Book Seven of the Clear Diagrams of the Book of Changes, compiled by Hu Wei of Deqing

《繫辭傳》曰：「八卦成列，象在其中矣；因而重之，爻在其中矣。」又曰：「《易》之為書也，廣大悉備，有天道焉，有人道焉，有地道焉，兼三才而兩之，故六。六者非他也，三才之道也。」《說卦傳》曰：「昔者聖人之作《易》也，將以順性命之理。是以立天之道曰陰與陽，立地之道曰柔與剛，立人之道曰仁與義，兼三才而兩之，故《易》六畫而成卦。分陰分陽，迭用柔剛，故《易》六位而成章。」

The Great Treatise of the Zhou Changes says: "The eight trigrams are arranged in rows, and all the myriad phenomena of heaven and earth are already contained within them; when the eight trigrams are combined two by two, the six lines are already contained within them." It also says: "The Book of Changes encompasses vastness and is complete in all things: it contains the way of heaven, the way of humanity, and the way of earth. By doubling the three principles of heaven, earth, and humanity, one trigram consists of six lines. This 'six' is not anything else but the way of the three principles." The Sayings on the Trigrams says: "In ancient times, the sage created the Book of Changes to follow the principles of life and destiny, so he established the way of heaven as 'yin' and 'yang,' the way of earth as 'flexibility' and 'firmness,' and the way of humanity as 'benevolence' and 'righteousness.' By doubling the three principles, the Book of Changes is composed of six lines. By distinguishing the positions of yin and yang, and alternately using flexible and firm lines, the Book of Changes forms its textual structure through six lines."

按：夫子曰「重」、曰「兼」，明是倍三為六，非逐爻漸生之謂。《本義》猶從舊解，云「因而重之」謂各因一卦而以八卦次第加之為六十四，又云三畫已具三才，重之故六。至《圖說》則與邵義並存，而以邵為善；及蔡氏草《啟蒙》，則専主《觀物外篇》，而顯背經文亦有所不顧矣。

Hu Wei's commentary: Confucius said "repetition" and "comprehensiveness," clearly indicating that the three lines are doubled to form six lines, not that the six lines are generated layer by layer one by one. Zhu Xi's "The Original Meaning of the Zhou Changes" still followed the old interpretations, explaining "thereby repeating" as each trigram serving as the lower part, and then successively adding the eight trigrams above to form the sixty-four trigrams. He also said that the three lines already contain the three elements of heaven, earth, and humanity, and that by repeating them, they become six lines. However, in the diagram section of "The Awakening of the Study of the Changes," he presented both the old interpretations and Shao Yong's view side by side, and even considered Shao's view better. When Cai Yuanping drafted "The Awakening of the Study of the Changes," he focused mainly on Shao Yong's "Outer Chapters of Observing Things," clearly disregarding the classical texts of "The Great Treatise" and "The Explanation of the Trigrams."

《大傳》但云包犧氏始作八卦，其因而重之以為六十四者不言其人。先儒或以為神農，或以為大禹，或以為文王，總無確證。然吾觀夫子所陳十三卦制器尚象之事，唯網罟創自包犧，取諸《離》之純卦，而耒耨之利取諸《益》，日中為市取諸《噬嗑》，皆神農之所為也，則謂神農重卦者庶幾得之。蓋伏羲雖有因重之意，而八卦成列之後未嘗復加之畫；至神農則始一一演之，以為六十四卦、三百八十四爻，而重卦之名至黃帝乃備耳。子曰：「聖人立象以盡意，設卦以盡情偽。」蓋立象即八卦成列，設卦即因而重之，伏羲略而神農詳也。

The Great Treatise mentions only that Fuxi first drew the Eight Trigrams, but does not say who first overlapped them and derived the sixty-four trigrams. Previous scholars have suggested different people: some say Shennong, others say Yu the Great, and others say King Wen. There has never been conclusive evidence. However, when Confucius lists in the Great Treatise the thirteen trigrams related to "making tools and taking images as models," only the part about tying knots and making nets comes from Fuxi, taking its image from the pure trigram Li, which is composed of two identical lines. The invention of the plow and hoe, taking its image from the Yì trigram, and the establishment of markets at noon, taking its image from the Shìkè trigram, are all attributed to Shennong. Therefore, it is probably correct to say that the overlapping of trigrams originated with Shennong. Although Fuxi had the idea of "overlapping," after the Eight Trigrams were arranged, he did not add more lines. It was Shennong who developed each trigram step by step, forming the sixty-four trigrams and the 384 lines. The term "overlapping trigrams" was only fully established during the time of the Yellow Emperor. Confucius said, "The sage establishes images to express meaning, and sets trigrams to reveal human nature and falsehood." What is meant by "establishing images" is the arrangement of the Eight Trigrams, and what is meant by "setting trigrams" is overlapping them. Fuxi did it simply, while Shennong did it in detail.

若夫重卦之次序，絶無可考。《連山》首《艮》，《歸藏》首《坤》，先儒雖有是說，而其書已亡，自《艮》《坤》以後六十三卦其次序不知如何，今可言者獨文王所演之易象耳。或云烈山氏之易，文王因之，烈山氏即神農也。首《乾》《坤》，終二《濟》，兩兩反對，皆有至理，安得於此外更造一圖以為伏羲六十四卦之次序哉？智者之鑿，孟子之所惡也。

After the creation of the sixty-four hexagrams, the order in which they are arranged is completely unattainable through historical verification. The book "Lianshan" began with the hexagram "Gen," while "Guicang" began with "Kun." Although previous scholars have mentioned these arrangements, both books have long since been lost. Therefore, no one knows how the remaining sixty-three hexagrams were ordered after "Gen" and "Kun." Today, the only hexagram sequence that can be clearly explained is the one developed by King Wen. Some people claim that Liushanshi had a book of "Yi," which King Wen used. Liushanshi is said to be Shennong. King Wen's hexagram sequence starts with "Qian" and "Kun," and ends with "Ji Ji" and "Wei Ji." The sixty-four hexagrams are paired in opposition, and each pair contains profound meaning. How can one create another diagram outside of this sequence and claim it to be the original order of the sixty-four hexagrams from Fuxi? This kind of artificial and clever fabrication is exactly what Mencius despised.

《本義圖說》曰：前《八卦次序圖》即《繫辭傳》所謂「八卦成列」者，此圖即其所謂「因而重之」者也。故下三畫即前圖之八卦，上三畫則各以其序重之，而下卦因亦各衍而為八也。若逐爻漸生，則邵子所謂「八分為十六，十六分為三十二，三十二分為六十四」者，尤見法象自然之妙也。《易學啟蒙》曰：八卦之上各生一竒一偶而為四畫者十六，於經無見，邵子所謂「八分為十六」者是也，又為兩儀之上各加八卦，又為八卦之上各加兩儀也。四畫之上各生一竒一偶而為五畫者三十二，邵子所謂「分為三十二」者是也，又為四象之上各加八卦，又為八卦之上各加四象也。

In Zhu Xi's "The Original Meaning of the Zhou Changes," the diagram explanation states: the previous diagram of the "Order of the Eight Trigrams" is what the "Great Treatise" refers to as "the eight trigrams arranged in order." This diagram, however, is what it calls "thereby stacking them again." Therefore, the three lines below each trigram correspond to the eight trigrams in the previous diagram, while the three lines above each trigram are stacked in the order of the eight trigrams, thus allowing each lower trigram to generate the eight trigrams again. If we follow the gradual generation of each line, this is what Shao Yong refers to as "eight divided into sixteen, sixteen divided into thirty-two, thirty-two divided into sixty-four," which more clearly reveals the natural elegance of the generation of trigrams. "The Awakening of the Study of the Changes" says: adding one odd and one even line above each of the eight trigrams results in sixteen figures of four lines—this is not supported by the text, which is exactly what Shao Yong refers to as "eight divided into sixteen." From another perspective, this is equivalent to adding the eight trigrams to the two principles, or adding the two principles to the eight trigrams. Adding one odd and one even line to each of the four-line figures results in thirty-two figures of five lines, which is exactly what Shao Yong refers to as "divided into thirty-two." From another perspective, this is equivalent to adding the eight trigrams to the four principles, or adding the four principles to the eight trigrams.

五畫之上各生一竒一偶而為六畫者六十四，則兼三才而兩之，而八卦之乘八卦亦周，於是六十四卦之名立，而易道大成矣。《周禮》所謂「三易之別皆六十有四」，《大傳》所謂「因而重之，爻在其中矣」，邵子所謂「三十二分為六十四」者是也。若於其上各卦又各生一竒一偶，則為七畫者百二十八矣；七畫之上又各生一竒一偶，則為八畫者二百五十六矣；八畫之上又各生一竒一偶，則為九畫者五百十二矣；九畫之上又各生一竒一偶，則為十畫者千二十四矣；十畫之上又各生一竒一偶，則為十一畫者二千四十八矣；十一畫之上又各生一竒一偶，則為十二畫者四千九十六矣。

Above the five lines, each one generates one odd and one even line, resulting in six lines with a total of sixty-four hexagrams. This is what the "Sayings on the Trigrams" refers to as "combining the three elements and doubling them." The multiplication of the eight trigrams with each other covers all possibilities completely, thus establishing the names of the sixty-four hexagrams. The Way of the Book of Changes is thus fully realized. The "Rites of Zhou" states, "There are three kinds of the Book of Changes, each different, but all have sixty-four hexagrams." The "Great Treatise" says, "By doubling the trigrams, the lines are included within." Shao Yong says, "Thirty-two divided into sixty-four." All these statements refer to the same concept. The "启蒙" continues with the same method of "doubling": if each hexagram is further doubled by adding one odd and one even line above the six lines, it results in seven lines with a total of one hundred and twenty-eight; doubling again above the seven lines results in eight lines with two hundred and fifty-six; doubling again above the eight lines results in nine lines with five hundred and twelve; doubling again above the nine lines results in ten lines with one thousand and twenty-four; doubling again above the ten lines results in eleven lines with two thousand and forty-eight; doubling again above the eleven lines results in twelve lines with four thousand and ninety-six. Each time a line is added, the number doubles.

此焦贛《易林》變卦之數，蓋以六十四乘六十四也，今不復為圖於此，而略見第四篇中。若自十二畫上又各生一竒一偶，累至二十四畫，則成千六百七十七萬七千二百一十六變，以四千九十六自相乘，其數亦與此合，引而伸之，蓋未知其所終極也。雖未見其用處，然亦足以見易道之無窮矣。

This is the number of changing hexagrams in Jiao Yanshou's "Yi Lin," which is the product of sixty-four multiplied by sixty-four. Here, no separate diagram is drawn, but a general account can be found in the fourth chapter. If one continues to add one odd and one even line above the twelve lines, and keeps adding them up to twenty-four lines, it would result in sixteen million seven hundred seventy-seven thousand two hundred and sixteen changes; multiplying four thousand and nine十六 by itself also gives the same number. If this process is extended further, it is impossible to know where it would end. Although it seems to have no practical use, it sufficiently demonstrates the boundless nature of the Way of the Book of Changes.

