I Ching Numerology Hidden Diagrams

天地之數五十有五，專為大衍之數五十張本，此蓍策之原，非畫卦之法。《易雅》云：九六七八為揲蓍策數，乃先有卦而後揲蓍，非先得數而後畫卦，夫子未嘗以是明河圗也。李泰伯云：天一至地十乃天地之氣降出之次第，而曰五十有五者，葢聖人假其積數以起算法，非實數也。譬如兄弟行第一至第十者乃十人耳，今《鉤隠》河圗有白黑四十五點，是九人而化為四十五人也；《啟蒙》河圗有白黑五十五點，是十人而化為五十五人也。以積數為實數，以算法為卦原，而寫之以成象，九圗十書、十圗九書，總無是處。

Hu Wei said: "The number fifty-five of heaven and earth" is specifically intended to set up the foundation for "the fifty numbers of the great derivation," which is the origin of the divination with yarrow stalks, not the method of drawing hexagrams. The "Yi Ya" says that nine, six, seven, and eight are the numbers of stalks obtained by divination, indicating that hexagrams come first and then the divination with yarrow stalks, not that numbers are obtained first and then hexagrams are drawn. Confucius never used these numbers to explain the Yellow River Chart. Li Gou said: from heavenly one to earthly ten, it is merely the order of the birth of the qi of heaven and earth; calling it fifty-five is the way of the sage to use this cumulative number to start the calculation, not that there are actually fifty-five numbers. For example, the order of brothers from first to tenth refers to ten people, but now the "Gou Yin Tu" draws the Yellow River Chart with forty-five black and white dots, equivalent to turning nine people into forty-five; the "Ming Gong" draws the Yellow River Chart with fifty-five black and white dots, equivalent to turning ten people into fifty-five. Taking the cumulative number as an actual number and taking the calculation method as the origin of drawing hexagrams, then drawing the figure accordingly—whether saying nine is the diagram and ten is the text or ten is the diagram and nine is the text, all of them make no sense.

然九宮猶存八卦之位，而五合缺其四隅，則與八卦一毫不相似矣。易有八卦而無五行，以《洪範》五行附會於翼傳，自漢儒始。《五行志》曰：天一生水，地二生火，天三生木，地四生金，天五生土。又曰：水之大數六，火七，木八，金九，土十。大數即成數，此以天地之數配五行也。坎水、離火、巽木見於夫子之大象，而坤艮不言土，乾為金惟見於《說卦》。據《左傳》莊二十二年周史曰「坤，土也」，《周語》太子晉曰「山，土之聚也」，是坤艮亦可言土矣，而震木兊金無聞焉。《五行志》曰：震在東方為木，兊在西方為金。震木兊金始見於此。《漢上易傳》云：京房以乾兊為金。然則震巽同為木，葢亦始於房。此以八卦方位配五行也，皆非夫子之意。

However, the Nine-square Diagram still retains the directional positions of the Eight Trigrams, while the Five Elements Generating Diagram lacks four corners, making it completely unlike the Eight Trigrams. The Book of Changes contains only the Eight Trigrams and not the Five Elements; attaching the Five Elements from the Hongfan (The Mandate of Heaven) to the Ten Wings of the Book of Changes began from the Han dynasty scholars. The "Book of Han · Five Elements Chapter" says: "Heaven produces water with the number one, Earth produces fire with the number two, Heaven produces wood with the number three, Earth produces metal with the number four, Heaven produces earth with the number five." It also says: "The great number of water is six, fire is seven, wood is eight, metal is nine, and earth is ten." "Great number" is the same as "completed number," which is matching the numbers of heaven and earth with the Five Elements. The associations of Kan with water, Li with fire, and Xun with wood are found in the Great Image Commentary written by Confucius, but Kun and Gen are not stated as earth. The association of Qian with metal is only mentioned in the "Sayings on the Trigrams." According to the "Zuo Zhuan" from the 22nd year of Duke Zhuang, the Zhou dynasty historian said, "Kun is earth." The "Zhou Yu" from the "Guoyu" says, "Mountains are the accumulation of earth." This shows that Kun and Gen can also be interpreted as earth. As for Zhen being wood and Dui being metal, there is no evidence in the classic text. The "Book of Han · Five Elements Chapter" says: "Zhen is in the east and belongs to wood, Dui is in the west and belongs to metal"—this is the first time the idea of Zhen as wood and Dui as metal appears. Zhu Zhen's "Han Shang Yijie" says: "Jingfang associated Qian and Dui with metal." Therefore, the association of Zhen and Xun with wood probably began with Jingfang. This method of matching the Eight Trigrams with the Five Elements is not in line with Confucius's original intention.

劉牧云：洛書之數五十有五，演五行而不述四象，謂禹則之以陳範，故專主五行也。今既以五十有五為河圗，而羲則之以畫卦，即與五行全無交涉，奚為拾漢儒之餘瀋而以五行生成之數附會於其間乎？劉歆言羲則圗、禹則書，而繼之曰「河圗洛書相為經緯，八卦九章相為表裡」，此真所謂畫蛇添足者，而《啟蒙》欲有以通之，吾未見其有可通之理也。

Liu Mu said: The number of the Luo Shu is fifty-five, and it only deduces the Five Phases without mentioning the Four Symbols, because Da Yu took it as a model to explain the Hong Fan, so it is exclusively about the Five Phases. Now, if we take fifty-five as the He Tu, and Fuxi took it as a model to draw the trigrams, then it has nothing to do with the Five Phases. Why should we pick up the leftovers of Han scholars and force the numbers of the generation of the Five Phases into it? Liu Xin said Fuxi took the He Tu as a model and Da Yu took the Luo Shu as a model, and then he said "the He Tu and Luo Shu are like the meridians and parallels, the Eight Trigrams and the Nine Categories are like the inside and outside," which is truly adding legs to a snake. The启蒙 also wants to integrate them, but I don't see any reason to integrate them.

然則聖人之則之也奈何？曰：則河圗者虛其中，則洛書者總其實也。河圗之虛五與十者，太極也；奇數二十、偶數二十者，兩儀也；以一二三四為六七八九者，四象也；析四方之合以為乾坤離坎，補四隅之空以為兊震巽艮者，八卦也。洛書之實：其一為五行，其二為五事，其三為八政，其四[四庫本此至「五十合」闕]為五紀，其五為皇極，其六為三德，其七為稽疑，其八為庶徵，其九為福極，其位與數尤曉然矣。

So how did the sage derive from them? The answer is: to derive from the Yellow River Chart, one should take the central part as empty; to derive from the Luo Writing, one should summarize the actual numbers. In the Yellow River Chart, removing the five and ten from the center, that is the Taiji; the odd numbers total twenty, and the even numbers also total twenty, that is the two principles; pairing one, two, three, and four with six, seven, eight, and nine, that is the four images; dividing the four cardinal directions to determine Qian, Kun, Li, and Kan, and filling in the four intercardinal directions to determine Dui, Zhen, Xun, and Gen, that is the eight trigrams. The actual numbers of the Luo Writing: the first is the Five Phases, the second is the Five Affairs, the third is the Eight Policies, the fourth (the Complete Library of the Four Treasuries edition begins here and continues to the section "fifty combined" below) is the Five Records, the fifth is the Imperial Center, the sixth is the Three Virtues, the seventh is the Inquiry into Doubt, the eighth is the Various Signs, the ninth is the Ultimate Blessing—its positions and numbers are even clearer.

又曰：洛書而虛其中，則亦太極也；奇偶各居二十，則亦兩儀；一二三四而含九八七六，縱橫十五而互為七八九六，則亦四象也；四方之正以為乾坤離坎，四隅之偏以為兌震巽艮，則亦八卦也。河圖之一六為水，二七為火，三八為木，四九為金，五十為土，則固洪範之五行，而五十有五者又九疇之子目也。是則洛書固可以為易，而河圖亦可以為範矣，且又安知圖之不為書、書之不為圖也耶？

It is also said that if the center of the Luo Writing is removed, it is also the Taiji; the odd and even numbers each total twenty, which is also the two principles; within the numbers one, two, three, and four there are nine, eight, seven, and six, and when added vertically and horizontally they all total fifteen, and they correspond to each other as seven, eight, nine, and six, which is also the four images; the four cardinal directions are assigned to Qian, Kun, Li, and Kan, while the four intermediate directions are assigned to Dui, Zhen, Xun, and Gen, which is also the eight trigrams. In the He Tu, one and six represent water, two and seven represent fire, three and eight represent wood, four and nine represent metal, and five and ten represent earth, which is originally the Five Phases of the Hongfan chapter. Moreover, the total number fifty-five is exactly the sum of the details of the nine categories. Thus, the Luo Writing can be used as the Yi, and the He Tu can be used as the Hongfan; and how can we be certain that the diagram cannot be the book, or the book cannot be the diagram?

玉齋胡氏方平《啟蒙通釋》曰：四方為乾坤離坎、四隅為兌震巽艮者，蓋一六老陰之數而畫卦為艮坤，反居六、坤居一也；三八少陰之數而畫卦為離震，離居三、震居八也；四九老陽之數而畫卦為乾兌，乾居九、兌居四也；二七少陽之數而畫卦為巽坎，巽居二、坎居七也，此洛書亦可以為八卦也。九疇子目者：五行五，五事五，八政八，五紀五，皇極一，三德三，稽疑七，庶徵十，福極十一，總五十五。

In the Yuan dynasty, Hu Fangping (styled Yu Zhai) wrote in "Yixue Qimeng Tongshi" that the four cardinal directions are Qian (Heaven), Kun (Earth), Li (Fire), and Kan (Water), while the four intermediate directions are Dui (Lake), Zhen (Thunder), Xun (Wind), and Gen (Mountain). This is because one and six are the numbers of old yin, and using them to draw the trigrams results in Gen and Kun, which are placed at the sixth and first positions respectively; three and eight are the numbers of young yin, and using them to draw the trigrams results in Li and Zhen, which are placed at the third and eighth positions respectively; four and nine are the numbers of old yang, and using them to draw the trigrams results in Qian and Dui, which are placed at the ninth and fourth positions respectively; two and seven are the numbers of young yang, and using them to draw the trigrams results in Xun and Kan, which are placed at the second and seventh positions respectively. This means that the Luo Writing can also be used to match the eight trigrams. As for the details of the nine categories: five for the Five Phases, five for the Five Affairs, eight for the Eight Policies, five for the Five Records, one for the Imperial Center, three for the Three Virtues, seven for the Deliberation of Doubts, ten for the Various Signs, eleven for the Ultimate Blessings, totaling exactly fifty-five.

