The Book of Changes clarifies distinctions through diagrams.

《仲氏易》（蕭山毛錫齡字天與，善言易，早卒，其季奇齡述之為《仲氏易》）曰：此為揲蓍三致意也。夫秖一揲蓍，而本乾坤而前民用，至於如是。是故未揲之先，合五十之數，聚而不分，有大中之道焉。說文：極，中也。屋極謂之中，言不分於一隅也。崔憬雲舍一蓍為太極，是也。而於是分之為二以象兩，則是太極生兩儀也。李氏《易解》秖四十九數而未分為太極，分之為陰陽，是也。而於是揲之以四以象四時，則是兩儀生四象也。虞翻謂四象即四時，是也。而於是一扐再扐、再變三變而八卦成焉，則是四象生八卦也。荀爽雲四時通變為八卦之所由始，是也。

The Zhongshi Yi (by Mao Xilin of Xiaoshan, who was skilled in explaining the Yi, but died young; his younger brother Mao Qilin compiled his teachings into the Zhongshi Yi) says: This section discusses the repeated process of divination with yarrow stalks. Just the method of divining with yarrow stalks, taking the Qian and Kun trigrams as its foundation, and guiding the people, can reach such a level. Therefore, before divining, fifty yarrow stalks are gathered together, unseparated, and this contains the principle of "Great Center." The Shuowen Jiezi says: "Ji" means the center; the ridge of a roof is called "ji," meaning it is in the center and not biased to any corner. Tang dynasty scholar Cui Jing said, "Discarding one yarrow stalk is the Taiji," which is exactly this meaning. Then the yarrow stalks are divided into two parts to symbolize the two principles, which is "Taiji produces the two principles." Li Dingzuo's Zhouyi Jijie says, "When there are only forty-nine stalks and they are not yet separated, it is Taiji; once separated, it becomes yin and yang," which is exactly this meaning. Then counting in groups of four to symbolize the four seasons, which is "the two principles produce the four images." Yu Fan said, "the four images are the four seasons," which is exactly this meaning. Then one division, two divisions, through two changes and three changes, the eight trigrams are formed, which is "the four images produce the eight trigrams." Xun Shuang said, "the change of the four seasons is the beginning of the eight trigrams," which is exactly this meaning.

夫如是而所生止八卦已哉？吉凶定則大業即於是生，而況其它乎？所謂生生之謂易，如是矣。其不及掛一象三、歸奇象閏者，略言之也，猶後文秖言象四時也。舊以太極兩儀泛指天地，則於「易有太極」「易有四象」兩「易有」不合，一；謂是伏羲畫卦時，則畫卦是作卦，不是生卦，繫辭凡言生，如生變化、生吉凶、生情偽、生利害，皆是筮卦非畫卦也，二；

So if this is the case, is the only thing produced the Eight Trigrams? Once good and bad fortune are determined, great undertakings arise from this, and what about other things? The phrase "the continuous generation is called the Book of Changes" is exactly what this means. Here, the expressions "hang one to symbolize three" and "return the odd to the handle to symbolize the leap month" are not mentioned, which is simply a concise narration, just as later it only says "to symbolize the four seasons." If the old interpretation takes "the Supreme Ultimate" and "the Two Principles" generally as heaven and earth, then this does not match the sentence structure "the Book of Changes has the Supreme Ultimate" and "the Book of Changes has the Four Images," which is the first point that does not make sense. If one says this is referring to Fuxi drawing the trigrams, then drawing the trigrams is "creating the trigrams" rather than "producing the trigrams." In the "Great Treatise" transmission, whenever the word "produce" is used, such as "produce change and transformation," "produce good and bad fortune," "produce human deceit," and "produce benefit and harm," it refers to the trigrams obtained by divination, not the trigrams drawn, which is the second point that does not make sense.

伏羲畫卦是由乾而坤而六子，而因重以至六十四，夫子本辭自言之，並無由一而二而四之法，三；太極秪中而不分之義，而為圗為說，聚訟不決，此必不可為訓者，四；四象從來無解，五。且後文明云「易有四象，所以示也」，與下「所以告」「所以斷」同，若指畫卦言，則陰陽老少但畫時取資之象，謂可以示世、告世、斷吉凶乎？

Fuxi drew the trigrams, starting from Qian to Kun, then proceeding to the six subsidiary trigrams, and finally combining them to form the sixty-four trigrams. Confucius' commentary explicitly states this, and there is no doubling method from one to two, then two to four, as mentioned in the third point, which does not make sense. The term "Taiji" merely means "residing in the center without division," yet later scholars have drawn diagrams and established theories about it, leading to endless disputes, which certainly cannot be taken as a standard, as mentioned in the fourth point. The term "four images" has never had a clear interpretation throughout history, which is the fifth point that does not make sense. Moreover, the text clearly states "The Book of Changes has four images, so it can be shown," with the same grammatical structure as the following sentences "so it can be told" and "so it can be judged." If this refers to the process of drawing the trigrams, then yin and yang as old and young are merely the images used in drawing the trigrams. Can they really be used to show the world, inform people, or judge fortune and misfortune?