康節先天之學，其病根全在小橫圖。蓋八卦之次序既乖，則其論方位亦誤，六十四卦之次序方位更不待言矣。而吾竊有怪於《啟蒙》之說也。數用加一倍法，可以推之百千萬億而無窮；若《易》卦則六畫而止，其變而之他亦不過六畫。

The root of the problem in Shao Yong's Earlier Heaven theory lies entirely in that small horizontal diagram of the Eight Trigrams. Since the order of the Eight Trigrams is wrong, the directions he talks about are also incorrect; the order and directions of the sixty-four Trigrams are even worse. What puzzles me most privately is a passage from his "Introduction to the Study of the Changes." Although using the "doubling method" can calculate numbers to infinity, the hexagrams in the Book of Changes only have six lines, and when one hexagram transforms into another, it still remains with six lines.

即如焦氏《易林》，每一卦變為六十四，至四千九十六，其本卦仍自為本卦，之卦別自為之卦，曷嘗屋上架屋，於六畫之上覆自七畫遞加至十二畫乎？而且云「自十二畫上又累至二十四畫，引而伸之，未知其所終極，足以見易道之無窮」也。夫易道無窮而卦畫則有窮，季通之藁荒謬至此，朱子曽不一是正，何歟？

Take Jiao Yanshou's "Yi Lin" for example. Each hexagram can transform into sixty-four hexagrams, resulting in a total of four thousand and ninety-six. However, the original hexagram remains a hexagram with six lines, and the transformed hexagram is also a hexagram with six lines. How could it be that they build upon six lines by adding seven lines up to twelve lines? The "Ming Guan" even says, "From twelve lines, they add up to twenty-four lines, and so on without end, showing that the Way of the Book of Changes is boundless." But we must know that although the Way of the Book of Changes is indeed boundless, the hexagrams themselves are limited. Cai Yuanping's (Zi Jitong) draft is so absurd, yet Zhu Xi did not correct a single word. Why is that?

《仲氏易》曰：夫兩儀四象者，生卦之序，非畫卦之序也。因而重之者，以三重三，非謂二可重一、四可重二、八可重四也。故就其成卦而觀之，則由兩而四，由四而八，由八而至六十四，未為不可；而就其畫卦而觀之則不然。夫伏羲但畫八卦耳，何曽畫六十四卦乎？《繫辭傳》曰「乾坤成列，易立其中」，則先畫乾坤；又曰「八卦成列，象在其中」，則次畫八卦；又曰「因而重之，爻在其中」，則於是不再畫也，第因其所畫而復配之為六十四卦，而易象終焉。故《周禮》經卦皆八，揚雄謂宓羲經以八卦，孔安國曰「伏羲氏之王天下也，始畫八卦」，皆以畫八卦為一截，未嘗一及重卦。

Ma Qilin's "Zhong Shi Yi" says that the concept of two principles and four images refers to the order in which trigrams were generated, not the order in which Fuxi drew the trigrams. The phrase "thereby stacking them" means using a three-line trigram to stack another three-line trigram, not that two principles can be stacked into one line, or four images can be stacked into two principles, or eight trigrams can be stacked into four images. Therefore, in terms of the generation of trigrams, it is possible to say that it proceeds from two principles to four images, from four images to eight trigrams, and from eight trigrams to the sixty-four trigrams. However, in terms of the actual order in which Fuxi drew the trigrams, it was not like that. Fuxi only drew the eight trigrams; he never drew the sixty-four trigrams. The "Xici Zhuan" says, "When Qian and Kun are arranged in order, the Book of Changes is established in the middle," indicating that Qian and Kun were drawn first. It also says, "When the eight trigrams are arranged in order, the images are contained within them," showing that the eight trigrams were drawn next. Furthermore, it says, "By stacking them, the lines are contained within them," indicating that at this point, no further drawing was done. Instead, the already drawn eight trigrams were combined with each other to form the sixty-four trigrams, and the images of the Book of Changes were thus complete. Therefore, the "Zhou Li" says that all the basic trigrams are eight, Yang Xiong says that Fuxi's fundamental trigrams were only the eight trigrams, and Kong An Guo says, "Fuxi ruled the world and began to draw the eight trigrams," all of them regard drawing the eight trigrams as a single stage, and none of them ever mention stacking trigrams.

而重卦之起，舊有歸之神農者（京房引孔子之言曰「神農重乎八純」，謂取伏羲八純卦而重之為六十四卦。《史記》亦云神農始作重卦），有歸之大禹者（《周禮》三易，一曰《連山》，即夏易，謂以重艮為連山也。晉孫盛曰「夏禹修用《連山》」，以艮之重卦為夏易首）。雖其說不可深信，然亦以見八卦與六十四卦縱成自伏羲，亦必不連次而加畫之，斷可識矣。故先天之圖其誤有八。一、畫繁（自一畫為陽，二畫為陰，三一為乾，三二為坤，而其畫已畢，未有畫至六十四卦者。今圖取巧便，但以黒為陰、白為陽耳，此非羲畫法也。若羲畫原法則黒皆兩畫，是六十四卦在陽有一百九十二畫、在陰有三百八十四畫，太不憚煩矣，此非自然因重之數也。其誤一也）。

As for the origin of the sixty-four hexagrams, old accounts attribute it to the Yellow Emperor (Shennong). Jing Fang cited Confucius' words saying, "Shennong repeated the eight pure trigrams," meaning that he combined the eight trigrams of Fuxi into hexagrams. The "Records of the Grand Historian" also states that Shennong first created the repeated trigrams. Others attribute it to the Great Yu. The "Rites of Zhou" mentions three types of the Book of Changes, the first being "Lianshan," which is the Book of Changes of the Xia dynasty. It says that "Lianshan" starts with the repeated trigram of Ken. Jin dynasty's Sun Sheng said, "Great Yu revised and used Lianshan," meaning that the repeated trigram of Ken was the first hexagram of the Xia Book of Changes. Although these accounts are not entirely reliable, they do show that even if both the eight trigrams and the sixty-four hexagrams were created by Fuxi, they could not have been drawn one after another, layer by layer. This can be definitely concluded. Therefore, the Earlier Heaven diagram has eight errors. The first is that the method is complicated. One line represents yang, two lines represent yin, three ones make Qian, three twos make Kun, and the drawing stops there, never continuing to the sixty-four hexagrams. The current diagram, for convenience, uses black to represent yin and white to represent yang, which is not the method of Fuxi. If we follow Fuxi's original method, each yin line would need to be drawn with two strokes. Then, in the sixty-four hexagrams, there would be 192 strokes for yang lines and 384 strokes for yin lines, which is too complicated. This is not the natural number that should result from "repeating" them. This is the first error.

二、四五無名（四象分四畫為太陽、少陰、少陽、太陰，今増至十六畫，又増至三十二畫，則可名十六象、三十二象乎？抑仍名四象乎？若仍名四象，則八卦又生四象矣。其誤二也）。三、三六無住法（惟只有三畫，並無四畫五畫之加，故三畫而止便可名之為八卦。如連翩加畫，則何以三畫有名，四畫五畫秖空畫更無名也？且何以見畫之當止於三、止於六也？其誤三也）。四、不因（乾坤成列畫八卦，八卦成列始作重卦，故曰「因而重之」。因者，因成列之卦也，若一連畫去，何所因乎？其誤四也）。五、父子母女並生（乾父坤母合生六子，此《繋辭》明言次第也，今八卦並生。其誤五也）。

Second, there is no name for the figures with four or five lines (the four trigrams are divided into four types of figures called Sun, Xiao Yin, Xiao Yang, and Tai Yin; now they have increased to sixteen figures and then to thirty-two figures. Can they be called "sixteen figures" or "thirty-two figures"? Or should they still be called the four trigrams? If they are still called the four trigrams, then the eight trigrams would have generated the four trigrams again. This is the second error). Third, there is no reason to stop at three or six lines (since there are only three lines, there is no level of four or five lines. Therefore, once the three lines are drawn, they can be called the eight trigrams. If one keeps adding lines layer by layer, then why do the three lines have names while the four and five lines are just empty lines without names? And on what basis can we decide to stop at three lines and not go further? This is the third error). Fourth, it does not conform to the word "because" (after the trigrams Kan and Qian are arranged, the eight trigrams are drawn; after the eight trigrams are arranged, the compound trigrams are made. Therefore, it is said "because they are repeated." The term "because" means to follow the already arranged trigrams. If one draws the lines continuously, then what is there to "because"? This is the fourth error). Fifth, the parents and children are born at the same time (Qian is the father and Kun is the mother, and together they produce six children, which is clearly stated in the Great Treatise. Now the eight trigrams are all born at the same time. This is the fifth error).

六、子先母，女先男，少先長（六子俱先坤，兌離先震，巽先坎，兌又先離，離又先巽，於一索再索之敘俱失盡矣。羲畫次第必不如是。其誤六也）。七、卦位不合（《說卦》卦位千古不蔑，今以第加之畫而環圖之，乾一右轉，巽五左旋，以乾南坤北離東坎西為象，此實本魏氏《參同契》乾坤運軸、坎離匡廓之圖而妄名先天，致邵子以「雷風相薄」「水火不相射」為證。其誤七也）。八、卦數杜撰無據（卦原無數，但以大衍之數推之，則乾西北卦正當地六相成之數，故曰乾六；坤西南卦正當天九相成之數，故曰坤九。今無故而為乾一、兌二、離三、震四之數，此何據乎？其誤八也）。具此八誤而以為伏羲畫卦次第如是，不可通矣。

Sixth, the children come before the mother, the daughter before the son, and the young before the elder (all six children trigrams are placed before the trigram of Earth, the trigrams Dui and Li are placed before Zhen, Xun before Kan, and Dui before Li, which in turn is before Xun. The order of the first, second, and third draws in the "Say on the Trigrams" is completely disrupted. The order in which Fuxi arranged the trigrams would not be like this. This is the sixth error). Seventh, the positions of the trigrams do not match the text of the classics (the positions of the eight trigrams as recorded in the "Say on the Trigrams" have been unchangeable since ancient times. Now, however, they are arranged in a circular diagram according to the order of successive additions. The trigram Qian one starts from the right and proceeds clockwise, while Xun five starts from the left and moves counterclockwise, forming a diagram in which Qian is in the south, Kun in the north, Li in the east, and Kan in the west. This is actually based on Wei Boyang's "Complementary Treatise," which uses Qian and Kun as the axis and Kan and Li as the frame, as found in alchemical diagrams. Yet it is mistakenly labeled as "Earlier Heaven." This has led Shao Yong to use the phrases "Thunder and Wind contend" and "Water and Fire do not oppose" from the "Say on the Trigrams" as evidence. This is the seventh error). Eighth, the numbers assigned to the trigrams are entirely fabricated without basis (the trigrams originally had no numbers. If we use the number of the Great Derivation, Qian is located in the northwest, which corresponds to the number of the earth's sixfold formation, thus Qian is six; Kun is located in the southwest, which corresponds to the number of the sky's ninefold formation, thus Kun is nine. Now, however, they arbitrarily assign the numbers Qian one, Dui two, Li three, Zhen four. Why is this done? This is the eighth error). With these eight errors, it is still claimed that this is the order in which Fuxi arranged the trigrams, which is not logical.

按：仲氏八誤之辯，剖析無遺，總由伏羲六十四卦次序元無可考而任意為之，所以來後人之彈射也。冠諸經首，不愈彰邵子之過乎？

Hu Wei commented: Mao Qiling's eight refutations are thorough and leave nothing out. Ultimately, it is because the order of the sixty-four hexagrams by Fuxi originally cannot be verified, yet someone made up a fabricated sequence, which led to later criticism. To place such a diagram at the very beginning of the Zhou Changes text would not only be inappropriate but also further highlight Shao Yong's mistake.

