Volume One: Notes on Collation

其雷風相薄者，即《怛》卦也。《怛》之《象》日：「雷風相與，巽而動。天地之道，恆久而不已也。日月得天而能久照，四時變化而能久成，聖人久於其道而天下化成：觀其所怛，而天地萬物之情可見矣。」

As for "Thunder and Wind interacting," this refers to the Hexagram of Constancy. The Commentary on the Judgment of the Hexagram of Constancy says: "Thunder and Wind interact, with Wind being yielding and Thunder causing movement. The way of Heaven and Earth is constant and unceasing. The sun and moon follow the way of Heaven and Earth and thus can shine for a long time, the four seasons change according to the way of Heaven and Earth and thus can sustain all things, and the sage follows the way for a long time and thus achieves success in governing the world. By observing its constancy, the nature of Heaven and Earth and all things can be understood."

迦求於下經之人道攸始，則《說卦》重卦其旨一毫不悖也。故愚謂重《易》斷自羲始。不然，《禮》謂三《易》其經卦皆八，其別皆六十四，其欺我哉？求《易》之道，試以是進之。

Taking the lower part of the Book of Changes, which begins with human affairs, as evidence, it is clear that what is discussed in the "Shuo Gua" does not contradict the meaning of the compound hexagrams. Therefore, I believe the creation of the compound hexagrams definitely began with Fuxi. If not, then why does the "Zhou Li" say that the simple trigrams were eight and the compound hexagrams sixty-four for the three dynasties of Xia, Shang, and Zhou? Those who seek to understand the Way of the Changes should start from this point.

《說卦》日：「昔者聖人之作《易》也，參天兩地而倚數，觀變於陰陽而立卦，發揮於剛柔而生爻。」因參稽其所以參兩者，其得於河像素問然矣。且帝出乎震一章，尤河圖之大講明也。特截自震起於春中，環周而訖於艮，寓夏正之歲更爾。

The Sayings on the Trigrams say: "Former sages composed the Book of Changes, using three to correspond to Heaven and two to correspond to Earth, thus establishing numbers. They observed the changes of yin and yang and established the trigrams, and displayed the roles of firmness and flexibility to produce the lines." Investigating the basis of their statement "three for Heaven, two for Earth," it is originally derived from the image of the River Chart. Moreover, the passage "The Emperor arises from Zhen" further elaborates on the River Chart. It merely takes a section starting from Zhen, beginning at the middle of the spring equinox, and proceeds in a circle until it reaches Gen, thus symbolizing the order of the new year in the traditional lunar calendar.

故曰：「終萬物，始萬物者，莫盛乎艮。」日：「艮，東北之卦，萬物之所成終而所成始。」意蓋謂又始於出乎震者也。此實孔子特以變通四時言也，而於通乎晝夜之道，而知則未及悉也。

Therefore, the "Shuo Gua" says: "There is nothing more profound than Gen in bringing about the completion of all things and initiating all things." It also says: "Gen is the hexagram of the Northeast, the place where all things complete their end and begin anew." This means that after completion, one must begin again from "Chu Hu Zhen." This is indeed what Confucius particularly emphasized regarding the transformation of the four seasons. As for the aspect of "understanding the way of day and night," it has not been explained in detail.

夫兩之制，並起於平地，以奉中參者，自春而秋以分，必極於夏之至者，亦晝之象也。始終之參，皆在地中者，自秋而春以分，必極於冬之至者，亦夜之象也。

The method of "two" begins from the horizon, used to honor the central "San" (Three), which moves from the spring equinox to the autumn equinox, necessarily reaching its peak at the summer solstice, which represents the image of daylight. The starting and ending "San" are both below the horizon, moving from the autumn equinox to the spring equinox, necessarily reaching its peak at the winter solstice, which represents the image of darkness.

請以日用常行變而通之，則出乎震者，人之始作於日一也。古謂震日一所以驗也。齊乎巽者，動而相與之交也。相見乎離，則交際之極也。致役乎坤，則動極徐靜也。說言乎兌，休且入也。自震至兌，此晝之體用，人所同見。

Take everyday life and understand it through practical application: "Emerging from Zhen" means people rise and work at sunrise. The ancients said Zhen represents "sunrise," which confirms this. "Harmonizing with Xun" means becoming active and interacting with others. "Meeting at Li" means socializing and engaging in affairs at their peak. "Employing K'un" means movement reaches its peak and then gradually turns to stillness. "Speaking at Dui" means resting and preparing to return home. From Zhen to Dui, this represents the body and function of the day, something everyone can observe.

至於戰乎乾，卒取終參之制。其數之九，則存兌餘之三，嚮晦入息於乾六以終也。陰陽相薄，閉塞不用之時也。然終則有始，至於勞乎坎，則夜分之氣復動，準於七日之復則同也。成言乎艮，則遠接兌餘之三，說言乎兌也。山澤通氣，感而相與，雖止於其所而時行則行，斯人事之又興始者也。

As for "fighting in Qian," this refers to using the last "San" according to its method. Its number is nine, so it retains the three remaining from Dui. When people return indoors at night to rest, it concludes with Qian's six and comes to an end. At this time, yin and yang approach each other closely, which is a time of closure and inactivity. However, if there is an end, there must be a beginning. When it reaches "exerting effort in Kan," the energy of the middle of the night begins to revive again, which is similar to the principle of the hexagram "Fu" that "after seven days, the energy returns." When it reaches "forming words in Gen," it connects far back to the three remaining from Dui, which is "speaking in Dui." The energies of mountain and marsh communicate with each other, interact, and associate. Although they temporarily stop at their respective places, once the right moment comes, they resume their movement, which is precisely the beginning of human affairs once again.

變化者，進退之象也；剛柔者，晝夜之象也。吾見自羲、文以來，河圖之一陰一陽，進退升降，往復循環，周流不息；開古迄今，遠之一歲之冬夏，邇之一日之晝夜，莫不由斯道也。

What is called change is the image of advance and retreat; what is called yin and yang is the image of day and night. I have observed that since Fuxi and King Wen, the River Chart has shown the alternation of yin and yang, the movement of advance and retreat, the rising and falling, the continuous cycle and circulation, which flows without ceasing. From ancient times until today, in the distant case of the seasons of winter and summer, and in the near case of day and night, there is nothing that does not follow this principle.