蠡吾李剛主塨與毛太史奇齡《訊易書》曰：易有太極一節，先儒舊說反覆思之不解。以兩儀為天地，然八卦之乾坤天地也，豈天地生天地乎？若以兩儀為陰陽，則乾坤陰陽也，亦陰陽生陰陽矣，一不解也。四象為木火金水等說，先生闢之詳矣，況乾坤之上，先儒以太極為主宰尚有理，若又有兩儀四象，則乾坤之上不容有許多對象也，二不解也。繫辭曰「天地設位而易行乎其中」，則易者從乾坤六子而名之者也，乃言易有太極以生天地，三不解也。

Li Nen, a man from Liwu, wrote to Ma Qilin, a historian, in his book "Xun Yi Shu" that the passage "The Book of Changes has the Taiji" has been a puzzle to previous scholars. If "two principles" are interpreted as heaven and earth, but the trigrams Qian and Kun already represent heaven and earth, then how can heaven and earth give birth to heaven and earth again? If "two principles" are interpreted as yin and yang, but Qian and Kun are already yin and yang, then it would be yang giving birth to yang, which is the first point of confusion. If "four images" are interpreted as wood, fire, metal, and water, the master has already refuted this thoroughly; moreover, if previous scholars placed Taiji as the master above Qian and Kun, that could be acceptable, but if between Taiji and Qian and Kun we insert two principles and four images, then there would be too many layers above Qian and Kun, which is the second point of confusion. The "Great Treatise" says, "Heaven and earth are set in position, and the Book of Changes operates within them," indicating that the Book of Changes is named after Qian and Kun and their six sons. Now, however, it says the Book of Changes has Taiji giving birth to heaven and earth, which is the third point of confusion.

先生直以太極為乾，兩儀為乾坤各三而成八卦，塨亦未了然。今忽從先生解「夫易何為」句，謂闡大衍五十之數，生一妄解：謂太極者，大衍之舍一不用者也（唐崔憬有此說）；兩儀者，分而為二以象兩也；四象者，揲之以四以象四時也（先儒以四象為老陽老陰少陽少陰，然亦揲之以四中事也）；八卦統六十四卦而言，四揲十有八變而成之者也。

Master Li Tun still does not fully understand when the Master directly equates the Taiji with Qian and the two principles with Qian and Kun, each generating three trigrams to form the Eight Trigrams. Now, following the Master's interpretation of the sentence "What is the Book of Changes?" I have come up with an immature explanation: the Taiji is the one line not used in the fifty numbers of the Great Derivation (a view already held by the Tang dynasty scholar Cui Jing); the two principles are "divided into two to represent the two," the four images are "divided by four to represent the four seasons" (previous scholars interpreted the four images as old yang, old yin, young yang, and young yin, but actually this is also part of the process of dividing by four); and the Eight Trigrams refer to all sixty-four trigrams, meaning that the divination process involves dividing by four four times, resulting in eighteen changes to form a hexagram.

言易大衍之數遞生以成八卦，而吉凶以定，趨吉避凶而大業以生，仍闡明揲蓍之故也。不言掛一歸奇者，即在兩四之內也。觀前文有「興神物以前民用」，後文有「定吉凶莫大乎蓍龜」及「易有四象所以示也，繫辭焉所以告也，定之以吉凶所以斷也」，似仍闡大衍之數者。惟先生敎之。（仲氏易舊主卦，後改主蓍，李未見，故有此訊。毛驚其闇合，答書大稱賞。）

This passage explains that the great derivation number of the Book of Changes arises in layers to form the eight trigrams, and through this, one determines fortune and misfortune, seeks good and avoids evil to achieve great accomplishments, still elucidating the principle of divination with yarrow stalks. The terms 'hang one' and 'return the odd' are not mentioned because they are already included within 'divide into two' and 'draw four'. Looking at the previous text, there is 'arouse the divine objects to serve the people', and later there is 'to determine fortune and misfortune, nothing is greater than yarrow and tortoise shells', as well as 'the Book of Changes has four images to show, with the Great Treatise to explain, and to determine fortune and misfortune to decide'. From this, it seems this section is still elaborating on the great derivation number. Please enlighten me. (The original version of Zhong Shi Yi argued that this section discusses trigrams, but later changed to focus on yarrow stalks. Li Nen did not see the revised edition, hence this letter of inquiry. Mao Qilin was surprised that the two were in agreement and replied with great praise.)

