Volume One: Notes on Collation

諦詳所置之數，正今圖所傳有四方而元四維之數者，是誇昌已元不識圖南所以標異，特因《太玄》準《易》取於《洪範》一水、二火、三木、四金、五土，而然鑿空元故，造端老子，增立怪論，以實圖南易置二、七、四、九之位爾，然猶未嘗以九疇分配九宮也。

Carefully examining the numbers he arranged, it is exactly the present version of the diagram that has only four directions and not the four cardinal directions. This shows that Fan Gechang originally did not understand why Chen Tuan was innovative. He merely fabricated this without cause, simply because the Tai Xuan followed the Yi and adopted the order of the Hong Fan, which lists one as water, two as fire, three as wood, four as metal, and five as earth. He even fabricated a strange theory, attributing it to Laozi, in order to justify Chen Tuan's arrangement of the numbers two, seven, four, and nine in those positions. However, he did not yet distribute the nine categories into the nine palaces.

究竅誇昌之取用，不過循納甲之緒餘，及五子歸庚之殊向，又謂天上八卦坎、離對中之外移，置乾、兌、坤於束，艮、震、巽於西，不謂五行之說，多起於《易》；後而反引五行以為定卦之原，此又其敢於創異之大端也。

He examined the methods used by Fan Echang, finding them to be merely remnants of the Najia stem assignment and an alternative approach called "five sons returning to Geng." He also stated that among the eight trigrams in the heavens, apart from Kan and Li which are positioned centrally opposite each other, the rest should be moved outward, placing Qian and Dui in the east and Gen, Zhen, and Xun in the west. He failed to understand that the theory of the Five Phases largely originated from the Book of Changes, yet he used the Five Phases as the fundamental principle for determining the trigrams, which was another bold innovation on his part.

是宜長民不獨增以五十五圖，又因誇昌坎、離、震、兌四正之外，而以四成數同於四方，謂坎六退本卦三數，以餘三數三畫為乾；離七退本卦三數，以餘四數四畫為巽；震八數退本卦三數，以餘五數五畫為艮；兌九數退本卦三數，以餘六數六畫為坤，皆以數為畫，標為河圖，是不揣本而齊末。

It's no wonder that Liu Mu not only added illustrations to make fifty-five pictures, but also followed Fan Ech Chang's method of placing Kan, Li, Zhen, and Dui in the four cardinal directions. He equated the four complete numbers with the four directions, saying: subtract the three numbers of the primary hexagram from the number six of Kan, and use the remaining three numbers and three lines to form Qian; subtract the three numbers of the primary hexagram from the number seven of Li, and use the remaining four numbers and four lines to form Xun; subtract the three numbers of the primary hexagram from the number eight of Zhen, and use the remaining five numbers and five lines to form Gen; subtract the three numbers of the primary hexagram from the number nine of Dui, and use the remaining six numbers and six lines to form Kun. He consistently used numbers to represent lines and called it the He Tu. This is truly not measuring the root, but only seeking uniformity at the periphery.

夫八卦各三畫，以剛柔生爻，未聞本卦只用三畫，而以其餘畫之多，反分為別卦也。所陳之數抑配偶然，且以坎、離、震、兌為四象，則尤非也。象本在未成卦之先，故曰：「四象生八卦」也。

The eight trigrams each consist of three lines, which are generated through the principles of yin and yang. There has never been a record of using only three lines for the primary hexagram and then using the remaining lines to form another hexagram based on their quantity. The numbers he arranged are merely arbitrary. Moreover, his classification of Kan, Li, Zhen, and Dui as the four trigrams is incorrect. The trigrams originally existed before the hexagrams were formed, which is why the Great Treatise states, "The four trigrams generate the eight trigrams."

又云：洛書之九疇，本河圖自然之數，虛皇極於中，而以八疇分佈四正、四維，五行置於坎一，五事置於坤二，五紀置於巽四，五福置於離九，一以九疇之次叔，陳列於河圖之卦次。夫九疇謂禹次第之者，直自初一、次一不次三、四而以次用之也。今隨河圖十五縱橫而置之，則成亂次矣。

He also said that the nine categories of the Luo Square are based on the natural numbers of the He Diagram, with the Emperor's Pole set in the center and the remaining eight categories arranged in the four cardinal directions and the four intermediate directions. The Five Phases are placed in the position of Kan one, the Five Affairs in the position of Kun two, the Five Records in the position of Xun four, and the Five Blessings in the position of Li nine, all arranged in the order of the nine categories on the hexagram positions of the He Diagram. However, the reason the nine categories are said to have been arranged by Great Yu is that they should be used in sequence, starting from the first day, then the second, then the third, and so on. Now, if we place them according to the fifteen grid pattern of the He Diagram, the order becomes completely disrupted.

