Yi Shu Gou Shen Tu (易數鉤深圖)

經名：易數鈞隱圖。原題三衢劉牧撰三卷。底本出處：《正統道藏》洞真部靈圖類。校版本：文淵閣四庫全書本經部易類（簡稱四庫本）。

This book is recorded in the Daozang under the title "Yishu Gouyun Tu." The original title attributes it to Liu Mu of Sanqu, divided into three volumes: upper, middle, and lower. The base text used for collation comes from the Ming Dynasty's Zhengtong Daozang, Dongzhen Bu Lingtu Leiyu; the collation text is a version included in the Wenyuan Ge Siku Quanshu, Jingbu Yi Leiyu, which is hereafter referred to simply as the "Siku Ben."

三衢劉牧撰。

This book was written by Liu Mu, who was from Sanqu (now Quzhou, Zhejiang Province).

夫《易》者，陰陽氣交之謂也。若夫陰陽未交，則四象未立；八卦未分，則萬物安從而生哉？是故兩儀變易而生四象，四象變易而生八卦、重卦六十四卦，於是乎天下之能事畢矣。

The Book of Changes discusses the interaction of yin and yang energies. If yin and yang had not yet interacted, the four images would not have arisen; if the eight trigrams had not yet been differentiated, how could all things have come into being? Therefore, the two principles (yin and yang) transform into the four images, the four images transform into the eight trigrams, and the eight trigrams combined in pairs form the sixty-four hexagrams. At this point, all the principles and phenomena that can be explored are fully established.

夫卦者，聖人設之觀於象也。象者，形上之應。原其本，則形由象生，象由數設；舍其數，則無以見四象所由之宗矣。是故仲尼之贊《易》也，必舉天地之極數，以明成變化而行鬼神之道。則知《易》之為書，必極數以知其本也。

A hexagram is something established by the sages for people to observe the forms and appearances of things. The 'form' refers to the 'supra-formal' principle that corresponds with all things in the universe. Investigating its origin: tangible things arise from forms, and forms are established through numbers; once numbers are set aside, one cannot perceive the origin from which the four trigrams emerge. Therefore, Confucius praised the principles of the Book of Changes, necessarily citing the extreme number of fifty-five to explain the principle of 'achieving transformation and movement, governing spirits and ghosts'. From this we can understand that the Book of Changes must thoroughly investigate numbers in order to recognize its fundamental nature.

詳夫註疏之家，至於分經析義，妙盡精研，及乎解釋天地錯綜之數，則語惟簡略，與《擊辭》不偶，所以學者難曉其義也。今採摭天地奇偶之數，自太極生兩儀而下，至於《復》卦，凡五十五位，點之成圖。於逐圖下，各釋其義，庶覽之者易曉耳。

If we look closely at the various scholars who have commented on and explained the text, they have carefully divided the passages, analyzed the meanings, and studied them in great detail. However, when it comes to explaining the part where the numbers of heaven and earth change and intermingle, their explanations become extremely brief, not matching the original text of the Great Treatise (originally written as "ji ci," a miswriting of "xi ci"). Therefore, scholars find it difficult to understand the meaning. Now I have collected various numbers of odd and even, starting from "the Taiji produces the two principles" down to the hexagram Fu, totaling fifty-five numbers. I have arranged them into a diagram using dots. Each diagram is followed by an explanation of its meaning, hoping that readers will find it easy to understand.

夫《易》道淵邈，雖往哲難窺於至跡。牧也，蕞生祖述，誠魄其狂簡，然則象有定位，變有定數，不能妄為之穿鑿耳。博雅君子，試為詳焉。

The Way of the Book of Changes is profound and difficult to measure. Even the sages of previous generations found it hard to grasp its most subtle aspects. I, Liu Mu, am but an insignificant scholar, able only to transmit the old teachings of others. I am truly ashamed that my understanding is crude and reckless. However, the nature of the images has a fixed order, and change follows a definite number; therefore, I dare not fabricate or impose my own interpretations. Esteemed and learned gentlemen, please examine my words carefully.

太極無數與象。今以二儀之氣，混而為一以畫之，蓋欲明二儀所從而生也。

The Taiji itself has no number and no image to describe. The Taiji diagram drawn here combines the two principles (Wu Wei) into one whole, representing it as an undivided unity. The intention is to show clearly from where the two principles originate.

《經》日：《易》有太極，是生兩儀。太極者，一氣也。天地未分之前，元氣混而為一，一氣所判，是日兩儀。《易》不云乎天地，而云兩儀者，何也？蓋以兩儀則二氣始分，天地則形象斯著；以其始分兩體之儀，故謂之兩儀也。

The Great Treatise says: "The Book of Changes contains the Supreme Ultimate, from which the two principles arise." The Supreme Ultimate refers to a unified vital energy. Before heaven and earth were differentiated, the original qi was undivided; once this qi was divided, it became the two principles. Why does the Book of Changes not directly say "heaven and earth," but instead say "the two principles"? Because when called the two principles, the two energies had just begun to separate; when called "heaven and earth," the forms and phenomena were already distinct. It takes the state when they had just split into two forms, hence it is called the two principles.

何以明其然？略試論之：夫氣之上者輕清，氣之下者重濁。輕清而圓者，天之象也。重濁而方者，地之象也。茲乃上下未交之時，但分其儀象耳。若二氣交，則天一下而生水，地二上而生火，此則形之始也。五行既備，而生動植焉，所謂在天成象，在地成形也。則知兩儀乃天地之象，天地乃兩儀之體爾。

How can we prove this? Let me briefly explain: the part of the qi that rises is light and clear, while the part that sinks is heavy and turbid. The light and clear part, which is round in shape, represents the image of heaven; the heavy and turbid part, which is square in shape, represents the image of earth. This is exactly when the upper and lower qi have not yet interacted, and only two forms of images are distinguished. When the two qi interact, the heavenly qi of the first kind descends to form water, and the earthly qi of the second kind ascends to form fire. This is the beginning of tangible things. After the five elements are fully present, animals and plants then come into being. This is what the Great Treatise says: "In heaven, images are formed; in earth, forms are created." From this we can understand that the two principles are the "images" of heaven and earth, while heaven and earth are the "substances" of the two principles.

今畫天左旋者，取天一、天三之位也。畫地右動者，取地二、地四之位也。分而各其處者，蓋明上下未交之象也。

This diagram depicts heaven rotating to the left, taking the positions of the odd numbers (yang numbers) 天一 and 天三; and earth rotating to the right, taking the positions of the even numbers (yin numbers) 地二 and 地四. By separating them and having each occupy one side, it shows the image of the two energies, heaven and earth, before they interact.

天一、地二、天三、地四，此四象生數也。至於天五，則居中而主乎變化，不知何物也，強名日中和之氣，不知所以然而然也。交接乎天地之氣，成就乎五行之質，彌綸錯綜，無所不周。三才之道既備，退藏於密，寂然無事，茲所謂陰陽不測之謂神者也。

The numbers one, two, three, and four are the "generative numbers" of the Four Symbols. As for the number five, it is located in the center and governs all changes. It is unclear what it really is, so it is merely named "the vitalizing energy of harmony and balance." It arises naturally without a clear cause. It connects the energies of heaven and earth, forms the physical manifestations of the Five Phases, pervades and interconnects everything, and is present everywhere. When the principles of heaven, earth, and humanity are all complete, it retreats to a hidden place, remaining still and inactive. This is precisely the "spirit" mentioned in the Great Treatise, which refers to "the indescribable nature of yin and yang." This diagram places the five points in the center, with empty space around them, depicting precisely this central number five that governs all changes.

《經》雖云四象生八卦，然須三、五之變易，備七、八、九、六之成數，而後能生八卦，而定位矣。

The Great Treatise says only that "the four images give rise to the eight trigrams," but in between there must be "combining three and five to produce change"—the interaction of the generating numbers with the number five of heaven, leading to the four completed numbers of seven, eight, nine, and six. Only then can the eight trigrams come into being, and their directions can be determined.

或問日：天地之數，何以由天五而生變化？答日：天地之生數足，所以生變化也。天地之數十有五，自天一至天五，凡十五數也。天一、天三、天五成九，此陽之數也，故《乾》元用九。地一不地四成六，此陰之數也，故《坤》元用六。兼五行之成數四十，合而為五十有五，備天地之極數也，所以能成變化而行鬼神。

Someone asked: Why does the number of heaven and earth require the number five of heaven to produce change? The answer is: When the number five of heaven is reached, the 'generative numbers' of heaven and earth are complete, so change can arise. The combined generative numbers of heaven and earth total fifteen: from the number one of heaven to the number five of heaven, adding one plus two plus three plus four plus five, the total is fifteen, which is exactly the number of points marked in this diagram. Among these, the three odd numbers, heaven one, heaven three, and heaven five, add up to nine, which is the number of yang, so the "Use of Nine" is mentioned in the Qian hexagram. The two even numbers, earth two and earth four, add up to six (the original text says "earth one not earth four," where "one not" is a mistake for the character "two"), which is the number of yin, so the "Use of Six" is mentioned in the Kun hexagram. Adding the completed numbers of the Five Phases, six, seven, eight, nine, and ten, which total forty, the total becomes fifty-five. At this point, the extreme numbers of heaven and earth are complete, so they can "accomplish change and operate the spirits."