四象，餘舊主東坡、漢上之說，乾坤為老陽老陰，三男三女為少陽少陰，葢以四象即八卦，八卦即六十四卦也。歲庚辰客京師，因金素公得交於李君，晨夕過從，間以此說就正。李君曰：八卦原該六十四卦，但經明曰四象生八卦，今乃以四象即八卦，是八卦生八卦矣，似難通也。因出《訊易書》並《仲氏易》以示余，餘參酌其說而為之解。

Regarding the "Four Symbols," I (Hu Wei) originally supported Su Shi's and Zhu Zhen's view, considering Qian and Kun as old yang and old yin, and three males and three females as young yang and young yin. Since the Four Symbols are the Eight Trigrams, and the Eight Trigrams are the sixty-four hexagrams. In the year Gengchen of the reign of Emperor Kangxi, while I was staying in the capital, I met Li Nuo through Jin Su Gong's introduction. We met every day, and during these times, I consulted him about this view. Li Nuo said: The Eight Trigrams originally included the sixty-four hexagrams, but the classics clearly state "the Four Symbols generate the Eight Trigrams." Now, if we take the Four Symbols as the Eight Trigrams, it would become the Eight Trigrams generating the Eight Trigrams, which seems inconsistent. Then he showed me his book "Xun Yi Shu" and Mao Qiling's "Zhong Shi Yi," and after considering their views, I made the following explanation.

謹按：天一地二至存乎德行四章，大抵言揲蓍求卦之事。此節上文曰「蓍之德圎而神」，而繼之曰「卦之德方以知，六爻之義易以貢」，是卦爻即揲蓍之所得，非易書已然之畫也。故又曰「神以知來」，曰「是興神物以前民用」，曰「利用出入，民咸用之謂之神」，皆指蓍言也。故唐一行以三變皆剛為太陽、三變皆柔為太陰，而朱子釋此節亦兼主揲蓍，訊易之解良是。

Carefully examined: The passage from the "Great Treatise" in the Upper Part of the "Commentary" from "Heavenly One and Earthly Two" to "Residing in Virtue" mainly discusses the process of divining a hexagram by means of divination with the yarrow stalks. The preceding text says "The virtue of the yarrow stalks is round and divine," then continues with "The virtue of the hexagram is square and knows, the meaning of the six lines is easy to offer," indicating that the hexagram lines here are derived from the divination process with the yarrow stalks, not the fixed hexagrams already drawn in the Book of Changes. Therefore, the following text says "The divine knows what comes," "It is the divine object used before the people's needs," and "It is called divine because it is useful for entering and exiting, and the people all use it," all of which refer to the yarrow stalk divination. Thus, the Tang dynasty monk Yixing interpreted the three changes all being yang as the sun and three changes all being yin as the moon, while Zhu Xi also explained this passage from the perspective of yarrow stalk divination. Li Nen's interpretation in his "Questions on the Book of Changes" is indeed correct.

但以分而為二為兩儀、揲之以四為四象，則其義猶未愜當。葢分而為二，不過分四十九策為左右，即不舍一為太極，其將不可分乎？安見此兩為一之所生乎？揲之以四，不過以左右手四四而數其策，即不分而為二，其將不可數乎？安見此四為兩之所生乎？

However, taking "fèn ér wéi èr" as the two principles (wàiyí) and "duó zhī yǐ sì" as the four images (sìxiàng) is not quite accurate. Because "fèn ér wéi èr" is merely dividing the forty-nine yao into two piles, left and right. Even without first removing one yao as the Taiji, could not two piles still be formed? How can one conclude that this "two" arises from that "one"? Similarly, "duó zhī yǐ sì" is simply counting the yao in groups of four, using both hands. Even without first dividing them into two piles, could not the counting still be done? How can one conclude that this "four" arises from that "two"?

且太極形而上者也，兩儀四象八卦皆形而下者也。八卦粲然成列，則兩儀四象亦必粲然成列。當分二揲四時，正在手中般運，其所謂天地、三才、四時、再閏者，特取譬之假象耳。若夫兩儀四象，則參伍錯綜之餘，通變而成文者也。四營未畢，格中無奇耦之數；三變未終，版上無老少之爻，又安見為兩儀四象哉？

Moreover, the Taiji belongs to the realm beyond form, while the two principles, four images, and eight trigrams belong to the realm of form. Since the eight trigrams are clearly arranged, the two principles and four images must also be clearly arranged. When dividing into two and counting four, the yarrow stalks are being manipulated in the hands, and the so-called heaven and earth, three realms, four seasons, and the leap month are merely metaphorical terms. As for the two principles and four images, they are the results of combining and interweaving, leading to the formation of patterns. Before the four camps are completed, the compartments do not contain odd or even numbers; before the three transformations are finished, the board does not have old or young lines. How then can the two principles and four images be discerned?

