On the seventh day the virtue returns, discussing the lower part.

詳夫《易緯稽覽圖》及鄭氏六日七分之說，蓋取《乾》、《坤》老陽、老陰之策配之也。《經》曰：《乾》之策二百一十有六，《坤》之策百四十有四，凡三百六十，當期之日。《疏》云：舉其大略，則不數五日四分之一也。

Examining the "Kilangtu" section of the "Yi Wei" and Zheng Xuan's "six days and seven parts" theory, it is largely a matter of matching the numbers of the old yang and old yin lines in the Qian and Kun hexagrams. The "Great Treatise" states: "The Qian hexagram has 216 lines, and the Kun hexagram has 144 lines, totaling 360, which corresponds to the period of a year." Kong Yingda's commentary explains that this is merely an approximate number and does not include the remaining five and four-fifths days.

又《疏》云：二篇之爻，總三百八十四，陰陽各半焉。陽爻一百九十二位，爻別三十六，總有六千九百一十二也；陰爻一百九十二位，爻別二十四，總有四千六百八也；陰陽總合，萬有一千五百二十，當萬物之數也。

Kong's commentary also states: The yao in the upper and lower parts of the Book of Changes total 384, with yin and yang yao each accounting for half. The yang yao amount to 192, each with a count of 36, totaling 6,912; the yin yao also amount to 192, each with a count of 24, totaling 4,608; when these two totals are added together, they amount to 11,520, which exactly corresponds to the number of all things.

且《經》為《乾》、《坤》二卦，老陽、老陰三百六十之數，當期之日，則不更別起數矣。卦之與爻，則未詳《易緯》、鄭氏六日七分之義也。夫陰陽之爻，總有三百八十四焉。且《易緯》及鄭氏雖以坎、離、震、兌四正之卦之爻，臧乎二十四之數，與當期之日相契，則又與聖人之辭不同矣。

The classic text only uses the old yang and old yin lines of the Qian and Kun hexagrams to form the number 360, which is taken as the number of days in a year. Therefore, it does not introduce another set of numbers. As for how the hexagrams and lines are distributed, the Yi Wei and Zheng Xuan's theory of "six days and seven parts" has never been clearly explained. The total number of yin and yang lines is 384. Although the Yi Wei and Zheng Xuan subtracted the 24 lines of the four cardinal trigrams Kan, Li, Zhen, and Dui (the original text says "臧" which is a mistake for "减"), making the remaining number match the number of days in a year, this approach does not align with the original words of the sage.

何以知之？且夫起子止亥，十二月之數，所以主十二卦之爻也。十二卦之爻者，自《復》至《坤》之位也。豈可取雜書、賢人之說，而破聖人之經義哉？或曰不然，其如《擊辭》何？

Why should it be said like this? From the month of Zi to the month of Hai, the twelve months' numbers are precisely used to divide the yao of the twelve message hexagrams; the so-called twelve hexagrams' yao refer to the sequence of hexagram positions from Fu to Kun. How can we use the miscellaneous sayings of the Wei texts and the interpretations of later sages to overturn the classics' meaning established by the sages? If someone were to say it is not so, then how would the clear statements in the Great Treatise be accounted for?

《臨》至于八月，有凶。《象》曰：臨，剛浸而長，說而順，剛中而應，大亨，以正天之道也。至于八月有凶，消不久。

The Hexagram 42, "Approach," states: "There will be calamity by the eighth lunar month." The Commentary on the Judgment (originally titled "Xiang") explains: "Approach" signifies the gradual increase of the yang lines. The inner trigram is Dui, representing Joy, and the outer trigram is Kun, representing順. Nine in the Second is a yang line in the middle, corresponding with Six in the Fifth, thus achieving great success. This is due to the proper alignment of the heavenly way. "There will be calamity by the eighth lunar month" indicates that the time when yang will decline is not far off.

原缺諸家之註解，各有異焉。且何氏云：從建子陽生，至建未為八月。褚氏云：自建寅至建酉為八月。孔氏《疏》又曰：今按此《注》云：小人道長，君子道消。宜據《否》卦之時，以《臨》卦建丑；而至《否》卦，則建申為八月也。理有未安，略試論之。

The original text here is missing. The interpretations of various scholars differ. He said: Starting from the month of Ji Zi (the eleventh month), when yang energy begins to arise, up to the month of Ji Wei (the sixth month), that is exactly eight months. Chu said: Starting from the month of Ji Yin (the first month) up to the month of Ji You (the eighth month). Kong Yingda's commentary further states: Now, looking at Wang Bi's annotation that "the way of the petty person grows, while the way of the gentleman declines," it should be determined according to the season corresponding to the hexagram "Pu" (Obstruction). The hexagram "Lin" (Approach) corresponds to the month of Ji Chou (the twelfth month), and counting up to the month of Ji Shen (the seventh month), which corresponds to "Pu," that is exactly the eighth month. These several interpretations are still not fully convincing, so I will briefly discuss them.