《經》曰：參伍以變，錯綜其數。通其變，遂成天地之文，極其數，遂定天下之象。義日：參，合也；伍，為偶配也，為天五合配天一，下生地六之類是也。以通其變化，交錯而成四象、八卦之數也。

The Great Treatise says: "By combining three and five, changes are produced; their numbers are interwoven. By comprehending these changes, the text of heaven and earth is formed; by reaching the limit of these numbers, the images of the world are established." These words mean that "参" refers to combination, and "伍" refers to pairing into even numbers—for example, the heavenly number five combines with the heavenly number one, giving rise to the earthly number six below, which is an instance of this. By relying on such combinations, the changes are connected, and they intermingle to form the four basic images and the eight trigrams. The above four diagrams illustrate this passage: the heavenly number one receives the heavenly number five and gives rise to the earthly number six below; the earthly number two receives the heavenly number five and gives rise to the heavenly number seven above; the heavenly number three receives the heavenly number five and gives rise to the earthly number eight on the left; the earthly number four receives the heavenly number five and gives rise to the heavenly number nine on the right. Each of the four generating numbers, when added to the central heavenly number five, becomes a completed number.

成天地之文者，為陰陽交而著其文理也。極其數者，為極天地之數也。天地之極數，五十有五之謂也。遂定天地之象者，天地之數既設，則象從而定也。

The phrase "forming the patterns of heaven and earth" means that after the interaction of yin and yang, their patterns and order became evident. "Exhausting the numbers" refers to investigating the numbers of heaven and earth to their utmost limit. The extreme number of heaven and earth refers to the total of fifty-five. "Thus establishing the images of heaven and earth" means that once the numbers of heaven and earth are arranged, their images are thereby determined.

《經》曰：兩儀生四象。孔氏《疏》謂：金、木、水、火稟天地而有，故云兩儀生四象。土則分王四季，又地中之別惟雲四象也。且金、木、水、火有形之物，安得為象哉？孔氏失之遠矣。

The Great Treatise says: "The two principles give rise to the four images." Kong Yingda's commentary in The Correct Meaning of the Zhou Changes explains that metal, wood, water, and fire are endowed with the qi of heaven and earth, hence they are called the four images. However, earth is strong in the last months of the four seasons and is a special category of the earth's center, so it is not mentioned among the four images. But metal, wood, water, and fire are all tangible things; how can they be called "images"? Kong's explanation is far from correct.

又云：《易》有四象，所以示者。莊氏云：四象謂六十四卦之中有實象，有假象，有義象，有用象也。今於釋卦之處已破之矣。

The Great Treatise also states: "The Book of Changes has four images, so as to show [things]." Zhuang explained that these four images refer to four types among the sixty-four hexagrams: real images, false images, meaningful images, and practical images. This view I have already refuted in my explanation of the hexagram structure.

何氏謂：天生神物，聖人則之，一也；天地變化，聖人效之，二也；天垂象，見吉凶，三也；河出圖，洛出書，聖人則之，四也。今謂此四事，聖人《易》外別有其功，非專《易》內之物。稱《易》有四象，且又云：《易》有四象，所以示也；擊辭焉，所以告也。然則象與辭，相對之物。辭既爻卦之下辭，象謂爻卦之象也。

He Fei regarded the four things listed in the Great Treatise as the four trigrams: the birth of divine objects such as the yarrow stalks and tortoise shells, which the sage took as a model, as the first; the transformation of heaven and earth, which the sage imitated, as the second; the heavenly signs appearing in physical forms to indicate auspiciousness and misfortune, as the third; and the emergence of the River Diagram and the Lake Book from the Yellow River and Luo River, which the sage took as a model, as the fourth. I believe these four things are the achievements of the sage outside the Book of Changes, and not exclusively internal to the Book of Changes, and thus cannot be used as evidence for the statement that "the Book of Changes has four trigrams." Moreover, the text also says: "The Book of Changes has four trigrams, so that they may be shown; and explanations are attached, so that they may be told." This clearly shows that "trigrams" and "explanations" are two distinct things: since "explanations" refer to the words attached below the hexagrams and lines, "trigrams" must refer to the images inherent in the hexagrams and lines themselves.

上兩儀生四象，七、八、九、六之謂也。諸儒有謂七、八、九、六，今則從以為義也。且疏家以七、八、九、六之四象，為所以示之四象，則駁雜之甚也。何哉？夫七、八、九、六，乃少陰、少陽、老陰、老陽之位，生八卦之四象，非《易》之所以示四象也。

The four images mentioned in the previous text "Two Principles give rise to Four Images" refer to the numbers seven, eight, nine, and six. Among various schools of thought, some have already proposed the idea that these four numbers represent the four images. I will now follow this interpretation. However, commentators have confused the group of four images consisting of seven, eight, nine, and six with the group of four images mentioned in "so as to illustrate," making the explanation very messy. Why? The numbers seven, eight, nine, and six correspond to the numbers of Young Yang, Young Yin, Old Yang, and Old Yin, respectively. They are used to generate the eight trigrams, and they are not the four images that the Book of Changes uses to convey its teachings to people.

略試論之：且夫四象者，其義有二：一者謂兩儀所生之四象，二者謂《易》有四象，所以示之四象，若天一、地一不天三、地四所以兼天五之變化，上下交易，四象備其成數，而後能生八卦矣。於是乎，坎、離、震、兌居四象之正位。不云五象者，以五無定位，舉其四則五可知矣。

Let me briefly discuss: the term "four images" has two meanings. The first refers to the four images generated from the two principles, and the second refers to the "four images of the Book of Changes, so as to show them." In the first sense, the four generating numbers, namely heaven one, earth two, heaven three, and earth four, each combine the transformation of heaven five. They interact with each other above and below, and the four images complete their numbers, thus giving rise to the eight trigrams. Therefore, the four trigrams Kan, Li, Zhen, and Dui occupy the central positions of the four images. The reason we do not say "five images" is that five has no fixed direction; by mentioning these four, five is naturally included among them.

夫五上駕天一，而下生地六；下駕地二，而上生天七；右駕天三，而左生地八；左駕地四，而右生天九，此河圖四十有五之數耳。斯則二儀所生之四象。

Heavenly Five moves upward to control Heavenly One, and generates Earthly Six below; it moves downward to control Earthly Two, and generates Heavenly Seven above; it moves right to control Heavenly Three, and generates Earthly Eight on the left; it moves left to control Earthly Four, and generates Heavenly Nine on the right—this is the number of forty-five points in the He Tu diagram (the numbers one through nine add up to forty-five). All of the above belong to the group of four images generated from the two principles.

所謂《易》有四象，所以示者，若《繫辭》云：吉凶者，失得之象，一也；悔吝者，憂虞之象，二也；變化者，進退之象，三也；剛柔者，晝夜之象，四也。且孔氏《疏》云：象之與辭，相對之物。辭既爻卦之下辭，象謂爻卦之象也。又上句云：《易》有四象，所以示也。下句云：擊辭焉，所以告也。

As for the four images mentioned in the phrase "The Book of Changes has four images, so as to show," these should be determined according to what is said in the Great Treatise. The first is jiu xiong, which refers to the image of gain and loss; the second is hui lin, which refers to the image of worry; the third is bian hua, which refers to the image of advancing and retreating; the fourth is gang rou, which refers to the image of day and night. Moreover, Kong Yingda's commentary itself states that images and words are two different things. Since words refer to the textual expressions attached to the hexagrams and lines, images refer to the symbolic representations of the hexagrams and lines. The previous sentence says "The Book of Changes has four images, so as to show," and the next sentence immediately follows with "attached are words, so as to inform."

詳其吉凶、悔吝、變化、剛柔四者之象，既《擊辭》所陳，則與爻卦正協其義也。而又孔氏復引二儀所生之四象，舉七、八、九、六之數，則其義非也，不亦失之甚乎？

Carefully examining the images of auspiciousness, misfortune, hesitation, and transformation, since all these are stated in the Great Treatise, they naturally correspond with the hexagrams and yao lines, and their meanings are coherent. However, the Master Kong introduced the four images generated by the two principles, bringing in the numbers seven, eight, nine, and six, which is incorrect. Is this not a serious mistake?

五行成數者，水數六，金數九，火數七，木數八也。水居坎而生乾，金居兌而生坤，火居離而生巽，木居震而生艮。巳居四正而生乾、坤、艮、巽，共成八卦也。

The completed numbers of the Five Phases are: water's completed number is six, metal's is nine, fire's is seven, and wood's is eight. Water resides in the position of Kan and gives rise to the Qian trigram, metal resides in the position of Dui and gives rise to the Kun trigram, fire resides in the position of Li and gives rise to the Xun trigram, and wood resides in the position of Zhen and gives rise to the Gen trigram. Once Kan, Li, Zhen, and Dui have occupied the four cardinal positions (the original text's "巳" is a mistake for "已"), each of these four cardinal positions gives rise to one trigram, resulting in the four trigrams of the corners: Qian, Kun, Gen, and Xun. Adding the four cardinal trigrams to the four corner trigrams, the Eight Trigrams are formed. This diagram distributes the numbers six, seven, eight, and nine among the four cardinal positions, and then draws one trigram from each cardinal position to the four corner positions.

