The Book of Changes clarifies distinctions through diagrams.

《魏志》博士淳于俊曰：「包羲因燧皇之圗而制八卦。」髙貴鄉公折之曰：「若使包羲因燧皇而作《易》，孔子何以不云『燧人氏沒，包羲氏作』乎？」俊不能荅。此妄談，不足深辨。

The Records of the Three Kingdoms: Wei Zhì states that the Doctor Chunyu Jun said: Fuxi made the Eight Trigrams based on the diagram passed down by Suirenshi. When Wei Emperor Gaoxianggong Cao Mao refuted him directly, he said: If Fuxi made the Zhou Changes based on Suirenshi, why does Confucius in the Great Treatise not say 'After Suirenshi died, Fuxi made it'? Chunyu Jun had no answer. Hu Wei commented: This is baseless talk and not worth further discussion.

《玉海》：姚信曰：「連山氏得河圗，夏人因之曰《連山》；歸藏氏得河圗，商人因之曰《歸藏》；伏義氏得河圗，周人因之曰《周易》。」（姚信，三國吳太常卿也。《周禮疏》云：案《世譜》等書，神農一曰連山氏、列山氏，黃帝一曰歸藏氏，並是代號。）王洙曰：「《山海經》云：伏羲氏得河圗，夏后因之曰《連山》；黃帝氏得河圗，商人因之曰《歸藏》；列山氏得河圗，周人因之曰《周易》。」（洙字原叔，著《易傳》十卷。）

Wang Yinglin, in his work "Yu Hai," cites the words of Yao Xin, a person from the Three Kingdoms period of Wu: Lianshan氏 obtained the Yellow River Chart, and the people of the Xia dynasty continued to use it, calling it "Lianshan"; Guicang氏 obtained the Yellow River Chart, and the people of the Shang dynasty continued to use it, calling it "Guicang"; Fuxi氏 obtained the Yellow River Chart, and the people of the Zhou dynasty continued to use it, calling it "Zhouyi." (Yao Xin was the Taichangqing of the Wu state during the Three Kingdoms period. "Zhou Li Shu" says: consult books on "Shi pu" (genealogical records), Shennong氏 is also called Lianshan氏 or Lieshan氏, and the Yellow Emperor is also called Guicang氏, all of which are alternative names for dynasties.) Wang Zhu of the Northern Song dynasty also said: "Shanhai Jing" states that Fuxi氏 obtained the Yellow River Chart, and the Xia dynasty continued to use it, calling it "Lianshan"; the Yellow Emperor obtained the Yellow River Chart, and the Shang dynasty continued to use it, calling it "Guicang"; Lieshan氏 obtained the Yellow River Chart, and the Zhou dynasty continued to use it, calling it "Zhouyi." (Wang Zhu, whose name was Yuan叔, wrote a ten-volume work called "Yi Zhuan.")

二說互異。漢上朱氏曰：「斯乃杜子春之所憑，姚信之言非口自出，但所從傳者異耳。梁武攻之，涉於率肆。仲尼曰『河不出圗，吾已矣夫』，葢聖人受命必有符瑞，若圗不再出，無勞嘆徯。」此言良是。然歴代所受河圗，豈必皆為卦畫之象而則之以作《易》？蒙有猜焉，未敢盡從也。

Yao Xin and Wang Zhu's two accounts conflict with each other regarding the imperial titles associated. Zhu Zhen of the Southern Song Dynasty (who lived in Hanzhou and was known as the Master of Hanzhou, author of "Hanzhou Commentary on the Changes") said: This was the old view based on which Du Zichun of the Han dynasty relied. Yao Xin's statements were not fabricated by himself, but rather he inherited a different tradition from his teacher. Liang Wu Di's refutation of such views was too hasty and reckless. Confucius said, "The Yellow River will not produce another chart, so my life is over," indicating that a sage's mandate must be accompanied by auspicious signs. If the Yellow River Chart will not appear again, Confucius would not have sighed and waited for it. Hu Wei remarked: Zhu Zhen's words are indeed correct. However, can all the Yellow River Charts passed down through the ages be considered as the images of hexagrams, and were they all used by sages to compose the Zhou Yi? I have doubts about this and dare not fully accept it.

按：《顧命》東西序之所陳，類皆玩好，唯大訓、河圗為載道之器。《周官》天府總謂之「大寶器」，祭祀陳之，示能守；喪紀陳之，示能傳也。河圗非必伏羲時出，猶鳳鳥不獨舜時來儀。然孔安國注《論語》云「河圗，八卦」，而《書·顧命》傳則直指為伏羲之河圗；姚信亦云伏羲得河圗，周人因之曰《周易》。朱子固有所本，非杜撰也。

Hu Wei said: In the "Gu Ming" passage, the items arranged in the eastern and western sequences are mostly things for appreciation, but "Da Xun" and "He Tu" are vessels that carry the great way. The "Zhou Li" refers to them collectively as "Da Bao Qi", which are displayed during worship to indicate the ability to preserve the ancestral legacy, and displayed during mourning rites to indicate the ability to transmit the way of the former kings. The He Tu did not necessarily appear only in the time of Fuxi, just as the phoenix does not only appear in the time of Shun. However, Kong An Guo's commentary on the "Lun Yu" only says "He Tu is the Eight Trigrams", but when he made a commentary on the "Shang Shu · Gu Ming", he directly pointed out that this is the He Tu obtained by Fuxi. Yao Xin also said that Fuxi obtained the He Tu, and the Zhou people based their "Zhou Yi" upon it. This shows that Zhu Xi's assertion that the He Tu appeared in the time of Fuxi was based on some grounds, and not made up out of nowhere.

但河圗不知載在何物，歴數千年至周而尚存。據《禮運》為馬圗，則《中候》云「龍馬銜甲，甲似龜背，袤廣九尺」，庶幾近之，而其所謂「甲」者，終不知為何物。據曹魏時張掖出石圗有八卦之狀，髙堂隆以比東序之世寶，則河圗當為石類。俞玉吾琰云：「天球，玉也。河圗而與天球並列，葢玉之有文者。」然則赤刀，金也，大訓而與赤刀並列，亦將為金之有文者乎？又有據大訓為簡策以證河圗之亦為簡冊者，則緯書九篇之說不為誕妄矣。

But no one can say for sure what material the River Chart was written on, since it has survived for thousands of years until the Zhou dynasty. If we take the "Horse Figure" mentioned in the "Liyun" as referring to the River Chart, then the description in the "Shangshu Zhonghou" that "a dragon horse with its mouth holding a tortoise shell, which was nine feet in length and breadth" is almost close to the truth. However, it remains unclear what exactly the "tortoise shell" referred to was. If we follow the inference from the stone chart with the Eight Trigrams found in Zhangye during the Cao Wei period, which was compared by Gao Tanglong to the precious treasures kept in the Eastern Hall, then the River Chart should be a stone. Yuan Dynasty's Yu Yan (styled Yuwu) said: the "Heavenly Sphere" was a jade object, and since the River Chart was displayed alongside the Heavenly Sphere, it was probably a piece of jade with patterns. However, following this logic, the "Red Knife" was metal, and since the "Great Instruction" was displayed alongside the Red Knife, would that not mean we should also say the "Great Instruction" was metal with patterns? Others argue that the "Great Instruction" was bamboo slips, so they use this to prove that the River Chart was also bamboo slips. In that case, the claim in the apocryphal texts that the River Chart consisted of nine chapters would not be entirely absurd. All these speculations about the material have their own evidence, but also their own flaws.

紛紛推測，終無定論。然河圗藏諸天府，不知何時遂亡。初意秦昭襄王取周九鼎寶器時，河圗併入於秦，及項羽燒秦宮室，與府庫俱為灰燼，此其所以不傳也。今年客京師，與四明萬君季野斯同論及此事，萬君曰：「幽王被犬戎之難，周室東遷，諸大寶器必亡於此時，河圗無論，後人恐夫子亦不及見。」餘聞而韙之。頃檢《周本紀》云：「犬戎殺幽王驪山下，虜褒姒，盡取周賂而去。」賂即珍寶貨財也，可見河圗實亡於此時。故自平、桓以下，凡《顧命》所陳諸寶器，無一復見於傳記；而王子朝之亂，其所挾以出者，周之寶珪與典籍而已，天府之藏無有也。（寶珪，典瑞所掌；典籍，太史掌之，並非大寶器。）

Various speculations have been made, but there has been no definite conclusion. However, the River Chart was kept in the treasury of the Zhou royal family, and it is unknown when it was lost. At first, I thought it was taken to the state of Qin by King Zhaoxiang of Qin when he seized the nine bronze tripods of the Zhou royal family. Then, when Xiang Yu burned the palaces of the Qin dynasty, the River Chart was destroyed along with the treasury and thus did not pass down to later generations. This year, while I was staying in the capital, I talked with Wan Siting (whose name is Jiyě, a famous historian of the Ming dynasty's history office). He said that when King You of Zhou was killed by the Qiong戎, the Zhou royal family was forced to move east, and all the great treasures must have been lost at that time. As for the River Chart, perhaps even Confucius did not have the chance to see it. I agreed with him. Recently, I checked the "Records of the Grand Historian: Annals of the Zhou Dynasty," which says that the Qiong戎 killed King You of Zhou at Lishan Mountain, took away the Concubine Bao Si, and took all the Zhou royal treasures away. "Lü" refers to precious treasures and goods. This shows that the River Chart was indeed lost at that time. Therefore, since the reign of King Ping of Zhou and King Huan of Zhou, all the treasures listed in the "Gu Ming" have not been mentioned again in historical records. And when Prince Zhaocao rebelled and fled, he only took away the Zhou royal jade and the official documents, but no great treasures were taken. (The royal jade was kept by the official in charge of ceremonial jade, and the official documents were kept by the Grand Historian, and neither of these belonged to the category of "great treasures.")