黃氏《象數論》曰：就二數通之於易，則十者有天一至地十之數可據，九者並無明文，此朱子爭十為河圖之意長於長民也。雖然，自一至十之數，易之所有也；自一至十之方位，易之所無也。一三五七九之合於天、二四六八十之合於地，易之所有也；一六合、二七合、三八合、四九合、五十合，易之所無也。天地之數，易之所有也；水火木金土之生成，易之所無也。試盡去後人之添入，依經為說，則此數仍於易無與，而況名之為河圗乎？

Huang Zongxi's "Discussion on the Images and Numbers of the Book of Changes" says: Using the numbers nine and ten to correspond with the Book of Changes, the number ten still has the classic text "Heaven one to Earth ten" to support it, but the number nine has no clear text. This is why Zhu Xi advocated that the number ten corresponds to the Yellow River Chart, and his reasoning is more convincing than Liu Mu's (whose courtesy name was Changmin). Nevertheless, the numbers from one to ten are originally present in the Book of Changes; however, the arrangement of these numbers in directions is not found in the Book of Changes. The odd numbers one, three, five, seven, and nine correspond to Heaven, while the even numbers two, four, six, eight, and ten correspond to Earth, and these are originally present in the Book of Changes. However, the pairing of one with six, two with seven, three with eight, four with nine, and five with ten is not found in the Book of Changes. The numbers of Heaven and Earth are originally present in the Book of Changes, but the generating numbers and completing numbers of water, fire, wood, metal, and earth are not found in the Book of Changes. If we try to remove all the additions made by later scholars and base our discussion solely on the classic texts, then these numbers still have nothing to do with the Book of Changes, let alone attaching the name "Yellow River Chart" to them.

天一至地十之數，儒者必欲言聖人則之以畫卦。崔憬曰：參天者，謂從三始順數而至五七九，不取於一；兩地者，謂從二起逆數而至十八六，不取於四。艮為少陽其數三，坎為中陽其數五，震為長陽其數七，乾為老陽其數九，兊為少陰其數二，離為中陰其數十，巽為長陰其數八，坤為老陰其數六。劉長民水六金九火七木八而生八卦[以坎離震兊為四正]：六居坎而生乾，謂三為坎、三為乾也；九居兊而生坤，謂三為兊、六為坤也；七居離而生巽，謂三為離、四為巽也；八居震而生艮，謂三為震、五為艮也。朱子曰：河圗之虛五與十者，太極也；奇數二十、偶數二十者，兩儀也；以一二三四為六七八九者，四象也；析四方之合以為乾坤離坎，補四隅之空以為兊震巽艮者，八卦也。同此一數，而三家所指不同如此。

The number system of "Heavenly One to Earthly Ten" has always been interpreted by Confucian scholars as the basis for the sage's drawing of the trigrams. Tang dynasty scholar Cui Jing said: the term "ascending to Heaven" refers to counting upward from three to five, seven, and nine, excluding one; the term "descending to Earth" refers to counting downward from two to ten, eight, and six, excluding four. Gen represents the Lesser Yang and is numbered three; Kan represents the Middle Yang and is numbered five; Zhen represents the Greater Yang and is numbered seven; Qian represents the Old Yang and is numbered nine; Dui represents the Lesser Yin and is numbered two; Li represents the Middle Yin and is numbered ten; Xun represents the Greater Yin and is numbered eight; Kun represents the Old Yin and is numbered six. Liu Mu said: water is six, metal is nine, fire is seven, wood is eight, and from these come the eight trigrams (with Kan, Li, Zhen, and Dui as the four cardinal trigrams). Six is in the position of Kan and gives rise to Qian, meaning three lines for Kan and three lines for Qian; nine is in the position of Dui and gives rise to Kun, meaning three lines for Dui and six lines for Kun; seven is in the position of Li and gives rise to Xun, meaning three lines for Li and four lines for Xun; eight is in the position of Zhen and gives rise to Gen, meaning three lines for Zhen and five lines for Gen. Zhu Xi said: in the Yellow River Chart, the numbers five and ten are removed, which is the Taiji; the odd numbers total twenty and the even numbers total twenty, which are the two principles; pairing one, two, three, and four into six, seven, eight, and nine, which are the four images; splitting the numbers of the four cardinal trigrams to determine Qian, Kun, Li, and Kan, and filling in the empty corners to determine Dui, Zhen, Xun, and Gen, which are the eight trigrams. It is the same number system, yet the interpretations of the three scholars differ greatly.

配卦之論始於崔憬。憬但言其數不言其位，乾坤震巽數有可據，其附會者坎離艮兊耳。長民兼位數而言，六為水而坎屬之，七為火而離屬之，八為木而震屬之，九為金而兊屬之，以四卦之五行遷就其位數，未為不可，至於乾坤艮巽則不可通矣。朱子祖先天之說，以乾南坤北者宓羲之卦位也，離南坎北者文王之卦位也，河圗出於宓羲，其時尚無離南坎北之位，硬以乾南坤北配之，則更無一合者矣。天下之物，一人以為然，千萬人以為然，其為物也不逺矣；一人可指之為此，又一人可指之為彼，其為物也無定名矣。故以天地之數配八卦者，皆非定名也。

The discussion of matching numbers with trigrams began with Cui Jing. Cui Jing only discussed numbers and not directions. Among the trigrams, the numbers for Qian, Kun, Zhen, and Xun have some basis, but the reasoning for Kan, Li, Gen, and Dui is forced. Liu Mu combined both numbers and directions: six is water and matches Kan, seven is fire and matches Li, eight is wood and matches Zhen, nine is metal and matches Dui. Using the Five Phases of these four trigrams to fit their directions and numbers makes some sense, but when it comes to Qian, Kun, Gen, and Xun, the reasoning fails. Zhu Xi followed the Earlier Heaven theory: Qian is in the south and Kun is in the north, which is the position of trigrams from Fuxi; Li is in the south and Kan is in the north, which is the position from King Wen. Since the Yellow River Chart originated in Fuxi's time, there was no concept of Li in the south and Kan in the north then. Forcing Qian to the south and Kun to the north to match the chart is even more inconsistent. In the world, if one person thinks something is so and a thousand others also think so, then that thing is close to the truth. But if one person calls it Jia and another calls it Yi, then that thing has no fixed name. Therefore, all the theories of matching the numbers of heaven and earth with the eight trigrams do not have fixed names.

毛氏《原舛編》曰：夫圗書非他，神聖之事也，豈有神聖之事而一人授之、一二人受之哉？授者無憑，受之者無據，而或四或五，或方或圎，或羲或禹，或卦或範，彼此可以爭先後，可以易，一室兩家，茫無定準，其為不足道亦可見矣。

Mo Shi's "Original Compilation of Errors" says: The Yellow River Chart and the Luo Writing are not anything else, but sacred matters; how could sacred matters be transmitted by only one person and accepted by just one or two people? The transmitter has no evidence, and the receiver has no basis. As for the accounts, some say four, some say five, some say square, some say round, some attribute them to Fuxi, some to the great Yu, some use them for drawing the trigrams, some for composing the "Hongan Fan" (the Nine Codes). They can argue about the sequence, they can interchange with each other; even within the same room there are two conflicting views, and there is no definite standard—this shows clearly that they are not reliable.

按：季通據先天八卦之方位，而附會以太極兩儀四象之名，曰「析四方之合以為乾坤離坎，補四隅之空以為兊震巽艮」[即闗《易》所云「正者全其位，隅者盡其畫」，然彼用後天卦位，此用先天卦位]。噫！伏羲上聖，其則河圗以畫卦，乃煩割裂補綴，費如許經營邪？雖至愚者亦知其無是理矣。劉歆所云相為經緯表裡者，不過以五行生成言之耳，季通發明其義，以為易之太極兩儀四象皆通於洛書，而洪範之五行、九疇之子目則又通於河圗，任意牽合，無所不可。然十圗九書本無定理，故結之曰「安知圗之不為書、書之不為圗」，終歸於鶻突無據而已矣。

Hu Wei said: Cai Yuan Ding based on the positions of the Earlier Heaven Trigrams, and attached the names of Taiji, two principles, and four images. He said, "Split the numbers of the four cardinal directions to determine the positions of Qian and Kun, Li and Kan, and supplement the empty corners to determine Dui, Zhen, Xun, and Gen." (This is what the fake "Guanzimi Yi Zhuan" said: "Those in the central positions occupy their proper places, and those in the corners use up the remaining lines," but there they used the Later Heaven Trigram positions, while here they used the Earlier Heaven Trigram positions.) Alas! Fuxi was an ancient sage, who took the form of the Yellow River Chart to draw the trigrams. Could he have needed to cut and patch things up, going through so much trouble? Even the most foolish person would know that there is no such reasoning. Liu Xin's statement of "mutual interweaving of meridians and moxibustion, inside and outside" was merely referring to the numbers of the Five Phases' generation. Cai Yuan Ding extended this meaning, believing that the Taiji, two principles, and four images of the Yi Classic could all be connected to the Luo Writing, and that the Five Phases and the nine categories of the Hongfan Classic could all be connected to the Yellow River Chart. He arbitrarily connected them, believing anything was possible. However, since "ten is the chart and nine is the writing" originally had no fixed meaning, in the end he could only say, "How do we know the chart cannot be the writing, or the writing cannot be the chart?" Eventually, he ended up with a vague and unsupported conclusion.