此乃五行生成數，本屬洛書，此畫之者欲備天地五十五數也。

This picture depicts the pairing of the generating numbers and the completed numbers of the Five Phases—the one with six, two with seven, three with eight, four with nine, and five with ten, which originally belong to the Luoshu diagram. Here, it is drawn to make up the total number of fifty-five for heaven and earth.

內十五，天地之用，九六之數也。兼五行之數四十，合而為五十有五，備天地之數也。

These three diagrams arrange the odd numbers of Heaven: one, three, five, seven, and nine, and the even numbers of Earth: two, four, six, eight, and ten, as well as the complete set of numbers combining both. The fifteen dots in the inner layer represent the sum of the Heaven and Earth generating numbers, which are the numbers based on the hexagram Qian's "All Nines" and Kun's "All Sixes." Adding the five elements' completing numbers makes a total of forty dots, resulting in a total of fifty-five, completing the numbers of Heaven and Earth.

《經》曰：凡天地之數五十有五，此所以成變化而行鬼神也。又日：大衍之數五十，則臧天地之數五也。韓氏日：演天地之數，所賴者五十也，則不言臧五之數。所以孔氏《疏》以為五十有五，乃天地陰陽奇偶之數，非是文演天地之策也。

The Great Treatise says: "All the numbers of heaven and earth total fifty-five, which is why they can produce changes and act as ghosts and spirits." It also says: "The great derivation involves fifty numbers." This shows that the number of the great derivation is obtained by subtracting five from the numbers of heaven and earth (the original text "臧" is a mistake for "减," meaning "to subtract"). Han Kangbo's commentary says that the derivation of the numbers of heaven and earth is based on fifty, but he does not explain why five is subtracted. Therefore, Kong Yingda's commentary argues that fifty-five is merely the total number of yin and yang odd and even numbers in heaven and earth, and not the actual number used by the sage in calculating the divination sticks (this sentence is missing a character in the original text, and the same is true in the Siku Quanshu edition).

且諸儒分大衍之數，分而為二之義中，則述天地之數五十有五之用，末則陳四營成易、十有八變而成卦之理。此豈可同乎本末，而異其中之數也？瓦乎蝶曹之數以象天地，豈可舍其數而求其象乎？斯亦疏家之失，不求天五退藏於密之義也。

Now, when various schools explain the "Great Derivation Number," they refer to the part about "dividing into two" based on the number fifty-five of heaven and earth. But when they reach the end, "four operations form the Book of Changes, and eighteen transformations form the hexagram," they rely on another set of numbers. Since the beginning and end both refer to the number of heaven and earth, how can the numbers in between be based on a different system? Moreover, the number used in divination with yarrow stalks is originally meant to symbolize heaven and earth (the original text's "蝶曹" is a mistake for "揲蓍"), so how can one ignore its numerical aspect and seek only its symbolic meaning? This is also a mistake in the commentary. The root of the problem lies in not investigating the meaning of "five of heaven hidden in secrecy."

且夫五十有五，天地之極數也。大衍之數，天地之用數也。蓋由天五不用，所以大衍之數少天地之數五也。

Fifty-five is the extreme number of heaven and earth; the great derivation number fifty is the number used by heaven and earth. Since the number five of heaven is not directly involved in use, the great derivation number is five less than the number of heaven and earth.

或曰：天五不用，何以明其不用之由？答日：天五不用，非不用也，是用四象者也。且天一、地二、天三、地四，此四象生數也，天五所以斡四象生數而成七、九、六、八之四象，是四象之中皆有五也。則知五能包四象，四象皆五之用也。舉其四，則五在其中矣。故《易》但言四象，以示不言五象也。

Someone asked: If it is said that the number five of Heaven is not used, on what basis can we explain why it is not used? The answer is: The statement that the number five of Heaven is not used does not mean it is truly unused, but rather that it is used in the four trigrams. The numbers one and two of Heaven and Earth, three and four of Heaven and Earth are the generating numbers of the four trigrams. The number five of Heaven coordinates these four generating numbers, transforming them into the four completed numbers seven, nine, six, and eight. That is, two plus five equals seven, four plus five equals nine, one plus five equals six, and three plus five equals eight. This shows that the number five is present in each of the four trigrams. Therefore, the number five encompasses the four trigrams, and the four trigrams are all the result of the number five. By mentioning these four, the number five is already included. Hence, the Book of Changes only mentions the four trigrams to reveal to people, and does not mention the fifth trigram.

今搽蓄之義，以筮而尚占者也，以象天地之用數，所以大衍之數臧天地之數五也。

The purpose of using the divination method of counting the yarrow stalks is to emphasize divination and inquiry, drawing upon the symbolic representation of the numerical patterns of heaven and earth. Therefore, the number of the Great Transformation is five less than the number of heaven and earth.

大衍之數五十，其用四十有九。韓氏注日：衍天地之數，所賴者五十。其用四十有九，則其一不用也。不用而用以之通，非數而數以之成，斯《易》之太極也。四十有九，數之極也。夫元不可以元明，必因於有，固嘗於有物之極，而必明其所由之宗也。

The Great Treatise says: "The number of the great derivation is fifty, but only forty-nine are actually used." Han Kangbo's commentary explains that the number used to deduce the principles of heaven and earth is fifty, but only forty-nine are actually employed, meaning one stalk of yarrow is left unused. This "one" does not participate in the actual use, yet all the use depends on it to be connected; it is not a number, yet all numbers depend on it to exist. This is the Taiji of the Book of Changes. Forty-nine represents the ultimate of numbers. "Nothing" cannot be made evident by "nothing" itself; it must rely on "something." Therefore, the origin of things is revealed precisely where the form reaches its extremity. (In the original text, every occurrence of the character "yuan" is a mistake for "wu," and the same applies below.)

孔氏《疏》：京房云：五十者，謂十日、十二辰、二十八宿也。凡五十其一不用者，天之生黑將欲以虛求實，故用四十九焉。馬季長云：《易》有太極，謂北辰。北辰生兩儀，兩儀生日月，日月生四時，四時生五行，五行生十二月，十二月生二十四黑。北辰居位不動，其餘四十九運而用之也。

Kong Yingda cites several previous scholars in his "Justice." Jing Fang says: fifty refers to the total number of ten heavenly stems, twelve earthly branches, and twenty-eight constellations added together; one is omitted because the qi generated by heaven requires emptiness to seek reality, so only forty-nine are used. Ma Rong (style name Jichang) says: The "I Ching" has the Taiji, which is the North Star; the North Star gives rise to the two principles, the two principles give rise to the sun and moon, the sun and moon give rise to the four seasons, the four seasons give rise to the Five Phases, the Five Phases give rise to the twelve months, and the twelve months give rise to the twenty-four solar terms; the North Star remains in its place and does not move, while the other forty-nine are in motion to be used by people. (In the original text, all instances of the character "he" are errors for "qi.")

荀爽云：卦各有六爻，六八四十八，加《乾》、《坤》二用，凡五十。初九潛龍勿用，故用四十九也。鄭康成云：天地之數，五十有五者，以五行黑通於萬物，故臧五；大衍又臧一，故用四十九。姚信、董遇云：天地之數，五十有五者，其六以象六畫之數，故臧而用四十九也。顧懼云：立此五十數以數神，神雖非數，因子而顯，故虛其一數，以明不可言之義也。

Xun Shuang said: Each of the eight trigrams has six lines, six multiplied by eight gives forty-eight. Adding the two special lines, 'Use Nine' in the Qian hexagram and 'Use Six' in the Kun hexagram, makes fifty. However, since the initial line of the Qian hexagram is 'The Dragon Hidden, Not to Be Used,' the actual number used is forty-nine. Zheng Xuan (styled Kangcheng) said: The number of heaven and earth is fifty-five because the five phases' energies permeate all things, so five is subtracted. Then again, the Great Derivation subtracts one more, resulting in forty-nine. Yao Xin and Dong Yu said: The number of heaven and earth is fifty-five, where six is used to symbolize the six lines of a single hexagram, so six is subtracted, resulting in forty-nine. Gu Huan said: The number fifty is established to calculate numbers in relation to the divine. Though the divine is not a number, it is revealed through numbers. Therefore, one number is left out to indicate the meaning that cannot be spoken.

今詳諸家所釋，義有多端，雖各執其說，而理則未允。敢試論之：韓氏《注》以虛一為太極，則未詳其所出之宗也。何者？夫太極生兩儀，兩儀既分，天始生一，肇其有數也。而後生四象五行之數，合而為五十有五，此乃天地之極數也。

Looking carefully at the various interpretations, they are all confused and contradictory, each holding to its own view, yet none of the reasons are convincing. Please allow me to attempt my own explanation. Han Kangbo took the 'one' that is empty and not used as the Taiji, but he did not clarify where this Taiji comes from. Why is this so? Taiji gives rise to the two principles, and after the two principles are separated, the 'one' is born from Heaven, and thus numbers begin. Then from this, the four images and the numbers of the Five Phases are generated, totaling fifty-five, which is the extreme number of heaven and earth.

