Zhou Yi Hang Shi Xue (周易杭氏學) · Volume 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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