展轉尋繹，終未豁然。竊意所謂太極者，一而已矣。命筮之初，奇偶未形，即是太極。迨夫四營而成易，合掛扐之策置之於格，或五或四則為奇，或九或八則為偶，是謂太極生兩儀。至於三變而成爻，畫之於版，三奇為□曰老陽，三偶為乂曰老陰，一奇二偶為一曰少陽，一偶二奇為--曰少陰，是謂兩儀生四象。至於九變而為三畫之小成，十八變而得二體之貞悔，是謂四象生八卦。由是各占其所值之卦爻，是謂八卦定吉凶。由是吉者趨而凶者避，是謂吉凶生大業。

I have thought about this repeatedly but still cannot understand it clearly. I privately believe that the concept of the Taiji (Supreme Ultimate) is simply "one." At the beginning of the divination process, before the odd and even numbers are formed, this is the Taiji. When the four camps (four transformations) are completed and one change is made, the yao (lines) are determined by combining the hanging and grasping sticks and placing them in the grid. If the result is five or four, it is odd; if it is nine or eight, it is even. This is called "the Taiji gives rise to the two principles (yin and yang)." When three changes are made to form one line, it is drawn on the board: if all three are odd, it is drawn as "□" and called old yang; if all three are even, it is drawn as "乂" and called old yin; if one is odd and two are even, it is drawn as "一" and called young yang; if one is even and two are odd, it is drawn as "--" and called young yin. This is called "the two principles give rise to the four images." When nine changes are made to form the three lines of the inner trigram, and eighteen changes are made to form the inner and outer trigrams (the贞 and 悔), this is called "the four images give rise to the eight trigrams." From this, one determines the fortune based on the trigrams and lines, which is called "the eight trigrams determine good and bad fortune." From this, one follows the good and avoids the bad, which is called "good and bad fortune lead to great achievements."

故下文結言之曰「定天下之吉凶，成天下之亹亹者，莫大乎蓍龜」，脈絡分明，辭旨融徹，其為揲蓍之序也何疑？總之四象二字苦無定說，今既主一行之剛柔太少，而更推得其所以然，始知四象與單稱象者不同。單稱象者，即易書已然之畫，八卦成列，象在其中是也；四象則蓍策過揲之數，爻所用之九六及不用之七八是也。故下文又曰「易有四象所以示」，謂示人以所值之卦爻也。章中兩言四象，朱子以前四象為聖人畫卦自然之次第，以後四象為揲蓍所得陰陽老少之爻，夫均此四象，且同在一章之中，豈容有二解哉？

Therefore, the following passage summarizes that "to determine the auspiciousness and misfortune of the world and to complete the earnestness of the world, nothing is greater than the divination with the tortoise shell and the yarrow stalks." The logic is clear and the meaning is coherent. This section discusses the order of divining with the yarrow stalks. What is there to doubt? In general, the term "four images" has been unclear throughout history. Now that we have adopted Yixing's interpretation of the four images as the combination of yin and yang, old and young, and further explained the reason behind it, we now understand that "four images" is different from simply "image." When we say "image" alone, it refers to the fixed hexagrams already drawn in the Book of Changes, as expressed in the phrase "when the eight trigrams are arranged, the image is already contained within them." The "four images," however, refer to the numbers obtained through the process of divining with the yarrow stalks, that is, the numbers used for the lines: nine and six for the used lines, and seven and eight for the unused lines. Therefore, the following passage says, "the Book of Changes has four images, so it can be shown," meaning that the hexagram and line obtained through the divination process are made clear to people. This chapter mentions "four images" twice, but Zhu Xi interprets the first "four images" as the natural order of the sage's drawing of the hexagrams and the second "four images" as the yin and yang old and young lines obtained through divining with the yarrow stalks. The term "four images" is the same, and both instances appear within the same chapter. How can there be two different interpretations?

太極兩儀四象之遞生，其為揲蓍之序益洞然而無疑矣。解成，以復於李君。李君答書曰：拙解雖成，然清夜思之，尚未自信，以舍一、分二、揲四是相連之事，非相生之物也。今得妙解，豁然真是相生之序矣，真是生生之易矣，何快如之。

This shows that the Taiji, two principles, four images, and so on, arise successively, exactly matching the sequence of the divination method with yarrow stalks. This makes the explanation clear and beyond doubt. After finishing the explanation, I wrote back to Li Nen. Li Nen replied saying: Although I have written my explanation, when I think about it late at night, I still cannot be confident. Because the steps of "abandoning one, dividing into two, and counting four" are connected in sequence, and are not things that generate each other. Now that I have received your exquisite explanation, I suddenly understand clearly. This is truly the order of mutual generation, truly "the easy is called the ever-renewing," and there is nothing more exhilarating than this.

此節於圗書之義似乎差緩，然《鉤隠》《啟蒙》以太極、兩儀、四象、八卦悉附會於圗書，傳習已久，世莫敢違，故詳著其說，以明此節與圗書無涉，且與畫卦亦無涉，而先天八卦次序之謬因以見雲。

This section seems somewhat distant in clarifying the meaning of the river chart and the lo book; however, liu mu's "yi shu gou yin tu" and zhu xi's "yi xue meng ting" have connected the taiji, two principles, four images, and eight trigrams to the river chart and the lo book. This interpretation has been passed down and taught for a long time, and people dare not contradict it. Therefore, I have detailed the above explanations to show that this section has nothing to do with the river chart and the lo book, nor with the process of drawing the trigrams. The error in the sequence of the earlier heaven trigrams is thus clearly revealed.