右論邵子伏羲六十四卦次序。

The above section examines the diagram of the "Fuxi Sixty-Four Trigrams Order" transmitted by Shao Yong.

《本義圖說》曰：右伏羲四圖，其說皆出於邵氏。蓋邵氏得之李之才挺之，挺之得之穆修伯長，伯長得之華山希夷先生陳摶圖南者，所謂先天之學也。此圖圓布者，乾盡牛中，坤盡子中，離盡卯中，坎盡酉中，陽生於子中，極於午中，陰生於午中，極於子中，其陽在南，其陰在北。方布者，乾始於西北，坤盡於東南，其陽在北，其陰在南。此二者陰陽對待之數。圓於外者為陽，方於中者為陰；圓者動而為天，方者靜而為地者也。

Zhu Xi's "The Original Meaning of the Zhou Changes · Diagram Explanation" says: The four diagrams of Fuxi mentioned above all originate from Shao Yong. Shao Yong learned from Li Zhici (whose courtesy name was Tengzhi), who in turn learned from Mu Xiu (whose courtesy name was Boyang), who learned from Master Chen Tuan of Huashan (whose courtesy name was Tunan). This is what is called "Earlier Heaven Learning." When this diagram is arranged in a circular form, the Qian trigram ends at the midpoint of the southern direction's midpoint (the original text's "Niu Zhong" should be "Wu Zhong"), the Kun trigram ends at the midpoint of the northern direction's midpoint, the Li trigram ends at the midpoint of the eastern direction's midpoint, and the Kan trigram ends at the midpoint of the western direction's midpoint. Yang energy originates from the midpoint of the Zi position and reaches its peak at the midpoint of the Wu position, while Yin energy originates from the midpoint of the Wu position and reaches its peak at the midpoint of the Zi position. Therefore, Yang is in the south and Yin is in the north. When arranged in a square form, the Qian trigram begins at the northwest corner, and the Kun trigram ends at the southeast corner. Yang is in the north and Yin is in the south. These two forms illustrate the mutual relationship between Yin and Yang. The circular diagram is external and belongs to Yang, while the square diagram is internal and belongs to Yin. The circle is active and represents Heaven, while the square is still and represents Earth.

邵子《觀物外篇》曰：夫易根於乾坤而生於姤復，蓋剛交柔而為復，柔交剛而為姤，自茲而無窮矣。又曰：復至乾凡百一十有二陽，姤至坤凡八十陽；姤至坤凡百一十有二陰，復至乾凡八十陰。邵氏伯溫曰：先君云，乾坤大父母也，故能生八卦；復姤小父母也，故能生六十四卦。

Shao Yong's "Outer Chapter of Observing Things" says: The Book of Changes takes Qian and Kun as its fundamental elements, from which the hexagrams of Gou and Fu arise. When a yang line enters the yin center, it forms the hexagram Fu; when a yin line enters the yang center, it forms the hexagram Gou. From this, changes are endless. He also says: From Fu to Qian, there are a total of 112 yang lines; from Gou to Kun, there are 80 yang lines. From Gou to Kun, there are a total of 112 yin lines; from Fu to Qian, there are 80 yin lines. Shao Bowen says: My father once explained that Qian and Kun are the "great parents," thus able to generate the Eight Trigrams; Fu and Gou are the "small parents," thus able to generate the 64 hexagrams.

《朱子語類》：董銖問：「先天圖有自然之象數，伏羲當初亦知其然否？」曰：「也不見得如何。但橫圖據現在底畫較自然，圓圖便是就這中間抝做兩截，恁地轉來者是竒，恁地轉去厎是偶，有些造作，不甚依他元初畫厎。」

The Shu Leiclass of Zhu Xi records: Dong Zhu asked, "The Earlier Heaven diagram contains naturally occurring images and numbers. Did Fuxi know it was like this originally?" Zhu Xi answered, "This cannot be seen clearly. The horizontal diagram arranged according to existing methods still appears natural. However, the circular diagram cuts the horizontal diagram in half down the middle, then turns one half clockwise representing odd (yang) and the other counterclockwise representing even (yin). This seems somewhat artificial and does not fully conform to the original way Fuxi drew the hexagrams."

黃氏宗炎曰：圖南本黃冠師，此圖不過仙家養生之所寓，故牽節候以配合，毫無義理。再三傳而堯夫受之，指為性天窟宅，千古不發之精蘊盡在此圖。《本義》崇而奉焉，證是羲皇心傳，置夫大易之首。以言乎數，則不逮京房、焦贛之可征；以言乎理，則逺遜輔嗣、正叔之可據。且曲為之說曰：此圖失自秦火，流於方外，自相授受，不入人間。夫《易》為卜筮之書，不在禁例，宜並其圖而不禁，豈有止許民間藏卦爻而獨不許藏圖之事？朱元晦與王子合書云：「邵氏言伏義卦位近於穿鑿附會，且當闕之。」乃《易學啟蒙》《本義》又如此其敬信，不可解也。

Huang Zongyan said: Chen Tuan originally came from a Daoist background, and this diagram was merely a symbolic representation of Daoist techniques for cultivating life. Therefore, forcing the connection between the twenty-four solar terms and the natural phenomena is completely meaningless. After passing through a couple of generations, Shao Yong (style name Yaofu) accepted it and regarded it as the dwelling place of the principles of life and death and the heavenly way, claiming that the profound and subtle secrets that no one in history had ever uncovered were all contained in this diagram. The "Original Meaning of the Zhou Changes" also praised and believed in it, claiming that it was the secret teaching passed down directly from Fuxi, and placed it at the beginning of the Zhou Changes text. However, in terms of numbers, it is not as verifiable as that of Jing Fang and Jiao Yanshou; in terms of principles, it is even far less coherent than that of Wang Bi (style name Fusi) and Cheng Yi (style name Zhengshu). Yet they still went out of their way to defend it, saying that this diagram was lost during the burning of books in the Qin dynasty, and fell into the hands of the Daoist sects, passed down secretly among them, and never entered the common people's hands. But we should know that the "Zhou Changes" is originally a book of divination, and was not among the books burned by the Qin dynasty, so the diagram should not have been banned either. How could it be that the common people were allowed to keep the hexagrams and lines, but not the diagram? Zhu Xi (style name Yuanhui) wrote in his letter to Wang Zihe: "Shao's explanation of the positions of the hexagrams of Fuxi is close to fabrication and forced interpretation; we may temporarily hold it in doubt." However, in his "Awakening of the Study of the Changes" and "Original Meaning of the Zhou Changes," he treated it with such reverence and belief, which is really confusing.

按：夫子云「八卦成列，象在其中矣；因而重之，爻在其中矣」，又云「八卦相蕩」「八卦相錯」，六十四卦皆三畫八卦之所生也。姤、復同在六十四卦中，豈能生諸卦乎？康節受學於李挺之，挺之《六十四卦相生圖》，凡五陰一陽、五陽一陰之卦皆自姤復而來，凡四陰二陽、四陽二陰之卦皆自臨遯而來，凡三陰三陽、三陽三陰之卦皆自泰否而來，此即姤復小父母之意。

Hu Wei commented: Confucius said, "When the eight trigrams are arranged in order, the images are already contained within them; by adding lines to them, the yao are also contained within them." He also said, "The eight trigrams interact with each other" and "The eight trigrams are in opposition to each other." This shows that the sixty-four hexagrams are all generated by the mutual generation of pairs of the three-line trigrams. The hexagrams of Gou and Fu are themselves among the sixty-four hexagrams; how can they then generate the other hexagrams? Shao Yong learned from Li Zhichai, who had a diagram called "The Diagram of the Generation of the Sixty-Four Hexagrams." According to this diagram, all hexagrams with five yin lines and one yang line, or five yang lines and one yin line, are generated from Fu, the hexagram of one yang line returning, and Gou, the hexagram of one yin line beginning. All hexagrams with four yin lines and two yang lines, or four yang lines and two yin lines, are generated from Lin, the hexagram of two yang lines, and Duan, the hexagram of two yin lines. All hexagrams with three yin lines and three yang lines, or three yang lines and three yin lines, are generated from Tai, the hexagram of three yang lines, and Po, the hexagram of three yin lines. This is the origin of what Shao Bowen called "Fu and Gou as the small parents."

蓋推乾坤三索之說，施之於六畫卦，故有是圖。然姤復所生止十卦，而康節舉臨遯否泰之所生悉歸之姤復，則又與挺之異。就今六十四卦觀之，逐爻變遷，義亦可通，伏羲作易之初實不爾也。其中間抝為兩截，左陽右陰，則又極其造作，而非法象自然之妙矣。

This diagram extends the idea from the "Three Searches" of the trigrams Qian and Kun in the "Shuo Gua" to the six-line hexagrams. However, according to Li Zhichai's diagram, the hexagrams generated by Guo and Fu are only ten, while Shao Yong included the hexagrams generated by Lin, Duan, Pi, and Tai under the names of Guo and Fu, which differs from Li Zhichai's approach. Considering the existing sixty-four hexagrams, it is reasonable to say they evolved line by line. But this was not the original method when Fuxi first created the Book of Changes. As for splitting the horizontal diagram into two parts, with the left side entirely yang and the right side entirely yin, this is clearly artificial and far from the "method of following nature" that is supposed to be its essence.

《擊壤集》詩曰：「耳目聰明男子身，洪鈞賦予不為貧。須探月窟方知物，未躡天根豈識人。乾遇巽時觀月窟，地逢雷處見天根。天根月窟閒來往，三十六宮都是春。」

Shao Yong's "Yichuan Jiyang Ji" contains a poem that says: "Heaven and earth have given me a body with keen hearing and sight, and their grant is not meager. Without exploring the 'Moon Cave,' one cannot understand all things; without stepping on the 'Heaven's Root,' one cannot know oneself. At the intersection of the Qian hexagram and the Xun hexagram, one can observe the Moon Cave; at the meeting of the Earth (Kun) hexagram and the Thunder (Zhen) hexagram, one can see the Heaven's Root. Moving freely between Heaven's Root and Moon Cave, every place among the thirty-six palaces is filled with spring."

石澗俞氏曰：月窟在上，天根在下，往來乎月窟天根之間者，心也。何謂三十六宮？乾一、兌二、離三、震四、巽五、坎六、艮七、坤八是也。「三十六宮都是春」，謂和氣周流乎一身也。如此則三十六宮不在紙上，而在吾身中矣。

Shi Jian Xiansheng Yu Yan said: The Moon Cave is above, and the Heaven Root is below. Those who can travel between the Moon Cave and the Heaven Root are the human heart. What is meant by 'thirty-six palaces'? It refers to Qian one, Dui two, Li three, Zhen four, Xun five, Kan six, Gen seven, Kun eight. When these eight numbers are added together, they total thirty-six. The phrase 'all thirty-six palaces are spring' means that harmonious energy circulates throughout the body. In this way, the thirty-six palaces are not confined to the diagram on paper, but are present on my own body.

