the Book of Changes: Qian Zao Du" says: "The name 'Changes' contains three meanings: transaction, change, and unchangeable." Zheng Xuan (styled Kangcheng) in his "Commentary on the Book of Changes" says: "Ease and simplicity is one, change is two, and unchangeable is three." These three meanings correspond exactly with the previous discussion of one, two, and three.

聖人以《易》立教，其道亦有三。上焉者道也，中焉者德也，下焉者占卜也。老子取其上，孔子取其中，焦京取其下，三者各有其用，而不相悖，且互相發明而不可離（道不准諸象數則失其鵠，德不原於道則失其統。占卜不合乎道德，則惑世誣民而已矣。）。後之學者，擇其一以為宗，而嚴立界說以明系統則可，若入主出奴，不揣其木妄自尊大，而排斥異己。執一不化，欲求其通也難矣。

The sages used the Book of Changes to establish teachings, and its path is divided into three layers: the highest layer is "Dao," the middle layer is "De," and the lowest layer is "divination." Laozi took the highest, Confucius took the middle, and Jiao Yanshou and Jing Fang took the lowest; each has its own use, and they do not contradict each other, but rather complement and support each other. (To talk about Dao without using images and numbers as standards would lose the target; to talk about De without basing it on Dao would lose the system; if divination does not conform to morality and ethics, it would merely be misleading the world and deceiving the people.) Later scholars chose one of these layers as their main focus, clearly defined their own system, which is acceptable. However, if they are biased from the beginning, favoring their own group and attacking others, without assessing their own foundation and presumptuously looking down on others, clinging to one aspect without flexibility, it would be difficult to achieve a comprehensive understanding.

孔子立教，雖為中人說法，然正所以立德以明道，以為下學上達之階梯。故《十翼》傳經，無一字一言不根據於象數（法象莫大乎天地，必合乎法象者，乃謂之法言者。經非先王之法言不敢言，非先王之法行不敢行，法言法行皆合乎天地法象者也。故曰“建諸天地而不悖，質諸鬼神而無疑，百世以俟聖人而不惑”。）。若舍法象以為言，則詩書執禮所雅言者，其為教焉詳矣。又何必韋編三絕，為此鉤深致遠之辭乎？子貢曰“夫子之文章可得而聞，”凡立言必有合乎法象者，乃謂之文章。孔子特於《易》象闡發之，以為萬世之準，此為學《易》者所不可不知者也。故論及之。

Confucius established his teachings, which although addressed to people of average ability, aimed at cultivating virtue in order to understand the Way, serving as a step from learning the basics to reaching higher understanding. Therefore, the Ten Wings interpreting the Classic did not use a single word or phrase that was not based on the principles of images and numbers. (There is no greater model than heaven and earth; only statements conforming to these principles can be called "model words." Words not in accordance with the words of former kings should not be spoken, and actions not in accordance with the deeds of former kings should not be done. Both model words and model deeds conform to the principles of heaven and earth, so the Doctrine of the Mean says, "Established between heaven and earth without contradiction, verified by spirits and deities without doubt, and even a thousand generations later when a sage appears, there will be no confusion.") If one were to establish arguments without reference to these principles, then the poems, books, and rites which Confucius often discussed would already be sufficiently detailed, and there would be no need to study the Book of Changes until the cords binding the bamboo slips broke three times, leading to profound and far-reaching statements. Zigong said, "The writings of the Master can be heard." — only statements conforming to the principles of heaven and earth can be called "writings." Confucius deliberately elaborated on the images of the Book of Changes, serving as a standard for all generations. This is something those studying the Book of Changes should not be unaware of, so I have discussed it here.

《易》之言“祭祀”“享祀”，均含有二義。一為祭神祀鬼，此祭祀之本義也。一為人群之集會，以謀一群公共之事，亦以祭祀行之。蓋古人風氣淳樸，而庶民之家，又無廣庭巨廈，足以為集會之地者。故凡有會議之事，往往藉祭祀以行之。一鄉一邑之事，則集之於社。一家一族之事，則集之於宗廟。所謂“利用祭祀”，“利用享祀”，及“孚乃利用禴”等象，不盡為禱祀求福，實含有會集群眾之意焉。

In the Zhou Yi, it speaks of "qifu" and "xiangsi," both of which contain two meanings. One refers to worshiping deities and spirits, which is the original meaning of sacrifice; the other refers to gatherings of people -- coming together to discuss public affairs of a group, also held under the name of sacrifice. Originally, the customs of ancient people were simple, and common households did not have spacious courtyards or tall buildings suitable for gatherings, so whenever there was a meeting, they often used sacrifice as an occasion: for matters of a village or town, they gathered at the community altar; for matters of a family or clan, they gathered at the ancestral temple. Therefore, the hexagrams of Kun and Cui, which speak of "using sacrifice" and "using worship," as well as the line "fu nai li yong yue" in Ji Ji (the line "fu nai li yong yue" refers to "yue," the simplest form of seasonal sacrifice), do not entirely mean praying for fortune. In fact, they all contain the meaning of gathering people together.

降及後世，厲行專制政治，普通人民，更不容有公然集會之事。幸有此祭祀成例可援，得藉事神為合群自衛之一道（上以神道愚民，民以神道自衛，可見“無平不陂”。《易》道之妙用，即寓於其間矣。）。近如各鄉之有社廟，各業與僑民之有會館，無不以祭祀為集合群眾之介，猶足以覘《易》之遺意焉。

In later dynasties, autocratic politics were strictly enforced, and ordinary people were not allowed to gather openly. Fortunately, there was the established practice of worship to refer to, allowing them to use the veneration of deities as a means of gathering and self-defense. Those in power used the divine to deceive the people, while the people themselves used the divine to protect themselves. This illustrates the meaning of the phrase "there is no flat ground that does not become a slope" from the line "Nine in the Third" of the Tai hexagram. The subtle application of the principles of the Book of Changes is embodied here. In modern times, each village has its local temple, and each trade and overseas community has its guild hall, all using worship as a means to gather people together. From this, we can glimpse the remnants of the principles of the Book of Changes.

《繫傳》：“聖人有以見天下之動，觀其會通以行其典禮，是故謂之爻。”“典禮”者，乃所以處斷萬事萬物之一切制度之謂也。故古聖王之所以治天下也，大而禮樂政刑，小而訓詁名物，無不下順民情。而上合法象，法象莫大乎天地，民受天地之中以生，能合乎天地法象者。民情自無不順。故謂之典禮。典者守也，禮者履也。必能會通乎天人，然後足以昭信守而見履行。

The Great Treatise says: "The sage observed the changes of all things under heaven, and found the places where they connect and communicate, using them to establish rites and regulations, hence called 'yao' (line)." What is meant by "communication" is to find the common principles amidst the myriad changes; what is meant by "rites and regulations" is to use them to decide on the systems for all things. Therefore, the ancient sage kings governed the world, whether in great matters such as rites, music, politics, and punishment, or in small matters such as names, objects, and explanations, all were in accordance with the people's sentiments below and in harmony with the heavenly patterns above. There is no greater model to follow than heaven and earth. The Zuo Zhuan says that the people receive the harmonious qi from heaven and earth and thus are born. Whatever conforms to the heavenly and earthly patterns will naturally have the people's sentiments in harmony, hence it is called "rites and regulations." "Dian" means to hold fast, and "li" means to practice; one must be able to connect heaven and humanity before it is sufficient to demonstrate what is held fast and to show it through practice.

孔子之周，問禮於老聃，即此禮也。蓋周自東遷而後，文武之道載於方策者，散佚殆盡。諸侯惡其害己焉，皆毀之以自便。孔子周流列國，雖得百二國之寶書，要皆屬各國之歷史故事，而所謂典禮者，迄不可得，故不得不求諸老聃。老氏世掌周史，耳熟能詳。先王之典禮，不啻若自其口出，而提綱挈領，鉅細畢賅，則莫備於《易》。

Confucius went to the capital of the Zhou dynasty to ask Lao Dan about ritual propriety, and it was precisely this kind of ritual that he was inquiring about. Originally, after the eastern migration of the Zhou royal house, the teachings of King Wen and King Wu recorded in official documents had largely been lost — the feudal lords found them inconvenient and even destroyed them for ease. Although Confucius traveled through many states and saw the collections of many feudal lords, most of them were merely historical anecdotes of the various states. The true ceremonial rites, however, were never obtained, so Confucius had to seek guidance from Lao Dan. The Lao family had long held the position of royal historian, and was well acquainted with these rites, as if they had flowed directly from the mouths of the former kings. As for a text that could summarize the essentials and cover all details comprehensively, none was more complete than the Book of Changes.

孔子受之，極深研幾，得其會通，又慮觸當世諸侯之忌也。正言之不可，乃寓微言於《十翼》之中。所謂“其稱名也小，其取類也大。其旨遠，其辭文。其言曲而中，其事肄而隱”者，非夫子之自道邪！於是更廣其旨以修《春秋》，刪《詩》、《書》，訂《禮》、《樂》，而古先聖王之典禮，乃燦然大備於六經。永如日月之經天，江河之行地，與天地法象，並昭千古。此孔子所以為述而不作，而功在生民者，非《易》又烏乎知之？

Confucius inherited this body of knowledge, delving deeply into its subtle aspects and mastering its comprehensive principles. He also considered the possibility of offending the contemporary feudal lords, so direct expression was not feasible. Therefore, he concealed profound meanings within the Ten Wings. The Great Treatise states, "The names mentioned are small, but the categories they represent are vast; the meaning is profound, the language is rich; the words are indirect yet accurate, the narration is elaborate yet restrained." Is this not a true reflection of the Master himself? He then expanded this principle to compile the Spring and Autumn Annals, edited the Book of Poetry and Book of Documents, and revised the Book of Rites and Book of Music. Thus, the ceremonial practices of the ancient kings were fully established in the Six Classics, shining brightly as the sun and moon in the sky and the rivers and streams on the earth, illuminating the ages together with the celestial patterns. Confucius' self-description of "recording without creating" and his contributions to the people of ten thousand generations, if not derived from the Book of Changes, where else could such understanding come from?

《訟·彖傳》曰：“上剛下險，險而健訟。”訟者爭也。君子平其爭則訟解。《傳》曰：“訟不可長。”訟不可長，則不至成獄矣。故訟者，民事之爭，尚情感理喻而不必恃乎用刑。九五曰“訟元吉”，是能平其爭而使無訟者也。訟之凶在終於訟而不可解，則成獄矣。噬嗑曰“亨利用獄”，《象傳》曰“君子以明罰勅法”，則不能不用刑以闢以止闢矣。

The Commentary on the Judgment of the Hexagram of Strife says: "The upper trigram is strong and vigorous, the lower trigram is dangerous and trapped; both danger and strength exist, hence strife arises." Strife means contention. A gentleman who resolves disputes brings an end to strife. The Image Commentary says, "Strife should not be prolonged" — contention should not be allowed to continue, for if it is not prolonged, it will not lead to legal punishment. Therefore, "strife" refers to civil disputes, which should be resolved through reasoning and emotion, without the need for punishment. The line statement of the fifth line says, "Strife brings great good fortune," which refers to the person who resolves disputes and brings about a world without strife. Strife brings misfortune because if contention continues without resolution, it becomes legal punishment. The Hexagram of Burning Through says, "It is prosperous, and punishment is useful." The Image Commentary says, "The gentleman uses clear punishment to enforce laws," at this point, punishment must be used to stop further punishment.

噬嗑之象上離下震。離者明也，萬物皆相見，則物無遁形，以示治獄者必明察庶物，一無壅蔽。中爻三四五為坎，坎為法律，為智，為水。二至四為艮，艮為手，為山，為止。下震為動，治獄者即明且智，用法如水之平，絕無偏倚（坎離皆中正象）。無論在下者變動百出，皆能明燭其隱。執法如山，止而不動，所以能止一切之動，而令悉合於法（噬嗑，合也）。只此六畫之象，已將近世司法之精義，包括無遺。

The hexagram Shìkè has the upper trigram Li (Fire) and the lower trigram Zhen (Thunder). Li represents brightness, and in this context, all things become clearly visible, with nothing hidden or concealed. This signifies that those who investigate cases must observe clearly and thoroughly, without any obstruction or concealment. The third, fourth, and fifth lines form the trigram Kan (Water), which represents law, wisdom, and water. The second to fourth lines form the trigram Gen (Mountain), which represents hands, mountains, and stopping. The lower trigram Zhen represents movement. The investigator is both clear-sighted and wise, applying the law like water, which is level and impartial (both Kan and Li are trigrams that represent correctness and centrality). Regardless of the various movements below, he can see into the hidden aspects. The enforcement of law is like a mountain, which remains still and thus can stop all disorder, bringing everything into conformity with the law (the term 'Shìkè' itself means 'to combine' or 'to harmonize'). Just these six lines of the hexagram already encompass the essential principles of modern jurisprudence.

蓋古聖王之治天下也，道之以德，齊之以禮，刑罰但以濟禮之窮。禮以待君子，刑以治小人。人之情無不樂為君子而甘為小人者，故人人能範圍於禮，而刑罰可以不用。自上失其道，君子弗用，小人譸張，不恥不仁，不畏不義，不見利不勸，不威不懲，始訟獄繁興。故睽之六三曰“其人天且劓（天同而）”，困初六曰“臀困于株木”，九五曰“劓刖”，睽“失道”，困“剛掩”。理窮數極（《雜卦》困數三十，睽數三十六。四九三十六而乾道窮，五六三十而天地之數極。），禮崩樂壞，不得不用刑以濟之。

Ancient sage-kings governed the world by guiding people with virtue and regulating them with ritual, using punishment only to supplement what ritual could not cover. Ritual was used to deal with the virtuous, while punishment was used to manage the petty. Human nature does not desire to be petty and instead longs to be virtuous, so everyone could be confined within the bounds of ritual, and punishment could be set aside. Since those in power lost the Way, the virtuous were not employed, and the petty acted deceitfully and tyrannically, without shame for unkindness or fear of injustice. They would not act unless they saw profit, and would not be punished unless threatened. Thus disputes and legal cases arose constantly. Therefore, the sixth line of the Kui hexagram says, "He has been branded and his nose cut off" (here "heaven" is used as "and," referring to the branding). The first line of the Kun hexagram says, "His buttocks are stuck on a dry tree," and the ninth line of the fifth says, "His nose and feet are cut off." The root of the problem in Kui is "losing the Way," and in Kun it is "the strong being concealed by the weak." When principles are exhausted and the time has come to an end (in the Zage hexagram, the number for Kun is thirty, and for Kui it is thirty-six; forty-nine makes thirty-six, which exhausts the Heaven's principle, and five and six make thirty, which reaches the extreme of the Heaven and Earth's numbers), when ritual and music collapse, punishment must be used to remedy the situation.

所謂窮則變，非《易》之常道也。聖人猶憂之，慮後世淫刑以逞者有所藉口也，特於豐著之。曰“君子以折獄致刑”，言刑非折獄者不能妄用也。於旅曰“君子以明慎用刑而不留獄”，言用刑者宜審慎迅速不可留滯也。於中孚曰“君子以議獄緩死”，恐折獄者之或猶有冤濫，更議擬之而求其當也。嗚呼！《易》道之生生，與聖人質《易》之深心，可以見矣。

This is what is meant by "when things reach their limit, they change," which is not the constant principle of the Book of Changes. The sage still felt uneasy about it, fearing that those in later generations who arbitrarily imposed punishments might use it as an excuse. Therefore, he specifically pointed this out in the Hexagram of Abundance: "The superior person acts with fairness in judicial cases and applies punishment appropriately," meaning that those who do not hold the position of judging cases should not arbitrarily use punishment. In the Hexagram of Travel, it says: "The superior person acts with clarity and caution in applying punishment and does not delay cases," meaning that punishment should be applied with care and speed, without delay or accumulation. In the Hexagram of Middle Trust, it says: "The superior person deliberates on cases and delays execution of death sentences," fearing that those who judge cases may still have instances of injustice or excess, so they add further deliberation and careful consideration to ensure the judgment is proper. Ah! The compassionate heart of the Way of the Book of Changes, which constantly generates and nurtures life, and the sincere efforts of the sages in examining the principles of the Book of Changes, can now be clearly understood.

司法獨立者，近三十年來之學說也。我國自三代以降，於古人設官分職之遺意。久已泯棼而莫可紀極。以行政官操生殺之柄，威福自恣，積非成是。恬焉安之而莫以為妄，而不謂《易》象已明著之，孔子贊《易》更一再言之。賁之《象》曰：“君子以明庶政無敢折獄。”明示以折獄之必有專職。行政者雖明，亦無敢越俎，非司法獨立之精義乎？

The concept of judicial independence is a theory that has only been introduced in the last thirty years. Since the Xia, Shang, and Zhou dynasties, the original intention of the ancients in setting up officials and dividing their duties has long been confused and cannot be clearly clarified: administrative officials hold the power of life and death, wielding authority arbitrarily, and this has become the norm, with everyone accepting it as natural without realizing its absurdity. Yet, the Book of Changes (Yi Jing) has already clearly revealed this principle. Confucius, in his commentary on the Yi, emphasized it repeatedly. The hexagram Bi (Brightness) represents the image of fire beneath a mountain, symbolizing the meaning of refining and embellishing governance. Its Image Commentary states: "The superior man thus clarifies all government affairs and dares not handle judicial cases." This clearly indicates that the handling of cases must be entrusted to a separate specialized body: even if administrative officials are intelligent, they dare not overstep their bounds to take on judicial responsibilities—this is precisely the essence of judicial independence.

《豐·象》曰：“君子以折獄致刑。”明示以用刑為折獄者之專責。凡非折獄者，皆不許有用刑之權，非司法獨立之明證乎？蓋豐與噬嗑為同體之卦（火雷噬嗑，雷火豐），噬嗑曰“利用獄”，故孔子更於豐申明其義以見除此之外，雖賁為噬嗑之往來卦，亦無敢折獄。其謹嚴如此。近世詡為新學說，而《易》象已深切著明於七千年之前。《易》道之廣大悉備，此其一端矣。

The Image Commentary of the Gua of Abundance says: "The superior man uses this to decide cases and carry out punishments." This clearly indicates that the use of punishment is the exclusive responsibility of those who judge cases. Anyone not in the position of judging cases is not allowed to have the authority to impose punishments—this is not precisely a clear evidence of judicial independence? Originally, the Gua of Abundance and the Gua of Eating the Cricket are formed by exchanging the upper and lower trigrams of the same pair (Fire-Thunder Eating the Cricket; exchanging upper and lower trigrams becomes Thunder-Fire Abundance). The Gua of Eating the Cricket says "It is advantageous to use litigation," so Confucius further explains this meaning in the Gua of Abundance, to show that even the Gua of Brightness, which is the reverse of the Gua of Eating the Cricket, does not dare to decide cases on its own. The rigor is to this extent. In modern times, those who claim to be new theories, the images of the Book of Changes have already explained deeply and clearly seven thousand years ago. The vastness and comprehensiveness of the Way of the Changes, this is only one aspect of it.

近世教育制度，發軔於歐西，裨販於日本。規模弘遠，成效彰著。適值我時衰俗敝之秋，以國力之不競，舍興學無以為圖強之本，遂盡棄其學而學焉。而不知現世所行之學制，為我國所採取而未能遍舉者，無不悉備於《易》象之中。河南張之銳氏，近世以新學講《易》者也。其論近世教育，足與《易》相印證者，略謂《易》之教育，約分五種：一曰“蒙養教育”，二曰“國民教育”，三曰“人才教育”，四曰“通俗教育”，五曰“世界教育”。

Modern educational systems originated in Western Europe and were later introduced to China through Japan. They are extensive and profound, with significant results. At a time when our country was in decline, with deteriorating customs and weak national strength, establishing schools was considered the fundamental way to strengthen the nation. Therefore, people abandoned their own traditional learning and focused entirely on learning from others. However, they did not realize that the current educational system being implemented, wherever it has been adopted but not yet fully implemented, was already fully contained within the imagery of the Book of Changes. Zhang ZhiRui from Henan is a modern scholar who uses new learning to interpret the Book of Changes. He discusses the aspects of modern education that correspond with the Book of Changes, roughly dividing the educational aspects of the Book of Changes into five categories: first, "early education," second, "national education," third, "talent education," fourth, "popular education," and fifth, "world education." These five categories extend from the family to the nation, from specialized talents to the customs of the common people, and continue to expand throughout the world, layer by layer.

“蒙以養正”，蒙養教育也。蒙養本於家庭，故九二曰“納婦吉子克家”，以明克家之子，必有賴於母教也。“包蒙”之包，亦作“彪蒙”，與革旁通，以明“豹變”“虎變”之大人，皆正始於彪蒙也。

The Commentary on the Judgment of the Hexagram of Enlightenment says, "Enlightenment nurtures correctness." This refers to the education of children in their early years. The foundation of this education lies in the family, so the Line Statement of the Second Line says, "Taking a wife is auspicious; the son can uphold the family," indicating that a son who can support his household must rely on his mother's guidance. The term "package enlightenment" in the Second Line, where "package" is also written as "彪," refers to the initial stage of a child's learning. The Hexagram of Enlightenment and the Hexagram of Revolution are complementary, which shows that the great figures mentioned in the Revolution Hexagram, such as "leopard transformation" and "tiger transformation," all began with proper education from childhood.

蠱之“振民育德”，國民教育也。國事之敗壞，由於民氣之萎靡頹喪。昧匹夫有責之義，故先甲後甲，教令一新，以振民氣。《傳》曰“蠱元亨而天下治”。六十四卦言天下治者，除乾元用九外，惟此一卦也。臨之“教思無窮容保民無疆”，人才教育也。政以臨民，培植政治之人才，非有專門教育不為功。蓋普通教育，有一定之教科，有不二之主義。而專門教育，則任學者自由研究。蓋人類之知識不可限量，不能限學者之思想，而範之以有盡之課程，故曰教思元窮也。

The Image Commentary of the Gua of蛊 says "to rouse the people and cultivate virtue," referring to national education. The Gua of蛊 represents a situation where long-standing evils have accumulated and require urgent reform; the decline of state affairs originates from the people's spirit being萎靡 and despondent, with everyone lacking the understanding of the principle "the rise and fall of the country concerns every common person." Therefore, the Gua of蛊 speaks of "before the first day of the stem Jia, and after the first day of the stem Jia," where Jia is the first of the ten heavenly stems, symbolizing the beginning of a fundamental change in laws and regulations. Three days before the action, the matter is clearly announced, and three days after, it is solemnly warned, thus renewing the edicts and rousing the people's spirit. The Commentary on the Judgment says "Gua of蛊 is original and prosperous, leading to the governance of the world." Among the sixty-four guas, only this Gua and the Gua of乾 mention "the world is well governed," apart from the "original use of nine" in the Gua of乾. The Image Commentary of the Gua of临 says "teaching and thinking are boundless, and the protection of the people has no limits," referring to the education of talent. Governance requires the ruler to be present among the people, and cultivating political talent can only be achieved through specialized education. General education has fixed subjects and a unified purpose, while specialized education allows scholars to study freely, because human knowledge is limitless and scholars' thoughts should not be restricted, nor should limited courses be used to confine them, hence saying "teaching and thinking are boundless."

《觀·象》之“省方設教”，通俗教育也。四方之風氣不齊，習尚亦異，故必省其方俗之所宜，觀其民情好尚而設教始當。《無妄·象》曰“君子以茂對時育萬物”，世界教育也。《中庸》曰“能盡人之性則能盡物之性，能盡物之性則可以贊天地之化育”，大亨以正，使天下萬物各正其性命，各全其天賦之能，而後教育之，道始達於圓滿之一境，則尚非近世言教育者可能幾及焉。以上張說之大旨如此，未知於近世師範之學，有當否也。

The Image Commentary of the Guan Hexagram says, "The former kings observed the customs of the four directions and studied the people's inclinations in order to establish education." This refers to popular education. Since the customs and habits of different regions vary, it is necessary to examine the appropriate ways of each place and observe the people's likes and dislikes, so that the education provided can be suitable. The Image Commentary of the Wuwang Hexagram says, "The former kings cultivated themselves in accordance with the seasons and nurtured all things." This refers to universal education. The Zhongyong says, "If one can fully understand human nature, one can also fully understand the nature of things; if one can fully understand the nature of things, one can assist heaven and earth in nurturing all things." This is a greatly smooth and harmonious process while remaining steadfast in the right path, enabling all things to properly fulfill their nature and fully realize their innate abilities. Only then can education be considered complete. This level of understanding is still beyond the reach of modern educators. This is the main idea of Zhang Zhihui's view. I wonder whether this is appropriate for modern teacher education.

死生亦大矣！《繫傳》曰：“原始反終，故知死生之說。”始終者數也，天也。萬物數，一始十終。始子一丑二，而終於酉十一，戌亥無數。萬物自有而入無，為死之候。乾居西北戌亥之地，故無方無體（太虛之象）人而克全其為人，則全受於始者，全歸諸終，終則反乎太虛。精氣不滅，與造化同遊者神也。是以君子有終（君子之死曰終）。終則有始，順乎天行，自有而入無者，亦自無出有。乾知大始，復藏於坎。一純二精（坎子一，坎艮之間丑二），至艮寅三而仍為人。此生死循環，佛家輪迴之說所自來也。

Death and life are truly the great matters of human existence! The "Great Treatise" says: "By tracing back the beginning of things and seeking their end, one understands the principle of death and life." The beginning and end belong to "number," which belongs to Heaven. The numbers of all things begin with one and end with ten: starting from the number one at the Zi position and the number two at the Chou position, up to the Wu position which is ten, completing one cycle and reaching its end. The Xu and Hai positions are not assigned numbers. All things move from "being" to "non-being," which is the moment of death. The Qian trigram resides in the Northwest Xu and Hai positions, thus having no fixed place or form (this is the image of the Great Void). If a person can preserve the way of being human, then what was originally fully received at the beginning will be fully returned at the end; returning to the end means returning to the Great Void. Those whose vital energy does not perish and who wander together with the workings of nature are called "spirit." Therefore, the "Guan" hexagram says, "The gentleman has an end" (the death of a gentleman is called "end"). Having an end means having a beginning. Following the movement of Heaven, moving from being to non-being, one will also move from non-being back to being. The Qian trigram governs the great beginning of all things, and then returns to be stored in Kan. Kan is associated with Zi and the number one, which is pure; the Chou position between Kan and Gen is associated with the number two, which is essence; when it reaches the Gen position of Yin, which is three, it becomes human again. This cycle of death and life is the source of the Buddhist concept of rebirth.

人而不能全其為人，則自失其人道，斫其生理。全受於始者，不能全歸於終。數盡則死（小人曰死），形消骨化，餘氣無歸，游魂為變者鬼也。變則失常，依其生前所自造之因而證其果，則為人為物，所趣各殊。此佛家輪迴六道之所由分也。

If a person cannot uphold the way of being human, they have abandoned the human path and harmed the principle of continuous generation and transformation. What was originally fully received from the beginning will not be fully returned at the end. When the vital energy is exhausted, death occurs (the death of a petty person is called 'death'). The physical form is destroyed, the bones disintegrate, and the remaining energy has nowhere to go. This becomes a 'ghost' through the process of 'transformation'. Since it is a 'transformation', it loses its normal course and can only be subject to the consequences of the causes they created in life, either being reborn as a human or as an object, with different destinations. This is the origin of the Buddhist concept of the 'six paths of rebirth'.

故生者死之始，死者生之終，死於此者生於彼。《易》道乾息於坤，坤即消於乾。莊子曰“方死方生，方生方死”，立論之最精者也。聖人作《易》，窮造化之原，洩陰陽之秘，無非示人以所以全其為人之道。原始反終者，即由終而反始。老氏佛氏，皆由終反始，皆由後天而反諸先天，由有而反諸無，由形而反諸氣，由氣而反諸神。實即由生而反諸死，故曰原始反終。

Therefore, birth is the beginning of death, and death is the end of birth. When one dies here, one is reborn there. In the Dao of the Book of Changes, Qian (Heaven) grows within Kun (Earth), and Kun retreats within Qian—'qi' (breath) signifies growth, and 'xiao' (retreat) signifies decline. One growth and one decline are two aspects of the same thing. The Zhuangzi says, 'Dying at the same time as being born, and being born at the same time as dying,' which is the most precise statement in its argument. The sages composed the Book of Changes to investigate the origin of creation and reveal the secrets of yin and yang, all in order to guide people in preserving the way of being human. What is meant by 'returning to the origin and reversing the end' is to return from the end to the beginning. Laozi and the Buddhist school both return from the end to the beginning, returning from the Later Heaven to the Earlier Heaven, from existence to non-existence, from form to qi, from qi to spirit—actually returning from life to death, hence it is called 'returning to the origin and reversing the end.'

反終者，不續終也（未濟不續終也）。不續終，則始無暨極。故老氏曰“元始乃長生而不死”，佛家曰“無始乃無始而無終”。（乾西北為無，乃由有而反諸無者也。故老氏之無為萬有之根，佛教之無為不生不滅之本。乾為金為圓為剛，老曰“金丹”，佛曰“金剛”，而《易》曰“終日乾乾”。乾乾者。上乾為咸乾，下乾為無恆乾。咸無也，恆有也。觀其所咸，而天地萬物之情可見。觀其所恆，而天地萬物之情可見。蓋斟酌於有無之間而用其中，而要皆殊塗而同歸者也。）

The concept of "reverse completion" refers to not continuing from the end (as stated in the Commentary on the Judgment of the Hexagram 60, "Not continuing from the end"). If one does not continue from the end, then the beginning has no limit. Therefore, Laozi speaks of "the beginning" as something that grows without dying; Buddhism speaks of "no beginning" as having neither beginning nor end. (The Hexagram Qian in the Northwest is "nothing," which is the place where from being it returns to non-being. Thus, Laozi's "nothing" is the root of all things, while Buddhism's "nothing" is the essence of non-arising and non-ceasing. Qian represents metal, roundness, and firmness. Therefore, Laozi speaks of "golden elixir," Buddhism speaks of "diamond," and the Book of Changes speaks of "constantly striving with Qian." The term "Qian Qian" refers to the previous Qian as "salty Qian" and the following Qian as "constant Qian." Salty Qian represents nothingness, while constant Qian represents being. The Commentary on the Judgment of the Hexagram 15 says that by observing what it connects with, one can see the forms of heaven and earth and all things; the Commentary on the Judgment of the Hexagram 30 says that by observing what it maintains constantly, one can also see the forms of heaven and earth and all things. In the end, it is about balancing between being and nothingness and taking the middle path. Ultimately, all these approaches differ in their paths but converge in their ultimate goal.)

無始無終，夫然後歸於太極，則無所謂《易》矣。《易》之立教，為中人說法，故執兩而用其中。然聖人致治之極功，則亦曰無為而治；德成而默契乎天，亦曰予欲無言。則亦與由有而反諸無者，初無二致焉。故《易》者逆數也。儒與佛老之立教雖異，而道無不同。蓋天地之數，至三而備。天地萬物，舉莫能外。損之六三，曰“三人行，則損一人，一人行則得其友”，始終生死之道，不外乎此三者。後之立教者，可等諸自檜以下矣。

Without beginning or end, it returns to the Taiji, and at that point, the Book of Changes becomes irrelevant. The establishment of the Book of Changes is for those of average capacity, so it grasps both extremes and takes the middle way. However, the highest achievement of the sage in governing the world is still to say "govern without action"; when virtue is perfected and one silently harmonizes with heaven, it is still to say "I desire to speak no words" — this is essentially the same as the path returning from being to non-being. Therefore, the Book of Changes is a reverse calculation. Although the teachings of Confucianism, Buddhism, and Taoism are established differently, their principles are all interconnected. The numbers of heaven and earth are complete at the number three, and nothing in heaven and earth can surpass it. The line Six in the Third of the Hexagram of Loss says: "When three people walk together, one should be reduced; when one walks alone, he finds a companion." The entire path of birth and death does not go beyond these three. Later generations who establish their own teachings are like季札 listening to music and realizing that what comes after the state of Guo is not worth commenting on anymore.

《中庸》曰：“鬼神之為德，其盛矣乎？”《繫下傳》曰：“過此以往，未之或知也。窮神知化，德之盛也。”然則鬼神之為德，又何以知之？曰：以幽明之故，坎幽離明，陽變陰化，天地萬物，無一非氣與形二者之相迭更。既原始反終而知死生之說，則精氣為物游魂為變，鬼神之情狀亦可由是以知矣。

The Doctrine of the Mean says: "The virtue of ghosts and spirits is truly great!" The Great Treatise says: "Beyond this point, it is beyond human knowledge; to exhaust the subtle and comprehend the transformations is the ultimate of virtue." Then, how can we know the virtue of ghosts and spirits? The answer is: by the principles of the hidden and the manifest. Kan represents the hidden, Li represents the manifest; Yang governs transformation, Yin governs change. All things in heaven and earth are formed by the alternation of "qi" and "form." Since we have understood the principle of "originating from the beginning and returning to the end," we can then comprehend that "the refined qi gathers to form objects, while the wandering souls disperse into transformations," and thus infer the nature of ghosts and spirits.

精坎也，魂離也。故天地八卦，六爻上下，上五天爻為天《易》，三四人爻為人《易》，二初地爻為地《易》。游魂歸魂，復取三四兩爻，則為鬼《易》。三四兩爻，有當不當之別。克全乎其生之德者，即不失其死之道，乃得當而為神。不能全乎其生之德者，亦失其死之，道即不得當而為鬼（生之德立人之道，曰仁與義是也）。敬生而既反乎人道，是不待其死已失其為人，尚何鬼神之有？

"The 'jing' (essence) belongs to the Kan trigram, and 'hun' (spirit) belongs to the Li trigram. Therefore, the eight trigrams of Heaven and Earth, with each trigram having six lines, are paired above and below: the top line and the fifth line, which are the heavenly lines, are called 'Heavenly Yi'; the third line and the fourth line, which are the human lines, are called 'Human Yi'; and the second line and the first line, which are the earthly lines, are called 'Earthly Yi'. The concepts of 'you hun' (wandering spirit) and 'gui hun' (returning spirit' are derived from the third and fourth lines, which are referred to as 'Ghost Yi'. The third and fourth lines have distinctions of being in proper position or not: if they preserve the virtue of life, they will not lose the way of death, and thus they are in proper position and become 'shen' (spirit); if they do not preserve the virtue of life, they lose the way of death and are not in proper position, thus becoming 'gui' (ghost). The virtue of life refers to the benevolence and righteousness that establish the human way. If someone has already violated the human way while alive, they are not even worthy of being called human, and how can they be called spirit or ghost?"

卦象天地生人，始乾三中爻坎子，終地十兌酉。終始死生，反覆有游魂歸魂，而以三歸之地十歸妹，為天地大歸魂卦，而六十四卦終焉。歸妹東震西兌，其先天為東離西坎，日魂月魄，合為天地中生人精氣。子一丑二，為天地始合（子丑日月。天地之數，合一二為始，合五六為中，合九十為終）。一主日，二主月。子一日，至酉十月。故人十月而生，此日月魂魄合，精氣始也。

The hexagram explains the generation of human beings from heaven and earth. It begins with the third line of the hexagram Qian (Heaven), with the middle line being Kan (Water) corresponding to the earthly branch Zi (Rat). It ends with the earthly branch You (Rooster) corresponding to Dui (Lake) in the number ten. The cycle of beginning and end, life and death, movement and return leads to the concepts of wandering soul and returning soul. The hexagram "Guimei" (Return of the Maiden), which is based on the number ten, is regarded as the great returning soul hexagram, marking the end of the sixty-four hexagrams. In "Guimei," Zhen (Thunder) is in the east and Dui (Lake) in the west; their earlier heaven positions are Li (Fire) in the east and Kan (Water) in the west. The soul of the sun and the body of the moon combine in the center of heaven and earth to form human essence and qi. Zi is one, Chou is two, representing the initial union of heaven and earth (Zi and Chou govern the sun and moon respectively. The numbers of heaven and earth, one and two combine to signify the beginning, five and six to signify the middle, and nine and ten to signify the end). One governs the sun, two governs the moon; counting from one (Zi) to ten (You) makes ten months, which is why human gestation lasts ten months—this is the principle of the union of the sun's soul and the moon's body, the beginning of essence and qi.

陰陽之道，始坎終離，魂升魄降。離午七未八，日魄七日不復，月魄八月有凶。離上坎下，歸魂不歸，而游魂為變者也。是故八卦之六變為游魂，仍為三爻變。至七變則復歸本宮，游魂乃有所歸。苟不復本宮，則遊而不歸（乾宮游魂為火地晉，七變復。下卦三爻乾，成火天大有若不復乾之三爻，而依次以四爻變，則成火山旅。遊入離宮，而游魂為變矣。），必七日而後來復（火山旅為離宮二世卦。再七變成天火同人，為歸魂上卦，始復為乾）。

The principle of yin and yang originates from the trigram Kan (Water) and concludes with the trigram Li (Fire). The soul ascends while the body descends. The trigram Li is associated with the number seven when paired with the hour Wu and with the number eight when paired with the hour Wei. Therefore, the daily soul (day魄) does not return after seven days, and the monthly soul (month魄) incurs misfortune in the eighth month. The hexagram Fu (Return) speaks of "returning after seven days," and the hexagram Lin (Approaching) mentions "misfortune occurs by the eighth month," both based on this principle. When Li is above and Kan is below, the soul returns but cannot find its original place, hence "the wandering soul changes." Therefore, when the eight trigrams change to the sixth transformation, they become the "wandering soul hexagram," still changing the third line. By the seventh transformation, they return to their original trigram, and the wandering soul finds its resting place. If they do not return to their original trigram, they wander without a place to rest. For example, the wandering soul hexagram of the Qian trigram is the hexagram Jin (Progress), and the seventh transformation should return to the original trigram by changing the third line of the lower trigram back to Qian, resulting in the hexagram Da You (Great Possession). If instead of changing the third line of Qian back, the fourth line is changed next, it becomes the hexagram Lu (Travel), entering the Li trigram, thus becoming a wandering soul. It must go through seven days to return. The hexagram Lu (Travel) is the second generation hexagram of the Li trigram. After changing seven more times, it becomes the hexagram Tong Ren (Union with the People), which serves as the upper trigram of the returning soul hexagram, thus returning to Qian.

復而反，丑而子，氣來信為神。復而不反，午而未，氣往屈為鬼。往來屈信，均以天地之數可推而知之。季路問事鬼神。子曰：“未能事人焉能事鬼。”問死。子曰：“未知生焉知死。”此即原始反終之說。言之所不能盡者，聖人以象顯之，以數明之。精氣為物，游魂為變，於六十四卦之象數推衍，皆合乎物理之自然。或有或無，各依其類，而未可概舉也。故經文有明言者，不明言者。明言者以舉其例，而不明言者皆觸類而知之矣。

Returning to its original position, such as from Chou back to Zi, signifies the coming of qi and extension, which is called "Shen"; returning without returning, such as from Wu to Wei, signifies the going of qi and contraction, which is called "Gui." The movement of going and returning, extension and contraction, can all be calculated using the numbers of Heaven and Earth. Zilu asked how to serve ghosts and spirits, and Confucius said, "If you cannot serve people, how can you serve ghosts?" When asked about death, Confucius said, "If you do not understand life, how can you understand death?" This is precisely the meaning of "returning to the beginning and concluding with the end." Matters that cannot be fully expressed in words are shown by the hexagrams and explained by numbers. "Fine qi becomes things, and wandering souls become transformations," and when these are extended through the sixty-four hexagrams, they all conform to the natural principles of things. There is presence and absence, each according to its category, and cannot be treated as a single case. Therefore, the classics have explicit statements and implicit ones: the explicit ones give examples, while the implicit ones require understanding through analogy.

如風火家人，夫夫婦婦父父子子而家道正，人情之各得其正者也。而反乎人情者，則為鬼之狀。故睽曰“見惡人”，曰“載鬼一車”。雷天大壯，大者壯也，大者正也，壯者狀也，即正大之狀也。能通乎正大之狀者，則知鬼神之情狀。故觀曰“觀天之神道”，曰“以神道設教”。此《易》言鬼神情狀之最著者也。

For example, the Wind and Fire "Family" hexagram illustrates a situation where husband is like a husband, wife is like a wife, father is like a father, son is like a son, and the family is properly ordered. This represents the proper state of human relationships. When human relationships are violated, it becomes the shape of a ghost. Therefore, the "Parting" hexagram says "seeing an evil person" and also "carrying a ghost in a cart." Thunder and Heaven "Great Strength" hexagram: "Great" means strength, "Great" means correctness, "Strength" means appearance, together meaning "the appearance of correctness." Those who understand the appearance of correctness also understand the appearance of ghosts and spirits. Therefore, the "Observing" hexagram says "observing the divine way of heaven" and also "establishing teaching through the divine way." These are the most prominent parts in the Book of Changes regarding the forms of ghosts and spirits.

乾坎艮震巽離坤兌八宮，六十四卦，終於雷澤歸妹。歸妹為兌宮歸魂，而兌又居八宮之終，故歸妹為天地大歸魂卦。歸妹上下錯為隨（澤雷隨），隨“元亨利貞，天下隨時，出門交有功，男之始也”，歸妹“女之終也”。（《雜卦傳》）《彖》言人之終始，則合男女而言之也。

There are eight palaces composed of the Trigrams Qian, Kan, Gen, Zhen, Xun, Li, Kun, and Dui, forming a total of sixty-four hexagrams, ending with the hexagram "Return of the Maiden" (归妹), which is the returning soul hexagram of the Dui palace. Since Dui is the last of the eight palaces, "Return of the Maiden" is the great returning soul hexagram of heaven and earth. When the upper and lower trigrams of "Return of the Maiden" are reversed, they form "Following" (随), which is the hexagram of "Lake and Thunder Following." "Following" speaks of "Original Greatness, Favorable to Correcting, Favorable to Crossing the Great," and the Commentary on the Judgment says "the world follows the time." The Nine in the Fourth position says "going out to meet people brings success." The Miscellaneous Commentary says that "Following" is the beginning of the male, and "Return of the Maiden" is the end of the female. The Commentary on the Judgment speaks of "the beginning and end of human beings," which combines the male and female together.

歸妹上卦震東甲乙，帝出乎震，甲不為首首乙，故曰“帝乙歸妹”。下卦兌西庚辛，前坤後乾，坤乾為地天泰，故泰之六五亦曰“帝乙歸妹”。泰反為否，《否·彖傳》亦曰“則是天地不交而萬物不通也”，而《歸妹·彖傳》亦曰“天地不交而萬物不興”，泰否“天地反類”，（《雜卦傳》曰：泰否反其類也。邵子曰：天地定位，泰否反類。）皆東西震兌出入反覆，而日月寒暑往來，（離日坎月，乾寒坤暑）循環不窮。

The upper trigram of 《Guī Mèi》is Zhen, located in the east, paired with the heavenly stem Jia and Yi. "The Emperor arises from Zhen," but here Jia is not first, Yi is first, so the line statement of the fifth line says, "The Emperor Yi marries off his sister"—Emperor Yi was a king of the Shang dynasty, who married off his sister. The lower trigram is Dui, located in the west, paired with the heavenly stems Geng and Xin. Before it is Kun, after it is Qian, so Kun above and Qian below forms the earth above and heaven below, which is the hexagram 《Tai》. Therefore, the line statement of the fifth line of 《Tai》also says, "The Emperor Yi marries off his sister." 《Tai》reversed becomes 《Pǐ》. The 《Commentary on the Judgment》of 《Pǐ》says, "This is when heaven and earth do not interact and all things are not in communication." The 《Commentary on the Judgment》of 《Guī Mèi》also says, "Heaven and earth do not interact and all things do not flourish." 《Tai》and 《Pǐ》are "heaven and earth reverse their categories" (the 《Zá Guà Zhuàn》says, "Tai and Pǐ reverse their categories"; Shao Yong says, "Heaven and earth are positioned, Tai and Pǐ reverse their categories"). These are the mutual coming and going between Zhen and Dui in the east and west, thus the coming and going of sun and moon, cold and heat (Li represents the sun, Kan represents the moon, Qian represents cold, Kun represents heat), continuing endlessly.

坎離既濟定，有歸妹在中，而南北離坎未濟不續終者。首尾續終，（《未濟·彖傳》曰“不續終也”。《雜卦》，歸妹在既濟未濟兩卦之中。）故曰“天地之大義也”。歸妹漸相錯成隨蠱，故《漸·彖》曰“女歸吉”，《蠱·彖傳》曰“終則有始”。蓋蠱之始，乃由故之已終而新復更始。歸妹之終始，乃續終其始。故《象傳》曰“永終知敝，天地大義”者，夫婦之道也。人類之所以不絕，以有男女夫婦，生生不已，終則有始。家人為夫婦之正，故《傳》曰“家人男正位乎外女正位乎內，天地之大義也”。

The trigrams Kan (Water) and Li (Fire) are paired to form the hexagram "Ji Ji" (Completion), and "Gui Mei" (Marriage) is positioned in the middle. The southern Li (Fire) and northern Kan (Water) trigrams together form "Wei Ji" (Not Yet Completed), which signifies "not continuing the end." The beginning and end connect to continue the cycle (the "Commentary on the Judgment" of "Wei Ji" says "not continuing the end"; in the "Miscellaneous Hexagrams," "Gui Mei" is exactly between "Ji Ji" and "Wei Ji"). Therefore, this is called "the great principle of heaven and earth." "Gui Mei" and "Zhen" (Gradual Progress) interweave to form "Sui" (Following) and "Gu" (Restoration), so the "Commentary on the Judgment" of "Zhen" says "a woman's return is auspicious," and the "Commentary on the Judgment" of "Gu" says "after the end comes the beginning." The "beginning" in "Gu" refers to the old having ended and a new beginning; the beginning and end in "Gui Mei" refer to continuing the end and then starting anew. Therefore, the "Image Commentary" says "eternally knowing the end and its decay," and the so-called "great principle of heaven and earth" refers to the relationship between husband and wife. Humanity continues without end because of the ceaseless cycle of male and female in marriage, constantly renewing itself. "Jia Ren" (Family) represents the proper relationship between husband and wife, so the "Commentary on the Judgment" says "the hexagram of Family: the man is upright in the outer position, the woman is upright in the inner position, this is the great principle of heaven and earth."

然天下之事，有常有變，有得有失。先王之制，女子十五而笄，男子二十而冠，為婚媾之始。女至二十而嫁，男至三十而娶，為最遲之限，此婚媾之常。得其時者也。逾此限則為失時。但或於此時而更遇變故，如父母之喪之類，則至二十三年而嫁。此婚媾之變，失其時者也。

However, matters in the world have both regularity and change, gain and loss. The system established by the former kings was that girls reach the age of fifteen and undergo the hairpin ceremony, and men reach twenty and undergo the cap ceremony, which marks the beginning of marriage. Girls marry at twenty, and men marry at thirty, which is the latest limit. This is the regular aspect of marriage, belonging to the timely. Exceeding this limit is considered losing the proper time. But sometimes, at the proper time, one encounters a change, such as the mourning for parents, in which case the girl would be married at twenty-three. This is the changing aspect of marriage, belonging to the loss of proper time.

處變失時，乃人情之大可憐也。故先王亦不以常制限之。能守正不阿，為漸之女歸，則固協於禮而得吉。即不能固守其正，如歸妹之說動而隨，而天地之大義。亦仍不可廢。所謂聘則為妻，奔則為妾。但以禮絀之，而不以法禁之也。故特著之曰“天地大義人之終始”，深望後之人能慎終於始，不至變常而失時，庶免乎凶，而維人道於不敝矣。意深哉！

Being caught in a period of change and missing the wedding date is the most pitiable situation in human affairs, so the ancient kings did not impose strict rules upon it. If one can remain upright and not be swayed by external influences, like the "female returning to her husband is auspicious" in the "Gradual" hexagram, and marry according to propriety, then it naturally conforms to the rites and brings good fortune. Even if one cannot maintain uprightness, like in the "Return of the Maiden" hexagram, where one acts out of joy and follows others, the great principle of heaven and earth should still not be abandoned. Therefore, the "Commentary on the Judgment" specifically emphasizes "the great principle of heaven and earth, the beginning and end of human affairs," earnestly hoping that future generations will think carefully about the outcome from the beginning, so as not to disrupt the established way and miss the proper time, thus avoiding misfortune and ensuring the continuity of human conduct. The intention is indeed profound!

《乾·九四·文言》曰“或躍在淵，乾道乃革”，以九四去內卦之終，而居外卦之始，為新陳代謝之際。故《雜卦傳》曰：“革去故也。”（乾二之坤五，乾成同人，坤成比。再以乾四之坤初，乾成家人，坤成屯。屯反蒙，蒙通革。家人反睽，睽上下交錯亦為革。）

The *Wenyan Zhuan* of the *Qian Hexagram* says: "Sometimes leaping in the abyss, the Qian path then changes." Because the Nine in the Fourth line has left the end of the Inner Trigram and is now at the beginning of the Outer Trigram, it is at the turning point of renewal, so the *Zagua Zhuan* says: "Change, abandoning the old." (The Second line of Qian and the Fifth line of Kui exchange positions, resulting in Qian becoming *Tongren* and Kui becoming *Bi*. Then the Fourth line of Qian and the First line of Kui exchange positions, resulting in Qian becoming *Jiaoren* and Kui becoming *Zun*. *Zun* reverses to become *Meng*, and *Meng* is connected with *Ge*; *Jiaoren* reverses to become *Kui*, and *Kui* with its upper and lower lines crossing becomes *Ge*.)

革上兌下離，《象》曰“澤中有火革，君子以治曆明時”。其所以治曆明時者，仍在九四之一爻，與乾之九四爻，實互相發明者也。（《周易折中》以革九五為成卦之主，於《彖》、《象》之義無當也。）

The Gé hexagram has Dui above and Li below. The Image Commentary says: "There is fire in the marsh, this is transformation; the superior man uses this to regulate the calendar and clearly distinguish the four seasons." Its ability to "regulate the calendar and clearly distinguish the seasons" depends crucially on the fourth line, which is mutually illuminating with the fourth line of the Qian hexagram. (The Yongzuan Zhouyi Zhizhong states that the fifth line of the Gé hexagram is the main line of the hexagram, but this does not align with the meaning of the Commentary on the Judgment and the Image Commentary.)