吾日用常行，不在他求，參天之道自艮始者，於是乎在其視《太玄》以七百二十九，贊之準《易》，《皇極》以元、會、運、世之旁通，各以一期之歲、月、日、時為數例，視今通其變、極其數於河圖，日可見之行也。豈不易簡而理得哉？斯非至精變而神者與？

The Way is present in our daily activities and ordinary actions, and we need not seek it elsewhere. The principle of "reaching the heavens" begins with the trigram Gen (Mountain), and this is precisely the reason. Comparing this to Yang Xiong's "Tai Xuan" which uses 729 verses to approximate the "Yi," and to Shao Yong's "Huang Ji Jing Shi" which employs the concepts of Yuan, Hui, Yun, and Shi to interconnect and use cycles of years, months, days, and hours as numerical examples, we can now observe the changes on the River Chart and exhaustively explore its numbers. This is truly a practical way that can be seen every day. Is this not both simple and easy to understand yet in harmony with reason? Is this not the most refined, the most changeable, and the most mysterious?

#1『亦類也』，此三字四庫本缺。 #2『爻』，原作『××』，據四庫本改。 #3『毫』，原作『豪』，據四庫本改。 #4『春中』，四庫本作『泰中』。 #5『他求』，四庫本作『它求』。

The first point: the three characters "亦类也" are not present in the Siku Quanshu edition. The second point: the character "爻" was originally written with two ink blots, but it is now corrected according to the Siku Quanshu edition. The third point: the character "毫" was originally written as "豪", but it is now corrected according to the Siku Quanshu edition. The fourth point: "春中" in the original text is "泰中" according to the Siku Quanshu edition. The fifth point: "他求" in the original text is "它求" according to the Siku Quanshu edition.

河之有圖，處犧則之以畫八卦，文王因之以繫卦辭，歷代寶而傳之。自見於《書》之《顧命》陳之束序者，而今乃謂其元，誰敢哉？然自《記》以思古，則云其出語之傷，今則云其不出《顧》已皆意之，而非其真見矣。秦火之後，獨見於《書傳》孔安國之雲而已。

The River Chart appeared on the Yellow River. Fuxi took inspiration from it and drew the Eight Trigrams. King Wen based his Hexagram Statements on it. Through the ages, it has been regarded as a precious treasure passed down from generation to generation. It was clearly mentioned in the Book of Documents, Gu Ming, as being displayed in the Eastern Hall. Now, however, some people even claim that such a thing never happened. Who dares to make such a statement? Yet since the Rites of Zhou reflected on ancient matters, it expressed a sorrowful sentiment about the River Chart not appearing. Modern people say it was never mentioned in Gu Ming. These are all speculations based on personal opinion, not genuine evidence. After the Qin Dynasty burned books, the idea of the River Chart was only found in one sentence from Kong An Guo's Commentary on the Book of Documents.

《漢志》雜以圖書，而徒謂其與《書》經緯表裹，《易緯》則徒又枝辭蔓引，愈違本旨，以至芒乎莫之究其有元形似之真為何如者，訖於唐五季也。

The Book of Han's Catalogue of Arts and Literature discusses the River Chart and the Lo Book together, merely stating that they are interrelated with the Book of Documents as vertical and horizontal threads; books like the Yijing Wei further complicate matters by adding speculative interpretations, further deviating from the original intent. As a result, there has been confusion, with no one able to investigate whether the River Chart actually has a form and, if so, what its true appearance is. This situation continued until the late Tang and Five Dynasties period.

及宋之初，陳傳圖南始創古推明象數，閔其賤用於陰陽家之起例，而蕪沒於《乾鑿度》大一取其數以行九宮之法，起而著為龍圖，以行於世。愚幸及其全書，觀其離合出入具於制數之說，誠若剖心而有以求羲、文之心者也，然皇有不得於羲、文之心者。

In the early Northern Song dynasty, Chen Tuan (styled Tunan) began to develop his own original ideas and clarify the principles of numbers and forms. He lamented that the River Chart had been misused by the yin-yang school as an example for divination, thereby diminishing its true value, and had also been obscured by the method described in the "Yi Wei · Qian Zao Du" that "the Great One takes its numbers to move through the nine palaces." Therefore, he wrote the "Longtu" and passed it down to later generations. I had the fortune of seeing his complete work, and observed how he discussed the coming together and separation of numbers, which indeed seemed to reflect his heartfelt pursuit of the original intentions of Fuxi and King Wen. However, there were still aspects that did not fully align with the original intentions of Fuxi and King Wen.

於本圖之外，就以五十有五之數別出一圖，自標之以為形洛書者已，是其初之失也。雖其縱橫、錯綜、分合、體用之意，皆在本圖，而五十有五之數，既離而別出，世遂舍本逐末，因疑圖書並出，雖是若非，元以究其詣極，而徒長紛紛之論。

He also drew another diagram with the number fifty-five, labeling it as the shape of the Luo Shu, which was his initial mistake. Although the meanings of vertical and horizontal, reversal and combination, division and integration, and the distinction between form and function are still present in this diagram, once the number fifty-five is separated from this diagram to form another one, people tend to abandon the original and focus on the secondary. As a result, they doubt that the He Tu and Luo Shu appeared at the same time, leading to confusion and endless disputes that are difficult to resolve, thus unnecessarily fueling continuous controversies.

至其傳及劉牧長民，因之泛出五十五圖，名以《鉤隱》，則又以增異。而時則李觀泰伯即駁其非是，然又自謂存其三圖。及見此三圖，則其首即所傳今謂河圖者，其二即所別出五十五數、漫標謂形洛書者，其三又止於八卦方位而已。是長民不揣其本，其事固非，而泰伯亦元不識此之三本之則一，而妄析以為三爾。

It came to Liu Mu (style name Changmin), who drew fifty-five pictures based on it, naming his work The Diagrams of Hidden Numbers in the Book of Changes. This led to the proliferation of strange theories. At that time, Li Gou (style name Taibo) wrote an article to refute his mistakes, but Li Gou also claimed he retained three of the diagrams. When he saw these three diagrams: the first one was said to be the so-called River Chart of today, the second was another set of fifty-five numbers, arbitrarily labeled as the shape of the Luo Book, and the third was merely the diagram of the eight trigrams' positions. This shows that Liu Mu did not investigate the fundamentals, and his action was indeed wrong. Meanwhile, Li Gou also did not understand that these three diagrams were originally one, yet he mistakenly split them into three.

自時已後，愈傳愈失，愈說愈鑿，至有因河出圖、洛出書見於《大傳》，而並致疑《大傳》非孔子所作者。不知圖本非書，書本非圖。至其甚者，以五十五數之圖，乃妄謂之河圖，而以圖南所傳之河圖反謂之洛書，顛倒迷繆，靡所底止。

From this point on, the transmission became increasingly distorted, and the interpretations became more forced. Even some people, because the phrase "the river produced the diagram and the Luo produced the book" appears in the Great Treatise, began to doubt the Great Treatise itself, claiming it was not composed by Confucius. They did not understand that diagrams are not books and books are not diagrams. Worse still, they arbitrarily called the diagram with the number fifty-five the River Diagram, and mistakenly referred to the River Chart passed down by Chen Tuan as the Luo Book, thereby reversing and confusing the two, leading to endless confusion.