粵若諸家之說，皆與《臨》卦之義不相偶契。何以知之？且卦、象之辭，所以各論一卦之體也。夫《臨》卦者，主建丑之月也。何氏從建子陽生而數，則卦辭當在《復》卦之下，不當屬《臨》卦也。褚氏從寅而數，則卦辭當在《泰》卦之下，亦不當屬《臨》卦也。孔氏宜據建申《否》卦為八月，則《否》之六三當消《泰》之九三，又與《臨》卦九三之不應也。

Examining the views of various scholars, they all fail to align with the meaning of the Hexagram "Qing" (Governing). Why is this so? Both the Hexagram Statement and the statements of the "Tuan" and "Xiang" are based on the nature of each individual hexagram. The Hexagram "Qing" governs the month of Chou (the second lunar month). He氏 starts from the month of Zi (the first lunar month) where yang energy begins to arise, so this Hexagram Statement should belong to the Hexagram "Fu" instead of "Qing." Chu氏 starts from the month of Yin (the third lunar month), so this Hexagram Statement should belong to the Hexagram "Tai" instead of "Qing." Kong氏 proposes to use the month of Shen (the seventh lunar month) and the Hexagram "Pi" for August, but in that case, the Nine in the Third of "Tai" would correspond to the Six in the Third of "Pi," which does not match the Nine in the Third of "Qing."

今若以建未為八月，取《逐》卦之六二，消《臨》卦之九二，則於義為允矣。何者？且《臨》卦之《象》曰：浸而長。《注》云：陽道轉進，陰道日消也。《遲》卦之《象》亦曰：浸而長。《注》云：陰道欲進而長，正道亦未全滅也。今以二卦之爻，既相偶合，又《象》辭皆有陰陽浸長之說，則其義不得不然也，所以稱建未為八月耳。

Now if we take the month of Wei as that "August," using the second line of the Duan hexagram to neutralize the second line of the Lin hexagram, it is appropriate in terms of meaning (the original words "zhú" and "chi" are both errors for "duan"). Why? The Lin hexagram's Commentary on the Judgment says "gradually increasing," and Wang Bi explains it as the yang force gradually advancing and the yin force gradually retreating. The Duan hexagram's Commentary on the Judgment also says "gradually increasing," and Wang Bi explains it as the yin force about to advance, while the correct path has not yet completely disappeared. Now since the lines of these two hexagrams correspond to each other—the second line of Lin facing the second line of Duan—the terms in the Commentary on the Judgment both refer to the gradual increase of yin and yang. Therefore, this meaning must be interpreted in this way, so the month of Wei is indeed that "August."

或問：當文王演卦之時，乃商之末世也。豈口口正月為義哉？答日：周公作爻辭，父基子構，所以爻辭多文王后事；則知文王之旨，周公述而成之，故以周正為定。

Someone asked: When King Wen was composing the hexagram statements, it was still the late Shang dynasty. How could he use the Zhou calendar's first month as the basis for his meaning (the original text is missing two characters here)? The answer was: The line statements were composed by the Duke of Zhou. The father laid the foundation, and the son completed it, so the line statements contain many events that took place after King Wen's death. This shows that King Wen's intentions were explained and completed by the Duke of Zhou. Therefore, all the months were determined according to the Zhou calendar's first month.

況乎《易》有二名，夏曰《連山》，商日《歸藏丫》，周曰《周易》。連山，則神農氏之號也。歸藏，則軒轅氏之號也。既連山、歸藏，並是代號，所以題周以別餘代，亦由《周禮》之謂也。且《易》既題周以正名，則公不得不以周之正朔定其月也。孰謂不然？

Moreover, the book of Changes (Yi) has had different names throughout the ages (the original text says "two names," but it should be "three names"): in the Xia dynasty it was called the "Lianshan," in the Shang dynasty it was called the "Guicang," and in the Zhou dynasty it was called the "Zhouyi." Lianshan refers to the title of the Yellow Emperor (Shennong), and Guicang refers to the title of the Yellow Emperor (Huangdi). Since Lianshan and Guicang were the names of different dynasties, marking the name with "Zhou" would be to distinguish it from the others, just as the "Zhouli" (Book of Rites of the Zhou) is named with "Zhou." Since the Yi is named with "Zhou," the Duke of Zhou naturally could not avoid using the official calendar of the Zhou dynasty to determine the months. Who could say otherwise?