朱子《書河圗洛書後》曰：世傳一至九數者為河圗、一至十數者為洛書，考之於古，正是反而置之，予於《啟蒙》辨之詳矣。近讀《大戴禮》，又得一證：其《明堂篇》有「二九四七五三六一八」之語，而鄭氏注云「法龜文也」。然則漢人固以此九數者為洛書矣。

Zhu Xi said in his "Commentary on the Yellow River Chart and the Luo Writing": The commonly circulated views take numbers from one to nine as the Yellow River Chart and numbers from one to ten as the Luo Writing. But when we examine ancient texts, it is exactly the opposite. I have already analyzed this thoroughly in my "Awakening to the Yi Classic." Recently, while reading the "Da Dai Li Ji," I found further evidence: its "Bright Hall Chapter" mentions "two nine four, seven five three, six one eight," and Zheng Xuan's commentary says "this is based on the patterns on the turtle's back." Thus, it appears that the Han dynasty people originally regarded these nine numbers as the Luo Writing.

《大戴禮·明堂篇》注云：「記用九室，謂法龜文，故取此數以明其制也。」朱子以為鄭氏語。餘姚黃先生云：鄭玄注小戴禮，未嘗注《大戴禮》，在《藝文志》可考，今之所傳亦後人假託為之也，甚疎略，不出於鄭氏明矣；況鄭氏明言河圗九篇、洛書六篇，豈又以九宮為洛書自背其說哉？今按《後漢書·鄭玄傳》，康成無《大戴禮》注；而《周書·盧辯傳》云：辯字景宣，以《大戴禮》未有訓詁，乃注之。《儒林傳》云：魏永熙三年，敕中書舍人盧景宣解《大載禮·夏小正》篇。然則「九室法龜文」乃景宣語，非康成語也。今之所傳葢出景宣，亦非假託。以洛書為龜文有數至於九，實始於晚出孔安國《書傳》，而景宣襲之。揚雄、張衡但言龜書，無九數之說。

The annotations to the "Mingtang Chapter" in the "Da Dai Li Ji" say: "This chapter records the use of nine rooms in the Bright Hall, which refers to taking the pattern of the tortoise's shell as a model, so using this number system to explain its system." Zhu Xi thought this was Zheng Xuan's view. Master Huang Zongxi of Yuyao said: Zheng Xuan annotated the "Xiao Dai Li Ji," not the "Da Dai Li Ji," which can be seen in the "Hanshu · Yiwen Zhi"; the annotations passed down today are also attributed to later people, and their content is very brief and obviously not from Zheng Xuan; moreover, Zheng Xuan clearly said that the He Tu had nine chapters and the Luo Shu had six chapters, so how could he again take the nine palace system as the Luo Shu and contradict himself? Now examining the "Hou Hanshu · Zheng Xuan Zhuan," Zheng Xuan (styled Kangcheng) did not annotate the "Da Dai Li." The "Rulin Zhuan" says: In the third year of Yongxi of the Eastern Wei, an imperial edict was issued ordering the middle secretary Lu Jingxuan to explain the "Xia Xiaozheng" chapter of the "Da Dai Li." Thus, it appears that the statement "nine rooms take the pattern of the tortoise's shell" is Lu Jingxuan's view, not Zheng Xuan's; the annotations passed down today are probably from Lu Jingxuan, and thus not a forgery. The idea of equating the Luo Shu with the tortoise's pattern and having numbers up to nine actually began with Kong Anguo's "Shangshu Zhuan" in later times, and Lu Jingxuan followed this idea. Yang Xiong and Zhang Heng only mentioned the tortoise script, without mentioning the number nine.

西山兩易圗書，援孔、劉、闗、邵以證已之說，其實唯孔安國以洛書為九數，而闗朗之圗書與所反悉同，劉不言其數，邵亦但以九為書而未嘗以十為圗也。《本義》雖列此二圗，終不能厭服天下之心。故呂伯恭與朱子友善而信劉牧龍圗之學，魏華父私淑朱子亦以戴九履一者為河圗，他如朱元升、葛同叟、李簡、胡一中皆生於朱子之後而不從《啟蒙》。宋末元初朱學盛行，始有從《啟蒙》者，而郝經、劉因、雷思齊猶以為非。迨明之中葉，士子舍《程傳》而專宗《本義》，天下於是惟知有卷首之圗書，而不復問其所從來矣。

Cai Yuanding reversed the River Chart and the Lo Shu, citing Kong Anguo, Liu Mu, Guan Lang, and Shao Yong to support his view. In reality, only Kong Anguo regarded the Lo Shu as the nine numbers, while the diagrams and texts in Guan Lang's writings completely reversed what he opposed. Liu Mu did not discuss that system, and Shao Yong only regarded nine as the Lo Shu, never taking ten as the River Chart. Although The Original Meaning of the Zhou Changes listed these two diagrams at the beginning, it could not convince the people. Therefore, Lu Zuguan, who was close to Zhu Xi, believed in Liu Mu's study of the Dragon Diagram; Wei Leoweng, who privately followed Zhu Xi, also regarded the diagram with "nine on top and one below" as the River Chart. Others like Zhu Yuansheng, Ge Tongshou, Li Jian, and Hu Yizhong, who were born after Zhu Xi, did not follow the启蒙. Only when Zhu Xi's learning became popular in the late Song and early Yuan dynasties did people begin to follow the启蒙. However, Hao Jing, Liu Yin, and Lei Siqi still thought it wrong. By the mid-Ming dynasty, scholars abandoned the Cheng氏 Commentary on the Zhou Changes and focused solely on The Original Meaning of the Zhou Changes. Thus, the world only knew about the two diagrams at the beginning of the book and no longer questioned their origins.

震川歸氏有光《易圗論》曰：或曰：子以易圗為非伏羲之舊，固已明矣，若夫「河以通乾出天苞，洛以流坤出地符」，所謂河圗洛書可廢耶？葢宋儒朱子之說甚詳：揭中五之要，明主客君臣之位，順五行生剋之序，辨體用常變之殊，合卦範兼通之妙，縱橫曲直無不相值，可謂精矣。曰：此愚所以恐其說之過於精也。夫事有出於聖人而在學者有不必精求者，河圗洛書是也。聖人聰明睿智，德通於天，符瑞之生出於世之所創見，而奇偶法象之妙足以為作易之本，理亦有然者。然曰「河圗洛書聖人則之」者，此大傳之所有也；「通乾流坤、天苞地符」之文，「五行生成、戴九履一」之數，非大傳之所有也。

In the "Commentary on the Diagrams of the Book of Changes" by Gu Yi Guang (styled Zhenchuan) of the Ming dynasty, someone asked: You have already clearly explained that you do not consider the diagrams of the Book of Changes to be original to Fuxi. As for the statements in the apocryphal texts that "the river water flows into Heaven and produces the heavenly bundle, and the Luo river flows into Earth and produces the earthly symbol," can the Yellow River Chart and the Luo Writing be discarded? Zhu Xi, a Song dynasty scholar, provided a very detailed explanation: He emphasized the central five numbers as the key, clarified the positions of host and guest, ruler and subject, followed the order of mutual generation and mutual control among the Five Phases, distinguished between essence and function, constancy and change, and combined the hexagrams of the Book of Changes with the nine categories of the "Huang Fan" to reveal their profound unity. In every direction, straight or curved, the correspondence is complete. This is indeed very precise. The reply was: This is exactly the point I am worried about, that his theory is "too refined." Some things are from the sage, but scholars need not pursue them in excessive detail. The Yellow River Chart and the Luo Writing are like that. The sage is wise and intelligent, with virtue reaching the heavens. The appearance of auspicious signs is rare. The subtlety of odd and even numbers as symbols is sufficient to serve as the foundation for the Book of Changes. This reasoning is reasonable. However, the statement "the sage took the Yellow River Chart and Luo Writing as models" is found in the "Great Treatise." As for the phrases "the river flows into Heaven and the Luo flows into Earth, heavenly bundle and earthly symbol" and the numbers "the number nine is on top and one is beneath," these are not found in the "Great Treatise."

以彼之名合此之跡，以此之跡符彼之名，不與大易同行，不藏於博士學官，而千載之下，山人野士持盈尺之書而曰「古之圗書者如是」，此其付受固已沈淪詭秘，而為學者之所疑矣。雖其說自以為無所不通，然此理在人，仁者知者皆能見之，龍虎之經、金石草木之卜、軌菥占算之術，隨其所自為說而亦無不合，豈必皆聖人之為之乎？大傳曰：「包羲氏之王天下也，仰則觀象於天，俯則觀法於地。」夫天地之間，何往非圗而何物非書也哉？揭其圗而示之曰「孰為上下，孰為左右，孰為乾兊離震，孰為巽坎艮坤」，天之告人也何其瀆；因其上下以為上下，因其左右以為左右，因其乾兊離震以為乾兊離震，因其巽坎艮坤以為巽坎艮坤，聖人之效天也何其拘。且彼所謂效變化則垂象者，毫而析之，又何所當也？

Using the names from one side to match the traces on the other, and using the traces on the other side to confirm the names from one side; this set of things neither circulated together with the Book of Changes nor was kept in the official schools of the scholars, yet after more than a thousand years, a person from the mountains and woods held a square foot of a diagram and said, "Ancient books were like this." Its transmission and reception have always been obscure and mysterious, and have long been doubted by scholars. Although this claim claims to be comprehensive, this point is clear in everyone's mind, and both the benevolent and the wise can see it: the alchemical text called the Dragon and Tiger Classic, the divination methods using metals, stones, herbs, and trees, and various systems of calculation and prediction, each set up their own theories at will, and none of them are without their own consistency. Could they all have been made by the sages? The Great Treatise says: "When Fu Xi ruled the world, he looked up to observe the patterns of heaven and looked down to study the principles of earth." Between heaven and earth, where is there not a diagram, and what is not a book? If one says that heaven raised a diagram to show people, pointing out where up and down, left and right, and where Qian, Dui, Li, and Zhen are, and where Xun, Kan, Gen, and Kun are, then the way heaven communicates with mankind is too careless; if one says that the sages followed its up and down to determine up and down, followed its left and right to determine left and right, followed its Qian, Dui, Li, and Zhen to determine Qian, Dui, Li, and Zhen, and followed its Xun, Kan, Gen, and Kun to determine Xun, Kan, Gen, and Kun, then the way the sages imitate heaven is too rigid. Moreover, their so-called "imitating change and revealing the images of things" requires every detail to be analyzed, which is not understandable at all.