殊不明河圖八卦明著五十五數，實指以天數五、地數五；而其數自天一、地二以至天五、地十，合而五十有五，有體有用，有虛有實，原始要終，而盡發於一圖，豈嘗別求合於洛書哉？洛書亦豈嘗謂五十五數哉？

They had no idea that the River Chart and the Eight Trigrams originally clearly contain the number fifty-five, which actually refers to "five heavenly numbers and five earthly numbers." These numbers, from heavenly one and earthly two up to heavenly five and earthly ten, altogether make fifty-five. Within them there is substance and function, emptiness and reality, origin and conclusion, all fully displayed in a single diagram. Why then would they need to combine it with the Lo Shu? Has the Lo Shu ever claimed to be about fifty-five?

今圖南既別元義例辭說，誤以圖之五十五數，別標一圖以為洛書，是其傳疑之始也。原其初意，蓋由漢儒襲傳《洪範》初一之五行，其二曰火，四日金。《太玄》準《易》實本之，亦以二為火，為南；四為金，為西。今河圖乃置二於西南，置四於束南，是火、金改次矣。

Now that Chen Tuan has not given any further explanations or examples, yet mistakenly took the fifty-five numbers of the River Chart and marked them in another diagram as the Lo Shu, this has become the beginning of a doubtful case. Investigating his original intention, it is probably because the Han scholars had passed down the passage from the "Huang Fan" in the Classic of Documents, which says "the first is the Five Phases," where the second is fire and the fourth is metal. Yang Xiong's "Tai Xuan" imitated the "Yi," and actually based itself on this, also taking two as fire located in the south and four as metal located in the west. However, the River Chart placed two in the southwest and four in the southeast, thus changing the order of fire and metal.

既不敢遂改河圖，乃別以其五十五數析為洛書，而以《洪範》二火次於南，四金次於西，且以七隨二，九隨四，而易置其南西焉。以故長民不識其由，至謂火、金易位也。

He did not dare to alter the He Tu directly, so he instead took out the fifty-five numbers and used them as the Luo Shu. According to the Hong Fan, he placed the two fire elements in the south and the four metal elements in the west. He also arranged the seven following the two and the nine following the four, swapping the positions of the south and the west. Because of this, Liu Mu did not understand the reason behind it and mistakenly claimed that fire and metal had exchanged their positions.

夫離之數九，居正南，為火；兌之數七，居正西，為金，乃天地自然參五以變之數，斷斷元以易之，豈容以漢儒任意比校《洪範》火、金之二、四，得而移易之乎？況《洪範》只有五行之數，今增以七、九，又以七隨二，九隨四，又何所本哉？若校以河圖之例，七附二，九附四，是七稽疑當隨二五事，九五福當隨四五紀，則成何義類也？

One must know that the number of Li is nine, it resides in the direction of Due South, and belongs to the element of fire; the number of Dui is seven, it resides in the direction of Due West, and belongs to the element of metal: this is the natural number of heaven and earth, "interwoven by five and three," which is absolutely unchangeable. How can one allow Han dynasty scholars to arbitrarily associate it with the "Five Constants" in the "Hóngfàn" where fire is assigned the number two and metal the number four, and then move them around? Moreover, the "Hóngfàn" only has the order of numbers for the five elements. Now, however, the numbers seven and nine are added, and seven is made to follow two, nine to follow four. What is the basis for this? If we check according to the pattern of the He Tu, seven is attached to two, nine to four, then the seventh category "Kexi" would follow the second category "Wushì," and the ninth category "Wufu" would follow the fourth category "Wujì." What kind of reasoning or classification is this?

二、七、四、九，徒論其數，元形象，元方位可定指，空移易之則可；離、兌之有方所，火、金之有體用，豈天地之造化，亦遂肯依附人之作為，亦為之變移乎？今圖南不謂圖書之數，校然不可相同，而欲以背理之人為比而同之，截截自分界限，是得指失肩背矣。

Two, seven, four, and nine, if considered merely as numbers, have no definite form or direction, so changing them around is not a problem. However, Li (Fire) and Dui (Lake) each have fixed directions, and fire and metal each have their own substance and function. Can the workings of heaven and earth be so accommodating as to change according to human arrangements? Now Chen Tuan refuses to acknowledge that the numbers of the River Chart and the Lake Chart are clearly different, yet he tries to force them into agreement by artificial means, and arbitrarily draws boundaries. This is like being able to take care of one finger but losing the whole shoulder.

且河圖之出，非徒謂四象、八卦之具文也，天地之體用固猶是也。離南象天，離中乃陰，陰所以降；坎北象地，坎中有陽，陽所以升。震陽在初，所以象腸木之束升；兌陰在上，故以象陰金之西降。乾、坤所以體天地，陰、陽所以用造化，而二卦乃寄於西南、西北之維，習於常見，是天地易位矣，不惟是也。

The appearance of the River Chart is not merely presenting the ready-made patterns of the Four Symbols and the Eight Trigrams. The essence and function of heaven and earth are also contained within it. The Trigram Li resides in the south and represents heaven, yet its middle line is yin, which is why yin governs descent; the Trigram Kan resides in the north and represents earth, yet its middle line is yang, which is why yang governs ascent. The Trigram Zhen has its yang line at the very bottom, thus symbolizing the rising yang wood from the east; the Trigram Dui has its yin line at the very top, thus symbolizing the descending yin metal from the west. The Trigrams Qian and Kun are originally used to represent heaven and earth, while yin and yang are originally used to govern the workings of the universe. Yet these two trigrams are placed in the southwest and northwest directions. People have become accustomed to this and do not notice, but in reality, this already signifies a reversal of heaven and earth. Moreover, the issue is not limited to this.

筮法又以震、巽為木，乾、兌為金，坤、艮為土，而坎獨為水，離獨為火，則坎、離得專水、火，而乾、坤乃不得專天、地，亦猶火、金之不可以執方求定也。坤二位於西南，乃地二生火；巽四位於束南，乃地四生金，皆陰也。而兌七位於西，離九位於南，皆陽也。是生數皆陰，必待陽數以成之也。

Divination methods also assign Zhen and Xun to wood, Qian and Dui to metal, Kun and Gen to earth, while Kan is alone assigned to water and Li alone to fire. In this way, Kan and Li can exclusively represent water and fire, whereas Qian and Kun cannot exclusively represent heaven and earth. This is similar to how fire and metal cannot rigidly be confined to a single direction for identification. Kun, with its two positions, is located in the southwest, which corresponds to 'earth two produces fire'; Xun, with its four positions, is located in the southeast, which corresponds to 'earth four produces metal'. Both of these belong to yin. Dui, with its seven positions, is located in the west, and Li, with its nine positions, is located in the south; both of these belong to yang. Thus, the generating numbers belong to yin and must await the completion by the yang numbers.