若何氏以建子至建未為八月，則是究其末而不原其本矣。至於孔氏引輔嗣之《注》，以君子道消，小人道長，必以《否》卦之義也。但陰則小人之道長，陽則君子之道長，不必專在《否》卦之義也昕矣。

As for He氏 counting from the month of Zi to the month of Wei as eight months, this approach only focuses on the surface without tracing back to the root. Kong Yingda cited Wang Bi's commentary, asserting that "the way of the gentleman declines and the way of the petty person prevails" must refer to the Hexagram of Obstruction. In reality, whenever there is yin, it is the growth of the petty person's way, and whenever there is yang, it is the growth of the gentleman's way. This does not necessarily have to be attributed solely to the Hexagram of Obstruction, which is quite clear.

又《王氏卦略》云：《逐》，小人浸長，難在於內，亨在於外，與《臨》卦相對者也。《臨》剛長則柔危，《運》柔長則剛危矣。《臨》，二陽居內，君子之道日長；《逐》，二陰在內，小人之道日進。

Wang Bi's "Outline of the Zhou Changes · Trigram Overview" says: The "Dun" hexagram represents the gradual growth of small people, with danger in the inner trigram and success in the outer trigram, exactly opposite to the "Lin" hexagram. In the "Lin" hexagram, the growth of strong lines brings danger to the weak lines; in the "Dun" hexagram, the growth of weak lines brings danger to the strong lines. In the "Lin" hexagram, two yang lines reside in the inner trigram, representing the gradual growth of the gentleman's way; in the "Dun" hexagram, two yin lines reside in the inner trigram, representing the gradual approach of the petty person's way.

且八月凶者，天之道火寒暑退陽長，至二得位居中，故於此時垂消退之戒。陽息於十一月，為《復》；至十二月，為《臨》；消於五月，為《娠》；至六月，為《逐》。自子至未，凡八月也。

The statement that there is calamity in the eighth month refers to the heavenly course. (The original text is missing several characters here, as is the case in the Siku Quanshu edition.) When cold comes and summer goes, yang wanes and yin grows. When the second line, six, is in the central position, it serves as a warning of decline at this time. Yang energy begins to arise in the eleventh month, corresponding to the hexagram "Return"; in the twelfth month, it corresponds to "Approach"; beginning in the fifth month, yang begins to decline, corresponding to "Encounter"; and in the sixth month, it corresponds to "Retreat." Counting from the month of Jiuzi to the month of Jiwei, there are exactly eight months.

或問日：洛書云：一日水，二日火，三日木，四日金，五日土。則與龍圖五行之數之位不偶者，何也？答曰：此謂陳其生數也。且雖則陳其生數，乃是已交之數也。下篇分土王四時，則備其成數矣。且夫洛書、九疇，惟出於五行之數，故先陳其已交之生數，然後以土數足之，乃可見其成數也。

Someone asked: The "Book of Documents · Hongfan" states in the Luo Shu that "one is water, two is fire, three is wood, four is metal, five is earth." This does not match the positions of the five elements' numbers in the Longtu (He Tu). Why is this so? The answer is: what is stated here is only the generating numbers of the five elements. Although they are called generating numbers, they are already numbers after yin and yang have interacted. In the next section, it will explain that earth is strong in the four seasons, and only when the completed numbers are added do they become complete. Both the Luo Shu and the nine categories of the Hongfan come from the numbers of the five elements, so they first present these already interacting generating numbers, and then add the number five for earth, making the completed numbers appear. The five pictures from the forty-ninth to the fifty-third in the He Tu, in order, depict the full numbers of the He Tu, the heavenly and earthly numbers in the He Tu, the four images' numbers contained in the He Tu, the eight trigrams generated from the He Tu, and the generating numbers of the five elements in the Luo Shu, one, two, three, four, and five. This picture adds the number five for earth to each generating number, resulting in the completed numbers six, seven, eight, nine, and ten.