使二圗者果在如今所傳，然其所謂精蘊者，聖人固已取而歸之易矣，求圗書之說於易可也。子產曰：「天道逺，人道邇。」天者，聖人之所獨得，而人者，聖人之所以告人者也。告人以天，人則駭而惑；告人以人，人則樂而從。故聖人之作易，凡所謂深微悠忽之理，舉皆推之於庸言庸行之間，而卦爻之象、吉凶悔吝之辭，不亦深切而著明也哉！聖人見轉蓬而造車，觀鳥跡而制字，世之人求為車之說與夫書之義則有矣，而必轉蓬鳥跡之求，愚未見其然也。

Even if these two diagrams were indeed as they are today, the profound meanings contained within them have already been incorporated by the sages into the Book of Changes. Therefore, seeking the meaning of the diagrams within the Book of Changes is sufficient. Zichan said, "The way of Heaven is distant, the way of humanity is near." The way of Heaven is understood solely by the sages, while the way of humanity is what the sages use to enlighten the people. To explain the way of Heaven to people would cause them confusion and fear; but to explain the way of humanity to people would make them willing to listen. Thus, the sages composed the Book of Changes, transferring all subtle and indistinct principles into everyday speech and actions. Therefore, the images of the hexagrams and the terms expressing fortune, regret, and hardship are both profound and clear. The sages observed the rotating thistle and invented the cart, and saw the tracks of birds and beasts and created writing. It is proper for people to seek the principles behind the cart and the meaning of writing, but if they insist on delving deeply into the thistle and the tracks, I do not see the necessity.

孔子贊易，刪《連山》《歸藏》而取《周易》，始於乾而終於未濟，則圗書之列粲然者莫是過矣。今夫冶之所貴者範，而用者不求範而求器也；耕之所資者耒，而食者不求耒而求粟也。有圗書而後有易，有易無圗書可也。故《論語》「河不出圗」，與鳳鳥同瑞而已；《顧命》「河圗在東序」，與兊弓和矢同寶而已。是故圗書不可以精，精於易者精於圗書者也。惟其不知其不可精而欲精之，是以測度摹擬無所不至，故有九宮之法，有八分井文之畫，有坎離交流之卦，與夫孔安國、向、歆、揚雄、班固、劉牧、魏華父、朱子發、張文饒諸儒之論，或九或十，或合或分，紛紛不定，亦何足辨也。

Confucius explained the principles of the I Ching, omitting the Lianshan and Guicang and choosing only the Zhouyi. He began with the Qian hexagram and ended with the Weijì hexagram. Therefore, the truly clear and visible parts in the theory of the River Chart and the Book of Changes are no more than this. For example, in metal casting, the most important thing is the mold, but those who use it do not seek the mold but the finished object; in farming, the plow is essential, but those who eat do not seek the plow but the grain. First there was the River Chart and the Book of Changes, but now that the Book of Changes exists, the River Chart is not necessary. Therefore, the saying in the Analects that "the Yellow River does not produce a chart" is merely another kind of auspicious omen, like the phoenix; and the statement in the Shangshu Guiming that "the River Chart is displayed in the eastern hall" is just another kind of treasure, like the bow and arrows of the earth. Therefore, the River Chart and the Book of Changes do not need to be pursued for perfection. Those who seek perfection in the Book of Changes are also seeking perfection in the River Chart. Because people do not understand that it is not necessary to pursue perfection, they go to great lengths in conjecture and imitation: thus arose the method of the nine palaces, the method of drawing the eight-part grid pattern, the theory of the mutual exchange of Kan and Li, and the discussions of various scholars such as Kong AnGuo, Liu Xiang, Liu Xin, Yang Xiong, Ban Gu, Liu Mu, Wei Le翁, Zhu Zhen, and Zhang Xingcheng, who hold different views, some advocating nine, some advocating ten, some combining, some separating, resulting in endless disputes without a definite conclusion. So why bother to argue about it?

自《本義》之圗書盛行，學者捲舌而不敢議，震川先生獨能昌言以正之，引繩批根，不遺餘力，真三百年來有數文字。

Since the theory of the Book and Diagram in the preface of The Original Meaning of the Zhou Changes became popular, scholars have all kept silent and dared not comment. Only Mr. Gui Youguang was able to speak out and correct it directly, straightening the measuring rope and uprooting the error completely, without any hesitation. This is truly an outstanding article among the three hundred years of writings.

秀水徐善敬可博覽精思，無所不通，而尤深於易，晚著書以發其蘊，有《天易》《羲易》《商易》《周易》。天易者，河圗洛書也；羲易者，先天古易也；商易者，《歸藏》首坤也；周易者，文王所演也。連山無傳，故不著夏易。同縣朱太史彝尊名其書曰《徐氏四易》而為之序。敬可與餘厚，向在京師出以示余，其言河圗洛書以劉牧得希夷之傳，而西山兩易殊可疑，餘深以為然，僭作題辭，要不出此意。

Xu Shanjie, a man from Xiushui, was well-read and deeply thoughtful, with profound understanding in all fields, but especially skilled in the study of the I Ching. In his later years, he wrote four books to explain his insights: The Heavenly I Ching, The Xia I Ching, The Shang I Ching, and The Zhou I Ching. The Heavenly I Ching discusses the Yellow River Chart and the Luo Writing. The Xia I Ching refers to the ancient Earlier Heaven I Ching. The Shang I Ching discusses the Guicang, with the Earth Trigram as the first. The Zhou I Ching refers to the I Ching developed by King Wen. The Lianshan has no surviving texts, so there is no separate section for the Xia I Ching. A historian from the same county, Zhu Yizun, named this collection The Four I Chings of Xu and wrote an introduction. Xu Jingke and I had a close friendship. When we were in the capital together, he showed me his books. He discussed the Yellow River Chart and the Luo Writing, believing that Liu Mu was the true inheritor of Chen Tuan's teachings, while Cai Yuanding's reversal of the charts was suspicious. I strongly agreed with him, so I wrote an introduction, which mainly expressed this view.

既而思之，河圗洛書自秦漢以來未有能言其狀者，至五季而始出，何可遽信？學者不能痛絶圗書之謬種，而徒辨劉蔡之是非，無為也。歲庚午，與敬可讀書莫釐峰下，方且效一得之慮，相與更定是書，而敬可尋以病歸，卒於家，吾欲言之無以為質矣。因復窮究其義，知圗書之形象自古無傳，當姑從漢孔劉之言而闕其疑，至於宋人之所傳，一槩難信。越七歲，為今丁丑，始成此五卷。追念舊好，歔欷者久之。嗟乎！郢人逝矣，誰與盡言？此嵇生所以致慨也。

Later, upon further reflection, I thought: since the Han dynasty, no one has been able to describe the shape of the Yellow River Chart and the Luo Writing, until the Five Dynasties period when they suddenly appeared. How can we easily believe them? Scholars who cannot eliminate these false doctrines at their roots and instead argue over whether Liu Mu or Cai Yuanping was right are wasting their efforts. In the year Gengwu, I was studying with Xu Jingke on the Molei Peak, intending to present my own opinion and revise this book together; but unfortunately, Jingke soon returned home due to illness and died there. I had no one to discuss my thoughts with. Thus, I once again thoroughly examined the meaning and principles, realizing that the image of the Book of Changes has never been passed down since ancient times. Therefore, we should only follow the interpretations of Han dynasty scholars like Kong AnGuo and Liu Xin, keeping doubts and not discussing them. As for the versions passed down by the Song dynasty, they are all difficult to believe. Seven years later, this year Dingchou, I have finally completed these five volumes. Thinking of my old friends, I have been sighing for a long time. Alas! The person who was matched with the master craftsman, Ying, has already passed away. Who else can I discuss this with freely? This is precisely the reason why Ji Kang felt deeply sorrowful over the loss of a true friend.

右論啟蒙圗書。

In the previous section, the discussion examines the interpretations of the Yellow River Chart and the Luo Writing as presented in the "Commentary on the Origins of the Book of Changes."

《繫辭傳》曰：「易有太極，是生兩儀，兩儀生四象，四象生八卦。」

The Great Treatise of the Zhou Changes says: The Book of Changes has a "Taiji" (Supreme Ultimate), from which arises "two yin and yang" (the Two Principles), from which arise the "Four Symbols," and from the Four Symbols arise the Eight Trigrams.

朱子曰：「一每生二，自然之理也。《易》者，陰陽之變；大極者，其理也。兩儀者，始為一畫以分陰陽；四象者，次為二畫以分太少；八卦者，次為三畫而三才之象始備。此數言者，實聖人作《易》自然之次第，有不假絲毫智力而成者。畫卦揲蓍，其序皆然。」

Zhu Xi explained that one must necessarily produce two, which is the natural principle. The "Book of Changes" discusses the transformation of yin and yang. The term "Great Ultimate" (i.e., "Taiji") refers to the principle behind these transformations. "Two Principles" (liang yi) are the first line drawn, used to distinguish yin and yang. "Four Symbols" (si xiang) are the second lines drawn, used to distinguish Taiyin, Taiyang, Xiaoyin, and Xiaoyang. "Eight Trigrams" (bagua) are the third lines drawn, and at this point, the images of heaven, earth, and humanity ("san cai") are fully complete. These statements truly reflect the natural order in which the sages created the "Book of Changes," without any artificial ingenuity. Whether drawing the trigrams or using the divination method with yarrow stalks, the sequence remains the same.

按：此節夫子本言揲蓍之序，與畫卦無涉，說見第一卷。

Hu Wei remarks: In this section of the Great Treatise, Confucius originally discussed the order of counting the yarrow stalks when seeking a hexagram, which has nothing to do with Fuxi drawing the trigrams. A detailed argument can be found in the first volume of this book.