地之生數自西而南，故坤而後巽；成數自南而西，故離而後兌。觀於火既熾而灰滅，是火既變而神化；金雖銷而質存，是金既化而精猶未變也。此火、金之所以互變化者，同而不同，故一不七、四、九之數，自是參伍錯綜之變，不可以執方究其竟也。

The earth's generating numbers move from west to south, so first comes Kun and then Xun; the completed numbers move from south to west, so first comes Li and then Dui. When fire burns extremely bright and then the ashes are extinguished, this shows that fire has transformed and its subtle nature is hard to find; although metal is melted, its substance remains, showing that metal has transformed but its essential quality has not changed. This is exactly where fire and metal transform into each other. They appear similar but are actually different. Therefore, the numbers two, seven, four, and nine are originally the "three and five interwoven and complex" changes, and one cannot rigidly pursue them to a single direction.

今五十五數之圖，以一、二、三、四置於四方之內，而以六、七、八、九隨置其外者，按其方而數之則可也。不知將何以循序迴環，以運行之乎？況不知五與十者，特有數寄於四方之位而虛用之也。

Now that diagram with fifty-five numbers places one, two, three, and four within the inner circle of the four directions, and six, seven, eight, and nine following them in the outer circle. Although counting them one by one according to the directions can be done, how exactly do they proceed in sequence, circulate, and flow? Moreover, the person who created the diagram did not understand that five and ten are merely numbers placed in the positions of the four directions as placeholders, waiting to be used.

且五與十雖謂土數，五行家於土，必以分王於四方辰、戌、丑、未之位；醫家謂土為脾，以五氣之運，每運七十二日，總三百六十為期之例，特以土之七十二日，四分之各十八日於四時之附末，謂為脾之主事。醫於人至為切已，以土之日四分而試之以為常驗，亦豈嘗專以土之五總之，而特設五於四方之外，與四方分位，而別立之五以為中五哉？

The numbers five and ten are called earth numbers, but when the Five Phases school talks about earth, it always says that earth rules the four directions, namely the months of Chen, Xu, Chou, and Wei. The medical school considers earth as the spleen, and according to the system of five cycles, each cycle lasts seventy-two days, totaling three hundred and sixty days. To conform to this system, they specially divide the seventy-two days of earth into four parts, each part being eighteen days, and attach them to the end of each of the four seasons, saying that this is the time period governed by the spleen. Medicine is most relevant to the human body, yet it still divides the days of earth into four parts for verification and regards it as a standard practice. How could it specifically place the number five of earth in a separate position outside the four directions, and set up a so-called 'central five' to stand equal with the four directions?

況筮法四營而成《易》，以十有八變而成卦；每變四營，總卦之成，凡七十有二營，亦與醫說胳合。今圖乃分五離立，而特設異五於中位，指以為中，則為此中者，又將孰適於用乎？故餘以為圖南之別出五十五數，標異謂之形洛書者，是其初作已自失之矣。

Moreover, the method of divination says "four operations form the Book of Changes, and eighteen transformations form a hexagram," with each transformation involving four operations, thus forming a hexagram through seventy-two operations, which coincides with the medical tradition. Now, this diagram separates the number five and places it independently, especially setting a different five in the central position, pointing to it as the "center." So, what practical use can this so-called center have? Therefore, I believe that Chen Tuan's separation of fifty-five numbers and his distinctive naming of it as the form of the Luo Book was already incorrect from the beginning.

《書》之九疇，各疇自有成數，如一五行，二五事，猶或得以五行、五用之數；從而強推引之，至於五皇極，則已不可指實之為何物、何事，而甚則九五福而附以六極，則將計九乎？計五福而兼計六極乎？

The Nine Categories of the "Nine Categories" in the "Book of Documents · Hongfan" each have a fixed number: for example, the first category is "Five Phases," the second is "Five Affairs," and perhaps the numbers of "Five Phases" and "Five Affairs" can be loosely connected. However, by the fifth category, "Huangji," it is already impossible to clearly identify what it refers to. Worse still, after the ninth category "Wufu" (Five Blessings), there is also "Liuji" (Six Evils) attached, so the question arises: should this be counted as nine, or should it be considered as five blessings combined with six evils?

皇極謂大中，而六極者，其極又可謂中乎，皇極本非物非事，故可指之為中。今徒實以五點，而五點者，乃遂得為中乎？疇自一至九，界界然各存本有之數，不知何自而可以合於五十有五之數？強謂其合者，蓋其人之妄也心。

"The term 'Huangji' refers to the concept of 'Great Center,' but the 'ji' in 'Liuji' can also be called 'center'? The original 'Huangji' was neither a specific thing nor a specific matter, so it could be called 'center.' Now, if we just draw five points on the ground, can these five points become 'center'? The nine categories range from one to nine, clearly defined, each maintaining its original number. How can they be combined to form fifty-five? Those who insist they can be combined are merely speaking without basis."

若其後而至於以書謂圖，以圖謂書者，又妄人中之妄人也。此餘特謂圖則有數可通，而書則有疇類可數，而不可布之以為圖也。

Later, some people even claimed that the Luo Shu was the He Tu and the He Tu was the Luo Shu, which is the talk of the most foolish. Therefore, I specifically want to point out: the He Tu can be understood through numbers, while the Luo Shu can only be counted through its categories and cannot be arranged into a single diagram.

凡餘所以專守河圖者，非敢自謂親見羲、文所以本之而作《易》者，而其五且十之數，橫、斜、旁、正相生相成之進、退、贏、縮，一陰一陽之奇、耦、分、合，八體二用之虛、實、變、通，殆有造化神明莫窮之蕙，非人之所能為；而殆乎天機之自然者，宜其為羲、文所以作《易》之本原也。

I devote myself exclusively to the River Chart not because I dare to claim to have personally seen the original object upon which Fuxi and King Wen based the Book of Changes, but because its numbers five and ten, arranged horizontally, diagonally, sideways, and straight, mutually generate and complement each other, advancing and retreating, expanding and contracting. They embody yin and yang, with odd and even numbers, division and union. The Eight Trigrams form the body, while the numbers nine and six serve as the function, with emptiness and reality, change and communication. It almost contains infinite and boundless meanings of creation and divine wisdom, not something human could fabricate, but close to the natural workings of heaven. It should be the original source from which Fuxi and King Wen derived the Book of Changes.