右論太極兩儀四象非圗書之所有。

In the previous section, it was argued that the concept of Taiji, two principles, and four images is not inherent in the Yellow River Chart or the Luo Writing.

天生神物，聖人則之。（秀巖李氏曰：《龜筴傳》天下和平，王道得，而蓍莖長丈，其生每百莖，漢儒之說如此。今犍為郡田野間生此蓍草，一本百莖，絶無餘支，愚親觀之，但長可二尺餘，不盡如先儒之說。問諸土人，雲其生亦如常草，但一本百莖，此為異也。）天地變化，聖人效之。（漢上朱氏曰：天地變化，四時行焉，萬物生焉，故聖人效之。）

The Great Treatise says: Heaven produces extraordinary things (the yarrow stalks and the turtle shell), and the sage takes inspiration from them. (Xiuyan Master Li Xinxin said: The Records of the Grand Historian, in the chapter on divination with turtle shells and yarrow stalks, states that when the world is at peace and the Way of the King is practiced, the yarrow stalks grow to a height of ten feet, each stalk producing a hundred stems. This was the view of Han dynasty scholars. Now in Jianwei prefecture, there are fields where such yarrow stalks grow, each stalk producing a hundred stems, with no extra branches. I have personally seen them, but they are not taller than two feet, not entirely as described by earlier scholars. I asked the locals, who said they grow like ordinary grass, but each stalk produces a hundred stems, which is indeed unusual.) Heaven and earth undergo changes, and the sage follows them. (Han Shang Master Zhu Zhen said: When heaven and earth undergo a change, the four seasons proceed, and all things grow, so the sage follows them.)

天垂象，見吉凶，聖人象之。（日月五星，天象也，天不言，示之以象，吉凶見矣，故聖人象之。）河出圗，洛出書，聖人則之。易有四象，所以示也。（朱子曰：四象謂陰陽老少，示謂示人以所值之卦爻。）繫辭焉，所以告也；定之以吉凶，所以斷也。

Heaven shows celestial phenomena to indicate good and bad fortune, and sages take inspiration from them. The sun, moon, and five planets are celestial phenomena; Heaven does not speak, but uses symbols to reveal good and bad fortune, so sages take inspiration from them. When the Yellow River produced a map and the Luo River produced a book, sages took them as models. The Book of Changes has four figures, which are used to reveal. Zhu Xi said: the four figures refer to yin and yang with old and young; "show" means to reveal the hexagram and line to people. Adding words below the hexagram and line is used to inform; using good and bad fortune to judge it is used for decision-making.

程氏遺書入闗錄曰：孔子感麟而作春秋，然麟不出，春秋豈不作？大抵須有發端處，如畫卦因見河圗洛書，果無河圗洛書，八卦亦須作。

The "Record of the Words of the Two Chengs: Entering the Pass" says: Confucius composed the "Spring and Autumn Annals" because he was moved by the appearance of the qilin. However, if the qilin had not appeared, would the "Spring and Autumn Annals" not have been composed? Generally speaking, things always require some initial trigger, just as the trigrams were drawn because of the Yellow River Chart and the Luo Writing. If there had been no Yellow River Chart or Luo Writing, the eight trigrams would still have been drawn.

紫巖張氏浚曰：天生神物，謂蓍龜之探賾索隠、鉤深致逺者是也，聖人則之以明易之象數；天地變化，謂陰陽之消息盈虛、往來進退者是也，聖人效之而為六十四卦；天垂象，謂天之經緯錯雜、縱橫昭著者是也，聖人象之而為三百八十四爻。夫易之象數卦爻，聖人皆得於心，而必參之天地者，葢聖人與天地之心相似，其愛人之心未嘗不同也。然天欲雨，山川必先雲氣，況易之興也，豈無先至之祥乎？

Ziyan Master Zhang Jun said: "Heaven produces divine things," referring to the yarrow stalks and the turtle shell, which can explore the profound, seek the hidden, draw out the obscure, and summon distant meanings; the sage took them as a model to explain the images and numbers of the Book of Changes. "Heaven and Earth change," refers to the waxing and waning, fullness and emptiness, coming and going, advancing and retreating of yin and yang; the sage imitated it to create the sixty-four hexagrams. "Heaven shows an image," refers to the intersecting and crossing, clearly visible constellations in the sky; the sage took their image to determine the 384 lines. The images, numbers, hexagrams, and lines of the Book of Changes, the sage originally obtained them from his own heart, yet he had to verify them against heaven and earth, because the sage's heart is similar to the heart of heaven and earth, and the love for humanity is the same. However, when heaven wants to rain, mountains and rivers must first produce clouds;何况 the emergence of the Book of Changes, could it not have preceded it with auspicious signs?