《語類》曰：「某嘗聞季通：『康節之數，伏羲也曽理會否？』曰：『伏羲須理會過。』某以為不然。伏羲只是據他見得一個道理，恁他便畫出幾畫，他也那裡知得疉出來恁地巧。此伏羲所以為聖。若他也恁地逐一推排，便不是天然意思。《史記》曰伏羲至淳厚，作《易》八卦，那裡恁地巧推排。」（此葉賀孫所録也。劉砥録以「伏羲至淳厚」為季通述太史公語，以規朱子。）

The *Zhu Zi Yu Le* records Zhu Xi's words: I once asked Cai Jitong (Cai Yuan ding): "Did Fuxi also investigate the system of numbers that Shao Kangjie discussed?" He replied: "Fuxi certainly did." I did not think so. Fuxi merely drew those trigrams based on the principle he himself understood, without knowing that layering them in sequence could result in such a neat and complete system. It is precisely for this reason that Fuxi can be called a sage. If he had also calculated step by step as later people did, it would not have been natural and spontaneous. The *Records of the Grand Historian* says that Fuxi was extremely simple and sincere, and he composed the *Book of Changes* and drew the Eight Trigrams. How could he have arranged them so cleverly? (This entry is recorded by Ye Hesun. Liu Di's record, however, takes the phrase "Fuxi was extremely simple and sincere" as Cai Jitong quoting Sima Qian's words, used to advise Zhu Xi.)

又董銖問：「《程易》乾繇辭下解云：『聖人始畫八卦，三才之道備矣，因而重之，以盡天下之變，故六畫而成卦。』據此說，卻是聖人始書八卦，每卦便是三畫，因而重之為六畫，似與邵子說不同。」曰：「程子之意，只雲三畫上疉成六畫，八卦上疉成六十四耳，與邵子說異。蓋康節此意不曽說與程子，程子亦不曽問之，故一向只隨他所見去。但他說聖人始畫八卦，不知其時先畫甚卦，此處便曉他不得。」

There is another question raised by Dong Zhu: "In the Hexagram Statement of the Qian hexagram, Cheng Yi explains that 'the sage first drew the Eight Trigrams, and thus the principles of Heaven, Earth, and Humanity were all complete. Then he overlapped the Eight Trigrams to exhaust all changes in the world, hence forming a hexagram with six lines.' According to this explanation, the original Eight Trigrams each had three lines, and they were overlapped to form six lines, which seems different from Shao Yong's view." Zhu Xi replied: "Cheng's meaning is simply that three lines were overlapped to form six lines, and the Eight Trigrams were overlapped to form the sixty-four hexagrams. This is indeed different from Shao Yong's view. Perhaps Shao Yong's idea was never communicated to Cheng, and Cheng never asked him about it, so Cheng always explained according to his own understanding. However, when he says the sage first drew the Eight Trigrams, he does not explain which trigram was drawn first, which is illogical."

按：康節先天八卦次序，伊川不用，以為聖人始畫八卦，每卦便是三畫。其後精通邵學者莫如漢上，而《集傳》釋兩儀、四象、八卦亦不從康節，意可知矣。朱子初亦疑之，謂伏義至淳厚，未必如此巧推排，而蔡季通堅執不移，故《本義》屈伊川而伸康節。蓋牧堂（季通父，名發，字神與）嘗以《皇極經世》授季通曰：「此孔孟正脈。」故季通篤信邵學不啻如孔孟，朱子方以為老友，不在弟子之列，往往曲從其言。至《啟蒙》則屬季通起藁，其《原卦畫》一篇敷暢邵學尤為詳備，而其說遂牢不可破矣。

Hu Wei said: Shao Kangjie's arrangement of the Earlier Heaven Trigrams was not adopted by Cheng Yi. He believed that when the sage originally drew the eight trigrams, each trigram was directly composed of three lines. Later scholars who thoroughly understood Shao Yong's teachings did not surpass Zhu Zhen (the Master of Han Shang). His Han Shang Commentary on the Zhou Changes did not follow Shao Kangjie when explaining the two principles, four images, and eight trigrams. His attitude towards this issue is evident. Zhu Xi initially also doubted, saying that Fuxi was extremely simple and sincere, and would not have arranged things so cleverly. However, Cai Jitong refused to yield, so The Original Meaning of the Zhou Changes finally compromised Cheng Yi's view and supported Shao Kangjie's. Originally, Cai Muting (Jitong's father, named Fa, with the style name Shenyu) once passed on the Huang Ji Jing Shi to Jitong, saying, "This is the orthodox lineage of Confucius and Mencius." Therefore, Jitong believed in Shao's teachings no less than he did in Confucius and Mencius. Zhu Xi regarded him as an old friend, not as a disciple, and often yielded to his opinions. When compiling the Yi Xue Ming Tong, he even entrusted Jitong to draft it. Among the chapters, the "Original Trigram Diagram" elaborated and developed Shao's teachings in a particularly detailed and complete manner, thus making this theory firmly established and unshakable.

朱子又疑伊川不知康節之意。愚謂程、邵在洛中晨夕往來，豈有邵不言而程亦不問者？此必伊川灼見其非，故《易傳》不從耳。又疑八卦不知先畫何卦。萬季野云：「讀《大傳》『成象之謂乾，效法之謂坤』，便見是先畫乾，次畫坤，然後以乾坤相索成六子，有何難曉？」李剛主亦云。

Zhu Xi also doubted that Cheng Yi did not understand Shao Kangjie's intention. I Hu Wei think that Cheng Yi and Shao Yong were both in Luoyang, living together day and night, so there could not be a situation where Shao Yong never spoke and Cheng Yi never asked. This must be because Cheng Yi clearly saw something wrong with it, so the Book of Changes Commentary did not adopt it. Zhu Xi also doubted that Cheng Yi could not explain which hexagram was drawn first. Wan Siting (style name Jiyě) said, "As long as one reads the two sentences from the Great Treatise, 'Forming the image is called Qian, following the pattern is called Kun,' one can see that Qian was drawn first, then Kun, and then the six subordinate hexagrams were generated through the mutual inquiry between Qian and Kun. What is there difficult to understand about it?" Li Nen (style name Gangzhu) also said the same thing.

邵子《觀物外篇》曰：「太極既分，兩儀立矣。陽下交於陰，陰上交於陽，四象生矣。陽交於陰，陰交於陽，而生天之四象；剛交於柔，柔交於剛，而生地之四象。於是八卦成矣。八卦相錯，然後萬物生焉。是故一分為二，二分為四，四分為八，八分為十六，十六分為三十二，三十二分為六十四。故曰：『分陰分陽，迭用柔剛，易六位而成章也。』」

Shao Yong said in "Guangwu Wai Pian" that after the Taiji is divided, the two principles are established. Yang goes down to meet Yin, and Yin goes up to meet Yang, thus the four images are generated. The meeting of Yang and Yin, and the meeting of Yin and Yang, produce the four celestial images; the meeting of hardness and softness, and the meeting of softness and hardness, produce the four terrestrial images. At this point, the eight trigrams are formed. The eight trigrams intermingle and combine, and then all things are generated from this. Therefore, it is said: one divides into two, two divides into four, four divides into eight, eight divides into sixteen, sixteen divides into thirty-two, thirty-two divides into sixty-four. Therefore, the "Shu Guan Zhuan" says: "Separating Yin and separating Yang, alternating the use of softness and hardness, the Book of Changes is completed through six lines."

「十分為百，百分為千，千分為萬，猶根之有乾，乾之有枝，枝之有葉，愈大則愈小，愈細則愈繁。合之斯為一，衍之斯為萬。是故乾以分之，坤以翕之，震以長之，巽以消之。長則分，分則消，消則翕也。」

Ten is divided into a hundred, a hundred into a thousand, a thousand into ten thousand, just as tree roots produce the trunk, the trunk produces branches, and branches produce leaves: the larger the whole, the smaller the units divided from it; the more detailed the division, the greater the number. When combined, it becomes one; when extended, it becomes myriad. Therefore, Qian is used for differentiation, Kun for convergence, Zhen for growth, and Xun for retreat; growth leads to differentiation, differentiation leads to retreat, and retreat leads to convergence.

《本義》圖說：右《繫辭傳》曰「易有太極，是生兩儀，兩儀生四象，四象生八卦」，邵子曰「一分為二，二分為四，四分為八也」。《說卦傳》曰「易逆數也」，邵子曰「乾一、兌二、離三、震四、巽五、坎六、艮七、坤八，自乾至坤皆得未生之卦，若逆推四時之比也」。後六十四卦次序仿此。（黒白之位本非古法，但今欲易曉，且為此以寓之耳。後六十四卦次序仿此。）

The diagram attached to The Original Meaning of the Zhou Changes is said to come from the Great Treatise, which states, "The Book of Changes has the Taiji, from which the two principles arise, from the two principles the four images, and from the four images the eight trigrams." Shao Yong explains this as "one divides into two, two divides into four, four divides into eight." The Sayings on the Trigrams also say, "The Book of Changes proceeds in reverse order." Shao Yong explains that Qian is one, Dui is two, Li is three, Zhen is four, Xun is five, Kan is six, Gen is seven, and Kun is eight. Counting from Qian to Kun, all the trigrams are those that have not yet been generated, like counting the seasons in reverse. The order of the sixty-four trigrams is also arranged in this way. (The diagram uses black and white to indicate the positions of odd and even numbers, which is not the ancient method, but is used here to make it easier for modern people to understand, serving merely as a way to represent the trigram figures. The order of the sixty-four trigrams is also arranged in this way.)