竊嘗心潛力索，觸類引伸，變而通之，由門入蘊，謂獨得一全之體用，僭著其說。然與漢諸儒事事必強推五行，以求合於《春秋》災異，傅會五十五數以為洛書者，實不敢謂然，不敢同也。

I have privately devoted myself wholeheartedly to exploration, drawing connections and making extensions, transforming and integrating, entering from the gate into the hall, believing myself to have attained a complete system of principles and applications, and thus dared to write these statements. However, regarding the Han dynasty scholars who insisted on forcibly linking everything to the Five Phases in order to associate with the Spring and Autumn Annals' omens and disasters, and those who forced the number fifty-five into the Lo Shu diagram, I really do not agree, and I dare not approve of such views.

世恐未悉，況此河圖或謂由《易緯·乾鑿度》謂太一取其數以行九宮，四正四維皆合十五。鄭康成又注引其所以行九宮者，至於環中之虛位，本非謂五，而乃謂皇為五之中宮。固其《緯》、《注》俱妄，又不知其為五若十，皆虛用以制其奇耦生成，雖有其數，皇元其位也。

People may not yet understand this, and some even claim that the River Chart comes from the Yi Zhuan · Gan Zao Du, saying that the number of Taiyi is used to move through the Nine Palaces, with the four cardinal directions and the four intermediate directions adding up to fifteen. Zheng Xuan also made annotations and cited the method of the movement of the Nine Palaces, mentioning the empty position in the center, which originally does not refer to five. Yet he called it the 'Huang', meaning the central palace of five. Both the Yi Zhuan and Zheng's annotations are baseless. They also do not understand that whether it is five or ten, these numbers are merely hypothetical and used to constrain the generation of odd and even numbers. Although there is such a number, there is no actual direction associated with it.

然其所謂之太乙者，與太極則元以異也。苟未識其然，《記》日：「夫禮必本於太一，分而為天地，轉而為陰陽，變而為四時，列而為鬼神。」其理固與太極元以異也，自可旁通而元問然者；《記》經之屬也，因附諸《傳》後以徵。

However, what they refer to as "Taiyi" is essentially the same as "Taiji." If one still fails to recognize this, one may refer to the passage in the "Book of Rites: The Ritual Propriety" which says: "Ritual must originate from Taiyi, which differentiates into heaven and earth, rotates into yin and yang, transforms into the four seasons, and arranges into ghosts and spirits." This principle is fundamentally the same as Taiji, so it can be understood through analogy without further doubt. The "Book of Rites" is a classic text, so this passage is appended after the "River Chart Transmission" as a verification.

#1『擊』，原作『縣』，據四庫本改。 #2『芒』，四庫本作『茫』。 #3『大一』四庫本作『太一』。 #4『雖』，原作『維』，據四庫本改。 #5『鉤隱』，原作『勾隱』，據四庫本改。 #6『其三圖』，四庫本空缺此三字。 #7『說』，四庫本作『失』。 #8『校然』，四庫本作『較然』。 #9『未變』，原作『存變』，據四庫本改。 #10『妄人』，原作『妄之』，據四庫本改。 #11『為』，原脫，據四庫本補。 #12『為』，原脫，據四庫本補。

First: The character 「击」 was originally written as 「县」, but has been corrected according to the Siku Quanshu edition. Second: The character 「芒」 in the Siku Quanshu edition is written as 「茫」. Third: The phrase 「大一」 in the Siku Quanshu edition is written as 「太一」. Fourth: The character 「虽」 was originally written as 「维」, but has been corrected according to the Siku Quanshu edition. Fifth: The phrase 「钩隐」 was originally written as 「勾隐」, but has been corrected according to the Siku Quanshu edition. Sixth: The three characters 「其三图」 are missing in the Siku Quanshu edition. Seventh: The character 「说」 in the Siku Quanshu edition is written as 「失」. Eighth: The phrase 「校然」 in the Siku Quanshu edition is written as 「较然」. Ninth: The phrase 「未变」 was originally written as 「存变」, but has been corrected according to the Siku Quanshu edition. Tenth: The character 「妄人」 was originally written as 「妄之」, but has been corrected according to the Siku Quanshu edition. Eleventh: The character 「为」 was originally missing, but has been added according to the Siku Quanshu edition. Twelfth: The character 「为」 was originally missing, but has been added according to the Siku Quanshu edition.

古聖人之王天下，創始公至理，以惠啟千萬世者，豈易易然率己見以自擅制作哉？此有天授，斷可識矣。故河之出圖，伏羲因之以則而畫八卦；洛之出書，大禹因之以則而叔九疇。孔子於《大傳》叔天生神物，聖人則之，而並及圖書，而謂其兼則之也。子不語怪、力、亂、神，豈元所見於真實，而自樂為虛誕，以愚欺天下後世哉？

In ancient times, the sage rulers governed the world, establishing universal principles to benefit and enlighten countless generations. Would they lightly and arbitrarily create their own private views and fabricate things on their own? There is certainly a heavenly mandate involved, which can be clearly recognized. Therefore, when the Yellow River produced a diagram, Fuxi took it as a model and created the Eight Trigrams; when the Luo River produced a book, Yu the Great took it as a model and established the Nine Categories. In the Great Treatise of the I Ching, Confucius explained, "Heaven produces divine objects; sages take them as models." He also mentioned the River Chart and the Luo Book, meaning that sages took both as models. Confucius never spoke of strange phenomena, violence, disorder, or ghosts and spirits. Could he, without seeing real evidence, willingly fabricate false stories to deceive and mislead the world and future generations?

自稱庖羲氏之王天下，仰則觀象於天，俯則觀法於地，觀烏獸之文，與地之宜，近取諸身，遠取諸物，始作八卦，以通神明之德，以類萬物之情。是豈先聖、後聖各以私意淺識得措乎其間哉？《易》之廣大配天地，變通配四時，陰陽之義配日月，其為書廣大悉備，與乾坤相為終始而元弊，非有天授，能為是乎？此孔子有見於圖書之出，特謂則之而已，元它說也。

The Great Treatise says that when Fu Xi ruled over the world, he looked up to observe the phenomena in the heavens, looked down to observe the principles on the earth, observed the patterns of birds and beasts and the suitability of the land, took the image of himself nearby and the images of all things far away. Only then did he create the Eight Trigrams, to connect with the virtue of the divine and to compare the forms of all things. How could it be that the sage ancestors and later sages could each act on their own private views and shallow insights? The Book of Changes is vast and corresponds with heaven and earth, changeable and corresponds with the four seasons, and the meaning of yin and yang corresponds with the sun and moon. It is vast and includes everything, and corresponds with the beginning and end of the principles of heaven and earth without any faults. Could one achieve this without receiving it from heaven? Therefore, Confucius indeed saw the records about the River Chart and the Lo Book, and thus only said "the sage followed it," without any other words.