是以聖人必終之以河出圗洛出書而又則之者，其則皇天以興其易者乎？又況「河圗不出，吾已矣夫」，孔子嘗有是嘆；「九洛之事，治成德備」，莊周嘗有是言。聖人則之，度其時以卜其道之將以興也。而鄭康成溺於緯書，乃云河圗有九篇、洛書有六篇；孔安國又以河圗為八卦、洛書為九疇，此皆蕪穢聖經者矣。甚至以神物、變化、垂象、圗書為四象，此尤不經，學者不可以不辨。

Therefore, the sage must finally say in this chapter, "The river produces the chart, the Luo produces the book, and the sage follows them," probably taking inspiration from heaven to establish the Way of the Book of Changes. Moreover, Confucius once lamented, "If the Yellow River Chart does not appear, my life is probably in vain." Zhuangzi also said, "The affairs of the nine Luo have been completed, and virtue is fully established." The sages taking inspiration from the chart and the book were using them to discern the times and predict the rise of their own Way. However, Zheng Xuan became immersed in the writings of the Waijia (esoteric doctrines), claiming that the Yellow River Chart had nine chapters and the Luo Book had six. Kong AnGuo further interpreted the Yellow River Chart as the Eight Trigrams and the Luo Book as the Nine Categories. These interpretations have made the sacred classics chaotic and corrupt. Even worse, some people equate the four statements "Heaven produces divine objects," "Heaven and Earth change," "Heaven shows signs," and "The river produces the chart and the Luo produces the book" with the "Four Symbols," which is even more absurd. Scholars must not fail to distinguish clearly.

按：此言聖人作易，準天地萬物之理而未嘗自用其私智。蓍草一本百莖，中分為五十，而大衍之數以定，四營之法以立，是謂天生神物，聖人則之。在天成象，在地成形，天地之變化也；剛柔相摩，八卦相蕩，鼓之以雷霆，潤之以風雨，日月運行，一寒一暑，乾道成男，坤道成女，則聖人效之之事也。日月五星，天之垂象也，順序而行則示人以吉，薄蝕陵鬬則告人以凶，聖人設卦觀象，繫辭焉而明吉凶，使占者知所趨避，所以象之也。

Hu Wei commented: This chapter explains that the sage composed the Book of Changes, always taking the principles of heaven and earth and all things as the standard, never acting on his own cleverness. A single plant of the yarrow grass produces one hundred stalks, from which fifty are selected, thus establishing the number of the great derivation, and the method of four camps. This is what is meant by "Heaven produces divine objects, and the sage follows them." In the heavens they become celestial phenomena, on the earth they become forms, which are the changes of heaven and earth. The intermingling of the strong and the weak, and the mutual movement of the eight trigrams, are moved by thunder and lightning, nourished by wind and rain, and guided by the movement of the sun and moon, with the alternation of cold and heat. The way of Heaven produces male, and the way of Earth produces female. These are the things the sage emulated. The sun and moon, and the five wandering stars, are the celestial signs. Their orderly movement indicates auspiciousness to mankind, while their occurrence of eclipses, conjunctions, and conflicts warns of misfortune. The sage set up trigrams to observe these signs, and connected them with words to explain auspicious and inauspicious outcomes, so that those who practice divination may know what to pursue and what to avoid. This is what is meant by "the sage emulated them."

河洛者，地之中也，聖人興必出圗書，伏羲則之以畫卦，文王周公則之以繫彖爻，而開物成務之道備矣。上三者無時不有，圗書則曠世而一出，故末言之。觀下文繫辭與四象並舉，則此實該三聖之事，不必專主伏羲，亦不必謂洛書禹時所出，於易無與也。

The Yellow River and Luo River area is the center of the world, and when sages arise, there must be a revelation of a sacred text: Fuxi took it as a model to draw the trigrams, King Wen and the Duke of Zhou took it as a model to compose the Great Treatise and the Line Statements, thus completing the great way of governing things and achieving all affairs. The three aspects mentioned above—divine objects, transformations, and celestial signs—are always present, but the sacred text appears only once in many generations, so it is mentioned last. Looking at the following text which mentions the Great Treatise together with the Four Images, we can see that this section actually includes the deeds of the three sages—Fuxi, King Wen, and the Duke of Zhou—without being limited to Fuxi alone; nor should we say it has nothing to do with the Zhou Changes just because the Luo Writing is said to have appeared during the time of King Yu of the Xia dynasty.