今若以太極為虛一之數，則是大衍當用五十有四也。不然，則餘五之數，元所設耳。況乎大衍衍天地之數也，則明乎後天地之數矣。大衍既後天地之數，則太極不可配，虛其一之位也明矣。

Now, if the Taiji is considered the empty and unused "one," then the Da yan should only subtract one from fifty-five, leaving fifty-four for practical use. If not calculated this way, the remaining five numbers would become idle numbers with nowhere to be placed. Moreover, Da yan is used to deduce the numbers of heaven and earth, indicating that it comes into being after the numbers of heaven and earth. Since Da yan comes after the numbers of heaven and earth, Taiji cannot be paired with it, and thus cannot serve as the empty and unused "one" position. This point is quite clear.

又元不可以元明，必因於有，是則以太極為元之稱。且太極者，元黑混而為一之時也。其黑已兆，非元之謂，則韓氏之《注》，義亦迂矣。

Han's commentary also says, "Nothing cannot be manifested by itself; it must rely on something existing." This equates the Taiji with the term "wu" (nothingness). However, the so-called Taiji refers to the stage where the primordial qi is unified as a whole; since the qi has already begun to manifest, it cannot be called "wu" anymore. In this view, Han's commentary appears to be overly convoluted.

或曰：韓氏之《注》，承輔嗣之旨。且輔嗣之《注》，獨冠古今，斐然議之，元乃不可乎？答曰：此必韓氏之寓言，非輔嗣之意也。且若愚以胸臆論之，是謂狂簡。今質以聖人辭，且《易》有太極，是生兩儀，《易》既言有，則非元之謂也。不其然乎？

Some people say: Han Kangbo's commentary follows the spirit of Wang Bi (styled Fusi). Wang Bi's "Commentary on the Yi" is unparalleled through the ages. How can you criticize it so extensively? The answer is: This statement must be Han's own way of expressing his views, not Wang Bi's original intention. Moreover, if I were to criticize merely based on my own opinion, that would be reckless and hasty. Now, I am using the words of the sages to challenge it — the "Great Treatise" says, "The Yi contains the Taiji, from which the two principles arise." The text says "has," not "does not have." Is it not so?

至於京、荀、馬、鄭眾賢之論，皆採摭天地名數，強配其義。□□□且若以天地之名數，強加配偶，則靡所不可。□然而天地之數，生成相因，理如貫珠，不可駢贅而設也。雖能強立其義，推而究之，則於所由之宗不會矣。試論於末篇。

As for the interpretations of sages such as Jing Fang, Xun Shuang, Ma Rong, and Zheng Xuan, they all selected existing names and numbers from heaven and earth, forcing them together to form a meaning. (The original text is missing several characters here, and the Siku Quanshu edition also notes this omission.) If names and numbers from heaven and earth can be forced into such pairings, then nothing would be impossible to pair. (The original text also has missing characters here.) However, the numbers of heaven and earth, the original numbers and the completed numbers, are interdependent and mutually generating, their order resembling a string of beads connected in sequence. They cannot be arbitrarily added like extra fingers or redundant warts. Although these interpretations maywith difficulty hold together a certain meaning, when pursued further, they ultimately fail to connect with the original source of the numbers. This point I will discuss in the final chapter.

天地之數十有五，居其內而外斡；五行之數四十也，今止用其四十九者，何也？蓋由天五為變化之始，散在五行之位，故中元定象。又天一居尊而不動，以用天德也。天德，九也。天一者，象之始也，有生之宗也，為造化之主，故居尊而不動也。

The numbers of Heaven and Earth amount to fifteen in total, located in the inner layer and rotating outward. The completed numbers of the Five Phases total forty, arranged in the outer layer. Now only forty-nine are used. This is because the number five of Heaven is the beginning of all changes, which has already been distributed among the five phases. Therefore, there is no fixed symbol in the center (the term "yuan" in "zhongyuan dingxiang" refers to "wu," meaning "nothing"). Furthermore, the number one of Heaven occupies the honorable position and remains still, used to express the virtue of Heaven. The virtue of Heaven is nine. The number one of Heaven is the starting point of symbols, the origin of all living things, and the master of creation, so it remains still in the honorable position.

惟天三、地二、地四之數，合而成九陽之數也。天三則乾之三畫，地二、地四則坤之六畫也。地道元成而代有終，陽得兼陰之義也。故乾之三兼坤之六，成陽之九，斡運五行成數，而通變化也，所以搽曹之義以象其數也。

Only when the numbers three from Heaven, two from Earth, and four from Earth are combined together can the yang number nine be formed. The three from Heaven corresponds to the three lines of the Qian hexagram; the two and four from Earth add up to six, corresponding to the six broken lines of the Kun hexagram. The Earth path itself achieves nothing, but can only take the place of Heaven to complete its affairs, which is precisely the reason why yang can encompass yin. Therefore, the three lines of Qian incorporate the six lines of Kun, forming the yang number nine, which governs the five phases' completed numbers and thus connects all changes. The method of divination with yarrow stalks is intended to symbolize this number.

或問日：《易》云《坤》元用六，今則乾三兼之，是坤之六元用乎？答日：非也，在其中矣。此蓋《易》舉其多數而言之也。數六是少數，舉其多則少可知矣。是知陽進而《乾》元用九，陽退則《坤》元用六也。亦由當期之日，惟合老陰、老陽之數，其少陰、少陽之數，則在其中。舉多兼少，《易》義皆然矣。

Someone asked: The Book of Changes clearly states that the hexagram Kūn has "use of sixes," but now it is said that the three lines of Qian have absorbed it. Then, is the six of Kūn not of any use? The answer is: Not at all useless, but it is already included within. This is how the Book of Changes speaks by emphasizing the greater aspect: six is a smaller number, so by mentioning the greater, the smaller is naturally understood. From this we can see that when yang energy advances, Qian has "use of nines," and when yang energy recedes, Kūn has "use of sixes." This is similar to the full count of 360 days in a year, which is composed only by the two extreme numbers, old yang (Qian's count of 216) and old yin (Kūn's count of 144). The counts of young yang and young yin are naturally included within. By emphasizing the greater and including the smaller, this is the consistent method used in the Book of Changes.

且夫七、八、九、六之數，以四位合而數之，故老陽四九則三十六也，少陽四七則二十八也，老陰四六則二十四也，少陰四八則三十二也。

The numbers seven, eight, nine, and six are calculated by grouping them in sets of four: old yang is four nines, totaling thirty-six; young yang is four sevens, totaling twenty-eight; old yin is four sixes, totaling twenty-four; and young yin is four eights, totaling thirty-two. The previous four figures of young yang, young yin, old yang, and old yin each show the number of dots for seven, eight, nine, and six respectively. This figure combines all four together, showing the number of each multiplied by four, resulting in the corresponding measure or count.

乾畫，奇也。坤畫，偶也。且乾、坤之位分，則奇偶之位列，則陰陽之位序矣。

The trigram Qian consists of a single continuous line, which is considered odd; the trigram Kun consists of two broken lines, which is considered even. Each trigram consists of three lines. Qian uses three odd lines arranged from bottom to top to form three positions, while Kun uses three even lines to form three positions. Once the positions of Qian and Kun are separated, the positions of odd and even are established, and the sequence of yin and yang is determined.

《經》日一陰一陽之謂道。韓氏《注》云：道者，元之稱，元不通也，元不由也。況之日道，寂然元體，不可為象，必有之用極，而元之功顯，故至於神元方，而《易》元體，而道可見矣。故窮變以盡神，因神而明道，陰陽雖殊，元一以待之。在陰為元陰，陰以之生，在陽為元陽，陽以之成，故日一陰一陽也。

The Great Treatise says: "One yin and one yang is called the Dao." Han Kangbo's commentary says: what is referred to as the Dao is the name of "wu" (nothingness); it is everywhere and through everything, so it is compared to the Dao. It is quiet and has no form, so it cannot be taken as an image; only when the "you" (being) reaches its extreme, does the function of "wu" become apparent. Therefore, when "shen wu fang er yi wu ti" (the spirit has no fixed form and the Book of Changes has no definite body), the Dao can be seen. Thus, by thoroughly investigating changes to exhaust the subtlety of the spirit, and then relying on the spirit to understand the Dao; although yin and yang are different, they are both supported by this "wu"—on the yin side, it is "wu yin," yin is born through it; on the yang side, it is "wu yang," yang is formed through it. Therefore, it is said, "one yin and one yang." (In the original text, every instance of the character "yuan" is a mistake for "wu.")

又孔氏云一謂元陰元陽，乃謂之道也。觀其註疏之家，祖述元以為義，不釋其道之妙用也。且道元形，亦必陳乎宗旨。《易》稱一陰一陽之謂道，必垂一陰一陽之義耳。

Kong Yingda also said: this "one" refers to the state without yin or yang, which is called Dao. Looking at these commentators who make annotations and commentaries, they all follow the concept of "nothingness" to establish their arguments, but they are unwilling to explain where the subtle application of Dao lies. Although Dao may have no form, its main idea must be clearly explained. Since the Book of Changes says "one yin and one yang is called Dao," it must be intended to illustrate the meaning of the four characters "one yin and one yang" themselves.