乾坤二策，合三百有六十，當期之日。變通在四時，時各九十日。八卦分值一年。一卦盡，得四十五日。（五日為一候，三候為一氣，八卦一爻主一氣，三氣四十五日而一卦畢。）

The combined number of策 (counting units) for the trigrams Qian and Kun is 360, exactly matching the number of days in a year. The principle of change and adaptability is reflected in the four seasons, with each season consisting of 90 days. The eight trigrams take turns to guard the year, each trigram taking charge for 45 days. (Five days make a候 (period), three候 make an气 (climate), each yao of the eight trigrams governs one气, and three气 total 45 days, completing the term of one trigram.)

乾九四已入外卦，內卦三爻之氣已盡，故曰“乾道乃革”。兌離為西南之卦，金火相乘，（四時：春木生夏火，秋金生冬水，冬水又生春木，惟夏秋為火克金，故金曰“從革”。）志不相得乃革，故《象》曰“己日乃孚”。己者土也，以坤土行離兌之間，孚而信之，革道乃成。《彖傳》曰：“天地革而四時成”。虞仲翔氏云：“曆象謂日月星辰。離為明，坎為月，離為日，蒙艮為星，（革通蒙）四動成坎離。日月得正，謂四爻動外卦變坎，成水火既濟。日月得正，曆象正而時序明矣。”王弼云：“曆數時會存乎變。”則渾括其意，義雖當，初學視之益蕩然矣。

The Nine in the Fourth of the Qian hexagram has already entered the outer trigram, and the energy of the third line of the inner trigram has been exhausted, so it is said, "The way of Heaven is transformation." The Dui and Li hexagrams belong to the western and southern trigrams respectively, and metal and fire mutually overpower each other. The sequence of the five phases is: spring wood generates summer fire, autumn metal generates winter water, and winter water generates spring wood; only between summer and autumn is fire overcoming metal. Therefore, the "Classic of Documents: Hongfan" says that the nature of metal is called "from transformation." Since the two trigrams have conflicting intentions, there is transformation, hence the hexagram "Gai" says, "Only on the day of Ji does trust arise." "Ji" belongs to the earth element, and the earth element moves between Li and Dui, thus gaining people's trust and completing the way of transformation. The Commentary on the Judgment says, "Heaven and Earth transform, and the four seasons are formed." Yu Fan (styled Zhongxiang) says, "Lixiang refers to the sun, moon, and stars. Li represents brightness, Kan represents the moon, and Li represents the sun. The mountain in the "Meng" hexagram represents the stars (the "Gai" and "Meng" hexagrams are yin-yang counterparts), and when the fourth line moves, it becomes Kan and Li. The phrase 'the sun and moon are in their proper places' means that when the fourth line moves, the outer trigram becomes Kan, and the whole hexagram becomes Water and Fire "Ji Ji." The sun and moon are each in their proper places, the Lixiang is correct, and the sequence of time becomes clear." Wang Bi says, "The reckoning of years and the conjunction of the seasons depend on transformation." This statement is only a general remark, though the meaning is correct, beginners may find it more confusing.

蓋革象下離為日，上坎為月，而九四一爻奇於其間，致日與月，不能相齊。日有餘而月不足，三為終，四連於三，歸餘於終之象，歸日之餘於終，積而成月，則閏也。積閏為章，（七閏十九年為一章）積章為蔀。（四章為一蔀，二十蔀為一遂，三遂為一首，七首為一極。詳《周髀算經》。）章蔀之名，不見於革而見於豐。豐六二、九四皆云“豐其蔀”，上六“蔀其家”，六五“來章”，蓋豐五變則成革也。孔子贊《易》，於一字一義，無不與卦爻往來脈絡貫通。非參互錯綜以求之，又烏能得其意之所在哉！（凌銳按：革五爻皆當位，惟九四一爻不當位。故曰“革而當其悔乃亡”。）

The image of the "Revolution" hexagram is formed by the lower trigram Li (Fire) representing the sun and the upper trigram Kan (Water) representing the moon, which has changed. The line nine in the fourth position is isolated in the middle, preventing the sun and moon from being properly aligned. The sun has an excess of days while the moon lacks sufficient days. The third line is called "the end," and the fourth line follows immediately after, symbolizing the transfer of the excess days to the end position. Accumulating these excess days forms a month, which is called "leap month." Accumulating leap months forms a "chapter" (a cycle of nineteen years with seven leap months), and accumulating chapters forms a "section" (four chapters make a section, twenty sections make a "sui," three "sui" make a "shou," and seven "shou" make a "ji," as detailed in the "Zhou Bi Suan Jing"). The terms "chapter" and "section" do not appear in the "Revolution" hexagram but appear in the "Brightness" hexagram: the line six in the second position and nine in the fourth position of "Brightness" both say "brightening the section," and the line six at the top says "sectioning the family," while the line six in the fifth position says "coming to the chapter." This is because the fifth line of the "Brightness" hexagram transforms into the "Revolution" hexagram. Confucius interpreted the Book of Changes, ensuring that every word and every level of meaning was connected with the flow of the hexagram lines. Without referring to mutual relationships and transformations, how could one understand his intent? (Ling Rui's note: The "Revolution" hexagram has five lines in proper position, except for the line nine in the fourth position, which is not in proper position. Therefore, the "Commentary on the Judgment" says, "Revolution in proper position, its regret will vanish.")

京氏卦納甲：乾貞子，坤貞未；乾納甲壬，內子外午；坤納乙癸，內未外丑；六子之卦，各按其所納之幹，而依乾坤之爻以為序。震貞子，坎貞寅，艮貞辰。巽從坤而內外相易，貞丑。離貞卯，兌貞己。乾子寅辰午申戌，左轉；坤未己卯丑亥酉，右行。陰陽相間，而周十二辰。

Jing Fang's method of assigning Heavenly Stems to hexagrams: The first line of the Qian hexagram is assigned to Zi, and the first line of the Kun hexagram is assigned to Wei. Qian hexagram is assigned the Heavenly Stems Jia and Ren, with the inner trigram starting at Zi and the outer trigram starting at Wu. Kun hexagram is assigned the Heavenly Stems Yi and Gui, with the inner trigram starting at Wei and the outer trigram starting at You. The remaining six hexagrams each follow their own assigned Heavenly Stems, arranging their lines according to the sequence of lines in Qian and Kun hexagrams: Zhen hexagram's first line is assigned to Zi, Kan hexagram's first line is assigned to Yin, Gen hexagram's first line is assigned to Chen. Xun hexagram follows Kun, with its inner and outer trigrams swapped, and its first line assigned to You. Li hexagram's first line is assigned to Mao, and Dui hexagram's first line is assigned to Si. Qian hexagram's lines are assigned in the order Zi, Yin, Chen, Wu, Shen, Xu, turning left in sequence. Kun hexagram's lines are assigned in the order Wei, Si, Mao, You, Hai, You, turning right in sequence. One yin and one yang alternate, exactly circling the twelve Earthly Branches.

鄭氏爻辰：乾貞於子左轉，子寅辰午申戌。間時而治六辰，與納甲同。坤貞於未亦同。乃由未而酉亥丑己卯，則與乾同為左轉。後學因此，每多歧誤。或謂康成說《易》本《乾鑿度》，故與京氏不同。然《乾鑿度》云“乾貞於十一月子，左行陽時六。坤貞於六月未，右行陰時六。歲終次從於屯蒙，屯蒙主歲。屯為陽，貞於十二月丑，其爻左行。以間時而治六辰。蒙為陰，貞於正月寅，其爻右行。亦間時而治六辰，歲終則從其次”云云。乃以六十四卦依《序卦》之次，前卦為陽，後卦為陰，每兩卦分主一歲。故三十二歲而一周，與爻辰之說不相蒙也。

Zheng Xuan's method of yao chen: The first line of the Qian hexagram is fixed at Zi, and moving left in a clockwise direction, it goes through Zi, Yin, Chen, Wu, Shen, Xu, assigning each line to one of six zhi, which is the same as Jing Fang's Najia method. The first line of the Kun hexagram is fixed at Wei, starting from the same point, but moving left in a clockwise direction as well, going through Wei, You, Hai, Chou, Si, Mao. Later scholars often made mistakes because some claimed Zheng Xuan's interpretation of the Book of Changes was based on the "Yi Wei Gan Zao Du," which is different from Jing Fang. However, the "Gan Zao Du" says: "The first line of the Qian hexagram is fixed at Zi in the eleventh month, moving left in a clockwise direction through the six yang positions; the first line of the Kun hexagram is fixed at Wei in the sixth month, moving right in a counterclockwise direction through the six yin positions. After one year, the order proceeds to the two hexagrams Zun and Meng: Zun belongs to yang, and its first line is fixed at Chou in the twelfth month, moving left, assigning each line to one of six zhi; Meng belongs to yin, and its first line is fixed at Yin in the first month, moving right, also assigning each line to one of six zhi; after one year, the order continues in sequence." This shows that the "Gan Zao Du" arranges the sixty-four hexagrams in the order of "Xu Gua," with the first hexagram being yang and the second being yin, each pair of hexagrams governing one year, completing a cycle of thirty-two years, which has nothing to do with Zheng Xuan's yao chen theory.

錢溉亭《述古錄》謂“京氏本律呂之合聲，鄭氏本月律”。其說具見《周官·太師》鄭氏注：“太師掌六律六同，（疏云：六律左旋，六同右轉）以合陰陽之聲。陽聲黃鐘子，太簇寅，姑洗辰，蕤賓午，夷則申，無射戌。子寅辰午申戌，其次與乾六爻左旋同也。陰聲大呂丑，應鐘亥，南呂酉，林鐘未，小呂己，夾鐘卯，則丑亥未酉己卯，其次與坤六爻不相合矣。鄭氏以律呂相生為主，則六律六同皆左旋。以律為夫，以呂為婦。婦從夫，故皆左旋。”是京氏之納甲，與《乾鑿度》同主合聲。而鄭之爻辰，則主相生，非本於《乾鑿度》者也。

Qiantang (nominated Gaiting) in his "Shu Gu Lu" said: "Jing Fang's theory is based on the harmonious sounds of the pitch pipes, while Zheng Xuan's theory is based on the monthly pitch pipes." This complete explanation appears in the Zheng Xuan commentary on "The Rites of Zhou · Spring Officials · Tai Shi": "The Tai Shi is in charge of the six pitch pipes and the six same pitch pipes (Jia Gongyan's commentary says: the six pitch pipes turn to the left, and the six same pitch pipes turn to the right), used to harmonize the sounds of yin and yang. The yang sounds are Huangzhong paired with Zi, Taicuo paired with Yin, Guxi paired with Chen, Rui Bin paired with Wu, Yizhe paired with Shen, and Wuyue paired with Xu. The order of Zi, Yin, Chen, Wu, Shen, Xu corresponds to the six yao of the Qian hexagram turning to the left. The yin sounds are DaLv paired with Chou, Yingzhong paired with Hai, Nanlv paired with You, Linzhong paired with Wei, XiaoLv paired with Si, and Jiazhong paired with Mao. The order of Chou, Hai, Wei, You, Si, Mao does not correspond to the six yao of the Kun hexagram turning to the right. Zheng Xuan takes the mutual generation of the pitch pipes as the main principle, so the six pitch pipes and the six same pitch pipes all turn to the left. This is because the pitch pipes are regarded as the husband and the same pitch pipes as the wife, with the wife following the husband, hence turning to the left." From this, we can see that Jing Fang's Najia and the "Qian Zao Du" both focus on "harmonious sounds," while Zheng Xuan's yao chen focuses on "mutual generation," and is not based on the "Qian Zao Du."

辛齋按：陰從於陽，陰陽之體也。河圖一三七九、二四六八皆左行者是也。（若陰陽分言，則陰逆陽順。陽自一三五七九，而陰則從四起，為四二十八六。故五位相得而各有合。若如舊說，則五與十無相合之理。詳見《易數偶得》）陽左旋陰右轉，陰陽之用也。洛書之一三九七左旋、二四八六右轉是也。非順行不能相生，非逆行不能相合，《易》之體用無不如是，明乎此，則聚訟不決之懸案，可片言而斷矣。

Xin Zhai says: Yin follows Yang, which is the "body" of yin and yang. In the Yellow River Chart, the generating numbers and the completed numbers are paired in pairs, with one, three, seven, and nine paired with two, four, six, and eight, all moving to the left, which is the reason for this. (If yin and yang are considered separately, then yin moves in reverse while yang moves in regular order: Yang is arranged as one, three, five, seven, nine, while Yin starts from four and proceeds as four, two, ten, eight, six, so that the five directions are paired in pairs and each has its match. If following the traditional arrangement, five and ten would not be compatible. See my work "Accidental Insights on the Changes".) Yang rotates to the left while Yin rotates to the right, which is the "use" of yin and yang. In the Luo Writing, one, three, nine, and seven rotate to the left, while two, four, eight, and six rotate to the right, which is the reason for this. Without moving in the proper direction, mutual generation cannot occur; without moving in the reverse direction, mutual compatibility cannot be achieved. The "body" and "use" of the Changes are all like this. Once this is understood, those cases that are in dispute can be decided with one sentence.

或問：既如子言，則京氏既主合聲矣，何以坤之未己卯丑亥酉，又與陰聲之丑亥酉未己卯不同也？曰：此即洛書七與九、二與八易位之理也。故巽之六爻則為丑亥酉未己卯矣。此中玄妙，具有至理。神而明之，非言所能盡焉。

Someone asked: According to your explanation, since Jing Fang advocates 'harmonizing tones,' then why do the hexagrams of the Kūn hexagram, which include the earthly branches of Wei, Si, Mao, Chou, Hai, and You, differ from the yin tones of Chou, Hai, You, Wei, Si, and Mao? The answer is: This is precisely the principle of the Luo Writing where the numbers seven and nine, and two and eight, exchange positions. Therefore, the order of the six lines of the Xun hexagram is exactly Chou, Hai, You, Wei, Si, and Mao. The subtlety here has extremely profound reasons, which can only be understood by individuals through inner realization, and cannot be fully expressed in words.

或問鄭康成氏爻辰說《易》，以星象證爻辭，而原注已佚。從《禮》注與《乾鑿度》注搜輯者，寥寥無幾。近世戴棠氏，撰《鄭氏爻辰補》。而全《易》三百八十四爻，各取《甘石星經》及《開元占經》所載諸星名，以印證爻辭，無不恰合。詎伏羲之播爻，文王之繫辭，果一一仰觀天文以取象乎，何巧合若是？

Someone asked: Zheng Xuan used the theory of yao chen to explain the Book of Changes, using celestial phenomena to verify the line statements. However, his original annotations have been lost, and only a few fragments have been collected from his commentaries on the Rites and his annotations on the Qian Zao Du. Recently, Dai Tang wrote the "Supplement to Zheng's Yao Chen," in which he matched each of the 384 lines of the Book of Changes with the names of stars recorded in the Gan Shi Star Classic and the Kaiyuan Treatise on Astrology, and found that they all coincided perfectly. Could it be that Fuxi arranged the line diagrams and King Wen composed the line statements of the upper trigrams by observing the heavens and taking their images? Otherwise, how could such a perfect coincidence occur?

曰：伏羲畫卦之時，文字未作，器用未備，又何有星名？蓋一畫開天，奇偶以生。仰觀俯察，法象於天地，變通乎四時。陰陽剛柔，動靜變化，而洽於造化數理之自然。而天地之運行，人物之遞演，自不能出此常軌之外。故先天而天不違。至黃帝以黃鐘定律，準度量，定權衡，悉本於伏羲之卦。而窺天測地，定日月星辰以紀歲時。

The response was: When Fuxi drew the trigrams, writing had not yet been invented, and utensils were not yet complete, how could there be the names of the star mansions? He merely drew the first trigram to open up the heavens, from which the odd and even lines originated. He looked up to observe the celestial phenomena and looked down to examine the geographical features, taking inspiration from the images of heaven and earth, and adapting to the order of the four seasons. The yin and yang, the firm and the flexible, the movement and stillness, all harmonize with the natural principles of creation and numbers. The operation of heaven and earth, and the successive transformation of human affairs and all things, have always followed this constant pattern. Therefore, it is said, "Before heaven, heaven does not violate." Later, the Yellow Emperor used the Huangzhong to establish the musical scale, calibrated measures and weights, and established standards, all based on Fuxi's trigrams. Afterwards, people explored the heavens and earth, determined the sun, moon, and stars to mark the passage of time.

然天廣無垠，既以象限立儀（象限儀分圓周為四，即法乎四象。儀者，分陰分陽，即法乎兩儀。），以分躔度次舍，而不可無以名之以資識別也。於是各按八卦之象數以定其名。故天星之名，大都出自卦象，非卦象之強合星名也。鄭氏爻辰以星名證其爻義，已不免倒果為因。必逐爻求象於星，而以爻辭附會之，以期或有一字一義之合；無論其未必盡合，即合矣，於經義仍未必有所發明。是亦可以不必矣。

But the heavens are vast and boundless; having already established a system using the quadrant instrument (which divides the circumference into four parts, thus following the principle of the Four Symbols; "instrument" refers to dividing yin and yang, thus following the principle of the Two Principles), it distinguishes the degrees of the sun and moon's movement and the sequence of the Twenty-Eight Mansions (where the sun and moon temporarily halt in their course). Therefore, it is necessary to have names for identification. Hence, they are named according to the numerical symbolism of the Eight Trigrams. Therefore, the names of the star mansions in the heavens mostly originate from the trigrams, and it is not the case that the trigrams are forced to conform to the names of the stars. Zheng Xuan used the names of the stars to verify the meaning of the lines, which already involves reversing cause and effect. If one insists on seeking symbolic correspondences from the star mansions for each line, and then force the line statements to fit, hoping for a one-to-one correspondence—regardless of whether such correspondences can actually be found, even if they can, it does not necessarily contribute to the elucidation of the classic's meaning. Therefore, such an approach is certainly unnecessary.

《易·彖傳》言“陰陽上下往來”，後儒或主卦變，或主錯綜，（此指來氏之所謂錯綜）眾論紛若，莫衷一是。而卦變之例，荀虞以下既各不同，而同一虞《易》，其為圖也又參差不一。朱子既圖卦變，又取《彖傳》之言往來者十九卦，編為歌訣。然與其圖，已不相符合。且《彖傳》之言往來上下者，亦不僅此十九卦。故證以經文，參諸卦象，自以主兩卦之一往一來者，（即來氏錯綜）其說較優。

The Commentary on the Judgment in the Book of Changes speaks of "yin and yang moving up and down." Later Confucian scholars have proposed different interpretations, some advocating the use of "changing hexagrams" and others advocating "interchange and reversal" (here referring to the concept of interchange and reversal as discussed by Lai Zhide). There are many conflicting views, and no consensus has been reached. As for the method of changing hexagrams, from Xun Shuang and Yu Fan down to other scholars, their approaches have varied greatly. Even within Yu Fan's own interpretation of the Book of Changes, later generations have drawn different diagrams. Zhu Xi both drew a diagram of changing hexagrams and compiled a mnemonic verse based on the nineteen hexagrams from the Commentary on the Judgment that discuss movement. However, the verse does not align with his own diagram. Moreover, the Commentary on the Judgment discusses movement up and down not only in these nineteen hexagrams. Therefore, using the text to verify and referring to the hexagrams for examination, it is still more reasonable to argue based on the mutual reversal of two hexagrams, one moving and one returning (which is what Lai Zhide called interchange and reversal).

蓋文王之《易》，本以兩卦反覆一往一來。則《彖傳》以釋《彖》，自必於此兩卦推勘其義，理至當也。上卦為外為上為往，下卦為內為下為來。（此卦之下即彼卦之上，此往則彼來，彼上則此下。）上卦二陽一陰者，陰上進而往。二陰一陽者，陽上進而往。下卦之為來亦然。

The original "Book of Changes" by King Wen was arranged by repeatedly reversing two trigrams, with movement going and coming. Since the "Commentary on the Judgment" explains the hexagram statements, it naturally seeks meaning between the two reversed trigrams, which is the most reasonable approach. The upper trigram belongs to the outside and is "going," while the lower trigram belongs to the inside and is "coming" (the lower trigram of this hexagram is the upper trigram of the other, so when one goes, the other comes; when one is above, the other is below). If the upper trigram has two yang lines and one yin line, the yin line moves upward and is considered "going"; if it has two yin lines and one yang line, the yang line moves upward and is considered "going." The situation for "coming" in the lower trigram follows the same pattern.

故《孔疏》云“凡言往來者皆據異類而言。”若三陰三陽之卦，則上下並言。泰否之兼言往來，咸蠱之兼言上下，噬嗑賁渙節言來言上言分是也。四陰四陽之卦，則以一陰一陽之在上下者言，晉升無妄大畜訟需是也。二陰二陽，則以陰陽之在上卦者言，賽解鼎睽是也。五陰五陽者，以一陰一陽言，復姤是也。似較卦變之茫無一定者，差可依據。

Therefore, Kong Yingda in The Correct Meaning of the Zhou Changes says: "Whenever there is talk of coming and going, it refers to the yao that differs from the majority." If the hexagram consists of three yin and three yang lines, then both the upper and lower trigrams are mentioned: The Tai and the Pi hexagrams both discuss coming and going, the Xian and the Gu hexagrams both discuss upper and lower, and the Shihe, Ben, Huan, and Jie hexagrams discuss coming, upper, and division, all belonging to this category. If the hexagram consists of four yin and four yang lines, then the yao in the upper or lower trigram is referred to: the Jin, Sheng, Wuwang, Daxu, Song, and Xu hexagrams are examples. If the hexagram consists of two yin and two yang lines, then the yao in the upper trigram is referred to: the Jian, Jie, Ding, and Kui hexagrams are examples. If the hexagram consists of five yin and five yang lines, then the single yin or yang line is referred to: the Fu and Guu hexagrams are examples. This is more grounded than the indeterminate nature of the theory of hexagram transformation.

然此但以上下兩象而言，間有以專重之一爻為主者，則又不在此例。乾坤為《易》之門，往來者必於此門。二陽一陰者坤體，而陰往來上下於其間也。二陰一陽者乾體，而陽往來上下於其間也。上下無常，剛柔相易，原非可執一例以求之。但初學者不可不先求一隅之可舉者以為根據耳。

However, this is only referring to the images of the two upper and lower trigrams; there are also cases where a particular important line is the focus, which are not included in this category. Qian and Kun are the gateways of the Book of Changes, and movement must pass through this gate. For a trigram with two yang lines and one yin line, the yin line is the main element, moving up and down within it. For a trigram with two yin lines and one yang line, the yang line is the main element, moving up and down within it. Since movement up and down is ever-changing, and the qualities of yang and yin constantly shift and transform, it is naturally impossible to follow a fixed rule. But for beginners, they cannot avoid using a concrete example as a reference.

《周禮·太卜》：“掌三《易》之法，《連山》、《歸藏》、《周易》。其經卦皆八，其別卦皆六十有四。”段若膺云：“《連山》、《歸藏》、《周易》三《易》，每《易》有八，每八分為六十四，故云其別卦。經卦即乾坤震巽坎離艮兌，別卦即因而重之之六十四卦也。”

The Zhou Li · Chun Guan · Tai Bu says: "The three books of Yi, namely the Lian Shan, Gui Cang, and Zhou Yi, all use the method of divination with yarrow stalks. They all have eight primary trigrams and sixty-four derived trigrams." Duanyucai (style name Ruoying) says: "The Lian Shan, Gui Cang, and Zhou Yi each have eight primary trigrams. Each set of eight trigrams is further combined in pairs to form sixty-four derived trigrams, which is called 'derived trigrams.' The primary trigrams are Qian, Kun, Zhen, Xun, Kan, Li, Gen, and Dui. The derived trigrams are formed by stacking two primary trigrams on top of each other to create the sixty-four trigrams."

楊用修《丹鉛錄》云：“別當作□。從重八。八八六十四，故云別卦。”蓋別訓分，八亦訓分。□從八八，謂分而又分。八八為六十四，正合八卦重為六十四卦之義。可見古人修辭之學，其用字之精當，迥非後人所可及也。

Yang Shen (style name Yongxiu) in his "Danqian Lu" said: "The character 'bie' should be written as '□', composed of two 'ba' characters superimposed. Since eight eights make sixty-four, it is called 'bie gua'. " Originally, the character 'bie' means to divide, and the character 'ba' also means to divide. The character '□' is made up of two 'ba's, meaning divided again and again. Eight times eight equals sixty-four, which exactly corresponds to the meaning of the eight trigrams being superimposed to form the sixty-four hexagrams. This shows that the rhetorical skills of ancient people were precise and appropriate in their word choice, far beyond what later generations can match.

《說卦傳》：震其究為健為蕃鮮，巽其究為躁卦。健為乾，蕃鮮指巽。躁卦即震也。考其他六卦，皆不稱究，獨於震巽兩卦言之何也？物有始有壯有究，震巽陰陽變化之始也。震以一陽變於坤，坤成震而乾成巽。原始要終，可得其究。至於坎離，為陰陽之壯，又得乾坤之中，不至極於一偏。艮兌已為陰陽之究，所謂其上易知。故艮成言，兌說言，皆無須推極其究者也。

The *Sayings on the Hexagrams* says: When the *Zhen* trigram is examined to its extreme, it becomes "strong" and "abundant and bright"; when the *Xun* trigram is examined to its extreme, it becomes "restless trigram." "Strong" refers to *Qian*, "abundant and bright" refers to *Xun*, and "restless trigram" refers to *Zhen*. The other six trigrams do not mention "examination," but only *Zhen* and *Xun* do. Why is this so? All things have three stages: beginning, flourishing, and culmination. *Zhen* and *Xun* are precisely the beginning of yin and yang transformation: *Zhen* is when one yang enters *Kun*, and *Kun* thus becomes *Zhen*; *Qian* thus becomes *Xun*. By tracing the origin and seeking the end, one can see its "culmination." As for *Kan* and *Li*, they are the flourishing stage of yin and yang, and they have the middle lines of *Qian* and *Kun*, so they do not reach an extreme. *Gen* and *Dui* have already reached the culmination of yin and yang, which is what the *Great Treatise* calls "easily known." Therefore, the *Sayings on the Hexagrams* says "it is fully expressed in *Gen*" and "it is explained in *Dui*," and there is no need to further examine their culmination.

惟巽之究為躁，似與其木性相反。而震之究為健，則為復其本性。為蕃鮮則為極其功用，其究同而究不同，則陰陽之分際然也。蓋陽為萬物之本，（天地五十五數，陽奇陰隅，而陰陽合數則仍為奇。一六合為七，二七合為九，三八合為十一，四九合為十三，總數五十五皆奇也。故曰陰必歸陽。）非若陰之為用有限也。

The trigram Xun reaches its extreme and becomes "zao" (restlessness), which seems to contradict its inherent gentle and flexible nature as wood. In contrast, the trigram Zhen reaches its extreme and becomes "jian" (strength), which restores its original yang nature. "Fan xian" (abundance and brightness) represents the full expression of its function. The same character "jiu" (to investigate to the extreme) leads to different results, which is due to the difference between yin and yang. Yang is the fundamental principle of all things (the total number of heavenly stems and earthly branches is fifty-five, with yang being odd numbers and yin even numbers; however, the combination of yin and yang still results in an odd number: one combined with the six harmonies makes seven, two combined with seven makes nine, three combined with eight makes eleven, four combined with nine makes thirteen, and the total number fifty-five is also odd, thus yin must return to yang). Unlike yin, whose function is limited, yang's function is boundless.

或問：《說卦傳》“坎為血卦”，《荀氏易》作“血衄”。說者謂血為人身之水，以病故衄然歟？曰：否。坎為血卦，猶離之為乾卦也。六子惟坎離得乾坤之中，特稱卦以別之。離為乾體，故曰“乾卦”。坎為坤體，故曰“血卦”。血坤也。《坤·上六》曰“其血玄黃”，《傳》曰“猶未離其類也，故稱血焉”。以見血為坤之類，是坎之稱血卦，與離之稱乾卦為例正同，未可以血衄改之也。

Someone asked: The "Commentary on the Hexagrams" says "Kan is the Blood Hexagram," but the "Xunshi Yi" of Xun Shuang's school writes it as "blood and nosebleed." Interpreters of the classics think that blood is the water in the human body, and nosebleeds occur when one is sick, so Kan also governs blood. Is this interpretation correct? Answer: No. The term "Blood Hexagram" for Kan is consistent with the term "Dry Hexagram" for Li. Among the six sub-hexagrams generated by Qian and Kun, only Kan and Li inherited the middle line from Qian and Kun, so they are specially named with the word "hexagram" to distinguish them from the other four sub-hexagrams. The outer two lines of Li are yang, and the middle line is yin, so its essence belongs to Qian, hence it is called the "Dry Hexagram." The outer two lines of Kan are yin, and the middle line is yang, so its essence belongs to Kun, hence it is called the "Blood Hexagram" — "blood" refers to Kun. The "Yao Ci" of the "Upper Sixth" line of the "Kun Hexagram" says "its blood is black and yellow," and the "Wenyan Zhuan" explains that "it has not yet separated from its category, hence it is called blood." This shows that blood belongs to the category of Kun. Therefore, the naming of Kan as the "Blood Hexagram" follows the same example as Li being called the "Dry Hexagram," and it is not correct to change it to "blood and nosebleed" as in the "Xunshi Yi."

或曰：離之為乾卦，乾讀若干，乃燥萬物者莫熯乎火，故曰乾卦。與乾坤之乾，音訓其可通乎？曰：鄭注云乾當為乾，陽在外作幹正也。虞《易》亦同。而張湛雲乾音乾，則音固可通。《易》之用字，恆以形聲相類者，分見互用，以相鉤貫。焦氏《通釋》言之詳矣。而《說卦》言象，尤往往舉甲以概乙，又或對舉相互以見意者。如乾為圓，則坤之為方可知。巽為臭，則震為聲可知。

Someone asked: The trigram 'Li' is called 'Qian', and the 'Qian' here should be read as 'Gan', based on the meaning in the 'Shuo Gua Zhuan' that 'the thing that dries all things is none other than fire', meaning fire can dry out all things, so it is called 'Qian' trigram. However, can the 'Qian' in 'Qian and Kun' be considered as the same in pronunciation and meaning? Answer: Zheng Xuan in his commentary said that 'Qian' should be read as 'Gan', with the yang line outside, and the character 'Gan' is considered correct. Yu Fan's commentary on the 'Zhou Yi' is also the same. However, Zhang Zhan of the Jin dynasty said that 'Gan' and 'Qian' have the same pronunciation, indicating that the pronunciation has always been the same. The use of characters in the 'Zhou Yi' often separates similar characters with similar radical and phonetic components, using them interchangeably to connect and link them, as explained in detail by Jiao Xuan's 'Yi Tong Shi'. As for the 'Shuo Gua Zhuan' discussing the images of the trigrams, it often uses one character to represent another, or pairs them to show their meanings: once it says 'Qian represents roundness', 'Kun represents earth', we can infer the rest; once it says 'Xun represents smell', 'Zhen represents sound', we can also infer the rest.

此以離為乾卦，以與坎之血卦相對。貞者事之幹也。乾貞在坎，而著乾之義於離，離其類為血，而存血之文於坎，交互見意，錯綜成文，可謂極天下之至精至變者矣！故《易》之為書，廣大悉備。孔子贊《易》之文，悉與相稱。一名一字，於形聲訓義，均鉤深致遠，無不各有精義存乎其間，非言語所能形容也。舉一三反，是在讀者之神而明之。

Here, the trigram Li is called "Qian" (Heaven), which is meant to contrast with Kan's "Xue" (Blood) trigram. The "Wenyan" section of the "Qian Hexagram" says, "Zhen refers to the main stem of a matter," where "Zhen" signifies the main part of something. The "Zhen" position of Qian falls on Kan (in the Later Heaven arrangement, Kan is located in Due North, which is precisely where Qian's "Zhen" position is). Yet the meaning of "dry" is assigned to Li; Li's category is originally associated with blood, but the character "blood" is preserved in Kan. The meanings are interchanged and interwoven, creating a complex and intricate text, truly exhausting the most subtle and changeable principles in the world. Therefore, the book of The Zhou Changes is vast and comprehensive, covering everything. Confucius' commentary on the Changes is also in harmony with it: each term and each character is deeply explored in both sound and meaning, each containing profound significance, beyond the reach of words. By understanding one, one can infer the rest, and it is up to the reader to grasp the meaning intuitively.

或問《說卦》之取象，震坎皆言馬，合之乾共三卦。巽為木，而坎於其木也堅多心，離其於木也為科上稿，艮於其木也為堅多節，凡四卦。乾又為木果，而震為蒼筤竹，又其於稼也為反生，亦木之類。何馬與木之取象獨多也？

Someone asked: The "Sayings on the Trigrams" mentions the image of a horse in both Zhen and Kan, and also mentions it in Qian, making a total of three trigrams that use the image of a horse. Xun represents wood, and Kan says "its image for wood is firm with many hearts" (the wood is hard with many knots), Li says "its image for wood is hollow in the middle and withered at the top" (the middle is hollow and the top is dry), and Gen says "its image for wood is firm with many knots" (the wood is hard with many knots), making a total of four trigrams that refer to wood. Qian also represents fruit trees, Zhen represents young bamboo, and Zhen also says "its image for crops is reverse growth" (the seeds of grain sprout in reverse), which also belongs to the category of wood. Why does the imagery of the eight trigrams focus so much on horses and wood?

曰：此為切於人生日用者言之。行者以馬，居者以木，為用廣，故取象多也。又周以火德王，馬為離午之精，行地無疆，周乎天下。故乾坤坎離皆言馬。伏羲以木德王，木者火之母也。損上益下，木道乃行。天施地生，其益無方者木也。故《易》言馬與木為獨多也。

This is talking about things most closely related to the daily lives of the people. Travel depends on horses, and dwellings depend on wood, both of which have the widest range of uses, so they are represented in many symbolic forms. Moreover, the Zhou dynasty ruled with the virtue of fire, and horses are the essence and qi of the fire element, corresponding to the午 position. The Commentary on the Judgment of the坤卦 says, "moving on the earth without boundaries," which means being able to travel everywhere, so the four trigrams Qian, Kun, Kan, and Li all mention horses. Fuxi ruled with the virtue of wood, and wood is the mother of fire; the Commentary on the Judgment of the益卦 says, "reducing from above to benefit below," "the way of wood is then established," and also says, "heaven gives, earth produces, its benefit has no limits." The thing capable of bearing the responsibility of nurturing all things without limit is wood. Therefore, the Zhou Changes speak extensively about horses and wood.

漢《易》之存於今者，惟虞氏注未盡亡佚。經勝清惠定宇、張惠言二氏之搜輯演繹，儼然首尾貫串，而規模畢具矣。顧宋學家及同為漢學之馬鄭者，悉力攻擊之。或謂其納甲之說，以魏伯陽《參同契》而擅改聖經之卦位；或謂其之正之說，全背《彖》、《象》傳義。王氏《經義述聞》，辯駁尤甚。

Han dynasty commentary on the Book of Changes has survived to the present day only in the works of Yu Fan. Through the efforts of Zhang Huiyan and Hui Dong of the Qing dynasty in collecting and deducing, Yu's commentary on the Book of Changes has become coherent and has a substantial framework. However, scholars of the Song dynasty school, as well as those following the Han school who revered Ma Rong and Zheng Xuan, all strongly criticized it. Some claimed that his theory of "Najia" was borrowed from Wei Boyang's Dan Classic, using alchemical correspondences, and that he arbitrarily altered the positions of hexagrams in the sacred classics. Others said his theory of "zhizheng" completely contradicted the meaning of the Commentary on the Judgment and the Image Commentary. Among them, Wang Yinzhi's refutation in his work "Jingyi Shuwén" was the most intense.

略謂仲翔發明卦爻，多以之正為義。陰居陽位為失正，則之正而為陽。陽居陰位為失正，則之正而為陰。蓋本《彖傳》之言位不當者而增廣之，變諸卦失正之爻以歸於既濟，可謂同條共貫矣。然經云位不當者，惟論爻之失正，以決其悔吝之由，示觀象玩辭、觀變玩占者，知所警耳。

Wang's general meaning is that Yu Fan (style name Zhongxiang) explained the hexagram lines by using the concept of 'returning to the correct position'—a yin line in a yang position is considered incorrect and should change to a yang line to return to correctness; a yang line in a yin position is considered incorrect and should change to a yin line to return to correctness. This is an extension of the Commentary on the Judgment's statement 'position is not appropriate.' It applies the idea of correcting incorrect lines to all hexagrams, changing all incorrect lines to the pattern of the hexagram Ji Ji, where all six lines are in their proper positions, making the reasoning coherent. However, the 'position is not appropriate' mentioned in the classics refers only to a single line being incorrect, used to determine the origin of regret and hardship, serving as a warning for those observing phenomena and interpreting divination.

夫爻因卦異，卦以爻分，各有部居，不相雜廁。若爻言初六、六三、六五，而易六以九；言九二、九四、上九，而易九以六言，則爻非此爻，卦非此卦矣。虞氏以為變而之正，實自失其本體，不且紊亂而無別乎？遍考《彖》、《象》傳文，絕無以之正為義者。既已無所根據，乃輒依附於經之言貞者，而以之正解之。

The statements of the lines vary according to the hexagram, and the hexagrams are distinguished by their lines, each having its own position, and they cannot be mixed up. If the line statements clearly mention initial six, sixth three, or fifth six, yet one changes 'six' to 'nine'; or if it mentions nine two, nine four, or top nine, yet one changes 'nine' to 'six', then the line is no longer that line, and the hexagram is no longer that hexagram. Yu Fan thought that 'changing to the correct' was the meaning, but in reality he lost the original essence, is it not causing confusion and disorder in the hexagrams and lines, making them indistinguishable? A thorough examination of the texts in the Commentary on the Judgment and the Image Commentary shows that there is not a single instance where 'changing to the correct' is used as a meaning. Since there is no basis for this, he simply attached himself to instances where the character 'zheng' appears in the classic text, and used 'changing to the correct' to explain everything.

如注“坤利牝馬之貞”，云“坤為牝，震為馬。初動得正，故利牝馬之貞”。注“安貞吉”，云“復初得正故貞吉”。案《彖》曰“牝馬地類，行地無疆，柔順利貞”，又曰“安貞之吉，應地無疆”，皆以坤純陰言之，未嘗以為初爻之正也。且如其說，文王於復卦繫於“利牝馬之貞”，不更合耶？何為紛紛然由此之彼，乃以彼釋此耶？以下逐卦指駁，斥謂盡亂聖人之成法。

For example, in commenting on the Hexagram Statement of the坤 (Earth) hexagram, "Beneficial to the faithful mare," Yu Fan said, "Kun represents the female, Zhen represents the horse, and the first line moves to become correct, hence it is beneficial to the faithful mare." In commenting on "Steadfastness brings good fortune," he said, "It transforms into the Fu hexagram, and the first line becomes correct, hence steadfastness brings good fortune." However, the Commentary on the Judgment of the坤 hexagram clearly states, "The female horse is of the earth kind, moving on the earth without boundaries, flexible, smooth, and faithful," and also says, "The good fortune of steadfastness is due to the earth having no boundaries." These statements are based on the overall nature of the pure yin lines in the坤 hexagram, never considering the first line changing to become correct. Moreover, according to Yu's interpretation, King Wen would have been better off directly associating "Beneficial to the faithful mare" with the Fu hexagram, which would have been more appropriate. Why go through the trouble of using one hexagram to explain another? Later scholars such as Wang criticized Yu's annotations for thoroughly disrupting the established methods of the sages.

又駁其旁通之說，謂《易》《彖》及《大象》惟取義於本卦。健順動巽陰明止說之德，天地風雷水火山澤之象，無不各如其本卦，義至明也。虞仲翔以卦之旁通釋之，雖極竟彌縫，究與《經》相牴牾。

Wang's school further refutes Yu Fan's theory of "parallel transmission," arguing that the Commentary on the Judgment and the Great Image in the Zhou Changes only derive meaning from the primary hexagram, taking the eight virtues of strength, smoothness, movement, entering, sinking, adhesion, stillness, and joy, and the eight natural phenomena of heaven, earth, wind, thunder, water, fire, mountain, and marsh, none of which fail to correspond with the primary hexagram. The meaning is originally very clear. Yu Fan, however, uses the "parallel transmission" of complete reversal of yin and yang between two hexagrams to explain it. Although he tries hard to reconcile the theory, it ultimately conflicts with the text of the classic.

如《履·彖》曰“履，柔履剛也”，虞曰“坤柔乘剛，謙坤藉乾，故柔履剛”。又“履帝位而不疚”，虞曰“謙震為帝，坎疾為病，至履帝位坎象不見，故履帝位而不疚”。此謂履與謙通，謙上體有坤，互體有震坎也。然《經》云說而應乎乾，謂下兌上乾也。若取義於下艮上坤之謙，則是止而應乎坤矣，豈說而應乎乾之謂乎？亦逐卦指駁，謂《彖》、《象》釋《易》也，不合於《彖》、《象》，尚望其合於《易》乎？

For example, the Commentary on the Judgment of the "Gua of Walking" says, "Walking, it means the softness walking upon the firmness." Yu Fan interprets this as "the yao of the softness in the坤 (Earth) trigram is riding upon the yao of the firmness, and the Gua of Humility, which is坤 on top, borrows from the乾 (Heaven), so it is called softness walking upon firmness." The Commentary on the Judgment also says, "Walking upon the imperial throne without guilt." Yu Fan interprets this as "the Zhen (Thunder) trigram in the Gua of Humility represents the emperor, and the Kan (Water) trigram represents illness. When reaching the position of the imperial throne, the Kan image disappears, so walking upon the imperial throne brings no pain." These are all explanations that the Gua of Walking and the Gua of Humility are connected through their mutual trigrams, since the Gua of Humility has the坤 trigram on top and contains Zhen and Kan in its interacting trigrams. However, the Commentary on the Judgment of the Gua of Walking clearly states, "It is said and corresponds to the乾 (Heaven)." This refers to the lower trigram being Dui (Lake) and the upper trigram being Qian (Heaven). If instead we take the meaning from the Gua of Humility, which has the lower trigram as Gen (Mountain) and the upper trigram as坤 (Earth), it would become "Stopping and corresponding to the坤 (Earth)." How could this still mean "It is said and corresponds to the乾 (Heaven)"? Wang also criticizes each hexagram in this way, saying that the Commentary on the Judgment and the Image Commentary were originally meant to explain the Zhou Changes. If even the Commentary on the Judgment and the Image Commentary do not align, how can we expect them to align with the Zhou Changes?

王氏之說，辨而詳矣。然六爻發揮旁通情也，辭也者各指其所之，而變卦以不當位之爻變而當位，又古今說《易》家所不廢，則旁通與之正，要不可謂非《易》中之一例。第必執此一例以概全《易》，其所不通者亦必強而通之，不得不謂虞氏之一蔽。必如王氏之說，則《彖》、《象》之外，更不容有一義之引伸比附，則廣大悉備之《易》象，恐學者更未易明也。

Wang Yinzhi's rebuttal is thorough and clear. However, the original text of the Wenyan section of the Qian hexagram says, "The six lines unfold, expressing the circumstances of the world." The Xici section also states, "The words each refer to their respective meanings." When changing hexagrams, moving an improperly positioned line to a proper position is a method that has never been abandoned by scholars throughout history. This shows that "bypassing" and "returning to the correct position" are indeed part of the structure of the Zhouyi. However, if one insists on using this structure to explain the entire Zhouyi, forcing explanations where they do not fit, then it cannot be denied that Yu Fan's interpretation has obscured the truth. But if one insists on Wang's view, allowing only interpretations from the Tuanchuan and Xiangchuan, and forbidding any further analogy or inference, then the vast and comprehensive imagery of the Yi would become even more difficult for scholars to understand.

況《彖》、《象》所釋，或含意待申，或僅舉一隅，或專重一事者，其例正多。故孔子曰“觀其彖辭則思過半矣”，又曰“書不盡言”，未嘗以《彖》、《象》所釋為已盡，更不容他人置喙也。

Moreover, the explanations in the Commentary on the Judgment and the Image Commentary are sometimes waiting for later scholars to elaborate on their meanings, sometimes only mention a single aspect, and sometimes focus on a particular matter. Such situations are quite common. Therefore, Confucius said in the Great Treatise, "Observing the judgment statements, one can think through more than half of it," and also said, "Written words cannot fully express speech." This shows that he never thought the explanations in the Judgment and Image Commentaries had exhausted all meanings, still less did he prohibit others from adding their own comments.

虞仲翔生於易代之際，世道人心，江河日下。說《易》大師，有曲說阿時以聖經為羔雁者矣。（如荀慈明輩是也。）故憤時疾俗，或不免有過激之論。如以坤初為“子弒其父臣弒其君”，謂坤陰漸而成遁弒父，漸而成否弒君，於象義亦未允當，（坤消至剝而乾象滅迷不復，常大變以其國君，凶方為家滅國滅之象。近書《周易指》已辨正之。）要皆有為而言。

Yu Fan was born during a period of dynastic change, when the world and people's morals were deteriorating day by day. Among the masters of the Zhou Changes at that time, some distorted the meaning of the classics and catered to the prevailing situation, using the sacred scriptures as gifts to gain favor and advancement (people like Xun Shuang were among them). Therefore, he was cynical about the world and his criticisms often went to extremes. For example, he interpreted the first line of the Kun hexagram, "Walking on frost, firm ice," as "a son killing his father, a minister killing his sovereign." He claimed that the gradual increase of the yin line in the Kun hexagram leading to the Duan hexagram represented a son killing his father, and the gradual increase leading to the Pǒ hexagram represented a minister killing his sovereign. This interpretation in terms of symbolic meaning is indeed not appropriate (according to reason, the yin should gradually decrease the yang until the Bo hexagram, with the yang image disappearing completely and not returning, thus producing the ominous image of a great change in the sovereign, the destruction of the state and family. Modern scholar Du Mu Guo Hu in his work "Zhou Yi Zhi" has already corrected this). However, what he said was all motivated by a purpose.

其納甲消息，皆與荀氏升降之說針鋒相對，意尤顯然。以之正立論，明天地大義。以既濟定也為歸，期人心之不正者胥歸於正，於是乎世亂或可少定。此虞氏之或苦心孤詣，千載而下猶皦然可見者也。

He discussed Najia and the concept of transmission and reception, constantly opposing Xu Shuang's theory of rising and falling. His intention was especially clear. He used the term "zhizheng" to argue for elucidating the great principles between heaven and earth; taking the six lines of the hexagram Ji Ji and establishing their respective positions as the ultimate goal, he hoped that all people with unrighteous hearts would return to the right path, so that the chaotic world might be somewhat stabilized. This was precisely Yu Fan's sincere and painstaking effort, and even a thousand years later, it remains clearly visible.

嗚乎！今之時何時乎？世道人心，視三國紛爭之際為何如？人材之消乏，視三國紛爭之際又何如？仲翔以梗直不見容流俗，被擯嶺表，尚不忘情於世，欲以《易》道濟之。相傳廣州六榕寺，猶仲翔講《易》之遺趾，流風未沫。今有其人，吾願執鞭以從之矣。

Alas! What kind of era is this today? How does the current state of the world and people compare to the time of the Three Kingdoms? How does the decline of talent compare to that time? Yu Fan was dismissed to Lingnan because of his upright nature, not being accepted by the prevailing customs, yet he never ceased to care about the world, wanting to use the principles of the Book of Changes to help it. It is said that the old site where he once explained the Book of Changes still remains at the Liu Rong Temple in Guangzhou, and his influence has not ceased. If there were such a person today, I would willingly take up the whip and drive the carriage to follow him.

虞仲翔氏說《易》，有半象與兩象易之兩例，後人多非議之。如解“小有言”為震象半見，解小畜“密雲不雨”為坎象半見，蓋皆以三畫卦之上兩畫，或下兩畫言之。後之說《易》者，駁詁非難，不勝備記。

Yu Fan interpreted the Yi Jing, establishing two methods: "half image" and "two images Yi." Later scholars often criticized these approaches. For example, he interpreted "small words" in the Gao卦 (Strife Hexagram) as a half-exposed Zhen image, and "thick clouds without rain" in the Xiao Xu卦 (Small Accumulation Hexagram) as a half-exposed Kan image. These interpretations focused on the upper two lines or the lower two lines of the three-line trigrams. Later commentators on the Yi Jing criticized and refuted these two methods extensively, making it impossible to list them all.

如焦理堂說《易》，固主虞氏旁通者也。乃於半象亦攻之甚力，謂“乾之半，亦巽兌之半；坤之半，亦艮震之半。震之下半，何異於坎離之上半？坎之半，又何異於兌艮之半？求其故而不得，造為半象，又造為三變受上之說。試思半象之說興，則履姤之下，均堪半坎；師困之上，皆可半震。究何從乎？朱漢上譏其牽合，非過論也”云云。

Jiao Xun, who originally advocated Yu Fan's theory of "pan tong" in interpreting the Yi Jing, strongly criticized the concept of "ban xiang." He said that half of Qian is also half of Xun and Dui, and half of Kun is also half of Gen and Zhen; what is the difference between the lower half of Zhen and the upper half of Kan and Li? Or between half of Kan and half of Dui and Gen? Yu Fan could not find the reason, so he invented the concept of "ban xiang" and also proposed the idea of "san bian shou shang." Imagine if the theory of "ban xiang" were established, then the lower trigrams of the Lu and Gou hexagrams could be considered half of Kan, and the upper trigrams of the Shi and Kun hexagrams could be considered half of Zhen. In the end, which one should be followed? Zhu Zhen, known as the Han Shang Master, criticized him for being forced and artificial, and his criticism was not unwarranted.

嗚呼！漢上固宋人之深於象數者，而焦理堂之《易通釋》，亦能貫串全經確有心得，非一知半解人云亦云者比，乃亦有此似是而非之論，可見解人難索。象學之發明，正未易言矣。焦氏所指駁者，驟觀之似極有理，實於象學茫然未辨也。虞氏半象之名，未能達意，且別無詳析之釋文，宜淺近者之詫為無理焉。

Alas! Zhu Zhen was a scholar of the Song dynasty who was particularly skilled in the imagery and numbers of the Yi Jing. Jiao Xun's "Yi Tong Shi" can connect the entire text and indeed has genuine insights, not someone who merely knows a little and follows others' opinions. Yet he still made such ambiguous remarks, showing how rare it is to find someone who truly understands the essence. It is indeed very difficult to clarify the study of imagery. What Jiao Xun criticized seems at first glance very reasonable, but in reality he did not clearly distinguish the principles of imagery study. Yu Fan's term "half imagery" did not clearly express his meaning, and he left no detailed explanatory writings, so it is not surprising that those with shallow learning find it strange and unreasonable.