天一、地六，地一不天七，天三、地八，地四、天九，天五、地十，合而生水、火、木、金、土。十日者，剛日也。相生者，金生水，水生木，木生火，火生土，土生金也。相剋者，金克木，木克土，土克水，水克火，火克金也。

Heavenly Stem one combines with Earthly Branch six, Earthly Branch two combines with Heavenly Stem seven (the original "Earthly Branch one" is an error for "Earthly Branch two"), Heavenly Stem three combines with Earthly Branch eight, Earthly Branch four combines with Heavenly Stem nine, Heavenly Stem five combines with Earthly Branch ten; these five groups combine with each other, respectively producing water, fire, wood, metal, and earth. The term "ten suns" refers to the ten Heavenly Stems, Jia, Yi, up to Ren, Gui. Heavenly Stems belong to Yang, so they are called "strong days." The order of mutual generation is: metal generates water, water generates wood, wood generates fire, fire generates earth, and earth generates metal. The order of mutual control is: metal controls wood, wood controls earth, earth controls water, water controls fire, and fire controls metal. This diagram illustrates the relationships of generation and control among the ten Heavenly Stems and the Five Phases.

《易》日：河出圖，洛出書，聖人則之。《春秋緯》云：河以通乾出天苞，洛以流坤吐地符。河龍圖發，洛龜書感。《河圖》有九篇，《洛書》有六篇。《書正義》日：洛書九類，各有文字，即是書也。而云：天乃錫禹。如此天與禹者，即是洛書也。

The Great Treatise says: "The Yellow River produced the map, and the Luo River produced the book, and the sage followed them." The Spring Annals says: the Yellow River connects upward to Heaven and spews out the heavenly essence, while the Luo River flows downward to Earth and spews out the earthly symbol; the Yellow River had a dragon carrying the map and appearing, and the Luo River had a turtle responding and presenting the book; it also says the River Chart consists of nine chapters, and the Luo Book consists of six chapters. The Correct Interpretation of the Book of Documents says: the nine categories recorded in the Luo Book each have their own characters, which are called "books"; the Hongfan says "Heaven then bestowed upon Yu," and such things bestowed by Heaven upon great Yu are called the Luo Book.

漢《五行志》，劉飲以為伏犧繼天而王，河出圖，則而畫八卦是也；禹治洪水，錫洛書，法而陳《洪範》是也。穎達共為此說，龜負洛書，《經》無其事。《中候》及諸《緯》多說黃帝、堯、舜、禹、湯、文、武受圖書之事，皆云龍負圖，龜負書。

In the "Book of Han · Five Phases Chapter," Liu Xin thought that Fuxi received the mandate of heaven and became king. When the Yellow River produced a divine map, he modeled the eight trigrams after it. When Yu the Great controlled the floods, heaven bestowed the Luo Book upon him, and he then composed the "Hong Fan." Kong Yingda also agreed with this view. However, the story of the turtle carrying the Luo Book is not recorded in the canonical texts. The "Shang Shu Zhonghou" and various ying texts often mention the Yellow Emperor, Yao, Shun, Yu, Tang, King Wen, and King Wu receiving the heavenly diagrams, all saying that a dragon carried the map and a turtle carried the book.

緯候之書，不知誰著，通人討竅，以為偽起哀、平者也。前漢之末，始有此書，不知起誰氏也。以前學者必相傳此說，故孔氏以《九類》是神龜負文而出，列於背，有數從一而至於九，見其文，遂因而第之以《九類》也。陳而行之，所以常道得其次叔也。言禹第之者，以天神言語必當簡要，不應曲有次第，丁寧若此，故以禹次而第之也。

Books of the type called "Wei Hou" are unknown in authorship; learned men have investigated and concluded that they were fabricated during the reigns of Emperor Ai and Emperor Ping of the Han dynasty. These books appeared only at the end of the Western Han dynasty, and it is unclear who first composed them. Scholars before this time must have passed down such accounts orally. Kong Anguo believed that the Nine Categories were revealed by a divine turtle carrying inscriptions on its back, with the characters arranged in order from one to nine. Emperor Yu the Great saw these characters and arranged them in sequence into nine categories, displaying them for implementation, thereby establishing the order of human conduct and moral principles. The reason for attributing this arrangement to Emperor Yu is that the words of heavenly spirits must be concise and not elaborate or detailed in their sequence and instructions. Therefore, it is concluded that Emperor Yu arranged them in order.

