Najia Diagram

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.