略試論之：且夫一陰一陽者，獨陰、獨陽之謂也。獨陰、獨陽且不能生物，必俟一陰一陽合，然後運其妙用，而成變化；四象因之而有，萬物由之而生，故日元不由之謂道也。

Let me briefly explain: what is meant by "one yin and one yang" refers to a single yin and a single yang. A single yin or a single yang cannot give rise to myriad things. Only when one yin and one yang come together can their subtle function be manifested and transformation occur. The four images thus arise, and all things are generated from this. Therefore, it is said that "the thing from which nothing is excluded is called the Dao."

若夫獨陰、獨陽者，天地所稟。天獨陽，地獨陰。至於五行之物，則各含一陰一陽之黑而生也。所以天一與地六合而生水，地二與天七合而生火，天三與地八合而生木，地四與天九合而生金，天五與地十合而生土，此則五行之質，各稟一陰一陽之黑耳。

As for pure yang and pure yin, these belong to heaven and earth respectively: heaven is entirely yang, and earth is entirely yin. When it comes to the five phases, each contains both yin and yang energies. Therefore, heaven one (yang) combines with earth six (yin) to produce water, earth two (yin) combines with heaven seven (yang) to produce fire, heaven three (yang) combines with earth eight (yin) to produce wood, earth four (yin) combines with heaven nine (yang) to produce metal, and heaven five (yang) combines with earth ten (yin) to produce earth—the forms of the five phases all arise from the combination of one yin and one yang. The two diagrams "Yang with Yin" and "Yin with Yang" illustrate the presence of yin within yang and yang within yin, while the two diagrams "Heaven alone Yang" and "Earth alone Yin" illustrate the pure, singular nature of heaven and earth.

至於動物、植物，又合五行之黑而生也。今欲明其義，故先布天地獨陰、獨陽之體，次列五行含二黑之象，末陳人稟五行之質也。

As for animals and plants, they also arise by combining the energies of the Five Phases. Now, in order to clarify this principle, we first outline the essential nature of Heaven and Earth as purely Yin and purely Yang. Next, we list the manifestations of each of the Five Phases, which contain two types of energies. Finally, we explain the diagram illustrating how humans receive the material essence of the Five Phases.

土，元象也，分王四季。地，則積陰之黑；黑稟獨陰，不能生物也。暨天五與地十合而生土，成其形質，附地而載，是為五行之一也。故《疏》云：土者，是地中之別耳。所以地則稱乎獨陰，土則稟乎二黑也。

The element of earth does not have its own specific symbolic representation, but it is dominant at the end of each of the four seasons. Earth is formed from accumulated yin energy, which is purely yin in nature and cannot generate things by itself. Only when the number five from heaven combines with the number ten from earth does earth come into being, thus acquiring its form and quality. It attaches itself to the earth and supports all things, thereby becoming one of the five elements. Therefore, Kong Yingda explained that earth is merely a category within the earth. This is why earth is called "sole yin," while earth (as an element) possesses both yin and yang energies. Previously, the diagrams for fire (Li), water (Kan), wood (Zhen), and metal (Dui) each combined numbers seven, six, eight, and nine respectively with the four directions. This diagram, however, combines five and ten to occupy the central position, thus completing the position of earth.

《易》之為書也，廣大悉備，有天道焉，有人道焉，有地道焉，兼三才而兩之，故六六者非他也，三才之道也。然則三才之道，上、中、下之位；三才之用舍五行，則斯須元以濟矣。

The book of Changes is vast and comprehensive, encompassing heavenly ways, human ways, and earthy ways. It combines the three fundamental elements of heaven, earth, and humanity, each represented by two lines, so that a single hexagram consists of six lines. These six lines are nothing else but the way of the three fundamental elements. The way of the three fundamental elements is divided into three positions: upper, middle, and lower. However, for the three fundamental elements to function, once the five phases are abandoned, they cannot accomplish anything at all.

至於人之生也，外濟五行之利，內具五行之性。五行者，木、火、土、金、水也。木性仁，火性禮，土性信，金性義，水性智，是故圓首方足，最靈於天地之問者，蘊是性也。人雖至愚，其於外也；日知由五行之用，其於丙也。或蒙其性而不循五常之教者，可不哀哉？

As for human survival, outwardly people take advantage of the benefits of the Five Phases to sustain themselves, while inwardly they possess the inherent nature bestowed by the Five Phases. The Five Phases are wood, fire, earth, metal, and water. The nature of wood is benevolence, fire is propriety, earth is trustworthiness, metal is righteousness, and water is wisdom. Therefore, humans, who are round-headed and square-footed, the most intelligent beings between heaven and earth, inherently contain these five qualities within themselves. Even the most ignorant person, in external matters, knows every day to rely on the functions of the Five Phases; however, in their inner nature, some people cover up their innate qualities and refuse to follow the moral teachings of benevolence, righteousness, propriety, wisdom, and trustworthiness. Is this not pitiable?

乾，天也，故稱乎父，下濟而光明。

Qian represents Heaven, so it is called the father. The father's way flows downward to assist all things, thus appearing bright. This diagram depicts the Yang line of Qian flowing from above into the body of Kun.

坤，地也，故稱乎母，卑而上行焉。

Kun represents the earth, so it is called the mother; the principle of the mother is to be lowly and to ascend. This diagram depicts the yin line of Kun moving upward from below into the body of Qian.

震一索而得男，故謂之長男。

The Zhen hexagram is the male hexagram obtained from the first interaction between Qian and Kun, hence it is called the Elder Son. This diagram depicts the yang of the first line of Qian entering the lower position of the Kun body to form Zhen.

巽一索而得女，故謂之長女。

The trigram Xun is the female trigram obtained from the first union and seeking of Qian and Kun, hence it is called the Elder Sister. This diagram depicts the yin of the first line of Kun entering the lower position of Qian's body to form Xun.

坎再索而得男，故謂之中男。

The Kan hexagram is the male hexagram obtained the second time when the Qian and Kun hexagrams interact and seek each other, hence it is called the Middle Male. This diagram depicts the Yang line of Qian entering the middle position of the Kun body to form Kan.

離再索而得女，故謂之中女。

The Li hexagram is the female hexagram obtained the second time when Qian and Kun interact, hence it is called the Middle Female. This diagram depicts the Yin line of Kun entering the middle position of Qian's structure to form Li.

艮三索而得男，故謂之少男。

The Gen hexagram is the male hexagram obtained for the third time through the interaction of Qian and Kun, hence it is called the Young Male. This diagram depicts the Yang line of Qian entering the upper position of the Kun body to form Gen.

兌三索而得女，故謂之少女。已上更布自然之象者，蓋欲明上下自然交易相生之理，成八卦變化之義也。

The Dui hexagram is the female hexagram obtained the third time through the interaction of Qian and Kun, hence it is called the Young Girl. The illustration shows the Yin line of Kun entering the upper position of Qian. The reason these natural images are arranged one by one in the above diagrams is to demonstrate the natural exchange between the upper and lower trigrams and the principle of mutual generation between them, thereby revealing the meaning of the transformation of the Eight Trigrams.

夫《易》有太極，是生兩儀，兩儀生四象，四象生八卦。八卦成列，象在其中矣；因而重之，爻在其中矣。則知太極乃兩儀之始，八卦則重卦之始也。重卦之首以《復》卦，何謂也？陽黑之始也。

The Great Treatise says: "The Book of Changes contains the Taiji, from which the two principles arise; the two principles give rise to the four images, and the four images give rise to the eight trigrams." It also says: "When the eight trigrams are arranged in order, the images are already contained within them; by adding layers to them, the lines are already contained within them." From this we can understand that Taiji is the beginning of the two principles, and the eight trigrams are the beginning of the compound trigrams. Then why is the hexagram of Fu used as the first hexagram? Because Fu is precisely the starting point of the emergence of yang energy.

略試論之：且夫四正之卦，所以分四時十二月之位，兼乾、坤、艮、震者，所以通其變化；因而重之，所以效其變化之用也。觀其變化之道，義有所宗，故其《復》卦生於坎中，動於震上，交於坤，變二震、二兌、二乾而終。自《復》至《乾》之六月，斯則陽爻上生之義也。

Let me briefly explain: the four trigrams Kan, Li, Zhen, and Dui are placed in the cardinal positions to correspond with the four seasons and twelve months. In addition, the trigrams Qian, Kun, Gen, and Xun (originally written as Zhen, but it should be Xun) are used to connect and express their transformations. By stacking the eight trigrams two by two, we are imitating the function of these transformations. Observing the pattern of these transformations, each has its origin: The hexagram Fu arises from the middle line of Kan, initiates from the upper line of Zhen, and interacts with Kun. Then the yang lines gradually ascend in position, undergoing two transformations each in Zhen, Dui, and Qian, until completion. From Fu to Qian, this process spans exactly six months, representing the gradual growth of the yang lines from the bottom to the top, month by month.