蓋八卦之象，惟乾坤坎離，反覆皆同。震艮巽兌四卦，則為二卦之反覆。震反即艮，兌反即巽。故孔子《雜卦》，曰“震起，兌見，巽伏，艮止”，又曰“離上而坎下也”。坎離雖不可反易，實即震艮巽兌之中體。下震起而上艮止即為離，下巽而上兌見即為坎。八卦之變化，皆此震起艮止巽伏兌見所往來。若去此四者，乾坤坎離皆為死物，無易可言矣。

The images of the Eight Trigrams are such that only Qian (Heaven) and Kun (Earth), along with Kan (Water) and Li (Fire), remain the same when turned upside down. The other four trigrams—Zhen (Thunder), Gen (Mountain), Xun (Wind), and Dui (Lake)—are paired and turn into each other when inverted: Zhen becomes Gen, and Dui becomes Xun. Therefore, Confucius said in the "Zagua Zhuan" that "Zhen initiates movement, Dui reveals, Xun conceals, and Gen stops." He also said, "Li is above and Kan is below." Although Kan and Li cannot be inverted, they are actually the intermediate forms of Zhen, Gen, Xun, and Dui. The lower part of Li is Zhen initiating movement, and the upper part is Gen stopping, forming Li. The lower part of Kan is Xun concealing, and the upper part is Dui revealing, forming Kan. All changes of the Eight Trigrams depend on the interaction of these four elements: Zhen initiating movement, Gen stopping, Xun concealing, and Dui revealing. If these four are removed, Qian, Kun, Kan, and Li would all become static and there would be no "Yi" (Change) to discuss.

故六爻之卦，初爻為震爻，二為坎爻，三為艮爻，四為巽丈，五為離爻，上為兌爻。虞氏所謂震體半見者，即震爻也。坎象半見者即坎爻也。六爻皆乾坤之體，故乾坤不可分爻。焦氏謂乾之半坤之半，正見其於卦象未通，未足以闢虞氏也。虞之失，在半象二字之辭不達意，謂其立名未當則可，謂為無所適從不可也。

Therefore, the six-line hexagram has the first line as the Zhen line, the second line as the Kan line, the third line as the Gen line, the fourth line as the Xun line (the original text says 'Xun zhang', where 'zhang' is a mistake for 'yao'), the fifth line as the Li line, and the top line as the Dui line. Yu Fan's statement 'Zhen body is half visible' refers to the Zhen line; 'Kan image is half visible' refers to the Kan line. All six lines of the hexagram are essentially composed of the Qian and Kun lines, so Qian and Kun themselves do not have separate lines. Zhao Xun's questioning with 'half of Qian and half of Kun' clearly shows his lack of thorough understanding of the hexagram images, making him insufficient to refute Yu Fan. Yu Fan's mistake lies only in the term 'half image' being imprecise; it is acceptable to say his naming is inappropriate, but it is not acceptable to say this approach leaves people confused.

至虞氏之所謂兩象易，實即上下錯。孔子《雜卦》亦即兩卦之上下交錯。六十四卦以交錯見義者，不勝枚舉。如履上下錯（上天下澤易上澤下天）為姤，履柔履剛也，姤柔遇剛也。屯上下錯為解，屯雷雨之動滿盈，解雷雨作而百果草木皆甲坼。恆上下錯為益，恆立不易方，益為益無方，皆兩象易也。苟以為非，則孔子之《彖傳》亦盡非乎？辛齋非宗虞氏《易》者，但以是非為去取，絕無成見。恫向之言《易》者，蔽於門戶之見，動輒是己而非人。故特著之，亦以自警焉。

As for Yu Fan's concept of "two images exchange," it simply refers to the reversal of the upper and lower parts of the hexagram. Confucius also used the method of interchanging the upper and lower trigrams in his "Commentary on the Miscellaneous Hexagrams." There are numerous examples in the sixty-four hexagrams where the meaning is revealed through such reversal: reversing the upper and lower trigrams of the "Gua" hexagram (changing upper Qian and lower Dui to upper Dui and lower Qian) results in the "Gou" hexagram. The "Commentary on the Judgment" of the "Gua" hexagram says "the soft follows the strong," while that of the "Gou" hexagram says "the soft meets the strong." Reversing the upper and lower trigrams of the "Zun" hexagram results in the "Jie" hexagram. The "Commentary on the Judgment" of the "Zun" hexagram says "the movement of thunder and rain fills the world," while that of the "Jie" hexagram says "thunder and rain arise, and all fruits and plants split open." Reversing the upper and lower trigrams of the "Heng" hexagram results in the "Yi" hexagram. The "Great Image" of the "Heng" hexagram says "standing firm without change," while the "Commentary on the Judgment" of the "Yi" hexagram says "the benefit has no fixed direction." These are all examples of the "two images exchange." If one insists that this method is wrong, can Confucius's "Commentary on the Judgment" be entirely incorrect? I, Hang Xinzhai, do not follow Yu's school of thought in interpreting the "Book of Changes," but I judge matters based on right and wrong, without any preconceived notions. I merely regret that those who interpreted the "Book of Changes" in the past were blinded by factionalism, often asserting their own views as correct and others as wrong. Therefore, I have written this explanation to clarify this point, and also as a warning to myself.

《說卦》象重出者三卦，“震為龍，艮為狗，兌為羊”，皆已見於第五章，而第八章又重出。八章“震為雷”之下，考《虞氏易》及《李氏集解》均作尨，注云幕色。震東方，故為尨。蓋馬八尺以上為尨，尨與龍，音亦同也。

In the "Say卦Transmission," the images of the hexagrams are repeated three times: "Zhen represents a dragon," "Gen represents a dog," and "Dui represents a sheep," all of which have already appeared in Chapter Five. They are repeated again in Chapter Eight. Under the entry "Zhen represents thunder" in Chapter Eight, the term "dragon" is recorded as "mang" in Yu Fan's commentary on the Zhou Changes and in Li Dingzuo's Collected Explanations of the Zhou Changes. The commentary explains that "mang" refers to a multicolored animal. Since Zhen is located in the East, "mang" is used as a symbolic image. According to Ma, a horse over eight feet tall is called "mang," and "mang" and "long" have the same pronunciation.

八章之“艮為狗”，虞氏及《李氏集解》，皆作拘。虞注云“指屈伸制物故為拘”（按：《隨·上六》“拘係之乃從維之”，即此拘也。），而朱氏《漢上易傳》曰“上言艮為狗，乃狗馬之狗。此言為狗者，熊虎子未有文猶狗也”。虞翻以兌艮為虎，艮寅位也，艮究成兌，故艮為虎子，未免迂曲矣。

Chapter Eight's "Geng Represents a Dog," both Yu Fan and the "Li Shi Ji Jie" write it as "ju." Yu Fan's commentary says, "The hand can bend and stretch to control external objects, so it is called 'ju.'" (Note: In the "Su Gu" hexagram's Sixth Line, "ju xi zhi, nai cong wei zhi," the character "ju" is used in this way.) Zhu Zhen's "Han Shang Yi Zhuan," however, says: In the fifth chapter, "Geng Represents a Dog" refers to the dog of horses and dogs; here, when it says "as a dog," it refers to the young of tigers and bears before their spots appear, which resemble dogs. Yu Fan takes You and Geng as tigers, because Geng is at the position of Yin, and when Geng is thoroughly examined, it transforms into You, so he says Geng represents tiger cubs, which is rather convoluted.

艮為羊之異說滋多，虞作“羔”，注云女使，《集解》同。鄭作“陽”，注云此陽謂養無家女行賃炊釁，今時有之，同於妾也。王氏《經義述聞》，謂“羔與羊，《書》、《傳》無訓女使”者。羔當為恙字之誤，恙亦通作養。

As for the entry 「as a sheep」 (the original text says 「Gen as a sheep」, actually referring to the Dui hexagram), there are many different interpretations. Yu Fan wrote 「gao」 and explained it as a female servant. The Li氏 Collection of Explanations agrees with this. Zheng Xuan wrote 「yang」 and explained that this 「yang」 refers to the practice of taking in an unmarried woman, employing her to cook and perform ritual sacrifices, a practice that existed at that time and was regarded as equivalent to a concubine. Wang Yinzhi's 「Narrative of Classic Interpretations」 states that there are no instances in the Shangshu or the commentaries of various schools where 「gao」 is interpreted as a female servant. Therefore, 「gao」 is likely a mistake for 「yang」, and 「yang」 can also be read as 「yang」 meaning to raise or nurture.

辛齋按以上諸說均有根據，惟無論為羔為恙為養，均須竄易經文，則不若依鄭說讀羊為陽。羊陽本通用，《春秋左氏傳》“夷養五”亦作“夷陽五”，可不必改經，而於諸家之義均可通矣。

I, Hang Xinzhai, remarked: The interpretations of the various scholars all have their basis, but regardless of whether one changes it to "gao," "yang," or "yang," it would require altering the text of the classics. Therefore, it is better to follow Zheng Xuan's interpretation and read "yang" as "yang." "Yang" and "yang" were originally interchangeable. For example, in the "Spring and Autumn Annals: Zuo Zhuan," "Yi Yang Wu" is also written as "Yi Yang Wu." This way, there is no need to alter the text of the classics, and the interpretations of all scholars can be made coherent.

八卦取象，精義入神，其微妙乃至不可思議。漢儒言《易》，不離象數，惜多散佚，已無完書。唐人以王弼為宗，言象者不著。其後如宋之邵子，及朱氏子發，與林氏黃中，鄭氏剛中，邱氏富國，黃氏東發；元之胡氏一桂，王氏申子，熊氏與可任重，龍氏仁夫；明之來氏矣鮮，黃氏道周；清之刁氏蒙吉，胡氏滄曉，惠氏仲儒定宇，萬氏彈峰諸家，皆於象義各有發明。

The eight trigrams take symbolic forms, with their subtle meanings reaching into the divine and marvelous. In their detailed aspects, they even reach an unimaginable level. Han dynasty scholars who interpreted the Book of Changes never separated from the principles of symbolic forms and numbers. Unfortunately, most of their writings have been lost, and there are no complete versions left. Tang dynasty scholars followed Wang Bi as their main authority, and those who interpreted the trigrams became less prominent. Later, figures such as Shao Yong of the Song dynasty, Zhu Zhen (zi fa), Lin Li (huang zhong), Zheng Gangzhong, Qiu Fuguo, Huang Zhen (known as Master Dongfa), in the Yuan dynasty, Hu Yigui, Wang Shenzi, Xiong Yuke (ren zhong), and Long Renfu; in the Ming dynasty, Lai Zhide (yi xian) and Huang Da Zhou; and in the Qing dynasty, Diao Bao (meng ji), Hu Xu (cang xiao), Hui Shiqi and his son Hui Dong (zhong ru, ding yu), and Wan Nianchun (tanjing) all made their own contributions to the interpretation of the symbolic meanings.

而姚氏與端木氏二家，（《姚氏易》及《周易指》）能原本經傳，發抒己見，不依傍昔賢門戶，尤為卓絕一時。雖或有所偏，其精到處皆確切不移，不可泯沒。辛齋為學日淺，僅就昔人之所未言，或言而未盡者，聊以助學《易》者之興趣也。

Among them, Yao Peizhong and Du Menguhu (i.e., the books "Yao Shi Yi" and "Zhou Yi Zhi") were able to take the classics as their foundation, express their own views, and not follow the schools of previous scholars. Their achievements were particularly outstanding at that time. Although they each had their own biases, their profound insights were accurate and unchangeable, and they should not be overlooked. My study of the Yi Jing is still shallow, so I only discuss a little on matters that previous scholars have not mentioned or have not fully explained, just to arouse the interest of those studying the Yi Jing.

凡言象者，不可忘《易》之義。《易》義不易者其體，而交易變易者其用。故八卦之象，無不交錯以見義。故乾為圜而形著於坤，離為日而光被於月。正秋者西也，而日行東陸。出震者東也，而日行西陸。執片面以言象，象不可得而見。泥一義以言象，象不得可而通也。

Anyone who talks about hexagram images must not forget the meaning of the character "Yi." "Yi" has three meanings: "Bu Yi" refers to its essence, "Jiao Yi" or "Bian Yi" refers to its function. Therefore, the images of the eight trigrams are always interrelated in expressing their meanings: Qian represents roundness, but the form of roundness is realized in Kun; Li represents the sun, but the light of the sun is applied to the moon. Dui represents the autumn season, located in the west, yet the sun in autumn moves eastward; Zhen represents the direction of spring growth, located in the east, yet the sun in spring moves westward. If one focuses only on a single aspect when discussing the images, the images will not be visible; if one rigidly adheres to a single meaning when discussing the images, the images will not make sense.

凡言象者，不可忘其數，天一地二天三地四天五地六天七地八天九地十。黃帝而後，皆以干支紀之。卦有定位，即有定數。（如坎子一，艮丑二寅三至兌酉十，乾戌亥數無。）《易》數乾元用九，乃天一不用，用地二至地十。數定而象之無定者，可因數而定。故觀象必倚數。如體物者必準諸度量，測遠者必察其角度。自舍數言象，而象茫如捕風矣。

All who discuss hexagrams must not forget the numbers behind them, which are referred to in the Great Treatise as the Heavenly One, Earthly Two, Heavenly Three, Earthly Four, Heavenly Five, Earthly Six, Heavenly Seven, Earthly Eight, Heavenly Nine, and Earthly Ten. After the Yellow Emperor, these numbers were marked with the Heavenly Stems and Earthly Branches. Since hexagrams have fixed positions, they also have fixed numbers (for example, Kan corresponds to Zi and is one, Gen corresponds to Chou and is two, and when it corresponds to Yin it is three, and so on, until Dui corresponds to You and is ten; Qian, located at Xu and Hai, is not counted). The use of numbers in the Zhou Changes is "Qian Yuan uses nine," meaning the Heavenly One is present but not used, and only the Earthly Two through the Earthly Ten are used. Once the numbers are fixed, the uncertain parts of the images can be determined by numbers, so observing images must rely on numbers, just as measuring objects requires a standard measure, and measuring distant objects requires observing angles. Since people have abandoned numbers to discuss images, the images have become indistinct, like grasping at wind.

凡言象者，不可不明其體。體者用之主也，故卜筮者亦曰取用。（每卦六爻，先取所用者一爻為主，即體也。）以所用者為主，而後察他爻之或從或違或動或靜，為利為害，吉凶始可得而斷焉。

Anyone who discusses hexagram images must first understand the concept of "body" (体). The body is the master of the use (用), so diviners also refer to it as "taking the use" (取用). Each hexagram has six lines; first, one selects the line that will be used as the main line, which is called the body. After determining this main line, one then examines the other lines to see if they are in harmony or opposition, whether they are active or still, and whether they are beneficial or harmful to me. Only then can one judge whether the outcome is auspicious or inauspicious.

用有大小，象則因其小而小之。因其大而大之，如乾也。大則為天，小則為木果，如坤也。大則為地，小則為布為釜，坎為大川，小則為溝瀆。離日大明，小亦為螢火。小大無方，各隨其體。明體以達用，象之用乃無窮矣。

The objects used in divination can be large or small, and the images used correspond accordingly—taking a small image when the object is small, and a large image when the object is large. For example, the trigram Qian (Heaven) can be considered as the vast sky when taken large, but when taken small, it may represent a single piece of fruit. The trigram Kun (Earth) can be seen as the entire earth when large, but when small, it may be a piece of cloth or a pot. The trigram Kan (Water) can represent great rivers and streams when large, but when small, it may be a ditch or a channel. The trigram Li (Fire) can be the brilliance of the sun when large, but when small, it may be a flicker of firefly light. There is no fixed standard of size; it all depends on the nature of the object being considered. Once the nature of the object is clearly understood, its functions can be inferred, and the applications of the images are limitless.

言凡象者，不可不視其所以。以者與也，及也。（《易》曰“不富以其鄰”及“剝床以足以其國君凶”，“拔茅茹以其匯”，諸“以”字皆與“及”字同訓。）卦因而重之，重為六畫，實具兩象。兩象必以其一為主，則必有所與。而六畫之二三四五中爻之象及其變動所生之象，無一而非與也。

Anyone who discusses hexagram images must consider their "reason" or purpose. "以" means "with," "and," or "as well as." In the "Zhou Yi," examples such as "not rich with its neighbor," "bed stripped away from the foot," "with its country ruler's misfortune," and "pulling out the rhizomes in their groups" all use "以" in the same way as "及." When the eight trigrams are combined to form a hexagram with six lines, it actually contains two images, upper and lower. Among these two images, one must be the main one, and the other is the object connected to it. Similarly, the intermediate image formed by the second, third, fourth, and fifth lines in a hexagram, as well as the new images formed by line changes, are all objects connected to the main image.

所與者而善，乃吉之幾。所與者而不善，乃凶之兆。而善惡又有大小之殊，所與者又有遠近之別，《繫傳》曰“遠近相取而悔吝生”，又曰“凡《易》之情，近而不相得，則凶或害之”。悔且吝，故必觀其所與者之善惡之大小，及情偽遠近，然後吉凶生而悔吝著，庶乎可得象之用焉。

The objects connected are good, then it is a favorable omen; if they are not good, it is a sign of misfortune. Good and evil also differ in degree, and the connected objects have distinctions of nearness and distance. The Great Treatise says, "Near and far relate to each other, and regret and hardship arise," and also says, "All the situations in the Book of Changes, if near but not in harmony, then misfortune occurs, there may be harm, and regret and hardship follow." Therefore, one must clearly discern the degree of goodness or evil in the connected objects, whether they are genuine or false, near or distant, only then will fortune and misfortune become evident, and regret and hardship be clear. Only then can one roughly grasp the use of the images.

凡言象者，不可不觀其所由。《繫傳》曰：“辭也者，各指其所之。”此有所之者，即彼有所由。《文言》曰：“臣弒其君，子弒其父，非一朝一夕之故，其所由來者漸矣。”蓋於坤之第一爻“履霜堅冰”，為三百八十四爻之所由來者，舉其例焉。

Anyone who discusses hexagrams must consider their origin. The Great Treatise says: "The words of the hexagrams each point to their destination." Where one end goes, the other end comes from. The Wenyan of the Qian Hexagram says: "A minister killing his sovereign, a son killing his father, is not the result of a single day or night; it has gradually developed over time." This is an example given under the first line of the Kun Hexagram, "Treading frost, the ice is already coming," illustrating that each of the 384 lines has its origin.

觀象者先明定其體象之所在。而更觀其所由來。如乾之姤，若用乾為天，則下巽為風，此風所由來為乾。乾為西北之卦，即西北風也。乾為冰為寒，則其風必寒。若用乾為木果，則巽不取象於風，當取象於蟲。因巽所由來為乾，既用為木果矣，則木果豈能生風？自應作蟲斷焉。舉其一例，餘可類推。不觀所由，象烏乎定哉！

The person interpreting the signs first needs to determine where the fundamental image falls, and then examine its origin. For example, if the first line of the Qian hexagram changes to become the Guo hexagram, then if we take Qian as Heaven, the lower trigram Xun would be Wind, and the origin of this wind is Qian. Since Qian represents the northwest, this wind would be a northwest wind. Moreover, since Qian also represents ice and cold, this wind must be cold. However, if we take Qian as a wooden fruit, then Xun should not be taken as Wind, but rather as insects; because the origin of Xun is Qian, and since Qian has already been used as a wooden fruit, a wooden fruit cannot produce wind. Naturally, it should be interpreted as producing insects. This is just one example, and the rest can be inferred in the same way. Without considering the origin, how can the image be determined?

凡言象者，不可不察其所安。安也者，位也。《繫傳》曰：“君子安其身而後動。”觀象者既定其主體之所在矣，必察其所在之處，能否得位。位得矣，必察其位之能否得時得用，而後其象始可得而言。

Anyone who discusses hexagram images must not neglect to examine their "position." By "position," it refers to the place. The Great Treatise says: "A gentleman stabilizes himself before he acts." When observing images, after determining the main subject in which line it resides, one must check whether its position is appropriate. Once the position is appropriate, one must further examine whether this position is timely and whether it is useful. Only then can the image of the hexagram be considered valid.

如用巽為木，則必察其所處之位為甲乙。或為丙丁壬癸，或為庚辛，為甲乙則當，為丙丁則相。為壬癸則生，而庚辛則死，既當或相與生矣，則更應察衰旺。並視所與者及所由者之如何，則象之情可畢見矣，如巽木處甲為剛木，所由來為乾，必為堅強之果木；所與者為艮，必是園林；為坤而壯者（如在四季月之終或戊己日時），為廣土；其衰者（如春令或甲乙日之類），則為盆缶。其他可準此。

For example, if we take Xun as wood, we must look at the position it occupies, whether it is in the position of Jia or Yi (wood), or Bing or Ding (fire), or Ren or Gui (water), or Geng or Xin (metal). If it is in the position of Jia or Yi, it is "in season" (when the element is strongest). If it is in the position of Bing or Ding, it is "supported" (being generated by the next element and in a secondary state of strength). If it is in the position of Ren or Gui, it is "generated" (being supported by its mother element). If it is in the position of Geng or Xin, it is "dead" (being overcome by the next element). Once we know it is in season, or supported, or generated, we must further examine its strength and weakness, and look at what it is connected to and what it comes from. In this way, the full situation becomes clear. For instance, if Xun wood is in the position of Jia, it is strong wood, and its origin is Qian, which means it is hard fruitwood. If it is connected to Gen, then it represents a garden. If it is connected to Kun and is in its prime (such as at the end of the four seasons or on a Wu or Ji day or hour), then it represents broad fields. If Kun is weak (such as in spring or on a Jia or Yi day), then it represents pots and containers. Other cases can be similarly inferred.

凡言象者，不可不明消息。消則滅，息則滋。如復姤臨遁之十二卦，消息之大焉者也。乾息坤，坤消乾。陰陽之大義，造化之橐龠，物理所莫能違，人事所莫能外。故物無大小，事無鉅細。言象者必先明乎消息盈虛之故，而象始可明。

Anyone who talks about hexagrams must understand the concept of yin and yang change. "Xiao" means decline, and "Xi" means growth. For example, the twelve hexagrams of change, such as Fu, Gu, Lin, and Duan, are the greatest examples of this principle. When the yang of Qian grows, it invades Kun; when the yin of Kun grows, it declines Qian. This is the great principle of yin and yang, the windbox of nature, which cannot be violated in physical phenomena or exceptions in human affairs. Therefore, whether the subject is big or small, the matter is great or minor, those who explain hexagrams must first understand the principle of growth and decline, fullness and emptiness, in order to explain the hexagrams clearly.

凡一卦本體之消息，或因時言之，或以位論之。當其消焉，象雖吉而未可言福。當其息焉，象若凶而益長其禍。其時值消而位當息，或位據息而時見消，則須辨其重輕，而異而分劑。或可亭毒均處而劑其平，或雖截短補長終莫齊其數。則又勢為之，未可泥於一端也。蓋勢之所趣，每善不敵惡，福不勝禍，一薰一蕕，十年尚猶有臭。一朝失足，而畢生之功盡棄。此君子之所以戒惡念之萌，而《易》道之所以扶陽而抑陰，嚴堅冰之防於履霜之始也。

The growth and decline of a hexagram's essence can be considered either in terms of the season or in terms of the yao positions. When the essence is in decline, even if the image is auspicious, it cannot bring about good fortune; when the essence is in growth, even if the image is ominous, it may instead increase misfortune. If the season indicates decline while the yao position suggests rest, or if the yao position indicates rest while the season indicates decline, one must distinguish between the two and handle them accordingly. Some cases can be balanced to achieve equilibrium between the two, while others, even with adjustments, cannot fully match the numbers. This is due to the situation at hand, and one must not be rigid in approach. Generally, the trend of circumstances often leads to good being overcome by evil, and fortune being surpassed by misfortune—just as a fragrant herb and a foul weed placed together will, after ten years, still leave the foul smell; a single misstep can cause the loss of a lifetime's achievements. This is precisely why a gentleman must be cautious and vigilant when evil thoughts first arise, and it is why the principles of the Book of Changes emphasize supporting yang and restraining yin, and why it warns against the formation of solid ice even at the beginning of a frosty step.

言象之大要如此。故夫陰陽之順逆，五行之休廢，氣數之盛衰，均不可不辨焉。向之言《易》者，曰吾治經，非以談休咎，奚用此術數為？而不知《易》以道陰陽，原本天地之數，以著天地之象，以通神明之德，以類萬物之情。非數則無以見《易》，非數即無以見象，未有象不明而能明《易》者也。

The main points of explaining the images (xiàng) are these. Therefore, the reversal and order of yin and yang, the decline and decline of the Five Phases, and the rise and fall of qi and numbers must all be distinguished. Previously, those who interpreted the Yi often said: "I am studying the classics, not coming to discuss good fortune, misfortune, blessings, and curses. What use is this system of numerology?" But they did not realize that the Zhuangzi's "Tianxia" had already said, "The Yi explains yin and yang." The Zhou Yi is originally dedicated to elucidating yin and yang; it originates from the numbers of heaven and earth, used to display the images of heaven and earth, used to connect with the virtue of the divine, and used to classify the forms of all things. Without numbers, one cannot see the Yi; without numbers, one cannot see the images. There has never been a person who could explain the Yi clearly without first understanding the images.

舍象以言《易》，故宋儒之性理，往往流於禪說而不自知。舍《易》以言象，方士之鼎爐，每每陷於魔道而殺其身。唯之與阿，相去幾何？然方士之說，不足以惑人，尚其為害之小者也。

Discarding the images to discuss the Yi, so the Song Confucian scholars who discussed principles of nature often fell into the path of Chan Buddhism without realizing it; discarding the Yi to discuss images, so the alchemists played with cauldrons and refined elixirs, repeatedly falling into wrong ways and losing their lives. The Dao De Jing says, 'Yes and Ah, how far apart are they?' The distance between these two is actually not far. However, the practices of the alchemists are not enough to confuse the people, so their harm is relatively minor.

易學自邵子以前，無八卦之圖。故言象者，除納甲以外，皆卦自為象。其有通兩卦又言者，即卦變及覆卦（來氏曰綜）耳。未有求之於八卦者，先天八卦無論矣。即後天八卦方位，亦鮮探索。惟“西南得朋”，“先甲”“先庚”等《彖》、《象》，注家或求諸卦位，餘則罕見矣。至先天八卦，更為言漢學者眾矢之的。焦氏之《易通釋》亦只以旁通貫串各卦，終不承認八卦之有先天也。

Before Shao Yong, there was no diagram of the eight trigrams with directional positions in the study of the Book of Changes. Therefore, those who discussed the images of the trigrams, apart from the method of assigning heavenly stems, considered each trigram to form its own image. Occasionally, there were discussions that connected two trigrams, but these were merely about changes between trigrams and their reversals, which Lai Zhide called 'comprehensive' or 'zong'. No one sought the positions of the eight trigrams. The Earlier Heaven Trigrams were even less considered. Even the directional positions of the Later Heaven Trigrams were rarely explored by predecessors. Only a few sentences in the Commentary on the Judgment and Image Commentary, such as 'southwest is where friends are found' in the Qian hexagram, 'three days before the first day of the month' in the Gu hexagram, and 'three days before the seventh day of the month' in the Xun hexagram, were occasionally used by commentators to find support from the trigram positions. As for the Earlier Heaven Trigrams, they became a target of criticism among scholars of the Han dynasty tradition. Jiao Xun's work 'Yi Tong Shi' only used 'parallel transmission' to connect the hexagrams and never acknowledged that the eight trigrams had an Earlier Heaven arrangement.

今按之六十四卦之《彖》、《爻》，其取象之所由，無不原本於先天後天兩圖。苟明其例，則逐卦逐爻象義相合。如按圖而索驥。否則各爻之象，有決非本卦與互卦及旁通所有者。如山風蠱，六爻有四爻言父，一爻言母。而父母之象，從何而來？不於先後兩圖求之，雖輾轉穿鑿，終不能得。迨考諸先後天，則知先天艮巽之位，即後天乾坤之位。乾父坤母，其所由來了如指掌矣。

Now that we use the sixty-four hexagrams' "Tuan Ci" and "Yao Ci" for comparison, their symbolic references all originate from the Earlier Heaven and Later Heaven diagrams. Once we understand this system, the images and meanings of each hexagram and its lines can be matched accordingly, just like finding a horse by following a map; otherwise, some of the images in the lines cannot be explained by the primary hexagram, the nuclear hexagram, or the related hexagrams. For example, in the hexagram "Gǔ" (Mountain Wind), four lines mention "father" and one mentions "mother." Where do the images of parents come from? Without referring to the Earlier Heaven and Later Heaven diagrams, no amount of interpretation can explain it. Only when we compare the Earlier Heaven and Later Heaven diagrams do we realize that the positions of Kūn (Earth) and Gèn (Mountain) in the Earlier Heaven correspond exactly to the positions of Qián (Heaven) and Kūn (Earth) in the Later Heaven—Qián represents father and Kūn represents mother, thus the source becomes clear.

又如《象傳》天火同人九五，曰“同人之先，以中直也”，“先”字從何而來？無從索解。考諸先後天，則後天離位，即先天乾位，更明析矣。故先天後天二圖，實闡發全《易》之秘籥。非但無可駁議，而先後二字，亦決不可易。或改先天為天地定位圖，後天為帝出乎震圖，乃昧於先後之義者也。

For example, the "Image Commentary" of "Heavenly Fire, Unity with Others" (Hexagram 13) explains the "Nine in the Fifth" as "The one who unites with others comes first, because of uprightness and centrality." Where does the character "first" (先) come from? According to traditional interpretations, there is no way to find an explanation. However, by comparing the Earlier Heaven and Later Heaven diagrams, we see that the position occupied by the Fire trigram (离) in the Later Heaven corresponds exactly to the position occupied by the Heaven trigram (乾) in the Earlier Heaven. Since the Heaven trigram is "first," the origin of "first" becomes clear. Therefore, the Earlier Heaven and Later Heaven diagrams are actually the key to understanding the entire "Zhou Changes" (I Ching). Not only are they irrefutable, but the terms "Earlier Heaven" and "Later Heaven" should not be changed. Those who would rename the Earlier Heaven diagram as the "Diagram of Heaven and Earth in Position" and the Later Heaven diagram as the "Diagram of the Emperor Emerging from the Thunder" do not understand the meaning of the words "earlier" and "later."

惟邵子以先天圖為伏羲所畫，後天圖為文王所定，則殊可議。蓋兩圖實體用相生，不能離拆。伏羲既作先天八卦，決不能無後天卦以通其用，故先天後天，與重卦六十四，皆一時並有。其六十四卦之大圓圖與方圖，或為邵子所發明，未必為伏羲氏之所畫也。

Only Shao Yong claimed that the Earlier Heaven Trigrams were drawn by Fuxi and the Later Heaven Trigrams were established by King Wen. This point is highly questionable. In fact, the two diagrams are mutually generative in essence and function, and cannot be viewed separately. Since Fuxi created the Earlier Heaven Trigrams, he certainly could not have failed to establish the Later Heaven Trigrams to realize their practical applications. Therefore, the Earlier Heaven Trigrams, the Later Heaven Trigrams, and the sixty-four hexagrams formed by their superposition all coexisted simultaneously. As for the circular and square diagrams of the sixty-four hexagrams, they might have been invented by Shao Yong himself, and were not necessarily drawn by Fuxi in ancient times.

漢《易》家駁先天圖者，曰：“離南坎北，《說卦傳》明定之方位也。乃以西北之乾置之南，西南之坤移之北。離為火故南方熱，坎為水故北方寒。今以乾居南方，則乾為寒為冰，豈不大謬？”當時以為名言。孰知南極北極，固皆為冰洋，今則三尺之童亦知之矣。駁議已不值一笑。然南北冰洋之發見，近三百年內事耳。乃何以伏羲畫卦時，已預有是象，謂非天下之至神乎？

The Han learning school refuted the Earlier Heaven diagram by saying: "Li is in the south, Kan is in the north, this is clearly established by the 'Sayings of the Guiguzi' regarding directions; yet the Earlier Heaven diagram places Qian, which should be in the northwest, in the south, and Kun, which should be in the southwest, in the north. Li is fire, so the south is hot; Kan is water, so the north is cold. Now placing Qian in the south, while the 'Sayings of the Guiguzi' also says Qian represents cold and ice, is this not a great mistake?" These words were once regarded as a famous argument. Who would have thought that the north and south poles were originally frozen seas, and today even a child knows that this argument is no longer credible. However, the discovery of the frozen seas in the north and south poles happened only within the last three hundred years. Why did Fuxi's diagram already contain this image? This is not precisely the most marvelous thing in the world?

乾為圜。圜者，渾圓，非平圓也。故《易》道之圓象，直四面凌空，不能僅觀其一面。鄉之言象者，目光不出於書外，泥於紙上之一圈，以為圓。錢竹汀至以地勢北高南下，駁乾南坤北之圖。具此目光以觀象，何異鄉愚觀李思訓山水。雖尺幅千里，以為不如春牛圖之得情，豈不辜負良工心苦！

The "Say on the Hexagrams" says, "Qian represents the circle." What is meant by "circle" here is a three-dimensional spherical shape, not a flat circular line. Therefore, the concept of "circle" in the "Book of Changes" refers to a sphere that extends in all directions, not merely a single plane. In the past, those who interpreted symbols were confined by books, fixating on the circle drawn on paper as the representation of a circle. Even Qian Daxin (pen name Zhuting) used the uneven terrain of north being higher than south to refute the "Earlier Heaven diagram" which places Qian in the south and Kun in the north. Observing symbols with such a narrow perspective is no different from a country bumpkin looking at a mountain landscape painting by Tang dynasty artist Li Sizhen. The painting captures a vast landscape within a small space, yet he prefers the familiar spring ox diagram posted in the government office, thus failing to appreciate the artist's painstaking effort.

乾為天，亦渾圓之天。故初潛而上亢。南極入地不見，潛也。北極出地，亢也。若在赤道以南觀之，則北極入地，而南極出地。若於正中赤道下觀之，則南北極皆不見，而成大過象。故大過曰“顛也，本末弱也”。

"Qian represents Heaven," which is also a round sphere. Therefore, the first line of the Qian hexagram is called "Qian" (hidden), and the top line is called "Kang" (exalted). When viewed from the northern hemisphere where China is located, the South Pole is buried underground and not visible, which is "Qian." The North Pole is above the ground, which is "Kang." If one were to view it from south of the equator, it would be reversed: the North Pole is buried underground, and the South Pole is above the ground. If one stands exactly on the equator, neither pole is visible, forming the image of the Da Guo hexagram, where the top and bottom lines are yin and the middle four lines are yang. Thus, the Commentary on the Judgment of Da Guo says, "Da Guo means overturning," and also says, "the beginning and end are weak."

六爻以三四兩爻為人爻，合言之，則上天下地中人。三極之道，與天地參者也。分言之，則人於天地間，只估三分之一。故乾以六爻言天行，則六龍皆為星象。言人道，則六龍以喻君子。言地勢，則中二爻為人居之地。初九、九二、九五、上九，皆龍之所宅。龍所宅，則海洋耳。即一卦分合言之，無不各具至理。舉乾而他卦可隅反矣。

In the six lines of a hexagram, the third and fourth lines are referred to as the human line. When considered together, the upper part represents heaven, the lower part represents earth, and the middle part represents humanity, which is exactly what the Great Treatise says: "the way of the three extremes." Humanity is thus placed on equal footing with heaven and earth as the third element. When viewed separately, humanity occupies only one-third of the space between heaven and earth. If the Qian hexagram is interpreted as describing the movement of celestial bodies, then the six lines represent the constellations of the eastern dragon (the Seven Stars of the Azure Dragon). If interpreted as describing human virtue, the six lines symbolize the gentleman. If interpreted as describing terrain, the middle two lines represent the land where humans reside, while the first, second, fifth, and top lines represent the places where dragons dwell—places that are the sea. In considering a single hexagram, whether viewed separately or together, there are always profound meanings to be found. Taking the Qian hexagram as an example, the same reasoning can be applied to all other hexagrams.

坎陷也，險也。說者謂以一陽陷兩陰之中，故險也。似矣，而未盡也。論卦象，坎為坤體，坤為順，何險之有？然正以上下皆順，如一人處至順之境，則陷溺其中而不自知。上下皆順，惟我是從，則更無匡弼輔導之資，其險莫險於是矣。反觀夫離，以一陰陷二陽之中，厥狀相等，何以不曰陷曰險，而乃曰麗？則離為乾體，乾德剛健，能匡輔之，乃剛柔相濟，自無險陷之虞矣。聖人取象之精，意極深遠。徒以陰陽言之，不免皮相之論也。

The trigram Kan represents a pit or a dangerous situation. Commentaries explain that because a yang line is trapped between two yin lines, it becomes dangerous. This seems plausible, but it does not fully capture the meaning. Considering the trigram itself, Kan is fundamentally associated with Kun, which represents compliance and smoothness. How then does danger arise? However, precisely because both upper and lower parts are compliant, it is like a person in a completely smooth and favorable environment, unaware of being trapped. When everyone follows one's will and there is no one to correct or support, there is no greater danger than this. In contrast, the trigram Li has a yin line trapped between two yang lines, which is the same shape as Kan. Why is it not called "trapping" or "danger," but instead "attachment" (li)? Because Li is fundamentally associated with Qian, which represents strength and vigor. Qian can correct and support Li, thus achieving a balance between yin and yang, and there is no danger of being trapped. The subtlety of the sage's use of imagery is profound; merely discussing the positions of yin and yang lines is superficial.

巽為雞，離為雉。雉俗呼為野雞，亦雞類也。巽既為雞，何不足以概雞，又特著於離？似近煩複矣。乃細察象義，則巽二陽在上，陽以象雞之翅。二陽重疊不分，故雞不能飛。離則兩陽在外，兩翅開張，故雉能飛。取象之妙，其細微不遺如此。

The *Shuogua* says that the trigram *Xun* represents a chicken and the trigram *Li* represents a pheasant. A pheasant is commonly known as a wild chicken and also belongs to the chicken family. Since *Xun* already represents a chicken, why is there a need to specially mention a pheasant under *Li*? It seems redundant. However, upon careful examination of the symbolic meanings, it becomes clear: the *Xun* trigram has two yang lines at the top, which symbolize the chicken's wings. The two yang lines are stacked together without separation, so a domestic chicken cannot fly. The *Li* trigram, on the other hand, has two yang lines arranged on the outside, resembling spread wings, so a wild pheasant can fly. The symbolism is so subtle and precise that even such fine distinctions are not overlooked.

兌為羊，說者謂羊性外柔內剛，故《陰符》曰“猛如虎狠如羊”。羊見死絕下畏避，且不號呼，切齒瞪目以就刃，剛狠極矣。而外極柔順，故以象兌之外柔內剛是也，猶未盡焉。兌，正秋也，五行屬金。土能生金，兌金為羊，故土可種羊，而土之怪亦曰羵羊。象理物理之妙合。實不可思議。

The *Shuo Gua* says that the trigram Dui represents a sheep. Interpreters explain that sheep are outwardly gentle and inwardly strong, hence the *Yin Fu Jing* says, "Fierce like a tiger, fierce like a sheep." When a sheep sees itself about to be slaughtered, it does not retreat or cry out, but instead clenches its teeth and stares bravely at the knife, showing extreme firmness while appearing extremely gentle on the outside. Therefore, it is used to symbolize the trigram Dui, which embodies outer softness and inner strength—this interpretation is correct, though not complete. Dui is the trigram of autumn, and it belongs to the metal element. Earth generates metal, so the image of the sheep is derived from the earth. The *Guoyu* records that Ji Hanzi dug a well and found a strange creature in the earth, and Confucius called it a "fengyang," which is a sheep found in the earth. The symbolic meaning and physical reality coinciding in this way is truly astonishing.

難者曰：坤土為牛，火能生土，何以火不能種牛？巽木為雞，水能生木，何以水不能種雞？曰：物各有理，非可概論。羊於辰屬未，坤貞未土，故土之生羊，不盡因於土金之相生焉。他物之生，各有原理。恨吾人學識尚淺，未能悉知之耳。

Someone raised a question: The Earth (Kun) represents soil and cattle, and fire generates earth, so why can't cattle grow out of fire? The Wind (Xun) represents wood and chickens, and water generates wood, so why can't chickens grow out of water? The answer is: All things have their own principles, and they cannot be treated in the same way. Sheep belong to the Earthly Branch 'Wei' and the correct position (Zhen) of the Kun hexagram is exactly at 'Wei' soil, so earth can generate sheep, not entirely because of the generation between earth and metal. The generation of other creatures also follows their own principles. We only regret that our knowledge is still shallow and we cannot understand them all.

坎為水，離為火。水火天地之大用，道家謂為人生之至寶。修道之功，歸結於取坎填離。而平時所致力者，所謂龍虎升降。二五交媾，皆不越坎離之功用。古來傳記，所載物類能煉形修道者，惟狐為最多。且其收效之易且速，恆為人類所不及。雖為經史所未載，然不盡為荒唐無稽之語，可斷言也。

Kan represents water, and Li represents fire. Water and fire are the greatest functions in the universe, and Daoist teachings regard them as the most precious treasures for human life. The practice of Daoist cultivation ultimately comes down to "taking Kan to fill Li." The daily efforts of so-called dragon and tiger rising and falling, and the union of the two five, all fall within the scope of the functions of Kan and Li. Throughout history, the records of creatures that can refine their forms and cultivate Dao are most commonly about foxes. Moreover, the effectiveness and speed of their transformation often surpass that of humans. Although these events are not recorded in official historical texts, they cannot all be dismissed as nonsense. This can be firmly stated.

要皆未能證明其理，乃考之於《易》，狐為坎象（《荀九家補》）。而水火既濟、火水未濟之兩卦，皆取象於狐。夫既濟未濟，非道家之乾坤，《參同契》之關鍵乎？乃文王作《彖》，周公繫《爻》，皆取象於狐。則狐之性靈形體，必與人近。或其內體有特異之機能，合於水火升降之作用，有非為人所及者，故能事半而功倍。古聖必已確知其故，因以繫諸離坎交媾之兩卦，非偶然也。

But no one has ever been able to prove the reasoning behind it. So we examine the Zhou Yi: the fox is the image of the Kan trigram (as seen in the supplementary images in the Xun Jiua Yi), and both the Ji Ji and Wei Ji hexagrams take their images from the fox. Are Ji Ji and Wei Ji not exactly the key concepts of the Daoist theory of Qian and Kun, as discussed in the Cang Tong Qi? King Wen composed the Tai Cis and the Duke of Zhou connected the line statements, yet they specifically took the image of the fox for these two hexagrams. Therefore, the fox's spirit and form must be very close to humans; perhaps it has some special function within its body that precisely corresponds to the rising and falling of water and fire, something beyond human capability, thus making cultivation much more effective. The ancient sages must have certainly known this reason beforehand, and that is why they connected the fox to these two hexagrams of mutual interaction between Li and Kan. It was certainly not by chance.

但非詳於動物生理學者，不能剖此疑團。在北京時，會以質諸大學教習日耳曼人沙某。沙亦向喜中國古學。而精於生理解剖者也。辛齋詳語其故，而沙乃鼓掌狂喜曰：“此足與吾國學者之研究相印證矣！近年解剖之學日精，凡人類與動物之身體之結構，無不明晰其作用：如人之腦筋有十二對，若者司觀，若者司聽司嗅，無不條分縷析。獨狐之腦筋，異常繁複。經多數博士之考驗，迄今尚未能解決。今由《易》象，可得其端倪。即從心腎兩臟以探察之，或可得其要領乎？”即此以觀，可見吾人於科學知識未能充分，而《易》象之精深奧衍，則斷非一知半解之腐儒所可擬議矣。

But if one is not an expert in animal physiology, one cannot unravel this mystery. When I was in Beijing, I once asked a German professor at the university, Mr. Sha, about this question. Mr. Sha had always been fond of Chinese antiquities and was skilled in anatomical studies. I explained the matter in detail to him, and he clapped his hands in delight, saying, "This is sufficient to corroborate the research of our scholars! In recent years, the study of anatomy has become increasingly precise, and the structure and functions of the human and animal bodies have all been clearly understood. For example, human cranial nerves are twelve pairs, and which pair controls vision, which hearing, which smell, are all clearly defined. However, the cranial nerves of the fox are exceptionally complex, and after many doctors have examined them repeatedly, the issue remains unsolved. Now, through the imagery of the Book of Changes, we may gain some insight—perhaps we should start by investigating the heart and kidney organs, and thus grasp the key to this mystery." From this incident, we can see that our scientific knowledge is still insufficient, and the depth and richness of the Book of Changes' imagery are far beyond the reach of those who only have a superficial understanding and dare to make hasty comments.

凡卦之象，合言之各有陰陽剛柔之別。陰陽以氣言，剛柔以形言。如乾為天為剛，坤為地為柔，坎為水為氣之形，離為火為形之氣，是也。而分言之，每卦又各自有其剛柔氣形之用。如乾為天為圜為父為君，又為玉為金為寒為冰，又為大赤，為良馬為老馬為瘠馬為駁馬，又為木果。

The images of all hexagrams, when considered together, each have distinctions of yin and yang, and of hardness and softness. Yin and yang refer to the nature of qi, while hardness and softness refer to form. For example, Qian represents Heaven and is considered hard, while Kun represents Earth and is considered soft. Kan represents water, which is a form condensed from qi, and Li represents fire, which is qi transformed into form. This is the meaning. When viewed separately, each hexagram also possesses various functions of hardness and softness, and of qi and form. For example, Qian is listed in the "Commentary on the Hexagrams" as representing Heaven, a circle, a father, a ruler, jade, metal, coldness, ice, a bright red color, a fine horse, an old horse, a thin horse, a spotted horse, and a tree fruit.

說者謂乾元資始，天與圜乾之體也，父與君，人之元也。玉與金，物之元也。寒與冰，氣之元也。大赤，色之元也。馬與木果，動物植物之元也。又來瞿唐云：“乾為馬，良馬其本體也。時變為老，形變為瘠，色變為駁，皆能得觀象之要者也。”學者由此類推，更可得無窮之精義。

Interpreters explain that Qian Yuan is the origin of all things, and Heaven and roundness are the essence of Qian; father and ruler are the fundamental elements in human relationships; jade and metal are the fundamental elements in material substances; cold and ice are the fundamental elements in qi; great red is the fundamental element in color; horse and fruit trees are the fundamental elements in animals and plants. Lai Zhide (also known as Qu Tang) further says: "Qian represents the horse, and a fine horse is its essence; as time changes, it becomes an old horse; as form changes, it becomes a thin horse; as color changes, it becomes a horse with mixed colors." These interpretations capture the essential principles of observing phenomena. Scholars can further infer from these and gain infinite profound meanings.

如為玉為金，金玉乃物質之最堅最精最純正者。《乾·文言》曰“剛健中正，純粹精也”，故以金玉象之。然物質之發明，日進無窮。近世所寶貴之金剛石，在畫卦時未必有是物也。而乾之剛純粹精，已酷肖其象。故自金剛石出世，而金玉失其貴。擬乾之象，當亦以金剛石為最肖矣。

For example, the Qian trigram is associated with "jade" and "metal." Metal and jade are the hardest, most refined, and most pure substances. The "Wenyan" section of the Qian hexagram states, "It is strong and upright, pure and refined." Therefore, metal and jade are used to symbolize it. However, discoveries in material substances are constantly evolving. Diamond, which is considered a treasure in modern times, may not have existed in the era when the hexagrams were drawn. Yet the virtue of Qian, being strong, upright, pure, and refined, has already closely resembled its form. Therefore, since the discovery of diamond, jade and metal have lost their former prestige. Today, when seeking to symbolize the image of Qian, diamond is the most appropriate representation.

蓋乾乃純粹之氣，而凝合成形，又極剛極堅，無物足以比擬。據近世化學家所考驗，金剛石乃純粹之炭氣所凝結，化之仍散而為氣，絕無渣滓。夫至精至純至剛至堅，又光明通達，聚之成質，而散仍復為氣。非乾之全德，又烏足以肖之？此象之可以物理之確當而補之者也。

The Trigram Qian represents pure qi condensed into form, and is extremely firm and hard, with nothing comparable to it. According to recent chemical analysis, a diamond is formed by pure carbon condensed, and when burned, it reverts back to gas without any residue. It is most refined, most pure, most firm, and most hard, yet also bright and transparent. When condensed, it forms a solid body; when dispersed, it returns to gas. Without possessing all these qualities of Qian, how could it be compared to it? This is an example where modern physical knowledge can be used to supplement the meaning of the hexagram.

凡卦之擬象，有自其陰陽之本體言者，有自其陰陽既合以後言者。如乾道成男，坤道成女，為男為女，是各就其本體言也。若乾為父，坤為母為婦，則自其陰陽既合以後而言也。凡卦之擬象，有取其全體者，有取三畫中之一畫者。乾坤為陰陽之宗，故取象皆以其全體。六子各分乾坤之一爻，故取象亦各就其一爻而言。如震巽以下爻，坎離以中爻，艮兌以上爻是也。

All divination hexagrams take their symbolic forms either from the fundamental nature of yin and yang or from their combination after they have interacted. For example, the Great Treatise says, "The principle of Heaven gives birth to the male, and the principle of Earth gives birth to the female," referring to their nature as male and female in terms of their fundamental essence. However, when it says Heaven represents the father and Earth represents the mother or wife, this refers to their interaction after yin and yang have combined. Furthermore, the symbolic forms of hexagrams may be taken from the entire hexagram or from a single line within the three lines. Heaven and Earth are the ultimate sources of yin and yang, so their symbolic forms are taken as a whole. The six subsidiary trigrams each receive one line from Heaven or Earth, so their symbolic forms are based on that particular line: Zhen and Xun take the lower line, Kan and Li take the middle line, and Gen and Dui take the upper line. This is the reasoning behind it.

六子既各分乾坤之一爻，故即分乾坤之象。如乾為馬，震坎皆言馬。坤為牛，離亦為牛。坤為腹，離為大腹。乾為首，坎為大首。“大腹”見於《傳》而不見於《經》，“大首”見於《經》而不見於《傳》，此尤見經傳互相發明之妙也。

The six sons each received one line from the trigrams Qian and Kun, thus each received part of the trigram imagery. For example, Qian represents a horse, and both Zhen and Kan also refer to a horse; Kun represents an ox, and Li also represents an ox; Kun represents the abdomen, and Li represents the great abdomen; Qian represents the head, and Kan represents the great head. The term "great abdomen" appears only in the Commentary on the Hexagrams but not in the classic text, while "great head" appears only in the classic text but not in the Commentary. One is in the Commentary, the other in the classic text, complementing each other perfectly. This clearly demonstrates the ingenious mutual clarification between the classic text and its Commentary.