河圗亡已久，雖老聃、萇弘之徒亦未經目覩，故夫子適周無從訪問，贊《易》有其名而無其義，所謂「疑者丘葢不言」也。若夫天地之數，夫子未嘗指為河圗，故自漢魏以迄隋唐，言河圗者或以為九宮，或以為九篇，未有指五十五數為河圗者。《乾鑿度》《參同契》雖皆以九宮為河圗，而終不敢摹一象名之曰河圗以附於其書。陳摶生於五季，去古彌逺，何從得其本真而繪圗以授人乎？漢景帝云「食肉不食馬肝，未為不知味」，今言《易》而不言河圗，亦未為不知道也。

The Yellow River Chart has been lost for a long time. Even old officials of the Zhou dynasty such as Lao Dan and Chang Hong did not see it with their own eyes, so when Confucius went to the Zhou court, he had no way to inquire about it. When he commented on the Zhou Changes, he only knew the name of the Yellow River Chart but did not understand its actual meaning. This is exactly what he said, "Where there is doubt, I Kong Qiu will leave it unspoken." As for the numbers from one to ten, Confucius never identified them as the Yellow River Chart. Therefore, from the Han and Wei dynasties up to the Sui and Tang dynasties, those who discussed the Yellow River Chart held various views, some thinking it was the Nine Palaces, others thinking it was the nine chapters of a supplementary text. No one ever regarded the number fifty-five as the Yellow River Chart. Although the "Yi Wei Gan Zao Du" and the "Zhou Yi San Tong Qi" both regarded the Nine Palaces as the Yellow River Chart, they never dared to draw an image and title it "Yellow River Chart" and include it in their own works. Chen Tuan lived in the Five Dynasties period, even further away from the ancient times, from where could he have obtained the original form of the Yellow River Chart and drawn a diagram to pass it on to others? Han Jingdi once said, "If you eat meat but do not eat horse's liver, you cannot be said to understand the taste." Today, if you talk about the Zhou Changes without mentioning the Yellow River Chart, it does not mean you do not understand the Way of the Changes. This passage is the key argument of Hu Wei's entire book: the Yellow River Chart had already been lost as a physical object by the late Western Zhou dynasty. Confucius had never seen it. The diagram of fifty-five points is a later development from Chen Tuan's school in the Song dynasty, and is certainly not the ancient Yellow River Chart.

右論古河圗之器。

In the above section, the author examines and discusses the ancient textual references to the Yellow River Chart as a physical object or utensil. This is a heading added by Hu Wei at the end of each section to indicate the scope of the topic covered in that section.

《書·洪範》：箕子乃言曰：「我聞在昔，鯀陻洪水，汨陳其五行。帝乃震怒，不畀洪範九疇，彝倫攸斁。鯀則殛死，禹乃嗣興，天乃錫禹洪範九疇，彝倫攸敘。初一曰五行，次二曰敬用五事，次三曰農用八政，次四曰協用五紀，次五曰建用皇極，次六曰又用三德，次七曰明用稽疑，次八曰念用庶徵，次九曰向用五福、威用六極。」

The Book of Documents, Hongfan section, records that Ji Zi (the uncle of King Zhou of Shang, who was consulted by King Wu of Zhou after the fall of Shang about the principles of state governance) said: I have heard that in the past Gun tried to control the floods by blocking them, which disrupted the order of the Five Phases of water, fire, wood, metal, and earth. Heaven therefore became angry and did not grant Gun the "Nine Categories of the Great Plan" (Hongfan Ji Chou), and the principles of human relationships and moral conduct were thus ruined. Gun was executed, and Da Yu took over to manage the floods. Heaven then gave Da Yu the Nine Categories of the Great Plan, and the principles of human relationships and moral conduct were restored. The first category is the Five Phases, the second is to perform the five duties with reverence and caution, the third is to diligently manage the eight state affairs, the fourth is to coordinate the use of the five celestial markers, the fifth is to establish the supreme standard of the Son of Heaven, the sixth is to govern using the three virtues, the seventh is to use divination to resolve doubts wisely, the eighth is to be attentive to various omens, and the ninth is to encourage virtue through the five blessings and to warn against calamity through the six extremes. This passage is the general summary of the Luo Writing case. Note that it mentions only "Hongfan Ji Chou" throughout and does not use the term "Luo Writing" at all.

孔氏安國曰：「天與禹，洛出書，神龜負文而出，列於背，有數至於九。禹遂因而第之，以成九類常道，所以次敘。」

Kong Anguo's commentary says: Heaven bestowed the Great Yu with the Book of the Great Plan, and the Luo River produced a book. A divine turtle carried the characters on its back, emerging from the water, with the characters arranged on the turtle's back, continuing up to nine. Great Yu then followed the order, forming nine categories of governing principles, thus establishing the order of human relationships. Kong Anguo's commentary was the first to connect the "Heaven bestowed Yu the Nine Categories of the Great Plan" from the Hongfan with the "Luo River produced a book" from the Xici. Later accounts of "a divine turtle carrying a book" all originated from this.

孔氏穎達曰：「《易·繫辭》云『河出圗，洛出書，聖人則之』，九類各有文字，即是書也。《漢書·五行志》劉歆以為『禹治洪水，錫洛書，法而陳之，洪範是也』，先達共為此說。龜負洛書，經無其事，《中候》及諸緯多說黃帝、堯、舜、禹、湯、文、武受圗書之事，皆云龍負圗、龜負書。緯候不知誰作，通人討核，謂偽起哀、平。雖復前漢之末始有此書，以前學者必相傳此說，故孔以九類是神龜負文而出，列於背有數，從一而至於九也。」

Kong Yingda said: The Great Treatise of the Zhou Changes speaks of "the Yellow River produced a map and the Luo River produced a book, and the sage kings took them as models." The nine categories of great principles each have their own characters, which is what is referred to as "the book." The Han Book's Five Phases Chapter records Liu Xin's view that "Yu controlled the great floods, and heaven bestowed upon him the Luo Writing, which Yu explained according to its principles, forming the Hongfan." Previous scholars of great learning all held this view. As for the divine turtle carrying the Luo Writing, there is no mention of this in the classic texts; the Shangshu Zhonghou and various writings of the Warring States period mostly speak of the Yellow Emperor, Yao, Shun, Yu, Tang, King Wen, and King Wu receiving the map and book. They all say that the dragon carried the map and the turtle carried the book. The writings of the Warring States period and the prophecies are unknown to whom they belong, but learned men have examined them and believe they were fabricated during the reigns of Emperor Ai and Emperor Ping of the Han dynasty. However, even if these writings appeared only at the end of the Western Han dynasty, scholars must have passed down this idea before that time, so Kong Anguo concluded that the nine categories were the characters on the turtle's back, emerging and arranged in order from one to nine.

「言『禹第之』者，以天神言語必當簡要，不應曲有次第丁寧若此，故以為禹次第之。又曰『初一』已下至『六極』，傳言此禹所第敘，不知洛書本有幾字。《五行志》悉載此一章，乃云『凡此六十五字皆洛書本文』。計天言簡要，必無次第之數，故孔以『第』是禹之所為，『初一曰』等二十七字必是禹加之也。其『敬用』『農用』等二十八字，大劉及顧氏以為龜背先有，總三十八字；小劉以為『敬用』等亦禹所第敘，其龜文惟有二十字。並無明據，未知孰是，故兩存焉。」（顧氏名彪，大劉名焯，小劉名炫，皆隋人。）

Kong Yingda then said: the reason for mentioning "Yu arranged the order" is that the words of heavenly spirits must be concise, not elaborate or detailed to such an extent. Therefore, it is concluded that the order was arranged by Yu. He also said that from "the first day" down to "the six extremes," Kong's commentary holds that Yu arranged the narration. As for how many characters the Luo Writing originally had, it is unknown. The full text of "The Book of Han · Five Phases Chapter" copied this section and stated, "these sixty-five characters are all the original text of the Luo Writing." However, considering that the words of heaven must be brief, they would not include terms like "first" or "second" indicating sequence. Therefore, Kong Anguo regarded the word "di" (meaning "sequence") as something added by Yu, and the twenty-seven characters starting with "chuyi" (the first day) must have been added by Yu. As for the twenty-eight characters starting with "jingyong" (respectfully used) and "nongyong" (used for farming), the Sui dynasty scholar Liu Zhuo (Big Liu) and Gu Biao believed these characters were originally on the turtle shell, making a total of thirty-eight characters. Liu Xuan (Little Liu), however, believed that the characters starting with "jingyong" were also arranged by Yu, and the original text on the turtle shell only had twenty characters. Neither view has clear evidence, so both are preserved. (Gu's name was Biao, Big Liu's name was Zhuo, and Little Liu's name was Xuan; they were all from the Sui dynasty.)