《娠》卦生於離中，消於巽下，交於乾，變二巽、二艮、二坤而終。自《娠》至於《坤》之六月，斯則陰爻下生之義也。自《復》至《坤》，凡十二卦，主十二月。卦主十二月，中分二十四黑二，爻分七十二候，以周其日月之數。是故離、坎分天地，子午以束為陽，子午以西為陰。若夫更錯以他卦之象，則總三百八十四爻，所以極三才之道。

The hexagram Gou (originally written as "shen", a mistake for "gou") arises from the middle line of Li (Fire). It begins to decline from the lower position of Xun (Wind) and intersects with Qian (Heaven). After that, the yao (line) of yin grows gradually from the top downward, undergoing two changes in Xun, two in Gen (Mountain), and two in Kun (Earth), thus completing the process. From Gou to Kun, there are exactly six months, which represents the meaning of yin lines growing from top to bottom. From Fu (Return) to Kun, there are twelve hexagrams, each corresponding to one month; within the twelve months, there are twenty-four solar terms, and each yao is divided into seventy-two "hou" (periods), used to encompass the entire cycle of the sun and moon's movements throughout the year. Therefore, Li (Fire) and Kan (Water) are positioned at the extremes of heaven and earth: divided by the line of Zi (Rat) and Wu (Horse), the eastern half belongs to yang, and the western half belongs to yin (the original text mistakenly wrote "shu" instead of "dong" for east). If we further incorporate the images of the other hexagrams, totaling three hundred eighty-four lines, they are used to exhaust the principles of heaven, earth, and humanity.

或問曰：合數圖以正之，卦之與爻分四時十二月之位，又兼乾、坤、艮、巽之卦通其變。且《復》卦生坎中，動於震，交於坤。《易》日：地中有雷，復。正協其義也。若《娠》卦則生於離之中，消於巽，交於乾。《易》日：天下有風，娠。且巽非四正之卦也，則與《復》卦不同其義。今卦體則是巽承於乾，而變易其位從兌者，何謂也？

Someone asked: By matching the numbers on the diagram, the hexagram and its lines are assigned to the directions of the four seasons and twelve months. It also incorporates the four cardinal trigrams, Qian, Kun, Gen, and Xun, to connect with the changes. The hexagram Fu arises from the middle line of Kan and moves to Zhen, crossing into Kun. The Great Image Commentary says "Thunder in the Earth, Fu," which exactly matches this explanation. As for the hexagram Gou, it arises from the middle line of Li and dissipates into Xun, crossing into Qian. The Great Image Commentary says "Wind over the World, Gou." However, Xun is not one of the four cardinal trigrams, so this is different from the case of Fu. Now the structure of Gou is clearly Xun below supporting Qian above, yet you have changed its position to Dui. Why is that?

答曰：斯則取《歸妹》之象。《易》曰：歸妹，天地之大義也。天地不交，則萬物不興。歸妹者，人之終始也。所以資長男交少女之義，交少女而長女主其卦者，明其妹繫於姊嫁，而妹非正也，所謂侄娣之義也。

The response says: This refers to the image of the hexagram "Return of the Maiden." The Commentary on the Judgment of the hexagram "Return of the Maiden" states: "Return of the Maiden" represents the great principle between heaven and earth. When heaven and earth do not interact, all things cannot arise. The matter of "Return of the Maiden" relates to the beginning and end of human relationships. Therefore, the hexagram uses the image of the eldest son (Zhen) and the young maiden (Dui) coming together. Although the one who comes together is the young maiden, the eldest daughter (Xun) is used as the main element of the hexagram, indicating that the younger sister follows the elder sister in marriage, and the younger sister is not the main wife, which reflects the ancient practice of the "zhi di" system, where the younger sister accompanies the elder sister as a bride.

若以長男交長女，雖曰夫婦常久之道，然未盡廣延之理也；則知能終其始者，必歸妹也，故《易》稱天地之大義。是以卦之變易，必從《歸妹》，妹非正室，必以姊主其卦也。是以其體則取兌合震，其名則以巽承乾也。變易之義，其在茲乎？

If only the eldest son and eldest daughter are paired together, although this conforms to the principle of a lasting marriage, it does not fully explain the principle of continuing the family line. Therefore, those who can maintain harmony from beginning to end must be represented by the image of "Returning to Marriage" (归妹). Hence, the Book of Changes calls it the great principle of heaven and earth. Therefore, the change of the hexagram must be determined according to the hexagram of "Returning to Marriage": since the younger sister is not the main wife, she must be guided by the elder sister. Therefore, in terms of the structure of the hexagram, it takes the union of the trigram of Joy (兑) and Thunder (震), which is exactly the structure of "Returning to Marriage." In terms of the name of the hexagram, it is called "Encountering" (姤) because the trigram of Wind (巽) follows the trigram of Heaven (乾). The principle of change is roughly this.

原缺前賢釋三才之義，皆以設剛柔兩畫，以布二黑，布以三位，而象三才。謂聖人率意以畫之矣。斯亦不詳《繫辭》之義也。夫卦者，天垂自然之象也。聖人始得之於河圖、洛書，遂觀天地奇偶之歟，從而畫之，是成八卦，則非率意以畫其數也。

In previous times, scholars explained the meaning of "three elements" as establishing two types of lines, yao, to distribute the energies of yin and yang, and then arranging them into three positions to symbolize the three elements. This is equivalent to saying that the sages arbitrarily drew them. This also fails to grasp the original meaning of the Great Treatise. A hexagram is the natural image revealed by heaven. The sages first obtained it from the River Chart and the Lake Chart, then observed the odd and even numbers of heaven and earth, and according to these numbers, they drew them, thus forming the Eight Trigrams; they did not draw these numbers out of a sudden whim.

略試論之：夫三畫所以成卦者，取天地自然奇偶之數也。乾之三畫而分三位者，為天之奇數三，故畫三位也。地之偶數三，亦畫三位也。餘六卦者，皆乾、坤之子，其體則一，故亦三位之設耳。

Let me briefly explain: the reason three lines can form one trigram is because they are derived from the odd and even numbers inherent in heaven and earth. The trigram Qian is drawn with three lines and divided into three positions, because the odd number of heaven takes 'three,' so it is drawn as three positions; the even number of earth is also arranged into three positions in the same way. The other six trigrams are all the children of Qian and Kun, and their structures all originate from the same source, so they are all set to have three positions.

且夫天獨陽也，地獨陰也。在獨陽、獨陰，則不能生物。暨天地之黑、五行之數定，始能生乎動植，故《經》日：有天地然後萬物生焉。豈一黑之中，有蘊三才之道邪？

Heaven is purely yang, and Earth is purely yin. If they remain in their purely yang or purely yin states, nothing can be generated. Only when the energies of Heaven and Earth and the numbers of the Five Phases are established can animals and plants come into being. Therefore, the "Xugua Zhuan" says: "Only after Heaven and Earth are formed can all things be generated." Could the concept of the Three Principles (Heaven, Humanity, and Earth) already be contained within a single line and a single breath?

所謂兼三才而兩之，蓋聖人重卦之義也，非八純卦之謂也。三才，則天、地、人之謂也；兩之，則重之謂也。上二畫為天，中二畫為人，下二畫為地；以人合天地之黑生，故分天地之黑而居中也。所以九二稱在田，明地道也；九五稱飛龍在天，明天道也。斯則其理坦然而明白矣。

The "Say on the Trigrams" says "combine the three elements and double them," which refers to the sages stacking the eight trigrams to form the sixty-four hexagrams, not the eight original trigrams each with three lines. The three elements are heaven, earth, and humanity. "Doubling them" means each element is represented by two lines. Thus, each hexagram has six lines: the top two lines belong to heaven, the middle two lines belong to humanity, and the bottom two lines belong to earth. Humanity is born from the union of heaven and earth's energies, so a portion of the energies of heaven and earth is placed in the middle. Therefore, the second line of the Qian hexagram, "Seeing the dragon in the field," clearly indicates the way of earth; the fifth line, "The dragon flying in the sky," clearly indicates the way of heaven. This makes the principle clear and straightforward.

如日不然，敢質之於《繫辭》，日：六爻之動，三極之道也。又曰：有天道焉，有人道焉，有地道焉，兼三才而兩之，故六。六者，非他也，三才之道也。又日：昔者聖人之作《易》，將以順性命之理，是以立天之道日陰與陽，立地之道日柔與剛，立人之道日仁與義，兼三才而兩之，故《易》六畫而成卦。

If you do not agree, please allow me to cite the classics as evidence. The Great Treatise says: the changes of the six lines in one hexagram embody the principles of heaven, earth, and humanity. The Great Treatise also says: a hexagram contains the way of heaven, the way of humanity, and the way of earth. It combines the three elements and uses two lines to represent each, hence six lines; these six lines are nothing else but the principles of the three elements. The Book of Changes also says: the ancients created the Book of Changes to follow the principles of life and destiny. Therefore, they established the way of heaven as yin and yang, the way of earth as flexibility and strength, and the way of humanity as benevolence and righteousness. By combining the three elements and using two lines for each, the Book of Changes forms a hexagram with six lines.

斯則皆云六畫包三才之義，則無三畫報三才之說，不其然乎？若夫六爻皆有人事者，為人倫則天法地之象，故初上皆包人事之義耳。

These passages all discuss the six lines encompassing the three elements, showing that there is no concept of 'three lines representing the three elements.' Is it not so? As for the six lines, which often refer to human affairs, this is because human relationships are originally based on following the heavens and emulating the earth. Therefore, even the first line and the top line contain the meaning of human affairs.