李剛主《學易》曰：「先天圖杜撰乾一、兌二、離三、震四、巽五、坎六、艮七、坤八之數，毛河右闢之是矣。若宗康成，以天地生成之數配八卦，則乾天也乃得地六數，坤地也乃得天九數，且中遺五數亦可疑也。蓋必分八卦次序之數，則畫卦自乾而終兌可為數，卦位自震而終艮可為數，然總不必也。何者？用九用六，爻有數；用四十有九，大衍有數，即卦數也。若乾一至坤八之數，聖人所不言，何為為渾敦畫眉乎？」

Li Neng said in his "Learning the Book of Changes": The Earlier Heaven diagram arbitrarily assigns the trigrams with numbers, starting with Qian as one, Dui as two, Li as three, Zhen as four, Xun as five, Kan as six, Gen as seven, and Kun as eight. Mao Qiling (He Yu) correctly refuted this. If we follow Zheng Xuan's (Kangcheng) method of matching the trigrams with the numbers of heaven and earth, then Qian, which is heaven, is assigned the number six of earth, and Kun, which is earth, is assigned the number nine of heaven. Moreover, the number five is missing in between, which is also suspicious. If we must assign numbers to the trigrams in order, then according to the method of drawing the trigrams, counting from Qian to Dui is one way of numbering; according to the positions of the trigrams, counting from Zhen to Gen is another way. However, these are actually unnecessary. Why? "Yong Ji" and "Yong Liu" already have numbers inherent in the lines. "The Great Derivation has a number of forty-nine," and the process of divination with yarrow stalks already has numbers, which are the numbers of the trigrams. As for the numbers from Qian to Kun eight, the sages never mentioned them. Why should we go out of our way to draw eyebrows on a chaos?

《易學啟蒙》曰：「盈天地之間莫非太極陰陽之妙，聖人於此仰觀俯察，逺求近取，固有以超然而黙契其心矣。故自兩儀之未分也，渾然太極，而兩儀、四象、六十四卦之理已粲然於其中。自太極而分兩儀，則太極固太極也，兩儀固兩儀也；自兩儀而分四象，則兩儀又為太極，而四象又為兩儀矣。自是而推之，由四而八，由八而十六，由十六而三十二，由三十二而六十四，以至於百千萬億之無窮，雖其見於摹畫者若有先後而出於人為，然其已定之形、已成之勢，則固已具於渾然之中，而不容毫髮思慮作為於其間也。」

The "Yixue Qimeng" says: Everything that fills the space between heaven and earth is nothing but the subtlety of the Taiji and the yin and yang. The sage observed the heavens above and examined the earth below, taking images from all things in the distance and from his own body in the near. Thus, he could naturally comprehend and have a silent harmony in his mind. Therefore, when the two principles had not yet separated, it was a single Taiji. But the principles of the two, the four images, and the sixty-four hexagrams were already clearly contained within it. When the Taiji splits into the two principles, the Taiji remains the Taiji, and the two principles remain the two principles. When the two principles split into the four images, then the two principles become the Taiji again, and the four images become the two principles. Continuing in this way, from four to eight, from eight to sixteen, from sixteen to thirty-two, from thirty-two to sixty-four, and so on endlessly. Although the diagram seems to show a sequence and an artificial order, the determined form and the established trend were already present in the unity of the whole, leaving no room for human thought or artificial creation.

「程子所謂『加一倍法』者，可謂一言以蔽之；而邵子所謂『畫前有易』者，又可見其真不妄矣。世儒於此或不知察，往往以為聖人作《易》蓋極其心思探索之巧而得之，甚者至謂凡卦之畫必由蓍而後得，其誤益以甚矣。」

Cheng Hao's "add one more" method can be summarized in one sentence the entire principle of generating hexagrams. Similarly, Shao Yong's statement "before drawing, there is the easy" can be seen as not mere empty talk. Later Confucian scholars sometimes fail to understand this point, often thinking that the sage composed the Book of Changes by exhausting his mind and achieving it through clever exploration. Worse still, some even claim that all hexagram diagrams must first be obtained through divination with yarrow stalks, which is an even greater mistake.

又曰：「太極者，象數未形而其理已具之稱，形器已具而其理無朕之目，在《河圖》《洛書》皆虛中之象也。周子曰『無極而太極』，邵子曰『道為太極』，又曰『心為太極』，此之謂也。」

The "Book of Changes: Awakening to the Teachings" also says: The term "Taiji" refers to a state where the image and numbers have not yet taken form, but its principle is already complete; it also refers to a state where the physical forms are already present, but the principle is not evident at all. In the "Yellow River Chart" and the "Luo Writing," it is represented by the image of the center being empty. Zhou Dunyi said "from non-polarity comes Taiji," Shao Yong said "the Dao is Taiji," and also said "the mind is Taiji," referring to this very concept.

「太極之判，始生一竒一偶而為一畫者二，是為兩儀，其數則陽一而陰二，在《河圖》《洛書》則竒偶是也。周子所謂『太極動而生陽，動極而靜，靜而生陰，靜極復動，一動一靜，互為其根，分陰分陽，兩儀立焉』，邵子所謂『一分為二』者，皆謂此也。」

The Taiji splits into two, producing two kinds of symbols, one odd and one even, which are called "the Two Principles" or "two yi." In terms of numbers, yang is represented by one and yin by two, corresponding to odd and even numbers in the Yellow River Chart and the Luo Writing. The "Taiji Diagram Explanation" by Zhou Dunyi describes how the Taiji, when it moves, gives rise to yang; when it moves to its extreme, it becomes still, and from stillness comes yin; when stillness reaches its extreme, it returns to movement. The alternation of movement and stillness forms the basis for distinguishing yin and yang, thus establishing the Two Principles. Similarly, Shao Yong's concept of "dividing one into two" refers to this same principle.

「兩儀之上各生一竒一偶而為二畫者四，是謂四象。其位則太陽一、少陰二、少陽三、太陰四，其數則太陽九、少陰八、少陽七、太陰六。以《河圖》言之，則六者一而得於五者也，七者二而得於五者也，八者三而得於五者也，九者四而得於五者也；以《洛書》言之，則九者十分一之餘也，八者十分二之餘也，七者十分三之餘也，六者十分四之餘也。周子所謂『水火木金』，邵子所謂『二分為四』者，皆謂此也。」

The *Yixue Qimeng* continues to say: Above the two principles, each generates one odd and one even, resulting in four symbols composed of two lines, which is called the "Four Images." In terms of position, the Sun is first, the Lesser Yin is second, the Lesser Yang is third, and the Great Yin is fourth. In terms of numbers, the Sun corresponds to nine, the Lesser Yin to eight, the Lesser Yang to seven, and the Great Yin to six. Using the *He Tu* (Yellow River Chart), these four numbers are each the base number plus the central five: six is one plus five, seven is two plus five, eight is three plus five, and nine is four plus five. Using the *Luoshu* (Luo Writing), these four numbers are derived by subtracting the base number from ten: nine is what remains after subtracting one from ten, eight is what remains after subtracting two from ten, seven is what remains after subtracting three from ten, and six is what remains after subtracting four from ten. What Zhou Dunyi discusses in his *Taiji Tu Shuo* as "water, fire, wood, metal," and what Shao Yong refers to as "dividing two into four," all refer to this level.

「四象之上各生一竒一偶而為三畫者八，於是三才略具而有八卦之名矣。其位則乾一、兌二、離三、震四、巽五、坎六、艮七、坤八。在《河圖》則乾坤離坎分居四實，兌震巽艮分居四虛；在《洛書》則乾坤離坎分居四方，兌震巽艮分居四隅。《周禮》所謂『三易經卦各八』，《大傳》所謂『八卦成列』，邵子所謂『四分為八』者，皆指此而言也。」

Above the Four Symbols, each generates one odd and one even, forming eight trigrams of three lines. At this point, the principles of heaven, earth, and humanity are largely complete, thus giving rise to the name of the Eight Trigrams. In terms of their positions, Qian is one, Dui two, Li three, Zhen four, Xun five, Kan six, Gen seven, and Kun eight. In the Yellow River Chart, Qian, Kun, Li, and Kan occupy four solid positions, while Dui, Zhen, Xun, and Gen occupy four empty positions. In the Luo Writing, Qian, Kun, Li, and Kan occupy the four cardinal directions, while Dui, Zhen, Xun, and Gen occupy the four corners. The "three books of Change" mentioned in the Zhou Li each have eight trigrams, the "Eight Trigrams in order" mentioned in the Great Treatise, and Shao Yong's "four divided into eight" all refer to this.

《語類》曰：「康節之書固自是好，而季通推得來又甚縝宻（觀此語則《啟蒙》仍季通之藁無所更定可知），若見於用，不知果如何，恐絶勝諸家也。」

The "Shuzi Yilu" records Master Zhu's words saying: Shao Kangjie's book was originally good, and Cai Jitong elaborated on it with great detail (from this statement alone, it can be seen that "Yixue Qimeng" is still Cai Jitong's original manuscript, and Master Zhu did not make any revisions). If applied in practice, it is uncertain how it would turn out, but it is likely to be far superior to other schools.

康節之學似揚子雲。《太玄》擬《易》，方、州、部、家皆自三數推之。玄之為首，一以生三為三方，三生九為九州島，九生二十七為二十七部，九九乘之斯為八十一家。首之以八十一，所以準六十四卦；贊之以七百二十有九，所以準三百八十四爻，無非以三數推之。康節之數，則是加倍之法。

Zhu Xi also said that Shao Kangjie's learning is somewhat similar to Yang Xiong. Yang Xiong's "Tai Xuan" was modeled after the "Yi Jing," where the four levels of "fang," "zhou," "bu," and "jia" were all derived according to the number three. "Tai Xuan" established "shou," beginning with one and generating three to form three fang, three generating nine to form nine zhou, nine generating twenty-seven to form twenty-seven bu, and then multiplying nine by nine to obtain eighty-one jia. It used eighty-one shou to correspond to the sixty-four hexagrams of the "Yi Jing," and seven hundred twenty-nine zan to correspond to the three hundred eighty-four lines of the "Yi Jing," with no part not derived by the number three. As for the numbers used by Shao Kangjie, he employed a method of doubling and adding.

程先生有一柬說先天圖甚有理，可試往聴他說看。觀其意甚不把當事，然自有《易》以來，只有康節說一個物事如此齊整。如揚子雲《太玄》便零星補湊得可笑，若不補又卻欠四分之一，補得來又卻多四分之三。如《潛虛》之數用五，只似如今算位一般，其直一畫則五也，下橫一畫則為六，橫二畫則為七，蓋亦補湊之書。

Zhu Xi also said that Cheng Yi once wrote a short letter saying that the Earlier Heaven diagram makes a lot of sense, and one could try to listen to his explanation. From his tone, it seems he did not take the matter very seriously. However, since the Book of Changes came into being, only Shao Kangjie (Shao Yong) has presented such a complete system. In contrast, Yang Xiong's Tai Xuan is a haphazard patchwork, which is laughable. If one does not supplement it, it is missing a quarter; if one does supplement it, it exceeds three quarters. Similarly, Sima Guang's Qian Xu uses five as the base number, which is like the way counting rods are arranged today: a vertical line represents five, adding a horizontal line below it represents six, adding two horizontal lines represents seven. In the end, it is also a book put together by patching things together.