黃氏《象數論》曰：康節因先天圖而創為天根月窟，即《參同契》乾坤門戸牝牡之論也。故以八卦言者，指坤震二卦之間為天根，以其為一陽所生之處也；指乾巽二卦之間為月窟，以其為一陰所生之處也。程前村直方謂天根在卯，離兌之中是也；月窟在酉，坎艮之中是也，引《爾雅》「天根，氐也」、《長楊賦》「西壓月窟」證之，然與「乾遇巽」「地逢雷」之義背矣。以六十四卦言者，朱子曰天根月窟指復姤二卦。有以十二闢卦言者，十一月為天根，五月為月窟。

Huang Zongxi's "Yixue Xiangshu Lun" says that Shao Yong created the concept of "tian gen" and "yue ku" based on the Earlier Heaven diagram. This is essentially the same as the ideas in the "Cantongqi" regarding the乾 and坤 as gateways, and the坎 and离 as male and female. Therefore, in the context of the Eight Trigrams, the relationship between the坤 and震 trigrams is called "tian gen," because it is where the first yang begins; and the relationship between the乾 and巽 trigrams is called "yue ku," because it is where the first yin begins. Cheng Zifang (who was called Qiancun) said that "tian gen" is located at the卯 position, that is, between the离 and兑 trigrams, and "yue ku" is located at the酉 position, that is, between the坎 and艮 trigrams. He also cited the "Erya" saying "tian gen is the Root Mansion" and Yang Xiong's "Changyang Fu" saying "the moon's cave is pressed westward" as evidence. However, this contradicts the meaning in Shao Yong's poem "When Qian meets Xun" and "When the earth meets Thunder." In the context of the sixty-four hexagrams, Zhu Xi believed that "tian gen" and "yue ku" refer to the hexagrams "Fu" and "Gou." There is also an interpretation based on the twelve great trigrams, taking the hexagram "Fu" in the eleventh month as "tian gen" and the hexagram "Gou" in the fifth month as "yue ku."

其三十六宮凡有六說。以八卦言者三：乾一、兌二、離三、震四、巽五、坎六、艮七、坤八之次第，積數為三十六；乾一對坤八為九，兌二對艮七為九，離三對坎六為九，震四對巽五為九，四九亦三十六；乾畫三，坤畫六，震坎艮畫各五，巽離兌畫各四，積數亦三十六。以六十四卦言者二：朱子曰卦之不易者有八（乾、坤、坎、離、頥、中孚、大過、小過），反易者二十八，合之為三十六；方虛谷回曰復起子左得一百八十日，姤起午右得一百八十日，一旬為一宮，三百六十日為三十六宮。

As for the "Thirty-six Palaces," there are six interpretations. In terms of the Eight Trigrams, there are three: first, adding the sequence of numbers assigned to the trigrams, which are Qian one, Dui two, Li three, Zhen four, Xun five, Kan six, Gen seven, and Kun eight, the total is thirty-six; second, pairing Qian one with Kun eight to make nine, Dui two with Gen seven to make nine, Li three with Kan six to make nine, and Zhen four with Xun five to make nine, four nines total thirty-six; third, Qian has three lines, Kun has six lines, Zhen, Kan, and Gen each have five lines, and Xun, Li, and Dui each have four lines, adding up to thirty-six. In terms of the sixty-four hexagrams, there are two: first, Zhu Xi said that eight hexagrams remain unchanged when reversed (Qian, Kun, Kan, Li, Yi, Zhongfú, Daguò, Xiaoguò), and twenty-eight pairs of hexagrams change when reversed, totaling thirty-six; second, Fang Hui (who took the号虚谷) said the hexagram Fu starts at the Zi position and moves left for one hundred eighty days, while Guo starts at the Wu position and moves right for one hundred eighty days, counting ten days as one palace, making three hundred sixty days equal to thirty-six palaces.

以十二闢卦言者一：鮑魯齋恂曰，自復至乾六卦，陽爻二十一、陰爻十五，合之則三十六；自姤至坤六卦，陰爻二十一、陽爻十五，合之亦三十六，陽爻陰爻總七十二，以配合言，故云三十六。按諸說雖異，其以陽生為天根、陰生為月窟無不同也。蓋康節之意，所謂天根者性也，所謂月窟者命也，性命雙修，老氏之學也（愚謂煉己是修性，進火是修命），其理為《易》所無，故其數與《易》無渉也。

With regard to the twelve trigrams of the Great Trigrams,鲍恂 (numbered as Lu Zhai) said that from the trigram 复 (Fu) to 乾 (Qian), there are six trigrams with twenty-one yang lines and fifteen yin lines, totaling thirty-six; from 姤 (Gou) to 坤 (Kun), there are six trigrams with twenty-one yin lines and fifteen yang lines, also totaling thirty-six. In total, there are seventy-two lines, yin and yang combined, hence called thirty-six, because they are calculated in pairs of yin and yang. Note: Although these statements differ, they all agree that the initial emergence of yang energy is called 天根 (heaven's root), and the initial emergence of yin energy is called 月窟 (moon's cave). This point is consistent. Shao Yong's original meaning is that 天根 refers to 性 (nature), and 月窟 refers to 命 (destiny). Cultivating both 性 and 命 is the practice of Daoist philosophy (I believe that 炼己 (refining oneself) is cultivating 性, and 进火 (advancing fire) is cultivating 命). This principle is not found in the Book of Changes, so its numbers have nothing to do with the Book of Changes.

按：天根月窟即《參同》納甲之說。天，陽也；月，陰也。以八卦言之，月三日生明於庚，納震一陽之氣，庚當乾終巽始，故曰「乾遇巽時觀月窟」；震一陽始交於甲，納乾初九之氣，甲當坤終震始，故曰「地逢雷處見天根」也。以六十四卦言之，純乾遇巽之一陰是為姤，於月為生魄，陽消陰息自此始，故謂之月窟，即乾盡午中而陰生之謂也；純坤遇震之一陽是謂復，於月為合朔，陰消陽息自此始，故謂之天根，即坤盡子中而陽生之謂也（《參同契》云「晦至朔旦，震來受符，當斯之時，天地媾其精，日月相撢持，雄陽播玄施，雌陰化黃包，混沌相交接，權輿樹根基」，邵子所謂「地逢雷處見天根」者是）。

Hu Wei commented: The concept of "tian gen" and "yue ku" is essentially the Najia stem assignment theory in the "Cantong Qi". Heaven belongs to yang, and the moon belongs to yin. In the eight trigrams, on the third day of the lunar month, the moon appears in the western position of Geng, receiving the yang energy of the Zhen trigram. Geng is exactly where the Qian trigram ends and the Xun trigram begins, so it is said "When Qian meets Xun, observe the yue ku". The Zhen trigram's initial yang energy first meets at the eastern position of Jia, receiving the initial yang energy of the first line of Qian. Jia is exactly where the Kun trigram ends and the Zhen trigram begins, so it is said "When earth meets thunder, see the tian gen". In the sixty-four trigrams, when the pure yang Qian meets the pure yin Xun, it forms the Guo trigram, which corresponds to the beginning of the moon's waxing phase, the start of yin growing and yang declining, so it is called yue ku, meaning the yang energy begins at the center of the noon position where Qian ends. When the pure yin Kun meets the pure yang Zhen, it forms the Fu trigram, which corresponds to the new moon, the start of yang growing and yin declining, so it is called tian gen, meaning the yang energy begins at the center of the midnight position where Kun ends. The "Cantong Qi" says: On the last day of the lunar month and the early morning of the first day, the Zhen trigram comes to receive the mandate, at this time, the heavens and earth meet and their vital energy combines, the sun and moon mutually attract and support each other, the yang of the male spreads out mysteriously, and the yin of the female nurtures the yellow placenta. In the chaos, they meet and exchange, thus the foundation of all things is established. Shao Yong's statement "When earth meets thunder, see the tian gen" refers exactly to this.

三十六宮，朱子之義較長。蓋人身之天根在尾閭，月窟在泥丸。修煉之法，夜子以心神注氣海，謂之生藥；子後則自尾閭進火以達於泥丸，午中則自泥丸還元以訖於尾閭。從復姤用功而諸卦皆到，上下往來，終而復始，和氣滿腔，盎然流溢，故曰「三十六宮都是春」也。邵子雖不事修煉，而其理固已洞徹，丹家秘寳和盤托出矣。

Discussing the "Thirty-six Palaces" is more coherent with Zhu Xi's explanation. The heavenly root on the human body is located at the tail闾 (the end of the spine), and the moon cave is at the mud ball (the top of the head, the brain palace). The method of cultivation is: at the moment of the midnight Zi hour, to concentrate the mind and spirit into the Qi sea, called "producing medicine"; after the Zi hour, to start a fire from the tail闾 and ascend it up to the mud ball, and at the noon Wu hour, to return from the mud ball back to its origin and descend down to the tail闾. Focusing on the hexagrams of "Reversal" and "Meeting," the sixty-four hexagrams are all covered, with movement up and down in a cycle, continuously returning to the beginning, thus harmonious energy fills the chest and abdomen, overflowing outward, so it is said "All thirty-six palaces are spring." Although Shao Yong himself did not practice cultivation, he had already thoroughly understood this principle, revealing the secret teachings of the alchemists completely.

或問：邵子既知此理，何不事修煉？曰：修煉亦是苦功，頗妨人作樂。邵子襟懷疎放，得蒙莊逍遙之趣，可以養生，可以盡年，無所待於修煉，故知而不為。其詩曰「不佞禪伯，不諛方士」，自是真實語，非因與二程遊而有所揜飾也。

Someone asked: Since Shao Yong understood this principle, why didn't he practice cultivation? The answer is: Cultivation is also a hard task, which greatly interferes with enjoying life's pleasures. Shao Yong had a broad and open mind, deeply understanding the carefree and effortless way of Zhuangzi. This in itself was sufficient for maintaining health and living out his natural lifespan, so he did not need to rely on cultivation. Therefore, he knew the truth but did not practice it. In his poetry, he said, "I do not flatter Buddhist masters, nor do I pay homage to those who practice esoteric arts," which is a straightforward statement, not something he intentionally concealed because of his interactions with Cheng Hui and Cheng Yi, his brothers.

《朱子語類》：周謨問：先天卦氣相接皆是左旋，蓋乾接以巽初姤卦，便是一陰生；坤接以震初復卦，便是一陽生。自復卦一陽生（十一月），盡震四、離三一十六卦，然後得臨卦（十二月）；又盡兌二凡八卦，然後得泰卦（正月）；又隔四卦得大壯（二月）；又隔大有一卦得夬（三月）；夬接乾（四月），乾接姤。自姤卦一陰生（五月），盡巽五、坎六一十六卦，然後得遯卦（六月）；又盡艮七凡八卦，然後得否卦（七月）；又隔四卦得觀（八月）；又隔比一卦得剝（九月）；剝接坤（十月），坤接復，周而復始，循環無端。

The Shu Leiclass records: Zhou Mo asked: In the Earlier Heaven diagram, the connection of the trigrams proceeds to the left. After the trigram Qian, it connects to the first trigram of the Xun palace, which is Guo, indicating the initial emergence of yin; after the trigram Kun, it connects to the first trigram of the Zhen palace, which is Fu, indicating the initial emergence of yang. Starting from Fu, which marks the initial emergence of yang in the eleventh month, after traversing four trigrams in the Zhen palace and three in the Li palace, totaling sixteen trigrams, we arrive at Lin in the twelfth month; then after traversing two trigrams in the Dui palace, we arrive at Tai in the first month of the year; then after four more trigrams, we arrive at Da Zhuang in the second month; then after one more trigram, Da You, we arrive at Guai in the third month; Guai connects to Qian in the fourth month, and Qian connects back to Guo. Starting from Guo, which marks the initial emergence of yin in the fifth month, after traversing five trigrams in the Xun palace and six in the Kan palace, totaling sixteen trigrams, we arrive at Dun in the sixth month; then after traversing seven trigrams in the Gen palace, we arrive at Po in the seventh month; then after four more trigrams, we arrive at Guan in the eighth month; then after one more trigram, Bi, we arrive at Po in the ninth month; Po connects to Kun in the tenth month, and Kun connects back to Fu, thus forming a cycle that continues endlessly.