震為聲。凡天下之聲，無不由動而發者也。震為群動之宗，故又為聲。然《說卦傳》未言震為聲者，以巽之為臭對照而可得者也。《說卦》一言象，往往於相對待者舉其一端。如舉坤為眾，知乾之為一。舉乾為寒，知坤之為暑。舉坎為憂，知離之為樂。此以對卦互見其義者也，亦有反對互見其義者。如震為大塗，而艮為徑路。巽為疑而兌為決。此皆《說卦》所明言者，則其未明言者可類推而知矣。如舉巽為長為高，則知兌為渺小為纖細。舉艮為門闕，則知震為盤桓。非神而明之，象義莫能見矣。

The trigram Zhen represents sound. All sounds in the world arise from movement; Zhen is the ultimate source of all movement, hence it also represents sound. However, the "Commentary on the Hexagrams" does not explicitly state that Zhen represents sound. This must be inferred by comparing it with Xun, which represents scent. The "Commentary on the Hexagrams" often explains the symbolic meanings by referring to one of two opposing or related trigrams. For example, it mentions Kun as multitude, so we know Qian as unity; it mentions Qian as cold, so we know Kun as heat; it mentions Kan as sorrow, so we know Li as joy. This is using the concept of mutual reference between opposing trigrams to understand their meanings. There are also cases where the meanings are understood through the opposition of trigrams: Zhen represents a broad road, while Gen represents a narrow path; Xun represents doubt, while Dui represents decision. These are explicitly stated in the "Commentary on the Hexagrams." Therefore, things not explicitly mentioned can be inferred by analogy. For example, since Xun represents length and height, we can infer that Dui represents smallness and fineness; since Gen represents gates and thresholds, we can infer that Zhen represents lingering or wandering. Without the ability to grasp the meaning intuitively, the symbolic meanings of the trigrams cannot be understood.

坎為水，離為火，其單象也。而陰陽既合，而離又為電為光為熱。物理之作用，非水不能溶解，非光熱不能融合。無論動物之生，不能離水火與光力熱力，為循環之挹注。既礦物諸質，其凝結之初，亦無不由此。故以電光熱之力，無物不可化分，亦無物不可以化合。故《易》以坎離為六十四卦之中樞，而殿之以水火既濟火水未濟。

The trigrams Kan (water) and Li (fire) represent their simple forms. But when yin and yang interact, Li becomes electricity, light, and heat. In terms of physical functions: without water, there can be no dissolution; without light and heat, there can be no fusion. Not only do animals depend on the continuous cycle of water, fire, light, and heat for their growth, but even the initial formation of various minerals comes from this process. Therefore, with the power of electricity, light, and heat, nothing can remain undecomposed, and nothing can fail to combine. For this reason, the Zhou Changes take Kan and Li as the central trigrams of the sixty-four hexagrams, and use Ji Ji (water and fire in harmony) and Wei Ji (water and fire not yet in harmony) as the concluding hexagrams of the entire book.

或問：乾為天，又為木果。小大之不倫，何懸絕若是？曰：天者元也，元無所不至。木果雖小，即乾之貞，而為元之所伏也。剝之上九曰“碩果不食”，反而為復，貞下起元，故終則有始也。其取象於木果者，以其形圓。圓內有核，核內有仁，仁內即元之所存，物雖小而生意無窮。至初爻變為巽，則元已不可見。故巽為不果，又為伏。伏者即謂元之伏藏而不可見，即無首之義也。《易》象之妙，極深研幾，無一字不有精義存乎其間。

Someone asked: The trigram Qian represents both Heaven and a fruit tree, yet the size is so different, why is there such a big difference? The answer: Heaven is "Yuan," which is everywhere. Although the fruit is small, it is precisely the "Zhen" of Qian, which is where Yuan is hidden. The upper ninth line of the Bao hexagram says "the large fruit is not eaten," and when Bao is exhausted, it returns to Fu, meaning that when Zhen is exhausted, Yuan arises again. Therefore, there must be a beginning when there is an end. The image of a fruit tree is taken because its shape is round: within the roundness is a kernel, within the kernel is the kernel, and within the kernel is where Yuan resides. Though the thing is small, its vitality is endless. When the first line of Qian changes to Xun, Yuan becomes invisible, so the Commentary on the Hexagrams says Xun "is not a fruit" and "is hidden." The term "hidden" means that Yuan is concealed and not visible, which is the meaning of "seeing a group of dragons without a leader" in the use of nine in Qian. The subtlety of the Book of Changes lies in exploring the profound and examining the subtle, with no single character lacking in profound meaning.

或問：乾為木果，即乾上爻之象乎？曰：碩果不食，上爻之象也。而窮上反下，則為初爻。故“木果”二字，須合兩爻以見義。經於剝上曰“碩果”，曰“不食”，二字均有分寸，不可不深思熟察也。

Someone asked: "The Qian hexagram is represented as 'wooden fruit,' is this the image of the top line of the Qian hexagram?" The answer: "The phrase 'large fruit not eaten' indeed represents the image of the top line, but when it reaches the top it must return to the bottom, thus becoming the first line again. Therefore, the two characters 'wooden fruit' must be understood in conjunction with both the top line and the first line to reveal their meaning. The classic text in the Bao hexagram's top line says 'large fruit,' and also says 'not eaten.' The expressions 'large' and 'not eaten' are both very precise, and one cannot help but think deeply and examine carefully."

或問：乾乃純陽，何以為寒為冰？曰：陽畜於陰，寒與冰，皆以陰畜陽。乾居西北，固陰沍寒。陰陽相薄，凝而為冰（所謂陰陽既合以後之象也）。故乾西北對東南巽。乾巽曰小畜，乾居西北，於先天之位為艮，艮乾曰大畜，大畜小畜而陽始生，猶必潛以養之，勿用以守之。剛健純粹，夫豈一朝一夕之故哉！

Someone asked: Qian is pure yang, so why does the "Shu Gu" say it represents cold and ice? The answer is because yang is restrained by yin - cold and ice both involve yin restraining yang. In the later heaven arrangement, Qian is located in the northwest, which is naturally cold and closed off due to the gathering of yin energy. The interaction between yin and yang leads to the formation of ice (this is precisely what is meant by the image after the union of yin and yang). Therefore, Qian being in the northwest corresponds to Xun in the southeast. With Xun above and Qian below, we have the hexagram Xiao Xu. In the earlier heaven arrangement, the position of Qian is艮 (Gen). With Gen above and Qian below, we have Da Xu. Only after going through Da Xu and Xiao Xu can yang energy begin to grow. Even then, it is still necessary to conceal it as in the first line of Qian, "Initial Nine," to nurture it, and to guard it by "not using" it. The strong and pure virtue of Qian cannot be achieved in a day or two!

或問：艮為虎，兌亦為虎。艮為虎，乃荀九家之說。按之於《經》，則履之“虎尾”，革之“虎變”，皆似兌象。究何從乎？曰：履與革，固有兌象。而頤之“虎視眈眈”，則艮象也。此即前文所謂以對卦而相通之一例也。

Someone asked: "Geng (Gon) represents the tiger, and Dui also represents the tiger. The representation of Geng as the tiger comes from the supplementary imagery in the Xun Jiye Yi. But if we check the classic texts, the phrase 'stepping on a tiger's tail' in the Lu卦 and 'the great man's tiger transformation' in the Ge卦 seem to be Dui imagery. So which one should we follow?" The answer is: The Lu卦 and Ge卦 indeed both contain Dui imagery, while the phrase "the tiger stares intently" in the Yi卦's line six in the fourth position is Geng imagery. This is exactly the example mentioned earlier, demonstrating how one can use the mutual correspondence between related trigrams.

考八卦之象，艮為狗，因艮外剛而內柔，狗之性似之，故為狗。然艮有成終成始之德，能與剛德相終始，則為虎。兌之本象為羊，履之“虎尾”，革之“虎變”，曰“尾”曰“變”，明非兌之本象也。至兌之為虎，乃另屬一義。兌居西方，上直昂宿白虎之位，亦如乾卦之取象蒼龍，則因位而取象。與剛柔之說無與矣。

Examining the symbolic representations of the Eight Trigrams: The Trigram Gen is associated with the dog because Gen is externally strong and internally gentle, and the dog's nature is similar, hence the dog is used as its symbol. However, Gen also possesses the virtue of "completing the beginning and the end," being able to maintain harmony with strong virtue throughout, so it can also be associated with the tiger. The original symbol of Dui is the sheep; the Book of Changes says "tiger's tail" in the hexagram Li and "tiger's transformation" in the hexagram Ge. One mentions "tail" and the other "transformation," clearly not referring to Dui's original symbol. As for why Dui is associated with the tiger, it is due to another reason: Dui is located in the west, precisely corresponding to the White Tiger constellation, the seven stars of Hairy Head mansion. This is similar to how the Trigram Qian is associated with the Eastern Blue Dragon, based on directional association, and has nothing to do with the idea of being externally gentle and internally strong.

或問：坤為布為釜，乃坤之本象乎？曰：非也。此皆陰陽化合而生之象也。坤與乾合，則陰陽經緯而有布象。坤得離坎，則水火濟用而有釜象或缶象。缶亦釜也。《易》有缶而無釜，因上古火化之始，未有釜也。觀比之盈缶，坎用缶，離鼓缶，可會通其義矣。曰：陰陽經緯，既乾坤相合之象，何獨於坤言之？曰：陽氣而陰質也。曰：乾亦有稱布乎？曰：有諸。乾施坤受，施亦布也。布五行於四時，乾之布也。布同而義殊矣。妙哉！《易》之為書也。

Someone asked: "Is 'Kun' associated with 'cloth' and 'vessel', which are its original images?" The answer was: No. These are images that arise after the combination of yin and yang. When Kun combines with Qian, yin and yang intermingle vertically and horizontally, thus producing the image of cloth. When Kun combines with Li and Kan, water and fire interact, thus producing the image of a vessel or a gu. A gu is also a vessel. The text of the Zhou Yi only mentions 'gu' and not 'fu', because when ancient people first learned to use fire for cooking, there was no such thing as a 'fu'. Looking at the line 'There is sincerity in the gu' from the top line of the Bi hexagram, 'Wine and food in two vessels, using the gu' from the sixth line of the Kan hexagram, and 'Singing without beating the gu' from the third line of the Li hexagram, one can understand the meaning. Another question: If the intermingling of yin and yang is the image of the combination of Qian and Kun, why is the image of cloth specifically mentioned under Kun? The answer is: Because yang is only qi, while yin is the substance. Another question: Can Qian also be called 'cloth'? The answer is: Yes. Qian gives out, and Kun receives. 'Giving out' is also 'cloth'. Distributing the five elements throughout the four seasons is precisely the action of Qian. The same character 'cloth' has different meanings. The Zhou Yi is truly marvelous.

或問：離為鼈、為蟹、為蠃、為蚌、為龜。此五者，惟龜象見於頤與損益，餘象皆不見經傳，其義何居？曰：五者皆水族也。不屬諸坎而屬諸離，以見陰陽互藏之妙焉。舊說以五者皆甲蟲，外剛內柔，故以取象。是矣，而未盡也。離中虛能受，故能納五行之精。得巽木之精為鱉，得震雷之精為蟹，得兌月之精為蚌，得乾金之精為蠃，得坎艮之精為龜，而畢受化於坤土。觀象於頤可得其義。推而廣之，其象可見也。（焦氏《易通釋》謂《易》之言敝即鱉也，言解即蟹也，言贏即蠃也，言邦即蚌也，於義亦通。）

Someone asked: The "Say on the Trigrams" says that the trigram Li (Fire) represents turtle, crab, snail, mussel, and tortoise. Among these five, only the tortoise is mentioned in the "Yi" (I Ching) and its commentaries, while the other four are not found in the classical texts. What is the purpose of using these as symbols? The answer: These five are all aquatic creatures, yet they are not associated with Kan (Water) but with Li (Fire), which clearly shows the profound mystery of yin and yang intermingling and containing each other. The old view considered these five to be creatures with hard shells and soft insides, so they were used as symbols—this is partly correct, but not entirely. The trigram Li is hollow in the center, and emptiness allows it to contain and receive. Therefore, it can hold the essence of the Five Phases: it receives the essence of Xun wood to become a turtle, the essence of Zhen thunder to become a crab, the essence of Dui metal to become a mussel, the essence of Qian metal to become a snail, and the essence of Kan mountain to become a tortoise. Finally, all of them are nurtured by the essence of Kun earth. Observing the images in the "Yi" (I Ching) in the "Yi" hexagram can clarify this meaning. Extending this understanding, these images can all be recognized. (Jiao Xun's "Yi Tong Shi" says that the character "bi" in the "Yi" text refers to turtle, "jie" refers to crab, "ying" refers to snail, and "bang" refers to mussel. These interpretations are also reasonable in terms of meaning.)

或曰：坎為月，今以兌為月，是非邵子之象乎？曰：非也。卦之言象，以相對見義。坎離相對，離為日，則坎為月。離為火，則坎為水。兌之為月，對於震巽取義。《易》之言月者，除日月對舉者則指坎。餘皆指兌言也。

Some people say: "Cann is the moon, but now it is Dui that is taken as the moon. Is this not the way of Shao Yong's school?" The answer is: No. In divination, the meaning is derived from the relations between the trigrams. Cann and Li are opposite to each other: since Li represents the sun, Cann represents the moon; since Li represents fire, Cann represents water. As for Dui being taken as the moon, it is in relation to Zhen and Xun. In the text of the Zhou Changes, whenever the moon is mentioned, it refers to Cann in cases where the sun and moon are mentioned together, but in other cases, it refers to Dui.

或問：《繫下傳》“龍蛇之蟄以存身焉”，是否指乾卦之象？曰：然。咸卦三爻至五爻互乾，乾四爻之“上不在天下不在田中不在人”者，以此四爻乃在乾卦之中。《咸·象》曰“君子以虛受人”者，即此一爻，故稱龍蛇。龍蛇者，未確指其為龍為蛇，與“或躍在淵”之或字相應者也。蓋乾之對宮為巽，巽於十二辰，貞在辰巳，辰為龍，巳為蛇。躍者，超越而上之名，言四爻能超躍越過巳之一位，即及於離午而為飛龍。不能及於離午，則在巳而為蛇。辭意極為明析。按之於象數，無不絲絲人扣者。聖人之文，真與造化同一工也！

Someone asked: The "Xici Xia Zhuan" says, "The dragon and snake hibernate to preserve themselves," does this refer to the image of the Qian hexagram? Answer: Yes. The third to fifth lines of the Xian hexagram together form the structure of the Qian hexagram. The Nine in the Fourth line of the Qian hexagram is said to be "not above Heaven, not below the field, not in the middle of people," precisely because this line is in a transitional position within the Qian hexagram. The "Great Image" of the Xian hexagram says, "The gentleman receives others with humility," which refers exactly to this line, hence it is called "dragon and snake." The term "dragon and snake" does not specifically refer to either a dragon or a snake, corresponding to the "or" in the line statement "or leap into the abyss." Originally, the opposite hexagram of Qian is Xun. In the twelve earthly branches, the position of Xun falls on the hours of Chen and Si: Chen is the dragon, and Si is the snake. "Leap" is a term meaning to transcend upward. It means that the Nine in the Fourth line can leap over the position of Si and reach Li and Wu to become a flying dragon; if it cannot leap over, it remains in the position of Si and is merely a snake. The meaning of the line statement is very clear. When verified with the principles of numbers and positions, everything fits perfectly. The words of the sage are truly in harmony with the workings of nature!

或問：《說卦》“離為龜”，乃六十四卦之有離者，均不言龜，獨見之於頤與損益何也？曰：頤與損益，皆剛外柔內，有離之象。來氏所謂大象是也。頤與損益，大象似離，故言龜。亦即聖人示人以取象之一例焉。

Someone asked: The "Sayings on the Trigrams" says "Li represents the tortoise," but among the sixty-four trigrams, none of the ones containing the trigram Li mention the tortoise, except for the trigrams Yi, Shen, and Yi. Why is this? The answer is: The trigrams Yi, Shen, and Yi all have a hard outer part and a soft inner part, and they have the shape of Li. This is what Lai Zhide referred to as "the great image." Since these three trigrams as a whole resemble Li, they are associated with the tortoise. This is exactly the example of taking a symbolic image that the sage demonstrated to people.

曰：在損益皆稱“十朋之龜”何也？曰：十者，取其最多之數，即天一至地十之數也。朋者，陰陽相合。以天一地二天三地四，數各有合，故曰朋。此“龜”字與震卦“億喪貝”之貝字同。古人無錢布，龜與貝皆寶貨之一類也，故以象言之。頤之龜乃活龜，而損益之龜則龜版耳。

Another question: Both the hexagrams "Zhen" (Loss) and "Yi" (Gain) mention "ten tortoises," why is this so? The answer is: "Ten" refers to the largest number, which is the end of the sequence from heavenly one to earthly ten. "Peng" refers to the pairing of yin and yang: heavenly one pairs with earthly two, heavenly three pairs with earthly four, and each number has its counterpart, hence called "peng." The word "gu" (tortoise) here is of the same category as the "bei" (shell money) in the line "yi sang bei" (countless loss of shell money) in the hexagram "Zhen." In ancient times, there were no copper coins or metal currency; tortoise shells and shells were considered valuable items, so they were used as symbols. The tortoises mentioned in the hexagram "Yi" (Nourishment) are live tortoises, but those mentioned in "Zhen" (Loss) and "Yi" (Gain) are merely the turtle shells used for divination.

或問：巽為寡髮，《李氏集解》作宣髮。虞注曰巽為白，故宣髮。將何說之從？曰：兩說皆可通也，巽為長女。凡女之愆時未嫁。及早嫁而生育過多者。血皆失其經而髮禿。故曰寡髮。禿必於前額，故亦可曰宣髮。《考工記》“半矩謂之宣”，似宣之義更能形容酷肖，較寡字尤周到也。

Someone asked: The "Say on the Trigrams" says that Xun is "of sparse hair," but Li Dingzuo's "Collected Explanations of the Zhou Changes" says "of spreading hair." Yu Fan's commentary says that Xun is associated with white, hence "spreading hair." Which should be followed? The answer is that both interpretations are reasonable. Xun is the elder sister, and any woman who has not married before her time or who has married early and given birth many times will lose her blood balance, leading to thinning hair, hence "sparse hair." However, baldness always begins at the forehead, so it can also be called "spreading hair." The "Rites of Zhou · Records of the Master of Works" says "half the square is called 'Xuan'," and "Xuan" implies a broad forehead, which seems to describe the condition more accurately and comprehensively than the word "sparse."

或問：巽為近利市三倍，其於象也何居？曰：此象之微妙，非通全卦而觀之，僅就巽之三畫以探索之，無從得其義焉。巽為入，有入而無出，得坤吝嗇之性。然坤柔順，故雖吝音，尚不致為貪。而巽之體，則乾體也。以乾體之健，行坤性之吝，更兼其本性之人。三者合之，所謂三倍也。

Someone asked: The "Say on the Trigrams" says that Xun represents "a profit threefold." What is the basis for this image? The answer: This image is very subtle. If one does not observe the entire trigram but only examines the three lines of Xun, one cannot understand its meaning. Xun represents "entering," which is only entering and not exiting, thus acquiring the nature of Kūn, which is stingy. However, Kūn is flexible and yielding, so although it is stingy, it does not become greedy. The original nature of Xun, however, is the nature of Qian: with the strength and vigor of Qian, acting with the stinginess of Kūn, and adding its own nature of "entering," the combination of these three is what is called "threefold." (The original text says "lìn yīn" should be read as "lìn sè" [stingy], and "běn xìng zhī rén" should be read as "běn xìng zhī rù" [nature of entering].)

然則近利市三字之象，又從何而來也？曰：此則須索之於八卦方位也。八卦巽居東南，其前則東震也，其後則南離也。離與震，火雷噬嗑。日中為市，致天下之民，聚天下之貨，交易而退，各得其所，蓋取諸噬嗑。今巽之方位，適介於噬嗑上下卦之間，非近利市而何？故聖人之於象，一字一義，必有根據。潛心以求之，多方以索之，方能知其妙。若以不解解之，其奧義終莫能得也。

So where does the image of "near profit and market" come from? The answer is to look for it in the positions of the Eight Trigrams. Among the Eight Trigrams, Xun is located in the southeast. In front of it is Zhen in the due east, and behind it is Li in the due south. Li and Zhen combine to form the Hexagram 21, Fire Over Thunder, Shi Ke. The "Xici Xia Zhuan" says: "At noon the market is held, gathering the people from all over the world and collecting goods from all over the world. They trade and then depart, each getting what they need. This is derived from Shi Ke." Now, the position of Xun is exactly between the upper and lower trigrams of Shi Ke. Is this not "near profit and market"? Thus, the sage established images, each character and each meaning must have its basis. One must diligently seek and search from many sides to understand its subtlety. If one explains it with partial knowledge and superficial understanding, those profound meanings will never be grasped.

或曰：宣髮與近利市三倍，其象義之妙既聞之矣。而巽又為多白眼，亦必有妙義，可得聞歟？曰：此則前人已有言之者矣。曰離柔居中，為目之正。巽陰反下，而二陽上，故多白眼。似為來氏之說。於義頗近，尚未明暢。請申言之。

Some people said: I have already understood the subtle meanings of the two divination lines "宣发" and "近利市三倍"; since the trigram Xun is said to "represent many white eyes," there must be some profound meaning, could you explain it to me? The answer was: this point has already been discussed by previous scholars. They said: the trigram Li has a yin line in the middle, which represents the upright eyes; while the trigram Xun has a yin line at the bottom and two yang lines above, thus representing many white eyes. This seems to be the view of Lai Zhide, and the meaning is quite similar, but not clearly explained. I will now elaborate further.

離為目，巽之下，即離之上也。離之下，即兌之上也。此即虞氏所謂半象。故經文於兌稱“眇目”，履與歸妹皆兌，皆曰“眇能視”是也。以兌例巽，則巽亦眇耳。惟巽又為白。白者，上二陽也。是巽之眇，白且占三分之二。非多自眼而何？“多白眼”二字，不啻將巽之眇活畫出來。神哉化工之筆也！

The trigram Li represents the eye. The lower half of Xun is exactly the upper half of Li; the lower half of Li is exactly the upper half of Dui — this is what Yu Fan referred to as "half-trigrams." Therefore, the classic text refers to "眇目" (blind eye) in the Dui hexagram: both the hexagram "Lu" (Following) and "Gui Mei" (Return of the Maiden) contain the structure of Dui, and both mention "眇能视" (blind in one eye yet able to see). By comparing Dui to Xun, Xun also possesses the quality of "眇." However, Xun is also associated with "white," referring to the two yang lines at the top. Thus, the "眇" in Xun is dominated by white, occupying two-thirds of it. It is not called "多白眼" (many white eyes) for nothing (the original text says "多自眼," where "自" is a mistake for "白"). The term "多白眼" vividly portrays Xun's eye that appears pale. Truly, it is a masterpiece of divine craftsmanship!

或問：坎，其於人為加憂，為心病，為耳痛。舊解為陽陷陰中，心危慮深，故加憂。憂之甚為心病，心以虛為體。剛畫梗於其中故病。惟耳亦然。坎為耳，外陰內陽，取象陽之總也。又為耳痛，象陽畫之梗於其中也。其說當乎？

Someone asked: The "Say on the Trigrams" says about Kan (Water): "It represents added worry, heart disease, and ear pain." Old commentaries explain that a yang line is trapped within yin lines, causing inner anxiety and deep thinking, hence "added worry"; when worry reaches its extreme, it becomes "heart disease," because the heart is based on emptiness, and a single strong yang line blocking in the middle causes illness. The ear is similar: Kan represents the ear, with outer yin and inner yang, symbolizing the gathering of yang energy; saying it "represents ear pain" also symbolizes that yang line blocking in the middle. Is this explanation appropriate?

曰：否否。坎曰惟心亨，正以陽之正中也。若以陽之梗於中為病，則天下之心，殆無不病者矣。陽梗於中為耳痛，則天下之耳，將無不痛者矣。其說之誣，不待辯矣。坎為耳為心，其本象也。其為加憂，為心病，為耳痛，則因所處之時與位而言。所謂陰陽既合以後之象，陰陽合則變化生，曰憂，曰病，曰痛，明明既動以後之事，烏得以本象之陰陽言之？

It's incorrect, incorrect. The Commentary on the Judgment of the Kan hexagram says, "Only with the heart being open is there smoothness." This is precisely because a yang line is in the proper central position. If one says that a yang line obstructing in the middle is a problem, then almost everyone's heart would be diseased; if one says that a yang line obstructing in the middle causes ear pain, then everyone's ears would be painful. The absurdity of such a statement is evident without argument. Kan represents ear and heart in its fundamental form; however, its associations with added worry, heart disease, and ear pain are based on its position and timing, which belong to the images that arise after the interaction of yin and yang. Once yin and yang interact, changes arise. Speaking of worry, disease, and pain clearly refers to situations after movement has occurred. How can one explain these in terms of the fundamental yin and yang of the hexagram?

比樂師憂，同一坎焉，何為於比則樂，於師則憂？豈比之坎剛畫梗於其中，而師之坎則無剛畫梗於其中耶？豈比之坎陽陷陰中而師之坎陽出陰外耶？同一坎也，同一坎與坤也，同為一剛而五柔也，乃優樂頓異者，則惟其所處之時與位之不同耳。

The Zage Zhuan says, "Bi is joy and Shi is sorrow." Both hexagrams contain a Kan trigram, yet Bi is associated with joy while Shi is associated with sorrow. Is it because the Kan in Bi has a strong line crossing through it, while the Kan in Shi does not? Or is it because the Kan in Bi has a yang line sinking into yin, while the Kan in Shi has a yang line moving outside yin? Both are Kan, both are paired with Kun, and both consist of one yang and five yin lines. Yet joy and sorrow are completely opposite. The reason is only that their positions and contexts are different.

然憂與樂固同此心焉。處憂則憂，當樂而樂。或先憂而後樂，或先樂而後憂。時與位無定，君子處之無成心焉。故曰加憂。加者非所固有，從而加之之辭。《坎·彖》曰“惟心亨，往有尚”，尚即加之義也。物失其中為病，艮之“危薰心”，心病也。不安其中亦病，咸之“憧憧往來”，亦心病也。坎者通也，失其通為痛。噬嗑之“荷校滅耳”，《傳》曰“聰不明也”，乃耳痛也。未聞剛梗於中之為病為痛也。

However, sorrow and joy both originate from the same mind: when in a situation that calls for sorrow, one feels sorrow; when in a situation that calls for joy, one feels joy; sometimes sorrow comes first and then joy, sometimes joy comes first and then sorrow. Time and position are not fixed, and the gentleman deals with them without clinging to fixed views, so the "Say on the Hexagram" says "add sorrow" — "add" means something that was originally not there but is added later. The "Commentary on the Judgment" of the "Gua of Water" says "the mind is open and thus communication is smooth, and action is commendable," where "commendable" also means "add." When things lose the middle, they become diseased: the "Nine in the Third" of the "Gua of Stillness" says "dangerous and the heart is scorched," which is a heart disease; being unsettled in the middle is also a disease: the "Nine in the Fourth" of the "Gua of Attraction" says "confused movement," which is also a heart disease. The meaning of "Kan" is communication; losing communication leads to pain: the "Top Nine" of the "Gua of Eating the Fire" says "a wooden staff on the head and ears cut off," and the "Image Commentary" says "the ears are not clear," which is actual ear pain. I have never heard of a yang line blocking the middle being considered a disease or a pain.

腐儒不明象義，又不熟經文，僅知於一卦三畫中求象。求而不得，於是以剛柔之卦畫，以己意揣測而附會之，而不顧其理之是非。此言象者之所以授人口實也。坎之為矯輮，亦非其本象也。凡物件之矯輮者，必先炙以火，而以水定之。故坎象之為矯輮，亦必在與離相合，或在與離通變之後，而弓輪則更因矯輮推而及之者也。蓋物之有弓與輪，乃為矯輮之最著者也。《易》象有相因而及者，如艮為門闕，因更為閽寺；兌為口舌，因更為巫，皆與此一例也。

The ignorant scholar does not understand the symbolic meaning of the hexagrams and is not familiar with the classics, yet he only seeks the image within the three lines of a single hexagram. When he cannot find the image, he resorts to interpreting the yao lines, which are either hard or soft, according to his own understanding, regardless of whether the reasoning makes sense. This is precisely why those who talk about images are criticized by others. For example, the trigram Kan is said to represent "bending and straightening wood," but this is not its original image. Any process of bending and straightening wood must first be heated with fire and then fixed with water, so the image of Kan as "bending and straightening wood" only makes sense after it has interacted with Li, or after a transformation involving Li. As for "bow and wheel," this is a further derivation from the image of bending and straightening. Among objects, bows and wheels are the most obvious results of bending and straightening. In the images of the Book of Changes, there are examples where one image leads to another in a connected way: for instance, Gen represents a gate, and thus also the gatekeeper; Dui represents mouth and tongue, and thus also the shaman. These are all examples of the same pattern.

或問：象之言數，是否即“七日來復”，“八月有凶”，與“十年不字”、“十年勿用”之類？曰：非也。此乃言爻與卦之數。雖與象不盡無關，然不可即謂象之數也。然則象之倚於數者如何，可略舉其例歟？曰：《易》之為書，參天兩地而倚數。三畫成卦，參天也。因而重之，兩地也。六畫而分三才，又參天也。三才而迭用柔剛，又兩地也。用九用六，又參天而兩地也。故《易》之立言，殆無一不倚於數。詳言之，非短辭所能罄，當別論之。

Someone asked: Are the numbers mentioned in the images referring to things like the "seven days to return" in the复卦, "eight months with misfortune" in the临卦, and "ten years to be able to write" in the屯卦, as well as "ten years without use" in the蒙卦? Answer: No. Those refer to the numbers of lines and hexagrams, although they are not entirely unrelated to the images, they cannot be called the numbers of the images. Then, what numbers does the image rely on? Can you give a few examples? Answer: The Sayings of the Hexagram explains that the Book of Changes is "three heavens and two earths, relying on numbers." Forming a hexagram with three lines is "three heavens"; stacking two hexagrams to form twelve lines is "two earths"; dividing the six lines into three elements is again "three heavens"; alternating the soft and hard lines among the three elements is again "two earths"; using nine and six still follows the pattern of three heavens and two earths. Therefore, the Book of Changes is almost entirely based on numbers. To explain in detail is not possible in a few words, it should be discussed in a separate treatise.

象之倚數，亦不能離乎陰陽。陽數參天，陰數兩地。參兩之數，無不原本天一至地十之五十五數，而折為五行，分寄於象。故象之言數，以根於五行及九宮之數為多。而五行各有始有壯有究，數又有別也。

The numbers on which images depend cannot be separated from yin and yang: the yang numbers take "ascending to heaven" with three as the base; the yin numbers take "two lands" with two as the base. The combination of these two kinds of numbers is based on the total of fifty-five, derived from the sum of the numbers from heaven one to earth ten. This total is then divided into the Five Phases, and each phase is associated with various images. Therefore, numbers mentioned in images mostly originate from the numbers of the Five Phases and the Nine Palaces. Each of the Five Phases has three stages: beginning, flourishing, and decline, and numbers vary in each stage.

《易》窮則變，窮於數也（天數極於二十有五，地數極於三十，天地之數窮於五十有五。故生數終於五，成數始於六，天地生成之數合於五。六乃為天地之中，七則反以天之五分陰分陽。故乾之數十。以地之六迭用柔剛，故支之數十二，十三則凶。陰九陽六，六九五十四，為窮之災。而五十六為凶之始，而九十六與一百零六皆凶數。）是故欲明象之數，必先別其時位。時有三候（即始壯究也），位有三等（即初中上也），明乎此，於象倚於數之理思過半矣。

The Great Treatise says, "The Book of Changes transforms when it reaches its limit." The limit refers to numbers: the heavenly numbers reach their peak at twenty-five, and the earthly numbers reach theirs at thirty. The total of heavenly and earthly numbers is fifty-five. Therefore, the numbers of generation end at five, and the numbers of completion begin at six. The numbers of generation and completion meet at five; six is the central number of heaven and earth. Seven, on the other hand, divides the five of heaven into yin and yang. Hence, the heavenly stems have ten numbers. Using the six of earthly numbers alternately with soft and strong, the earthly branches have twelve numbers, and thirteen is considered ominous. Yin reaches its peak at nine, and yang is used at six. Multiplying six by nine gives fifty-four, which is the peak of calamity. Fifty-six is the beginning of misfortune, and ninety-six and one hundred and six are also considered ominous numbers. Therefore, to understand the numbers of the images, one must first distinguish their time and position. Time has three phases: beginning, flourishing, and ending. Position has three levels: initial, middle, and upper. Once this is understood, one will grasp a large part of the principle that images depend on numbers.

《易》象掌於太卜，周室版蕩，典章散迭。東遷而後，未能盡復故物。孔子《說卦》所傳，即為掇拾殘闕之遺，而又歷經劫火，簡策散失。比及西漢，兩篇《十翼》，猶闕《說卦》三篇。後得河內女子發於廢屋，即今之《說卦》是也。

The divination texts of the Book of Changes were originally managed by the official in charge of divination. During the turmoil of the Zhou dynasty, the rituals and systems were lost. After the Eastern Migration of the Son of Heaven, the old records could not be fully restored. The text passed down by Confucius in the "Commentary on the Hexagrams" was already collected from fragmented remains. Later, it was repeatedly damaged by wars, and the bamboo slips were lost. By the Western Han dynasty, among the ten appendices, the three chapters of the "Commentary on the Hexagrams" were still missing. Later, they were discovered by a woman from Henan in a destroyed old house, which is the version of the "Commentary on the Hexagrams" we have today.

卦象殘闕，自所不免。《荀九家》補象，乾有四，坤八，震三，巽二，坎八，離一，艮三，兌二，都三十有一。朱子已取以列入《本義》。而孟氏之逸象，文十倍於《九家》。計乾之象六十有一，坤八十一，震四十九，坎四十七，艮三十七，巽二十，離十九，兌九，共三百二十三，亦云夥矣。

The omissions in the hexagrams are inevitable. The lost images restored by the "Nine Schools of the Zhou Changes" include four for Qian, eight for Kun, three for Zhen, two for Xun, eight for Kan, one for Li, three for Gen, and two for Dui, totaling thirty-one. Zhu Xi has already included these in his "Original Meaning of the Zhou Changes." The lost images transmitted by the school of Meng Xi are ten times longer than those of the Nine Schools: Qian has sixty-one, Kun eighty-one, Zhen forty-nine, Kan forty-seven, Gen thirty-seven, Xun twenty, Li nineteen, and Dui nine, totaling three hundred and twenty-three. This is already a considerable number.

而後儒如何妥、於令升、侯果、朱震、來知德，及勝清毛錫齡，亦均有補象。要皆採自二篇《十翼》者為多。如《九家》所補之三十一象，惟坤之帛與漿，震之為鵠，巽之為鶴，未見於經，餘皆經傳所有者也。《易》道廣大，無所不包，象足以盡物，物不足以盡卦。《易·說卦》於《象》曰其於物也，其於人也，亦舉一隅而已。觸類旁通，非列舉所能盡也。

Later scholars such as Guan Bao (Zhi Sheng), Hou Guo, Zhu Zhen, Lai Zhide, and Mao Qiling of the Qing dynasty all contributed their own interpretations, though most of their additions were drawn from the two chapters of the Ten Wings. For example, among the thirty-one images added by the "Nine Schools," only the images of the Earth (Kun) "as silk" and "as soup," the Thunder (Zhen) "as a goose," and the Wind (Xun) "as a crane" are not found in the original text; the rest are already present in the classic texts. The Way of the Book of Changes is vast and encompasses everything. The images are sufficient to exhaust all things, yet all things are insufficient to exhaust a single hexagram. The "Sayings on the Hexagrams" mentions "its relation to things" and "its relation to people," but these are merely examples from one corner; the full understanding depends on drawing connections and applying principles, which cannot be exhausted by listing each case individually.

（《荀九家》者，荀慈明集九家《易》解，為書十卷，見於《班書》。而《文獻通考》引陳氏說，謂漢淮南王所聘明《易》者九人，荀爽嘗為之集解。但陸氏《釋文序錄》列九家姓氏為京房、馬融、鄭玄、宋衷、虞翻、陸績、姚信、翟子元、荀爽，與前說不同。但考陸氏所列諸家，無論時代後先，且立說各異，有相冰炭，決非可合而為一者。姑錄其說以備參考可耳。）

The so-called "Xun Jiujia" is a commentary on the Book of Changes compiled by Xun Shuang (style name Ciming) collecting the interpretations of nine schools. The entire work consists of ten volumes and is recorded in Ban Gu's "Book of Han · Catalogue of Arts and Literature." However, the "Comprehensive Survey of Literature and Records" cites Chen Zhenzun's statement, saying that it was nine scholars proficient in the Book of Changes who were hired by Prince Huainan of the Han dynasty, and Xun Shuang once made a collective commentary for them. But Lu Deming's "Sequencing of the Classics · Preface" lists the names of the nine schools as Jing Fang, Ma Rong, Zheng Xuan, Song Zhong, Yu Fan, Lu Ji, Yao Xin, Zhai Zixuan, and Xun Shuang, which differs from the previous account. Upon careful examination of the families listed by Lu, regardless of their chronological order, their doctrines are mutually conflicting, some opposing each other like water and fire, and it is impossible for them to be combined into a single work. Therefore, these different accounts are recorded here for reference only.

《坤·彖》曰“君子有攸往”。讀者於此一句，往往忽略，順口讀過。而自漢以後，講《易》者無慮千數百家，亦均未著眼於此。宋儒或以為占辭，以君子指筮者，則更為無稽。須知此卦為六十四卦之第二卦，上承六十四卦第一卦之乾卦。

The Hexagram Statement of the Qian Hexagram says, "The gentleman has a course to take." Readers often overlook this sentence, reading it carelessly; since the Han dynasty, there have been more than a thousand scholars interpreting the Book of Changes, but none have focused on this point. Some Song dynasty Confucian scholars took it as a divination statement, considering "the gentleman" to refer to the person casting the divination, which lacks proper basis. One must understand that the Qian Hexagram is the second among the sixty-four hexagrams, following the first hexagram, Qian.

文王於《乾·彖》，只繫以“元亨利貞”四字，以概括乾德，即以概括六十四卦。以乾為天行，蕩蕩莫名。舍此四字，實無可以表示乾德而概括無遺者。坤以承乾，故亦首繫以“元亨利牝馬之貞”。“牝馬”二字，綰合乾坤，以示陰陽合德，剛柔有體。所謂立天之道，立地之道者，皆以此“元亨利貞”四字挈其綱矣。

King Wen attached only the four characters "Yuan, Heng, Li, Zhen" to the Hexagram Statement of Qian. He used these four characters to summarize the virtue of Qian, and also to summarize the entire sixty-four hexagrams. Since Qian represents the movement of Heaven, which is vast and beyond description, there are no other words besides these four that can fully express the virtue of Qian without omission. K'un follows Qian, so the Hexagram Statement of K'un also begins with "Yuan, Heng, Li, Zhen of the female horse." The two characters "female horse" connect Qian and K'un, indicating the union of yin and yang, and the distinct nature of yang and yin. The "establishing the way of Heaven" and "establishing the way of Earth" mentioned in the "Shuo Gua Zhuan" are all summarized and guided by these four characters "Yuan, Heng, Li, Zhen."

然天地之道，非人莫明；天地化育，非人莫參。先聖作《易》，原以明人道以立人極。故於《坤·彖》“貞”字之下，即大書特書曰“君子”，所以正名定分，乃《周易》開宗明義之第一特筆也。

However, the way of heaven and earth cannot be made clear without people; the nurturing and transformation of heaven and earth cannot be participated in without people. The sage ancestors composed the Zhou Changes, originally to clarify human conduct and establish the standards of being a person. Therefore, in the Hexagram Statement of the Qian Hexagram, immediately following the character "Zhen," they prominently inscribe the term "junzi" (gentleman), to properly name and define roles—this is the first distinctive emphasis in the Zhou Changes.

讀者疑吾言乎？試即文王六十四卦之《彖辭》索之，可比較而得之矣。謙為人道之卦，曰“君子有終”。否曰“不利君子貞”，同人曰“利君子貞”，皆此君子也。周公繫爻於乾三之“君子終日乾乾”。孔子贊《易》，六十四卦《大象》之“君子”，皆述文王之意，所以闡發此一句“君子”兩字者也。乃後人猶不注意，不將前聖後聖垂教之苦心，一筆抹煞乎？

Does the reader doubt my words? Just check the sixty-four hexagram statements of the hexagrams systematized by King Wen, and a comparison will make it clear. The hexagram of Humility discusses human conduct, and its statement says, "The gentleman has a proper end." The hexagram of Non-Alignment says, "It is not advantageous for the gentleman to be steadfast." The hexagram of Fellowship says, "It is advantageous for the gentleman to be steadfast." All of them refer to this term "the gentleman." The Duke of Zhou composed the line statements, and in the third line of the hexagram of Heaven, he wrote, "The gentleman remains diligent all day." Confucius commented on the Book of Changes, and in the Great Image Commentary of the sixty-four hexagrams, the term "the gentleman" is also used to convey the meaning of King Wen, explaining the two characters in the statement of the hexagram of Earth. How could later generations still fail to pay attention, thereby wiping out the sincere efforts of the sages past and present in imparting teachings and guiding people?

“有攸往”者，乃鄭重指導之辭，三字具有無窮深意，亦不當忽略讀過。此“有”字，乃全《易》開卷第一“有”字，即《序卦》“有天地然後有萬物”與“有男女有夫婦有父子及禮義有所錯”之有。言既有“乾元亨利貞”，既有“坤元亨利牝馬之貞”，而後君子始“有攸往”之可言矣。

"The 'There is something to go toward' (you you wang)" is a solemn word of guidance. These three characters contain infinite meaning and should not be overlooked. The character 'you' here is the first 'you' in the entire I Ching, that is, in the "Xugua Zhuan" (the "Sequence of Changes" commentary), "When Heaven and Earth exist, then all things come into being," and also "There are men and women, there are husband and wife, there are father and son," up to "Rites and righteousness have their place." The meaning is that first there is the "Yuan, Heng, Li, Zhen" (the four virtues) of Qian (Heaven), then there is the "Yuan, Heng, Li, the贞 of the female horse" of Kun (Earth), and only then can the gentleman speak of "there is something to go toward."

攸者，安也，久也；往者，進也。上言乾坤之“元亨利貞”，乃天地之道，循環而無端者也。而君子以參贊天地，乃進化而不已者也。故曰“有攸往”。與近世哲學家所謂天行之往復為循環線，人治之進化為螺旋線，其理正相吻合。以下六十四卦皆根此立言，以明人事之是非得失而定吉凶。

"Yu" means to be secure and enduring, "wang" means to advance forward. The "yuan heng li zhen" of Qian and Kun mentioned earlier represent the way of heaven and earth, which is cyclical and continuous without beginning or end. However, the gentleman's participation in the nurturing of heaven and earth is a constant process of advancement, hence it is said "there is a proper direction to go." This aligns with the modern philosopher's statement that "the movement of heaven is a circular cycle, while human governance is a spiral ascent." All sixty-four hexagrams are based on this principle, used to explain the right and wrong of human affairs and to determine fortune and misfortune.

自讀者將此重要之經文滑口讀過，宋人不得其解，更以君子二字為指筮者而言。於是全《易》，《彖》、《象》，皆索然毫無生氣。孔子之《大象》所謂“君子以”者，亦味同嚼蠟矣。

Since readers have lightly passed over this most important passage, the Song scholars found it difficult to understand, so they simply took the term "junzi" to mean the person performing the divination. As a result, the entire Zhou Yi along with the Commentary on the Judgment and the Image Commentary have become dull and lifeless; even the "junzi yi" phrases in Confucius' Great Image Commentary read like tasteless wax.

“坤利西南得朋，東北喪朋”二語，註解不一。王肅以下，大概以朋為陰類，西南離巽兌皆陰卦，故“得朋”。東北震坎艮皆陽卦，故“喪朋”。以喻女子在室得朋，猶迷而失道；出嫁喪朋，乃順而得常。陰必從陽，離喪其朋類，乃能成化育之功，而有安貞之吉。史徵、崔憬，及程朱《傳》、《義》之解釋，大略如此。其於文義，終覺牽強。言虞氏學者，以納甲為言。以坤之得朋，為月之得明，則以朋為陽矣。辛齋以為欲解釋此二語，必先定朋字之確詁。究竟指陽說，抑指陰言？

The hexagram statement of the "Kun" hexagram, "In the southwest we gain companions, in the northeast we lose companions," has had various interpretations by commentators. Since Wang Su of the Wei dynasty, most have regarded "companions" as referring to like elements of yin. The hexagrams associated with the southwest direction, Li (Fire), Xun (Wind), and Dui (Lake), are all yin hexagrams, hence called "gaining companions"; those in the northeast direction, Zhen (Thunder), Kan (Water), and Gen (Mountain), are yang hexagrams, hence called "losing companions." This is used as an analogy for a woman who, while unmarried and living at home, is with her peers, which is called "gaining companions," yet this is seen as straying from the right path; when she marries and leaves her peers, which is called "losing companions," she becomes gentle and conforms to the norm. Yin must follow yang, and by abandoning her own kind, she can achieve the function of nurturing all things, thus resulting in the auspiciousness of "safety and sincerity." The explanations of Tang dynasty scholars such as Shi Zheng and Cui Jing, as well as Cheng Yi's "Yichuan Commentary on the Changes" and Zhu Xi's "Original Meaning of the Zhou Changes," largely follow this approach, but when compared with the literal text of the classic, they still seem forced. Those who follow Yu Fan's school of thought, however, reinterpret the statement using the "Najia" system, interpreting "gaining companions" as the moon receiving light, thus making "companions" refer to yang. Hang Xinzhai believes that to make sense of these two sentences, one must first determine the exact meaning of the character "companions": does it refer to yang or yin?

按西南固坤之本位，坤中爻二三四為益坤(益卦二三四爻為坤)，三四五為損坤(損卦二三四爻為坤)。故損之五，益之二，皆曰“十朋之龜”。此十朋，即《坤·象》“得朋”“喪朋”之朋也。而損之六三，曰“三人行則損一人，一人行則得其友，”以損之義為損下益上。損泰下卦之三，以益上卦之上，泰變為損，下乾(乾，子丑寅三人)去其一爻，故曰“三人行則損一人”。損此一爻以益坤上，雖成損，而上與三仍得陰陽相應，故日“則得其友”。據此以觀，則陰以得陽為朋，陽以得陰為友，其例甚明。

His analysis begins with the trigram images. The southwest direction is originally the position of the Trigram Earth (Kun); and the Trigram Earth has another source: the Trigram Increase (Yi) with its second, third, and fourth lines forms the Trigram Earth, and the Trigram Decrease (Sun) with its third, fourth, and fifth lines also forms the Trigram Earth. Therefore, the line statements of the sixth line of the Trigram Decrease and the second line of the Trigram Increase both mention "ten tortoises," and the "ten friends" in this context refers to the "friends" mentioned in the "Tuan" statement of the Trigram Earth. Now looking at the third line of the Trigram Decrease: "If three people walk, one is lost; if one walks, he gains a friend." The meaning of the Trigram Decrease is to reduce the lower trigram to increase the upper trigram: by removing the third line of the lower trigram Tai, it is added to the top line of the upper trigram, transforming Tai into Sun. Originally, the lower trigram was Heaven (Qian), which corresponds to the stems Zi, Chou, and Yin, matching the "three people." Now one line is removed, hence "three people walk and one is lost." This line is added to the upper trigram Earth (Kun), so although the trigram becomes Sun, the top line and the third line still correspond in yin and yang, hence "then he gains a friend." From this we can see that when yin receives yang, it is called "friend," and when yang receives yin, it is called "friend" as well. The principle is clear. This is the key point where his interpretation differs from the old commentaries: the old commentaries interpreted "friend" as a kind of yin, but he deduced from the line statements of the Trigrams Decrease and Increase that "friend" must refer to yang.

而《坤·彖》之“朋”可得言矣。坤方於十二辰為未申之位，於消息卦為否為遁。否下卦坤，故“先迷”。上卦乾，故“後得主”。坤間辰六爻，未巳卯逆行，自西至南，由遁至乾，皆陽爻日增，故曰“西南得朋”。自乾以後，而東而北，夬壯泰臨復。陽爻遞減，故曰“喪朋”。至戌亥歸坤，純陰無陽，朋喪盡矣。更逆行至酉，為坤之終位(兌酉數十，十亦為終)。值兌之正位，兌九四之喜有慶也。故曰“乃終有慶”。

Once the grammatical meaning is established, the word "friend" in the "Tuan" statement of the "Kun" hexagram makes sense. The "Kun" hexagram is located in the western-southwest direction, corresponding to the Earthly Branches "Wei" and "Shen," and in the twelve changing hexagrams, it corresponds to "Pu" and "Dun." The lower trigram of "Pu" is "Kun," so the hexagram statement says "first being lost"; the upper trigram is "Qian," so it says "later obtaining a master." The six lines of the "Kun" hexagram correspond to the Earthly Branches "Wei," "Si," and "Mao" in reverse order, moving from west to south, and the hexagram image progresses from "Dun" to "Qian," with the number of yang lines gradually increasing, hence "friendship is found in the southwest." After "Qian," moving east and north, the sequence is "Gua," "Da Zhuang," "Tai," "Lin," and "Fu," with the number of yang lines gradually decreasing, hence "friendship is lost." When reaching "Xu" and "Hai," they return to "Kun," which is entirely yin with no yang, and friendship is completely lost. Reversing again to "You," this is the final position of "Kun" ("Dui" corresponds to "You," and its number is ten, which signifies the end), and it coincides with the proper position of "Dui." This matches the "Nine in the Fourth" line of "Dui" saying "there is joy," hence the hexagram statement continues with "finally there is celebration."