易有筮無卜，而卜筮蓍龜並言；伏羲所則者河圗也，而並及洛書，學者疑之。蔡季通云：易豈有龜卜之法乎？亦言其理無二而已。愚竊謂上文雖蓍龜並言，而此但云神物，即專指蓍亦無不可。圗書原不止羲禹時出。漢《五行志》劉向曰：昔三代居三河，河洛出圗書。《武帝紀》元光元年詔曰：昔在唐虞，畫象而民不犯；周之成康，刑錯不用，德及鳥獸，麟鳳在郊藪，河洛出圗書。《李尋傳》對災異曰：天下有道，則河出圗，洛出書。《溝洫志》谷永上言：河，中國之經瀆，聖王興則出圗書，王道廢則竭絶。由是觀之，歴代有道之君皆受圗書，非獨羲禹時出也。

The Zhou Yi contains only the method of divination with yarrow stalks and does not include the method of divination with turtle shells. However, the Xici Zhuan mentions both divination with turtle shells and divination with yarrow stalks, and places them side by side. Fuxi's method was based on the He Tu, yet the text also mentions the Luo Shu. Scholars have raised questions about this. Cai Yuanzheng said: How could the Yi contain the method of divination with turtle shells? He argued that it is merely saying that the principles of the two methods are the same. I personally think that although the text mentions both yarrow stalks and turtle shells together earlier, here it only refers to "divine objects," and it is acceptable to interpret this as referring specifically to the yarrow stalks. As for the He Tu and Luo Shu, they did not appear only during Fuxi's and Yu's time. The Han Shu, Wuxing Zhi records Liu Xiang's statement: In the past, the Xia, Shang, and Zhou dynasties were all located in the area of the three rivers. The Yellow River and Luo River produced the He Tu and Luo Shu. The Han Shu, Wu Di Ji records the edict of the first year of Yuan Guang in the reign of Emperor Wu: In the time of Yao and Shun, they only used painted symbols as laws and the people did not commit crimes; during the time of King Cheng and King Kang of Zhou, punishments were not used, and virtue extended to birds and beasts, with qilin and fenghuang appearing in the outskirts of the capital and the marshes. The Li Xin Zhuan records Li Xin's answer to questions about disasters and anomalies: When the world is in order, the Yellow River produces the He Tu and the Luo River produces the Luo Shu. The Gou Xu Zhi records Gu Yong's memorial: The Yellow River is the great river of China. When sage kings arose, it produced the He Tu and Luo Shu. When the Way of the King declined, it dried up and ceased to flow. From this, we can see that throughout history, virtuous rulers have received the He Tu and Luo Shu, not only appearing during the time of Fuxi and Yu.

河圗，象也，故則之以畫卦；洛書，文字也，故則之以繫辭。河圗非必八卦，洛書不盡九疇也。墨子言周文王時河出錄圗，故易緯《乾鑿度》有入戊午蔀二十九年受錄應河圗之說。沈約《宋書·符瑞志》云：周公攝政七年，制禮作樂，鳳凰見，乃與成王觀於河洛，沈璧，禮畢，榮光幕河，青龍臨壇，銜玄甲之圗，坐之而去；禮於洛亦如之，玄龜止於壇，背甲刻書，赤文成字，其言自周公至於秦漢盛衰之符。此皆本諸緯候，殊不足信。

The River Chart belongs to the category of 'images' and thus was used as a model for drawing the eight trigrams. The Luo Writing belongs to the category of 'text' and thus was used as a basis for the Great Treatise. The River Chart is not necessarily the eight trigrams, and the Luo Writing is not limited to the nine categories in the Hongfan chapter. Mozi said that during King Wen's time, a chart appeared in the Yellow River, so the Yi Jing commentary, the Gan Zao Du, mentions 'in the 29th year of the Wuwu cycle, receiving a symbolic record to correspond with the River Chart.' Shen Jue's Song Shu, Fu Rui Zhi says: In the seventh year of Duke of Zhou's regency, he established rites and music, and the phoenix appeared. Then he went with King Cheng to the Yellow and Luo rivers to observe rituals, and sank a jade bi into the water. After the rites, a brilliant light of five colors covered the river surface, and the Azure Dragon appeared on the altar, holding a dark blue script chart in its mouth, then dropped it and left. The same happened at the Luo River, where a black tortoise stood on the altar, its shell engraved with characters, red patterns forming sentences, which spoke of the rise and fall of the Zhou dynasty up to the Qin and Han dynasties. All these are based on the apocryphal writings of the Wai Jing and the Hou Jing, and are not reliable.

然漢書言之鑿鑿，夫子亦有嘆徯之思，是圗書必非不再出之物，安知文王周公不有所則以繫彖爻乎？紫巖以圗書為易興先至之祥，正與夫子鳳鳥河圗並舉之意相合。大傳曰「易之興也其於中古乎」，又曰「當殷之末世周之盛德」，然則二聖繫辭，亦當有先至之祥，易興於中古，豈徒以羑里東山憂患之故哉？

However, the "Book of Han" speaks with certainty, and Confucius himself expressed a longing for the Yellow River Chart, indicating that such a chart is not something that appears once and then disappears. How can we be sure that King Wen and the Duke of Zhou did not take it as a model for composing the Great Treatise and the Line Statements? Zhang Jun regarded the chart as a auspicious omen preceding the emergence of the Way of the Book of Changes, which aligns with Confucius' parallel mention of the phoenix bird and the Yellow River Chart. The "Great Treatise" states, "The emergence of the Book of Changes was probably in the middle ancient times," and also says, "It was precisely during the late Shang dynasty and the flourishing era of the Zhou dynasty." Therefore, the two sages, King Wen and the Duke of Zhou, in composing the Great Treatise, should have also had prior auspicious signs. If the Book of Changes emerged in the middle ancient times, was it merely because King Wen was imprisoned in Youli and the Duke of Zhou conducted eastern campaigns, suffering these hardships?