卦氣左旋，而一歲十二月之卦皆得其序。但陰陽初生各歴十六卦而得一月，又歴八卦再得一月，至陰陽將極處只歴四卦為一月，又歴一卦遂一併三卦相接，其初如此之疎，其末如此之密，此陰陽盈縮當然之理歟？然此圖於復卦之下書曰「冬至子中」，於姤卦之下書曰「夏至午中」，此固無可疑者；獨於臨卦之下書曰「春分卯中」，則臨卦本為十二月之卦，而春分合在泰卦之下；於遯卦之下書曰「秋分酉中」，則遯卦本為六月之卦，而秋分合在否卦之下，是固不可曉者。答曰：伏羲易自是伏羲說話，文王易自是文王說話，固不可交互求合。所看先天卦氣盈縮子細，某亦嘗如此理會來，而未得其說。

The trigram energies rotate to the left, and the twelve months of the year each have their proper position in the trigrams. However, when yin and yang first begin to arise, each requires passing through sixteen trigrams to complete a month, then passing through the eight trigrams again to complete another month. When yin and yang are about to reach their peak, they only require passing through four trigrams to complete a month, and then passing through one trigram followed by three trigrams in succession. At the beginning, the trigrams are sparse, but at the end, they are dense. Is this not the natural way of yin and yang waxing and waning? Also, this diagram notes under the hexagram "Fu" (Return) "Winter Solstice at the midpoint of the Zi hour," and under "Gou" (Meeting) "Summer Solstice at the midpoint of the Wu hour," which is without doubt. However, it notes under "Lin" (Approaching) "Spring Equinox at the midpoint of the Mao hour"—but "Lin" is actually the hexagram of the twelfth month, and the Spring Equinox should be noted under "Tai" (Great). Similarly, it notes under "Dun" (Retreating) "Autumn Equinox at the midpoint of the You hour"—but "Dun" is the hexagram of the sixth month, and the Autumn Equinox should be noted under "Pǐ" (Obstruction). This is truly confusing. Zhu Xi replied: The "Book of Changes" of Fuxi is Fuxi's own interpretation, and the "Book of Changes" of King Wen is King Wen's own interpretation. They are fundamentally different and cannot be forced to fit together. If you look carefully at the expansion and contraction of the earlier heaven trigrams, I have also considered this, but have never been able to find a satisfactory explanation.

黃氏《象數論》曰：《易緯》有卦氣之法，京房精於其學。以坎、震、離、兌主二十四氣，其餘六十卦起自中孚。卦有六爻，爻主一日，凡主三百六十日，餘五日四分日之一。每日分為八十分，五日得四百分，四分日之一得二十分，積四百二十分，均於六十卦，六七四十二，每卦得六日七分。又於六十卦之中別置復、臨、泰、大壯、夬、乾、姤、遯、否、觀、剝、坤十二以為闢卦，每爻各主一候。自復至乾為息卦曰太陽，自姤至坤為消卦曰太陰，息卦所屬者曰少陽，消卦所屬者曰少陰。

Huang Zongxi in his "Discussion on the Imagery and Numerical Calculations of the Book of Changes" says that the "Book of Changes' Writings" contains a method called "Hexagram Qi" (卦气). Jing Fang was particularly skilled in this discipline. It uses the four cardinal hexagrams, Kan (Water), Zhen (Thunder), Li (Fire), and Dui (Lake), to govern the twenty-four solar terms. The remaining sixty hexagrams are arranged starting from Zhongfou (Middle Trust). Each hexagram has six lines, with each line governing one day, thus governing a total of three hundred and sixty days, leaving five and one fourth days remaining. A day is divided into eighty parts. Five days make four hundred parts, and one fourth of a day is twenty parts, totaling four hundred and twenty parts. These are evenly distributed among the sixty hexagrams. Six multiplied by seven gives forty-two, so each hexagram governs six days and seven parts. In addition, among the sixty hexagrams, twelve hexagrams, namely Fu (Return), Lin (Approach), Tai (Great Benefit), Da Zhuang (Great Strength), Guai (Approaching), Qian (Heaven), Gou (Meeting), Duan (Retreat), Pǒ (Obstruction), Guan (Observation), Po (Decrease), and Kun (Earth), are established as "Bi Hexagrams" (sovereign hexagrams). Each line of these hexagrams governs one "hou" (a period of five days). From Fu to Qian are the hexagrams of yang qi growth, called "Taiyang" (Great Yang); from Gou to Kun are the hexagrams of yang qi decline, called "Taiyin" (Great Yin). Those belonging to the growth hexagrams are called "Shaoyang" (Less Yang), and those belonging to the decline hexagrams are called "Shaoyin" (Less Yin).

故孔穎達《復·彖》「反復其道，七日來復」之疏，謂剝卦陽氣之盡在於九月之末，十月純坤用事，坤卦之盡則復卦陽來，坤卦有六日七分，舉成數故言七日。王昭素駁之曰：坤卦之盡復卦陽來，則十月之節終一陽便來，不得到冬至之日矣；據其節終尚去冬至十五日，則卦七日之義難用《易緯》之數。某以為昭素駁之是矣，然昭素未悉卦氣之法，不能針其錮疾也。

Therefore, Kong Yingda, in his commentary on the "Fu" hexagram's zhuangci, "Reversing its path, the yang returns after seven days," explained that the yang energy of the "Bo" hexagram ends by the end of the ninth lunar month, and in the tenth month, the pure Kun hexagram prevails. Once the Kun hexagram is completed, the "Fu" hexagram's single yang returns. Since the Kun hexagram lasts six days and seven parts, taking an integer, it is said "seven days." Wang Zhaozu refuted this, saying: if the yang of the "Fu" hexagram returns immediately after the Kun hexagram is completed, then the yang would return on the day the tenth lunar month ends, which would be before the winter solstice. According to the solar terms, there are still fifteen days until the winter solstice, showing that the idea of "seven days" for the hexagram is not applicable to the system of the "Yi Wei." I (Huang Zongxi) think Wang Zhaozu's refutation is correct, but he did not fully understand the method of hexagram energies, so his criticism did not address the core issue.

以十二闢卦言之，剝之至復所隔唯坤六爻，其一爻當一候，一候得五日五十六分分之五，六爻得三十日三十五分，非七日也。以六十卦言之，一卦六日七分，剝之至復中隔艮、既濟、噬嗑、大過、坤、未濟、蹇、頤、中孚九卦，計五十四日六十三分，非一卦也。孔氏牽合兩者，故其說不能合。《易》之「七日來復」，取卦之反易為義，反剝為復，所歴七爻，以一日為一爻，故曰「反復其道」，反覆即反覆也，與卦氣何與？即使孔氏之疏能合卦氣，則《易》之辭無乃為卦氣圖說乎？為卦氣之法者，宓戲耶？文王耶？

If calculated according to the twelve trigrams of the heavenly stem, from the trigram "Bao" to "Fu" there are only six lines of the trigram "Kun" in between. Each line corresponds to one period, and one period is five days and five parts, so six lines total thirty days and thirty-five parts, which is not seven days. If calculated according to the sixty trigrams, each trigram corresponds to six days and seven parts. From "Bao" to "Fu" there are nine trigrams in between: Gen, Ji Ji, Shi He, Da Guo, Kun, Wei Ji, Jian, Yi, Zhong Fu. The total is fifty-four days and sixty-three parts, which is more than one trigram. Kong Yingda combined the two calculation methods, so his explanation does not match. The "Yi" says "seven days to return," which refers to the meaning of reversing and turning over the trigrams: turning the trigram "Bao" upside down gives the trigram "Fu," and in between there are seven lines. Taking one line as one day, it is said "reversing its path." "Reversing" means turning over, so how is this related to the trigram qi? Even if Kong Yingda's commentary matches the trigram qi, can the trigram line statements really be explanations of the trigram qi diagram? Moreover, who established the method of trigram qi, Fuxi or King Wen?

先儒之議卦氣者，謂卦氣不起於中孚而起於復，中孚為大雪之終氣，至冬至而始盡，故繫於冬至之下，中孚之於冬至，於象於名兩無當也。然觀《太玄》之辭曰「陽氣藏於黃宮，信無不在其中」，則中孚之直冬至者，顧以其名耳。《太玄》之釋卦序，自闢卦之外，無不以其名為義也，又何獨疑於中孚乎？所謂六日七分者，六日既盡，七分便為來日之始，非必取足八十分而自為一日也。趙汝楳乃以餘算歸之一卦，於是有一卦直七日者，失其意矣。葉氏則以七分為之氣盈，六十卦餘五日二十分，若積餘以置閏者，是一卦直六日，且並京、焦之學失其傳也。

Earlier scholars discussed the concept of "gu qi" (卦气), arguing that the sequence should start from the hexagram "Fu" (复) rather than "Zhongfu" (中孚). This is because "Zhongfu" corresponds to the end of the "Daxue" (大雪) solar term, and it would not be completed until the "Dongzhi" (冬至) solar term. Therefore, it was placed under "Dongzhi," but "Zhongfu" neither matches the symbolic meaning nor the name of "Dongzhi." However, according to Yang Xiong's "Tai Xuan," which says, "Yang qi is hidden in the Yellow Palace, and sincerity is present throughout," it shows that "Zhongfu" is appropriate for "Dongzhi" because of its name. The "Tai Xuan" explains the order of hexagrams, using the names of the hexagrams to derive meaning, except for the "bi gua" (辟卦). So why should we doubt "Zhongfu" alone? The term "liu ri qi fen" (六日七分) means that six days are completed, and the remaining seven parts are considered the beginning of the next day. It does not mean that one must complete eighty parts to form a day. Zhao Ru Mei, however, assigned all the remaining parts to a single hexagram, leading to the idea that one hexagram corresponds to seven days, which deviates from the original meaning. Ye Shi, on the other hand, treated the seven parts as surplus of the solar terms, saying that the sixty hexagrams exceed five days and twenty parts, similar to accumulating surplus to perform intercalation. This led to the idea that one hexagram corresponds to six days, and thus the teachings of Jing Fang and Jiao Yanshou were also lost.

六日七分之說相傳最久，其餘卦氣皆自後起。有自乾至未濟並依《易》書本序，以一卦直一日，乾直甲子，坤直乙丑，至未濟直癸亥，乃盡六十日，六周而三百六十日；四正卦則直二分二至，坎冬至、離夏至、震春分、兌秋分，不在六十卦輪直之列者，焦氏之法也。有以乾坤坎離四卦為槖鑰，餘六十卦依序卦，一爻直一時，一月有三百六十時足其數者，又以十二闢卦每卦管領一時，魏伯陽之法也。

The idea of "six days and seven parts" has been around the longest, while other methods of卦气 are later developments. One method follows the original order of the sixty hexagrams in the Zhou Changes, assigning each hexagram to one day: Qian (Heaven) corresponds to Jiazi, Kun (Earth) to Yichou, and so on until Wei Ji (Completion) corresponds to Guihai, making exactly sixty days. Six cycles of this make up three hundred and sixty days. The four main hexagrams, Kan (Water), Zhen (Thunder), Li (Fire), and Dui (Lake), each correspond to two solstices and two equinoxes—Kan governs the winter solstice, Li the summer solstice, Zhen the spring equinox, and Dui the autumn equinox, and they do not participate in the sixty-hexagram cycle. This is Jiao Yanshou's method. Another method treats Qian, Kun, Kan, and Li as the windbox (tuo yue), with the remaining sixty hexagrams arranged according to the "Sequence of Hexagrams." Each trigram corresponds to an hour, and a month of three hundred and sixty hours fits perfectly. Then the twelve great hexagrams each govern an hour. This is Wei Boyang's method.