則自“先迷後得主”以下，可一氣貫串，無一字不腳踏實地矣。至“十朋”之義，原為天一至地十之數，各相有合。在坤言坤，以陰得陽，故曰“十朋”，與前說亦相合也。(以消息言之，“得”者息也，“喪”者消也。得喪者，即消息二字之代名也。以坤消乾至東北而乾陽消盡，反為純坤。喪朋之為消陽，可無疑義矣。)

According to this, the hexagram statements from "First losing then gaining the master" onwards can be connected in a continuous manner, with no single character left hanging without a concrete meaning. As for the meaning of "ten friends," it originally refers to the set of numbers from heaven one to earth ten, paired two by two with each having a corresponding match; in the context of the Hexagram Kūn, it refers to the attainment of yang by yin, hence called "ten friends," which also fits perfectly with the previous explanations. Hang Xinzhai added a comment saying: if viewed from the perspective of the message hexagrams, "gaining" is "rest," meaning the growth of yang energy; "losing" is "decline," meaning the retreat of yang energy; the two characters "gaining" and "losing" are actually substitutes for the two characters "message" and "decline." Using the Hexagram Kūn to decline the Hexagram Qián, when reaching the northeast direction, the yang lines of Qián are completely declined, and the entire hexagram becomes pure Kūn. Thus, "losing friends" is indeed the decline of yang, and there is no doubt about this.

《坤·初六》：“履霜堅冰至”。舊說尚無悖於義，惟以“堅冰”二字為疑。於是臆說紛紜，妄相揣測。而於聖人立言之本旨，相去愈遠矣。須知此爻乃坤卦初爻，乃六十四卦陰爻之第一爻，亦即以陰消陽之第一爻也。剛柔始變，陰陽大化根本所自立之初，豈可輕易忽略看過？周公繫艾，鄭重言之曰“履”。履者何？踐履也。以“履”冠六十四陰爻之初，以明人生涉世之初步也。

The line statement of the first line of the Hexagram Kūn says, "When you walk on frost, you know ice is coming." Previous interpretations have not entirely deviated from the meaning, but they have doubted the word "ice," leading to many speculative interpretations. These guesses have only moved further away from the original intention of the sage. We must realize that this line is the first line of the Hexagram Kūn, which is the first line among all the yin lines in the sixty-four hexagrams. It is also the first line where yin begins to overcome yang. Here the transformation between hardness and softness starts, and the fundamental principle of yin and yang is established. How can we lightly dismiss this? The Duke of Zhou attached this line statement with great seriousness, using the character "履" ("to walk"). What does "履" mean? It means to walk with firm steps, to tread the ground. By placing the character "履" at the beginning of all the yin lines in the sixty-four hexagrams, it clearly points out the first step one takes in entering the world.

離卦之初曰“履錯然”，以殿《上經》，以示有始必有終。兩“履”字遙相呼應，非泛文也。孔子韋編三絕，深能契合文周之心，故《繫傳》於三陳九德，獨舉一履。再三反覆，推勘盡致。以明立德之本。雖僅舉九卦，而六十四卦可以意推之矣。故“履”之一字，即以為全《易》之綱領，為聖人以《易》立教精義之所在，亦無不可也。豈可輕易忽略看過哉！

In correspondence with this, the line statement of the initial line of the "Li" hexagram says, "To tread in disorder," which is used to conclude the Upper Canon, indicating that there must be an end to any beginning. The two instances of the character "履" (tread) echo each other from beginning to end, clearly not mere incidental words. Confucius, having studied the "Zhou Yi" so thoroughly that he wore out the thongs of his satchel, deeply understood the intent of King Wen and the Duke of Zhou. Therefore, in the "Great Treatise" section of the "Xici Zhuan," the part discussing "three presentations and nine virtues" uniquely places the "Lv" hexagram first, elaborating it repeatedly and thoroughly exploring the principle until its full meaning is revealed. This is done to clarify the fundamental aspect of establishing virtue. Although only nine hexagrams are mentioned there, the principles of the sixty-four hexagrams can be inferred from them. Therefore, considering the character "履" as the main idea of the entire "Zhou Yi" and as the essential meaning of the sages' teaching through the "Yi" is not unreasonable. Such an important character, how could it be easily overlooked!

“堅冰至”，原非坤初爻之候，乃周公以繫於初爻者。雖曰防微杜漸之意，然實《周易》之一種特別筆法，學者更不可不知也。陽順陰逆，坤乃陰卦之宗。故聖人繫辭，皆用逆筆，特由“至”字反說到“初”。觀乾曰“元亨利貞”，坤曰“元亨利牝馬之貞”，其文氣亦皆一順一逆。孔子贊坤，亦以“至”字開口，真能與文王周公心心相印者矣。觀象玩辭，不可不於此等處加之意也。

The time referred to by "坚冰至" does not originally belong to the first line of the Hexagram坤 (Earth). It was intentionally attached by the Duke of Zhou. Although old interpretations viewing it as a warning against neglecting small matters are correct, this is also a special writing style in the Zhou Yi. Those studying the Yi should be aware of it. The movement of yang is smooth, while that of yin is reverse. Since坤 is the master of all yin hexagrams, the sage used reverse expressions in its commentary. It deliberately starts from the result "至" and goes back to the beginning "初". For example, the Qian hexagram says "元亨利贞", while the坤 hexagram says "元亨利牝马之贞". The style is one smooth and one reverse. When Confucius wrote the Commentary on the Judgment for the坤 hexagram, he began with the word "至" in "至哉坤元", truly reflecting the mind of King Wen and the Duke of Zhou. When observing the hexagram and contemplating the line statements, one must pay special attention to such points.

《坤·六二》“習”之一字，亦《周易》最要之眼目也，亦不可忽略看過。初曰“履”，以明人生涉世之始也。二曰“習”，以明涉世後必至之一境也。繫接上文，一氣而來。霜猶履也，堅冰至則已習矣。人之生性相近也，習則遠矣。善惡分途，積微成著，無不由習之一字而來。聖人慎所習，惟立教以濟之，故坎特著曰“習坎”(坤二爻坎位也)。孔子《大象》曰“君子以常德行習教事”，而《論語》曰“學而時習之”，此皆善用其習以立人道者也。

The character "xi" in the second line of the "Kun" hexagram is also one of the most important elements in the "Zhou Yi," and should not be overlooked. The first line mentions "lu," highlighting the beginning of a person's entry into the world. The second line mentions "xi," indicating the inevitable state one enters after becoming involved in the world. The meaning of these two lines continues in a connected manner: stepping on frost is still "lu," but when solid ice forms, it becomes "xi." Human nature is originally similar, but once habits are formed, they become very different; good and evil then diverge, accumulating from small beginnings into obvious distinctions, and all of this comes from the character "xi." The sage understands the danger of habits and can only remedy this through education, so the "Kan" hexagram specifically names its hexagram "Xi Kan" ("Practice of Difficulty"), as the second line of the "Kun" hexagram is precisely in the position of the "Kan" hexagram. Confucius in his "Great Image Commentary" says, "The superior man uses constant virtue and practices teaching and affairs." The opening of the "Analects" says, "Learning and reviewing it from time to time," which are examples of using "xi" to establish the way of human beings.

自世運遞遞降，天德王道已成故事(蠱，故事也)。後世雄才大略之君相，恆利用“習”之一字，為操縱斯民之具。非常之原，黎民懼焉。乃施之以漸，今習而安之，則習非且可以勝是矣！(如革命之說，初聞者無不掩耳卻走，駭為非常。乃一再試之輿論，和之。曾幾何，時昔之掩耳卻走者，或且醉心從之矣。此即習之說也。近世歐美大政治家，欲有所設施，恆先建議以造成輿論，使人民習見習聞而後行之。舉重若輕矣。)

However, the world's circumstances have gradually declined through generations, and the Heavenly Virtue and the Way of the King have long become outdated matters (the image taken from the "Guzh" hexagram precisely represents accumulated old practices). Later rulers and ministers with great talent and ability often reversed this, using the concept of "habit" as a tool to control the people. Whenever extraordinary measures were taken, the people at first were always fearful; thus, they would gradually implement them step by step, allowing people to become accustomed to them and accept them as normal, eventually leading to the wrong becoming dominant over the right. Hang Xinzhai, in his own notes, gave an example: when the idea of revolution was first proposed, those who heard it would all cover their ears and flee, shocked and horrified; but after repeated trials and endorsements by public opinion, soon those who had once covered their ears and fled were even沉迷 and followed it, which is precisely the effect of "habit." In modern times, great politicians in Europe and America also often begin by proposing bills to create public opinion, allowing the people to become accustomed to seeing and hearing about it before implementing it, thus making heavy tasks seem light.

然聖人之化民成俗，尚道德不尚事功。操縱之術，非所屑焉。端民習於就學之始，薰陶而善良之，化行而俗美，則施之於事。不習自無不利，此豈一朝一夕之故哉！周公繫“習”於坤之二爻，以承“履霜堅冰”之後，其用意至深遠矣！

But the sage cultivates the people and shapes the customs, valuing morality rather than achievements. Such manipulative tactics are beneath him. The sage's approach is to correct the people's learning from the very beginning of their schooling, using gradual influence to guide them toward goodness. Once education is widely implemented, the customs will naturally become refined. Only then can governance be applied. At that point, there is no need for deliberate practice, and everything will naturally proceed smoothly. How could such a thing be achieved in a day or two! The Duke of Zhou associated the character "习" with the Second Line of the "Kun" hexagram, following "Footsteps of frost, ice forms," intending something profoundly significant.

乾，天行也。坤，地道也。天運於虛，地徵諸實。故乾以言道，坤以言德。道運於虛，德徵諸實也。詳玩兩卦《彖》、《象》，乾曰“元亨利貞”，坤則曰“元享利牝馬之貞”。全卦六爻，乾則象以“潛見躍飛亢”及“乾乾”“惕若”，皆用虛筆。而坤則曰“履”，曰“習”曰“可貞”，曰“括囊”曰“黃裳”，曰“血”，筆筆皆徵實矣。

The hexagram Qian discusses the movement of heaven, and the hexagram Kun discusses the principles of earth. Heaven operates in the void, while earth manifests in the tangible, so Qian is used to explain "the Way" and Kun to explain "virtue." The Way operates in the void, while virtue must be verified through actual deeds. Looking closely at the Commentary on the Judgment and the Image Commentary of these two hexagrams: Qian speaks of "origin, prosperity, advantage, and uprightness," while Kun adds a specific image, "origin, prosperity, advantage, and the uprightness of a mare." The wording of the six lines is also similar: Qian uses "hidden," "emergent," "leaping," "flying," "excess," and "diligently striving" and "cautious vigilance," all abstract expressions; Kun, however, uses "walking," "practice," "suitable uprightness," "binding the bag," "yellow undergarment," and "blood," each phrase grounded in reality.

聖人之筆，妙極神化。孔子贊《易》，為衰世之救濟，略天道而言人事，由下學以希上達。故首重立德，由立德以明道。然明道與立德，均非辭無以見焉。是以《文言》曰“修辭立其誠”。上下兩篇之《繫辭》，又各為之傳，又特表而出之曰“以言者尚其辭”，又曰“所樂而玩者爻之辭焉”，皆教人以學《易》之方也。卦有小大，辭有險易，言小大而陰陽可知，言險易而順逆虛實可知。學者必潛心玩索，始能微顯闡幽。茲略舉乾坤兩卦之字法，餘卦可類推，而《十翼》之辭亦可類及矣。

The precision with which the sage writes is so subtle that it seems supernatural. Confucius composed the "Commentaries on the Changes," originally intending to seek relief for a time of decline and disorder, so he omitted discussions on heavenly principles and focused more on human affairs. He started from practical learning to pursue higher understanding, thus emphasizing moral cultivation first, and then using moral cultivation to explain the Way. However, whether seeking to understand the Way or cultivating virtue, it cannot be expressed without words. Therefore, the "Commentary on the Literary Changes" says, "Refine your expressions and establish sincerity." Both the Upper and Lower "Great Treatises" specially emphasize "those who speak should value words," and also say, "what they enjoy and play with is the words of the hexagrams," all teaching the way to study the Changes. Hexagrams have small and great ones, and their words have dangerous and easy ones: speaking of small and great allows one to understand yin and yang; speaking of danger and ease allows one to understand order and disorder, emptiness and reality. Those who study the Changes must deeply ponder and explore, so as to move from the obvious to the subtle and reveal hidden meanings. Here we only briefly mention the use of words in the hexagrams of Qian and Kun; the other hexagrams can be understood in the same way, and the writings of the Ten Wings can also be compared similarly.

《乾·彖》曰：“首出庶物，萬國咸寧。”《坤·彖》曰：“含弘光大，品物咸亨。”此以贊乾坤化育之功，皆陰陽合德，交相為用。乾用九以變坤，坤用六以承乾。僅一咸字，已將乾坤兩卦綰合，有天地絪縕之妙。咸者上兌下艮之卦，乾在坤中，所謂二氣感應以相與，天地感而萬物化生者也。

The Commentary on the Judgment of the Qian hexagram says, "It leads all creatures and brings peace to all nations." The Commentary on the Judgment of the Kun hexagram says, "It contains and expands, and all things are able to flourish." Both sentences praise the nurturing power of Qian and Kun. Yet both are based on the harmonious union of yin and yang, and their mutual use: Qian transforms into Kun through the use of all nines, and Kun receives Qian through the use of all sixes. The single character "xian" (all) connects the Qian and Kun hexagrams together, embodying the subtle intermingling of the energies of heaven and earth. "Xian" itself is the hexagram composed of Dui above and Gen below, and its structure is precisely Qian within Kun. This is what the Commentary on the Judgment of the Xian hexagram says: "The two energies respond to each other," and "Heaven and earth feel each other and all things are generated."

夫庶物與萬國，皆坤象焉。乾元首出，久道化成。於是乎有咸寧之慶。弘與大，皆乾象焉，而坤能含之光之(凡陽必得陰而始光。如日，必遇地與月，或其他能受光之質，而光始見也。)，於是乎品物有咸亨之象。然而乾之咸寧，寧於坤焉。而坤之咸亨，亨於乾焉。交互錯綜，妙合無間。神哉化工之筆也！至臨之“咸臨”，姤之“咸章”，皆以一“咸”字以形容陰陽構合之妙。臨數一二，一二為子丑，子丑陰陽始合。姤數七八，七八為午未，午未天地相遇，為陰陽中合。與乾坤兩卦之“咸”字，互相印證，互相發明者也。

Looking at them separately: "Shu wu" and "wan guo" both belong to the image of the Hexagram Kun. The principle of the Hexagram Qian, which is at the beginning and leads to enduring and nurturing, thus brings about the auspiciousness of "xian ning" (peace and stability). "Hong" and "da" both belong to the image of the Hexagram Qian, while the Hexagram Kun can contain and illuminate them. (For any yang, it must be combined with yin to show light. For example, the sun must meet the earth, the moon, or other objects that can receive light, for the light to be seen.) Thus, all things have the image of "xian heng" (harmonious and prosperous). However, the "xian ning" of the Hexagram Qian is actually peace resting upon the Hexagram Kun; the "xian heng" of the Hexagram Kun is actually prosperity arising from the Hexagram Qian. They interact and interweave in a perfect and seamless way, truly a marvel of nature. As for the "xian lin" in the line statement of the Hexagram Lin and the "xian zhang" in the line statement of the Hexagram Guo, they both use the character "xian" to describe the subtlety of the union between yin and yang. The Hexagram Lin corresponds to the numbers one and two, which correspond to the earthly branches Zi and Chou, the very beginning of the union between yin and yang. The Hexagram Guo corresponds to the numbers seven and eight, which correspond to the earthly branches Wu and Wei, the very point where heaven and earth meet and yin and yang meet halfway. These instances of the character "xian" along with the "xian" in the Hexagrams Qian and Kun can be used to confirm and illuminate each other.

《咸·彖傳》曰“咸，感也。(舊說：咸感無心，兌說無言。無心之感，其感始至。無言之說，其說乃大。)二氣感應以相與”。蓋物理必異性者乃能相感，而善感者莫如人。人之善感者，莫如男女，尤莫如少女少男。故以少女少男之卦名之曰咸。而咸卦六爻，又均取象於人身，則以感覺之最靈且捷者，更莫過於一身焉。

The Commentary on the Judgment of the Hexagram Xian says: "Xian means感应 (response). ... Two energies respond to each other and interact." (Old interpretations point out that the character "Xian" lacks a "heart" component compared to "gan" (response), and the character "Dui" lacks a "speech" component compared to "shuo" (speech); without a heart, the response is most sincere; without speech, the joy is most extensive.) In general, physical phenomena require things of different natures to respond to each other, and among all things, humans are most adept at responding. Among humans, the most sensitive to sensation are men and women, especially young girls and young boys. Therefore, the Book of Changes takes the hexagram with the young girl Dui above and the young boy Gen below, and names it Xian. Moreover, all six lines of the hexagram Xian are taken as symbols of the human body, because nothing is more sensitive and quick in sensation than one's own body.

六爻初拇，二腓，三股，五脢，六輔頰舌。四當為心，乃不曰心，而曰“憧憧往來”。以心不可見，且咸之感，本無心也。卦爻取象之精細，可謂剖拆毫芒。至義蘊之妙，更有非言語所能形容。細玩逐爻之辭，見深見淺，必有所得焉。(物理：異性則相感相吸。兩性既感而吸合，則原有之兩性相消而等於無。故咸又為無。又咸從戌從口，戌亥數無。先天卦艮居戌口，與兌相對，故兌艮為咸，而咸為無。後天卦乾居戌亥，故乾亦為無。)

The six lines of a hexagram correspond to specific parts of the body: the first line (initial six) represents the big toe, the second line (six in the second) represents the calf, the third line (nine in the third) represents the thigh, the fifth line (nine in the fifth) represents the back muscles, and the sixth line (six at the top) represents the cheek and tongue. In order, the fourth line (nine in the fourth) should represent the heart, but the line statement does not mention the heart, instead saying "chong chong wai lai" (a state of confusion and coming and going), because the heart is invisible, and thesympathetic response (response or mutual influence) of "Xian" (咸) is originally a feeling without a specific object. The detailed imagery used in the hexagram lines can be analyzed down to the finest detail; as for the profound meaning contained within, it is beyond words, and one can only carefully contemplate each line's wording, whether seeing it deeply or shallowly, and eventually gain some understanding. Hang Xinzhai added in his commentary: from a physical perspective, opposite elements attract and respond to each other; once the two elements have responded and combined, their original dual nature cancels each other out and becomes nothing. Therefore, "Xian" (咸) also has the meaning of "nothing." Furthermore, looking at the character "Xian," it is composed of "Xu" and "Kou." The numbers associated with Xu and Hai are "nothing." In the Earlier Heaven arrangement, the trigram "Gen" (Geng) is located at Xu, facing "Dui" (De), so "Dui" and "Gen" together form "Xian," and thus "Xian" represents "nothing." In the Later Heaven arrangement, "Qian" (Qian) is located at Xu and Hai, so "Qian" also represents "nothing."

“大哉乾元！萬物資始”，“至哉坤元！萬物資生”。此言盈天地間之事事物物而約其大數，即上下二篇之策，萬有一千五百二十以當萬物之數者是也。《乾·彖》曰“品物流形”，《坤·彖》曰“品物咸亨”。品物者，物之既成，可以類而別之，故曰“品”。“品物流形”者，乾流坤形也，坎也。“品物咸亨”者，坤承乾亨也，離也。可見乾坤二《彖》，無一字不互文見義者也。

The Commentary on the Judgment of the Qian hexagram says, "How great is the Qian Yuan! All things draw their origin from it." The Commentary on the Judgment of the Kun hexagram says, "How profound is the Kun Yuan! All things draw their sustenance from it." Here, "all things" refers to the generalization of everything existing between heaven and earth as a single number, which is the total of the counts in the Upper and Lower Classics mentioned in the Great Treatise. The number is eleven thousand five hundred and twenty, used as the number representing all things. Furthermore, the Commentary on the Judgment of the Qian hexagram also says, "The myriad things flow into form," while the Commentary on the Judgment of the Kun hexagram says, "The myriad things all achieve success." The term "myriad things" refers to things that have already taken form and can be classified into categories, hence the term "category" or "kind." "The myriad things flow into form" signifies the movement of the Qian energy and the shaping by the Kun, symbolizing the trigram Kan. "The myriad things all achieve success" indicates the Kun receiving the Qian and achieving success, symbolizing the trigram Li. Thus, every word in the Commentaries on the Judgment of the Qian and Kun hexagrams is interdependent and mutually explanatory.

至“首出庶物”，不曰“萬”，不曰“品”者，乃合萬與品而兼言之，對於首而言也。通言萬物，未分類也。物而曰品，則“方以類聚物以群分”矣。既類聚以群分，則必有一焉超乎其類統乎其群者。即首出之義，而不為首者皆庶也。故曰“庶”者，對於首而言也。不曰“首出萬物”，“首出品物”，而必曰“首出庶物”。可見聖人修辭之精，無一字虛設，無一字苟且焉。

As for the phrase "shou chu shu wu," it does not say "wanwu" (all things) or "pinwu" (classified things), but instead uses "shu wu" (common things). This combines the meanings of "wan" (ten thousand) and "pin" (categories), and it is in contrast with the character "shou" (first). To refer generally to "wanwu" is to speak without classification; to call them "pinwu" is as the "Xici Zhuan" says, "things are grouped by their kind, and objects are categorized by their class." Once things are grouped and categorized, there must be one that transcends the category and leads all others, which is the meaning of "shou chu" (first to emerge). Those that are not in the leading position are all called "shu" (common). Therefore, using the word "shu" is precisely in contrast with "shou." It does not say "shou chu wanwu" or "shou chu pinwu," but insists on "shou chu shu wu." This shows the meticulousness of the sage's rhetoric; no word is superfluous, and no word is used carelessly.

《下經》之損益，猶《上經》之泰否也。《上經》始乾坤，至小畜履凡十卦。陰陽爻各三十，而繼之以泰否，為乾坤變。《下經》始咸恆至蹇解亦十卦。陰陽爻各三十，而繼之以損益。咸恆為乾在坤中，損益乃坤在乾中也。天行人事，均不外乎否泰往來損益盈虛而已。舊說泰損下益上，(損下卦之九三以益上卦之上六)則成損。否損上益下，(損上卦之上九以益下卦之六三)則成益。然則否泰往來，損益盈虛，其所以轉移變化之機關，俱在三爻。三爻者，人爻也。以明否泰損益皆在於人，而天地無與焉。天行之否泰，人得而轉移之。人事之否泰，天地無如何也。

The two hexagrams "Xin" and "Yi" in the Lower Classic are equivalent in status to the two hexagrams "Tai" and "Pou" in the Upper Classic. The Upper Classic begins with "Qian" and "Kun," proceeding through "Xiao Xu" and "Lv," totaling ten hexagrams, with thirty yao of yin and thirty yao of yang. Following these are "Tai" and "Pou," which are variations of "Qian" and "Kun." Similarly, the Lower Classic starts with "Xian" and "Heng," proceeding through "Jian" and "Jie," also totaling ten hexagrams, with thirty yao of yin and thirty yao of yang. Following these are "Xin" and "Yi." "Xian" and "Heng" represent "Qian" within "Kun," while "Xin" and "Yi" represent "Kun" within "Qian." The operation of heaven and the affairs of the world cannot escape the alternation of "Tai" and "Pou" and the waxing and waning of "Xin" and "Yi." According to old interpretations, "Tai" hexagram involves reducing the third line of the lower trigram to increase the sixth line of the upper trigram, transforming into "Xin"; "Pou" hexagram involves reducing the sixth line of the upper trigram to increase the third line of the lower trigram, transforming into "Yi." Thus, the transformation between "Tai" and "Pou," and between "Xin" and "Yi," hinges entirely on the third line. The third line is the human line, indicating that "Tai," "Pou," "Xin," and "Yi" all depend on human actions and have nothing to do with heaven and earth. The operation of heaven's Tai and Pou, can be altered by human effort; the Tai and Pou of human affairs, however, are beyond the control of heaven and earth. This is the key point of Hang Xinzhai's argument—he seeks to transfer the responsibility for disorder and order from heavenly fate to human affairs, hence emphasizing that the pivot lies in the human line rather than in heaven and earth.

孔子於乾之九三，反覆申明其義。曰“與時偕行”，在損曰“與時偕行”，在益曰“與時偕行”。否泰者時也，損益者人也。與時偕行，則否可轉泰。不能與時偕行，而與時偕極，則無泰而非否矣。與時偕行者何？即所謂“終日乾乾，乾行”者是也。然而經文於損，獨曰“有孚元吉”者何也？曰“損上益下”，其理近而易明，其事順而易行。故否泰之轉移尚易，然否轉為泰，泰復轉為否，泰否往復循環不已。又烏能日進無疆？

Confucius repeatedly emphasizes this point in the "Wenyan" section of the "Qian" hexagram's Nine in the Third, saying "to move in harmony with the times." He also mentions "to move in harmony with the times" in the "Commentary on the Judgment" of the "Sun" hexagram and again in the "Commentary on the Judgment" of the "Yi" hexagram. "Po" and "Tai" belong to "time," while "Sun" and "Yi" belong to "human action." If one moves in harmony with the times, "Po" can be transformed into "Tai"; if one does not move in harmony with the times and instead follows the trend to an extreme, then there will be no place of "Tai" and everywhere will be "Po." What does "to move in harmony with the times" mean? It refers to the continuous effort described in the "Qian" hexagram as "to be diligent day and night." However, the classic text only mentions "having sincerity and original good fortune" in the "Sun" hexagram. Why is that? Because the principle of "reducing from above to benefit below" is simple and easy to understand and carry out, so the transformation between "Po" and "Tai" is relatively easy. However, "Po" transforms into "Tai," and "Tai" turns back into "Po," and the cycle between "Tai" and "Po" continues without end. How then can we talk about continuous progress without bounds?

吾國數千年曆史皆一治一亂，循環往復致人事永無進步，不能與世界列強相抗衡者，正以吾人只知以益求益，而不能以損求益。故極其功只能轉否，而不能化否。能化否，則否變同人。同人而進於大有，世運始有進步。始避泰否之循環線而入於傾否之螺旋線，然後得合於進化之正軌也。故孔子又於益之《彖傳》申明之。曰“益動而巽，日進無疆”。此損益之大道，(天行先泰而後否，人事先損而後益)先聖之象已明示之。

The history of our country for thousands of years has always been characterized by cycles of peace and chaos, with human affairs never making real progress, and thus unable to compete with the world's major powers. The root of the problem lies in our tendency to pursue gain only through "benefit" (益), without understanding the necessity of "loss" (损) in order to achieve gain. Therefore, even when the effects of such efforts reach their peak, they can only lead to a reversal of the unfavorable situation (转否), but not a transformation of it (化否). If we can transform the unfavorable situation, then the hexagram of "Opposition" (否) would become "Harmony with Others" (同人); from there, we could progress to "Great Possession" (大有), and the world would indeed make real progress, escaping the cycle of alternation between peace and chaos (泰否循环), and entering an upward spiral, such as the line "Inverting Opposition" (倾否) in the upper ninth line of the hexagram of "Opposition." Only then would we be on the correct path of evolution. Therefore, Confucius explicitly states in the "Commentary on the Judgment" (彖传) of the hexagram of "Benefit" (益): "Benefit is dynamic and compliant, advancing daily without limit." This is the great principle of gain and loss (天道运行是先泰而后否, 人事经营则应先损而后益). The ancients, through the hexagrams, have clearly indicated this. What he seeks to refute is the ingrained habit of seeking only benefit without understanding the necessity of loss. The evidence he relies on is the line "Inverting Opposition" (倾否) in the upper ninth line of the hexagram of "Opposition" and the statement "Advancing daily without limit" (日进无疆) from the "Commentary on the Judgment" of the hexagram of "Benefit."

孔子贊《易》，又一再言之。乃三千年來竟無一人能察聖人之象，昧聖人之言，以求日進而無疆，坐令錦繡之乾坤，困於一治一亂之輪迴，而無發展之機，不亦深可痛哉！辛齋何人，於古先大師大儒之學，會不能仰望其肩背，詎謂能發前人所未發，明前人所未明，以補數千年之罅漏？或者時事相催，劫運當復，天誘其衷，困諸囹圄，導諸良師，開其一隙之明，畀引其端。庶聖意不致終晦，後人得藉此發揮而光大之，以臻世界之大同，未可知也。九仞之山，成於螘垤。辛齋其亦一蟻而已。

Confucius wrote the "Commentaries on the Book of Changes," and he repeatedly spoke about this matter. However, for three thousand years, no one has been able to understand the sage's hexagrams or grasp the sage's words, to pursue continuous progress without limit. Instead, the splendid mountains and rivers have been trapped in the cycle of peace and chaos, without the opportunity for development. Is it not deeply regrettable? Hang Xinzhai modestly said: Who am I? I have not even been able to look up to the shoulders of the great scholars and sages of the past, how dare I claim to have discovered what others have not discovered or clarified what others have not clarified, to fill the gaps of thousands of years? Perhaps it is due to the urgency of the times and the turning of the calamitous era, that Heaven has guided my aspirations, putting me in prison and bringing me good teachers who have enlightened me, opening a small ray of light and handing over this thread to me. Perhaps the intention of the sages will not ultimately remain obscure, and later generations may be able to use it to develop and expand, achieving world-wide harmony. This is also possible. A mountain nine li high is built up by small heaps of earth like an ant's hole. I, Hang Xinzhai, am no more than one ant among them.

八卦播五行於四時，木金土各二，惟水與火各一。震糞木有二也，兌乾金有二也，坤艮土有二也，惟離火坎水各一。先儒謂離坎居中，中不可有二，故水火均一也。又謂木金土皆有剛柔，惟水火無剛柔可分，故不能有二。然以十干分配五行，則水火木金土各有二。以十二辰分屬五行，則水火木金各有二，而土有四，則水火不二之說又不可通。

The eight trigrams distribute the five phases across the four seasons, with wood, metal, and earth each having two trigrams, while water and fire each have only one: The trigrams Zhen and Xun both belong to wood, hence wood has two; Dui and Qian both belong to metal, hence metal has two; Kun and Gen both belong to earth, hence earth has two; only Li belongs to fire and Kan belongs to water, each having only one trigram. Earlier scholars have offered two explanations for this: one says that Li and Kan are in the central position, and since the center cannot have two, water and fire can only each have one; the other says that wood, metal, and earth can be divided into yin and yang, but water and fire cannot be divided into yin and yang, hence they cannot have two. However, when using the ten heavenly stems to match the five phases, water, fire, wood, metal, and earth each have two; when using the twelve earthly branches to match the five phases, water, fire, wood, and metal each have two, while earth has four. In this case, the idea that water and fire cannot have two becomes inconsistent.

辛齋以為八卦於水火，亦各有二，與木金土無異焉。離為火，震為雷，雷亦火也。坎為水，兌為澤，澤亦水也。震為雷，震之一陽出於坎。陰根於陽，《內經》所謂“龍雷之火”，乃真火也。故於十干屬丙，而離火屬丁。兌之一陰麗於離，故曰麗澤兌。陽根於陰，其義取明水於月，乃真水也。於十干屬壬，而坎水屬癸，水火同源，陰陽互根，皆歸本於太一。俗儒未察五行之原理，以卦只有八，而五行之分陰分陽，其數有十，遂無可措置。曲為之解，遂有水火不二之說，而不自知其不可通也。

Hang Xinzhai believes that the Eight Trigrams also contain two instances of water and fire, just like wood, metal, and earth. The Trigram Li represents fire, and the Trigram Zhen represents thunder, which is also fire. The Trigram Kan represents water, and the Trigram Dui represents marsh, which is also water. The Trigram Zhen represents thunder, and its one yang line comes from Kan, which is yang arising from yin, exactly as the "Yellow Emperor's Inner Canon" describes "dragon fire and thunder fire," which is true fire, so it is paired with the heavenly stem Bing. The Trigram Li fire is paired with Ding. The Trigram Dui has one yin line attached to Li, so the Trigram Dui's "Great Image" says "beautiful marsh," which is yin arising from yang, taking the ancient practice of using a vessel to collect moonlight to obtain "bright water," which is true water, so it is paired with the heavenly stem Ren, while the Trigram Kan water is paired with Gui. Water and fire originate from the same source, and yin and yang are interdependent, ultimately returning to "Taiyi." Common scholars fail to grasp the principles of the Five Phases, seeing only eight trigrams, while the Five Phases have ten numbers divided into yin and yang. Therefore, they are unable to reconcile them, and they resort to forced interpretations, creating the idea of "water and fire not being two," without realizing their reasoning is flawed. His argument is based on the fact that the lines of the Trigrams Zhen and Dui come from Kan and Li respectively, so thunder can be paired with Bing fire and marsh with Ren water, thus making the Eight Trigrams and ten heavenly stems correspond perfectly.

八卦坎一，離九，震三，兌七，乾六，巽四，坤二，艮八，乃九宮之數，即洛書數也。後人不得其解，異說紛紜，各執一是，而互相駁難，究莫能得其要領。此由於不知九宮之真諦，無怪其開口便錯也。九宮本於太一，以一行九，如乾坤之周流六虛，分陰分陽，循環無端。一九三七二四六八，即陰陽太少之四位焉。

The Eight Trigrams are paired with numbers: The Trigram Kan is one, Li is nine, Zhen is three, Dui is seven, Qian is six, Xun is four, Kun is two, and Gen is eight. This is the number system of the Nine Palaces, also known as the number system of the Luo Writing. Later scholars failed to understand its principles, leading to various conflicting interpretations, each holding their own view and contradicting others, yet never grasping the essence. This is because they did not understand the true meaning of the Nine Palaces. It is no wonder they made mistakes as soon as they spoke. The Nine Palaces originally come from "Taiyi." With the number one moving around the Nine Palaces, it is like the energies of Qian and Kun circulating through the six lines, distinguishing yin and yang, cycling endlessly without beginning or end. The pairs one and nine, three and seven, two and four, six and eight correspond to the four forms of yin and yang: Yang, Lesser Yang, Lesser Yin, and Great Yin.

陽為氣，陰為形，氣與形有純駁，而太與少別也。一九太陽，純乎氣者也。故坎離居之。二八少陰，純乎形者也。故坤艮居之。三七少陽，氣與形相兼者也。故震兌居之。四六太陰，純乎形亦純乎氣者也，故乾巽居之。(巽為柔木，得氣之初，成形最早。乾為金剛，得氣最純，成形最堅。故柔木燒之而無炭，金剛化之而無質。此所以為太陰，陰極生陽，而玄牝為萬化之根也。)支支節節而解之，一卦一象以求之，其泥而不能通也宜矣。

Heavenly Stems: Jia, Yi, Bing, Ding, Wu, Ji, Geng, Xin, Ren, Gui Earthly Branches: Zi, Chou, Yin, Mao, Chen, Si, Wu, Wei, Shen, You, Xu, Hai Trigrams: Qian (Heaven), Dui (Lake), Li (Fire), Zhen (Thunder), Xun (Wind), Kan (Water), Gen (Mountain), Kun (Earth) Hang Xinzhai explains in his own notes that the last point refers to the fact that Xun is a flexible wood, which receives energy first and takes form first; Qian is a diamond, which receives energy most purely and takes form most firmly. Therefore, flexible wood, when burned, leaves no charcoal, and diamond, when melted, leaves no substance. This is why they belong to the category of Taiyin. When Yin reaches its extreme, it gives rise to Yang, and thus "Xuanpu" becomes the fundamental source of the transformation of all things. If one were to explain each section separately and rigidly match each hexagram to a single image, it would inevitably lead to being confined and unable to understand properly.

《上經》首乾坤，《下經》首咸恆。咸恆天地合體之卦也。泰否損益，亦天地合體之卦也。乾坤合德，見於咸恆。泰否交構(泰否為天地交)，見諸損益。故“天地絪縕，萬物化醇。男女媾精，萬物化生”，贊諸損之六三。天地絪縕，陰陽首交，而物以氣化。男女媾精，雌雄尾接，而物以形化矣。形能奪氣，物既成形，專於形化，而氣不復化，亦致一也。

The Upper Classic begins with the hexagrams Qian and Kun, while the Lower Classic begins with Xian and Heng. Xian and Heng are hexagrams representing the union of heaven and earth. Tai, Pinyin, Shen, and Yi are also hexagrams representing the union of heaven and earth. The harmonious virtue of Qian and Kun is expressed in Xian and Heng; the mutual interaction of Tai and Pinyin (both representing the intermingling of heaven and earth) is expressed in Shen and Yi. Therefore, the passage in the Great Treatise, "Heaven and earth blend together, and all things are transformed into purity; the union of male and female leads to the generation of all things," is the commentary on the sixth line of the third hexagram, Shen. The blending of heaven and earth's energies is the initial meeting of yin and yang, leading to the transformation of all things through energy; the union of male and female is the meeting of male and female forms, leading to the generation of all things through form. Form can take away the function of energy: once things have taken form, they proceed solely through transformation by form, and energy transformation ceases, which is the reason for becoming specialized.

是故天下之物，其初生者無不以氣化，天地之始合也。天地終合，萬物畢具，形成名立，氣為形奪，而氣化者少矣。然終則復始，氣機之流行，仍無少異。即氣化之用終不可絕，不但形之微者仍歸氣化(如無骨之蟲類是也)，即形化者亦或感於氣。而蛻化，而變化(如雀化蛤，魚化雀，沙魚化鹿化虎，人亦有時化虎之類)。生生化化，神妙莫測，皆資始於乾元，資生於坤元，實資於天元一(數學以立天元一御無窮不盡之數，亦此理也)。

Therefore, all things in the world, when they first came into being, were all transformed from qi. That was the stage when heaven and earth first came together. When heaven and earth were fully united, all things had fully formed, their forms were established, and their names were set. At that time, qi was taken by form, and the process of transformation through qi became less evident. However, the cycle continues, and the movement of qi remains the same as before. The function of transformation through qi never ceases. Not only do minute forms still rely on the transformation of qi (for example, creatures without bones), but even those that have already taken form may sometimes be transformed and changed by qi (for example, the ancient saying that a sparrow turns into a clam, a fish turns into a sparrow, a sandfish turns into a deer, then into a tiger, and even humans are said to occasionally turn into tigers). Thus, the continuous process of generation and transformation, which is mysterious and unfathomable, all originate from the beginning of the Trigram Qian, and from the generation of the Trigram Kun. In reality, they all draw upon the "Heavenly Origin One" (the concept of "Heavenly Origin One" in mathematics is used to manage infinite numbers, and it is the same principle).

天元一不用(以不用為用，故其用不窮)，用地元二(一二天地合，三三生萬物)。天元一子，地元二丑，子丑天地始合。絪縕氣化之候，在卦子一復丑二臨。復一小不用(復小而辨於物)，用臨二大(臨下兌。兌數十。十數盈數也。故大。)。故臨之初九、九二，皆曰“咸臨”(咸，乾在坤中，以陰含陽。陽動陰中，陰陽合德。資始資生，二而一矣。)。而乾坤二《彖傳》，孔子皆以一“咸”字形容之。

"The Heavenly Stem 'Jia' (天元一) is not used in itself (using non-use as use, thus its utility is boundless), but it uses 'Yi' (地元二). The combination of one and two represents the union of heaven and earth, and when three and three are multiplied, all things are generated. The Heavenly Stem 'Jia' is paired with the Earthly Branch 'Zi', and the Earthly Stem 'Yi' is paired with the Earthly Branch 'Chou'. 'Zi' and 'Chou' are precisely the beginning where heaven and earth first come together. During the process of mingling and generating qi, in the trigrams, this corresponds to the trigram 'Fu' (复) at the 'Zi' position and the trigram 'Lin' (临) at the 'Chou' position. 'Fu' is one, and its trigram is small and not used (as stated in the 'Great Treatise' (系辞传), 'Fu' is small but discerning in things). What is used is 'Lin', the two, which is called 'great' (the lower trigram of 'Lin' is 'Dui' (兑), and the number of 'Dui' is ten, which is the number of fullness, hence it is called 'great'). Therefore, the line statements of the first and second lines of the trigram 'Lin' both say 'Xian Lin' (咸临). 'Xian' refers to the 'Qian' trigram within the 'Kun' trigram, with yin containing yang; yang moves within yin, and yin and yang combine in harmony, thus the two functions of origin and generation are combined. Both the 'Commentary on the Judgment' (彖传) of the trigrams 'Qian' and 'Kun' also use the character 'Xian' to describe them."

咸臨於初爻，初應四四曰“至臨無咎”，即“至哉坤元”之“至”也。咸臨於二爻二應五，五曰“知臨大君之宜”，即“大哉乾元”之“大”也。乾大坤至，天地之氣，充滿流行，密合無間。天地絪縕，萬物化醇也。一二合生三，天地合生人。一氣而二形一精而二純，子丑二而寅三為人道。在卦為泰，泰為通。天地之氣，以人而通。乾道成男，坤道成女。乾交於坤，坤交於乾，而咸恆夫婦之道立。損益盈虛，相為消息，男女媾精，萬物化生也。故孔子於損之六三爻言之。

"Xian Lin" in the first line, the first line corresponds with the fourth line, and the sixth line of the fourth says "Zhi Lin, Wu Jiu," where "Zhi" is the same as "Zhi Zai Kun Yuan" in the "Zhi." "Xian Lin" in the second line, the second line corresponds with the fifth line, and the sixth line of the fifth says "Zhi Lin, Da Jun Zhi Yi," where "Da" is the same as "Da Zai Qian Yuan" in the "Da." The "Qian" hexagram represents "Da," and the "Kun" hexagram represents "Zhi." The energies of Heaven and Earth are fully present and flow continuously, closely combined without interruption, which is "Tian Di Yin Yun, Wan Wu Hua Chen." One and two combine to produce three, and Heaven and Earth combine to produce human beings; one is energy and two is form, one is essence and two is purity. Zi and Chou represent two, while Yin represents three, and Yin is the way of human beings. In the hexagram, this is the "Tai" hexagram, which means communication: the energies of Heaven and Earth pass through human beings to connect. The "Qian" way produces male, and the "Kun" way produces female; "Qian" interacts with "Kun," and "Kun" interacts with "Qian," thus establishing the way of husband and wife as established by "Xian" and "Heng." "Sun" and "Yi" represent the mutual increase and decrease of fullness and emptiness, which is exactly "Nan Nu Gou Jing, Wan Wu Hua Sheng," so Confucius attached this sentence to the sixth line of the third line in the "Sun" hexagram.

二與四，三與五，全《易》之重要關鍵也。不明乎此，則《象》《彖》終莫得而解。故孔子於“原始要終”一章，特詳言之。然此章文義深奧，學者莫明其妙，甚或不能句讀，因之異說蜂起。易傳燈甚至疑為偽作。是二三四五之說終不能明，故特將此章全文詮釋之。而後剛柔變易之道，始可得言也。《繫傳》曰：“《易》之為書也，原始要終，以為質也。六爻相雜，唯其時物也。其初難知，其上易知。本末也。初辭擬之，卒成之終”。此一節明設卦觀象之法。

The relationship between the second line and the fourth line, as well as between the third line and the fifth line, is a crucial point in the entire Zhou Yi. Without understanding this, the explanations in the Image Commentary and the Commentary on the Judgment cannot be properly understood. Therefore, Confucius particularly elaborates on this in the chapter "Original and Final" of the Great Treatise. However, this chapter is very profound and difficult to grasp, and those studying the Yi often fail to understand its subtleties, even unable to correctly punctuate the sentences, leading to various conflicting interpretations. Even the book "Yi Transmission Lamp" doubts that this chapter is a forgery. As a result, the concepts of the second, third, fourth, and fifth lines remain unclear. Therefore, Hang Xinzhai specially interprets the entire chapter, only then can the principles of change between yin and yang be discussed. The Great Treatise says: "The Yi is a book that traces the origin and considers the end, taking this as its essence. The six lines are mixed together, corresponding to the time and things. At the beginning, it is difficult to know; at the end, it is easy to know. This is the beginning and the end. The initial words are used to imitate, and the final outcome is formed." This passage explains the method of setting up hexagrams and observing their images.

《易》之為書，上下二篇，皆原始要終。《上經》以乾坤始，坎離終。《下篇》以咸恆始，既未濟終。即全《易》以乾坤始而坎離終(乾坤坎離為先天，南北東西之中。乾坤純陽純陰，其體始終不易。坎離為陰陽之中，其體亦始終不易。故後天以離坎代乾坤之位。六十四卦原始要終，皆乾坤坎離而已。六十四卦有其始終，一卦亦各有其始終。乾坤坎離以為之體，而離變其終則為震。震反則為艮坎，變其始則為兌。兌反為巽而離，變其始亦為艮。坎變其終亦為巽，巽艮反仍為兌。震則六爻相雜矣。六爻相雜，唯其時之不同，而陰陽之變化，其成象各異。其初難知，變之始也。其上易知，物之終也。初立其本終得其末。初率其辭，而揆其方。既有典常，卒能成其終。而一卦之體用可見矣。)，而一卦六爻相雜，唯其時物，亦各自有其始終。

The book of The Zhou Changes consists of two parts, both of which trace the origin and the end. The Upper Classic begins with the hexagrams Qian and Kun and ends with Kan and Li, while the Lower Classic begins with Xian and Heng and ends with Ji Ji and Wei Ji. When viewed together, the entire book begins with Qian and Kun and ends with Kan and Li. Hang Xinzhai added a long explanatory note here: Qian, Kun, Kan, and Li are the Earlier Heaven hexagrams, located in the center of the four cardinal directions. Qian and Kun are entirely yang and entirely yin, respectively, and their structures remain unchanged throughout. Kan and Li are the middle of yin and yang, and their structures also remain unchanged. Therefore, the Later Heaven positions use Li and Kan to replace the positions of Qian and Kun. The origin and end of the sixty-four hexagrams ultimately depend on the four hexagrams Qian, Kun, Kan, and Li. The entire book has its beginning and end, and each hexagram also has its own beginning and end: taking Qian, Kun, Kan, and Li as the foundation, when Li changes its end it becomes Zhen, and when Zhen is reversed it becomes Gen. When Kan changes its beginning it becomes Dui, and when Dui is reversed it becomes Xun, which connects with Li, and also becomes Gen when changing its beginning. When Kan changes its end it becomes Xun, and when Xun and Gen are reversed, they return to Dui. When reaching Zhen, the six lines become mixed. The six lines being mixed is due to the different times they occupy, and the images formed by the changes of yin and yang differ accordingly. The first line is difficult to know, because it is the beginning of change; the top line is easy to know, because it is the end of a matter. The first line establishes the foundation, and the top line represents the conclusion. By following the words of the first line to infer the direction, there is a regular pattern to follow, and ultimately it can reach its end. Thus, the nature and function of a hexagram become clear. Returning to the main text: the six lines of a hexagram are intermingled with each other, depending on the time they occupy and the things they represent, and each has its own beginning and end.

初難上易，有本末之分。知其所先後，則擬之於初者，卒能成其終。此就全卦六爻而言之也。然初者物之始，而用未著。上者時已過，而用或窮。故又曰“若夫雜物撰德，辨是與非，則非其中爻不備”。(物者，陰物陽物之總名。雜物則陰陽迭居其位而文生矣。撰者有選撰擬議之意。因陰陽之雜居，其德不同，則是非可辨矣。)

The first line is difficult to know, while the top line is easy to know; here there is a distinction between the beginning and the end. Knowing the order of precedence, the intention proposed on the first line can ultimately achieve its completion. This is speaking in terms of the entire hexagram's six lines. However, the first line is the beginning of things, and its function has not yet manifested; the top line is when the time has passed, and its function may have already reached its limit. Therefore, the Great Treatise says: "If one is to deal with various things and compose virtue, distinguish right from wrong, then it is not the middle lines that are complete." Hang Xinzhai's own commentary says: "The term 'things' refers to the general term for yin and yang things; 'miscellaneous things' means that yin and yang alternate in occupying the positions of the lines, and the beauty of the text arises from this. 'Compose' includes the meaning of selection and proposal; because yin and yang dwell together, the virtue of each line differs, so right and wrong can be distinguished."

又曰：“噫！亦要存亡去凶，則居可知矣。知者觀其彖辭，則思過半矣。”(此又詠歎以長言之，而申明上文意也。來知德氏以亦要為句，而要讀腰，謂即指中爻，似屬牽強。亦要者，即大要云爾猶言約舉其大概也。居者，剛柔迭居屯見而不失其居，即二四三五是也。)二四三五，已過全卦之半，此四爻皆謂之中者。以二五乃上下卦之中，三四又二與四，三與五之中也。

The Great Treatise continues by saying: "Alas! The main point is to preserve existence, prevent destruction, and avoid misfortune; this can be known by observing the positions of the lines. Those who understand will observe the meaning of the hexagram's lines and have already thought through more than half of it." This means that the main idea is simply to preserve existence, prevent destruction, and avoid misfortune; one can know this by looking at the positions of the lines. Hang Xinzhai's own note says that this uses a sighing, long sentence to further explain the previous meaning. A Ming dynasty scholar, Lai Zhide, divided "yi yao" as a separate sentence and read "yao" as "yao," suggesting it refers to the middle lines, which seems forced. "Yi yao" simply means "the main point," equivalent to saying roughly summarizing the main idea. "Ju" refers to the positions of the lines where yin and yang alternate, gathering and manifesting while each remaining in its proper place, that is, the second, fourth, third, and fifth lines. The second, fourth, third, and fifth lines have already exceeded half of the hexagram, and can all be called "zhong" (center): because the second and fifth lines are the centers of the lower and upper trigrams respectively, while the third and fourth lines are the middle of the pairs of second and fourth, and third and fifth lines.

故又曰：“二與四同功而異位，其善不同。二多譽，四多懼。近也，柔之為道，不利遠者。其要無咎，其用柔中也。”此即所謂下中爻也。二至四合成三畫卦一。既成一卦，又自有其上下之位。既分上下，其善與不善，便有不同。統觀六十四卦，凡二爻每多佳譽，而四爻每多恐懼。何哉？因四之位近於五，而四為柔爻。柔之為道，逼近於剛者不利，故多懼。而二雖同為柔爻，則遠於五矣。遠者大要可以無咎，況二又為下卦之中，柔而得用，此其所以多譽也。

Therefore, the Great Treatise also says: "The second and fourth lines have the same function but different positions, hence their good outcomes differ: the second line is often praised, the fourth line is often fearful, because it is close. The way of the flexible is not favorable to the distant; its main point is to avoid blame, for it uses flexibility in the center. " Here it refers to the middle lines in the lower trigram. The second line to the fourth line together form a three-line trigram; since they form a trigram, they themselves have a distinction between upper and lower. Once there is a distinction between upper and lower, good and bad differ. Observing all sixty-four trigrams, the second line often has praise, while the fourth line often has fear. Why is this? Because the fourth line is close to the fifth line, and the fourth line is a flexible line. The way of the flexible is not favorable when it approaches the strong, hence it is often fearful. The second line, although also a flexible line, is farther from the fifth line; the distant is generally without blame, and moreover, the second line is in the center of the lower trigram. Flexible yet properly used, this is why it is often praised. In other words, the good or bad of the same flexible line does not depend on the line itself, but on how close it is to the nine-five line and whether it is in the center and properly positioned.