按：《隋志》云「濟南伏生之傳，唯劉向父子所著《五行傳》是其本法」。歆以洛書為文字，葢亦本伏生。伏生嘗為秦博士，習聞古訓，洛書即九疇，必三代以來相傳之學，非臆說也。天地之文理當簡要，劉炫謂本文惟有二十字，是為得之。

Hu Wei remarked: The "Book of Sui · Catalogue of Literature" says, "The transmission of the Book of Documents by Fu Sheng of Jinan only follows the "Transmission of the Five Phases" written by Liu Xiang and his son." Liu Xin believed that the Luo Writing was a system of characters, which probably originated from Fu Sheng. Fu Sheng served as a Doctor in the Qin dynasty and was familiar with ancient interpretations. He regarded the Luo Writing as the Nine Categories, which must have been the traditional learning passed down since the Xia, Shang, and Zhou dynasties, not an arbitrary invention. The principles and patterns revealed by heaven and earth should be concise. Liu Xuan's assertion that the original text of the Luo Writing consists of only twenty characters is correct.

但孔疏云「天神言語」，世或疑焉，以為如此則頗似崔浩稱寇謙之所受《錄圗真經》「人神接對，手筆粲然」者，事涉妖妄，不可以說經。故林之奇《書傳》云「『帝乃震怒，不畀洪範九疇』猶言天奪之鑑，『天乃錫禹洪範九疇』猶言天誘其衷」，而趙汝楳《易雅》謂「不過如『天錫王勇智』『天錫公純嘏』之類，非真有物負之以錫諸人也」。王褘祖述其意，極論禹無受洛書之事，而據《繫辭傳》以為河圗、洛書皆伏羲所則以作《易》。總由「天神言語」四字有以滋其疑而莫之釋耳。孔子曰：「天何言哉？四時行焉，百物生焉。」孟子曰：「天不言，以行與事示之而已矣。」禹治水得其道，天錫之洛書以昭瑞應，此實「時行物生」「以行與事示之」之理。洛書，文也，非言也，而穎達以為天神之言語，則誣矣。

Kong Yingda's commentary mentions "the words of heavenly spirits," but people have doubts, thinking that this is similar to Cui Hao of the Northern Wei Dynasty's praise of Kuo Qianzhi's receiving the "Record of True Scripture," which claims that humans and spirits converse face to face and write clearly with their own hands. Such ideas are considered absurd and cannot be used to explain the classics. Therefore, Lin Zhiqi of the Southern Song Dynasty's "Complete Explanation of the Book of Documents" says: "Heaven's anger did not give the Nine Categories of the Mandate of Heaven to Gun," which is equivalent to saying that Heaven took away his insight; "Heaven then gave the Nine Categories of the Mandate of Heaven to Yu," which is equivalent to saying that Heaven inspired his mind. Zhao Ru'mei's "Yi Ya" also says that this is no different from statements in the classics such as "Heaven gave the king courage and wisdom" or "Heaven gave the public great blessings," which are not really about something carrying the Nine Categories to give to people. Wang Yi of the Yuan Dynasty inherited this idea and strongly argued that Yu did not receive the Luo Book. Instead, he used the "Great Treatise" to conclude that both the He Tu and the Luo Book were models that Fuxi used to compose the Zhou Yi. These doubts, in the end, all stem from the four words "words of heavenly spirits," yet no one has ever explained them clearly. Confucius said, "What has Heaven said? The four seasons still proceed in order, and all things still grow." Mencius said, "Heaven does not speak; it only shows through its actions and facts." The great Yu governing the waters in accordance with the right way, and Heaven giving him the Luo Book to show a sign of auspicious response, is exactly the meaning of "the four seasons proceeding in order and all things growing" and "showing through actions and facts." The Luo Book is "wen" (meaning), not "yan" (speech). Kong Yingda called it the words of heavenly spirits, which is wrong.

《說文》序云：「倉頡之初作書，葢依類象形，故謂之文；其後形聲相益，即謂之字。字者，言孳乳而浸多也。」然則文與字不同，文之點畫少，字之點畫多。洛書之文，葢與蒼頡初制相類。《左傳》：仲子有文在手，曰「為魯夫人」；成季、唐叔有文在手，曰「友」、曰「虞」。《正義》曰：「石經古文『虞』作□，『魯』作表，手文容或似之。」朱子亦云「古字畫少，恐或有模樣」。觀於此言，可以悟洛書成文之理矣。

The preface of the Shuo Wen Jie Zi says: Cang Jie first created characters by depicting the forms of things according to their categories, so they were called "wen"; later, when radicals and phonetic components were combined, they were called "zi." The meaning of "zi" is that it proliferates like reproduction. Thus, "wen" and "zi" are different: "wen" has fewer strokes, while "zi" has more. The "wen" in the Luo Shu is probably of the same kind as the original "wen" created by Cang Jie. The Zuo Zhuan records that Song Zhongzi was born with a pattern on his hand that formed the characters for "being the wife of Lu"; Duke Cheng Ji of Lu and Duke Tang Shuyu of Jin were also born with patterns on their hands, one forming the character "you" and the other "yu." The commentary says that the ancient text "yu" in the stone classics was written in a certain form, and "lu" in another form, and the patterns on the hands may have resembled these forms. Zhu Xi also said, "Ancient characters had few strokes, and perhaps they really looked like that." By reading these words, one can understand the principle of how the Luo Shu "forms characters."

馬圗見於《禮運》，人不以為怪；龜書見於緯候，世或疑其妄。然天地間耳目之所不及，未可斷以為必無。《魏志》明帝青龍四年，張掖有寶石負圗，狀像靈龜，文字告命，粲然著明；《水經注》引車頻《秦書》，苻堅建元十二年，髙陸縣民穿井得龜，大二尺六寸，背文負八卦古字。物固有然，無足怪者。

The image of a horse appears in the "Book of Rites: The Ritual of the Great Harmony," and people do not find it strange; however, the appearance of turtle scripts in the writings of the Wujing and Houjing schools is regarded by the world as absurd. Yet, things beyond the reach of human eyes and ears in the universe cannot be definitively said to not exist. The "Records of the Three Kingdoms: Wei Ji" records that in the fourth year of Qinglong during the reign of Wei Mingdi, a gemstone with a pattern on its back was found in Zhangye, resembling a spiritual turtle, with characters on it as clear as a heavenly decree; the "Commentary on the Water Classic" cites Che Pin's "Qin Book" that in the twelfth year of Jianyuan during Fu Jian's reign of the Former Qin, a peasant in GaoLu County dug a well and found a turtle two feet six inches long, with ancient characters in the shape of the Eight Trigrams on its back. Such things naturally occur, and there is no need to be overly surprised.

然世風衰薄，間有作偽之事。如三國吳孫晧時，鄱陽歴陵山石文理成字凡二十，乃人以朱書石作之，言天下當太平。（《吳志》：孫晧天璽元年，鄱陽言歴陵山石文理成字凡二十，曰「楚九州島渚，吳九州島都，揚州士，作天子，四世治，太平始」。注：《江表傳》曰：歴陵長上言石印發，晧遣使以太牢祭之。巫言石印三郎說天下方太平。使者作髙梯上看印文，詐以朱書石作二十字，還以啟晧，晧大喜。）

However, in times of declining morals, there were indeed cases of forgery. For example, during the time of Sun Hao, the ruler of Wu in the Three Kingdoms period, there was a stone in Liling Mountain in Pengyang that had a pattern forming twenty characters. In reality, someone had written these characters in vermilion on the stone to fake them, saying that the world was about to become peaceful. (The "Book of the Later Han" records: In the first year of Tianxi, during Sun Hao's reign, Pengyang reported that the stone in Liling Mountain had a pattern forming twenty characters, which read "Chu's nine islands, Wu's nine capitals, the people of Yangzhou will become emperor, the world will be ruled for four generations, and peace will begin." The annotation by Pei Songzhi cites the "Jiangbiao Zhuan," which says that the magistrate of Liling reported "stone printing." Sun Hao sent envoys to perform a sacrificial ceremony with the grand offering. The witch said that the stone printing was a sign that the heavens were declaring the world would soon be peaceful. The envoys set up a high ladder to examine the inscription, secretly writing the twenty characters in vermilion on the stone, and then reported back to Sun Hao, who was greatly pleased.)