然大禹既得《九類》，常道始有次叔；未有洛書之前，常道所以不亂者，世有澆、淳，教有疏、密，三皇以前無文亦治，何止元洛書也。但既得《九類》以後，口口法而行之則治，違之則亂也。

However, according to this explanation, after Da Yu received the nine categories, human relationships and the common ways of conduct became orderly. Then, before the Luo Book appeared, why were the common ways not chaotic? In fact, the customs of the world differ between being refined and pure or declining and shallow, and the governance and education differ between being rough and loose or detailed and meticulous. Before the Three Emperors, there were no written characters, yet the world was still peaceful, let alone the absence of the Luo Book. The point is that once the nine categories were obtained, following them led to order, while violating them caused chaos.

且不知洛書本文計天言簡要，必元次第之數。上傳云：禹因而次之。則孔氏以第是禹之所為，初一日等二十八字，必是禹加之也。其敬用、農用等一十八字，大劉及顧氏以為龜負也。小劉以為敬用等亦禹所第叔。其龜文惟有二十字，並元明據，未知孰是，故兩存焉耳。

Furthermore, no one knows the original text of the Luo Shu. Since the words of Heaven are concise, there must not be a fixed sequence of numbers. The transmitted text of the Shang Shu says "Yu then arranged them in order," so Kong An Guo believed that the arrangement was done by Yu. The twenty-eight words in the Hong Fan, such as "First is the Five Phases," must have been added by Yu. As for the eighteen words "Respectfully use" and "Agricultural use," Liu Xiang and Gu Shi thought they were originally on the turtle shell, while Liu Xin believed that the words "Respectfully use" and so on also came from Yu's arrangement, and that the turtle shell only had twenty characters. These views lack clear evidence, and it is unknown which is correct, so both views coexist.

詳夫眾賢之論，多背經書之旨。觀其大法，凡《九類》，蓋是禹叔洛書，因而第之，遂著成法則，非是神龜負書出於大禹之時也。何以明其然？略試論之。

Careful examination of the discussions of the ancients shows that most of them contradict the original meaning of the classics. Looking at the great principles for governing the world: the so-called Nine Categories were surely the content of the Luo Book as described by the great Yu, who arranged them in order and thus wrote down the principles. (The original text "shu" means "to narrate.") It was not that a divine turtle carrying a book happened to appear in the time of Yu. On what basis can this be proven? Let me briefly explain.

箕子日：在昔鯀陘洪水，汨陳其五行，帝乃震怒，不界《洪範》、九疇，彝倫攸教，鯀則趣死，禹乃嗣興，天乃錫禹《洪範》、九疇，彝倫攸叔，則不載神龜負圖之事。惟孔氏《注》稱天與禹洛書，神龜負文而出，列於背有數至九也。

Jizi in the "Hongfan" said: In the past, Gun blocked the floodwaters, thereby disturbing the order of the Five Phases. Heaven was angry and did not grant the Nine Categories of the "Hongfan" to him, leading to the collapse of the established principles of human relations. Gun was executed, and Yu rose to take his place. Then Heaven bestowed the Nine Categories of the "Hongfan" upon Yu, and the established principles of human relations were thus restored in order. This passage does not mention the story of a divine tortoise carrying a diagram. Only Kong AnGuo's commentary says: Heaven gave the great Yu the Luo Shu, which was carried out by a divine tortoise. The characters were arranged on its back, and the numbers were arranged up to nine.

諸儒更演載天書言語字數之說，後乃邊相祖述，遂以禹親受洛書，而陳《九類》。且《經》元載圖書之事，惟《易擊辭》云：河出圖，洛出書，聖人則之。此蓋仲尼以作《易》而云也。則知河圖、洛書出於犧皇之世矣。

Various Confucian scholars later developed the idea that the Heavenly Book contains words and numbers arranged in order, and later generations passed this down, thus believing that Yu the Great personally received the Luo Book and used it to explain the nine categories. In reality, the classic texts do not mention anything about the Heavenly and Earthly Books. Only the "Great Treatise" of the Book of Changes says, "The River produced the diagram, the Luo produced the book, and the sage followed them," which was originally a statement by Confucius regarding his composition of the Book of Changes. From this we can see that the River Diagram and the Luo Book originated in the time of Fuxi.