按：《太玄》方、州、部、家表贊皆自三數推之，全從「三生萬物」得來，不待清靜寂寞等語而始知其為老氏之學也。《易》之為書，廣大悉備，天象厯數之理皆包括其中，然伏羲作《易》之本，夫子仰觀俯察數語盡之，天象厯數非其本也。雄因覃思渾天而作《太玄》以擬之，與《太初厯》相應。

Hu Wei said: The sections of "Tai Xuan" such as Fang, Zhou, Bu, Jia, as well as the Biao and Zan, are all derived according to the number three. They completely originate from Laozi's statement "three gives rise to all things." One does not need to see the words like "quiet and solitary" in the text to know that it comes from the school of Laozi. The Book of Changes is vast and comprehensive, containing the principles of celestial phenomena and calendar systems; but the fundamental idea of Fuxi's creation of the Book of Changes was fully explained by Confucius in the few words "looking up to observe the heavens and looking down to examine the earth." Celestial phenomena and calendrical calculations are not its fundamental basis. Yang Xiong composed the "Tai Xuan" to parallel the Book of Changes, based on his deep contemplation of the theory of the浑天 (hun tian, a cosmological theory). Therefore, it corresponds exactly with the Han dynasty's "Tai Chu Li" (Great Initial Calendar).

《易》太極生兩，兩生四，四生八；《玄》太極函三為一，一生二，二生三，三生萬物：其所據者固老氏之《易》，而非聖人之《易》矣。列子言太易自一而七而九，亦皆竒數，卻不言三。夫子所言自一而兩而四而八皆偶數，故康節用加一倍法。子云之乘法以參，康節之倍數以兩，故蔡季通云：「使康節為之，定是四公、八辟、十六侯、三十二卿、六十四大夫，都是加倍法也。」

The Book of Changes arises from the Taiji generating two principles, the two principles generating four images, and the four images generating the Eight Trigrams; the TaiXuan, however, originates from the Taiji containing three as one, one generating two, two generating three, and three generating all things. This shows that it is based on the Book of Changes of Laozi's tradition, not the Book of Changes of the sages. Liezi speaks of "Taiyi" originating from one, then seven, then nine, using only odd numbers, but does not mention three. Confucius, on the other hand, speaks of originating from one, then two, then four, then eight, using only even numbers, so Shao Kangjie adopted the method of doubling. Yang Zhonglin's method involves multiplying by three, while Shao Kangjie's method involves doubling, hence Cai Jitong said, "If Kangjie were to compose the TaiXuan, he would certainly arrange it as four publics, eight divisions, sixteen peers, thirty-two ministers, and sixty-four scholars, all following the method of doubling."

子云草《玄》，自丑至午得七百二十九而止，《玄》其所自造，任意可也。康節著先天圖，自兩至八，《易》之所有也；自八而為十六、三十二、六十四，以至於百千萬億而無窮，又豈《易》之所有乎？是亦邵子之數學，而非古聖人之《易》矣。

Yang Zi Yun composed the "Tai Xuan" starting from the Chou position up to the Wu position, obtaining seven hundred and twenty-nine zan and then stopping; since the "Tai Xuan" was a book he himself created, the arrangement was entirely up to his own will. Shao Kangjie composed the Earlier Heaven diagram, deriving the Eight Trigrams from the Two Principles, which is something already present in the "Yi"; but starting from the Eight Trigrams and proceeding to sixteen, thirty-two, sixty-four, and so on infinitely, is this also something originally present in the "Yi"? This is also merely Shao Yong's own mathematics, not the "Yi" of the ancient sages.

朱子嘗云「康節之學似揚子雲」，又云「康節數學源流於陳希夷」。希夷，老氏之徒也，不啻若子云之小疵。朱子斥《太玄》學本老氏，而顧以出自希夷者為聖人之《易》，獨何與？

Zhu Xi once said that Shao Kangjie's learning was like Yang Xiong's, and also said that Kangjie's mathematical origins came from Chen Tuan (Xiyi). Chen Tuan was originally a figure from the Daoist Laoshang school, and his faults were far more serious than just the minor flaws of Yang Xiong. Zhu Xi on one hand criticized the study of Tai Xuan as being based on Laoshang, yet on the other hand regarded things originating from Chen Tuan as the sacred Book of Changes. Why was this so?

嗟乎！仲尼沒而微言絶，七十子喪而大義乖。漢世崇尚黃老，至謂《老子》兩篇過於五經，子云擬《易》，所以墮其玄中也。魏晉諸人皆以老、易混稱，歴唐宋而未艾。伊川始闢異端，専宗十翼，《易》道昌明如日月之中天矣，而希夷之徒以象數自鳴，復從而亂之。蓋自孔子贊《易》之後二千年間，其不以老氏之《易》為聖人之《易》者無幾。迨宋末元初，《啟蒙》之說盛行，以至於今，則反謂文王、周公、孔子之《易》非伏羲之《易》，而老、列、希夷、康節之《易》乃真伏羲之《易》矣。晦盲否塞五百餘年，非屏絶先天諸圖而専宗程氏《易》，不可得而明也。

Alas! After Confucius' death, the subtle teachings were cut off, and the seventy disciples declined, distorting the great principles. During the Han dynasty, the doctrines of the Yellow Emperor and Laozi were esteemed, even claiming that the Upper and Lower Chapters of the Dao De Jing surpassed the Five Classics. Yang Xiong imitated the Yi Jing to compose the Tai Xuan, thus falling into the Daoist path of mysticism. The scholars of the Wei and Jin dynasties further confused Laozi's teachings with the Yi Jing, and this trend continued through the Tang and Song dynasties without ceasing. It was only Cheng Yi who began to reject heresies and focused solely on the ten wings of Confucius, making the Yi Jing's principles as clear as the sun and moon. However, the school of Chen Tuan once again claimed the image and number methods as their own, causing further confusion. In general, for two thousand years since Confucius praised the Yi Jing, few people regarded the Yi Jing of Laozi as the true Yi Jing of the sage. By the late Song and early Yuan dynasties, the teachings of the "Yi Xue Ming Cong" became popular and have continued to the present day. People now claim that the Yi Jing of King Wen, the Duke of Zhou, and Confucius is not the Yi Jing of Fuxi, but rather the Yi Jing of Laozi, Liezi, Chen Tuan, and Shao Yong is truly the Yi Jing of Fuxi. This darkness and confusion has lasted for more than five hundred years. Without completely rejecting the earlier heaven diagrams and focusing solely on Cheng Yi's "Yi Zhuan," the principles of the Yi Jing cannot be clarified again.

鯤溟黃氏曰中曰：「卦之短長闊狹彼此如一，若依橫圖畫法，下畫一竒一偶，以視四象，每竒偶當截為二段，八卦當截為四段，十六當截為八段，三十二當截為十六段，六十四當截為三十二段。其四象、八卦、十六、三十二亦各各當截。若不截下，以一竒一偶牽連上之六十四，竒偶長短不倫，且圓圖如何抝轉？方圖如何堆疉？」

Huang Yu Zhong, who goes by the name Hao Kunming, said: The length and width of the trigrams are originally all the same. If we follow the method of drawing the horizontal diagram, the lowest line is divided into one odd and one even. When compared with the four trigrams, each odd or even line must be divided into two parts; when compared with the eight trigrams, divided into four parts; when compared with sixteen, divided into eight parts; when compared with thirty-two, divided into sixteen parts; and when compared with sixty-four, divided into thirty-two parts. Among the layers of four trigrams, eight trigrams, sixteen, and thirty-two, each also needs to be divided. If the lowest line is not divided, then one odd or even line would have to connect to the upper sixty-four trigrams. In this case, the odd and even lines would be of uneven length, making it impossible for the circular diagram to bend smoothly or for the square diagram to be stacked properly.

「若依六十四截之，截竒則竒仍是竒，截偶則偶已非偶矣。何也？偶之為畫，中斷者也，自兩儀一截而後，偶固蚤化而為竒矣。今觀橫圖，亦自知其法不可通，不得已而以黒白分竒偶，大失畫竒偶之本色矣。」

If the sixty-four hexagrams are divided according to their structure, when a yī (odd line) is cut, it remains an odd line. But when an è (even line) is cut, the even line is no longer an even line. Why is this? Because the even line was originally a single broken line in the middle. After being divided from the two principles (yīn and yáng) at the level of the two trigrams, the even line has already been transformed into two short odd lines. Now, looking at the horizontal diagram, the person drawing the diagram himself realizes that this method does not make sense. Therefore, he is forced to use black and white colors to distinguish between odd and even lines. This greatly distorts the original appearance of odd and even lines.

按：橫圖逐爻漸生之法，唯揲蓍三變而成爻、十八變而成卦，自初而二、而三、而四、而五、而上，六爻次第得之，誠有然者。然兩儀主一變言，但分竒偶；而初畫則兼三變，三變之餘或老或少，各視其所得之九六七八以為名，則初畫便當為四象，不可謂兩儀。四象三畫皆有，獨以中畫為四象，尤不可也。然則就揲蓍言之，其義亦有難通者矣。

Hu Wei said: The method of generating lines one by one in a horizontal diagram only makes sense when using the divination with yarrow stalks: three changes produce one line, eighteen changes produce one hexagram. From the first line to the second, third, fourth, fifth, and top line, the six lines are obtained in order, and this is indeed the case. However, the concept of "two principles" refers only to one change, distinguishing between odd and even. But the first line requires three changes, and the remaining number of stalks after three changes, whether old or young, is named according to nine, six, seven, or eight. Therefore, the first line should be considered as "four principles," not "two principles." Moreover, the four principles are present in each of the three lines of the trigram, yet only the middle line is regarded as the four principles, which is even more unreasonable. Thus, even when considering the method of divination with yarrow stalks, this theory has inconsistencies.