臨朝，武承嗣使鑿白石為文凡八字以獻，稱獲之於洛水，太后命其石曰「寶圗」。（《通鑑》：唐垂拱元年，武承嗣使鑿白石為文，曰「聖母臨人，永昌帝業」，末紫石雜藥物填之，使雍州人唐同泰奉表以獻，稱獲之於洛水。太后喜，命其石曰「寶圗」，尋更命為「天授聖圗」。十二月己酉，太后拜洛受圗。）

For example, when Wu Zetian was ruling the country as empress regnant, Wu Chengsi had people carve eight characters on a white stone and present it to her, falsely claiming that it was obtained from the Luo River. The empress named this stone "Baotu" (Precious Map). (The Zizhi Tongjian records: In the first year of Taichang during the Tang dynasty, Wu Chengsi had people carve the eight characters "Shengmu Linren, Yongchang Diyeye" (The Holy Mother governs the people, the imperial cause will be eternal) on a white stone. The carving was finished with purple stone mixed with medicinal substances to fill in the gaps. He sent Yongzhou's Tang Tongtai to present it with a memorial, claiming that it was obtained from the Luo River. The empress was greatly pleased and named this stone "Baotu" (Precious Map). Soon after, she changed its name to "Tianshu Shengtu" (Heavenly Granting Sacred Map). On the twelfth day of the twelfth lunar month in that year, the empress personally went to the Luo River to receive the map.) Note: The text originally had "Linchao" (taking the throne) with the subject "Tang Wuhou" (Wu Zetian), but this has been omitted in the current edition.

林少穎、趙汝楳、王子充有見於此類，故深斥洛書。然以末世之偽而疑上古之真，不可也。《東都事略·杜鎬傳》：王欽若勸真宗為祥瑞以鎮服四夷，真宗疑焉，因問鎬「河出圗，洛出書，果何事」，鎬遽對曰：「此聖人以神道設敎耳。」真宗意遂決。是猶曹丕簒漢而以為舜、禹之事當亦如此也。鎬之言，不惟成君之惡，且大得罪於聖人矣。

Lin Zhiqi (style name Shaoying), Zhao Rumei, and Wang Yi (style name Zichong) clearly recognized this kind of forgery, so they strongly opposed the Luo Writing. However, using forgeries from the late period to doubt authentic ancient relics is not acceptable. The "Eastern Capital Affairs" records that Wang Qinruo advised Emperor Zhenzong of the Song Dynasty to create omens to intimidate the world. Zhenzong hesitated, and thus asked Du Hao, "What really happened with the river producing a map and the Luo producing a writing?" Du Hao immediately replied, "This is merely the sages using divine ways to carry out education." Zhenzong then decided to create omens. This is like Cao Pi's usurpation of the Han dynasty, yet he still claimed that the abdication of Shun and Yu was done in the same way. Du Hao's words not only helped the ruler commit evil deeds, but also greatly offended the sages.

《仲氏易》曰：「考禹治河所得，名為洪範九疇，不名洛書。觀《書》云『天乃錫禹洪範九疇』，並不及洛書，可驗也。若云天所錫者洛書，禹因而衍之，始名洪範九疇，則《書》又云『天不畀鯀洪範九疇』，是以禹所更定之名而天反豫竊之也，可乎？」

In the early Qing dynasty, Mao Qiling in his work "Zhong Shi Yi" said: examining the things obtained by Da Yu in governing the river, they are called "Hong Fan Ji Chou," not "Luo Shu." The Book of Documents says, "Heaven then bestowed upon Yu the Hong Fan Ji Chou," entirely without mentioning Luo Shu. This can be verified. If it were said that what Heaven bestowed was originally Luo Shu, and Yu deduced from it and then named it Hong Fan Ji Chou, then the Book of Documents also says, "Heaven did not give the Hong Fan Ji Chou to Gun," which would mean that Heaven preemptively used the name that Yu later established. Is this a coherent explanation?

渭按：《洪範》者，《尚書》之篇名也。《書序》云「武王勝殷，以箕子歸，作《洪範》」，是《洪範》乃箕子之所命，以其為治天下之大法，故謂之《洪範》。其「九疇」則大禹所命，亦猶包犧之八卦耳。羲皇受河圗而始作八卦，文王演之，其書名《易》，不名《河圗》；大禹第洛書為九疇，箕子演之，其書名《洪範》，不名《洛書》，其義一也。

Hu Wei said: The "Hongfan" is the title of a chapter in the "Shangshu". The "Shu Xü" says, "King Wu defeated the Shang dynasty and brought back Ji Zi, who composed the "Hongfan"." This shows that the name "Hongfan" was given by Ji Zi, because it is the great law for governing the world, hence called "Hongfan". As for the term "jiu chou", it was established by the Great Yu, just as the name "Ba Gu" was given by Fuxi. Fuxi received the Yellow River Chart and began to draw the Eight Trigrams, and King Wen further developed it, and the book was called "Zhou Yi", not "He Tu". Similarly, Great Yu arranged the Luo Writing into the nine categories, and Ji Zi further developed it, and the book was called "Hongfan", not "Luo Shu". The reasoning behind these two matters is exactly the same. Mao Qilin used the fact that the term "Luo Shu" does not appear in the text of the classic to deny the existence of the Luo Writing, which is confusing the name of the book with the original object.

葢河圗、洛書乃《易》《洪範》所由作，非即《易》《洪範》也。以彖、爻無河圗之文而疑八卦非感河圗而作，以《洪範》無洛書之文而疑九疇非法洛書而陳，然則夫子所謂「聖人則之」者，果何所則而何所作邪？至於「天不畀鯀洪範九疇」而「錫禹洪範九疇」，此箕子追序之辭，謂鯀失治水之道，天不錫之以洛書；禹得治水之道，天乃錫之以洛書耳。而顧以辭害意，謂禹所更定之名而天反豫竊之也，不已戲乎！

To know that the Yellow River Chart and the Luo Writing are the sources from which the Zhou Changes and the Hongfan were derived, not equivalent to the Zhou Changes and Hongfan themselves. If one doubts that the Eight Trigrams were inspired by the Yellow River Chart merely because the hexagram statements and line statements do not contain the word 'Yellow River Chart'; or doubts that the nine categories of Hongfan were based on the Luo Writing merely because the Hongfan does not contain the word 'Luo Writing', then what exactly did Confucius mean by 'sages took them as models'? What exactly did they produce? As for the statement that 'Heaven did not give the Hongfan nine categories to Gun, but gave them to Yu', this is a way of speaking used by Ji Zi when recounting events later. It means that Gun lost the way of water control, so Heaven did not give him the Luo Writing; Yu mastered the way of water control, so Heaven gave him the Luo Writing. Ma Qilin, however, clung to the literal wording and obstructed the true meaning, interpreting it as if Heaven had preemptively used the name that Yu later revised. Is this not too childish?

總之，河圗、洛書特推原當時《易》《範》所由作。今欲明《易》，八卦具在，焉用河圗？欲明《範》，九章具在，焉用洛書？宋人崇尚圗書，自以為補苴罅漏，張皇幽渺，若非此則無以明《易》《範》，遂成千古笑柄。然「河圗洛書」三語實出於夫子，又不可如歐公軰斥之以妖妄，故不得不一核其源流。

In summary, the Yellow River Chart and the Luo Writing are merely attempts to trace the origins of the Zhou Changes and the Hong Fan. Today, if we want to understand the Zhou Changes, the Eight Trigrams are available, so why use the Yellow River Chart? If we want to understand the Hong Fan, the nine chapters are available, so why use the Luo Writing? The Song dynasty scholars praised the study of these charts, believing they were filling in the gaps of the classics and revealing profound and mysterious meanings. They seemed to think that without them, the Zhou Changes and the Hong Fan could not be properly explained. In the end, however, their approach became a subject of ridicule throughout history. Nevertheless, the statement "the river produced the chart, the Luo produced the writing, and the sage followed them" is indeed attributed to Confucius. We cannot simply dismiss it as superstition as Ouyang Xiu and his contemporaries did. Therefore, we must thoroughly examine its origins. This is precisely Hu Wei's position: he does not believe in the charts favored by the Song scholars, yet he does not discard Confucius's words.