《正義》曰：陽黑始《剝》盡，謂陽黑始於《剝》盡之後，至陽黑來《復》時，凡七日也。其釋注分明。如褚氏、莊氏並云：五月一陰生，至十一月一陽生，凡七月。而云七日不云月者，欲見陽長須速，故變月而言日也。

Kong Yingda in The Correct Meaning of the Zhou Changes says: The phrase "the yang energy begins to be stripped away completely" refers to the period starting from when the yang energy is completely stripped away in the Hexagram of Stripping, up to when the yang energy returns and forms the Hexagram of Reversion, which takes a total of seven days. He explains Wang Bi's commentary in a clear and explicit manner. As for Chu's and Zhuang's interpretations, they both state that in the fifth month, the first yin energy begins to arise, and in the eleventh month, the first yang energy begins to arise, spanning a total of seven months. The classic text says "seven days" rather than "seven months" in order to emphasize that the growth of yang energy must be rapid, hence changing "month" to "day."

一今瀚嗣云：《剝》盡。至來《復》，是從《剝》盡至來《復》時經七月也。若從五月言之恤何得雲始盡也？又《臨》卦亦是陽長言八月，今《復》卦亦是陽長，何獨變月而稱日？觀《注》之意，必為不然，亦甩《易緯》六日七分之義，同鄭康成之說，但於文省略，不復具言。

Now Wang Bi says, "After the hexagram of 'Breaking' (Pei), the hexagram of 'Returning' (Fu) comes." This means that from the hexagram of Pei, where the yang energy is completely stripped away, to the hexagram of Fu, where yang energy returns, it takes seven months. If we follow the views of Chu and Zhuang, who start counting from May, how can they say that this happens after the yang energy is completely stripped away? Moreover, the hexagram of Ling also talks about the growth of yang energy, yet it says, "There is danger by August." Now the hexagram of Fu also speaks of the growth of yang energy, so why does it change "month" to "day"? Looking at Wang Bi's annotations, it is clear that he does not follow the views of Chu and Zhuang. He probably adopts the meaning from the "Yi Wei" that "six days and seven parts," which is the same as Zheng Xuan's view, but he expresses it more briefly without elaborating fully.

按《易緯稽覽圖》云：卦黑起於艮、巽、離、坎、震、兌，各主一方；其六十卦，卦有三百六十爻，日凡主三百六十日，餘有五日四分日之一，每日分為八十分，五日分為四百分；四分日之一，又為二十分，是四百二十分。六十卦分之，六七四十二，各得七分是每卦得六日七分也。

According to the *Yi Wei·Ji Lan Tu*, the trigrams' energies begin with Gen, Xun, Li, Kan, Zhen, and Dui, each governing one direction; excluding these trigrams, the remaining sixty trigrams contain a total of three hundred and sixty lines, exactly matching the three hundred and sixty days of a year. There remains five and one fourth days in a year: dividing one day into eighty parts, five days make four hundred parts; the one fourth day is equivalent to twenty parts, totaling four hundred and twenty parts. Dividing these four hundred and twenty parts among the sixty trigrams, six multiplied by seven equals forty-two, so each trigram receives seven parts, meaning each trigram corresponds to six days and seven parts.

《剝》卦陽黑之盡，在九月之末，十月當純《坤》用事，《坤》卦在六日七分之前，從《剝》盡至腸黑來《復》、隔《坤》之一卦六日七分。舉成數言之，故輔嗣言：凡七日也。

The hexagram of "Breaking Up" indicates the complete exhaustion of yang energy, occurring at the end of the ninth month; the tenth month is governed by the hexagram of "Earth" which is entirely yin. The hexagram of "Earth" occupies a position of six and seven parts. From the complete exhaustion of yang in the hexagram of "Breaking Up" to the return of yang, the interval exactly corresponds to the six and seven parts of the hexagram of "Earth." When considering whole numbers, Wang Bi says "a total of seven days."

且今七日來《復》之義，詳夫孔氏之《疏》，雖得之於前，而又失之於後也。何哉？且《易》云七日來《復》，輔嗣之《注》又言七日，雖則引《經》、《注》破褚氏、莊氏之誤，於義為得。末又引《易緯》一鄭氏六日七分，則其理文背《經》、《注》之義。且《易緯》、鄭氏言每卦得六日七分，財未詳六日七分能終一卦之義。

Now looking at the meaning of "seven days to return," we find that Kong Yingda's commentary is correct in the first part but wrong in the latter. Why? The classic text says "seven days to return," and Wang Bi's annotation also mentions seven days. Kong's commentary cites the text and Wang's annotation to refute the errors of Chu and Zhuang, which is correct. However, in the end, he cites the "Yi Wei" and Zheng Xuan's "six days and seven parts," which contradicts the original meaning of the text and Wang's annotation. Moreover, the "Yi Wei" and Zheng Xuan only mention that each hexagram takes six days and seven parts, but they never clearly explain how six days and seven parts can complete a hexagram.

略試論之：且坎、離、震、兌四正之卦也，存四位，生乾、坤、艮、巽之卦，每位統一時，每爻主一月，此則四純之卦也。又若重卦自《復》至《乾》六爻，而經六月也；自《娠》至《坤》亦六爻，而經六月也，則一爻而主一月也照昭矣。而云六日七分為義，則作《疏》者不思之甚也。

Let me briefly discuss this: Kan, Li, Zhen, and Dui are the four cardinal trigrams, occupying the four cardinal positions, from which the trigrams Qian, Kun, Gen, and Xun are generated. Each cardinal position governs a season, and each line corresponds to a month, which is how the four pure trigrams are divided. Now considering compound trigrams: from Fu to Qian, the yang lines increase from one to six, totaling six lines, spanning six months; similarly, from Guo to Kun, the yin lines also increase from one to six, taking the same six months. This clearly shows that one line corresponds to one month. Yet they insist on establishing meaning based on six days and seven parts, which shows that the commentators were clearly not thinking carefully.

且夫七日來《復》者，十月之末，坤卦既終，陰已退，陽黑復生也。為天有十日，陽上生也。至七為少陽，陰陽交易而生，當陽復來之時，為老陰。待經陰之數盡，至七日少陽。七日來復，則合《經》、《注》之義也。

As for the phrase "seven days to return": by the end of the tenth month, the Hexagram of Earth (坤) has been completed, and the yin energy has entirely receded, allowing yang energy to begin to emerge again. Heaven has ten days (the ten Heavenly Stems), and yang energy grows upward from the bottom. When it reaches the seventh position, it becomes the Lesser Yang. Yin and yang alternate in generation: when yang energy returns, the previous stage was Old Yin; when the count of yin reaches its end, on the seventh day it transforms into Lesser Yang. Thus, the concept of "seven days to return" aligns with the meaning of the classic text and Wang Bi's commentary. (This passage has several missing sections in the original source, and the same is true of the Siku Quanshu edition.)

《繫辭》曰天一、地二，天三、地四，天五、地六，天七、地八，天九、地十，此乃五行生成之數也。天一生水，地二生火，天三生木，地四生金，天五生土，此其生數也。如此，則陽無匹，陰無偶，故地六成水，天七成火，地八成木，天九成金，地十成土。於是陰陽各有匹偶，而物得成矣。故謂之成數也。又曰：天數五，地數五，五位相得，而各有合，此所以成變化而行鬼神謂此也。

The Great Treatise says: "Heaven is one, Earth is two; Heaven is three, Earth is four; Heaven is five, Earth is six; Heaven is seven, Earth is eight; Heaven is nine, Earth is ten." These ten numbers are the generating numbers and the completing numbers of the Five Phases. Heaven one generates water, Earth two generates fire, Heaven three generates wood, Earth four generates metal, Heaven five generates earth. These five are the generating numbers. However, only the generating numbers would not allow the yang numbers to have their counterparts, nor would the yin numbers form pairs. Therefore, the Earth six completes water, Heaven seven completes fire, Earth eight completes wood, Heaven nine completes metal, and Earth ten completes earth. In this way, yin and yang each have their counterparts, and things are formed. Hence, the latter five are called the completing numbers. The text also says: "Heaven has five numbers, Earth has five numbers, the five positions correspond to each other and each has its match." What is meant by "achieving transformation and operating as ghosts and spirits" is precisely this.

又數之所起，起於陰陽；陰陽往來，在於日道。十一月冬至，以及夏至，當為陽來。正月為春，木位也，日南極，陽來而陰往。冬，水位也，當以一陽生為水數。五月夏至，日北極，陰進而陽退。夏，火位也，當以一陰生為火數。但陰不名奇數，必六月二陰生為火數也。

Another school of thought says that the origin of numbers lies in yin and yang, and the movement of yin and yang depends on the path of the sun. From the winter solstice in the eleventh month until the summer solstice, this period is considered the arrival of yang energy. The first month is spring, belonging to the wood position. At this time, the sun reaches the southernmost point, and yang comes while yin retreats. Winter belongs to the water position, so the number 'one', representing the initial emergence of yang, is used for water. In May, at the summer solstice, the sun reaches the northernmost point, and yin advances while yang retreats. Summer belongs to the fire position, so the number representing the initial emergence of yin should be used for fire. However, yin cannot be called an odd number, so the number 'two', representing the emergence of two yins, is used for fire instead.