若夫畫卦之法，三才一時俱備，豈有先畫一竒一偶，其上覆為一竒一偶之理？康節以揲蓍之序為畫卦之序，又何怪乎世儒謂凡卦之畫必由蓍而後得也哉！《儀禮》注云「卦者主畫地識（音志）爻，爻備以方寫之」，方即牘也。伏羲時書契未興，其始作八卦不知畫在何處，然亦必有一物焉以載此八卦之象可知也。

As for the method of drawing the trigrams, the three elements of heaven, earth, and humanity are all present at the same time, so how could there be a method of first drawing one odd and one even, and then adding another odd and even on top of it? Shao Kangjie took the sequence of divining with yarrow stalks as the sequence of drawing the trigrams, which is why later Confucian scholars claimed that all trigram diagrams must be obtained through the process of divining with yarrow stalks. Zheng Xuan's commentary on the "Rites of Zhou" says, "A trigram is used to record the lines on the ground, and after the six lines are complete, they are copied down on a square board" (the character "识" is read as "zhì", meaning "to record"). Here, the term "方" refers to a wooden tablet. In the time of Fuxi, written characters and records had not yet emerged, so we do not know exactly where Fuxi originally drew the eight trigrams. However, it is certain that there must have been some medium used to carry the imagery of the trigrams.

信如康節所圖，則初畫最長，巾畫半之，終畫又半之。吾不知伏羲既作此象，將截為八段以示人乎？將連者仍連而聴人之自為識別乎？抑亦殫其智力以為之初，如今人之起藁，繼乃更定，劃然分列為八乎？揆諸事情，決無是理。鯤溟之辯良足解頤。吾不知季通何以極贊其妙，而朱子舍己從之也。

If it is indeed as Shao Kangjie depicted, then the lowest line is the longest, the middle line is only half of it, and the top line is only half of the middle line. I really do not know: since Fuxi created such a diagram, was it intended to be divided into eight parts for people to see? Or was it meant to keep the connected lines as they are, leaving it to others to distinguish on their own? Or perhaps he first used his full intellect to draw a rough draft, like modern people do when sketching, and then revised it later, making the Eight Trigrams clearly separated? By common sense, there is no such thing. Huang Kunming's argument is truly amusing. I do not understand why Cai Jitong praised this method so highly, while Zhu Xi abandoned his own view and followed it instead.

林黃中栗與朱子論《易》，以一卦之全體為太極，內外為兩儀，內外及互體為四象，又顛倒取為八卦。朱子曰：「如此則不是生，卻是包也。」林曰：「惟其包之，所以生之。」朱子曰：「包如母之懷子，子在母中；生如母之產子，子在母外。」此特據康節之圖以為言耳。

Lin Li (style name Huangzhong) discussed the Book of Changes with Zhu Xi, advocating that the whole hexagram should be considered as the Taiji, the inner and outer trigrams as the two principles, and the inner trigram, outer trigram, and mutual trigrams together as the four images. He also suggested taking the hexagram in reverse order to form the eight trigrams. Zhu Xi said, "If it is explained this way, it is not 'birth' but 'containment.'" Lin Li replied, "Exactly because it contains, it can give birth." Zhu Xi said, "Containment is like a mother carrying a fetus, where the child is within the mother's body; birth is like a mother giving birth, where the child is outside the mother's body." In fact, Zhu Xi's remarks were based solely on Shao Kangjie's diagram.

若希夷太極圖作白黒回互之狀，函兩儀、四象、八卦，皆子在母中。譬諸歲時，一歲本一氣耳，析之而為寒暑則二氣矣，又析之而為春夏秋冬則四氣矣，又析之而為分至啟閉則八節矣，皆一分為二、子在母中者也。

If we talk about Chen Tuan's Taiji diagram, which is drawn in a black and white interlocking pattern, containing the Two Principles, the Four Symbols, and the Eight Trigrams, all of these belong to the situation of "a child within the mother's body." Taking the twelve months of the year as an analogy: originally, a year is just one kind of energy. When it is divided, it becomes the cold and hot energies; further divided, it becomes the four seasons: spring, summer, autumn, and winter; and further divided, it becomes the eight solar terms: spring equinox and autumn equinox, summer solstice and winter solstice, and the beginning of spring, summer, autumn, and winter. All of these are cases of division into two, which belong to the situation of "a child within the mother's body."

至康節變為橫圖，則兩儀、四象、八卦皆子在母外：初畫為儀，中畫為象，終畫為卦，而太極一畫更居其先，是猶一歲之外別有寒暑，寒暑之外別有四時，四時之外別有八節也，其謬不已甚乎？雖名為先天，而實失希夷之意矣。

When Shao Kangjie changed it into a horizontal diagram, then the two principles, four images, and eight trigrams all became "a child outside the mother's body": the lowest line represents the two principles, the middle line represents the four images, and the top line represents the eight trigrams, while the single line representing the Taiji is placed before them. This is like saying there is another cold and heat beyond a year, another four seasons beyond cold and heat, and another eight solar terms beyond the four seasons; how absurd is that! Although it carries the name "Earlier Heaven," it has actually lost the original meaning intended by Chen Tuan.

《仲氏易》曰：「趙宋専襲陳摶先天圖，謂老陽、少陽、老陰、少陰為四象，而世共遵之。考陰陽老少仍是揲蓍所用，與畫卦不同。惟卦有動靜，爻有貞變，老動少靜，老變少不變，故立此數。」

Ma Qiying's "Zhong Shi Yi" says: The Song dynasty specifically inherited Chen Tuan's Earlier Heaven diagram, treating old yang, young yang, old yin, and young yin as the four trigrams. Everyone followed this tradition. However, upon examination, the terms old and young yin and yang were originally names used in the process of divining with yarrow stalks, and were separate from the act of drawing the hexagrams. It was only because the hexagrams have movement and stillness, and the lines have unchanging and changing ones, that old yang and old yin were considered active, while young yang and young yin were considered still. Old ones are meant to change, while young ones remain unchanged, hence these numbers were established.

「今繪圖者先以兩儀為一重，則自兩畫始，非一畫也；若又加一虛中夾畫於兩儀之前以為太極，則又別一畫，非卦畫也。乃以兩陰兩陽作四象而以為二重。夫老之與少並從已成之卦所推，故乾為老陽，非老陽而後乾也。當庖羲作乾畫時，雖有二畫，然尚未知所成為何等，而乃先曰此當為純陽之卦、此畫為老陽，有是理乎？此說之必不可通者也。」

Nowadays, those who draw diagrams first consider the two principles as one layer, starting from two lines rather than one; if they add another intermediate broken line before the two principles to represent the Taiji, that would form another line, but that is not a trigram. Then they take two yin and two yang as the four images, considering them as the second layer. One must know that the distinction between old and young is derived from the already formed trigrams, so it is only after the Qian trigram is formed that it is called old yang, not that old yang exists first and then the Qian trigram comes into being. When Fuxi was drawing the Qian trigram and reached the second line, although there were already two lines, he still did not know what trigram it would eventually become. How could he possibly say in advance, "This will become a pure yang trigram" or "This line belongs to old yang"? This is a fundamental flaw in this theory.

「乃作三重畫而並以乾、兌、離、震、巽、坎、艮、坤一齊出之為八卦，是一畫之後不必成乾，已先作兌離諸卦之畫；及成乾之後，又不必繼坤，而反以六子之卦成之坤前。將夫子《大傳》所云『成象乎乾，效法乎坤』，與『乾坤成列』『因而重之』『一索再索』『得男得女』諸語顯然抵梧（去聲），是敢於悖聖，而以此解經，真鹵莽之甚者也。」

So he then drew the third layer, arranging Qian, Dui, Li, Zhen, Xun, Kan, Gen, and Kun all together as the Eight Trigrams. In this way, after completing the first line, one did not necessarily have to start with the Qian trigram first; instead, the Dui, Li, and others were drawn first. Moreover, after the Qian trigram was formed, one did not immediately proceed to the Kun trigram, but instead placed the six subsidiary trigrams before the Kun trigram. This directly contradicts what Confucius said in the Great Treatise, such as "forming the image is called Qian, following the pattern is called Kun," and phrases like "Qian and Kun are arranged in order," "thereby doubling them," "one inquiry, then another," and "receiving a male or female." ("Contradict" is written as "抵梧," where "梧" is pronounced in the falling tone.) This is daringly opposing the sage, yet using it to explain the classics, which is extremely crude and reckless.

按：卦，象也；蓍，數也。《左傳》韓簡曰：「物生而後有象，象而後有滋，滋而後有數。」蓋數即象之分限節度處，生於象而不可以生象。康節加一倍法欲以數生卦，非也。四象唯揲蓍三變成爻後有之，乾坤男女即是八卦，不得稱四象，専屬第二畫尤無理，說見上文。

Hu Wei said: The trigrams belong to the category of "xiang" (image), while the yarrow stalks belong to the category of "shu" (number). In the "Zuo Zhuan", Han Jian said: "Things first come into being, then there is an image; with the image, there is growth; with growth, there is number." Number is merely the boundary and measure of the image, originating from the image, and not the other way around. Shao Kangjie's method of doubling aims to generate trigrams through number, which is incorrect. The four trigrams only come into being after the yarrow stalks are divided three times to form a line; the trigrams Qian and Kun and the six subsidiary trigrams are themselves the eight trigrams, and cannot be called the four trigrams. To specifically assign the four trigrams to the second line is even more unreasonable, as explained in the previous text.

《說卦傳》曰：「雷以動之，風以散之，雨以潤之，日以晅之，艮以止之，兌以說之，乾以君之，坤以藏之。」

The Sayings on the Trigrams states: Thunder is used to move all things, wind is used to scatter all things, rain is used to nourish all things, the sun is used to dry all things, mountain is used to stop all things, lake is used to make all things joyful, heaven is used to govern all things, and earth is used to store all things.