又曰：“三與五同功而異位。三多凶，五多功，貴賤之等也。”此即所謂上中爻也。三至五，亦合成三畫卦一。而六十四卦之三爻，多凶，而五爻多功。何哉？則以五貴而三賤。五得位得中，而三則非所論也。綜二四三五而言之，二與四柔爻也，三與五剛爻也。故又曰：“其柔危，其剛勝耶？”二四雖同為柔，惟四獨危。三五雖同為剛，而五獨勝。此總論二四三五之位。而成卦以後，則剛柔雜居。柔者或以柔而益見其危，剛者或過剛而更著其凶。存亡凶吉，觀其居，則可知矣。

The Great Treatise also says: "The third and fifth lines have the same function but different positions; the third line is often凶 (dangerous) while the fifth line is often功 (beneficial), which reflects the distinction between the noble and the humble." Here it refers to the middle lines in the above group. The third line to the fifth line also form a three-line trigram together. In the sixty-four trigrams, the third line is often dangerous while the fifth line is often beneficial. Why is this so? Because the fifth line is noble and occupies the central position, while the third line does not have these advantages. If we consider the second, fourth, third, and fifth lines together, the second and fourth lines are yin positions, while the third and fifth lines are yang positions. Therefore, the Great Treatise concludes: "Is it the yin that is dangerous, and the yang that prevails?" The second and fourth lines, although both yin, are particularly dangerous; the third and fifth lines, although both yang, are particularly successful. This is a general discussion of the positions of the second, fourth, third, and fifth lines. Once the trigram is formed, the yin and yang lines are mixed in their positions. The yin lines may become even more dangerous due to their yin nature, while the yang lines may become even more凶 (dangerous) due to their excessive yang. Whether something is present or not, whether it is凶 or吉 (beneficial), can be determined by the position it occupies. This shows that the second, fourth, third, and fifth lines are the key to determining the survival, destruction, danger, or benefit of a trigram. This is also the reason why Hang Xinzhai carefully explains this entire passage in detail.

《易》柔乘剛之爻，皆二三五。始於屯之六二，陰陽始交而難生。難由於六二之乘剛也。(乘非二乘初之謂，乃坤六二之柔爻乘乾九二之剛爻。以柔敵剛，剛為所覆，而伏於下，故曰“乘剛”。)凡柔乘剛有其漸，始則柔遇剛。(姤，遇也，柔遇剛也。)遇而不以為異，漸而柔乘剛。(履，柔履剛也)履而不止，漸而柔乘剛。乘剛而不止，終之即柔變剛。(剝，柔變剛也)至柔變剛而乾爻二二五，均為柔乘。乃柔乘五剛。六十四卦終於柔變剛，乃剛決柔矣。

In the Zhou Changes, instances where a yao of yin (soft) overpowers a yao of yang (hard) occur at the second, third, and fifth positions. This example begins with the second line of the Zun hexagram: when yin and yang first meet, difficulty arises, and this difficulty comes from the yin line six in the second position overpowering the yang line nine in the second position. Hang Xinzhai explains: here, the term "multiplying over" does not refer to the second line multiplying over the first line, but rather to the yin line six in the second position of the Kun hexagram multiplying over the yang line nine in the second position of the Qian hexagram. This is a confrontation between soft and hard, with the hard being covered and hidden below, hence called "multiplying over the hard." Generally, when a soft line multiplies over a hard line, it is a gradual process: at first, the soft and hard merely meet (the Gou hexagram's Commentary on the Judgment says, "Gou means meeting, and it is the meeting of the soft with the hard"); when they meet, there is no noticeable difference, and gradually the soft steps on the hard (the Liu hexagram's Commentary on the Judgment says, "the soft steps on the hard"); when the soft steps on the hard and does not stop, it gradually becomes the soft dominating the hard; if the soft continues to multiply over the hard without stopping, it finally changes the hard into soft (the Po hexagram's Commentary on the Judgment says, "the soft changes the hard"). When the soft has changed the hard, the second, third, and fifth lines of the Qian hexagram, which are all hard lines, are all multiplied over by the soft, forming a situation where one soft line multiplies over five hard lines. Among the sixty-four hexagrams, the process ends with the soft changing the hard, and finally the hard comes to decisively overcome the soft.

始柔遇剛，而姤柔壯，壯震起，不艮止之，而震起者皆乘剛爻矣。二三五乘剛爻，天地三人爻睽不同人，遇剛敵剛而乘剛，莫凶於三爻矣。是故乘剛，始《屯·六二》“乘馬”。屯“乘馬”出之井，井二三五剛爻不可柔乘。柔乘則剛掩，剛掩則困。故乘剛莫凶於困之六三爻也。是以《震·六二》，乘剛也；《噬嗑·六二》，乘剛也。天地乘剛爻皆於六二。乘剛難始，即難在三五。三五天地日月候。三柔乘，困剛掩。五柔乘，豫貞疾。皆日月掩食象也。

The beginning is of soft meeting hard, but the softness in the hexagram Gou once becomes strong it turns into Dazhuang. The lower trigram of Dazhuang is Zhen, which signifies movement. If there is no Gen to stop it, any movement becomes a yao that rides on hardness. The second, third, and fifth lines are all positions of riding on hardness. In the three elements of heaven, earth, and humanity, the human yao is in the third position, its image is the hexagram Kui, which signifies discord, not the hexagram Tongren which signifies harmony. Meeting hardness, opposing hardness, and riding on hardness, there is no position more dangerous than the third line. Therefore, when discussing riding on hardness, it begins with the line six two in the hexagram Zun, which says "riding on horses, hesitating." The image of "riding on horses" in Zun comes from Jing. The second, third, and fifth lines in Jing are all yang lines, which cannot be ridden upon by yin. Once ridden upon by yin, yang is obscured, and when yang is obscured, it becomes Kunn. Therefore, the danger of riding on hardness is no greater than the line six three in Kunn. In addition, the line six two in Zhen is riding on hardness, and the line six two in Shike is also riding on hardness. All instances of riding on hardness in heaven and earth fall on the line six two. The difficulty of riding on hardness begins with the second line, but the real difficulty lies in the third and fifth lines. The third and fifth lines are the times when heaven and earth and sun and moon move. When the third line is ridden upon by yin, it is like the yang being obscured in Kunn; when the fifth line is ridden upon by yin, it is like the line "Zhen Ji" in Yu, which is like the sun and moon being obscured leading to an eclipse.

柔乘剛，則坤有尤，而乾有悔。故《易》無尤之爻，恆在二四五。尤，異也。睽，異也。(睽三五柔)西南坤柔道，以物見異為有尤，乃乘剛也。東北艮終止之，以終止坤柔，不見異，不乘剛，而終以無尤。故於天地西南(離兌)睽異，而終於東北蹇難，艮止之。二三五震起，而柔乘剛者，皆二四五。反震而艮止之，則終無尤矣。

Softness once takes over strength, and the line of the Earth (Kun) has "you," while the line of Heaven (Qian) has "regret." Therefore, in The Zhou Changes, the line without "you" is always in the second, fourth, or fifth positions. "You" means "difference," and the hexagram of Kui is one of divergence. The third and fifth lines of Kui are all soft. The southwest belongs to Kun, which follows the path of softness. When encountering things, it produces divergence, which is called "having you," which is precisely taking over strength. The northeast belongs to Gen, which can stop it—stopping the softness of Kun, so there is no divergence, and thus no taking over strength, ultimately achieving "no you." Therefore, in the directions of heaven and earth, the southwest (Li, Dui) is the source of divergence, and it ends with the difficulty of Jian in the northeast, which is stopped by Gen. The second, third, and fifth lines are stirred up by Zhen. All instances of softness taking over strength occur in these positions. By turning Zhen into Gen and stopping it, ultimately there is no you.

是以屯二，乘剛也。屯震反艮，屯成蹇，蹇二終無尤也。噬嗑二，乘剛也。噬嗑震反艮，噬嗑成旅。旅二，終無尤也。豫五，乘剛也。豫震反艮，豫成剝，剝五終無尤也。柔剛二三五終無尤，二四五天地中，三四反類，故困三乘剛也。困反類賁，賁四終無尤也。是以無尤皆二四五柔以艮止，乘剛皆二三五柔以震起也。

By following this method step by step: In the hexagram Zhun, the line six in the second is riding on a yang line. The Zhun hexagram, with its Zhen trigram reversed, becomes Gen, thus transforming Zhun into Jian. In Jian, the line six in the second is "finally without blame." In the hexagram Shihe, the line six in the second is riding on a yang line. The Shihe hexagram, with its Zhen trigram reversed, becomes Gen, thus transforming Shihe into Lu. In Lu, the line six in the second is "finally without blame." In the hexagram Yu, the line six in the fifth is riding on a yang line. The Yu hexagram, with its Zhen trigram reversed, becomes Gen, thus transforming Yu into Bo. In Bo, the line six in the fifth is "finally without blame." The reason why the yin lines in positions two, three, and five can finally be without blame is that positions two, four, and five are in the center of heaven and earth. However, positions three and four must instead take their kind from the opposite, so in the hexagram Kun, the line six in the third is riding on a yang line. The Kun hexagram, by reversing its kind, becomes Ben, thus transforming Kun into Ben. In Ben, the line six in the fourth is "finally without blame." This shows that all instances of "without blame" are due to the yin lines in positions two, four, and five being stopped by Gen. All instances of "riding on a yang line" are due to the yin lines in positions two, three, and five being stirred by Zhen.

二三五不柔乘，二四五終無尤，於是坤無尤而乾悔亡，為貞吉悔亡。故《易》貞吉悔亡爻，恆為二四五。乃坤柔不乘剛，乾剛不柔乘，是以坤貞吉而乾悔亡。坤貞吉，貞於坎；乾悔亡，悔於離。天地南北離坎，《易》日月一二明始，故正北方卦子丑，坎艮蹇貞吉；南方卦午未，離坤晉悔亡；而晉以下子丑二初貞吉，上午未三五日月明悔亡。

Two, three, and five are not being multiplied by the soft, so two, four, and five ultimately have no blame. Thus, the hexagram of Kūn has no blame and the hexagram of Qián has no regret, combining to form the line statement "Zhen Ji" and "Hui Wang." Therefore, in the Zhou Changes, the lines that say "Zhen Ji" and "Hui Wang" always fall on two, four, and five. This is because the soft of Kūn does not multiply the strong, and the strong of Qián is not multiplied by the soft, so Kūn attains "Zhen Ji" and Qián attains "Hui Wang." The "Zhen Ji" of Kūn is based on Kan; the "Hui Wang" of Qián is based on Li. The north and south of heaven and earth correspond to Li and Kan. The Zhou Changes take the sun and moon, and the numbers one and two as the beginning of brightness. Therefore, the position of Zi and Chou in the north, where Kan and Gen form Jian, speaks of "Zhen Ji." The position of Wu and Wei in the south, where Li and Kūn form Jin, speaks of "Hui Wang." From Jin onwards, all hexagrams that belong to Zi and Chou have the lines two and one often speaking of "Zhen Ji," while those that belong to Wu and Wei have the lines three and five, due to the brightness of the sun and moon, speaking of "Hui Wang."

內子丑一二，家人內也。外午未七八，睽外也。家人二貞吉而初悔亡，內也。睽五悔亡，外也。天地內外陰陽，陰不可過乎陽，內陰壯不可也。故家人內有恆不可有壯。是以家人二貞吉，而恆二悔亡。恆二悔亡，爻止二字；即大壯二悔亡，爻止二字。為內陰不可壯而止之。於是正北方坎卦內正，而南方離卦無悔。

The inner trigram corresponds to Zi and Chou, and to the first and second lines, taking the image of "inner" from the hexagram Family. The outer trigram corresponds to Wu and Wei, and to the seventh and eighth lines, taking the image of "outer" from the hexagram Kui. The line statement of line six-two in Family speaks of "uprightness and good fortune," and the line statement of line initial nine in Family speaks of "regret disappearing," both belonging to the inner. The line statement of line six-five in Kui speaks of "regret disappearing," belonging to the outer. Heaven and earth have a distinction between inner and outer, and yin and yang have a boundary: yin cannot surpass yang, so the yin in the inner trigram is not allowed to be strong. Therefore, the "inner" represented by Family can only have the constancy of the hexagram Hex, but not the strength of the hexagram Great Strength. Thus, the line statement of line six-two in Family says "uprightness and good fortune," while the line statement of line nine-two in Hex only says "regret disappearing," with the line statement consisting of only these two words. The line statement of line nine-two in Great Strength also only says "regret disappearing," with the line statement consisting of only these two words, in order to restrain the yin in the inner trigram from becoming strong. In this way, the hexagram Kan in the direction of true north gains its proper inner aspect, and the hexagram Li in the southern direction is free from regret.

可大壯往外，是為大壯內二貞吉，而外四五貞吉悔亡而無悔也。天地坤始柔不可壯，壯則乘剛，坤有尤。乾後剛不可不壯，不壯剛柔乘剛，乾有悔。是以大壯於坤柔壯止，於乾剛晉進。大壯正大，天地之情可見，而二四五貞吉悔亡而無悔可也。《易》於南北離坎，乃未濟上下卦。大壯二四五剛柔爻，即未濟離坎二四五剛柔爻，故大壯二貞吉。坎貞吉，大壯四貞吉悔亡，坎離貞吉悔亡，大壯五無悔，離貞吉無悔，故南北乃天地未濟離坎六十四卦終也。故二三五二四剛柔中爻，為全《易》至要關鍵。不明乎此，《易》不可得而言也。

Only when strength is vigorous and outwardly expressed can it be effective. This is why in the Inner Trigram of "Great Strength" (大壮), the line "Nine in the Second" says "Zhen Ji" (贞吉), while the lines four and five of the Outer Trigram respectively say "Zhen Ji Hui Wang" (贞吉悔亡) and "Wu Hui" (无悔). In the space between Heaven and Earth, the Trigram "Kun" (坤) comes first, and its softness cannot be strong; once strength is applied, it must ride upon the strong, and "Kun" then becomes "You" (有尤). The Trigram "Qian" (乾) comes later, and its strength cannot be weak; if it is not strong, then its strength is reversed by the softness, and "Qian" then becomes "You Hui" (有悔). Therefore, the hexagram "Great Strength" (大壮) stops the vigorous growth of "Kun" and allows the strength of "Qian" to advance like in "Jin" (晋). The "Commentary on the Judgment" (彖传) of "Great Strength" says, "Righteousness and grandeur, and the truth of Heaven and Earth can be seen." The lines two, four, and five of "Great Strength" speaking of "Zhen Ji," "Zhen Ji Hui Wang," and "Wu Hui" are exactly in line with this meaning. The "Zhou Yi" (周易) uses the Trigrams "Li" (离) and "Kan" (坎) in the north and south as the upper and lower trigrams of "Wei Ji" (未济). The lines two, four, and five of "Great Strength" which are yao (爻) of yin and yang are the same as the lines two, four, and five of "Li" and "Kan" in "Wei Ji." Therefore, the line "Nine in the Second" of "Great Strength" saying "Zhen Ji" corresponds with the "Zhen Ji" of "Kan"; the line "Nine in the Fourth" of "Great Strength" saying "Zhen Ji Hui Wang" corresponds with the "Zhen Ji Hui Wang" of both "Kan" and "Li"; and the line "Six in the Fifth" of "Great Strength" saying "Wu Hui" corresponds with the "Zhen Ji Wu Hui" of "Li." Therefore, the north and south trigrams are the "Li" and "Kan" of the "Wei Ji" and also the final hexagrams of the sixty-four. From this we can see that the middle lines two, three, and five, and the lines two and four of yin and yang are the most important elements in the entire "Zhou Yi." Without understanding this, one cannot even begin to speak of the "Yi."

乾陽二三五在井，(乾初九天一勿用，用地二陰陽合德。故乾陽不曰一三五，曰二三五。)故井初下也，時舍也。與乾初下也時舍同也。三多凶，惟井三王明受福。(坤陰晉二“受茲介福”，《既濟·九五》“東鄰殺牛不如西鄰之禴祭實受其福”。《象》曰“實受其福吉大來也”。《困·九五·象傳》“利用祭祀受福也”。經傳言福者，只此四爻而已。)坤陰二三五在噬嗑，故曰“噬嗑合也”，言陰與陽相合也。先王分疆畫界取諸井，日中為市，取諸噬嗑。燮理阻陽，以養萬民，得二四三五之用也。井反為困，二與五同也。而三則變九為六。《彖傳》曰“困剛掩也”，即井九三之陽為柔所掩，故曰“剛掩”。困數三十六。天地數窮，窮則變，變則通，而通在井二三五。乾陽出用，俱在三四人爻反覆。故二與四三與五內重要之關鍵，尤在三四也。

The yang of the Qian hexagram falls on the second, third, and fifth lines, and its image is seen in the Jing hexagram. The first line of the Qian hexagram is the heavenly one, "the dragon is hidden and not used," and the line used is the earthly two, where yin and yang combine. Therefore, the yang of the Qian hexagram is not called one, three, and five, but rather two, three, and five. Thus, the first line of the Jing hexagram, which is at the bottom and "abandons the time," is the same principle as the first line of the Qian hexagram, which is at the bottom and "abandons the time." The third line is usually dangerous, but in the Jing hexagram, the third line says, "the king is wise and receives his blessing." Hang Xinzhai's self-commentary lists the references to "blessing" in the classics: the yin of the Kun hexagram is seen in the Jin hexagram's line two, "receives this intermediate blessing"; the Ji Ji hexagram's line five says, "the eastern neighbor sacrifices an ox, but the western neighbor's simple sacrifice is actually blessed"; the Image Commentary says, "actually receives the blessing, which is a great coming"; and the Kun hexagram's line five in the Image Commentary says, "using worship brings blessing." The references to "blessing" in the classics are only in these four lines. The yin of the Kun hexagram falls on the second, third, and fifth lines, and its image is seen in the Shi He hexagram. Therefore, the Commentary on the Judgment says, "Shi He means union," which refers to the union of yin and yang. The Great Treatise says that the ancient kings divided territories by taking the image of the Jing hexagram, and the market at noon by taking the image of the Shi He hexagram, both of which regulate yin and yang to nourish the people. These are based on the use of the second and fourth lines, and the third and fifth lines. When the Jing hexagram is reversed into the Kun hexagram, the second and fifth lines remain unchanged, but the third line changes from nine to six. The Commentary on the Judgment says, "Kun means being covered by strength," which is exactly the yang of the Jing hexagram's third line being covered by yin. The number of the Kun hexagram is thirty-six, and the numbers of heaven and earth reach their limit here. When the limit is reached, change occurs, and change leads to communication, and communication again comes back to the second, third, and fifth lines of the Jing hexagram. The function of the yang of the Qian hexagram is revealed in the repeated changes of the second and fourth lines, and the third and fifth lines. Therefore, among these key pairs, the most important are the third and fourth lines.

卦用七八，爻用九六。七八其體，九六其用。故六十四卦無一非九六之用。孔子首以乾坤發明之，以示六十四卦無一非九六之用，實無一非乾坤之用也。然坤以從乾，地道無成，坤之用皆乾之用，六之用皆九之用，故特於《乾·文言》一再申明其義，曰“乾元用九，天下治也”，“乾元用九，乃見天則”，又曰“天德不可為首也”。

The hexagram itself uses seven and eight, while the lines use nine and six: seven and eight represent the essence, while nine and six represent the application. Therefore, none of the sixty-four hexagrams are without the use of nine and six. Confucius first used the hexagrams of Qian and Kun to illustrate this principle, indicating that since none of the sixty-four hexagrams are without the use of nine and six, none are without the use of Qian and Kun. However, Kun's function is to follow Qian, and the way of the earth does not claim success for itself. Therefore, the application of six is actually the application of nine, and the use of six is actually the use of nine. Hence, Confucius particularly emphasized in the Wenyan Zhuan of the Qian hexagram, saying, "The primordial power of Qian uses nine, and the world is governed," and again, "The primordial power of Qian uses nine, and thus the principle of heaven is revealed," and also said, "The virtue of heaven cannot be first."

先儒於用九用六二語，解釋不一。或以占變，或以剛柔，或泛論君臣之道，或比附天地之氣，或以“群龍無首”四字望文生義，或以“用六永貞”一言互明其旨，而皆未有確切不移之說，為至當不易之論者。揆厥原因，實由蔡墨之一語，曰乾之坤“見群龍無首吉”。故主占變之說者，皆以用九為純乾變純坤，用六為純坤變純乾。其他泛言義理言君臣，更悠悠無可捉摸矣。

Previous scholars have offered various interpretations of the phrases "use nine" and "use six," with no consensus. Some have explained them from the perspective of changing lines in divination, others from the concepts of yin and yang, some have discussed them in general terms regarding the relationship between sovereign and minister, others have compared them to the energies of heaven and earth, and still others have taken the phrase "a multitude of dragons without a leader" literally, or used the phrase "use six and maintain purity" to elaborate on the meaning. None of these interpretations have been definitive. The reason for this is that the "Zuo Zhuan" records a statement by Cai Mo, who said that the divination phrases for the hexagrams "Qian" and "Kun" are "a multitude of dragons without a leader, auspicious." Therefore, those who advocate for the theory of change in divination interpret "use nine" as the transformation of pure "Qian" into pure "Kun," and "use six" as the transformation of pure "Kun" into pure "Qian." As for those who discuss the meaning in general terms or in terms of the relationship between sovereign and minister, their interpretations are even more vague and difficult to grasp.

夫經文既明明曰九曰六，則釋經者自當先從九六二字研究，得其確詁，然後推究用九用六及所以用九用六之原，而證之以經，方為有據。端木鶴田氏曰：“用九者，天一不用，用地二至地十。”誠為最扼要之論矣。夫先聖既以九六命爻，自無爻非用九用六也。既稱之曰九曰六，則必根據於天一地二之數可知也。

The text clearly states "nine" and "six," so those interpreting the text should first study the characters "nine" and "six" to obtain an accurate explanation. Then they should investigate the meanings of "using nine" and "using six," as well as the reasons for using nine and six, and verify these interpretations with the text itself. Only then can their interpretations be considered valid. Qing dynasty scholar Du Menghu (styled Hetaian) said: "所谓用九" means "heavenly one is not used, while earthly two up to earthly ten are used." This is indeed a concise and accurate statement. Since the ancient sages used "nine" and "six" to name the lines, it is certain that no line is without the use of nine or six. Since they are called "nine" and "six," they must have been based on the system of heavenly one and earthly two, which can be definitely concluded.

今以天一地二之數推之，惟一與九不變。一不變者體也，(以一乘十乘百皆仍為一，而乘三乘四仍為三四。與二合則生三，而一之本數乃不見，故一不用。)九不變者用也。(凡以九遍乘他數，無一非九。如二九十八，一八九也。三九二十七，二七亦九也。至九九八十一，八一亦九也。)故自九乘一以至十，其積數為三百八十四，乃全《易》六十四卦之爻數也。而自一以後遞加至十，積數為九十九，加至百為九千九百九十九，而皆虛其一。故一不用，不為首，而《易》之全數皆用九之數。

Now using the system of "Heavenly One and Earthly Two," only one and nine remain unchanged. The unchanging nature of one is in terms of substance (when one is multiplied by ten, hundred, or any multiple, it remains one; when multiplied by three or four, it results in three or four; when combined with two, it produces three, and the original number one disappears, so one is not used). The unchanging nature of nine is in terms of function (when nine is multiplied by any other number, the result always adds up to nine: two times nine is eighteen, one plus eight is nine; three times nine is twenty-seven, two plus seven is nine; until nine times nine is eighty-one, eight plus one is still nine). Therefore, multiplying nine by one up to nine by ten and adding them all together results in three hundred and eighty-four, which is exactly the total number of lines in the sixty-four hexagrams of the Zhou Changes. Adding from one up to ten gives ninety-nine; adding up to one hundred gives nine thousand nine hundred and ninety-nine, both of which are one digit short of a full number. This shows that one is not used, does not occupy the first position, while the entire numerical system of the Zhou Changes is based on nine. This calculation provides solid evidence for the concept of "All Nines" (用九): not relying on divination or abstract reasoning, but proving through numbers that nine is used and one is the substance.

坤之用六曰“利永貞”，天下之道貞夫一者也，則正與九對。由此推之，自二至八，其五位之相得相合，與卦位爻數之相得相合，均可次第而明。然後驗之於日月，征之於四時，考之於聲音律呂，發而為禮樂政治，人倫道德，皆一以貫之。而八卦六十四卦三百八十四爻，亦一以貫之。持論皆有實據，而非徒託之空言矣。(九六之用皆出於數理之自然，非人力可能加減。參看《易數偶得》各圖自明。)

The hexagram "Kun" says "it is advantageous to pursue uprightness forever" under the use of six. The "Great Treatise" explains that the way of the world returns to "uprightness as one," which corresponds precisely to the nine. From this, we can proceed downward, from two to eight, and understand how these numbers relate to each other, as well as how the positions of the hexagrams and the numbers of the lines correspond. Then, using the sun and moon for verification, the four seasons for confirmation, and the tones and pitch-pipes for examination, we can extend this to the rites, music, politics, and human relationships, all of which can be unified. Thus, this argument has solid foundation, not empty talk. Hang Xinzhai's own note: the use of nine and six comes from the natural order of numbers, not from human intervention. Refer to his work "Accidental Gains on the Numbers of the Book of Changes" for further clarification.

《大學》、《中庸》，皆本於大《易》。以象證之，幾無一句無一字，不與卦義卦數相合。數始於天一，卦始於坎子。(八卦之位，坎北方子，其數一；艮東北丑寅，其數二三；震東方卯，其數四；巽東南辰巳，數五六；離南方午，其數七；坤西南未申，其數八九；兌西方酉，其數十；乾西北戌亥，其數無。乾無也，於文天屈西北為無。)子天一不用，乾初勿用，用始丑地二。(用地二至地十而一勿用，是為乾元用九)子天一復，復小。丑地二臨，臨大。坎習教事，(《坎·象》曰：“君子以常德行習教事。”)教者斆也。臨內卦兌，兌為學。子一至兌十，一始十終，而艮成終成始，念終始與於學，故曰“大學”。

The chapters "Great Learning" and "Meaning of the Middle Way" both originate from the "Zhou Yi" or "I Ching." When verified through hexagram symbols, there is hardly a sentence or a single character that does not align with the meanings and numbers of the hexagrams. The numbers begin with the heavenly stem "Jia" (天一), and the hexagrams start from the position of the hexagram "Kan" (坎) which corresponds to the position "Zi" (子) in the north. Hang Xinzhai himself annotated the positions and numbers of the eight trigrams: "Kan" is in the north, at "Zi" position, with the number one; "Gen" (艮) is in the northeast, at "Chou" and "Yin" positions, with numbers two and three; "Zhen" (震) is in the east, at "Mao" position, with the number four; "Xun" (巽) is in the southeast, at "Chen" and "Si" positions, with numbers five and six; "Li" (离) is in the south, at "Wu" position, with the number seven; "Kun" (坤) is in the southwest, at "Wei" and "Shen" positions, with numbers eight and nine; "Dui" (兑) is in the west, at "You" position, with the number ten; and "Qian" (乾) is in the northwest, at "Xu" and "Hai" positions, with the number "wu" (nothing) — "Qian" is "wu" (nothing), as the character "tian" (heaven) is curved in the northwest, forming the character "wu." The position "Zi" with the number one is not used, just as the first line of the hexagram "Qian" (乾) says "the hidden dragon does not act." The actual beginning of use is from the position "Chou" with the number two (using the number two up to ten, but not using one, which is why it is called "Qian Yuan Yu Ji" (the origin of heaven uses nine)). The position "Zi" with the number one corresponds to the hexagram "Fu" (复), which is called "small"; the position "Chou" with the number two corresponds to the hexagram "Lin" (临), which is called "great." The hexagram "Kan" governs "learning and teaching" (as the "Great Image" of "Kan" says, "the gentleman maintains constant virtue and practices teaching and learning"). "Teaching" is also "xiao" (敩), which includes both teaching and learning. The inner trigram of "Lin" is "Dui" (兑), which represents learning. From the number one at the position "Zi" to the number ten at the position "You" (兑), one is the beginning and ten is the end. "Gen" (艮) can both complete the end and begin again, constantly focusing on learning without separating the beginning and the end, hence it is called "Great Learning."

大學終始在艮，即在於《乾·九二》。(乾初一子勿用，用地二丑。地二丑乃坤二之數，乾坤合德，故坎子隱伏丑二。兌見故乾二曰“利見大人”。)九二“君子學以聚之，問以辨之，寬以居之，仁以行之”，大人之學也。大人之學，由於謹小而慎微。庸言之信，庸行之謹，閒邪存其誠，善世而不伐，德博而化，乃龍德而正中者也。故曰“中庸”。故《大學》、《中庸》皆本於《易》，皆始於乾之九二。九二乃坎離爻。坎離南北正中，君子中道而行。《大學》由離而至坎，《中庸》由坎而至離。離坎上下，水火既濟。聖功王道，備於此矣。

The beginning and end of the Great Learning are based on the Gen trigram, which corresponds to the Nine in the Second line of the Qian hexagram. Hang Xinzhai explains: The first line of the Qian hexagram is one, which corresponds to the Zi branch, and it is not suitable for use. What is used is the second line of the Earthly Branch, which is Chou. The second line of Chou corresponds to the second line of the Kun hexagram. The Qian and Kun trigrams are in harmony, so the Kan trigram is hidden within the second line of Chou. The Dui trigram has already appeared, so the Nine in the Second line of the Qian hexagram says, "It is advantageous to see a great man." The Wenyan commentary on the Nine in the Second line says, "A gentleman studies to gather knowledge, asks questions to distinguish truth, lives with broad-mindedness, and acts with benevolence." This is the learning of a great man. The learning of a great man is achieved through careful attention to small details: in ordinary speech, one must be sincere; in ordinary actions, one must be cautious; one must guard against evil to preserve sincerity; one must benefit the world without boasting; one must have broad virtue and be able to influence others. This is called "dragon virtue and correct center," hence it is called "the Mean." Thus, both the Great Learning and the Doctrine of the Mean are based on the Zhou Changes and originate from the Nine in the Second line of the Qian hexagram. The Nine in the Second line is the line of the Kan and Li trigrams. The Kan and Li trigrams are located at the center of the north and south respectively, so the gentleman follows the middle path. The Great Learning proceeds from the Li trigram to the Kan trigram, and the Doctrine of the Mean proceeds from the Kan trigram to the Li trigram. The Li and Kan trigrams, one above the other, form the hexagram of Water and Fire in Completion. The achievement of sainthood and the way of the sovereign are both complete here.

大學之道，道本於天。(乾為天戌亥數無。以無出有，乾知大始，冒天下之道，貞下起元，而元在坎子天一。)天一坎數，由一生二，陰陽合德，故曰“一陰一陽之謂道”。子一丑二，於天象為日月，子與丑合，(一二天地始合)天地合德，日月合明。明也者，離也。離坤(八卦離之右為坤，火地晉)乃晉卦，《晉·象》曰“君子以自昭明德”。“自昭明德”者，乃君子戒謹恐懼慎獨之功。其象著於西南離坤，而其本則仍在東北。故坎與艮，水山蹇，君子以反身修德。艮與坎，山水蒙，君了以果行育德。坎艮反覆，蒙以養正，而聖功基於此矣。然君子之德，非獨善其身己焉。己立立人，己達達人，重離繼照。《象》日“明兩作離，大人以繼明照于四方”。故曰“在明明德”。

The "Dao" in "The Great Learning" originates from Heaven. Hang Xinzhai explains: The trigram "Qian" represents Heaven, which resides in the positions of Xu and Hai, and its number is "wu" (nothing). From nothingness comes being. "Qian" governs the great beginning of all things, covering the world, and through "zheng xia qi yuan" (establishing the beginning and initiating the cycle), this "yuan" is found in the trigram "Kan" (Water), specifically the "tian yi" (Heavenly One). "Tian yi" is the number of "Kan." From one comes two, and yin and yang combine to form virtue, hence the "Great Treatise" states, "One yin and one yang is called Dao." The trigram "Zi" represents one, and "Chou" represents two, corresponding to the sun and moon in the celestial phenomena. "Zi" and "Chou" combine (one and two are the initial union of heaven and earth), and heaven and earth combine their virtue, while the sun and moon combine their brightness. This brightness is represented by the trigram "Li" (Fire). "Li" connects with "Kun" (Earth) in the eight trigrams, forming the hexagram "Jin" (Progress). The "Great Image" of "Jin" says, "The gentleman cultivates his own brightness and virtue." "Cultivating one's own brightness and virtue" is the practice of the gentleman being cautious and respectful, carefully self-cultivating. This image is evident in the southwest trigrams "Li" and "Kun," but its root lies in the northeast. Thus, "Kan" and "Gen" combine to form the hexagram "Jian" (Obstruction), and the "Great Image" says, "The gentleman returns to himself and cultivates virtue." "Gen" and "Kan" combine to form the hexagram "Meng" (Youth), and the "Great Image" says, "The gentleman acts decisively and nurtures virtue." "Kan" and "Gen" repeatedly combine, cultivating virtue in the state of ignorance, thus laying the foundation for becoming a sage. However, the virtue of the gentleman is not only about self-cultivation but also about establishing others when oneself is established, and guiding others when oneself is successful. Just as two "Li" trigrams overlap, the light continues, and the "Great Image" says, "Two lights shining, the great man continues the brightness and illuminates the four directions." Therefore, the "Great Learning" says, "To manifest the bright virtue."

離南方之卦，在先天乃乾之位也。乾與離，天火同人。同人親也。乾君坤民，乾施坤受。離以乾體包孕坤陰，其親也至矣。故曰“在親民，在止於至善”。善者，乾之元也。(《文言》曰“元者善之長也”)至者，坤之元也。(《坤·彖》曰“至哉坤元”)乾元一，坤元二。乾一勿用，用在坤二。乾坤合德，則至善也。一生二，二生三，三乃艮之數。艮，止也，止於至善者也。(一二三三生萬物，子丑寅天地人。建子一復丑二臨寅三泰，泰通而天地人之道通，萬物咸備於我。此所以為君子立德之本，三者為《大學》之綱領焉。)

The hexagram Li is the southern hexagram. In the Earlier Heaven arrangement, it originally occupied the position of the hexagram Qian. The hexagram Qian and Li combine to form the hexagram Tongren, which signifies intimacy. Qian represents the ruler, and Kun represents the people; Qian gives and Kun receives. Li contains the yao of Kun within its structure, indicating a profound intimacy. Therefore, the Great Learning says, "To care for the people, to attain the highest good." The term "good" refers to the original principle of Qian (as stated in the Wenyan Zhuan: "The original principle is the beginning of goodness"). The term "highest" refers to the original principle of Kun (as stated in the Commentary on the Judgment of the hexagram Kun: "The original principle of Kun is indeed profound"). The original principle of Qian is one, and the original principle of Kun is two. The one of Qian is not used; the two of Kun is used. When Qian and Kun share the same virtue, it is called "the highest good." One gives rise to two, and two gives rise to three. Three corresponds to the number of Gen. Gen signifies stopping, which is "to attain the highest good." Hang Xinzhai notes: one, two, and three, and from three all things arise. Zi, Chou, and Yin correspond to Heaven, Earth, and Humanity. The beginning of Zi is the hexagram Fu, the beginning of Chou is the hexagram Lin, and the beginning of Yin is the hexagram Tai. When Tai is harmonious, the way of Heaven, Earth, and Humanity is all harmonious, and all things are complete within me. This is the fundamental basis for a gentleman to establish virtue. To illuminate the bright virtue, to care for the people, and to attain the highest good are the three main principles of the Great Learning.

知止而後有定，(乾為知，艮為止，知止為乾坎。艮三位，艮反身修德，反諸坎。所謂含三為一是也。)知止反身修德，止於至善，則陰陽合德而既濟定，(既濟定也。既濟六爻皆當位，皆一陰一陽，此之謂道。)定而後能靜，(乾動坤靜，止於至善。以乾合坤，由動而返諸靜矣。)靜而後能安，(坤先迷後得主，後順得常。安貞之德，應地無疆。)安而後能慮，(由艮而返諸坎者，復由坎而出諸艮。坎為思慮。《傳》曰“能說諸心”，坎也。“能研諸侯之慮”，艮也。)慮而後能得。(乾坤合德，乾以易知，坤以簡能，易簡天下之理得矣。)

"Knowing where to stop leads to determination" —— The hexagram "Qian" represents knowledge, and "Gen" represents stopping. Knowing where to stop combines "Qian" and "Kan"; "Gen" is in the third position, representing self-reflection and cultivating virtue, which is returning to "Kan," that is, the concept of "containing three as one." Knowing where to stop and returning to self-cultivation, stopping at the highest good, leads to the harmonization of yin and yang, achieving the stability of "Ji Ji" (The Completed). The "彖传" of "Ji Ji" says "stability"; all six lines of "Ji Ji" are in proper positions, each consisting of one yin and one yang, which is called the Way. "After determination comes stillness" —— "Qian" represents movement, and "Kun" represents stillness; stopping at the highest good is combining "Qian" with "Kun," returning from movement to stillness. "After stillness comes peace" —— The "Kun" hexagram says first being lost and then gaining mastery, later being harmonious and attaining constancy, the virtue of maintaining steadfastness should be in harmony with the vastness of the earth. "After peace comes contemplation" —— Returning from "Gen" to "Kan," and then from "Kan" back to "Gen"; "Kan" represents thought, and the "Great Treatise" says "being able to express in the heart" is "Kan," "being able to examine the thoughts of feudal lords" is "Gen." "After contemplation comes attainment" —— "Qian" and "Kun" harmonize in virtue; "Qian" knows through simplicity, "Kun" acts through ease, simplicity and ease encompass all the principles of the world. Hang Xinzhai's method of matching each sentence with a hexagram is to explain that the five stages of practice in the "Great Learning" —— "determination, stillness, peace, contemplation, attainment" —— are not merely arbitrary sequences, but each stage has a corresponding hexagram and position that can be clearly identified.

物有本末，(天地之數，子一丑二寅三，三生萬物，皆始於丑二。丑屬牛，牛大物也。故物從牛星，紀起於牽牛。本末皆從木，木下為本，上為末。寅與卯屬木，《易》象三才天地人，乾天坤地艮人，三才之數不齊，皆齊於巽木。故巽也者齊也。齊之以巽，巽震成益，木道乃行。象也者，材也。材成輔相而天地，人之用以彰。)

"The phrase 'things have their origins and their ends' is explained by Hang Xinzhai as follows: the numbers of heaven and earth, with Zi representing one, Chou two, Yin three. Three generates all things, and everything begins with Chou two. Chou belongs to the ox, which is a large creature, so the character 'wu' (thing) includes the radical 'niu' (ox). The star system also begins with the constellation Niutou (the Ox). The characters 'ben' (origin) and 'mo' (end) both contain the radical 'mu' (wood); the lower part of 'mu' is 'ben' and the upper part is 'mo'. Yin and Mao both belong to wood. The Zhou Changes take their imagery from the three elements of heaven, earth, and humanity. The Qian hexagram represents heaven, the Kun represents earth, and the Gen represents humanity. The numbers of the three elements are uneven, so they rely on the Xun hexagram, which represents wood, to harmonize them. Therefore, the 'Say on the Hexagrams' states that Xun is the one that harmonizes. Using Xun to harmonize, Xun and Zhen combine to form Yi, and thus the way of wood is established. 'Xiang' (image) is also 'cai' (material), and once the material is complete, it assists heaven and earth, and thus the function of humanity is revealed."

事有終始，(坤為有，乾為事。坤以從乾，故坤曰從事，從乾之事也。乾以統坤，故乾用格物，格坤之物也。乾始坤終，一始十終，而成終成始於艮。則終則有始，物無盡而事無窮。)知所先後。(有本末終始則有先後。先者體也，後者用也。先後一德。明德體也，在所先也。明明德，用也。在所後也。艮其止，止其所也。故所先所後皆在艮，而知其所先後則在乾。乾知太始。)知所先，則先天而天不違。知所後，則後天而奉大時。則庶幾近乎道矣。

The sentence "things have beginning and end" is explained in the self-commentary as follows: The hexagram "Kun" represents having, and the hexagram "Qian" represents things; "Kun" is responsible for following "Qian," so "Kun" discusses "engaging in things," which means engaging in the matters of "Qian." "Qian" is responsible for governing "Kun," so "Qian" discusses "investigating things," which means investigating the things of "Kun." "Qian" represents the beginning, and "Kun" represents the end. One represents the beginning, ten represents the end, and both the completion of the end and the beginning are found in "Gen." Thus, after the end comes the beginning again, and things have no end, and matters have no end. The sentence "knowing what comes first and what comes later" is explained in the self-commentary as follows: Once there is beginning and end, there is also order of precedence and succession; what comes first belongs to the essence, and what comes later belongs to the function. Precedence and succession are actually the same virtue. "Mingde" is the essence, which belongs to what comes first; "Mingmingde" is the function, which belongs to what comes later. The "Commentary on the Judgment" of the hexagram "Gen" says, "Gently stopping, stopping at its place," so both what comes first and what comes later are found in "Gen." Knowing the order of precedence is found in "Qian," because "Qian" governs the great beginning of all things. Knowing what comes first allows one to be as the "Commentary of the Literary Meaning" says, "acting before heaven does not contradict heaven"; knowing what comes later allows one to be "acting after heaven and following the timing of heaven," thus approaching the Dao.

古之慾明明德於天下者，(乾坤一古今。乾以先坤，古以鑑今。乾鎮而靜，性也。感於坤而動性之慾也。人各有欲，欲貴知止。欲能知止，知止於至於善，足以自昭明德矣。)明明德者，明兩作離，大人以繼明照于四方，是所謂由離而到坎者也。知所先，必先治其國。由離而巽(南方離，東南巽)鼎，鼎通屯，屯建侯，鼎凝命，治其國也。由巽而震，巽為齊，震巽恆，夫婦之道。上承巽離風火家人，齊其家也。

The Great Learning says, "In ancient times, those who wished to manifest their bright virtue throughout the world," and the commentary explains: The trigrams Qian and Kun represent ancient and modern times, with Qian preceding Kun, just as ancient times serve as a mirror for the present. Qian is deep and still, representing nature; when it feels the movement of Kun, it becomes active, which is the desire arising from nature. Everyone has desires, but what is precious is knowing where to stop; when desire knows where to stop, stopping at the highest good, it is sufficient to manifest one's bright virtue. What is called "manifesting bright virtue" is "the two lights shine together, the great man continues the bright illumination to the four directions," which is the transition from Li to Kan mentioned earlier. Once the order of precedence is understood, one must first govern the state: from Li to Xun (South is Li, Southeast is Xun) forms the Ding trigram, which is connected to Tun. Tun speaks of "favorable for establishing a feudal lord," while Ding speaks of "correct position and receiving mandate," which is governing the state. Then from Xun to Zhen, Xun represents order, and together with Zhen, they form Heng, which is the way of husband and wife; above them, Xun and Li form the wind and fire family, which is harmonizing the family.

震反為艮，反身修德，修其身也。修身為本，自離至艮，由天下國家而反諸身，德之由用而歸之體也。更由艮而坎，坎維心亨，正於天一，正其心者也。由坎而乾，意出於心。乾為言，而艮成之。從成從言，誠也。誠其意者也。知者徹始徹終，聞一知十。由乾而兌，乾知大始，智至至之。從坎一至兌十，致其知者也。由兌而坤，坤為物，與艮對。艮手格之，故曰“致知在格物”。自艮而至坤終焉。此德之體也，皆知所先也。

The hexagram Zhen turned upside down becomes Gen. The Gen hexagram in the Great Image says "reverse oneself and cultivate virtue," which refers to cultivating oneself. Cultivating oneself is the fundamental aspect: from Li to Gen, moving from the world and state back to oneself, virtue moves from its application back to its essence. Then from Gen to Kan, the Kan hexagram's Commentary on the Judgment says "maintaining the heart is smooth," aligning with the position of Heaven's first principle, which is to correct one's heart. From Kan to Qian, the mind originates from the heart, Qian governs speech, and Gen makes it complete; the character "cheng" (sincerity) is composed of "cheng" (completion) and "yan" (speech), which is precisely to sincere one's intention. A wise person can carry through consistently, understanding ten things from one: from Qian to Dui, Qian governs knowing the great beginning of all things, and wisdom reaches there, from the number one in Kan to the number ten in Dui, which is to attain knowledge. Then from Dui to Kun, Kun represents things, opposite to Gen, which represents the hand; using the hand to investigate it, hence the Great Learning says "attaining knowledge lies in investigating things." From Gen to Kun, this path concludes. All of the above belong to the essence of virtue, all being the aspect of "knowing what comes first."

知所先，則知所後。物格而後知至，(至者坤也。)知至而後意誠，意誠而後心正，心正而後身修，身修而後家齊，家齊而後國治，國治而後天下平。是由本而及於末，由體而達諸用。於八卦從坤而兌，兌而乾，乾而坎，坎而艮。艮為修身，修身齊家之始，成終成始。而震而巽而離，更復於坤。所謂全體大用，無不明矣(坤為地，天之下也。坤體承乾坎，平也，亦由終而反始也。)。故大學之道，首明明德。明兩作離也。終天下平，祗既平坎也。坎離正中，由體達用，則水火既濟功成，剛柔正而位當，知止而後有定(既濟定也。)，《易》道備矣。

Knowing the beginning, one also knows the end. "When things are thoroughly understood, then knowledge is complete" (the term "to reach the utmost" belongs to the Hexagram 63, the Earth). "When knowledge is complete, then the mind is sincere; when the mind is sincere, then the heart is upright; when the heart is upright, then the person is cultivated; when the person is cultivated, then the family is harmonious; when the family is harmonious, then the state is well governed; when the state is well governed, then the world is at peace." This is a process from the fundamental to the external, from the essence to the application. In the Eight Trigrams, it proceeds from the Hexagram 63 (Earth) to the Hexagram 58 (Lake), then to the Hexagram 1 (Heaven), then to the Hexagram 64 (Water), then to the Hexagram 19 (Mountain); the Hexagram 19 governs self-cultivation, which is the beginning of family harmony, capable of both concluding and beginning again. Continuing from the Hexagram 19 to the Hexagram 21 (Thunder), then to the Hexagram 22 (Wind), then to the Hexagram 31 (Fire), and finally returning to the Hexagram 63 (Earth). This is called the complete essence and full application, and at this point, everything is clear. The Hexagram 63 (Earth) is the Earth, beneath the Heaven; the essence of the Hexagram 63 receives the influence of the Hexagram 1 (Heaven) and the Hexagram 64 (Water), embodying the meaning of "peace," and thus returning from the end to the beginning. Therefore, the Way of the Great Learning begins with "brightening the bright virtue," symbolizing the image of "two lights shining, the Fire"; it ends with "the world is at peace," which is simply the image of "the Water" after peace has been achieved. The Hexagrams 64 (Water) and 31 (Fire) are in the central position, moving from essence to application, forming the Water and Fire Containing Each Other (Hexagram 60), where success is achieved, and the strong and the weak each hold their proper position. "When one knows where to stop, then one has stability" (the Commentary on the Judgment of the Water and Fire Containing Each Other says "stability"), and the Way of the Book of Changes is thus complete. Clearly, the sequence from investigating things to achieving world peace in the Great Learning corresponds exactly to a full cycle through the Eight Trigrams, returning to the starting point, with the beginning and end corresponding precisely to the Hexagrams 64 (Water) and 31 (Fire).

自天子以至於庶人，一是皆以修身為本，言人類階級至不齊焉，惟道能齊之。名類大小至不一焉，惟道能一之。齊之一之，故曰壹是以修身為本。艮為身，艮止，止其所所先所後，無不歸於至善矣。其本亂而末治者否矣。修身為本，身不修，既濟道反，初吉終亂(既濟“初吉終亂”)，本末易位。二之五亦五之二，為天地否矣。否泰反覆損益，益下不厚事，而損錯雷風相薄，天地變化，治亂之消息甚微。君子明乎消息盈虛，知所先後，明乎厚薄(剝上“以厚下安宅”則反覆。)，安土敦仁(修身)，而治可保矣。故曰“其所厚者薄而其所薄者厚，未之有也”。

"From the Son of Heaven down to the common people, all should take self-cultivation as the foundation," meaning that human ranks are extremely uneven, and only the Way can bring them into order; the distinctions of names and categories are also extremely inconsistent, and only the Way can unify them. By ordering them and unifying them, it is said "all should take self-cultivation as the foundation." The Hexagram of Gen represents the body, and Gen also signifies stillness. Stillness at the proper place ensures that what comes first and what comes later is all directed toward the highest good. As for "if the foundation is disorderly and the branches are orderly, it is impossible," self-cultivation is the foundation. If the body is not cultivated, the Way of Ji Ji reverses, becoming "initially auspicious but eventually disorderly" (the Hexagram Ji Ji's statement indeed says "initially auspicious but eventually disorderly"). The foundation and the branches are reversed; the second line moves to the fifth, and the fifth line moves to the second, turning into the Hexagram of Po. The alternation of Po and Tai and the mutual dependence of Shen and Yi: the Great Image of Yi says "benefiting the lower does not involve heavy affairs," while Shen, which is opposite to Yi, is thunder and wind colliding, thus causing changes in heaven and earth. The rise and fall of order and disorder are actually extremely subtle. The gentleman understands the waxing and waning of things, knows the order of precedence and succession, and understands the boundaries of thickness and thinness (the upper ninth line of the Hexagram Bao says "by being generous to the lower and securing the house," which is the meaning of reversal). Being settled in one's place and being earnest in benevolence is self-cultivation, and thus peace can be maintained. Therefore, the Great Learning says "if what is esteemed is made light and what is made light is esteemed, there has never been such a thing."