況圖之自見於成、康，《顧命》陳之束序之後，元所復聞。孔子固已自悲其不出，而有已夫之嘆。漢儒之始，孔安國乃由《書傳》於河圖束序之下，謂伏羲王天下，龍馬負圖出河，遂則其文，謂之河圖；

Moreover, the River Chart has been recorded since the time of King Cheng and King Kang of the Zhou dynasty. After it was mentioned in the "Gu Meng" as being displayed in the Eastern Hall, there is no further record of it. Confucius himself felt sorrowful about its disappearance and sighed, "Alas!" It was not until the early Han dynasty that Kong AnGuo, a Han scholar, noted in his "Shangshu Zhuan" that when Fuxi ruled the world, a dragon horse emerged from the Yellow River carrying the chart, and Fuxi took its patterns as a model, which is called the River Chart.

於天乃錫禹《洪範》九疇之下，謂天錫禹洛書，神龜負文而出，列於背，有數汰一至九，禹因而第之以成九類，類即疇也。是二說自分載於《洪範》、《顧命》各篇本語之下，亦未之有它說也。

It also notes below the sentence "Heaven bestowed the Huafan Nine Categories to Yu" that Heaven gave Yu the Luo Book, which was a pattern on the back of a divine turtle, arranged in numbers from one to nine. Yu compiled these into nine categories, with "category" meaning the same as "category" in the text. These two accounts are originally recorded separately in the texts of Huafan and Gu Ming, and there are no other accounts elsewhere.

至鄭康成始引《春秋緯》合注《大傳》之圖書云：「河以通乾出天苞，洛以流坤吐地符。河圖龍發，洛書龜感。《河圖》有九篇，《洛書》有六篇。」已是詭說之開端；然仍引安國之注，以為河圖八卦是也，洛書九疇是也。其後王輔嗣、韓康伯於此並元所註釋，惟孔穎達《易疏》雖全篇寫鄭注，亦謂輔嗣之義未知何風，是必未以鄭注為然也。

Zheng Xuan was the first to cite the "Chunqiu Wei" in commenting on the "Great Treatise" mentioned in the "Zhou Changes," saying: "The He River rises to the Heaven Trigram and produces the heavenly bundle, while the Luo River flows down to the Earth Trigram and emits the earthly symbol. The He Diagram is initiated by the dragon, and the Luo Book is responded to by the tortoise. The He Diagram consists of nine chapters, and the Luo Book consists of six chapters." This already marks the beginning of obscure and strange interpretations. However, he still cited Kong AnGuo's commentary, believing that the He Diagram is the Eight Trigrams and the Luo Book is the Nine Categories. Later, Wang Bi and Han Kangbo did not comment on this passage, while Kong Yingda's "Zhou Changes Justice" although fully quoting Zheng's commentary, also stated that Wang Bi's meaning was unknown in origin, indicating that he certainly did not endorse Zheng's commentary.

及其疏《書》之《洪範》，乃又引《繫辭》云：「河出圖，洛出書，聖人則之。」九類各有文字，即是書也。而云天乃錫禹，知此天與禹者，即洛書。就引《漢書·五行志》劉飲以為伏羲擊天而王，河出圖，則而畫之，八卦是也；禹治洪水，錫洛書，法而陳之，《洪範》是也。河圖、洛書，相為經緯；八卦、九章，相為表裹。

When Kong Yingda commented on the "Hongfan" section of the "Shangshu," he cited the "Great Treatise" saying, "The river produces a map, the Luo produces a book, and the sage follows them." He explained that the nine categories each have their own characters, which are referred to as "book." The text says, "Heaven bestowed the Book of Hongfan upon Yu," indicating that what Heaven gave to Yu was the Luo Book. He then cited Liu Xing's account from the "Hanshu · Wuxing Zhi," stating that Fuxi inherited the mandate of Heaven and became king; when the Yellow River produced a map, he followed it and drew the Eight Trigrams. Yu controlled the floods, and Heaven bestowed the Luo Book upon him, which he followed and recorded as the "Hongfan." The River Map and Luo Book form the vertical and horizontal threads, while the Eight Trigrams and Nine Chapters form the inner and outer parts.

先達共為此說。龜負洛書，經無是事。《中候》及諸《緯》多說黃帝、堯、舜、禹、湯、文、武受圖書之事，皆云龍負圖，龜負書。緯候之書，不知誰作，通人討竅，謂偽起哀、平，雖復前漢之末始有此書，已前學者必相傳此說，故孔以為九類是神龜負文而出，列於其背，有數仄一至九，禹見其文，因而第之以成九類法也。

Eminent scholars of the past all hold this view. In fact, the story of the divine turtle carrying the Luo Book is not mentioned in the canonical texts. The Shangshu Zhonghou and various ying books often talk about the Yellow Emperor, Yao, Shun, Yu, Tang, King Wen, and King Wu receiving the Tu and Shu. They all say that the dragon carried the Tu and the turtle carried the Shu. These ying and hou texts are unknown in origin, and learned scholars have investigated them, believing they were fabricated during the reigns of Emperor Ai and Emperor Ping of the Western Han dynasty. Even if these texts appeared only in the late Western Han, scholars before that time must have passed down this story orally. Therefore, Kong Anguo thought that the nine categories were formed when the divine turtle carried the patterns and arranged them on its back, with numbers from one to nine. Yu saw these patterns and thus arranged them into the nine categories.

言禹第之者，以天神言語必當簡要，不應曲有次第，丁寧如此，故以為禹第之也。

This is why it is said the order was compiled by Yu the Great, because the words of heavenly spirits must necessarily be concise and should not be arranged in a roundabout way or explained so meticulously. Therefore, it is concluded that this arrangement was made by Yu the Great.

其疏《顧命》之河圖束序，及疏《記》之出馬圖，詳略雖小有殊同，指意大校若此，是則所謂河圖為八卦，所謂洛書為九疇，並無改議也。

Kong Yingda, in his commentary on the sentence "The River Chart is in the eastern hall" from Gu Ming, and also in his commentary on the sentence "The River does not produce the Map of the Horse" from the Li Ji, although there are slight differences in detail, the general meaning is the same. This shows that the so-called River Chart refers to the Eight Trigrams, and the so-called Luo Book refers to the Nine Categories. This interpretation has never been changed by anyone throughout history.