至宋而後有所謂先天圖者，於是邵子以六日七分之法施於其圖，黜卦起中孚之說，以復起冬至、姤起夏至，其以坎離震兌四正卦主二十四氣者，改為乾坤坎離，此圓圖之卦氣也。張理以方圖覆背置之，泰處於東北，乾處於東南，否處於西南，坤處於西北，亦以冬至起復，至泰而正月，至乾而四月；夏至起姤，至否而七月，至坤而十月，此方圖之卦氣也。張氏又以一陰一陽至六陰六陽類而並列，六陽處南，六陰處北，陽自下而升，陰自上而降，廣闢卦之法也。

The concept of the "Earlier Heaven Diagram" appeared only after the Song Dynasty. Shao Yong applied the method of six days and seven parts to this diagram, abandoning the old idea that the hexagram qi began with the hexagram Zhongfou, and instead changed it so that the hexagram Fu began at the winter solstice and the hexagram Gou began at the summer solstice. Originally, the four cardinal hexagrams Kan, Li, Zhen, and Dui were used to correspond to the twenty-four solar terms, but this was changed to the four cardinal hexagrams Qian, Kun, Kan, and Li, forming the circular diagram of hexagram qi. Zhang Li further rotated the square diagram and placed the hexagram Tai in the Northeast, the hexagram Qian in the Southeast, the hexagram Pǒ in the Southwest, and the hexagram Kun in the Northwest. Similarly, starting from the winter solstice with Fu, reaching Tai in January and Qian in April; starting from the summer solstice with Gou, reaching Pǒ in July and Kun in October, forming the square diagram of hexagram qi. Zhang Li also arranged the hexagrams in groups of one yin and one yang up to six yin and six yang, placing the six yang hexagrams to the south and the six yin hexagrams to the north. Yang qi rose from below to above, while yin qi descended from above to below, which is an extension of the method of dividing hexagrams.

邵子又以方圖乾兌離震各重之為六十四卦，共二百五十六卦，以之算大運，亦以算小運，二十四氣每氣六十四爻，積一千五百六十二爻，合乾兌離震掛一之數，謂之掛一圖，所謂皇極之學也。諸家之不同如此。蓋初無一定之理，各以意之所見為之，是故六日七分之外，有一卦直一日者，兩卦直一日者，有一爻直一日者，四爻三分強直一日者，總卦與日之大數而後分配其小數，或多或少，不顧其果否如是也。

Shao Yong then took the four palaces of Qian, Dui, Li, and Zhen in the square diagram and each of them was repeated six times to form sixty-four hexagrams, totaling two hundred and fifty-six hexagrams, which were used to calculate great destiny and small destiny. Each of the twenty-four solar terms was paired with sixty-four lines, accumulating a total of fifteen hundred and sixty-two lines, exactly matching the number of "one hexagram" in the four palaces of Qian, Dui, Li, and Zhen, known as the "One Hexagram Diagram." This is referred to as the study of the "Huang Ji Jing Shi." The differences among various schools are like this. Originally, there is no fixed and unchanging principle; each person arranges according to their own opinion, so besides the six days and seven parts, there are also cases where one hexagram corresponds to one day, two hexagrams correspond to one day, one line corresponds to one day, and four lines plus three parts and more correspond to one day. In general, one first determines the approximate number of hexagrams and days, then distributes the remaining small numbers, more or less, without considering whether it actually corresponds to reality.

其卦之排比，惟《序卦》可據，《序卦》之義於時日不可強通，故漢儒別求其義於卦名，而有中孚之起。然揚雄氏所傳之卦義未免穿鑿附會，未嘗為《易》之篤論也。宋儒始一變其說，以竒偶之升降消長為言，而於經文可據之方位一切反之。然則宋儒之畫、漢儒之義，猶二五之為十也，孰分其優劣哉？

As for how the sixty-four hexagrams are arranged, only the "Sequence of Hexagrams" can be relied upon; however, the principles in the "Sequence of Hexagrams" cannot be forced to correspond with time and days. Therefore, Han scholars sought justification from the names of the hexagrams, leading to the idea that the hexagram qi originates from Zhongfou. However, the interpretation of hexagrams passed down by Yang Xiong is overly speculative and cannot be considered an accurate explanation of the Book of Changes. Starting from the Song dynasty, scholars changed the old approach, focusing exclusively on the rise and fall of odd and even lines, yet they completely reversed the established positions of the eight trigrams as recorded in the text. In this light, the method of the Song scholars and the interpretation of the Han scholars are like two times five and five times two, both resulting in ten. Who can determine which is superior or inferior?

按：《說卦傳》有經卦之方位，而無別卦之方位。蓋文王所演六十四卦，其八卦之貞錯綜而敘，不以其卦為類，故無方位之可言。京房六日七分法，卦氣起於中孚，亦不過取卦名之義以為當直冬至，非謂中孚方位在子之半也。自魏伯陽以乾坤坎離牝牡、震艮巽兌，先天八卦之方位端倪始見，而邵子演之曰：「乾坤定上下之位，離坎列左右之門，天地之所闔闢，日月之所出入。」於是有乾南坤北、離東坎西之圖，又推之於六十四卦為大橫圖以定其次序，又規夫橫圖而圓之以為六十四卦之方位，更有方圖居其中。

Hu Wei commented: The "Sayings on the Trigrams" only discusses the orientation of the three-line primary trigrams, but does not mention the orientation of the six-line composite trigrams. The sixty-four trigrams derived by King Wen have their lower trigrams (Zhen trigrams) arranged in a crosswise and intersecting manner, not grouped according to the same eight trigrams, so there is no mention of orientation. Jing Fang's method of six days and seven parts starts the trigram qi from Zhongfu, but this is merely taking the meaning of the trigram name Zhongfu, believing it should correspond to the winter solstice, not meaning that the trigram Zhongfu is located in the position of Zi. Since Wei Boyang used Qian, Kun, Kan, and Li as male and female, and paired them with Zhen, Gen, Xun, and Dui to explain the stem assignment, the beginning of the orientation of the Earlier Heaven trigrams started to appear; Shao Yong further developed this, saying: "Qian and Kun determine the upper and lower positions, Li and Kan form the left and right gates, the heavens and earth thus open and close, the sun and moon thus rise and set." Thus, a diagram was formed with Qian in the south, Kun in the north, Li in the east, and Kan in the west, and this was extended to the sixty-four trigrams to form the Great Horizontal Diagram to determine the order, then the horizontal diagram was bent into a circle as the orientation of the sixty-four trigrams, with a square diagram placed in the center.

於是經卦既非乾坤三索之序，別卦又失文王所演之舊。雖用京、焦分卦直日之遺法，而次序方位參錯不齊，其卦氣所自起，不得不黜中孚而用復姤；坎離震兌四正卦之主二十四氣者，亦改為乾坤坎離，固其所矣。然京房分卦直日以候災異，實有其用；而邵子大圓圖則但如《參同契》以六十卦象一月升降往來之氣，非真有分卦直日之事也。故闢卦相去之疎密前後不同，而二分卯酉之中乃繋之臨遯，蓋此圖惟明丹道，不主占候，固不必一一求合於卦氣也。

This way, the three-line trigrams no longer follow the order of the six sons generated by the trigrams Qian and Kun as described in the "Shuo Gua" text, and the six-line composite trigrams lose the original appearance as presented by King Wen. Although the method of assigning trigrams to days, inherited from Jing Fang and Jiao Yanshou, is still used, the sequence and positions are disordered, so the starting point of the trigram qi must be abandoned from Zhongfou and changed to Fu and Gu. Originally, the twenty-four solar terms were governed by the four main trigrams Kan, Li, Zhen, and Dui, but now they are replaced by Qian, Kun, Kan, and Li. This is naturally inevitable. However, Jing Fang's method of assigning trigrams to days was used for predicting disasters and anomalies, and indeed had practical use. Shao Yong's great circle diagram, on the other hand, is similar to the "Cantongqi" text, using the sixty trigrams to symbolize the rising and falling of yin and yang qi throughout the month, and did not actually intend to assign trigrams to days. Therefore, the spacing and order between the trigrams on the diagram are inconsistent, and the positions of Mao and You, corresponding to the spring and autumn equinoxes, are instead associated with the trigrams Lin and Dun. This shows that this diagram was intended to explain the Dao of alchemy and not for divination, and thus it was not necessary to align it with the trigram qi in every detail.

其極數知來之學全在加一倍法，與此圖無涉。至於方圖，則內外疉作四層，意在明十六卦兩隅尖射之巧妙，難用分卦直日法，而張仲純亦仿圓圖之例，起復姤，終乾坤，以定十二闢之卦氣，其舛謬不更甚乎？

As for Shao Yong's system of divination which aims to exhaust all numbers and predict the future, it entirely depends on the "Doubling Method," and has nothing to do with this circular diagram. As for the square diagram, it is composed of four layers overlapping from the inside out, intended to show the ingenious way in which the sixteen hexagrams shoot out from two opposite corners, and it is inherently difficult to apply the method of assigning daily values to hexagrams. Moreover, Zhang Li (style name Zhongchun) also followed the precedent of the circular diagram, arranging the twelve great hexagrams from the hexagram of "Returning" (Fu) and "Meeting" (Gou) to the hexagram of "Heaven" (Qian) and "Earth" (Kun), but this is not only incorrect but even more so than before.

「冬至子之半，天心無改移。一陽初動處，萬物未生時。玄酒味方淡，太音聲正希。此言如不信，更請問庖犧。」又曰：「何者謂之機？天根理極微。今年初盡處，明日起頭時。此際易得意，其間難下辭。人能知此義，何事不能知？」

Shao Yong wrote a poem saying: "At the midpoint of the Zi hour on the winter solstice, the heart of heaven and earth remains unchanged. This is the beginning of the first yang, and also the time when all things have not yet begun to sprout. It is like the taste of the dark wine, which is very mild, and like the sound of the highest music, which is almost imperceptible. If you do not believe this, then go and ask Fuxi again." In another poem he said: "What is called 'the mechanism'? It is the principle of the beginning of heaven, extremely subtle. It is at the moment when this year is about to end, and the next day is about to begin. This is the easiest to understand intuitively, yet the hardest to explain in words. If a person can understand this, then what else could he not understand?"

石澗俞氏曰：朱紫陽云「子之半是未成子，方離於亥之時」，又云「一陽初動處，在貞元之間」。愚謂此處正是造化之真機。程伊川云「若非竊造化之機，安能長生」，至哉言乎！

Master Shi Jian, Yu Yan said: Zhu Xi, who was known as Ziyang, explained "the half of Zi" as the moment when Zi had not yet fully formed and was just leaving the hour of Hai. He also spoke of "the beginning of the first yang" as occurring precisely at the junction between the last part of the old year and the beginning of the new year. I believe this is exactly where the true secret of nature lies. Cheng Yi, known as Master Yichuan, said, "If one is not stealing the key to the workings of nature, how could one attain longevity?" These words are truly profound!