是故《易》稱《乾》貞於十一月，《坤》貞於六月，來而皆左行。由此冬至以及夏至，當為陽來也。正月為春，木位也，三陽已生，故三為木數。夏至以及於冬至為陰進。八月為秋，金位也；四陰以生，故四為金數。三月春之季，土位五陰以生，故五為土數。此其口口口也。

Therefore this school of thought says: The hexagram Qian is in its proper position in the eleventh month, and the hexagram Kun is in its proper position in the sixth month. Both move in a counterclockwise direction. From the winter solstice to the summer solstice, yang energy is rising: the first month is spring, belonging to the wood position, at which time three yang energies have emerged, so the number three is taken as the number for wood. From the summer solstice to the winter solstice, yin energy is increasing: the eighth month is autumn, belonging to the metal position, at which time four yin energies have emerged, so the number four is taken as the number for metal; the third month is the last month of spring, belonging to the earth position, at which time five yin energies have emerged, so the number five is taken as the number for earth. This is their (the original text is missing three characters) explanation.

又萬物之本有生於元，著生於微。萬物成形，必以微、著為漸；五行先後，亦以微、著為次。五行之體，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，亦是次序之宜矣。劉氏與顧氏皆以為水、火、木、金得土數而成，故水數成六，火數成七，木數成八，金數成九，土數成十，義亦然也。

There is another view: the origin of all things comes from "non-existence" to "existence," from subtle to prominent. All things take form necessarily by progressing from subtle to prominent; the order of the Five Phases is also arranged according to their subtlety and prominence. In terms of their physical forms, water is the most subtle, hence it is ranked first; fire becomes gradually more prominent, hence it is ranked second; wood already has a tangible form, hence it is ranked third; metal has a solid body, hence it is ranked fourth; earth has a vast and broad quality, hence it is ranked fifth—this order is also considered appropriate. Liu and Gu both believe that water, fire, wood, and metal each require the number five of earth to be complete, so the completed number of water is six, fire is seven, wood is eight, metal is nine, and earth is ten, and the reasoning is the same.

今詳眾賢之論，以天一至天五為五行之生數，則不釋所以能生之之義也；以地六至地十為五行之成數，則不釋所以能成之之義也，故學者莫洞其旨。蓋由象與形，不析有元之義也；道與器，未分上下之理也。

Now looking carefully at the discussions of the ancients: they take the numbers from Tian Yi to Tian Wu as the generating numbers of the Five Phases, but do not explain why these numbers can "generate"; they take the numbers from Di Liu to Di Shi as the completing numbers of the Five Phases, but also do not explain why these numbers can "complete." Therefore, scholars have always failed to grasp the true meaning. The root of the problem lies in: when discussing "xiang" and "xing," they have not analyzed the distinction between "you" and "wu"; when discussing "dao" and "qi," they have not clearly distinguished the boundary between the transcendental and the material.

略試論之：《易》曰：形而上者謂之道，形而下者謂之器。則地六而上謂之道，地六而下謂之器也。謂天一、地一不天三、地四，止有四象，未著乎形體，故日形而上者謂之道也。

Let me briefly discuss this. The Great Treatise says: "What is above form is called the Way, and what is below form is called the vessel." Following this reasoning, the numbers one to five above six in the earthly stem belong to the Way, while the numbers six to ten below six in the earthly stem belong to the vessel. This means that the Heaven One, Earth Two, Heaven Three, and Earth Four only form the four images, but have not yet descended to the physical form, so they are called "what is above form is called the Way."

天五運乎變化，上駕天一，下生地六，水之數也；下駕地二，上生天七，火之數也；右駕天三，左生地八，木之數也；左駕地四，右生天九，金之數也；地十應五而居中，土之數也。此則已著乎形數，故日形而下者之謂器。

Heavenly Five operates within to generate transformation: it governs Heaven One above and produces Earth Six below, which is the number of water; it governs Earth Two below and produces Heaven Seven above, which is the number of fire; it governs Heaven Three to the right and produces Earth Eight to the left, which is the number of wood; it governs Earth Four to the left and produces Heaven Nine to the right, which is the number of metal; Earth Ten corresponds with Heaven Five and resides in the center, which is the number of earth. At this point, the numbers have taken form, so it is called "what is formed is called an object."

所謂象之與形者，《易》云：見乃謂之象，河圖所以示其象也。形乃謂之器，洛書所以陳其形也。本乎天者親上，本乎地者親下，故日：河以通乾出天，洛以流坤吐地。《易》者，報道與器，所以聖人兼之而作《易》。《經》云：河出圖，洛出書，聖人則之。斯之謂矣。

The distinction between "xiang" (image) and "xing" (form): The Great Treatise says "when something is seen, it is called xiang." The River Chart is used to display this xiang. "When something takes shape, it is called qi" (object). The Lake Chart is used to arrange this xing. Based on the heavens, things are attached above; based on the earth, things are attached below. Therefore, the Spring Annals says: The Yellow River connects with Heaven and releases the heavenly seed, while the Luo River flows downward to Earth and releases the earthly symbol. The Book of Changes encompasses both the way (dao) and objects (qi) (the original text says "bao" which is a mistake for "bao" meaning "encompass"). Therefore, the sage combined the River Chart and the Lake Chart to compose the Book of Changes. The Great Treatise says "the River produced the chart, the Luo produced the book, and the sage followed them," which refers to this meaning.

且夫河圖之數，惟四十有五，蓋不顯土數也。不顯土數者，以河圖陳八卦之象，若其土數，則入乎形數矣。是兼其用而不顯其成數也。洛書則五十五數，所以成變化而著形器者也。故河圖陳四象而不言五行，洛書演五行而不述四象，然則四象亦金、木、水、火之成數也。

The total number of the He Tu is only forty-five, because it does not display the completed number of Earth. The reason it does not show the Earth number is that the He Tu presents the images of the Eight Trigrams; once the Earth number is included, it would become a tangible number. Therefore, it only incorporates the function of Earth but does not display its completed number. The Luo Shu, on the other hand, has fifty-five numbers, used to achieve transformation and to manifest form and objects. Thus, the He Tu presents the Four Symbols but does not discuss the Five Phases, while the Luo Shu deduces the Five Phases but does not mention the Four Symbols. Therefore, the Four Symbols are actually the completed numbers of Metal, Wood, Water, and Fire.

在河圖，則老陽、老陰、少陽、少陰之數是也；在洛書，則金、木、水、火之數也。所以異者，由四象附土數而成質，故四象異於五行矣。然而皆從天五而變化也。

The same numbers nine, six, seven, and eight: when arranged in the River Chart, they represent the numbers of old yang, old yin, young yang, and young yin; when arranged in the Lo Shu, they represent the numbers of metal, wood, water, and fire. The difference between them lies in the fact that the four trigrams need the number of earth to take form, so the four trigrams and the five elements are divided into two layers. However, both are generated through the movement of the number five from heaven.

至於天數五，地數五，五位相得而各有合焉者，此備陳五行相生之數耳。且五行雖有成數，未各相合，則亦未有所從而生矣。故天一與地六合而生水，地二與天七合而生火，天三與地八合而生木，地四與天九合而生金，天五與地十合而生土。伏犧而下，但乘其數，至黃帝始名，原缺乙丙丁也。

As for the statement 「Heavenly numbers are five, earthly numbers are five, the five positions mutually generate and each has its counterpart」, it fully explains the numerical relationships of the Five Phases. Although each of the Five Phases has its own numerical value, without mutual coordination, they cannot produce tangible things. Therefore, Heaven One combines with Earth Six to generate Water, Earth Two combines with Heaven Seven to generate Fire, Heaven Three combines with Earth Eight to generate Wood, Earth Four combines with Heaven Nine to generate Metal, and Heaven Five combines with Earth Ten to generate Earth. From Fuxi onwards, these numbers were simply used; it was not until the time of the Yellow Emperor that they were given names (the original text here is missing), namely the names of the Ten Heavenly Stems such as Jia, Yi, Bing, Ding, and so on.

今眾賢以一陽生為水數，二陰生為火數，三陽生為木數，四陰生為金數，五陽生為土數，原缺說強配之也，則非天地自然之數也。至於以微、著為漸者，亦非通論，何哉？且以堅固言之，則土不當後於金也；以廣大言之，則火不當後於水也；蓋五行之質，各稟自然，偶合而生，相因於數；微、著之論，實非《經》旨矣。

Nowadays, all the sages have taken one yang as the water number, two yin as the fire number, three yang as the wood number, four yin as the metal number, and five yang as the earth number (the original text here is missing), which are all forced interpretations and not the natural numbers of heaven and earth. As for using "from subtle to manifest" to arrange the order, this is also not a thorough understanding. Why? If we consider firmness, earth should not come after metal; if we consider vastness, fire should not come after water. The forms and qualities of the five phases each receive their nature from the natural world, coming together by chance to produce each other, and they depend on each other according to their numbers. The discussion of ordering them by subtle to manifest is certainly not the original meaning of the classic text.

又若十一月一陽生為奇數者，謂天一動乎坎之中也；五月一陰生為偶數者，謂地二動乎離之中也；以六月二陰生為偶數，則未知所出之宗也。

Furthermore, the statement that the first yang in November is considered an odd number refers to the heavenly stem Tianyi (天一) arising in the middle line of the Kan trigram. The statement that the first yin in May is considered an even number refers to the earthly branch Di'er (地二) arising in the middle line of the Li trigram. As for the claim that the two yins in June are considered even, it is unclear where its basis comes from.

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 An Guo'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 An Guo, 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?