由漢而唐，《易經》行世，凡經、傳、疏、釋之外，未有及於圖、書之文刊列經首者。迨故宋之初，陳搏圖南始創意推明象數，自謂因玩索孔子三陳九卦之義，得其遠旨，新有書述，特稱龍圖，離合變通，圖餘二十，是全用《大傳》天一地二至天五地十、五十有五之數，雜以納甲，貫穿《易》理。

From the Han dynasty to the Tang dynasty, the Book of Changes was widely circulated, and apart from the canonical text, commentaries, interpretations, and annotations, no one ever placed diagrams such as the River Chart and the Lo Book at the beginning of the text. It was not until the early Song dynasty that Chen Tuan, who was known by the courtesy name Tu Nan, innovatively emphasized the principles of figures and numbers. He claimed that after repeatedly pondering Confucius' three mentions of the nine trigrams in the Great Treatise, he grasped the profound meaning, and thus composed a new book, specially naming it The Dragon Diagram. The book discusses the combination, separation, transformation, and adaptability, containing more than twenty diagrams. These diagrams entirely adopted the fifty-five numbers from the Great Treatise, starting from Heaven One and Earth Two up to Heaven Five and Earth Ten, and incorporated the Han dynasty method of assigning stems, known as Najia, to connect the principles of the Book of Changes.

內一圖謂形九宮，附一圖謂形洛書者，則盡去其五生數，祇起地六至地十。自釋十為用，十為成形，故《洪範》陳五行之用數語而已。及終其書，再出兩圖，其一形九宮者，元無改異，標為河圖；其一不過盡置列《大傳》五十有五之數於四方及中，而自標異謂為洛書，並無傳例言說。

Among them there is a diagram called the Nine Palace Form, and another called the Luo Book Form, which removes all five generating numbers and starts from the earth number six up to the earth number ten. His own explanation is merely a few words: "Ten is used, ten forms the shape, so the 'Great Plan' states the numbers used for the Five Phases." At the end of the entire text, he lists two more diagrams: one of the Nine Palace Form remains unchanged from before but is now labeled as the He Tu; the other simply arranges the fifty-five numbers from the 'Great Treatise' in the four directions and the center, yet he boldly names it the Luo Book without any traditional rationale or explanation.

特移二、七於南，四、九於西，莫可知其何所祖法而作，而標以此名，大抵因如前說《洪範》五行之二火、四金，《太玄》準《易》因之為二南、四西而然。然其流傳未遠，知者亦鮮。

He merely moved the numbers two and seven to the south, and four and nine to the west, but no one knows what principle he used to create this diagram or why he gave it this name. Perhaps, as mentioned earlier, it is because the Five Phases in the "Hóngfàn" associate two with fire and four with metal, and Yang Xiong's "Tàxuán" follows the "Yì" by adopting this same system, placing two in the south and four in the west. Therefore, he arranged it this way. However, this system did not spread widely, and few people knew about it.

自圖南五傳而至劉牧長民，乃增至五十五圖，名以《鉤隱》。師友自相推許，更為唱述，各於《易》問有註釋，日《卦德論》，日《室中語》，日《記師說》，日《指歸》，曰《精微》，曰《通神》，亦總謂《周易新注》。每欲自神其事及跡，而究之未見其真能有所神奇也。

From Chen Tuan, the tradition passed down through five dynasties to Liu Mu, who was known by the name Changmin, and it was then increased to fifty-five diagrams, titled The Diagrams of Hidden Numbers in the Book of Changes. They mutually praised and responded to each other's teachings, passing them on, and each person had their own commentary on the Book of Changes. The titles of their works included The Discourse on the Virtues of the Hexagrams, The Words Within the Room, The Record of the Teacher's Teachings, The Return to the Origin, The Subtleties, and The Communication with the Divine. Collectively, they were also called The New Commentary on the Book of Changes. They always tried to present these matters and their actions as highly mysterious and divine, but upon close examination, there was not really anything truly miraculous to be found.

時則有李觀泰伯，著《六論》以駁其非是，至謂恩其志誤學子，壞爨世教，而刪其圖之復重存之者三焉：河圖也，洛書也，八卦也。夫長民之多為圖畫，固未知其是，而泰伯亦無未識此圖之三本之則一爾。河圖本列八卦，而數五十有五也。

At that time there was Li Gou, who took the name Tai Bo, and he wrote the "Six Discussions" to refute their errors, even saying that these people intended to mislead students and corrupt the world's teachings. Therefore, he deleted the repeated diagrams and kept only three: the River Chart, the Lo Shu, and the Eight Trigrams. In fact, Liu Mu's addition of more diagrams was not necessarily correct; yet Li Gou also did not understand, for these three diagrams were originally just one diagram—the River Chart itself already arranged the Eight Trigrams, and its numbers totaled fifty-five.

及長民輩始破洛書古說，謂非只是《洪範》，必別有書出於羲之上世，羲乃得而並則之以作《易》也。泰伯之見，則又與之同，此愚又莫能知何為其然也。

By the time of Liu Mu, the old views about the Luo Shu were first broken, and they believed that the Luo Shu was not only the Hong Fan but must have been another book that appeared in the time before Fuxi. Fuxi was then able to take both the Luo Shu and the He Tu as models to compose the Yi. Li Gou's view was also the same as theirs, and I really don't understand why they should see it this way.

蓋嘗夷考《大傳》此章，自有法象天地，變通四時，縣象日月，而又有及於蓄龜，故因謂之天生神物，聖人則之者，正謂曹也。《易》惟曹是用，所謂曹之德員而神，幽贊於神明而生曹，《易》豈有龜事哉？因其均可以占，故牽聯及龜爾。

I once carefully examined this chapter of the Great Treatise. It originally discusses the principles of the cosmos, the transformation of the four seasons, and the celestial phenomena of the sun and moon. Then it goes on to mention the yarrow stalks and the tortoise shell. Therefore, it says, "Heaven produces divine objects; sages follow them." Here, the term "divine object" clearly refers to the yarrow stalks. The Book of Changes only uses the yarrow stalks, as it says, "The virtue of the yarrow stalks is round and divine," and also states, "It is in the profound communion with the divine that the yarrow stalks arise." Where in the Book of Changes is there mention of the tortoise shell? It is only because the yarrow stalks and the tortoise shell can both be used for divination that the tortoise shell is mentioned by association.

以上文謂法象天地，變通四時，故申之曰：「天地變化，聖人效之。」上文謂縣象日月，故申之日：「天垂象，聖人象之。」至於天生神物，乃申謂之如河出圖，洛出書，聖人亦得以則之也。

Because the previous text discussed the principles of law and phenomena mirroring heaven and earth, and transformation in accordance with the four seasons, it then proceeds to explain: "Heaven and earth change, and the sage follows their example." Since the previous text mentioned the suspension of celestial phenomena such as the sun and moon, it then continues: "Heaven displays signs, and the sage imitates them." As for the phrase "Heaven produces divine objects," the explanation that follows means that events such as the Yellow River producing a map and the Luo River producing a book are also things that the sage can take as a model.