乃是古者河出龍圖，洛出龜書，犧皇口□□畫八卦，因而重之，為六十四卦。口□□□□口□□□□口口□□口口□口□口□口口□□文王作《卦辭》，周公作《爻辭》，仲尼輔之《十翼》，《易》道始明。

That is to say: In ancient times, a dragon appeared in the Yellow River, bringing the diagram, and a tortoise emerged in the Luo River, bringing the script. Fuxi drew the Eight Trigrams based on them. He then combined the Eight Trigrams two by two to form the sixty-four Hexagrams. (The original text is missing several sentences here, as is the case in the Siku Quanshu edition.) Later, King Wen composed the Hexagram Statements, the Duke of Zhou composed the Line Statements, and Confucius further supplemented the Book of Changes with the Ten Wings, thereby making the doctrine of the Book of Changes widely known throughout the world.

觀今龍圖，其位有九，四象八卦皆所包組。且其圖縱橫皆合天地自然之數，財非後人能假偽而設之也。夫龍圖呈卦，非聖人不能畫之；卦含萬象，非聖人不能明之。以此而觀，則洛出書，非出大禹之時也。

Looking at the dragon diagram transmitted today, it contains nine numbers, encompassing the four symbols and the eight trigrams within it (the original text says "zu" but should be "luo"); moreover, the numbers along both the horizontal and vertical directions conform to the natural numbers of heaven and earth, which could not have been fabricated by later people. The dragon diagram presents the trigrams, which are not something the sage could fail to draw; the trigrams contain all phenomena, which are not something the sage could fail to explain. From this, we can see that the book emerging from Luo River did not originate in the time of Great Yu.

《書》云天錫禹九疇者，蓋是天生聖德於禹，誠明洛書之義，因第而次之，垂範後世也。今河圖相傳於前代，其數自一至九，包四象八卦之義，而兼五行之數；洛書則惟五行生成之數也。然犧皇但畫卦以垂教，則五行之數未顯，故禹更陳五行而顯九類也。

The Book of Documents says, "Heaven bestowed upon Yu nine categories." This means that Heaven endowed the great Yu with virtue, enabling him to truly understand the principles of the Luo Book. Thus, he arranged them in order, establishing them as a model for future generations. Now, the transmitted River Chart from earlier times has numbers from one to nine, containing the meanings of the Four Symbols and the Eight Trigrams, and also includes the numbers of the Five Phases. The Luo Book, however, contains only the generating numbers and the completed numbers of the Five Phases. Fuxi originally drew the trigrams to teach people, but the numbers of the Five Phases were not yet clear, so Yu re-explained the Five Phases and made the nine categories clear.

今諸儒以禹受洛書，書載天神言語，陳列字數，實非通論。天何言哉，聖人則之必不然也。或日：未可，敢質於《經》。且堯任九子，各主其一。九疇之數，九子之職也。至農用八政，司空、司徒之官，唐虞世設之矣。協用五紀，羲氏、和氏已正之矣。斯則非俟禹受洛書之後設其官也。

Nowadays, various scholars of Confucianism believe that Yu the Great received the Luo Book, which contains the words of heavenly spirits and is arranged in a fixed number of characters. This is certainly not a reasonable view. Has heaven ever spoken? To say that sages modeled themselves after such things is surely wrong. Perhaps someone might object: this argument may not hold, let me use the classics to prove it. Yao appointed nine ministers, each responsible for a particular task, and the number nine of the nine categories exactly matches the nine ministers' duties. As for the "eight administrative affairs" in "agricultural use of the eight administrative affairs," the offices of the Minister of Works and the Minister of War were already established in the time of the Xia and Shang dynasties; the "coordinating with the five celestial phenomena" in the calendar system was also already corrected by Xi and He. This shows that these offices were not established only after Yu received the Luo Book.

且夫天垂象，見吉凶，聖人象之；河出圖，洛出書，聖人則之。天象則□口□口□□口。□雖組其義，非至聖不能明之。口□河圖、洛書，非羲皇不能畫之。卦合其象，非文王不能伸之。爻象之興，非周公不能著之。

The Great Treatise says: Heaven manifests signs and images, revealing auspicious and inauspicious omens, and the sage takes inspiration from them. The river黄河 produces a diagram, and the Luo River produces a book, and the sage takes them as models. Although the heavenly signs encompass this meaning, it is not understandable unless by the highest sage; the river diagram and the Luo book could not have been drawn unless by Fuxi. The hexagrams and their images are in harmony, which could not have been explained unless by King Wen. The emergence of the lines of the hexagrams could not have been written down unless by the Duke of Zhou.