此謂知本，此謂知之至也。古本《大學》經文之末有此二句，今本移此二句於“大畏民志此謂知本”之下，作第五章。與“親民”之為“新民”，皆程子所改定者也。實則“親民”親字，含有教養二義。改作“新”字，僅有教之一義。則《傳》所稱如保赤子及同好同惡諸義，均贅文矣。證之於《易》，親字非訛尤確而可信，故並及之。

"These words, 'This is knowing the root, this is knowing thoroughly,' are located at the end of the classical text of the Great Learning. However, in the present version, they have been moved below 'Great fear of the people's will, this is knowing the root,' and are made into a fifth chapter. This change, like the alteration of 'care for the people' to 'renew the people,' was made by Cheng Yi. In fact, the character 'qin' in 'care for the people' includes both teaching and nurturing. Changing it to 'xin' leaves only the aspect of teaching. Thus, the meaning of 'as caring for a newborn child' and the idea of sharing the people's joys and sorrows in the transmission text become redundant. Using the Zhou Changes as a reference, the character 'qin' is not an error, which is even more convincing. Therefore, I mention this together here."

“中庸”之中，即離坎中正之中。庸者從庚。陰陽之義，用始乙庚(故蠱先甲後甲，巽先庚後庚。)。後天震出東方，首出庶物，萬象更新，故納甲以震納庚。而庚之本位則屬西方，西正秋兌，震仁兌義，立人之道。故庸字之義，乃合震兌二象，兼仁義之用者也。程子曰“不易之謂庸”，朱了曰“庸平常也”，均非確詁。《乾·九二》“庸言之信庸行之謹”，兌言震行，取象尤極顯明。

The "zhong" in "Zhongyong" refers to the middle and upright nature of the trigrams Li (Fire) and Kan (Water). The character "yong" contains the radical "geng." In terms of yin and yang principles, it is used in relation to Yi and Geng (thus the hexagram Gu explains "three days before Jia and three days after Jia," and the hexagram Xun explains "three days before Geng and three days after Geng"). In the Later Heaven arrangement, the trigram Zhen (Thunder) is located in the East, where all things first emerge, marking the beginning of renewal, so the method of Najia assigns Geng to Zhen. However, Geng's original position belongs to the West, which corresponds to the trigram Dui (Lake) and the autumn season. Zhen represents Ren (benevolence), and Dui represents Yi (righteousness), which are the two fundamental aspects of human conduct. Therefore, the meaning of "yong" is to combine the images of Zhen and Dui and to incorporate the functions of Ren and Yi. Cheng Yi said "yong refers to something unchanging," and Zhu Xi said "yong means ordinary," but these interpretations are not accurate. The "Wenyan" of the second line of the hexagram Qian states "ordinary words are trustworthy, ordinary actions are cautious." "Words" belong to Dui, and "actions" belong to Zhen, and the symbolic meaning is especially clear.

天命之謂性，惟天之命，於穆不已。天者，乾也。天命則乾元資始，而始於坎，即坎中之一陽，所謂性也。孔子贊《易》，利貞者性情也。又曰“一陰一陽之謂道，繼之者善也，成之者性也”，又曰“成性存存道義之門”，又曰“窮理盡性以至於命”。言簡意賅，源委分明，直截了當。後之言性理者，累千百萬言，枝枝葉葉，糾紛纏繞，其本根反不易尋覓矣。

The Zhongyong says, "Heaven's mandate is called nature." The Book of Poetry, Zhou Songs, says, "Only Heaven's mandate, profound and unceasing." Here, the term "Heaven" refers to the Qian hexagram. Heaven's mandate means the Qian hexagram's original yang line, which is the source of all things. This beginning falls on the Kan hexagram, specifically the central yang line of the Kan hexagram, which is referred to as "nature." Confucius wrote the Commentary on the Yi, and in the Wenyan, it says, "Beneficial constancy is the nature and disposition." In the Great Treatise, it says, "One yin and one yang is called the Way; what continues it is goodness, and what completes it is nature." It also says, "Maintaining nature consistently is the gate to the Way and righteousness," and again, "Exhausting principles, completing nature, and reaching the mandate." These words are concise and to the point, clearly distinguishing the beginning and end, the source and flow. Later scholars who discussed nature and principle wrote millions of words, but their discussions became tangled and complicated, making the fundamental principles difficult to find.

率性之謂道。率者率也，即成性存存也。率性之謂道，非性之謂道也。道本於天，性亦受於天。人能不失天賦之性，即能合於天之道矣。於《易》象坎為性，性隱伏不可見者也。坎常德行，習教事，教人明於天之道而察於民之故，凡皆所以成其性也。故曰修道之謂教。

The Zhongyong continues saying, "To follow one's nature is called the Way." "Follow" means to adhere to, which is exactly what the Great Treatise says, "To realize one's nature and maintain it steadfastly." One should note that it says "to follow one's nature is called the Way," not "nature is called the Way." The Way originates from Heaven, and human nature also receives its origin from Heaven. When a person does not lose his innate nature, he can harmonize with the Way of Heaven. In the symbolic imagery of the Zhou Changes, the Kan hexagram represents nature, which is hidden and not visible. The Great Image of the Kan hexagram says, "To practice constant virtue and to become accustomed to teaching and learning," which teaches people to understand the Way of Heaven and to observe the affairs of the people. All these are for the purpose of realizing one's nature. Therefore, the Zhongyong continues, "To cultivate the Way is called teaching."

性不可見，感於物而動，則情也。情亦不可見，而見乎色(喜怒哀樂見於色)，見乎辭，見乎行。性貞天一者也。動則情見乎色見乎辭見乎行。其為喜怒哀樂者，則不一矣。於是由艮而震，而以巽齊之。則不一者一，而合乎道。故道也者，不可須臾離也，可離非道也。此象之由坎而至於離者也。

Human nature itself is invisible; when it is touched by external things, it becomes emotion. Emotion is also invisible, but it appears in expressions (joy, anger, sorrow, and happiness are seen on one's face), in speech, and in actions. Human nature is fixed and constant as heaven's one principle. Once it moves, emotion appears in expressions, in words, and in actions, manifesting as joy, anger, sorrow, and happiness, which differ greatly. Thus, from the hexagram of "Stillness" (Gèn) it moves to "Thunder" (Zhèn), then uses "Wind" (Xùn) to regulate it, bringing disorder back to order and aligning with the Way. Therefore, the "Doctrine of the Mean" says, "The Way cannot be separated for a moment; if it can be separated, it is not the Way." This passage in terms of hexagram imagery corresponds precisely to the transition from "Water" (Kǎn) to "Fire" (Lí).

戒慎乎其所不睹(離目睹)，恐懼乎其所不聞(坎耳聞)，莫見乎隱，莫顯乎微者，皆坎為心，隱而顯微而著者也。坎心天地中，故喜怒哀樂之未發謂之中。坎一發而十至(兌十)。坎兌為節，故曰發而皆中節。先天乾坤南北中，後天震兌東西和(萬物出震)，故曰“致中和天地位焉，萬物育焉”(《易》與天地準，東震西兌，準平震卯兌西。日月出入，天象半顯半隱。正北坎，西北乾，東北艮，皆隱而不見也。天地之氣，始於亥子之間微也。)。

The Zhongyong says, "Be cautious in what is not seen" (the Li trigram represents the eye, which governs sight), "and be fearful in what is not heard" (the Kan trigram represents the ear, which governs hearing). "Nothing is more visible than the hidden, and nothing is more evident than the subtle" — all of this is because the Kan trigram governs the heart, which is hidden yet can become visible, subtle yet can become prominent. The heart governed by Kan is located in the center of heaven and earth, so it says, "When joy, anger, sorrow, and joy have not yet been expressed, this is called the middle." The Kan trigram is one, and when it is expressed, it reaches ten (the Dui trigram is ten); since Kan and Dui combine to form the Jie trigram, it says, "When expressed, they all conform to the proper measure." In the Earlier Heaven arrangement, the Qian and Kun trigrams are located in the north and south, forming the center; in the Later Heaven arrangement, the Zhen and Dui trigrams are located in the east and west, forming harmony (all things originate from Zhen). Therefore, it says, "Achieving the middle and harmony, heaven and earth are in their proper places, and all things flourish." Hang Xinzhai's own note: The Zhou Changes correspond to heaven and earth. The east is Zhen, the west is Dui; this perfectly matches Zhen corresponding to Mao and Dui corresponding to You. The rising and setting of the sun and moon, heavenly phenomena are always half visible and half hidden — the Kan trigram in the due north, the Qian trigram in the northwest, and the Gen trigram in the northeast are all hidden and not visible. The vital energy of heaven and earth arises at the intersection of Hai and Zi, which is the most subtle.

坎一復小，故小德川流。丑二臨大，故大德敦化。一二天地中，天下之大本也。天一勿用，用丑二艮成言。成言為誠，先坎後震。雲雷屯，經綸，故唯天下之至誠，為能經綸天下之大經，立天下之大本。天一勿用，用二至十。故凡為天下國家有九經，所以行之者一也。

The Trigram Kan is paired with one, and its hexagram is Fu, which is called small, so the Zhongyong says "small virtue flows like a river." Chou is paired with two, and its hexagram is Lin, which is called great, so it says "great virtue promotes transformation." One and two are located in the center of heaven and earth, which is exactly "the great root of the world." Heaven one is not used; instead, Chou two is used. Gen is called "formed words"; "formed words" is sincerity. The order is first Kan and then Zhen. Kan and Zhen together form the hexagram Zun, which is Cloud and Thunder. The Great Image of Zun says "the gentleman is skilled in planning and organizing," so the Zhongyong says "only those with the highest sincerity can plan and organize the great principles of the world and establish the great root of the world." Heaven one is not used, but two is used up to ten, so it says "for governing the world and state there are nine principles, and they are all carried out by one."

正北坎，西北乾，東北艮。乾天道，對巽為直。來者信也，由亥出子。坎一兌十，動而直，直而中節，唯聖者能之。其二屈往(往者屈也)，故曰其次致曲。本東方艮人道，艮成言，曲能有誠。艮寅泰通，震出用事，萬物甲坼。誠則形也，巽物絜齊。形則著也，離皆相見，著則明也，皆由坎以至離者也。明動變化，由離坤而兌乾，故曰“唯天下至誠為能化”。

Due north is Kan (Water), northwest is Qian (Heaven), and northeast is Gen (Mountain). Qian governs the heavenly way and is opposite to Xun (Wind), its nature being straight. "Coming" means extension (as stated in the Great Treatise, "Going is bending, coming is sincerity"). It originates from the亥 position and emerges at the Zi position. Kan represents one, Dui represents ten; movement enables straightness, and straightness conforms to measure, something only the sage can achieve. The next level is bending and going (going is bending), so the Zhongyong says "the next level is to pursue the subtle." This path originates from the human way governed by Gen in the east. Gen can "form words," even though it begins with bending, it can still be sincere. Gen is paired with寅 and connects with Tai (Peace), while Zhen (Thunder) emerges and takes action, causing all things to break forth from their shells. "Sincerity becomes form" is due to Xun making all things clean and orderly; "form becomes evident" is due to Li (Fire) causing all things to appear; "evident becomes clear"—these are all the path from Kan to Li. Further down, "clearness leads to movement, movement leads to change, change leads to transformation," which is the path from Li and Kun (Earth) to Dui and Qian, so the Zhongyong says "only the supremely sincere can bring about transformation."

誠者艮也，不誠無物，是故君子誠之為貴，與《大學》之壹是皆以修身為本，象義皆同，後先一貫者也。蓋艮寅為人位，曾子稱思不出其位，惟日三省，故獨得孔子一貫之傳。《大學》、《中庸》，皆端本於修身，即皆本於艮寅之一位，重乾爻辰二爻在寅，故《大學》、《中庸》之義，皆出於乾之九二也。顧孔子贊《易》，於立人之道，其樞機又在於三四兩爻何也？曰：此六爻之義也。論六爻三極，三四為人爻曰人極；而三四兩爻，居內外之際，合言之，則為兩卦之中；分言之又為內之終而外之始。六十四卦之反覆上下，無不由此。故《易》之言人道於三四兩爻。“中庸”“大學”，以卦位言之。故均以艮寅明修道之本，皆所謂同條而共貫者也。(誠者物之終始。艮者成終而成始也。)

"Cheng" belongs to the trigram Gen, and the "Zhongyong" says "Without Cheng, there is nothing," so the gentleman values Cheng above all; this is consistent with the "Daxue" saying "All things should be based on self-cultivation," and the symbolic meaning and rational principles are entirely the same, maintaining continuity. Gen corresponds to the branch Yin, which is the position where humans reside; Zengzi said "Thoughts should not go beyond one's position," and he also examined himself three times daily, so he alone received the heart transmission of Confucius. Both the "Daxue" and "Zhongyong" take self-cultivation as the fundamental starting point, meaning they both originate from the position of Gen and Yin; the emphasis on the second line of the trigram Qian, which falls exactly on Yin, so the principles of the "Daxue" and "Zhongyong" both come from the second line of the trigram Qian. However, when Confucius wrote the "Yi Zhuan" and discussed establishing the human way, the key was in the third and fourth lines, so why is that? The answer is: this refers to the six lines of a single trigram. Considering the three extreme lines, the third and fourth lines are called the human lines, referred to as the human extreme; and the third and fourth lines are located at the junction of the inner and outer trigrams. When viewed together, they are the middle of the upper and lower trigrams; when viewed separately, they are the end of the inner trigram and the beginning of the outer trigram. The reversal and inversion of the sixty-four trigrams all originate from here, so the "Yi" discusses the human way by focusing on the third and fourth lines. As for "Zhongyong" and "Daxue," they refer to the trigram positions, so they both use Gen and Yin to explain the fundamental of cultivating the Dao. In fact, they are originally the same principle and the same lineage (Cheng is the beginning and end of all things, while Gen becomes the end and also the beginning). In other words, when discussing the lines of a trigram, it leads to the third and fourth lines; when discussing the trigram positions, it leads to Gen and Yin. Although they seem different, they are actually talking about the same thing: the key to the human way lies within oneself, and the starting point of practice is self-cultivation.

誠為艮，而至誠則為乾。至誠之道，是反身修德。由艮而反諸坎，由三而反諸一，即所謂涵三為一也。涵三為一，太極之象。太極以無含有，自坎至乾，是即由有而入無(乾西北戌亥數無)。無思也，無為也。寂然不動，感而遂通天下之故，不疾而速，不行而至，乃天下之至神，故至誠之道可以前知。

"Cheng" belongs to the trigram Gen, while "Zhi Cheng" belongs to the trigram Qian. The way of Zhi Cheng is to turn inward and cultivate virtue: from Gen returning to Kan, from three returning to one, which is called "Han San Wei Yi." Han San Wei Yi is precisely the image of the Taiji. Taiji contains nothingness to encompass existence, from Kan to Qian, it moves from existence into nothingness (Qian resides in the Northwest, its number is nothingness). When reaching this stage, it is what the Great Treatise says: "Without thought, without action, still and unmoving, yet responsive to all things and understanding the causes of the world." "Without haste yet swift, without movement yet reaching," this is the most marvelous state in the world, so the Zhongyong says that the way of Zhi Cheng can foresee the future. The difference between "Cheng" and "Zhi Cheng" is the difference between Gen and Qian, between existence and nothingness.

西北乾天道，東北艮人道。天地人，子丑寅，三建用中，建中立極。丑艮為身，寅艮為庶，三庶也，故曰“本諸身，徵諸庶民”，子天建，丑地建，寅人建，為“三王”、“三統”，故曰“考諸三王而不謬”。於乾知天，故曰“質諸鬼神而無疑”。“於艮知人”，故曰“百世以俟聖人而不惑”。此天地子丑而本諸戌亥，君子以一誠終始之，即以艮終始之也。誠則形，形則著，著則明，明則動，動則變，變則化。

The trigram 乾 (Qian) in the Northwest represents the Way of Heaven, and the trigram 艮 (Gen) in the Northeast represents the Way of Humanity. Heaven, Earth, and Humanity are assigned the three branches 子 (Zi), 丑 (Chou), and 寅 (Yin). By using these three branches together and taking the middle one, the concept of the center is established, which defines the standard for human conduct. 丑 (Chou) corresponds to 艮 (Gen) as the body, and 寅 (Yin) corresponds to 艮 (Gen) as the common people. The number three represents the common people, so the Classic of Rites (Zhongyong) says, "Begin with the self, and verify with the common people." 子 (Zi) represents the Heaven's establishment, 丑 (Chou) represents the Earth's establishment, and 寅 (Yin) represents the Human's establishment, which corresponds to the Three Kings of Xia, Shang, and Zhou and the Three Dynasties. Therefore, it says, "Examining the Three Kings does not lead to error." By observing 乾 (Qian), one understands Heaven, so it says, "Consulting ghosts and spirits brings no doubt." By observing 艮 (Gen), one understands Humanity, so it says, "Waiting for a sage for a hundred generations brings no confusion." The fundamental principle of the Heaven and Earth and the branches 子 and 丑 lies in 戌 (Xu) and 亥 (Hai). A gentleman upholds the character of "Sincerity" throughout, which is to uphold 艮 (Gen) throughout. Therefore, the Classic of Rites (Zhongyong) says, "When sincerity is present, it takes form; when it takes form, it becomes evident; when it becomes evident, it becomes clear; when it becomes clear, it leads to action; when it leads to action, it brings change; when it brings change, it leads to transformation."

西北乾庸言庸行終之，乾戌遠，坤申近，知遠之近也。東南巽辰，風自乾亥，知風之自也。乾亥微，艮寅顯，知微之顯也。君子入德深藏乾亥下，人所不見，潛也。西北隅屋漏相在爾室，乾為斧為鉞，不怒而民威於斧鉞也。西北乾天至神道，丑用中本末盡以在之。乾天神道，於震無聲，於巽無臭，故曰“聲色之於以化民末也，上天之載無聲是無臭至也”。

Finally, it concludes with the northwest trigram 乾 (Qian) and its concept of 'ordinary words and actions'. 乾 (Qian) resides in戌 (Xu), representing distance, while 坤 (Kun) resides in申 (Shen), representing proximity. Therefore, the Zhongyong says 'knowing the distant as near'. The southeast trigram 巽 (Xun) is paired with 辰 (Chen), while wind originates from 亥 (Hai), where 乾 (Qian) resides. Hence, it says 'knowing the source of the wind'. 乾 (Qian) at亥 (Hai) is subtle and profound, while 艮 (Gen) at寅 (Yin) is manifest and clear. Therefore, it says 'knowing the subtle and making it manifest'. A gentleman in the initial stage of cultivating virtue hides deep beneath 乾 (Qian) at亥 (Hai), which is unseen by others, corresponding to the initial line of 乾 (Qian), 'qian' (hidden). The northwest corner is where the roof leaks, as the Book of Poetry says 'when you are in your room, do not feel ashamed even in the place where the roof leaks'. 乾 (Qian) represents axes and halberds, hence 'without anger, the people fear it more than axes and halberds'. The northwest trigram 乾 (Qian) represents the most divine way of Heaven. The position of 丑 (Chou) uses the middle, encompassing both beginning and end. The divine way of Heaven, in 乾 (Qian), is silent in 震 (Zhen) and odorless in 巽 (Xun). Therefore, the final chapter of Zhongyong says 'sound and color are not the way to transform people, they are the lesser things', 'Heaven's carrying on is silent and odorless, that is the ultimate'.

此“中庸”乾九二正中，庸言庸行，閒邪存其誠，善世而不伐，德博而化。《中庸》一篇，以化終之也。

Here the term 「中庸」 refers to the second line, nine two, of the Qian hexagram. Nine two is located in the middle of the lower trigram's third line, which is the position of 「正中」, from which the character 「中」 is derived. The Wenyan commentary on the Qian hexagram explains nine two as follows: 「Ordinary speech is trustworthy, ordinary conduct is cautious, guarding against evil thoughts and preserving sincerity, benefiting the world without self-praise, having broad virtue and being able to transform all things.」 Being trustworthy in ordinary speech and cautious in ordinary conduct is called 「庸言庸行」, from which the character 「庸」 is derived. Preventing evil thoughts to preserve sincerity, benefiting the world without boasting, and having broad virtue that can transform all things. The concepts of 「sincerity」 and 「transformation」 discussed throughout the Zhongyong text are derived from these statements, so its conclusion also ends with the character 「化」.

泰西之十字架，相傳以為耶穌代眾人受刑釘死於十字架上，故尊奉之，以為耶穌流血之紀念。此宗教家附會之說，不足信也。其實十字架者，乃數學之交線也。數不交不生，如兩線平行，各不相交，雖引之至於極長，縱環繞地球一周，仍為兩平行線而已，不生數也。惟兩線相交，成十字形，動則為圓，靜則為矩，而三角勾股八線，皆由此生焉。此乃幾何原本之原本，實數學之初祖。

The cross in the West is said to have originated because Jesus suffered crucifixion on a cross-shaped scaffold, and believers revere it as a memorial of Jesus' sacrificial death. This is a fanciful explanation by religious people, not reliable. In reality, the original meaning of the cross is the intersection of two lines in mathematics. Numbers cannot be formed without intersection; for example, two parallel lines go their separate ways and never meet, even if extended infinitely around the Earth, they remain just two parallel lines, producing no numbers. Only when two lines intersect, forming a cross, can they rotate to create a circle, and when stationary, form a right angle ruler. Triangles, the Pythagorean theorem, and trigonometric functions such as sine and cosine all originate from this. Therefore, this cross is the fundamental basis of Euclid's Elements, truly the ancestor of mathematics.

我國相傳之兩儀圖（今通俗皆稱為“太極圖”，其實此圖分陰分陽，有黑有白不可謂之太極，當名為兩儀圖，校為愜當。北方亦有稱之為陰陽魚兒者，魚字亦儀字之傳訛也），天然之配偶也。兩儀為理學之祖，由兩儀生四象，四象生八卦，變化無窮，莫不肇端於此一陰一陽。一陰一陽之謂道。道也者，形而上者也。

The traditional Chinese "Two Principles Diagram" (now commonly called the "Taiji Diagram") is actually a natural counterpart to the Western cross. One represents numbers, the other principles; one from the West, one from the East, perfectly complementary. The Two Principles are the origin of Neo-Confucianism. From the Two Principles come the Four Symbols, from the Four Symbols come the Eight Trigrams, and the transformations are endless, all originating from the interplay of one yin and one yang. The "Great Treatise" states, "Yin and yang together are called the Dao," and "Dao" belongs to the realm of the ultimate reality.

交線成勾股成三角八線，推衍無盡，莫不導源於此一縱一橫。一縱一橫數也。數也者，成器之所先也。形而下者也。故道運於虛，而數徵諸實。我國數千年來，專尚儒家以空言談經，鄙術數為小道，崇虛黜實，末流之弊，舉國皆無用之學。所謂形而上者，幾墜於地矣。

As for the intersection of lines, it gives rise to right angles, triangles, and trigonometric functions, and its derivations are endless, yet all originate from a single vertical and a single horizontal line. The vertical and horizontal lines belong to 'numbers'. Numbers are the prerequisite for making objects and belong to the level of the material world. Therefore, 'Dao' operates in the abstract, while 'numbers' must be verified through concrete facts. For thousands of years in our country, we have only praised Confucian scholars who talk about classics in abstract terms, and regarded numerical methods as a minor and inferior discipline. We have favored the abstract and rejected empirical verification, leading to the consequence that the whole nation's learning has become useless. Even their own proclaimed metaphysical Dao has almost fallen into oblivion, with no one to carry it forward.

泰西之學，則不尚空談，立一說必徵諸實驗，制一器必極其效用，不以理想為止境，不以無成而中輟，千迴百折，精益求精，於是科學功能，幾俟造化；器物利用，無阻高深；形學發達，於斯為盛。然極其弊，則謂世界將可以力爭，強權兒足以勝天演。物慾無限，而生人者適以殺人，殺人者即以自殺。物質之文明，浸成□焉不可終日之勢。此倚重於數之一偏，與倚重於理之一偏，各趨極端。其末流之失，亦正相等也。

Western scholarship does not emphasize empty talk; when establishing a theory, it must be verified by experiment, and when making an object, it must fully utilize its function, not taking imagination as the end, nor abandoning it halfway due to lack of immediate success. Through repeated trials and continuous refinement, the function of science almost rivals nature. The use of tools is not hindered by their complexity, and geometry thus flourishes greatly. However, pushing this to an extreme brings about drawbacks: people come to believe that worldly matters can be decided by force, and that power alone can overcome the laws of natural evolution. Unlimited desires, originally means for sustaining life, are now used for killing; the means for killing ultimately become self-destruction. When material civilization reaches this stage, it gradually becomes precarious, unsustainable. This is the extreme of the aspect of 'numbers,' while our country's emphasis on 'principles' also leads to extremes, and the errors of their respective extremes are equally severe.

夫理與數，本不可以須臾離。故聖人倚數，必參天而兩地。故形上之道，與形下之器，雖相生相成，無偏重亦無偏廢。舍道而言器，則器為虛器。離器而言道，則道盡空談。三代傳統，一揆諸道（故曰“道統”），不但禮樂政刑，悉本度數（度生於律，律本黃鐘，子丑一二），即德行言語（言語即文章也），亦無不各有其典則。（《孝經》“先王之法言法行”。法者，即合於度數者也。）故節以制度，以議德行，而《大學》治國平天下之道，必本於絜矩也。

Reason and numbers have never been separated for a moment. Therefore, the sage established numbers by following the principle of "participating in heaven and dividing by two," using the heavenly number three and the earthly number two to match. Although the formless Dao and the formed objects (qi) are interdependent and complementary, neither should be overemphasized nor neglected. If one discards Dao and talks only about objects, the objects become empty shells; if one leaves objects and talks only about Dao, Dao becomes mere empty talk. The traditions of the Xia, Shang, and Zhou dynasties all return to the root of Dao (hence called the "Dao tradition"), not only because rites, music, politics, and punishment are based on measurements and numbers (measurements come from the pitch, which is based on the Huangzhong tone, matching the number of Zi one and Chou two), but even virtues and speech (speech is literature) have their own rules and standards. (The "Xiao Jing" says, "The methods of the former kings' words and deeds," where "method" refers to conformity with measurements and numbers.) Therefore, the "Great Treatise" says to "regulate by institutional rules and discuss virtue," and the "Great Learning" also states that the way to govern the country and pacify the world must be based on "the principle of the square measure."

道不可見，故聖人示之以象。象無可稽，故聖人又準之以數。數與象合，而道無不可見。制器尚象，而器以立。載道以器，而道不虛。理象數一貫之道，皆出諸《易》。自王弼以玄理說《易》，後世畏象數之繁，因靡然從之，創掃象之說。（弼以玄理說《易》，運實於虛，歸有於無。芻狗天地，糟粕仁義，更何有於象？後儒既主其說，乃闢其玄談，是買櫝而還珠，亦非弼之所及料也。）自是象數與《易》，又離為二。

The Way is invisible, so the sage used "xiang" to display it; since "xiang" cannot be examined, the sage then used "shu" to define it. When "shu" and "xiang" are combined, the Way becomes visible. By using "xiang" to make objects, objects can be formed; by using objects to carry the Way, the Way does not become empty. The study that integrates principle, xiang, and shu all comes from the Book of Changes. Since Wang Bi explained the Book of Changes with metaphysical principles, later people feared the complexity of xiang and shu, and followed him blindly, creating the doctrine of "sao xiang" (rejecting xiang). (Wang Bi used metaphysical principles to explain the Book of Changes, transforming the concrete into the abstract and the existent into non-existence, viewing heaven and earth as straw dogs and benevolence and righteousness as dregs, leaving no room for xiang. Later Confucian scholars adopted his views but attacked his metaphysical discussions, which is like buying the box and returning the pearl, something Wang Bi could not have foreseen.) From then on, xiang and shu have been separated from the Book of Changes.

周子傳太極圖（實即兩儀，以為繼述道統之圖），道果在是矣，而器已無存（禮樂政刑皆器也），則道亦不亡而亡矣。諺曰“皮之不存，毛將焉附”，其是之謂歟？是故三代而後，易學晦盲，數學流於西方（西人於借根方名之曰“東來法”），理學顯於有宋。即此一縱一橫之十字架，分陰分陽之兩儀圖，足以為東西近世學術源流之代表矣。

The Taiji diagram passed down by Zhou Dunyi is actually the diagram of the two principles (two yi), using it as a model to inherit the transmission of the Dao. The Dao is indeed present here, but the instruments have completely disappeared (rituals, music, politics, and law are all instruments). Therefore, the Dao has only a name but no real existence. The proverb says, "If the skin is gone, where can the hair attach?" This is exactly the situation described. Therefore, after the Three Dynasties, the study of the Book of Changes became obscure and unclear. Mathematics was passed on to the West (Westerners call algebraic methods such as the method of solving equations by radicals the 'Eastern method,' showing their origin in the East). Meanwhile, Neo-Confucianism became prominent only during the Song Dynasty. On one side there is only numbers, on the other only principles. This vertical and horizontal cross and the diagram of the two principles (yin and yang) can serve as two representative symbols of the development of modern scholarship in both Eastern and Western traditions.

近西人極物質文明之益，即倦而知返，更探其原於哲學。我受理學空疏之害，尤備嘗苦痛力求自拔於沉淪。是東西人心，已同有覺悟之機。所謂通其變使民不倦，《易》窮則變變則通通則久，其在斯乎！故合中西之學，融會而貫通之。以此所有餘，助彼所不足；截此之所長，補彼之所短，一轉移間而各劑其平，各得其當，非《易》道又烏能貫而通之！

In recent times, Westerners have enjoyed the benefits of material civilization to the fullest, then become weary and turn to philosophy to seek the fundamental principles. We, on the other hand, have suffered greatly from the emptiness of Neo-Confucianism and are striving desperately to free ourselves from thispredicament. It is evident that the hearts of people in both East and West have now reached a moment of awakening. The Great Treatise says, "To understand the changes, so that the people will not grow weary," and "The Book of Changes reaches an end, then changes; changes lead to smoothness; smoothness leads to longevity." These words precisely describe the current situation. Therefore, we must integrate Eastern and Western learning, combine them and make them coherent. Use the excess of one side to compensate for the deficiency of the other, take the strengths of one to make up for the weaknesses of the other. With a single turn, both sides will achieve balance and appropriateness. If it is not the Way of the Book of Changes, what else could unify them?

夫十字架與兩儀圖，各產生於數千年前。一東一西，不相謀面。自西教東漸，於是天然配偶之兩代表，乃日相接近。又迭經幾許之歲月，始得消除種種之障害隔閡，而日即親洽，今殆去自由結婚之期會不遠矣。結婚以後，必能產生新文明之種子，為我全世界放一異彩。吾將摻券期之，拭目俟之矣。

The cross and the diagram of the Two Principles originated thousands of years ago, one in the East and one in the West, never having met before. Since the spread of Western religion to the East, these natural partners have gradually drawn closer. After many years, they have progressively overcome various obstacles and misunderstandings, becoming more and more intimate and harmonious. Now, the day when they can freely marry is probably not far off. After the marriage, they will certainly produce seeds of a new civilization, bringing a brilliant light to our whole world. I wish to hold this paper marriage contract as evidence, waiting for that day to come, watching with eager eyes.

宋以前言《易》者，未有圖也，而太極更不可圖。自周濂溪始為太極圖，又於太極之上添一無極，曰“無極而太極”。後儒因之，遂以太極為第二位，似乎太極之前，更有一無極之圖恍然在於心目間者，而不知其說之不可通也。

Before the Song dynasty, those who explained the Book of Changes never drew diagrams, let alone the Taiji (Supreme Ultimate). After Zhou Dunyi drew the Taiji diagram, he added the concept of "Wují" (Ultimate Void) above the Taiji, saying "Wují gives rise to Taiji." Later Confucian scholars followed this idea, placing Taiji in second position, as if there was another diagram of Wují floating vaguely in the mind before Taiji. But they did not realize that this notion is fundamentally incoherent.

《繫傳》曰“《易》有太極”。極者，至極而無對之稱。物各有極，故曰“天極”，曰“地極”，曰“人極”。陽有陽極，陰有陰極，所以別之曰“太極”。太者，至尊無上之稱，原以對三極及其他諸極而言也。即曰太極，則太字之上，又何能更有所加？況無者，有之對也。既可名之曰無，則無之對便是有。若云無極而有極則可，無極而太極，則文不當而辭不順也。

The *Great Treatise* says, "The *Book of Changes* has the Supreme Ultimate." "Ultimate" refers to the utmost limit, something without a counterpart. All things have their own ultimate, so there is a "heavenly ultimate," a "terrestrial ultimate," and a "human ultimate"; yang has its yang ultimate, and yin has its yin ultimate. In order to distinguish these, it is called the "Supreme Ultimate." "Tai" means supreme and exalted, and originally it is a name established in contrast to the three ultimates and other various ultimates. If it is already called the Supreme Ultimate, what can be added above the character "Tai"? Moreover, "wu" (nothingness) is in contrast to "you" (being). Since it can be called nothingness, then the opposite of nothingness is being. If one says "from nothingness to the ultimate of being," the reasoning is still coherent. But to say "from nothingness to the Supreme Ultimate" is inconsistent in terms of meaning and also awkward in expression.

夫太極者，渾淪無端，立乎天地之先，無名可以名之，無象可以象之。老子所謂“有物無形，先天地生，無以名之，強名之曰道”者，庶乎其近之。《易》道元亨利貞，而太極者，乃元之所自出。今之言幾何學者，曰點線面體，此物質之元亨利貞也。故物之形皆起於一點，謂之起點。而以精神上言之，則必有以立乎此起點之前者。

The Taiji is a single, undivided entity, without beginning or end, existing before heaven and earth. It cannot be named or imaged. Laozi said, "There is something that has substance but no form, born before heaven and earth. It cannot be named, so it is called Dao." This is almost the same meaning. The Book of Changes speaks of four virtues: Yuan, Heng, Li, and Zhen. The Taiji is the source from which Yuan originates. Today, those who study geometry say that points, lines, surfaces, and solids are four elements, which correspond to the four virtues in the material world. Therefore, any form begins with a point, called the "starting point." But from the spiritual perspective, there must be something that exists before this starting point.

言能得此起點，譬有二人於此，甲繪平圓圖，而乙繪立方圖。平圓立方，各有其起點，起點之形式同也。而繪成以後，則圓者自圓，方者自方。則因甲於起點之前，其胸中之所蘊蓄者，已完具一平圓之形象。乙於起點之前，其胸中之所蘊蓄者，已完具一立方之形象。此蘊蓄者，即為平圓與立方之太極也。然當其未落筆以前，又烏從而見之？烏從而聞之？

This principle can be explained from the starting point. For example, here are two people: Jia draws a circle, and Yi draws a square. Both the circle and the square have their own starting points, and the form of the starting point is exactly the same. However, after they are drawn, the circle remains naturally circular, and the square remains naturally square. This is because before Jia begins to draw, the complete image of a circle already exists in his mind; before Yi begins to draw, the complete image of a square already exists in his mind. This stored image in the mind is the Taiji of the circle and the square respectively. However, before they start to draw, where can this stored image be seen or heard? How can it be perceived? Clearly, although it is real, it cannot be sought after in terms of sound or form.

所以雲萬事萬物各有其太極，而《易》有太極，則在兩儀未判陰陽無始以前，先天渾沌之中，自有此肫然穆然、孕育萬物，具足萬理之渾淪元氣，以立乎天地之先，而為造化之主宰者，無形可象，無名可稱。孔子稱之為太極，已至矣盡矣。更何能於此外再加一字，再著一筆乎？加一字，著一筆，即非太極矣。

Therefore, all things and phenomena have their own Taiji. As for the Taiji mentioned in the Book of Changes, it exists before the two principles (yin and yang) have been differentiated and before the beginning of yin and yang, within the primordial chaos of the Earlier Heaven. There is inherently a single, sincere and tranquil primordial qi that nurtures all things and contains all principles. It stands before heaven and earth, as the master of creation. It cannot be depicted in form or named. Confucius gave it the name 'Taiji', which already expresses the ultimate and the extreme. How could there be another character or stroke added to this name? Once a character is added or a stroke is made, it falls into words and forms, and thus is no longer Taiji.

惟周子之所謂太極者，即有其圖，圖中有黑有白，有陰有陽，是即兩儀四象，實已不可謂之曰太極。故又加一無極於其上。蓋為中人以下說法，非有跡象可指，不能以言語形容，乃繪此圖以明一陰一陽之道所由來，使人可一覽而得，其用心亦良苦矣。

Zhou Dunyi said that since the Taiji had already been represented in a diagram, which contained black and white, yin and yang, it was actually the two principles and four images, and could no longer be called Taiji. Therefore, he added the term "wuji" above it. He did this primarily for those with average or lower intellectual capacity: since Taiji has no form or trace and cannot be described with words, he drew this diagram to explain the origin of the principle of yin and yang, so that people could understand it at a glance. His intention can be said to have been very thoughtful.

但以本無跡象之太極，以跡象求之，終有語病，無論如何設辭，終覺似是而非。（太極沖溟無形，可以意會，不可以言傳。言傳則有聲，有聲非太極也。著筆則有象，有象非太極也。）若讀者不善體會，以辭害意，是將使太極之真相，終無由瞭解。所謂“差以毫釐，謬以千里”矣。可不慎哉！

But to seek the formless Taiji with forms and traces inevitably leaves linguistic flaws. No matter how one phrases it, it always seems somewhat ambiguous. Taiji is vast and empty, indistinct and formless; it can only be understood by the mind and not transmitted through words. Once expressed in words, it has sound, and once it has sound, it is no longer Taiji; once written down, it has form, and once it has form, it is no longer Taiji. If readers are not good at grasping the meaning, they may be hindered by the words, and thus the true nature of Taiji will forever remain unknown. This is precisely what is meant by "a slight error at the beginning leads to a great mistake later." How can we not be cautious!

生生之謂《易》，故《易》道遏惡而揚善，好生而惡殺，此所以扶陽而抑陰也（陽以象善，陰以象惡也）。自專制帝王，借經術以愚民，而頭巾腐儒，又逢惡助長，曲借經文為乾祿固寵之具，於是正義湮晦。古聖救世之經文，幾反為賊民之愛書矣。尊君而抑臣，貴君而賤民，受誣之甚，莫過《易》與《春秋》。蓋《春秋》亦原本於《易》者也。

The Great Treatise says, "To produce life is called the Book of Changes." Therefore, the principles of the Book of Changes restrain evil and promote goodness, favor life and detest killing. This is why it supports Yang and restrains Yin (Yang symbolizes goodness, and Yin symbolizes evil). Since autocratic emperors have used Confucian classics to deceive the people, and those corrupt scholars in square hats have flattered the authorities and encouraged their wickedness, twisting the classics and using them as tools for seeking official positions and securing favor, the righteous principles within the classics have become obscured and forgotten. The ancient sages' writings meant to save the world have almost become evidence for harming the people. The doctrines of honoring the sovereign and suppressing the ministers, valuing the sovereign and despising the people, have been most misinterpreted and slandered, none more so than the Book of Changes and the Spring and Autumn Annals—the Spring and Autumn Annals itself was originally derived from the Book of Changes.

來瞿塘氏《易注》，尚為善本。乃其釋乾元用九，亦云為人君者體春生之元，用秋殺之元，一張一弛，為天道之法則。道千古人君以殺人者，皆此等曲說階之厲也。夫春生秋殺，《易》固無此明文。後儒以此明天地之氣，盈虛消息，亦如陽死陰生，陰死陽生之類。非春以生之者，至秋必殺之，天地預存一必殺之心也。

Lai Zhide's "Collected Commentaries on the Zhou Changes" is still considered a good edition, but he explains the term "Yuan" and "Yong Ji" in the Qian hexagram, saying that a ruler should observe the "Yuan" of spring's generation and use the "Yuan" of autumn's severity, alternating between relaxation and restraint, which is the principle of the Way of Heaven. Throughout history, those who have provided rulers with paths to kill people have all been caused by such twisted interpretations. In fact, the phrase "spring generates, autumn kills" is not explicitly stated in the "Zhou Changes." Later Confucian scholars used it to explain the waxing and waning of the energies of heaven and earth, similar to the idea of yang dying and yin being born, or yin dying and yang being born. It does not mean that because something is generated in spring, it must necessarily be killed in autumn, as if heaven and earth had a predetermined intention to kill.

帝王亦人耳，以人殺人而謂之道，而謂之天道之法則，可謂誣聖蔑經之甚矣。孔子懼人之誤解也，故特於《繫辭傳》鄭重以明之，曰“吉凶與民同患”，又曰“其孰能與於此哉！古之聰明睿知神武而不殺者夫”！聖意之深遠，亦可謂周且至矣，而謬誤仍若此。諸注類是者，不勝枚舉。聊舉一二，以見讀注者，當具隻眼。以辭害意且不可，況經本無其辭，而以意出入之，其誤天下後世也大矣。

Emperors are merely human beings; to kill people and call it the Dao, or the principle of the heavenly Dao, is an extreme defamation of the sages and a desecration of the classics. Fearing that later generations might misunderstand, Confucius deliberately emphasized in the Great Treatise that "good fortune and misfortune are shared by the people," and also said, "Who could possibly be involved in this? It must be the ancient wise and enlightened ruler who was both divine and martial yet did not resort to killing." How profound and comprehensive the sage's meaning is, yet misunderstandings remain as prevalent as ever. There are countless examples of such misinterpretations in the annotations of various schools. Here I will mention just a couple, so that those reading the annotations of the Book of Changes may know that they must have their own independent perspective. Using words to obstruct the meaning of the classics is already unacceptable, and how much worse it is when the classics themselves do not contain such words, yet people add or subtract according to their own interpretations, thereby causing even greater confusion for future generations.

日光具七色光線，而此七色之光線，動而合成一色，則為白色，此近世泰西科學家所發明也。現時學校儀器中，有一種圓形之平面版，其上分繪七色。附一機輪，以皮帶聯之，搖其輪令此圓版之旋轉極速，則只見白色。（另以青黃二色之版轉動則成綠色，紅青二色者則成紫色，其他之色之配合亦各如其應得之色，而色之深淺則以兩色所占面積之多寡而分，與兩色之顏料相調合者無異。惟七色則只成白色。）即所以證明七色變白之說也。凡高等小學以上之學生，殆無不知有此者矣。

Sunlight contains seven colors: red, orange, yellow, green, blue, indigo, and violet. When these seven colors are mixed together, they form white, a discovery made by modern Western scientists. Nowadays, there is a round flat disc in school laboratories, with each side painted in one of the seven colors. It is connected to a wheel by a belt. When the wheel is turned rapidly, the seven colors overlap quickly, making it impossible to distinguish them, and the eye perceives only a single white color. If green and yellow are mixed, green is produced; if red and green are mixed, purple is produced. Similarly, other color combinations produce their respective colors. The brightness or darkness of the resulting color depends on the proportion of the areas of the two colors, just like mixing two pigments. However, when all seven colors are combined, none of them is visible, and only white is seen. This instrument is used to demonstrate the principle that seven colors combine to form white. Almost all students in higher elementary schools know about this.

然我國舊學家，固未有言之者也。不料《易經》於數千年以前，早已發明之。象義明晰，確切不移，與西人之說正相吻合。其象即見於山火賁之一卦，賁離內艮外，離為日，離居九位，九宮之色：一白，二黑，三碧，四綠，五黃，六白，七赤，八白，九紫。數雖九，而白居其三，並之仍為七色。離為日而居九位，則自當有七色，與西說正相同也。

However, our old scholars had never discussed this principle before. Unexpectedly, the Book of Changes revealed it thousands of years ago: the meaning of the hexagrams is clear and definite, consistent with the Western theory. This image is seen in the hexagram of "Brightness" (Zhen). In the hexagram of Zhen, the trigram Li is inside and the trigram Gen is outside. Li represents the sun. In the nine palaces, Li is in the ninth position. The colors corresponding to the nine palaces are: one white, two black, three green, four green, five yellow, six white, seven red, eight white, and nine purple. Although there are nine colors, white appears three times, making a total of seven colors. Since Li represents the sun and is in the ninth position, it naturally should have seven colors, which coincides exactly with the Western theory.

由九三至六五，中爻為震。震，動也。震動而離之七色皆變為白，故六四曰“白馬翰如”（翰如即轉動極速之狀也），至上九曰“白賁無咎”。曰“白賁”，則全卦皆變白矣。與七色變白之新學說，完全吻合，無一絲一毫之勉強穿鑿。而“翰如”二字，則幾將近日學校所用之儀器，並其轉動之狀曲繪而出，可謂神妙不可思議矣。子曰“《易》之為書也，廣大悉備”，略指其一而已可見矣。惜我國讀《易》者，皆忽略讀過，更無科學之知識與眼光以研究之，宜乎其不可解者多矣。

Taking the lines nine in the third, six in the fourth, and six in the fifth to form the interacting structure, the middle layer of the hexagram is Zhen. Zhen means movement. When Zhen moves, the seven colors of Li turn completely white. Therefore, the line statement of six in the fourth says, "A white horse gallops swiftly" ("gallops swiftly" means moving very fast). By the time we reach the line statement of nine at the top, it says, "White purity without blame" — meaning the entire hexagram has turned white. This perfectly matches the new theory that seven colors turn white. There is not the slightest forced or artificial interpretation. The two characters "gallops swiftly" almost depict the instrument used in schools today and its spinning motion, in a winding and intricate way. It is truly amazing beyond measure. Confucius said, "The Book of Changes is vast and comprehensive," and merely citing this example from the hexagram of Ben shows that this praise is not empty. Unfortunately, those who study the Book of Changes in our country have easily overlooked it, and lack scientific knowledge and insight to investigate it, which is why so many parts remain difficult to understand.

（朱子注《易》，至理有不可通，輒以不可解或未詳二字了之。然尚能闕疑者也。後人或錯綜其象以求之，或為卦變、爻變以附會之。但求於象可以聯屬，不顧義理之是否可通，與本卦之才物是否應有此理者，蓋比比矣。如賁卦之白字，或以為巽為白。而本卦無巽，則曰艮錯兌，兌反巽也。或以六五變則上卦為巽，故言白也。而不顧巽之義為入為伏，與本卦之義固皆無當也。唯中爻為震，震下伏巽，動而為白，義尚較近。然不以新說參證之，又烏知古聖取象之妙，實與造化同工，斷非拘拘於一爻一卦之單辭所能悉解也。）

Zhu Xi annotated the Book of Changes, and when he encountered passages whose meanings did not make sense, he often simply used the words "inexplicable" or "unknown" to pass over them, which was still considered a way of preserving doubt. Later commentators, however, attempted to solve problems by misinterpreting the hexagram images, or by using changes in hexagrams and yao changes to force interpretations, seeking only to connect the images together, regardless of whether the meaning made sense or whether the subject matter of the original hexagram could logically have such a meaning. Such examples are common among commentators. For instance, the character "white" in the hexagram Bi is said by some to be associated with Xun, but since Xun is not present in the original hexagram, they argue that Xun and Gen are opposite, and that Xun is the reverse of Xun. Others say that the fifth line changes, making the upper trigram Xun, thus explaining "white." They all ignore the meaning of Xun, which is "entering" or "hidden," and the meaning of the original hexagram, which has nothing to do with it. Only those who take the middle line as Zhen, with Xun hidden beneath Zhen, and a movement resulting in "white," offer an interpretation that is somewhat closer to the meaning of the original hexagram. However, without referring to new theories, how could one know that the subtle imagery used by the ancient sages was truly in harmony with the workings of nature, and not something that could be fully understood by merely clinging to isolated phrases from a single line or hexagram?

西教士花之安氏，頗注意於中國之經籍，曾著《自西徂東》一書，謂畫卦之伏羲，乃巴比倫人。巴比倫高原，為西洋文化策源地。伏羲八卦，以乾為天，以坤為地，至今巴比倫人猶稱天為乾，地為坤，此一證也。又巴比倫亦有十二屬象，與中國之十二辰大略相同，其證二也。

The missionary Hua Zhi'an from the West paid close attention to Chinese classics and wrote a book called "From West to East," claiming that the Fuxi who drew the trigrams was a Babylonian. His reasoning was that the Babylonian highlands were the origin of Western culture; Fuxi's eight trigrams used Qian for Heaven and Kun for Earth, and the Babylonians still call Heaven "Qian" and Earth "Kun" today, which is the first piece of evidence. Babylon also has twelve zodiac animals, which are largely the same as China's twelve earthly branches, which is the second piece of evidence. Based on this, he concluded that the study of the eight trigrams originated from Babylon and not from China itself.

或因花氏之說，更加推求，謂伏羲畫卦，以備萬物之象。宇宙偉大之象，無不列舉，如天地水火風雷山澤，以配八卦。而海為天地間最大之一象，獨付闕如。而舉澤以為山之對，則亦一疑問也。巴比倫介歐亞之間，四面皆大陸，距海最遠。其間惟裡海死海，為瀦水最大之區，故稱之為澤，亦足證花氏之說不盡無因。花氏更稱巴比倫古代之王，有號福巨者，與伏羲二字音亦相近。當即為始畫八卦之人，亦可謂讀書得間矣。

Some followed Huazhi'an's view and went further to explore, saying that Fuxi's drawing of the eight trigrams was intended to include all the images of things in the universe, listing all great phenomena, such as heaven, earth, water, fire, wind, thunder, mountain, and marsh, assigning them to the eight trigrams. However, the sea, which is the largest phenomenon between heaven and earth, is missing from the eight trigrams, and there is no place for the sea in the trigrams. Instead, "marsh" is used to oppose "mountain," which raises a question. Babylonia is located between Europe and Asia, surrounded by land on all sides, and is farthest from the sea. Within its territory, the largest bodies of water are the Caspian Sea and the Dead Sea, which are considered "marshes." This shows that Huazhi'an's view is not entirely without basis. Huazhi'an also said that in ancient Babylonia, there was a king known as "Fujü," whose name is phonetically similar to "Fuxi," and should be the one who first drew the eight trigrams. This can be considered reading between the lines and understanding the meaning from the text.

但我國上古之史，雖無可稽考，然自伏羲而後，代有傳人。一畫開天，即文字所造始。儷皮為禮，已姓氏之足徵。在中國之佚聞古蹟，無有可為伏羲來自遠方之證者。況伏羲之陵，猶在中州，至今無恙。其果否為伏羲埋骨之所，雖無從徵實，但有一事足以參證，有決非人力所能為者，則古聖揲以求卦之蓍草是也。

But although the history of ancient China cannot be verified, there have been continuous records since the time of Fuxi. The "one line opening the heavens" refers to the beginning of writing; using pairs of deer skins as gifts already indicates the existence of surnames that can be verified. In China's legends and remains, there is no evidence that Fuxi came from afar. Moreover, Fuxi's tomb is still intact in the central plains. Whether or not it is indeed where Fuxi was buried cannot be confirmed for certain. However, there is one thing that can be used as evidence, and it is certainly not man-made. That is the yarrow stalks used by ancient sages for divination.