未暇一一辯詁，且以初一之口五行言之。既謂五行，自當分配五方，何得以五者限萃一方？不以推行，惡得謂五行哉？以至謂火、金易位，與河圖不同，其顛倒迷繆不可訓知若此。

I didn't have time to argue point by point, so let's just take the first category, "Five Phases," as an example. Since it is called the Five Phases, they naturally should be distributed among the five directions. How could these five elements be confined and gathered in one direction? Without allowing them to move and transform, how can they be called the Five Phases? It even goes so far as to say that fire and metal have exchanged positions, differing from the He Tu diagram. The confusion and disorder have reached such an extent that it is utterly illogical.

其後楊次公自著《洞極經》，託名於關子明，其叔本篇稱子曰：「河圖之本，七前六後，八左九右，聖人觀之以畫八卦，是故全七一之三以為離，奇以為巽；全八之三以為震，奇以為艮；全六之三以為坎，奇以為乾；全九之三以為兌，奇以為坤。正者全其位，偶者盡其畫。」而謂四象生八卦，此謬之尤者。

Later Yang Cigong himself wrote the "Dongji Jing," but falsely attributed it to Guan Ziming. When explaining this passage, he cited "Zi Yu" (the Master said): "The fundamental principle of the River Chart is that seven is in front, six is behind, eight is on the left, and nine is on the right. The sage observed this and drew the eight trigrams. Therefore, taking the full number of seven, three lines were used for Li (Fire); taking its remainder, three lines were used for Xun (Wind). Taking the full number of eight, three lines were used for Zhen (Thunder); taking its remainder, three lines were used for Gen (Mountain). Taking the full number of six, three lines were used for Kan (Water); taking its remainder, three lines were used for Qian (Heaven). Taking the full number of nine, three lines were used for Dui (Lake); taking its remainder, three lines were used for Kun (Earth). Those in the central position preserved their direction, while those in the even position used up their line numbers." And he said this was the "Four Symbols giving rise to the Eight Trigrams." This is truly the most erroneous statement.

乾、坤相索而生六子，今為男女者，反能生父母之卦邪？況泛言一不七為火，四、九為金，猶可饅所未識者。今至明言離九為七，兌七為九，是河圖一可變置矣而可乎？

Heavenly Stem and Earthly Branches are used to generate the six sons' trigrams, which are derived from the interaction between Heaven and Earth. Now, these six sons' trigrams, being male and female, can generate the parents' trigrams? Moreover, it is possible to generally say that numbers two and seven are fire, and four and nine are metal, which can deceive those who do not understand. But now it is clearly stated that Li nine is seven and Dui seven is nine, which is equivalent to saying that the He Tu can be arbitrarily rearranged. How can that be acceptable?

又謂洛書之文，五處其中，九前一後，三左七右，四前左二，前右八後，左六後右，後世稽之以為三象，因而九變之以二十七象。今按其說，惟五處其中一語，於洛書不悖，餘悉河圖之數，而河圖之數乃因洛書以五處中，而盡失其所以為五之理爾。

He also said that the pattern of the Luo Shu is such that the number five is in the center, nine is in front, one is behind, three is on the left, seven on the right, four is in the front left, two in the front right, eight in the back left, and six in the back right; later generations studied it and established three images, and through nine transformations, it became twenty-seven images. Now according to his statement, only the phrase "five is in the center" does not contradict the Luo Shu; the rest are all numbers from the He Tu. Once the number five in the He Tu is placed in the center according to the Luo Shu, it completely loses the meaning of five being five.

《書》之九疇，以皇極之五處中，固元別用，是可以定位也。至河圖之有天五，乃兼地十以為十五，其五乃四分於成數之內而合於十，豈嘗有五虛點而實置於圖之中位哉？圖之傳誤正由此五。

The nine categories of the *Shangshu* (Book of Documents) have the fifth category, the Supreme Center (huangji), in the middle, which originally had no other function, so it was positioned that way. As for the number five in the River Chart (hetu), it is meant to combine with the number ten of the earth to form fifteen. This number five is divided into four parts and scattered within the formed numbers, then combined with ten. How could there ever have been five empty dots actually placed at the center of the chart? The error in the transmission of the River Chart originates from this number five.