侏儒問天髙於修人，修人曰「不知」。侏儒曰：「子雖不知，猶近於我。」孔安國、劉歆，修人也；陳摶、劉牧，侏儒也。天髙幾許，豈修人所能知？然必無修人不知而侏儒反知之理。況修人所言畧有端倪，而侏儒所言無非夢囈，又安得不舍侏儒而從修人邪！

There is an analogy: a short man asks a tall man how high the sky is, and the tall man says "I don't know." The short man replies, "Although you don't know, you are closer to the sky than I am." Kong Anguo and Liu Xin are the tall man, while Chen Tuan and Liu Mu are the short man. How high the sky is is something even the tall man cannot know. But there is no way that the tall man, who doesn't know, could be right while the short man, who does know, is wrong. Moreover, what the tall man says has some clue, while what the short man says is all nonsense. How could one abandon the short man and follow the tall man?

右論古洛書之文。

In the previous section, the discussion examines the textual form of the Luo Writing as found in ancient texts. This is the heading added by Hu Wei for this section.

《書·洪範》曰：「一、五行：一曰水，二曰火，三曰木，四曰金，五曰土。」

The Shangshu · Hongfan says: The first of the nine categories is "Wuxing" — the first is water, the second is fire, the third is wood, the fourth is metal, and the fifth is earth. This is the earliest occurrence of the term "Wuxing" and its fixed order in the classic texts. All later discussions about "Wuxing shengshu, chengshu" (generative and completed numbers of the Five Phases) originated from these five numbers. Therefore, Hu Wei began his study of the divination classics by examining this.

《正義》曰：「萬物成形，以微著為漸；五行先後，亦以微著為次。水最微為一，火漸著為二，木形實為三，金體固為四，土質大為五。」

Kong Yingda explains in his "Shangshu Zhenyi" that the order is based on the gradual development from subtle to prominent. The Five Phases are arranged in the same way. Water is the most subtle, so it comes first; fire is somewhat more prominent, so it comes second; wood has a substantial form, so it comes third; metal has a firm body, so it comes fourth; and earth has a thick and vast quality, so it comes fifth. This sequence refers to the weight and substance of forms, and has nothing to do with the so-called "shengshu" and "chengshu."

按：五行之名肇見於《洪範》，其一二三四五以微著輕重為次，自氣而形而質具在其中，未見此但為生數而必待六七八九十以成之也。《易》有四象而無五行，此與天地、大衍之數絶無交涉。

Hu Wei said: The term "Five Phases" first appears in "Hong Fan." Its first, second, third, fourth, and fifth are arranged in order from subtle to manifest, from light to heavy, covering from qi to form and then to substance. Therefore, these five numbers are not merely so-called "generative numbers," and it is not necessary to wait until six, seven, eight, nine, and ten to "complete" them. The "Zhou Yi" only includes four images: Taiyang, Taiyin, Shaoyang, and Shaoyin, and does not include the Five Phases. Therefore, the Five Phases numbers in "Hong Fan" have nothing to do with the "Heaven and Earth numbers" (one to ten) and the "Great Derivation numbers" (fifty) in the "Xici." This point is the first foundation for Hu Wei to refute the Song dynasty's theory of the Yellow River Chart with fifty-five points.

右論古五行之序。

The previous section examines the original meaning of the order of the Five Phases in ancient times.

《漢書·五行志》：《左氏傳》鄭裨灶曰「火，水妃也，妃以五成」（妃音配，或讀如字）。說曰：「天以一生水，地以二生火，天以三生木，地以四生金，天以五生土。五位皆以五而合，而陰陽易位，故曰『妃以五成』。然則水之大數六，火七，木八，金九，土十。故水以天一為火二牡，木以天三為土十牡，土以天五為水六牡，火以天七為金四牡，金以天九為木八牡。陽奇為牡，陰耦為妃，故曰『水，火之牡也』（左傳魯梓慎語），『火，水妃也』。於《易》，坎為水、為中男，離為火、為中女，葢取諸此也。」

The Han Shu's "Five Phases" section cites a statement from the Zuo Zhuan, in which the Zheng state official Bi Zao says: Fire is the spouse of water, and spouses are matched by "five." ("Fei" is read as "pei," but some read it as the original character.) The "Five Phases" section explains further: Heaven produces water with one, Earth produces fire with two, Heaven produces wood with three, Earth produces metal with four, and Heaven produces earth with five. These five directions must all be combined with "five" to be compatible, and after compatibility, yin and yang switch positions, so it is said that "spouses are matched by five." Thus, the number of water is six, fire is seven, wood is eight, metal is nine, and earth is ten. Therefore, water takes Tian Yi (Heaven One) as the "mu" (male) of Fire Two, wood takes Tian San (Heaven Three) as the "mu" of Earth Ten, earth takes Tian Wu (Heaven Five) as the "mu" of Water Six, fire takes Tian Qi (Heaven Seven) as the "mu" of Metal Four, and metal takes Tian Jiū (Heaven Nine) as the "mu" of Wood Eight. Odd numbers are "mu" (male) for yang, and even numbers are "fei" (female) for yin. Therefore, the Zuo Zhuan says "water is the male of fire" (this is the statement of Lu state official Zi Chen), and "fire is the female of water." In the Zhou Yi, Kan represents water and is the middle male, Li represents fire and is the middle female, which is derived from this meaning.

白雲郭氏雍曰：「《漢志》言『天以一生水，地以二生火，天以三生木，地以四生金，天以五生土』，故或謂天一至天五為五行生數，地六至地十為五行成數。雖有此五行之說，而於《易》無所見，故五行之說出於歴數之學，非《易》之道也。」

In the Southern Song dynasty, Guo Yong (also known as Master Baiyun, author of "Guo Shi Chuanjia Yishuo") said: The "Wu Xing Zhi" section of the "Hanshu" states, "Heaven produces water with one, Earth produces fire with two, Heaven produces wood with three, Earth produces metal with four, and Heaven produces earth with five." Therefore, some refer to the numbers from heaven one to heaven five as the "sheng shu" (generative numbers) of the Five Phases, and the numbers from earth six to earth ten as the "cheng shu" (completed numbers) of the Five Phases. Although there is this theory of the Five Phases, it is nowhere to be found in the "Zhou Yi." This shows that the theory of the Five Phases comes from the system of calendar calculations, and is not part of the principles of the "Yi."

梨洲黃氏宗羲《象數論》曰：「世之言五行者，莫不本於生成之數，皆以為造化之自然，無容複議也。某則以九流之失，由此數失之於始。夫太虛絪縕相感，止有一氣，無所謂天氣也，無所謂地氣也。自其清通而不可見，則謂之天；自其凝滯而有形象，則謂之地。故曰『資始』『資生』，又曰『天施地生』，言天倡而不和，地和而不倡。今所謂『生』者倡也，所謂『成』者和也。一三五，天之生數；六八十，地之成數；二四，地之生數；七九，天之成數。是天倡而復和，地和而復倡，真若太虛之申兩氣並行，天氣、地氣其為物貳矣。

In the Ming and Qing dynasties, Huang Zongxi, who was known as Li Zhuo, wrote in his work "Yixue Xiangshu Lun" that those who talk about the Five Phases all take "the generating numbers and the completed numbers" as the fundamental principles, believing that this is the natural order of creation, and that there is no room for objection. I, however, believe that the errors of the nine schools of thought originated from the very beginning of this system of numbers. In the state of Tai Xu, the two energies intertwine and interact, and there is only one kind of energy, not two separate energies called "heavenly energy" and "earthly energy." When referring to its clear, empty, and unobstructed aspect, it is called heaven; when referring to its condensed, obstructed, and tangible aspect, it is called earth. Therefore, the Book of Changes speaks of "Qian provides the beginning, Kun provides the growth," and also says "heaven spreads, earth produces," meaning that heaven only initiates and does not respond, while earth only responds and does not initiate. Now, what is called "sheng" (growth) is actually initiation, and what is called "cheng" (completion) is actually response. The numbers one, three, and five are the generating numbers of heaven, while six, eight, and ten are the completed numbers of earth. The numbers two and four become the generating numbers of earth, and the numbers seven and nine become the generating numbers of heaven. In this way, heaven both initiates and responds, and earth both responds and initiates, which is like two kinds of energy emerging from Tai Xu, existing side by side, and treating heavenly energy and earthly energy as two separate things.

是故一氣之流行，無時而息。溫之殺而涼為秋，是金之行；涼之至而寒為冬，是水之行；寒之殺則又和。木火金水之化生萬物，其凝之之性即土。葢木火金水土，目雖五而氣則一，皆天也；其成形而為萬物，皆地也。若以水木土天之所生，火金地之所生，則春冬屬天，夏秋屬地，五行各有分屬，一氣循環，忽截而為天，忽截而為地，恐無此法象矣。

Therefore, this qi flows without ceasing. As warmth gradually fades and turns cool, it becomes autumn, which is the movement of metal; as coolness reaches its extreme and turns cold, it becomes winter, which is the movement of water; as coldness gradually fades and returns to mildness, it becomes spring. Wood, fire, metal, and water generate and nurture all things, while the nature that causes things to take form is earth. Thus, although the names of wood, fire, metal, water, and earth are five, the qi is one, belonging to heaven; when they take form and generate myriad things, they belong to earth. If we say that water, wood, and earth are born from heaven, and fire and metal are born from earth, then spring and winter belong to heaven, while summer and autumn belong to earth. The five phases each have their own domain. Yet this single qi circulates endlessly, yet is suddenly divided into heaven and suddenly divided into earth. There is probably no such phenomenon in the universe of heaven and earth.