蓋由河之出圖，羲前既得以則而畫卦，因及於洛之出書，禹後復得以則而叔疇爾。又豈害於比類而互言之哉？豈嘗直欲以圖書之數、之義、之條貫比而同之哉？豈嘗直謂圖書並出於一時哉？

In general, this is because the Yellow River produced the diagram, and Fuxi came first, having taken it as a model to draw the trigrams. Thus, it naturally leads to the discussion of the Luo River producing the text, with Yu coming later, who took it as a model to establish the nine categories. By comparing and interweaving these two, what harm is there? Confucius never necessarily required that the numbers, meanings, and connections of the River Diagram and the Luo Book be entirely the same. Nor did he ever say that the diagram and the text appeared at the same time.

且不惟漢儒引《洪範》以為洛書，雖圖南之初謂形洛書者，亦不過謂十為用，十為成形，故《洪範》陳五行之用也者，是明指洛書為《洪範》矣。不知長民輩不本其初，故倍其師傳，而謂洛書非出於禹之時，益使後之人迷亂而失所據依，何也？

Moreover, not only did Han dynasty Confucian scholars use the "Hongfan" chapter to explain the Luo Shu, but even Chen Tuan's original statement about the "form of the Luo Shu" merely said, "Ten is used, ten forms the shape, so the 'Hongfan' chapter explains the use of the Five Phases." This clearly indicates that the Luo Shu is the same as the 'Hongfan'. It is surprising that Liu Mu and his contemporaries did not trace back to the source, but instead deviated from the teachings passed down by their predecessors, claiming that the Luo Shu did not originate in the time of Great Yu. This further confuses later generations and causes them to lose their basis. Why is this so?

又不謂孔子之謂聖人之則之也。非特去羲之時將幾世、幾年，雖祇去禹之世固已千數百年矣。其稱書之出洛，以比羲之圖之出河，於理惡乎而不可？長民故為此說，是且並孔子之《大傳》不之信邪。

They do not think about what Confucius meant by "the sage follows it." Confucius lived many generations and many years after the time of Fuxi; even if we count only from the time of the Great Yu, it would have been thousands of years. He speaks of the book emerging from the Luo River, comparing it with the map emerging from the Yellow River during Fuxi's time. How is that unreasonable? Liu Mu insists on this claim, but is he not then refusing to believe Confucius' Great Treatise?

考圖南之為龍圖，雖自謂得於孔子三陳九卦之旨而作，然其序日：「龍圖者，天散而示之，羲合而用之，孔默而形之。」且明稱始圖之未合，惟五十五數，則是謂《大傳》天數二十有五，地數三十，合而言之，不知何以於其末改標之以為洛書，殆其始誤也。

Chen Tuan's work, the Dragon Chart, though he claimed to have understood the meaning of Confucius's three times nine hexagrams, his own preface says, "The so-called Dragon Chart is dispersed by Heaven and displayed by Earth, Fuxi combined it and applied it, and Confucius silently revealed it." Moreover, he clearly states that the original chart had not yet been combined, only the number fifty-five, which refers to the number mentioned in the Great Treatise, that Heaven's number is twenty-five and Earth's number is thirty, combined together. It is really unclear why he later changed it to the Luo Book at the end of the book, which is probably the original mistake.

長民輩乃承誤而益增其誤，遂真以為洛書，而有五十五圖以實其誤；以至泰伯已後，悉以圖南標異之五十五數為真洛書也。不思圖南標洛書之始偶謂用十，夫洛書所叔九疇，其十數當何汰而起哉？

Liu Mu and his contemporaries inherited this mistake and made it worse, actually treating it as the Luo Shu, and even drew fifty-five diagrams to confirm this error; so from Li Gou onwards, everyone regarded the fifty-five numbers that Chen Tuan introduced as the real Luo Shu. They never considered: when Chen Tuan first referred to the Luo Shu, he only casually mentioned 'using ten'; yet the number ten in the nine categories described in the Luo Shu, from where should this number ten be counted?

意豈謂《大傳》之河、圖既可出而示世，則洛書亦可以並出示之，因假《大傳》五十五數，托為《書》之九疇乎？九疇所言皆用縱比而同之謂五十五數，其用又安在哉？此不可之大者也。

Are they not thinking that since the River Chart mentioned in the Great Treatise can be presented to others, the Lo Shu should also be presented? Therefore, they have borrowed the number fifty-five from the Great Treatise and falsely attributed it to the Nine Categories of the Book of Documents? The Nine Categories discuss practical applications. Even if one forcefully equates them with the number fifty-five, where would this number be applied? This is the most illogical point of all.

故嘗因長民之事討其原，圖南之後，种放、許堅、李溉，未及見其它有著述。若其所親授之師，如範誇昌所著《太易源流》，其稱龍馬負圖出河，羲皇窮天人之際，復位五行生成之數，定地上八卦之體，故老子自西周傳授孔子造《易》之原，天一正北，地二正南，天三正束，地四正西，天五中央，地六配子，天七配午，地八配卯，天九配酉，地十配中，寄於末，乃天地之數五十有五矣。

So I once investigated the origin of Liu Mu's theory. After Chen Tuan, the scholars Zong Fang, Xu Jian, and Li Gai did not have any other writings. As for Liu Mu's direct teacher Fan Echang, in his work "The Origin of Taiyi," he said: the dragon horse carried the diagram from the Yellow River, and Fuxi explored the connection between heaven and humanity, reordering the numbers of the Five Phases' generation. He established the forms of the Eight Trigrams on earth. Therefore, Laozi passed down the original principles of the Book of Changes to Confucius during the Western Zhou dynasty. These principles are: Tianyi (Heavenly One) is located in the due north, Di'er (Earthly Two) in the due south, Tian San (Heavenly Three) in the due east, Di Si (Earthly Four) in the due west, Tian Wu (Heavenly Five) in the center. Di Liu (Earthly Six) corresponds to Zi (the first Earthly Branch), Tian Qi (Heavenly Seven) corresponds to Wu (the fifth Earthly Branch), Di Ba (Earthly Eight) corresponds to Mao (the second Earthly Branch), Tian Jiug (Heavenly Nine) corresponds to You (the eighth Earthly Branch), and Di Shiy (Earthly Ten) corresponds to the center, with the position of the center being assigned to the last position. This is the total of fifty-five numbers of heaven and earth.

因考其既以圖之前五數置於北、南、束、西之正及中，復以後五數配子、午、卯、酉及中，何也？夫子、午、卯、酉，非四方之正邪？地十配中雲寄於末，夫中抑有末邪？

I therefore examined this: since he placed the first five numbers in the north, south, east, west, and center, yet assigned the last five numbers to zi, wu, mao, you, and center, why is this so? Zi, wu, mao, you are not precisely the four cardinal directions? It is also said that the ten heavenly stems are paired with the center and reside in the last position; does "center" have another "end"?