故仲尼日：文王既沒，文不在茲乎。又日：天生德於予，則知天生睿哲於聖人，默究乎幽跡，是謂錫之也。故仲虺之誥日：天乃錫王勇智，表正萬邦之謂也。

Therefore Confucius said, "After King Wen's death, is the culture not in me?" He also said, "Heaven bestowed virtue upon me." From this we can see that Heaven grants wisdom to the sage, enabling him to silently investigate the hidden traces. This is called "xi," which means to bestow. Therefore the Book of Documents, in the section "Zhonghui Zhi Gao," says, "Heaven then bestowed upon the king courage and wisdom, to exemplify the myriad states," which expresses exactly this meaning.

且孔氏以箕子稱天乃錫禹九疇，便謂之洛出龜書，則不思聖人云河出圖，洛出書，在作《易》之前也。又唐法九疇，唐虞之前已行之矣。而云禹受洛書之後，始有常道次叔，不日誣之者乎？

Confucius mentioned "the river produced the map, the Luo produced the book," referring to events before the composition of the Book of Changes. Kong AnGuo, however, simply assumed that the statement by Ji Zi, "Heaven bestowed the nine categories upon Yu," meant that the turtle book emerged from the Luo River. He did not consider that the system of the nine categories was already in practice before the time of Yao and Shun. To claim that human ethics and principles only became orderly after Yu received the Luo book is not a truthful statement.

《春秋緯》日：《洛書》六篇。孔氏云：洛書，神龜負文而出，列於背，有數一至九。今代之所傳龜書，惟總五行生成之數，未知孰是。略試論之：《春秋緯》喜一《洛書》六篇，則與五行、九疇之數不偶，亦未明其義。孔氏云洛書有數一至九，謂《書》之九疇自一五行至五福、六極之數也。

The Spring and Autumn Wai (external commentary) says: The Luo Shu consists of six chapters. Kong An Guo said: The Luo Shu is a divine turtle carrying characters, with the characters arranged on the turtle's back, numbered from one to nine. However, the Luo Shu currently passed down only combines the generating numbers and completing numbers of the Five Phases, and it is unclear which account is correct. Let me briefly discuss this. The Luo Shu mentioned in the Spring and Autumn Wai, with the words 「xi yi」 (meaning 'joy one') being a later addition and error, does not match the numbers of the Five Phases or the nine categories (jiu chou). Its meaning is also unclear. Kong An Guo's statement about the Luo Shu having numbers from one to nine refers to the order of the nine categories in the Shang Shu · Hong Fan, starting from the first category 「Five Phases」 up to the ninth category 「Five Blessings, Six Evils」.

且《書》之九疇，惟五行是包天地自然之數，餘八法皆是禹參酌天時、人事類之耳，射非龜所負之文也。今詳《洪範五行傳》，凡言災異，必推五行為之宗。又若鯀元聖德，汨陳五行，是以彝倫攸教。

In the nine categories of the "Hong Fan," only the first category, "Wuxing" (Five Phases), contains the numbers of heaven and earth in nature. The other eight categories were classified and arranged by the Great Yu according to the timing of heaven and the affairs of people, and they are not originally inscribed on the turtle shell (the original text "she" should be "shu"). Looking closely at the "Hong Fan Wuxing Zhuan," whenever it discusses calamities and anomalies, it always traces them back to the Five Phases. For example, Gun lacked virtue and disturbed the order of the Five Phases, thus causing the collapse of the principles of human relations and the common ways of people.

則知五行是天垂自然之數，其文負於神龜；餘八法皆大禹引而伸之，猶龍圖止負四象八純之卦；餘重卦六十四，皆伏犧仰觀俯察，象其物宜，伸之以爻象也。

From this we can see that the Five Phases are the natural numbers revealed by Heaven, and this part of the text is indeed what the divine turtle carried. The other eight principles were all elaborated upon by the Great Yu based on this. This is like the Dragon Pattern only carrying the Four Symbols and the eight pure trigrams, while the other sixty-four trigrams formed by overlapping are all derived by Fuxi observing the heavens above and examining the earth below, taking the appropriate images from all things, and elaborating them one by one with the yao symbols.

況乎五行包自然之性，八卦報自然之象，聖人更為之變易，各以類分，而觀吉凶矣。若今世之所傳者，龜書不為妄也。尚或疑焉者，試精之於問答。

Moreover, the Five Phases include the inherent nature of all things in the natural world, and the Eight Trigrams encompass the manifestations of all things in the natural world (the original text's "报" is a mistake for "包"). The sages further applied change and differentiated them according to categories, thus observing auspiciousness and inauspiciousness. In this way, the divination texts passed down in the present age are not fabricated. If anyone still has doubts, let me clarify further through a question and answer format.