原其『一水二火三木四金五土』，不過以質之輕重為數之多寡，第之先後，故土重於金，金重於木，木重於火，火重於水。然方其為氣，豈有輕重之可言？未聞涼重於溫、寒重於和也。則知天一至地十之數，於五行無與矣。是故言五行天生地成可也，言地生天成不可也；言奇數屬天、偶數屬地可也，言某行屬奇數、某行屬偶數不可也。此千古不解之惑，儒者不免，況於術數家乎！」

Tracing back the original meaning of "one water, two fire, three wood, four metal, five earth," it is merely determining the number of each based on the weight of their physical forms and arranging them in order. Therefore, earth is heavier than metal, metal heavier than wood, wood heavier than fire, and fire heavier than water. However, when they are still in the form of qi, how can there be a question of heaviness or lightness? There is no mention of cool qi being heavier than warm qi or cold qi heavier than mild qi. From this we can see that the system of heavenly one to earthly ten has nothing to do with the Five Phases. Therefore, saying that the Five Phases originate from heaven and are formed by earth is acceptable; but saying that some originate from earth and are formed by heaven is not acceptable. Saying that odd numbers belong to heaven and even numbers to earth is acceptable; but saying that a particular phase belongs to an odd number or an even number is not acceptable. This has been a confusion for thousands of years, even the Confucian scholars cannot avoid it, let alone those who practice numerology!

按：《大傳》曰「在天成象，在地成形」，又曰「乾知大始，坤作成物」，又曰「成象之謂乾，效法之謂坤」，然則氣象皆在天，形質皆在地。地道無成而代有終，五行無地生天成之理也。梨洲之言，可謂明且清矣。

Hu Wei remarked: The Great Treatise says, "In heaven it becomes an image; in the earth it becomes a form." It also says, "The Qian trigram governs the beginning of all things, while the Kun trigram is responsible for shaping them." Furthermore, it states, "That which manifests an image is called Qian, and that which follows and takes shape is called Kun." From this, it appears that qi and images belong to heaven, while forms and substance belong to the earth. The Wenyan commentary on the Kun hexagram explains that the way of the earth does not claim credit for success, but merely completes the final stage on behalf of heaven. Therefore, there is no such thing as the five phases being produced by the earth and completed by the heaven. Huang Zongxi's remarks can be said to be both clear and thorough.

《禮記·月令》孟春之月曰「天氣下降，地氣上騰，天地和同，草木萌動」，孟冬之月曰「天氣上騰，地氣下降，天地不通，閉塞而成冬」，是固有天氣、地氣之說矣。然地氣即向之所受於天而藏焉者也，以其在地，因謂之地氣，猶臣子受君父之賜予以為己有，不可謂其物本吾之所有也。故朱子謂「地二而虛，所以其中容得天許多氣」，豈天氣之外別有所為地氣哉！《孔子閒居》謂子夏曰「地載神氣，神氣風霆，風霆流行，庶物露生」，其所謂神氣，即天之氣也。況太虛之中、絪縕之始，安得地氣與天氣並行邪？

The *Book of Rites: Monthly Ordinances* describes the first month of spring as "the heavenly qi descends, the earthly qi ascends, heaven and earth interact harmoniously, and grass and trees begin to sprout," and the first month of winter as "the heavenly qi ascends, the earthly qi descends, heaven and earth are not connected, and thus become closed and blocked, forming winter." This indeed mentions the concept of "heavenly qi" and "earthly qi." However, the so-called earthly qi is originally the qi received from heaven and stored within the earth. Since it resides in the earth, it is called earthly qi. This is like a minister receiving a reward from the sovereign and father, treating it as his own, yet he cannot claim that the reward originally belonged to him. Therefore, Zhu Xi said, "The earth is divided into two parts with the middle being empty, so it can contain a great amount of heavenly qi." How could there be a separate kind of qi called earthly qi outside of heavenly qi? In *Book of Rites: Confucius in Retirement*, Confucius told Zi Xia, "The earth carries the divine qi, which transforms into wind and thunder. Wind and thunder spread throughout, and all things become visible and are born." The "divine qi" mentioned here is the qi of heaven. Moreover, in the initial state of the great void and the mingling of qi, how could there be both heavenly and earthly qi existing together?

《左傳》昭九年裨灶曰「火，水妃也，妃以五成」，注云「火畏水，故謂之妃。妃，合也。五行各相妃合，得五而成」。疏云：「陰陽之書有五行妃合之說：甲乙木也，丙丁火也，戊巳土也，庚辛金也，壬癸水也。木克土，土克水，水克火，火克金，金克木。木畏金，以乙為庚妃也；金畏火，以辛為丙妃也；火畏水，以丁為壬妃也；水畏土，以癸為戊妃也；土畏木，以己為甲妃也。」杜用此說，故云「火畏水，故為之妃」。

The *Zuo Zhuan* records in the ninth year of Duke Zhao that Bi Zhao said, "Fire is the spouse of water, and spouses are matched through the five elements." Du Yu's annotation explains, "Fire fears water, so it is called the spouse of water. 'Fēi' means to match. The five elements each combine with one another, and they require the number 'five' to be matched." Kong Yingda's commentary explains that the school of yin and yang has a theory about the combination of the five elements—Jia and Yi belong to wood, Bing and Ding to fire, Wu and Ji to earth, Geng and Xin to metal, and Ren and Gui to water. Wood overcomes earth, earth overcomes water, water overcomes fire, fire overcomes metal, and metal overcomes wood. Wood fears metal, so Yi is paired with Geng; metal fears fire, so Xin is paired with Bing; fire fears water, so Ding is paired with Ren; water fears earth, so Gui is paired with Wu; and earth fears wood, so Ji is paired with Jia. Du Yu used exactly this theory, hence saying, "Fire fears water, so it becomes its spouse."

十八年梓慎曰「水，火之牡也」，注云「牡，雄也」。疏云：「陰陽之書有五行嫁娶之法：火畏水，故以丁為壬妃，是水為火之雄。」今按此文，則水妃火牡，辭雖不同，理實一致。陰陽家五行嫁娶之法，取十於妃合為義：甲與己合，乙與庚合，丙與辛合，丁與壬合，戊與癸合，是為「妃以五成」。此皆陰陽家言，與《易》道本不相謀，而《漢志》以天一地二之數釋「火牡水妃」之義，又證之於卦，以坎為火牡、離為水妃，是則然矣。獨不思乾兊之金、坤艮之土、震巽之木，將孰為牡而孰為妃邪？豈乾兊之金可以牡震巽之木，震巽之木可以牡坤艮之土邪？就其言推之，己有不可得通者，而後之人顧猶據以為洛書，爭以為河圗，真不足當劍首之一吷矣。

In the eighteenth year of Duke Zhao's reign, Zi Chen said, "Water is the male of fire." Du Yu's annotation explained, "Male means the male." Kong's commentary explained further: In the books of the School of Yin and Yang, there is a method of marriage among the Five Phases. Fire fears water, so they take Ding as the spouse of Ren, which is why water is considered the male of fire. Now looking at these two statements, one says "water is the wife of fire's male," and the other says "fire is the wife of water's male." Although the wording is different, the meaning is essentially the same. The method of marriage among the Five Phases according to the School of Yin and Yang is based on the pairing of the ten heavenly stems: Jia pairs with Ji, Yi with Geng, Bing with Xin, Ding with Ren, and Wu with Gui. Two stems separated by five positions are considered a pair, which is called "spouses are formed by the five." All of this is the view of the School of Yin and Yang, and has nothing to do with the Way of the Zhou Changes. However, the "Five Elements" section of the "Book of Han" uses the system of Tian Yi and Di Er (Heaven One and Earth Two) to explain the meaning of "fire's male and water's wife," and then uses hexagrams to verify it, taking Kan as fire's male and Li as water's wife, which seems to make sense. But he never considers: Qian and Dui belong to metal, Kun and Gen belong to earth, Zhen and Xun belong to wood. So who is the male and who is the wife among them? Can metal from Qian and Dui be the male of wood from Zhen and Xun, and wood from Zhen and Xun be the male of earth from Kun and Gen? Following his reasoning further, it already makes no sense, yet later people still take it as the Luo Writing and compete to claim it as the Yellow River Chart. It is truly not worth the effort to pay attention to it.