孔子曰：昔者聖人之作《易》也，幽贊於神明而生蓍。至今蓍草所產之地，厥惟伏羲文王周公孔子之墓，而他處無有也。（惟近今所生之蓍不及古時之長，余嘗採蓍於孔林，最長者乃不滿今尺三十寸，以合周尺僅四尺餘。所謂六尺及盈丈者，詢之孔氏，雲久未得見矣。）夫文周與孔子之墓，固確為聖穴，決無可疑。則伏羲之陵而有蓍草，亦斷然足證其非妄矣。其非巴比倫產，可不辨自明。

Confucius said in the "Shuo Gua Zhuan" that in ancient times the sages composed the Book of Changes, receiving divine assistance and producing the yarrow stalks. Up to the present day, the only places where yarrow stalks grow are the tombs of Fuxi, King Wen, the Duke of Zhou, and Confucius. Elsewhere, there are none. (Recently grown yarrow stalks are not as long as in ancient times. I once gathered yarrow stalks in the Confucius family graveyard, and the longest ones were no more than thirty inches long today, which is only four feet and more in Zhou measurements. Ancient texts mention six feet or even up to a zhang, but when I asked the descendants of Confucius, they said such stalks had long since disappeared.) The tombs of King Wen, the Duke of Zhou, and Confucius are indeed the resting places of sages, without any doubt; therefore, the fact that yarrow stalks grow on the tomb of Fuxi is sufficient to confirm that this tomb is not fabricated. If this is the case, then Fuxi is not from Babylon, and this can be clearly established without argument.

或者當伏羲之時，西北之人物殷繁（其時東南皆水陸地不多），治化流被於歐亞兩州之交，故巴比倫得有伏羲之學說（逮洪水為災，地形改變，流沙阻隔，西道遂不復通，故禹域西限流沙），未可知也。至八卦之象無海，則有說焉。夫江河海洋，皆後起之名辭。伏羲時文字未興，烏得有此析類之名？卦象水火山澤，皆以對舉為文。海固無可對也，故以澤對山。洪荒之世，世界一澤國耳。舉目所見惟山與澤，則亦以山澤象之耳。《周易》為中古之書，取象較廣。坎為大川，大川亦即海也。焉得以數千年後之名詞，而致疑於上古之世哉！

Perhaps during the time of Fuxi, the area to the northwest was densely populated, while the southeast was mostly water and had little land. The teachings spread to the border of Eurasia, so Babylon preserved Fuxi's doctrines. Later, due to floods and changes in the terrain, shifting sands blocked the western route, hence the western boundary of the territory set by Yu the Great was marked by shifting sands. This may be possible. As for the absence of the sea in the imagery of the Eight Trigrams, there is another reason. The terms river, river, sea, and ocean are later names. Writing had not yet emerged in Fuxi's time, so how could there be such specific classifications? Moreover, in the trigrams, water, fire, mountain, and marsh are paired. Since the sea has nothing to pair with, it is paired with marsh. In the age of chaos and wilderness, the whole world was merely a marshland, and all that could be seen were mountains and marshes, so they used mountain and marsh as symbols. The Zhou Yi is a book from the middle ancient times, and its imagery is broader. The trigram Kan represents a great river, which is also the sea. How can we use terms that appeared only thousands of years later to question the ancient times?

西人物質之化分，譯之為化學者，乃近世紀所發明者也。不謂地隔三萬里，時閱七千年，而吾《易》之象數，能與之一一吻合無毫釐之差。嗚呼！是所謂範圍天地而不過，曲成萬物而不遺者，豈空談性理所能悉其奧旨哉！張氏之銳《易象闡微》，取氣之分劑性質，以卦位爻數乘除推衍，無不妙合。尤奇者，陽三而陰二，足證古聖參天兩地之數，固俟之萬世而不惑者也。

Westerners study matter by breaking it down, and they call this study "chemistry," a discipline that has only recently emerged in the last one or two hundred years. It is amazing that, despite being three thousand miles apart and seven thousand years apart in time, the images and numbers in our Book of Changes can correspond with it one by one, without any error at all. How regrettable! The "Great Treatise" says, "It encompasses all transformations in heaven and earth without exceeding, and skillfully completes all things without omission." How could such profound meanings be understood by those who merely talk about the nature of the mind and principles? Zhang Zhiui's work, "Explanations of the Images of the Book of Changes," uses the proportions and properties of various kinds of qi (i.e., atomic weights) and applies them through hexagram positions and line numbers for calculations, and they all perfectly match. Especially remarkable is the use of the number three for yang and two for yin, which clearly proves that the ancient sages' principle of "three for heaven and two for earth" is indeed something that will never be doubted in future generations.

《易》以陽為氣而陰為質，乾坤氣質之總綱，六子乃氣質之分類。故氣質之分晰，當於六子求之。輕氣（亦曰水素）比較各氣重量為最輕，於《易》為震象，以乾通坤初，出於震之卦氣也。震初一陽始復，其幾甚微，故其氣甚輕。（地山謙，坤艮皆重也。乃曰謙輕者，亦以三四五爻之互震也。）震為動為陽，陽之氣輕清而上升，故坤變為震。動而氣升，則乾即成巽而為風。蓋乾陽之坤，熱漲上騰，而乾之本體反虛。他處空氣入而補之，因動盪而為風也。

The Book of Changes takes yang as qi and yin as substance. The two trigrams Qian (Heaven) and Kun (Earth) are the general principles of qi and substance. The six trigrams Zhen (Thunder), Kan (Water), Gen (Mountain), Xun (Wind), Li (Fire), and Dui (Lake) are the specific classifications of qi and substance. Therefore, to distinguish between qi and substance, one should look to these six trigrams. Light qi (also called water element, which is today's hydrogen) is the lightest among all qi. In the Book of Changes, it is associated with the trigram Zhen. This is because it is the first line of Qian, the initial yang line that emerges from Zhen, representing the qi that flows from Heaven to Earth. The first line of Zhen is a single yang line that has just begun to arise, which is extremely subtle, hence its qi is very light. (The hexagram "Modesty" (Earth over Mountain) has both Kun and Gen, which are heavy, yet it is called "Modesty" and "Light," because the third, fourth, and fifth lines together produce the trigram Zhen.) Zhen represents movement and yang. Yang qi is light and rises, so Kun transforms into Zhen. When there is movement, the qi rises, and Qian transforms into Xun, becoming wind. This is because the yang of Qian enters the yin of Kun, expands due to heat, and rises. As a result, the original body of Qian becomes empty, and air from elsewhere flows in to fill the space. Because of this movement and turbulence, wind is produced.

凡卦爻本體，不能互成他卦者，當為獨立之原點。其可以互成他卦者，即為化合之合點。如坎（六畫卦）五陽以上無互體，為獨立養氣（亦曰酸素）原點。下互艮為淡氣，此即養氣當與淡氣相合之象也。若五陽下降至四，則亦互震體，而變為雷雨作解。此即輕氣上升，與天空養氣化合而成雨之象也。又如震初陽無互體，為輕氣獨立原點。四陽互艮互坎，此亦與淡氣相和，及化合成雨之象也。

Any hexagram line that cannot generate other hexagrams is considered an independent origin, just like chemical elements; if it can generate other hexagrams, it is a point of combination. For example, the hexagram of Kan (Water), with its nine in the fifth line, has no further interrelated hexagram above it, making it an independent origin of yang energy (also called acid element, i.e., oxygen); below it, it generates Gen (Mountain), which represents neutral energy (i.e., nitrogen), exactly reflecting the combination of yang energy with neutral energy. If the nine in the fifth line descends to the fourth position, it then generates Zhen (Thunder), transforming the hexagram into Jie (Release), which represents light energy rising and combining with yang energy in the sky to form rain. Similarly, the initial line of Zhen (Thunder) has no interrelated hexagram, making it an independent origin of light energy; the nine in the fourth line generates Gen and Kan, reflecting the combination with neutral energy and the formation of rain.

坎五之陽由乾二來也，以陽三（爻體陽三陰二）與五位相加為八，以二乘八得數十六。震初之陽，由乾四來也。以陽三與初位相減為二，以二除四，仍得二二：十六二一：八，故輕氣之分劑數（亦曰原子量）為一，養氣之分劑數為八，一以乘得數，一以除得數也。

The Yang of the fifth line in the Kan hexagram comes from the Yang of the second line in the Qian hexagram. Using the Yang number three (Yang takes three, Yin takes two) and adding it to the fifth position, we get eight. Then multiplying eight by two gives sixteen. The Yang of the first line in the Zhen hexagram comes from the Yang of the fourth line in the Qian hexagram. Using the Yang number three and subtracting it from the first position, we get two. Then dividing four by two still gives two. The ratio of two to sixteen reduces to one to eight, so the numerical value for the light element (also called atomic weight) is set to one, and the numerical value for the nourishing element is set to eight: one is derived from multiplication, and the other from division.

淡氣（亦曰窒素）者，愛力甚小。而其性安靜無為，其作用但在節止養氣之太過，故知此氣必為艮之卦氣（艮靜而止）也。如艮九三上九兩陽爻，皆為淡氣。上九之陽由乾三來，九三之陽由乾上來。以陽三與上位六相加則為三，三以陽三加入三位，則為二三。

The affinity of the subtle energy (also called inert gas, i.e., nitrogen) is very weak, and its nature is quiet and inactive. Its function is only to restrain and regulate the vital energy so that it does not become excessive. From this we can infer that this kind of energy must belong to the Qian trigram (Gen), since Gen's nature is quiet and capable of stopping. For example, in the Gen hexagram, the ninth line in the third position and the ninth line at the top are both yang lines that belong to the subtle energy. The yang line at the top comes from the ninth line in the third position of the Qian trigram, and the yang line in the third position comes from the top line of the Qian trigram. Adding the yang number three with the upper position six gives the divisor three used later; adding the yang number three with the number three gives the multiplier two used later.

艮下體之卦位，其和數為六（初二三之和）。上體之卦位，其和數為十五（四五六之和）。六與十五之和數為二十一，以三除之得七，後以二乘七得十四（以三除者陽，加於上位得三，陽數也。以二乘者陽，加於三位得二陽數也），為淡氣一分劑數。輕養二氣之乘除，以反對為用，淡氣則自為乘除。由此推之，可見卦氣每生一物，必變化其方式。方式不同，故形質有異也。

The third line of the lower trigram in the "Gen" hexagram adds up to six (the sum of the first, second, and third lines). The third line of the upper trigram adds up to fifteen (the sum of the fourth, fifth, and sixth lines). Adding six and fifteen gives twenty-one. Dividing twenty-one by three results in seven. Then multiplying seven by two gives fourteen. The reason for using three as the divisor is that the yang number three is added to the upper position, making it three, which is a yang number. The reason for using two as the multiplier is that the yang number three is added to the third position, resulting in two, which is also a yang number. The number fourteen is thus a component number of the "dàn qì" (thin qi). The multiplication and division of "qīng qì" (light qi) and "yǎng qì" (nourishing qi) are used in opposition to each other, while "dàn qì" uses multiplication and division within itself. From this, it can be seen that whenever a hexagram generates an object, it must change its calculation method. Since the calculation methods differ, the forms and substances produced are also different.

輕淡養為三少陽氣類原點。此三氣者，常混合瀰漫於空中者也。試以三類氣質合成卦象如□，即蒙卦也。上艮為淡氣，下坎為養氣。九二六三六四互震為輕氣，九二至上九共歷五位。陽自初至二進一位，自初至上進五位。養氣即生，則應消去淡氣一位。故養氣居空氣五分之一，淡氣居空氣五分之四，而輕氣體積則甚小。輕養淡三氣混合瀰漫而成蒙象。蒙象者，其地球表面之蒙氣乎？

The three types of qi, light qi, thin qi, and nourishing qi, originate from the category of the three yangs. These three types of qi often mix together and spread throughout the air. If we combine these three types of qi into a single hexagram (the original hexagram is now missing), it forms the Hexagram of Enlightenment. The upper trigram is Gen (Mountain), representing thin qi, and the lower trigram is Kan (Water), representing nourishing qi. The lines nine in the second, six in the third, and six in the fourth interact to form Zhen (Thunder), representing light qi. Counting from nine in the second to nine at the top, there are five positions. Yang moves from the initial position to the second position, advancing by one position, and from the initial position to the top position, advancing by five positions. When nourishing qi is generated, it should decrease by one position from thin qi. Therefore, nourishing qi occupies one fifth of the air, thin qi occupies four fifths of the air, and the volume of light qi is extremely small. The mixture of light, nourishing, and thin qi forms the hexagram of Enlightenment. The term 'Mont' probably refers to the layer of misty qi that envelops the Earth's surface.

綠氣（亦曰鹽素）能漂白物色，其臭甚烈，能傷人，此巽之象也。《說卦傳》“巽為白，又為臭”，又曰“巽也者言萬物之絜齊也”，皆綠氣之性能功用也。如巽□象，下體陽爻，積與位之和為十一（陽三加二位為五，陽三加三位為六，合之為十一也）。上體陽爻積與位之和為十七（陽三加五位為八，陰三加上位為九，合之為十七也），下體陰爻積與位之和為三（陰二加初位為三），上體陰爻積與位之和為六（陽二加四位為六），以三減六得三，以初加四得五。三五相加，再與十一十七相和，即等三十六，為綠氣之一分劑數（綠氣之一分劑數或作三五一五）。

Green gas (also called salt, which is today's chlorine) can bleach the color of objects, has a very strong smell, and can injure people when inhaled. This is exactly the image of Xun. The "Say on the Hexagrams" says, "Xun represents white," and also says "Xun represents smell," and further says, "Xun is the one who speaks of the purity and order of all things." "Purity and order" refers to the function and ability of green gas. According to the image of the Hexagram Xun (the original hexagram diagram is now missing), the sum of the number of yang lines and their positions in the lower trigram is eleven (three yang lines plus two positions equal five, three yang lines plus three positions equal six, altogether eleven); the sum of the number of yang lines and their positions in the upper trigram is seventeen (three yang lines plus five positions equal eight, three yang lines plus six positions equal nine, altogether seventeen); the sum of the number of yin lines and their positions in the lower trigram is three (two yin lines plus the first position equal three); the sum of the number of yin lines and their positions in the upper trigram is six (two yin lines plus the fourth position equal six). Subtracting three from six gives three, adding the first position and the fourth position gives five, and three plus five equals eight. Adding this eight to eleven and seventeen gives exactly thirty-six, which is a number representing green gas (there is also a version of the number for green gas as thirty-five point fifteen, which is slightly different from this).

炭氣（亦曰炭素）為有形質之氣，故化學家謂之非金類，而煤炭所含者為最多。若在氣質內，則常與養氣化合，所謂炭養二是也。蓋炭氣之原點屬離，離陰卦也。陰常附陽（離麗也，必附麗於他物而始見。離為火，火必附於物始燃），是為有形質之物。故炭氣與綠氣，不能如輕淡養三氣，能卓然獨立於空氣界也。

Carbon gas (also called carbon, which is a tangible gas) is classified by chemists as a non-metal, and it is most abundant in coal. When carbon gas exists in a gaseous state, it often combines with vital gas, known as "carbon and vital," with one part carbon combining with two parts vital. The origin of carbon gas is associated with the hexagram Li, which is a yin trigram. Yin often depends on yang (the term "Li" means "adhering," meaning that it must adhere to something else to be visible. Li represents fire, which also needs to be attached to an object in order to burn). Therefore, carbon gas is a tangible substance. Because of this, carbon gas and green gas cannot exist independently in the air like the light, thin, and vital gases.

□離卦二陰自坤五而來，下體陽爻積與位之和為十（陽三加初位為四，陽三加三位為六，合為十也）。上體陽爻積與位之和為十六（陽三加四位為七，陽三加上位為九，合為十六）。以上體陽五位數，除下體陽爻積與位之和，得數二。以下體陰二位數，除上體陽爻積與位之和得數八。二與八之較六，即為炭氣之一分劑數（綠氣一分劑數由和而得，炭氣一分劑數由較而得方式亦不同也）。

In the hexagram Li (Fire), the two yin lines are both derived from the fifth line of the hexagram Kun (Earth). The sum of the number of yang lines and their positions in the lower trigram is ten (three for yang plus the initial position gives four, three for yang plus the third position gives six, totaling ten). The sum of the number of yang lines and their positions in the upper trigram is sixteen (three for yang plus the fourth position gives seven, three for yang plus the top position gives nine, totaling sixteen). Using the fifth position occupied by the yang lines in the upper trigram to divide the sum of the lower trigram, which is ten, the result is two. Using the second position occupied by the yin lines in the lower trigram to divide the sum of the upper trigram, which is sixteen, the result is eight. Subtracting eight from two gives a difference of six, which is the numerical component of the charcoal qi. The numerical component of the green qi is obtained by addition, while that of the charcoal qi is obtained by subtraction. The calculation methods differ, hence their forms and qualities are also different.

六子之卦，震坎艮巽離，皆有其自成之原點。惟兌獨無，蓋陽數大，陰數小，陽順生，陰逆生，陽始於震，陰始於兌。震之原點為一，則兌始生之陰數，必更小於一，退入零位，幾不可見，必不能成為獨立之原點矣。求之於化學氣類中，惟喜氣於兌象為近。兌為悅，悅喜意也（喜氣嗅之令人狂笑）。考喜氣為淡養所合成，西名為NO。此亦足證兌無自生之原點矣。

Among the six sons' hexagrams, Zhen, Kan, Gen, Xun, and Li each have their own independent origin, but Dui does not. This is because the yang number is large and the yin number is small, with yang generating in a forward direction and yin generating in a reverse direction: yang begins with Zhen, while yin begins with Dui. If the origin of Zhen is counted as one, then the initial yin number of Dui must be smaller than one, retreating to zero, which is almost imperceptible and therefore cannot serve as an independent origin. In terms of chemical qi types, only the qi of joy is most similar to Dui. Dui represents joy, which means happiness (the scent of joy can cause laughter). Investigating the nature of joy, it is composed of a light qi and a nurturing qi, known in Western terms as NO. Since it is formed by the combination of two qis, it is not a fundamental substance itself, which precisely demonstrates that Dui does not have an independent origin.

喜氣之分劑數為二十二，即八與十四所合之數（養氣一分劑數為八，淡氣一分劑數為十四）。淡氣為艮象，養氣為坎象。艮之上體三爻積與位之和為二十二（陰二加四位為六，陰二加五位為七，陽三加上位為九，合之為二十二也），坎之上體三爻積與位之和亦二十二（陰二加四位為六，陽三加五位為八，陰二加上位亦八，合之亦為二十二也）。以艮之上體，合兌之下體，則為□損卦。以坎之上體，合兌之下體，則為□節卦。

The numerical value of the joyful qi is twenty-two, which is exactly the sum of the numerical values of the nurturing qi (eight) and the mild qi (fourteen). This confirms that it is indeed composed of two qis. The mild qi belongs to the image of Gen, and the nurturing qi belongs to the image of Kan, so the numbers must be taken from the hexagrams Gen and Kan. The sum of the yao numbers and their positions in the upper trigram of Gen is twenty-two (the sum of two yin lines added to the fourth position gives six, two yin lines added to the fifth position gives seven, and three yang lines added to the upper position gives nine, totaling twenty-two). Similarly, the sum of the yao numbers and their positions in the upper trigram of Kan is also twenty-two (two yin lines added to the fourth position gives six, three yang lines added to the fifth position gives eight, and two yin lines added to the upper position also gives eight, totaling twenty-two). When the upper trigram of Gen is combined with the lower trigram of Dui, it forms the hexagram Shen; when the upper trigram of Kan is combined with the lower trigram of Dui, it forms the hexagram Jie (the original hexagram figures are now missing). These two hexagrams serve as the basis for the subsequent calculations.

兌下體三爻積與位之和為十四（陽三加初位為四，陽三加二位為五，陰二加三位為五，合之為十四也），以下體兌之十四，減上體艮之二十二，即得坎養之八。以坎養之八，復減上體坎之二十二，即得艮淡之十四。故八與十四之和，即喜氣之分劑數。其數之妙合，極參伍錯綜之致，而無不吻合，誠不可思議矣。

The third line of the lower trigram兑 (Dui) has a total of fourteen when the number of lines and their positions are added together (a yang line three plus the first position gives four, a yang line three plus the second position gives five, and a yin line two plus the third position gives five, totaling fourteen). Using fourteen from the lower trigram兑 to subtract from the upper trigram艮 (Gen) which is twenty-two, we get exactly eight, which corresponds to the nurturing energy of坎 (Kan). Then using the eight from坎 to subtract from the upper trigram坎 again, we get fourteen, which corresponds to the subtle energy of艮. By subtracting each pair, the results exactly match the respective energies. Therefore, adding eight and fourteen gives twenty-two, which is the number of the joyful energy. The elegance of these numbers fitting together is so intricate and complex that it is truly beyond comprehension.

以上輕（震象）養（坎象）淡（艮象）綠（巽象）炭（離象）喜（兌象）六氣，即乾坤二元所化生，震坎艮三少陽，巽離兌三少陰之六元象也。然三少陽所成之原質有三類，而三少陰所成原質只有兩類。可見陽三陰二之定則，離造物者亦不能越此範圍（五行之數亦天三地二，天地之生數亦天三地二）也。此外之原質，若碘，若砩，若金類，若非金類，為數甚夥。苟能各按其天然分劑之數與其品性，依卦象變化之條理，以方程求等之法細繹之，當無不有一定之公式，可斷言矣。

The six kinds of qi, namely light qi (Zhen image), nourishing qi (Kan image), mild qi (Gen image), green qi (Xun image), charcoal qi (Li image), and joyful qi (Dui image), are derived from the two fundamental principles of Heaven and Earth. These correspond to the three lesser Yang trigrams, Zhen, Kan, and Gen, and the three lesser Yin trigrams, Xun, Li, and Dui, making up the six fundamental elements. Each type of qi corresponds to one trigram, and there is a perfect match. However, the original substances formed by the three lesser Yang trigrams are categorized into three types: light, nourishing, and mild. In contrast, the original substances formed by the three lesser Yin trigrams are only categorized into two types: green and charcoal. This shows that the principle of "Yang three, Yin two" is a fixed rule that even the Creator cannot transcend (the Five Phases also follow the principle of Heaven three and Earth two, and the generating numbers of Heaven and Earth are also Heaven three and Earth two). As for other original substances, such as iodine, fluorite, metals, and non-metals, there are many of them. As long as each is classified according to its natural division and properties, following the logic of trigram transformations, and carefully deduced using equations, there must be a definite formula for each. This can be confidently asserted, and it is not only these six kinds of qi that conform to the principles of images and numbers.

《化學鑑原》云：輕氣與諸質化合，其性大似金類（與鋅或銅化合，顯此性尤大），故疑為氣質金類，如汞為流質金類是也。輕氣與汞若汞與鉑，雖視無金光，而叩之不堅，亦不足為必非金類之據。汞加熱可化為明氣質，亦與金類為例，是可見輕氣亦或為金類也。

The Chemical Origin says: Light gas combines with various substances in a manner similar to metals, especially when it combines with zinc or copper. Therefore, it is suspected to be a gaseous metal, just as mercury is a liquid metal. Although light gas and mercury, as well as mercury and platinum, do not appear to have a metallic luster and are not hard when struck, this is not sufficient to conclude that they are definitely not metals. Mercury can be turned into a transparent gas when heated, which is similar to metals. Therefore, it is possible that light gas is also a type of metal.

又云：輕氣雖為萬物中至輕至稀之品，而分劑數為最小者，然依其分劑數而計其愛力，則甚大也。如一分重之輕氣，能與綠氣三十六分之重化合，能與溴八十分之重化合，與碘一百二十五分之重化合。極少之數，亦足支配此各質而變化其性。且所成之質，最難分析。化學以為極少之分劑，而生極大之愛力性，為甚奇也。

It is also said that light gas, though the lightest and rarest of all things with the smallest proportion, has a very great affinity when calculated by its proportion. For example, one part of light gas can combine with thirty-six parts of green gas, eighty parts of bromine, and one hundred and twenty-five parts of iodine—the combined weight being many times heavier than itself. A very small amount is sufficient to control these substances and change their properties, and the resulting compounds are extremely difficult to decompose. Chemists find it strange that such a small proportion can produce such a great affinity.

按化學家疑輕氣為金類，而不敢下確定之斷語。又奇其分劑數小而愛力極大，此由不明輕氣所以化生之原理也。若以《易》象證之，則所疑者皆渙然冰釋矣。蓋輕氣為震象，震者乾始交坤，其象恆通乾（震為乾之長子）。《說卦傳》“震其究為健”，健即乾也。乾為金，震者金氣之初發動者也。知輕氣之為震，則知輕氣為氣類之金可無疑矣。

Note: Chemists suspect that hydrogen is a metal and are hesitant to make a definite conclusion, also finding it strange that its atomic weight is small while its affinity is very great. This is because they do not understand the principle by which hydrogen is generated. If we use the imagery of the Book of Changes to verify this, all their doubts will be clearly resolved. Hydrogen belongs to the image of Zhen (Thunder), which is formed when Qian (Heaven) first interacts with Kun (Earth). The image of Zhen always connects with Qian (Zhen is the eldest son of Qian). The "Commentary on the Hexagrams" says, "Zhen, when pursued to its conclusion, becomes Qian," meaning that Zhen, when examined thoroughly, ultimately returns to Qian, "Qian" meaning strength. Qian represents metal, so Zhen represents the initial movement of metal energy. If we know that hydrogen belongs to Zhen, then hydrogen is a gaseous metal, and there is nothing to doubt.

一陽初復，故分劑數最小，所謂復小而辨於物是也。其感動力反甚大者，以乾健而震動也。震為物之始生，此天地之仁氣也。且又為最尊最大之乾卦最肖之長子，然則能以至小之分劑數化合最大之分劑數，而顯最大之愛力者，又何足怪乎！

A single yang line has just begun to revive, so its dividing number is the smallest. The Great Treatise says, "Recovery is small yet distinct in things," which exactly expresses this meaning. Its power of influence is actually great because the Qian trigram is strong and vigorous, and Zhen trigram is the master of movement. Zhen is the place where all things begin to grow, which is the benevolence of heaven and earth; moreover, it is the eldest son most similar to the greatest Qian trigram. Therefore, it can combine the largest dividing number with the smallest one, showing the greatest affinity, so what is strange about it?

以上諸說，不但足與物理相發明，尤足以證明象之切切實實，非模糊影響而意為擬議者也。向來說《易》者，以空談性理為高，能精研象數者已不可多得。間有談象數者，又莫明象數之原理，於是東牽西扯，曲折附會以求合，而不知去《易》之道愈遠，而象數反為說《易》之累矣。故顯明象數，必知物理。離物理以言象數，亦與離象數而談性理者，敝正相等耳。

The above statements are not only sufficient to complement physics, but also sufficient to prove that the images in the Book of Changes are concrete realities, not vague or subjective inventions. In the past, those who interpreted the Book of Changes often regarded discussions on moral principles and human nature as refined, while those who studied the principles of images and numbers were already rare. Occasionally, those who discussed images and numbers did not understand their underlying principles, so they twisted and forced interpretations to fit, yet they did not realize that this only took them further away from the true path of the Book of Changes. Thus, to explain images and numbers clearly, one must first understand physics. To discuss images and numbers without reference to physics is just as flawed as discussing moral principles without reference to images and numbers; both approaches are equally faulty, and neither is superior to the other.

《易》之為書也，廣大悉備。範圍天地，曲成萬物，故凡世界所有，無遠近，無今古，均不能出於《易》教之外。道教佛教，皆後起者也，而佛教創始於西域，更與中國之文化無關。乃聖人之作《易》，早定其數於三千年以前，而概括其教於卦象之中，並其科儀名類，亦皆一一列舉而豫定之。乃後來者冥然罔覺，順天地之理數，以自力進行。初未與《易》相謀，而事事物物胥一一準之，莫能相悖。始信孔子“天且不違況於人乎況於鬼神乎”之贊，為確有徵驗，而非以虛義為頌美之辭焉。

The book of Changes is vast and comprehensive, encompassing all aspects of the transformation of heaven and earth, and thoroughly revealing the nature of all things. Therefore, anything that exists in the world, regardless of its distance or time, falls within the scope of the teachings of the book of Changes. Taoism and Buddhism are later developments, and Buddhism originated in the West, having little to do with Chinese culture. However, the sages composed the book of Changes three thousand years ago, establishing the numbers of things beforehand, and including both religions within the hexagrams. Even their rituals, subjects, names, and classifications are all listed and predetermined without any omission. Later people were unaware of this, merely following the principles of heaven and earth and their own efforts, without consulting the book of Changes. Yet, everything they did coincided with the book of Changes, and could not be opposed. This is why they came to believe that Confucius' words in the "Commentary on the Literary Changes" of the Book of Changes, "Heaven does not violate, how then could people? How then could spirits and gods?" are indeed verified, and not just empty praise.

蓋天地之數，自天一地二至天九地十，八卦之入用準之。至乾而數為無，黃帝甲子，乾五支六，各分陰陽，以合八卦之用。至乾終戌亥，而數有孤虛（子一丑二至酉十盡於兌，至乾數無而於辰為虛。其對宮則為孤）。故乾坤陰陽皆極於己亥，己陽極陰始，亥陰極陽始。陰陽終始於己亥，而己亥實為天地陰陽之兩端（端者始也）。

The numbers of heaven and earth start from Tian Yi (Heaven One) and Di Er (Earth Two), continuing up to Tian Jiū (Heaven Ten) and Di Shí (Earth Ten), and the use of the Eight Trigrams follows these numbers. When reaching the position of Qian (Heaven), the number becomes "nothing." The Yellow Emperor created the Jiazi system, with five pairs of heavenly stems and six pairs of earthly branches, each divided into yin and yang to match the use of the Eight Trigrams. When reaching Qian, the sequence ends at Xu and Hai, and the numbers have "gū" (solitude) and "xū" (emptiness). Counting from Zi (one) to You (ten), the sequence ends at Dui (the last trigram). When reaching Qian, the number becomes nothing, but at Chen, it is "xū" (emptiness), and the corresponding trigram is "gū" (solitude). Therefore, the trigrams Qian and Kun (Heaven and Earth) both reach their extremes at Ji (six) and Hai (twelve). Ji is the end of yang and the beginning of yin, while Hai is the end of yin and the beginning of yang. Since yin and yang begin again at Ji and Hai, Ji and Hai are the two ends of heaven and earth ("end" meaning beginning).

聖人合陰陽之撰，通神明之德，先後皆履端伊始。己上先天乾兌卦，己履端始；亥下後天乾兌卦，亥履端始。是以聖人於己亥萬物終始，執其兩端，而用其中於民（天地子午正中，子一勿用。用子正在丑，用午正在未）。乃子丑中，天地協，使民協於中。南北乾坤坎離正中，堯舜通變宜民，垂衣裳而天下治。取諸乾坤，坎離水火，百姓日用而不知是也。

The sage harmonizes the system of yin and yang, comprehends the virtue of the divine, and begins both before and after with "starting at the beginning." Above the position of Ji is the Qian and Dui trigrams of the Earlier Heaven, so Ji is the beginning of starting at the beginning; below the position of Hai is the Qian and Dui trigrams of the Later Heaven, so Hai is also the beginning of starting at the beginning. Therefore, the sage takes both ends of the cycle of all things, Ji and Hai, and applies the concept of "center" to the people. (The天地 take Zi and Wu as the central positions; Zi is the "not to be used" position, but the use of Zi actually falls on Chou, and the use of Wu actually falls on Wei.) Thus, taking the middle between Zi and Chou, heaven and earth harmonize, and the people also harmonize with the center. The trigrams Qian, Kan, Li, and Kun are all located at the central positions. Yao and Shun understood their variations and made the people suitable, governing with ease and bringing great order to the world. The Great Treatise says this is taking the image of Qian and Kun. As for the use of Kan and Li, water and fire, these are daily uses of the people without their awareness.

故“人心惟危，道心惟微。惟精惟一，允執厥中”（子坎一，道心寅；艮三，人心子。一純丑，二精子，丑天地正中）。“中庸”乾二用中，皆天地大中之道，帝王立極，聖人立本，於己亥執其兩端，子丑用其中於民。斯堯舜之道，文周孔子所繼述，即《易》道用中之旨也。

Therefore, the "Book of Documents · Great Yu's Plan" says, "The human heart is perilous, the way heart is subtle; only by being meticulous and unified can one truly hold the middle." (The Son is Kan one, the way heart belongs to寅; the mountain is three, the human heart belongs to子. One is pure, paired with丑; two is meticulous, paired with子; 丑 is precisely the central point of heaven and earth.) "The Doctrine of the Mean" takes the use of the middle from the Nine in the Second line of the Qian hexagram, which represents the great middle way of heaven and earth. Emperors established their standard based on this, sages established their foundation based on this: holding both extremes on the Jihai positions, applying the middle at the 子丑 positions for the people. This is the way of Yao and Shun, also the way inherited and explained by King Wen, the Duke of Zhou, and Confucius. This is the essence of the "Yi" doctrine of "using the middle."

兩端各倚於一偏。東南偏辰巳，有陽無陰，主有生無死，道教是也（道教主長生不死）。西北偏戌亥，無陰無陽（乾數無），主無死無生，佛教是也。以其偏於一端也，對於用中而言，謂之異端。然天地既有其數，既開其端，即皆有其教。天地南北，子一陽，物出有，道教始。午一陰，物入無，佛教始。故子出而辰巳有者陽，於午一陰未生，入無之佛未見，其象有，有者皆道教。

Since they are both extremes, each tends to one side. The Southeast is biased toward Chen and Si, possessing yang but no yin, advocating life but not death, which is the doctrine of Taoism (Taoism takes immortality as its principle). The Northwest is biased toward Xu and Hai, possessing neither yin nor yang (the number of the乾 position is void), advocating neither death nor life, which is the doctrine of Buddhism. Because they each lean to one extreme, they are called heterodoxies in relation to the principle of the center. However, since heaven and earth have these numbers and have set these extremes, each has its own religion. Heaven and earth are divided into north and south: the Zi position has one yang, and all things emerge as "being," from which Taoism begins; the Wu position has one yin, and all things return to "non-being," from which Buddhism begins. Therefore, from the Zi position to Chen and Si, what is seen is all yang; at that time, the one yin of the Wu position has not yet emerged, and the Buddha, which returns to non-being, is not yet visible. Its image is "being," and all that belongs to "being" is Taoism.

孔子刪書斷自唐虞。唐虞日中天，南北用中，日未過中，其唐虞以上書是道教（黃帝為道家之祖，廣成空同皆道家言），非用中之道，故刪書刪之。而《易》之書所以明道，不明道教，是缺南北一偏，則《易》不備，不足以明道，故《易》象往來。自子一出有，其數逆來，起子西北來，而午東南，其卦為水天需，為火風鼎，其象為水火逆運，而以求有生無死。此其有陽無陰之一偏也，東南象也。

Confucius edited the Book of Documents, beginning from the time of the Yao and Yu Shun dynasties. The Yao and Yu Shun periods are like the sun at its zenith, with both north and south returning to the center, and the sun has not yet passed the meridian. The books prior to the Yao and Yu Shun belong to Daoism (the Yellow Emperor is the ancestor of Daoism, and figures like Guangchengzi and Kongtong are all Daoist teachings), which do not conform to the principle of the center, so Confucius deleted them when editing the Book of Documents. However, the Book of Changes is used to clarify the Dao. If Daoism is not explained, then the north and south are missing, and the Book of Changes would be incomplete and insufficient to clarify the Dao, hence the Book of Changes has both movement and return. Starting from the Zi position, one yang emerges and becomes existence, its number moves in reverse: coming from the northwest and going to the southeast, its hexagram is Water above Heaven, the Hexagram of Necessity, and Fire above Wind, the Hexagram of Tripod, its image is the reverse movement of water and fire, used to seek existence without death. This is one-sided with yang without yin, belonging to the image of the southeast.

是以西北來東南，其對卦言姤（西北乾對東南巽，為天風姤）言復（西南坤對東北艮，反震為地雷復），姤奼女而復嬰兒，需鼎服食以求長生之道者也。變則鼎折足需于泥而道敗，有生有死，有需“不速之客三人來”，道家所謂“三尸”“三彭”是也。故《易》四三為人爻，而游魂歸魂為鬼《易》（遊歸亦在四三兩爻。凡上五爻為天《易》，四三爻為人《易》，二初爻為地《易》，游魂歸魂為鬼《易》）。

Therefore, coming from the northwest to the southeast, in terms of the opposing trigrams, one is the hexagram "Gou" (the northwest trigram Qian opposing the southeast trigram Xun, forming the hexagram Tian Feng "Gou"), and the other is the hexagram "Fu" (the southwest trigram Kun opposing the northeast trigram Gen, reversed to Zhen, forming the hexagram Di Lei "Fu"). "Gou" is what the alchemists call "Chachan," and "Fu" is what they call "Infant." "Xu" and "Ding" represent the path of taking nourishment and cultivation to seek long life. Once things turn bad, it becomes "Ding" with "the tripod breaks its leg" and "Xu" with "waiting in the mud," indicating the decline of the Dao and the return to the cycle of life and death. The hexagram "Xu" also has "three unexpected guests come," which is what the Daoists refer to as "three corpses" and "three Peng." Therefore, the "Book of Changes" takes the third and fourth lines as the human lines, and the categories of "youhun" and "guihun" hexagrams as the ghostly hexagrams (both "youhun" and "guihun" are located on the third and fourth lines. All the top line and fifth line hexagrams are heavenly hexagrams, the third and fourth lines are human hexagrams, the second and first lines are earthly hexagrams, and the "youhun" and "guihun" hexagrams are ghostly hexagrams).

精氣為物，游魂為變，是故知鬼神之情狀。精氣為物者神，其道所謂神仙是也（艮寅人道，艮為山，故仙字從山從人。艮止其所，人極所自立也）。游魂為變者鬼，其道所謂尸彭是也。先天乾坤之位，而後天離坎居之。火上水下，其道未濟，魂升魄降（離魂坎魄），是死道也。故道以逆行。

The "Great Treatise" says, "Spiritual essence forms things, while wandering souls cause change; thus we know the nature of ghosts and spirits." The spiritual essence that gathers to form things is the divine, which in Taoism is called a celestial being. Since the position of "Geng Yin" (the second trigram of the Earthly Branches) represents the human realm, and "Geng" (Gen) represents mountain, the character for "celestial being" (xiān) includes "mountain" and "person." "Geng" signifies stopping at its place, which is precisely where human beings establish their own limits. The wandering soul that disperses to cause change is the ghost, which in Taoism is called "shi" (corpse) or "peng" (a mythical creature). In the Earlier Heaven arrangement, the trigrams for Heaven and Earth are positioned in certain directions, but in the Later Heaven arrangement, the trigrams for Fire and Water occupy those positions. Fire is above and Water is below, forming the hexagram "Not Yet Completed" (Wèi Jì). The soul ascends upward, while the body descends downward (Fire governs the soul, Water governs the body), which is the path toward death. Therefore, Taoist cultivation requires going against this path.

降炎上之火，升潤下之水，龍飛在天（震為龍，震下一陽由坎而出，龍飛在天，即取坎填離之說。丹家所謂龍從火裡出者是也。震位東方，亦青龍之位，其德為仁。仁屬陽，主升，乾九五爻其候也），虎履其尾（兌為虎，兌上一陰為陰之始，而位於正西白虎之位，其德為義。義屬陰，陰主降，降則變兌見為巽伏。故道家曰伏虎，又曰虎向水中生也），皆於三四兩爻反復其道。

To bring down the fire that naturally ascends and to raise up the water that naturally descends is called "Dragon Soaring in Heaven." (The trigram Zhen represents the Dragon; the yin line below Zhen comes from Kan. "Dragon Soaring in Heaven" corresponds to the Daoist practice of "taking Kan to fill Li," which is also referred to as "the Dragon emerging from fire." The position of Zhen is in the East, which is the position of the Azure Dragon; its virtue is benevolence. Benevolence is yang and is associated with rising, which corresponds to the ninth line of the fifth position in the Qian hexagram.) This is also called "Tiger Treading Its Tail." (The trigram Dui represents the Tiger; the yang line above Dui is the beginning of yin. Its position is in the West, the position of the White Tiger; its virtue is righteousness. Righteousness is yin and is associated with descending. When it descends, Dui transforms into Xun, which is hidden. Therefore, Daoists speak of "subduing the Tiger" and also say "the Tiger is born from water.") All of these involve the repetition of the principles in the third and fourth lines.

九四六三，陰陽反覆，是為雷澤歸妹，故歸妹天地大義人終始，為六十四卦之大歸魂卦也。先天乾，後天離，火天大有；先天坤，後天坎，地水師。大有眾也，師眾也。三人為眾，皆需之不速之客三人，故魂魄具而三尸即伏於中，是必損之三人損一，而後致一得天地之道。是《易》於道教明著其象，而魏伯陽之《參同契》，借《易》卦以明丹學，與《易》義無涉者，猶不與焉。儒者禁言異端，於他書則是，於《易》則非。《易》備萬物萬象，此道教東南一偏象，不可不知者也。

Nine in the Fourth and Six in the Third exchange their yin and yang, resulting in the trigram of Thunder over Marsh, known as "Return of the Maiden." Therefore, "Return of the Maiden" represents "the great principle of heaven and earth" and "the beginning and end of human beings," making it the largest returning soul hexagram among the sixty-four hexagrams. In the Earlier Heaven arrangement, the position of Heaven is occupied by Fire in the Later Heaven arrangement, forming the hexagram of Fire in Heaven, "Great Possession"; and the position of Earth in the Earlier Heaven is occupied by Water in the Later Heaven, forming the hexagram of Water on Earth, "The Army." "Great Possession" represents the multitude, and "The Army" also represents the multitude. Three people make a multitude, which corresponds to the three people mentioned in the hexagram "Need" with the line "Three unexpected guests come." Therefore, when the soul and spirit are complete, the three corpses are hidden within, and it is necessary to follow the principle of "One person is lost among three travelers" from the hexagram "Loss," reducing one person to achieve the unity of one, thus attaining the principle of heaven and earth. This is the image of the Book of Changes clearly displayed in Taoism. As for Wei Boyang's "Three Coinciding Treatise," which uses hexagrams to discuss alchemy but has nothing to do with the meaning of the Book of Changes, it should not be included. Scholars who prohibit discussion of heterodox views are correct when applied to other books, but incorrect when applied to the Book of Changes. The Book of Changes encompasses all things and phenomena. This southeastern aspect of Taoism is something that should not be unknown.

天地南北子一陽物出有，為恆有象（先天西南巽，東北震，為雷風恆象）。午一陰物入無，為咸無象（先天東南兌，西北艮，為澤山咸象）。咸無佛教也。午一陰生，午而戌亥，萬物歸無，為後天西北乾象。咸無反恆有，《春秋·莊七年》“夏四月夜，恆星不見”，為周莊王甲午，即佛誕生之日矣。佛誕生，天地咸象感，而恆星不見，而《易》已早徵其兆於先後天卦矣。

Heaven and earth are divided into north and south. The position of Zi (the rat) is where one yang begins to arise, and all things emerge into existence, which represents the image of "having" in the Hexagram 18 (Heng). In the Earlier Heaven arrangement, the southwest is Xun (wind) and the northeast is Zhen (thunder), together forming the Hexagram Heng (Thunder over Wind). The position of Wu (the horse) is where one yin begins to arise, and all things return to non-existence, which represents the image of "non-being" in the Hexagram 2 (Xian). In the Earlier Heaven arrangement, the southeast is Dui (lake) and the northwest is Gen (mountain), together forming the Hexagram Xian (Lake over Mountain). The "non-being" governed by Xian corresponds to Buddhism. When one yin arises at Wu, from Wu to Xu and Hai, all things return to non-existence, which is exactly the image of the northwest in the Later Heaven, represented by Qian (heaven). The "non-being" of Xian and the "having" of Heng are opposites. The Spring and Autumn Annals records that in the seventh year of Duke Zhuang of Zhou, during the summer fourth month, the night was so dark that the fixed stars were not visible. That year was Jiawu, the year of the birth of the Buddha. At the time of the Buddha's birth, heaven and earth responded to the image of Xian, hence the fixed stars were not visible. The Yi Jing had already revealed this sign in the Earlier Heaven and Later Heaven hexagrams.

故八卦於咸無順往，自東南午，而西北子，其卦為風火家人，為天水訟。家人由內出外，訟違行不親，其象為火水順滅，而以歸無死無生。此其無陰無陽之一偏也。西北乾剛乾金，故佛金剛不壞。佛說經金剛獨顯，為咸感應象。西北戌入夜明火，而佛始燃燈，西北天地以濟不通，而佛度彼岸（《易》利涉大川，皆由坎之乾東北往西南卦）。

Therefore, the Eight Trigrams in the hexagram "Xian" (咸) move in a forward direction on the "wu" (无) line: from the Southeast position of Wu to the Northwest position of Zi, resulting in the hexagram Wind Fire "Jiaoren" (家人) and Heaven Water "Song" (讼). "Jiaoren" represents movement from within to outside, while "Song" indicates conflicting actions that do not harmonize. The image is of fire and water successively extinguishing, returning to a state of neither death nor life. This is one aspect of the absence of yin and yang. The Northwest belongs to Qian (乾), which is strong and represents metal, so Buddhism refers to "Jingang bu huai" (金刚不坏), meaning "diamond-like indestructibility." The Sutra of Diamond (金刚经) is most prominent among the sutras spoken by the Buddha, precisely reflecting the image ofsympathetic response (induction) in the hexagram Xian. The position of Xu (戌) in the Northwest lights up at night, hence the Buddhist concept of the lamp of illumination. The Northwest is where heaven and earth are separated and do not communicate, so Buddhism speaks of crossing to the other shore. In the Book of Changes, whenever it says "li shexia chuan" (利涉大川), it refers to moving from Kan to Qian, from the Northeast to the Southwest.

天地數有無，以輔相左右民。左為輔，天地數甲三庚九，三九為二十七輔，是乾震無妄卦，乃天地有之數，而知無者妄也。右為相，天地數辛四乙八，四八為三十二相，是巽坤觀卦，乃天地無之數，而知觀者空也。故佛說以三十二相觀，不可以三十二相觀。

The numbers of Heaven and Earth have both "existence" and "non-existence," used to assist and guide the people. On the left is "auxiliary": the numbers of Heaven and Earth, Jia is three and Geng is nine; three and nine combine to make twenty-seven, which represents the "auxiliary" aspect. The trigram is Qian below and Zhen above, the hexagram of "Without Delusion," which represents the number of Heaven and Earth as "existence." Thus, what is called "non-existence" is delusion. On the right is "reflection": the numbers of Heaven and Earth, Xin is four and Yi is eight; four and eight combine to make thirty-two, which represents the "reflection" aspect. The trigram is Kun below and Xun above, the hexagram of "Observation," which represents the number of Heaven and Earth as "non-existence." Thus, what is observed is emptiness. Therefore, Buddhism says on one hand to observe with thirty-two aspects, and on the other hand, not to observe with thirty-two aspects.

是以戌西北巽入無，辛四西北物往來入無。有乙八辛四，坤巽入，升不來，而四於東南巽不果。西北乾木果，故佛說四果，謂入而實無所入。往來而實無往來，不來而實無不來，有法而實無有法，為四果，皆西北四戌入無數。四西北右相合一（合子一），即是一合相，而無見有，即非一合相，皆西北數西北相也。

Therefore,戌 is located in the northwest. The trigram Xun governs entry and return to nothingness. The number Xin, which is four, resides in the northwest. All things come and go, ultimately returning to nothingness. With Yi eight and Xin four, the trigrams Kūn and Xun govern entry, ascending without returning. The number four in the southeast trigram Xun is called 'not completed,' while in the northwest trigram Qian it is called 'wood fruit.' Therefore, Buddhism speaks of 'four fruits': entering yet there is nowhere to enter, coming and going yet there is no coming or going, not arriving yet there is no not arriving, having a method yet there is no method. These four aspects are the four fruits, all resulting from the number four and the戌 entering nothingness in the northwest. The number four in the northwest is the right 'aspect,' combining with the number one (i.e., the position of Zi), forming 'one combined aspect.' From nothingness, one perceives existence, hence it is also said 'it is not one combined aspect.' All these are the numbers and aspects of the northwest.

西北戌亥數無為空，而乾為門，故佛教曰空門。先天西北艮，艮為山，故佛門曰山門，佛祖曰開山。先後天乾艮合為遁，故又曰遁入空門。全《易》陰陽爻數，各一百零八，故佛之紀數，皆一百零八。西北陰，陰數窮於六，故佛至六祖而止（陰數窮於九，故道家丹以九轉）。西北咸，神無方而《易》無體，不疾而速，不行而至。咸感至神，故佛道感應至神。《易》備萬物萬象，此佛教於西北一偏象，不可不知者也。以上據端木鶴田氏之說而推衍之，其義尚多未盡，然亦可見其大概矣。

The numbers of the western and northwestern directions,戌 and 亥, are considered empty and void, and since the乾 represents a gate, Buddhism refers to it as the "empty gate." In the Earlier Heaven arrangement, the western north is associated with 艮, which represents a mountain, so the Buddhist gate is called the "mountain gate," and the Buddha is called the "mountain opener." In the Earlier Heaven, the乾 combines with the Later Heaven's 艮 to form the Hexagram of Retreat, so it is also said that one "retreats into the empty gate." The entire Book of Changes has 108 yin and yang lines, so Buddhist counting uses 108. The western north belongs to yin, and the extreme of yin numbers is six, so the Chan school of Buddhism stops at the sixth patriarch. The extreme of yang numbers is nine, so Taoist alchemy talks about nine transformations. The western north is associated with the Hexagram of Attraction, which says "the spirit has no fixed form and the Book of Changes has no fixed body." It does not hurry but naturally becomes fast, does not move but naturally arrives; the Hexagram of Attraction is aboutsympathetic response and reaches a miraculous level, so both Buddhism and Taoism talk about the miraculous nature ofsympathetic response. The Book of Changes encompasses all things and phenomena, and this western north aspect in Buddhism is something that should not be unknown. The above is based on the explanation of the scholar Du Mu Hetian, with further deductions. There are many meanings not fully explained, but one can get a general idea.