或問日：且云圖、書皆出於犧皇之世，則九疇亦陳於犧皇之代，不當言禹第而次之也？答曰：河圖八卦，垂其象也，故可以盡陳其位；洛書五行，含其性也，必以文字分其類。玄犧之世，世質民淳，文字未作，故九疇莫得而傳也，但申其數耳。至大禹聖人遂演成《九類》，垂為世範。九疇自禹而始也。

Someone asked: Since it is said that the River Chart and the Lake Chart both emerged during the time of Fuxi, then the Nine Categories should have been displayed during Fuxi's time, and not be attributed to the arrangement by the sage Yu. The answer is: The River Chart is paired with the Eight Trigrams, and it reveals the 'image' (xiang), so it can list out the directions one by one. The Lake Chart discusses the Five Phases, containing the 'nature' (xing), which must be distinguished by means of characters. During Fuxi's time, the customs were simple and the people's sentiments were sincere, and writing had not yet been created, so the Nine Categories could not be passed down, and only the number of them could be stated. It was only with the sage Yu that they were elaborated into nine categories, established as a standard for all generations. Therefore, the Nine Categories began with Yu.

或問曰：既云龍圖兼五行，則五行已具於龍圖矣。不應更用龜書也。答日：雖兼五行，有中位而無土數，唯四十有五，是有其象，而未著其形也，唯四象、八卦之義耳。龜書乃具五行生成之數五十有五矣。《易》者，包象與器，故聖人資圖、書而作之也。

Someone else asked: Since it is said that the Dragon Chart includes the Five Phases, then the Five Phases must already be complete within the Dragon Chart, so why is the Turtle Book needed? The answer was: Although the Dragon Chart includes the Five Phases, it only has the central position and lacks the number ten representing Earth, so the total is only forty-five. This shows the image but not the form. What is discussed is only the principles of the Four Symbols and the Eight Trigrams. The Turtle Book, however, fully contains the numbers of the generation of the Five Phases, totaling fifty-five. The Book of Changes includes both the "image" and the "object," so the sage used both the River Chart and the Lake Chart to compose the Book of Changes.

或問日：《書》云天乃錫禹《洪範》、九疇，必洛書，今臆說破之，元乃□□□。答曰：仲尼稱河出圖，洛出書，於玄犧畫《易》之前，不當云出夏禹之世也。如日不然，是洛書復出於夏禹之時矣。誠如是，禹之前元九疇也。又何以《堯典》之九法坦然明白乎哉？

Someone else asked: The Book of Documents says, "Heaven bestowed the Nine Categories of the Great Plan upon Yu," which must mean the Luo Book. Now you use speculative reasoning to overturn it, is that not (the original text here is missing several characters)? The answer was: Confucius said, "The River produced the diagram, and the Luo produced the book," referring to events before Fuxi drew the Book of Changes. It should not be interpreted as occurring during the time of the Xia Dynasty's Yu. If one says otherwise, then it would mean the Luo Book appeared again during the time of Yu. If that were truly the case, then before Yu there would have been no Nine Categories. How then can we explain the Nine Categories of law already being clearly implemented in the Yao Classic?

問曰：今《書》世之傳者龍圖、龜書，《經》所不載，緯候之書蔑聞其義，誠誕說也？曰：龍圖、龜書，雖不載之於《經》，亦前賢迭相傳授也。然而數與象合位，將卦偶不盈不縮，符於自然，非人智所能設之也。況乎古今陰陽之書，靡不宗之。至於通神明之德，與天地之理，應如影響，豈曰妄乎？

Another question was asked: Now, the dragon diagram and turtle script that are passed down in the world are not mentioned in the classics, and the books of the 'wai' and 'hou' (supplementary) also do not explain their meaning clearly. Are they not really absurd talk? The answer was: Although the dragon diagram and turtle script are not recorded in the classics, they were passed down by the virtuous people of previous generations. Moreover, the numbers and symbolic positions in the diagram correspond exactly with the trigrams, matching them in pairs without any excess or deficiency, and everywhere conforming to nature. This is certainly not something that human ingenuity could arrange. Furthermore, all the books throughout history that discuss yin and yang have regarded them as their fundamental principles. As for using them to connect with the virtue of the divine and to harmonize with the principles of heaven and earth, their effectiveness is like a shadow following its form or an echo responding to a sound. How can this be called absurd?