次公之假設此妄例，特以蓋其所祖者，乃楊子云三方、九州島而二十七部，私以為書耳。於斯二者，固已真易置圖、書矣。而朱元晦、蔡季通反祖之，信以為關子明作也。不計子明之《易傳》精詣，豈此摹擬者比，乃循此膚臆之見，因扶其說，亦謂河圖七前六後，八左九右；洛書之文，九前一後，三左七右，四前左，二前右，八後左，六後右。

Yang Cigong assumed this false example merely to cover up what he actually followed, which was actually Yang Xiong's "Ta Xuan" with its three directions, nine states, and twenty-seven parts, which he privately regarded as a classic. From these two points, he indeed completely reversed the River Chart and the Lo Shu. However, Zhu Xi (Zhu Yuanhui) and Cai Yuanding (Cai Jitong) instead followed him, believing that this was truly composed by Guan Ziming. They did not think about how profound Guan Ziming's "Yi Zhuan" was, which could not be compared to such imitative work; yet they followed this shallow and speculative view, further supporting it, and also explained that the River Chart has seven in front and six behind, eight on the left and nine on the right, while the Lo Shu has nine in front and one behind, three on the left and seven on the right, with four in front-left, two in front-right, eight in back-left, and six in back-right.

謂《大傳》既陳五十有五數，《洪範》又謂天乃錫禹《洪範》九疇，而九宮之數戴九履一，左三右七，二、四為肩，六、八為足，正龜背之象。劉牧意見以九為河圖，十為洛書，託言出於希夷，與諸儒舊說不合；又引《大傳》以為二者皆出於伏羲之世，其易置圖、書並元明驗。

They say: Since the Great Treatise presents the number fifty-five, and the Hongfan states "Heaven gave Yu the Hongfan Nine Categories," the nine-square grid number is said to have the number nine on top, one at the bottom, three on the left, seven on the right, two and four as the two shoulders, and six and eight as the two feet, forming exactly the shape of a tortoise's back. As for Liu Mu's view, he took nine as the He Tu and ten as the Luo Shu, attributing them to Chen Tuan, which differs from the old views of the scholars. He also cited the Great Treatise to say both originated in the time of Fuxi, but his reversal of the He Tu and Luo Shu lacks clear evidence.

其朱、蔡之指斥又如此，而直以圖南始標誤之洛書為河圖，而以其初正指河圖，反以為洛書，則朱、蔡實自誤而反罪長民之先誤。專己自是，張其辯說，不克自反，一至於此。

Zhu Xi and Cai Yuan ding criticized Liu Mu in this way, yet they themselves directly took the Luo Book that Chen Tuan had mistakenly labeled as the He Tu, and instead took the one Chen Tuan originally correctly identified as the He Tu as the Luo Book. In this way, Zhu and Cai actually made their own mistakes, yet they blamed Liu Mu for having made the error first. They were stubborn and self-willed, believing themselves to be right, and they spread their arguments without self-reflection, reaching such a point.

惟程泰之《易原》時能理到，至鄭束卿輩尋邇依傍，一意誕饅，廣增圖說，皆非實指，徒使後之人失其真是，信其所不當信，疑其所不當疑，並與本來宗旨樊然擾亂，是其所非，而非其所是。

Only Cheng Dachang (style name Taizhi) of "The Origins of the Changes" (Yi Yuan) could consistently address the principles. As for those of the generation of Zheng Dongqing, they only knew how to attach themselves closely to existing interpretations, indulging in sheer absurdity and deceiving people. They added a great deal of illustrations and diagrams, but all were not genuine references. This caused later generations to lose the true meaning: they did not believe what should be believed, and doubted what should not be doubted. The original purpose was also thoroughly confused, mixing right and wrong, taking the wrong for the right and the right for the wrong.

跡究其始，不過由圖南用十之一語立一圖之誤，至於為此紛紛，始猶借河圖以相因依，而為洛書之說，久則舍圖取書，又久乃遂以書為圖，荒然莫知河圖為何物，所以有圖者，寫為何事，執其五十五數以為圖，不知其五十五數其始特以誤及洛書，今及執之為圖，是圖既非興；其謂書以為圖者，書益非其書者矣。

Tracing back the origin of all this, it was merely Chen Tuan's mistaken statement of "using ten" that led to this endless confusion. At first, they still relied on the River Chart to support the theory of the Lo Shu; over time, they abandoned the River Chart and focused solely on the Lo Shu; eventually, they even took the Lo Shu to be the River Chart, completely unaware of what the River Chart actually was and why it was originally created. They took the number fifty-five as representing the River Chart, but did not realize that these fifty-five numbers were originally mistakenly added to the Lo Shu. Now, using them as the River Chart, this "chart" is no longer the true chart, and the "book" that claims the Lo Shu is the River Chart is also no longer the original Lo Shu.