鄭氏《易注》曰：「天地之氣各有五。五行之次，一曰水，天數也；二曰火，地數也；三曰木，天數也；四曰金，地數也；五曰土，天數也。此五者，陰無匹，陽無耦，故又合之：地六為天一匹也，天七為地二耦也，地八為天三匹也，天九為地四耦也，地十為天五匹也。二五陰陽各有合，然後氣相得施化行也。」（注「五位」。）

In the Han dynasty, Zheng Xuan's commentary on the Zhou Yi says: The energies of heaven and earth each have five elements. The order of the Five Phases is first water, which belongs to the heavenly numbers; second fire, which belongs to the earthly numbers; third wood, which belongs to the heavenly numbers; fourth metal, which belongs to the earthly numbers; and fifth earth, which belongs to the heavenly numbers. These five numbers, the yin ones have no counterparts, and the yang ones have no pairs, so they are each given a counterpart: the earthly six becomes the counterpart of the heavenly one, the heavenly seven becomes the pair of the earthly two, the earthly eight becomes the counterpart of the heavenly three, the heavenly nine becomes the pair of the earthly four, and the earthly ten becomes the counterpart of the heavenly five. With these two groups of five numbers, yin and yang are matched, and then the energies can harmonize, and generation and transformation can proceed. (This is Zheng Xuan's commentary on the Great Treatise's statement: "The five positions are in mutual accord and each has a corresponding element.")

又曰：「凡五行減五，大衍又減一，故四十九也。天一生水於北，地二生火於南，天三生木於東，地四生金於西，天五生土於中，陽無耦，陰無配，未得相成。地六成水於北，與天一併；天七成火於南，與地二並；地八成木於東，與天三並；天九成金於西，與地四並；地十成土於中，與天五並也。」（注「大衍」。）

Zheng Xuan also said: The number of the Five Phases is fifty-five, subtract five, so the great derivation number is fifty, then subtract one more, thus using forty-nine stalks of yarrow. Heaven One is in the north and produces water, Earth Two is in the south and produces fire, Heaven Three is in the east and produces wood, Earth Four is in the west and produces metal, Heaven Five is in the center and produces earth; at this time, the yang numbers have no counterparts, and the yin numbers have no partners, so they cannot achieve each other. Therefore, Earth Six in the north completes water and combines with Heaven One; Heaven Seven in the south completes fire and combines with Earth Two; Earth Eight in the east completes wood and combines with Heaven Three; Heaven Nine in the west completes metal and combines with Earth Four; Earth Ten in the center completes earth and combines with Heaven Five. (This is Zheng Xuan's commentary on the sentence "the great derivation number is fifty" in the Great Treatise.)

按：《漢志》說本劉歆《洪範五行傳》，但據天一至地十之數以釋《左氏》水妃火牡之文，初不為《易》而設，亦未有五方之位也。自康成取以注《易》，而七八九六為《易》之四象，水北火南木東金西土中，一生一成各為配耦（亦是配以五成，然但取生成，不取克畏，與《漢志》小異），雖未寫以為圗而圗已具，此與揚子《玄圗》皆偽《闗易》、河圗之粉本也。

Hu Wei said: The approach in the "Five Elements Chapter" of the "Book of Han" is based on Liu Xinxin's "Transmission of the Five Elements in the Hongfan," which used the numbers from heavenly one to earthly ten to explain the passage "water is the female and fire is the male" in the "Zuo Zhuan." Originally, this was not intended for the "Zhou Yi," and it had not yet been associated with the five cardinal directions of southeast, northwest, and the center. Since Zheng Xuan adopted this approach to annotate the "Zhou Yi," the numbers seven, eight, nine, and six became the four trigrams of the "Zhou Yi." Water is located in the north, fire in the south, wood in the east, metal in the west, and earth in the center. A generating number is paired with a forming number (this is also called "matching with five forms," but Zheng Xuan only took the generating and forming relationships, not the mutual control and mutual fear, which is slightly different from the "Book of Han" approach). Although Zheng Xuan did not draw a diagram, the structure of the diagram was already complete. This Zheng annotation, combined with Yang Xiong's "Xuan Tu," became the basis for the later false "Guanglang Yi Zhuan" and the Song dynasty's so-called "He Tu." This was a crucial link in Hu Wei's investigation into the origin of the Song dynasty's diagram.

《禮記·月令》：孟春之月，其日甲乙，其數八，立春盛德在木，迎春於東郊；孟夏之月，其日丙丁，其數七，立夏盛德在火，迎夏於南郊；季夏之月中央土，其日戊巳，其數五；孟秋之月，其日庚辛，其數九，立秋盛德在金，迎秋於西郊；孟冬之月，其日壬癸，其數六，立冬盛德在水，迎冬於北郊。

The Li Ji · Yue Ling records that in the first month of spring, the heavenly stems paired are Jia and Yi, and the number associated is eight. On the day of Beginning of Spring, the virtue of the season is in wood, and the Son of Heaven goes to the eastern outskirts to perform the ceremony of welcoming spring. In the first month of summer, the heavenly stems paired are Bing and Ding, and the number associated is seven. On the day of Beginning of Summer, the virtue of the season is in fire, and the Son of Heaven goes to the southern outskirts to perform the ceremony of welcoming summer. In the middle of summer, the season belongs to the central earth, the heavenly stems paired are Wu and Ji, and the number associated is five. In the first month of autumn, the heavenly stems paired are Geng and Xin, and the number associated is nine. On the day of Beginning of Autumn, the virtue of the season is in metal, and the Son of Heaven goes to the western outskirts to perform the ceremony of welcoming autumn. In the first month of winter, the heavenly stems paired are Ren and Gui, and the number associated is six. On the day of Beginning of Winter, the virtue of the season is in water, and the Son of Heaven goes to the northern outskirts to perform the ceremony of welcoming winter.

按：《月令》，呂不韋作也，而東木之數八，南火之數七，中土之數五，西金之數九，北水之數六，則似戰國時已有以天地之數附會於《洪範》而為五行生成之說者矣，不待劉歆、班固也。其於木火金水皆以成數言之，而土則獨言生數者，葢舉五以例其餘，以見六七八九之尚有一二三四也。

Hu Wei remarked: The "Monthly Orders" was compiled by Li Si, the chancellor of the Qin dynasty. In it, the number for the East (Wood) is eight, the number for the South (Fire) is seven, the number for the Center (Earth) is five, the number for the West (Metal) is nine, and the number for the North (Water) is six. This shows that during the Warring States period, someone had already connected the heavenly and earthly numbers from the Great Treatise with the Five Phases in the "Hóng Fàn," creating the concept of "originative numbers" and "completed numbers." This was not something that had to wait until Liu Xin and Ban Gu. It used the completed numbers for Wood, Fire, Metal, and Water, but used the originative number for Earth. Perhaps this was to use the number five as a model to infer the others, so that people could see that the numbers six, seven, eight, and nine still contained one, two, three, and four within them.

且一乘五即為六，二乘五即為七，三乘五即為八，四乘五即為九，五者六七八九之所由成也；六除五即為一，七除五即為二，八除五即為三，九除五即為四，六七八九者又一二三四之所藏也；五乘五即為十，十除五即為五，其數互相備，雖不言十而十在其中矣。鄭康成以木火金水為四象，實本於此。唐仲友《經世圗譜》云「《月令》，河圗之數也，故土藏十」，此據劉牧之《龍圗》而為言耳。然《龍圗》九宮之數也，南九西七，而《月令》以七居南、以九居西，則固與九宮易位矣。以是知不韋所言乃五行生成之數，非明堂九室縱橫十五之數也。（中央言五不言十，與《玄圗》同。）

Moreover, adding one to five gives six, two to five gives seven, three to five gives eight, and four to five gives nine, showing that the number five is the key to the generation of six, seven, eight, and nine. Subtracting five from six gives one, from seven gives two, from eight gives three, and from nine gives four, showing that within six, seven, eight, and nine there are also one, two, three, and four. Adding five to five gives ten, and subtracting five from ten brings it back to five. These numbers contain each other. Although the "Monthly Orders" does not mention ten, ten is actually included within it. Zheng Kangcheng paired wood, fire, metal, and water as the four images, which is based on this principle. The Southern Song scholar Tang Zhongyou in his "Classic World Diagram" said, "The numbers used in the 'Monthly Orders' are those of the Yellow River Chart, so ten is hidden within the earth," which is merely based on Liu Mu's "Dragon Chart." However, the "Dragon Chart" uses the numbers of the nine-square grid, with nine in the south and seven in the west. The "Monthly Orders," on the other hand, places seven in the south and nine in the west, thus reversing the directions of the nine-square grid. From this we can see that what Lu Buwei spoke of was the numbers of the generation of the Five Phases, not the numbers of the nine chambers of the Bright Hall, which are based on the principle that the sum of the numbers in each row and column is fifteen. (The "Monthly Orders" mentions only five in the center and not ten, which is the same as Yang Xiong's "Mysterious Diagram.")