《大易吟》曰：「天地定位，否泰反類；山澤通氣，損咸見義；風雷相薄，恆益起意；水火相射，既濟未濟。四象相交，成十六事；八卦相蕩，為六十四。」

Shao Yong's "Da Yi Yin" says: "Heaven and Earth are positioned above and below, and the hexagrams of 'Po' and 'Tai' are exactly opposite; mountains and marshes communicate their energies, and the hexagrams of 'Sun' and 'Xian' reveal this meaning; wind and thunder interact with each other, and the hexagrams of 'Heng' and 'Yi' elaborate on this idea; water and fire mutually shoot at each other, which is represented by the hexagrams of 'Ji Ji' and 'Wei Ji'. Four hexagram images interacting in pairs form sixteen matters; the eight trigrams interacting with each other become the sixty-four hexagrams."

《朱子語類》曰：此是說方圖中兩交股底。且如西北角乾、東南角坤，是天地定位，便對東北角泰、西南角否；次乾是兌，次坤是艮，便對次否之咸、次泰之損，後四卦亦如是，共十六卦。又曰：方圖自西北之東南，便是自乾以之坤；自東北之西南，便是由泰以之否。其間有咸恆損益、既濟未濟，所以又於此八卦見義，蓋為是自兩角尖射上與乾坤相對，不知怎生恁地巧。

Master Zhu Xi says: This refers to the situation where the two diagonals cross in the square diagram. For example, the northwest corner is the Trigram Qian (Heaven) and the southeast corner is the Trigram Kun (Earth), which represents 'Heaven and Earth are positioned.' This directly faces the northeast corner's Trigram Tai and the southwest corner's Trigram Po. Adjacent to Qian are the Dui trigrams, and adjacent to Kun are the Gen trigrams, which in turn face the trigrams adjacent to Po, namely Xian, and those adjacent to Tai, namely Shen. The following four trigrams are also arranged in this way, making a total of sixteen trigrams. He also says: The line from northwest to southeast in the square diagram is from Qian to Kun; the line from northeast to southwest is from Tai to Po. In between are Xian, Heng, Shen, Yi, Ji Ji, and Wei Ji, so the 'Great Yijing' also reveals meaning through these eight trigrams. It is probably because this is shot directly from the two corners, facing Qian and Kun, and it is truly amazing how this coincides.

天台董氏楷曰：愚因邵子《大易吟》，欲以方圖分作四層看。其第一層四隅乾坤否泰四卦，所謂「天地定位，否泰反類」也，然以周圍二十八卦橫直觀之，皆乾一坤八之卦，此見天地定位之不可易也。其第二層四隅兌艮咸損四卦，所謂「山澤通氣，損咸見義」也，然以周圍二十卦橫直觀之，亦皆兌二艮七之卦，此見山澤通氣之象也。

Heavenly Master Dong Kai of TianTai said: I read Shao Yong's "Great Yi Odes" and wanted to divide the diagram into four layers. The four corners of the outermost layer are the trigrams Qian, Kun, Po, and Tai, which is exactly what is said as "Heaven and Earth are positioned, Po and Tai are opposites"; and looking at the twenty-eight trigrams around this layer horizontally and vertically, they are all the trigrams from the first palace of Qian and the eighth palace of Kun, thus showing that the positioning of Heaven and Earth cannot be changed. The four corners of the second layer are the trigrams Dui, Gen, Xian, and Shen, which is exactly what is said as "Mountains and marshes communicate, the trigrams Xian and Shen illustrate this meaning"; and looking at the twenty trigrams around this layer horizontally and vertically, they are all the trigrams from the second palace of Dui and the seventh palace of Gen, thus showing the image of mountains and marshes communicating.

其第三層四隅為坎離既濟未濟四卦，所謂「水火相射，既濟未濟」是也，然以周圍十二卦橫直觀之，亦皆離三坎六之卦，此足以見水火不相射之象也。其最裡一層為震巽恆益四卦，所謂「雷風相薄，恆益起意」，其象亦可見矣。以此言之，邵子之詩曉然，足以見先天法象自然之妙。

The four corners of the third layer are the trigrams Kan, Li, Ji Ji, and Wei Ji, which are precisely referred to as "water and fire opposing each other, Ji Ji and Wei Ji"; when looking at the twelve trigrams surrounding this layer both horizontally and vertically, they are all trigrams from the three trigrams of Li and the six trigrams of Kan. This clearly demonstrates the image of water and fire not opposing each other. The innermost layer consists of the trigrams Zhen, Xun, Heng, and Yi, which are exactly called "thunder and wind colliding, Heng and Yi arising from intention," and their trigram images can also be seen. Thus, Shao Yong's poem is clear in meaning, sufficiently revealing the natural subtlety of the Earlier Heaven trigram arrangements.

按：方圖自西北至東南兩隅尖射為八純，自西南至東北兩隅尖射為否泰等卦，是為十六事。然後於四正各布十二卦，共四十八，合前十六為六十四，而八卦相錯徧焉。此亦邵子之巧推排，《易》無此卦位也。

Hu Wei remarked: The diagram shows eight pure trigrams radiating from the diagonal line running from northwest to southeast, namely Qian, Dui, Li, Zhen, Xun, Kan, Gen, and Kun. On the other diagonal from southwest to northeast, the trigrams such as 'Pu' and 'Tai' are arranged. Together they make up the 'sixteen trigrams'. Then, on each of the four cardinal directions, twelve trigrams are arranged, totaling forty-eight. Adding the sixteen trigrams mentioned earlier gives a total of sixty-four, thus covering all eight trigrams comprehensively. This is another clever arrangement by Shao Yong. The 'Book of Changes' originally did not have such positions for the trigrams.

《觀物外篇》曰：先天學，心法也，故圖皆從中起，萬化萬事生於心也（胡玉齋云：此明圖之所謂太極）。又曰：圖雖無文，吾終日言而未嘗離乎是，蓋天地萬物之理盡在其中矣。

Shao Yong's "Guānwù Wài Piān" says: The study of the Earlier Heaven is a system of "mental practice," so all the diagrams start from the center. All changes and transformations, all things and phenomena in the world arise from the mind. (Hu Yigui, who called himself Yu Zhai, said: Here the term "zhong" refers to the Taiji in the diagram.) It also says: Although there are no characters on the diagram, I have been talking about it all day long without ever leaving it, because the principles of heaven and earth and all things are contained within it.

前村程氏直方曰：邵子云「先天圖心法也，圖皆從中起」，曰「皆」者其故何也？兼方圓圖而言也。「天地定位」，圓圖之從中起也；「雷以動之，風以散之」，方圖之從中起也，皆五與十所寄之位也。故圓圖左旋起於六十四之坤，右轉起於一之乾，是中起於天地之定位也；方圖西北與東南之交也起於震巽，東北與西南之交也起於恆益，南北相直也則起於恆震巽益，東西相直也則起於震益恆巽，是中起於雷風之動散也。由此而論，圓者動，以定位為本；方者靜，以動散為用。故動而無動，靜而無靜，固先天之心法歟！是不可不皆求之圖也。

Master Cheng Zhifang of the Qiancun School said: Shao Yong said, "The Earlier Heaven Diagram is the heart method, and the diagram starts from the center." Why did he use the word "all" (都)? Because it refers to both the square diagram and the circular diagram. The sentence "Heaven and Earth are positioned" in the "Say on the Hexagrams" refers to the circular diagram starting from the center. The two sentences "Thunder moves it, Wind disperses it" refer to the square diagram starting from the center. These are all based on the central position of the number five and ten in the Yellow River Chart. Therefore, the circular diagram turns left, starting from the hexagram Kūn (Earth), which is the 64th; it turns right, starting from the hexagram Qián (Heaven), which is the first. This is starting from the center of the positioning of Heaven and Earth. For the square diagram, the intersection of the northwest and southeast corners starts from the two trigrams Zhen (Thunder) and Xun (Wind); the intersection of the northeast and southwest corners starts from the hexagrams Héng (Permanence) and Yì (Benefit). When looking along the north-south line, it starts from Héng, Zhen, Xun, and Yì; when looking along the east-west line, it starts from Zhen, Yì, Héng, and Xun. This is starting from the center of the movement and dispersion of Thunder and Wind. Thus, the circular diagram belongs to motion, with positioning as its foundation; the square diagram belongs to stillness, with movement and dispersion as its function. In motion there is no further motion, and in stillness there is no further stillness. This is probably the heart method of the Earlier Heaven. Therefore, both diagrams must not be neglected in seeking this meaning.

雙湖胡氏一桂曰：案程氏此論甚的。愚因推之：「天地定位」，起南北子午之中；「山澤通氣」，次西北東南之卦；「雷風相薄」，次東北西南之卦；「水火不相射」，又次東西之卦，圓圖自南北之中起也。「雷以動之，風以散之」，正居方圖中心；「雨以潤之，日以晅之」，則坎次巽、離次震；「艮以止之，兌以說之」，則艮次坎、兌次離；「乾以君之，坤以藏之」，則乾次兌、坤次艮，實由中而達乎西北東南，方圖亦自中起也。

Shuhu Xiansheng Hu Yigui said: Cheng Zhifang's remarks are very appropriate. I therefore proceeded to deduce further: The "Say on the Trigrams" states "Heaven and Earth are positioned," which begins from the central points of the north-south axis; "Mountains and marshes communicate with each other," which follows with the trigrams in the northwest and southeast corners; "Thunder and wind contend with each other," which comes next with the trigrams in the northeast and southwest corners; "Water and fire do not oppose each other," which follows with the trigrams in the due east and due west directions. This shows that the circular diagram originates from the center of the north-south axis. "Thunder moves it, wind disperses it," with Zhen and Xun located at the center of the square diagram; "Rain moistens it, sun brightens it," so Kan is adjacent to Xun, and Li is adjacent to Zhen; "Mountain stops it, Lake delights it," so Gen is adjacent to Kan, and Dui is adjacent to Li; "Heaven rules it, Earth conceals it," so Qian is adjacent to Dui, and Kun is adjacent to Gen. Thus, the path proceeds from the center to the northwest and southeast corners. This shows that the square diagram also originates from the center.

鄱陽董氏真卿曰：愚按畫卦之始，不過太極生兩儀，每一生二，以至於六十四卦，此說固不待贅矣。若夫邵子方圓圖，則又不過以六畫大橫圖中分，移右邊陽儀上生三十二卦自上而下居左，左邊陰儀上生三十二卦自上而下居右，規而圓之以象天而周其外，則自然有節氣之流行，而乾坤陰陽之極與復姤陰陽之始適居上下之中，而有以合乎「天地定位」之章。

A man from Poyang named Dong Zhenqing said: I think the beginning of drawing the hexagrams is simply the Taiji producing the two principles, and each principle producing two, continuing in this way until reaching the sixty-four hexagrams. This idea does not need to be explained further. As for Shao Yong's square diagram and circular diagram, they are merely taking the large horizontal hexagram diagram of six lines and cutting it in the middle. The thirty-two hexagrams generated by the yang principle on the right side are moved downward to the left, and the thirty-two hexagrams generated by the yin principle on the left side are moved downward to the right. Then they are bent into a circle to symbolize heaven, surrounding the outer circle. In this way, the movement of the twenty-four solar terms naturally appears. The hexagrams Qian and Kun, which represent the extreme of yin and yang, and Fu and Guo, which represent the beginning of yin and yang, are exactly placed in the middle of the top and bottom ends. This corresponds with the passage in "Shuo Gua" that says "Heaven and Earth are positioned."