徒自言人人，殊使學者亡羊多歧，求馬唐肆，紛如聚訟，吾誰適仄？不啻三百年於此，故推原致誤之由，疏列莘疑之妄，直以河圖本數討正之，庶幾學者見之瞭焉，會心自斷，知圖南之謂其由三陳九卦而得者，類於饅；陰腸家襲於以一、六、八白取以為起例者，流於末，若《乾鑿度》謂太一取其數以行四正四維皆合十五者。《鑿》於《緯》之拘贅，亦不盡然。

Everyone has their own opinions, leaving scholars confused, like searching for a sheep in a crossroad or buying a horse in an empty stable. They argue endlessly, like in a lawsuit. Who should I believe? This situation has persisted for more than three hundred years. Therefore, I trace back the causes of these errors, list various questionable and false theories, and directly use the original numbers from the River Chart to correct them. I hope scholars can understand at a glance and make their own judgment. One must know that Chen Tuan claimed he derived his method from "San Chen Ji Guà" (Three Chens and Nine Hexagrams), which is almost a deception. The Yin-Yang school followed the idea of one white, six white, and eight white to serve as examples for divination, which is merely a superficial technique. As for what is said in the "Qian Zao Du" (The Book of the凿ing of the Heaven), that the Taiyi (Supreme Oneness) takes numbers to move through the nine palaces, and that the four cardinal directions and four secondary directions add up to fifteen, this is an overly rigid and cumbersome interpretation in the "Yi Wei" (Commentaries on the Changes), and not entirely reliable.

然從昔儒先莫不斷斷然謂非人所能偽作者，今以餘自本觀之，直謂不必它求，特以《說卦》帝出乎震一□一章，環中往復參究之，以天一至地四，地六至天九求其實體，天五與地十明其虛用，則參伍以變，參天兩地，錯綜倚數，莫不左右逢原，一皆胳合乎孔子繫《易》之初旨。

However, all the distinguished Confucian scholars throughout history have firmly stated that the River Chart could not have been forged by human beings. Now, from the source, I can simply say: there is no need to seek elsewhere. Just take the passage in the "Shuo Gu" chapter that says "The Emperor arises from Zhen," and examine it thoroughly by considering the circular repetition. Use the numbers from Heaven One to Earth Four and from Earth Six to Heaven Nine to seek its substance, and use Heaven Five and Earth Ten to clarify its function. Thus, "Three and Two to produce change," "Three heavens and two earths," and "Interweaving and reversing numbers" will all be naturally in harmony, fully aligning with the original intent of Confucius in interpreting the Book of Changes.

是之謂參。淆亂抓論，轟明；河之出圖，通古不妄，足以見《易》矣。因洞悉洛之出書，一汍疇之外，豈復有圖有數之妄作者，誠古今之一大快事也。

This is what is truly called "participation" (参). It clears up confusion and exposes fallacies, making the principles clearly evident: the emergence of the River Chart (黄河出图) throughout history is not baseless, and from this we can see the origin of the Book of Changes (《易》). Therefore, we can fully understand that the emergence of the Luo Book (洛水出书) involved only the Nine Categories (九畴), and there is no other fabricated diagram or number. This is indeed a great event for both past and present.

#1『平』，原作一乎』，據四庫本改。 #2『禹』，四庫本作『語』。 #3『祇』，原作一祇，據四庫本改。 #4『非特』，仰庫本誤把後文自『八疇分佈四正、四維』至『是可以定位也』一段倒置於此處之後。特此說明。 #5『太易』，四庫本作『大易』。 #6『謬』，原作『繆』，據四庫本改。 #7『不啻騙』，原作『不趨』，據四庫本改。

The first point: the character "平" was originally written as "乎", and has been corrected according to the Siku Quanshu edition. The second point: the character "禹" in the Siku Quanshu edition is written as "语". The third point: the character "祇" originally had a distorted form, and has been corrected according to the Siku Quanshu edition. The fourth point: the phrase "非特" has been misplaced in the original text, with the passage from "八畴分布四正、四维" to "是可以定位也" appearing after it, which is an error in the Siku Quanshu edition. The fifth point: "太易" in the Siku Quanshu edition is written as "大易". The sixth point: the character "谬" was originally written as "缪", and has been corrected according to the Siku Quanshu edition. The seventh point: the phrase "不啻" was originally written as "不趋", and has been corrected according to the Siku Quanshu edition.