揚子雄《太玄·玄圗》篇曰：「一與六共宗（范望解云：在北方也），二與七為朋（在南方也），三與八成友（在東方也），四與九同道（在西方也），五與五相守（在中央也）。」

In the Western Han dynasty, Yang Xiong's "Classic of Supreme Mystery · Diagram of Supreme Mystery" states: "One and six share the same origin (as explained by the third-century Wu scholar Fan Wang, referring to the north), two and seven are friends (in the south), three and eight are companions (in the east), four and nine travel together (in the west), and five and five remain together (in the center). These four sentences are precisely the textual origin of the later Song dynasty concept of the "Yellow River Chart" regarding the arrangement of black and white dots. Hu Wei will later prove that the Song dynasty diagram was derived from this source."

張子曰：「天下之數止於十，窮則自十而反一。又數當止於九，其言十者，九之耦也。揚雄亦曰『五復守於五』者，葢地數無過天數之理，孰有地大於天乎？故知數止於九，九是陽極也；十也者，姑為五之耦焉耳。」

Zhang Zai of the Northern Song dynasty said: The numbers in the world end at ten, and when they reach the end, they return from ten back to one. Moreover, numbers should actually end at nine; the reason for mentioning ten is merely to pair it with nine. Yang Xiong also said, "Five remains with five," because there is no reason for the numbers of earth to exceed those of heaven -- how could the earth be larger than the heavens? Therefore, it is known that numbers end at nine, and nine is the extreme of yang; as for ten, it is only temporarily used to pair with five.

按：《太玄》演五行之數，不曰「五與十相守」而曰「五與五相守」，隠其十而不言，何也？葢子云覃思渾天，參摹而四分之，極於九九八十一首，每首九贊，以五行之數分隸九贊之下，勢不得復用十矣。故其說曰「鴻本五行，九位施重」，此十之所以隠而不言也與。（今九九算法遇十則變為一十，常隠而不見，即是此理。）

Hu Wei said: The Tai Xuan text derives the numbers of the Five Phases, not saying "five and ten hold together" but instead "five and five hold together," omitting the number ten. Why is this so? Perhaps Yang Xiong (whose courtesy name was Ziyun) devoted himself deeply to the study of the浑天 (hun tian) system, using the method of "three layers and four divisions" to derive the text. In the end, he arrived at eighty-one chapters, each with nine "zans." To distribute the numbers of the Five Phases among the nine zans, it was no longer possible to use the number ten. Therefore, he himself said, "The great fundamental lies in the Five Phases, and the nine positions are layered upon each other," which is why the number ten was omitted. (Today, in the algorithm of multiplication and division by nine, when reaching ten, it is carried over to become "one ten," and the number ten itself often disappears, which is the same principle.)

劉、鄭五行配合之說與天地之數相符，然未嘗名之曰圗也。至《太玄》始有《玄圗》篇，而其所謂「一六共宗，二七為朋，三八成友，四九同道，五五相守」者，葢即其圗也。圗雖不見於今，既名為圗，則圗固具是矣，而奇偶各配與劉、鄭同，惟五不配十為小異耳。

Liu Xin and Zheng Xuan's theory of the Five Phases combined with the Heavenly Stems and Earthly Branches agrees with the celestial and terrestrial numbers in the Great Treatise, but they never called it a 'Diagram'. It was only in the Tai Xuan that there is a section called the 'Xuan Tu' or 'Diagram of Tai Xuan'. What it says, 'one and six share the same origin, two and seven are friends, three and eight are companions, four and nine are on the same path, and five and five stay together', is probably the content of that diagram. Although the diagram itself is no longer available today, since it is called a 'Diagram', its form is fully described in these few sentences. The odd and even numbers are paired in the same way as Liu Xin and Zheng Xuan, except that five is not paired with ten, which is a slight difference.

范諤昌以是為伏羲復位生成之位，而劉牧目之曰洛書；闗子明以是為龍馬所授伏羲之數，而蔡元定宗之為河圗。其粉本皆用《太玄》而加以地十。然《玄》雖擬《易》，實老子之學，本名《玄圗》，非河圗也，安得附會《大傳》，指為聖人之所則哉！奇白偶黑之點，非子云意中所有，今欲示共宗同道之形，姑借《龍圗》之法以立象爾。

In the Northern Song dynasty, Fan Ech Chang regarded this set of numbers as the directional arrangement of Fuxi's "restitution and generation," while Liu Mu named it "the Luo Writing." A book attributed to Guan Ziming described it as numbers bestowed upon Fuxi by the dragon horse, while Cai Yuanding (a student of Zhu Xi, and the actual author of "The Awakening of the Yi") revered it as "the Yellow River Chart." Their sources all came from "The Tai Xuan," but they added an extra "ten on earth." However, although "The Tai Xuan" imitated "The Zhou Yi," its essence was based on Laozi's philosophy. Its original name was "The Xuan Tu," not the "Yellow River Chart," so how could it be forced into the "Great Treatise" and claimed as something the sages emulated? As for using white dots to represent odd numbers and black dots for even numbers, this was not something Yang Xiong had in mind. Now, in order to show the shape of "common origin" and "shared path," they merely borrowed the diagramming method from the "Dragon Tu" to create an image.

自春秋以迄兩漢，言五行者，禆灶、梓慎主占候，呂不韋主時令，劉向主災異，劉歆兼主歴數，揚雄草《玄》亦與《泰初歴》相應，雖皆言生成之數，卻非為《易》而設。至鄭康成始援以注《易》，而四象之義乃定，要之未有以此數為河圗洛書者。

From the Spring and Autumn period to the Two Han dynasties, those who discussed the Five Phases each focused on different aspects: Bi Zao and Zi Shen emphasized divination and observing the qi of the seasons, Lu Buwei focused on seasonal and monthly order, Liu Xiang concentrated on portents and anomalies, and Liu Xin integrated both calendar calculations and mathematics. Yang Xiong's composition of the Tai Xuan also coordinated with the Tai Chu calendar. Although they all discussed the generating numbers and completing numbers, none of them used these numbers specifically to interpret the Zhou Yi. It was only Zheng Kangcheng who introduced these numbers to annotate the Yi, thereby establishing the meaning of the four images. In summary, none of these people regarded this set of numbers as the He Tu or the Luo Shu.

何則？劉歆以河圗為八卦，洛書為九章；鄭康成以九篇為河圗，六篇為洛書；劉瑜以《乾鑿度》九宮之數為河圗；蜀隠者以希夷之先天太極為河圗。彼既自有其圗書，必不於其外更標一圗書可知也。自偽《龍圗》出，而始以五十有五為羲皇復位之數矣；自偽《闗易》出，而直以五行生成為龍馬所負之圗矣。劉牧、蔡元定從而揚其波，抑又甚焉。自此以後，劉、蔡迭為興廢，或以此為河圗，或以此為洛書，謬種流傳，變怪百出，原其弊，實《漢志》有以啟之。愚故先辨五行，次及九宮、《參同契》、先天太極，而以《龍圗》《鉤隠》《啟蒙》終焉。

Why is it said this way? Because Liu Xin believed that the Yellow River Chart was the Eight Trigrams and the Luo Writing was the Nine Categories; Zheng Kangcheng believed that the nine chapters of the apocryphal writings were the Yellow River Chart and the six chapters were the Luo Writing; Liu Yu of the Eastern Han dynasty regarded the nine-square numbers in the "Qian Zao Du" as the Yellow River Chart; another hermit in Sichuan Province regarded Chen Tuan's (who was known as Master Xiyi) Earlier Heaven Diagram and the Taiji Diagram as the Yellow River Chart. Since each of them already had their own system of "book and diagram," they would certainly not create another system outside of this, which is obvious. It was not until the forged "Longtu" appeared that the number "fifty-five" was claimed to be the number of Fuxi's reestablishment; it was not until the forged "Guan Lang Yi Zhuan" appeared that the five-phase generating numbers were directly said to be the diagram carried by the dragon and the horse. Liu Mu and Cai Yuan ding further promoted this, making it even worse. From then on, the school of Liu Mu and the school of Cai Yuan ding alternated, with some taking this set of numbers as the Yellow River Chart and others as the Luo Writing, spreading errors in various forms. Tracing the origin of this problem, it really started with the "Five Elements Chapter" in the "Book of Han." Therefore, I first distinguish the five elements, then discuss the nine-square grid, the "Zhou Yi Cang Tong Qi," the Earlier Heaven Diagram, and the Taiji Diagram, and finally conclude with the "Longtu," "Gou Yin Tu," and "Yi Xue Qimeng" — this is the order in which I examine and refute forgeries throughout the entire book.

右論洪範五行傳生成之數。

In the previous section, we examined the concepts of generating numbers and completed numbers discussed in the "Transmission of the Five Phases in the Hongfan Classic."