又以六畫大橫圖從三畫乾至坤各上生八卦者，自右而左分割作八段，自下重起，矩而方之以象地，而居圓圖之內，以取地囿天中之象。而由中及外，自然有雷風雨日、山澤天地對待之象，且縱橫斜正，以三畫六畫卦數之，莫不有以合乎「雷動風散」之章。而十二闢卦皆左旋於圓圖之間，右轉於方圖之外，雖疎密之不均，莫不有自然之妙焉。以此觀之，邵子「皆從中起」之說，蓋指圓圖方圖而言，新安程氏最為得之。邵子只據已成之橫圖，或規而圓，或矩而方，以見卦畫之用耳，又何論乎卦畫之所由生哉？固不以橫圖畫卦之始例論也。

He then divided the part of the six-line large horizontal diagram from the three-line Qian to the three-line Kun, each generating the eight trigrams, into eight sections from right to left, and rearranged them starting from the bottom. He arranged them into a square with a measuring tool to symbolize the earth, placing it inside the circular diagram, representing the image of "the earth being embraced by the heaven in the center." Thus, looking outward from the center, there naturally appeared the images of thunder, wind, rain, sun, and mountain, marsh, heaven, and earth, each pair opposing each other. Moreover, whether looking vertically, horizontally, diagonally, or straight, counting according to the three-line trigrams and six-line hexagrams, everything aligned with the passage in "Shuo Gu" that says, "Thunder moves it, wind disperses it." The twelve trigrams of the twelve divisions are arranged in a counterclockwise direction within the circular diagram and in a clockwise direction outside the square diagram. Although the spacing is uneven, they all possess natural elegance. From this, we can see that Shao Yong's statement "all begin from the center" refers to both the circular and square diagrams. Cheng Zhi Fang's understanding is most accurate. Shao Yong merely used the already drawn horizontal diagram, either bent into a circle or arranged into a square, to demonstrate the function of the trigrams. He did not discuss how the trigrams were generated. It was never appropriate to use the principles of the initial drawing of the horizontal diagram to universally interpret it.

《觀物外篇》曰：圓數有一（一為心），方數有二（或以一為心，或以四為心），竒耦之義也。六即一也，十二即二也（兩其六為十二，以六視十二，猶之乎一與二也）。天圓而地方，圓之數起一而積六（眾圓簇聚，一外得六），方之數起一而積八（眾方簇聚，一外得八），變之則起四而積十二也（以四為心，四外得十二）。六者常以六變，八者常以八變，十二者亦以八變，自然之道也。八者天地之體也，六者天之用，十二者地之用也。天變方為圓而常存其一，地分一為四而常執其方；天變其體而不變其用也，地變其用而不變其體也。六者並其一而為七，十二者並其四而為十六也。

Shao Yong's "Outer Chapters of Observing Things" says: The number of a circle has only one center (this "one" is the center), while the number of a square has two methods of calculation (some take one as the center, others take four as the center). This is the distinction between odd and even. Six is equivalent to one, and twelve is equivalent to two (two sixes make twelve; comparing six and twelve is like comparing one and two). Heaven is round and Earth is square: the number of a circle begins with one and accumulates to six (when many circles are gathered together, with one center, exactly six can be arranged around it), while the number of a square begins with one and accumulates to eight (when many squares are gathered together, with one center, exactly eight can be arranged around it). If changed, it begins with four and accumulates to twelve (taking four as the center, exactly twelve can be arranged around it). Six always changes by six, eight always changes by eight, and twelve changes by eight. This is the natural principle. Eight is the essence of Heaven and Earth, six is the function of Heaven, and twelve is the function of Earth. Heaven transforms the square into a circle while always preserving the "one," and Earth divides one into four while always maintaining the square. Heaven changes its essence but does not change its function, and Earth changes its function but does not change its essence. Adding the center one to six makes seven, and adding the center four to twelve makes sixteen.

又曰：五十者，蓍之數也；六十者，卦數也。五者，蓍之小衍也，故五十為大衍也；八者，卦之小成，則六十四為大成也。蓍徳圓，以況天之數，故七七四十九也，五十者存一而言之也；卦徳方，以況地之數，故八八六十四也，六十者去四而言之也。蓍者用數也，卦者體數也；用以體為基，故存一也；體以用為本，故去四也。圓者本一，方者本四，故蓍存一而卦去四也。

It is also said that fifty refers to the number of the yarrow stalks, and sixty refers to the number of hexagrams. Five is the 'small development' of the yarrow stalks, so fifty is called 'great development'; eight is the 'small completion' of the hexagrams, so sixty-four is called 'great completion'. The yarrow stalks have a round nature, used to symbolize the heavenly numbers, so seventy times seven is forty-nine; saying fifty includes the one that is kept aside and not used. The hexagrams have a square nature, used to symbolize the earthly numbers, so eight times eight is sixty-four; saying sixty refers to removing the four that are not used. The yarrow stalks are the 'used' numbers, and the hexagrams are the 'substantial' numbers; the used numbers take the substantial numbers as their foundation, so one is kept aside; the substantial numbers take the used numbers as their basis, so the four are removed. Roundness is based on one, squareness is based on four, so the yarrow stalks keep one and the hexagrams remove four.

按：《書·洪範》「五皇極」傳云「極，中也」，《漢·律歴志》「太極元氣，函三為一。極，中也」，極皆訓中（不從此訓自朱子始）。邵子曰「先天學，心法也，故圖皆從中起」，又曰「心為太極」，可見極即中，中即心，從中起謂從太極起也（《觀物詩》云「天向一中分造化，人於心上起經綸」，亦即此意）。天地萬物之理有一不本於太極者乎？有一不具於人心者乎？故曰「吾終日言而未嘗離乎是」。先儒以「圖皆從中起」兼方圓圖言之，當矣，然其義猶有所未盡也。

Hu Wei's commentary: In the "Book of Documents · Hongfan," the section on "Five, the Supreme Principle" was traditionally interpreted as "the 'ji' means 'zhong' (center)." The "Book of Han · Laws and Measures Chapter" says "the Taiji original qi includes three and becomes one," also stating "the 'ji' means 'zhong'." This shows that "ji" has always been interpreted as "zhong." The use of this interpretation began from Zhu Xi. Shao Yong said, "The Earlier Heaven studies are based on the mind, so all diagrams start from the center," and also said, "the mind is the Taiji." This shows that "ji" is "zhong," and "zhong" is "xin," so "starting from the center" means starting from the Taiji. In his poem "Guanwu," he says, "Heaven differentiates creation from the single character 'zhong,' and humans unfold their governance from their own minds," which is exactly this meaning. The principles of heaven, earth, and all things, which one is not derived from the Taiji? Which one is not present in the human mind? Therefore, he said, "I have spoken all day long but have never departed from it." Previous scholars interpreted "all diagrams start from the center" to refer to both square and circular diagrams, which is correct, but the meaning is not fully explained.

蓋先天方圓之圖皆由一四之積數來也。天圓而地方，其在《易》則圓主蓍，方主卦。圓之數起一而積六，一在中，六在外也，蓍徳圓象之。六並一為七，六者常以六變，六七四十二，並初七為四十九，大衍之數五十而其一為太極不用，故曰「五十者存一而言之」，此蓍策也，與卦圖無涉。

In fact, both the square and circular diagrams of the Earlier Heaven are derived from the two numbers "one" and "four." The concept of "heaven round and earth square" applies to the Book of Changes, where the circular aspect relates to the number of stalks used in divination, and the square aspect relates to the number of lines in a hexagram. The circular numbers start from one and accumulate to six, with one at the center and six at the perimeter, symbolizing the circular nature of the stalks used in divination. Adding the central one to six gives seven, but six always remains six during the process. Multiplying six by seven gives forty-two, and adding the initial seven results in forty-nine. The number of stalks used in divination is fifty, with one representing the non-used part of the Taiji. Therefore, fifty includes the unused one. This discussion concerns the method of divination with stalks, and has nothing to do with the hexagram diagram.

方之數起一而積八，一在中，八在外也，卦徳方象之，小圓圖是也。八並一為九，中為太極，故一不用也。八者常以八變，積為八八六十四，太圓圖是也，乾坤坎離四正卦不用，故曰「六十者去四而言之」也。乾坤當南北之中，坎離當東西之中，圖從中起，中為太極，故不用而止於六十，猶小圓圖之虛其一也。

The number of the square starts from one and accumulates to eight, with one in the center and eight surrounding it. The virtue of the trigrams is square, which is symbolized in this way, hence the small circular diagram of the eight trigrams is formed. Adding the one in the center to eight gives nine, and the center is the Taiji. Therefore, that one is present but not used. The eight trigrams always change in groups of eight, accumulating to sixty-four, forming the large circular diagram of the sixty-four trigrams. Among these, the four trigrams of Qian, Kun, Kan, and Li are present but not used, so it is said that 'sixty' refers to the number after excluding these four. Qian and Kun are at the center of north and south, while Kan and Li are at the center of east and west. The diagram starts from the center, which is the Taiji, so these four trigrams are not used and only sixty are counted, just as the small circular diagram of the eight trigrams leaves the central one empty.

方之數變之則起四而積十二，四在中，十二在外也。十二者亦以八變，故四之外累加之，第一圍必十二，第二圍必二十，第三圍必二十八，併為六十四，方圖是也。圖從中起，中為太極，故震巽恆益四卦亦不用而止於六十，猶大圓圖之去其四也。卦徳本方，象地之體，而其中又有方圓之別。天變方為圓而常存其一者，謂大小圓圖也，地中之天，方中之圓也；地分一為四而常執其方者，謂方圖也，地中之地，方中之方也（邵子取渾天之象，天周地外，地在天中，故作方圓合一之圖。朱子謂圓圖中間虛者便是太極，不合方圖在中間塞卻，待挑出放外，如此恐失作者之意）。

The number of squares changes, starting from four and accumulating up to twelve, with four in the center and twelve on the outside. Twelve also changes in groups of eight, so adding layer by layer around the central four: the first layer must be twelve, the second twenty, the third twenty-eight, totaling exactly sixty-four hexagrams. This is how the figure of the sixty-four hexagrams is formed. The figure starts from the center, where the center represents the Taiji (Supreme Ultimate). Therefore, the four hexagrams at the center—Zhen (Thunder), Xun (Wind), Heng (Continuity), and Yi (Benefit)—are not counted, resulting in a total of sixty, just like the large circle diagram excludes the four cardinal hexagrams. The nature of the hexagrams belongs to the square, symbolizing the body of the earth, yet within the square there is a distinction between square and circle: "Heaven transforms the square into a circle while always preserving the one," referring to the two circular diagrams, which represent the sky within the earth and the circle within the square; "Earth divides one into four while always preserving the square," referring to the square diagram, which represents the earth within the earth and the square within the square. (Shao Yong's diagram is based on the concept of the浑天, where the sky surrounds the earth externally, and the earth is located within the sky, thus forming a diagram that combines square and circle. Zhu Xi said that the empty space in the circular diagram is the Taiji, and it should not be blocked by the square diagram in the center; instead, it should be removed and placed outside. However, this might have lost the original intention of the diagram's creator.)