易將興而圗書出，所謂先天而天弗違也；圗書出而易遂作，所謂後天而奉天時也。記曰：清明在躬，志氣如神，耆欲將至，有開必先，天降時雨，山川出雲。聖人一天而已，時至事起，何容心焉？

The Book of Changes was about to arise and the diagrams and texts appeared, which is what the Wenyan section of the Qian hexagram says: "Before the time of heaven, heaven does not contradict it." When the diagrams and texts appeared and the Book of Changes was subsequently composed, this is "after the time of heaven, yet following the heavenly way." The Li Ji, in the section "Confucius in Leisure," says: When one possesses the virtue of clarity and brightness within oneself, one's aspirations and spirit become like those of a deity; when what one desires is about to arrive, there must first be a sign, just as when heaven intends to send timely rain, mountains and rivers first raise clouds. The sage is originally one with heaven; when the time comes, things naturally occur, so why would one need to exert deliberate effort?

鄭氏玄易注曰：春秋緯曰：河以通乾出天苞，洛以流坤吐地符，河龍圗發，洛龜書成。河圗有九篇，洛書有六篇。（隋經籍志：緯書《河圗》二十卷、《河圗龍文》一卷，其書出於前漢，有河圗九篇、洛書六篇，自黃帝至周文王所受本文；又別有三十篇，雲自初起至於孔子，九聖之所増演以廣其意；又有七經緯三十六篇，並云孔子所作，並前合為八十一篇。）

Zheng Xuan's commentary on the Zhou Yi says: The Spring and Autumn Waijing states that the Yellow River communicates with the Heaven Trigram Qian and thus emits the heavenly symbol, while the Luo River flows through the Earth Trigram Kun and thus emits the earthly mandate. In the Yellow River, a dragon diagram appears, and in the Luo River, a turtle script is formed. The He Tu has nine chapters, and the Luo Shu has six chapters. (According to the Sui Shu, the Catalogue of the Classics, the Waijing texts on the He Tu include twenty volumes of the He Tu and one volume of the He Tu Longwen, which originated in the Western Han dynasty. Among these, the He Tu consists of nine chapters and the Luo Shu six chapters, which are the original texts received by emperors from the Yellow Emperor to King Wen of Zhou. There are also thirty additional chapters, said to have been added and interpreted by nine sages from the beginning up to Confucius, to expand their meanings. There are also seven Jingwei and thirty-six chapters, all said to have been composed by Confucius. Adding these together, there are a total of eighty-one chapters.)

邢昺論語疏云：鄭玄以為河圗洛書龜龍銜負而出，如中候所說龍馬銜甲，赤文綠字，甲似龜背，袤廣九尺，上有列宿斗正之度、帝王錄紀興亾之數是也。今案史記秦始皇三十二年，燕人盧生奏錄圗書曰「亡秦者胡也」，此即所謂錄紀興亡之數，葢圗讖之術自戰國時已有之。

Xing Bing's Commentary on the Analects says: Zheng Xuan believed that the Yellow River Chart and the Luo Writing were brought out by turtles and dragons, as mentioned in the Shang Shu Zhonghou. A dragon horse with a red pattern and green characters in its mouth presented the chart, which was shaped like a turtle's back and measured nine feet in length and width. It recorded the positions of the twenty-eight constellations, the movement of the Big Dipper, and the omens of the rise and fall of emperors. According to the Records of the Grand Historian, in the thirty-second year of Qin Shi Huang's reign, a man from Yan named Lu Sheng presented a book of maps and charts, which read "The one who will destroy Qin is a man from the Hu tribe." This is exactly the kind of book that records the numbers of rise and fall, showing that the art of divination through maps and prophecies existed as early as the Warring States period.

漢武表章聖籍，諸不在六藝之科者皆不得進。及其衰也，哀平之際，緯候繁興，顯附於六藝而無所忌憚。王莽矯用符命，光武尤信讖言，鄭興、賈逵以附同稱顯，桓譚、尹敏以乖忤淪敗，自是習為內學（其事秘密，故稱內）。康成號一代儒宗，不能違眾而獨立，乃據此以注易。

During the Han Dynasty, Emperor Wu honored the sages and their scriptures, and any works not belonging to the Six Arts were excluded from official use. By the time the Han Dynasty declined, during the reigns of Emperor Ai and Emperor Ping, a large number of books called "Wei Shu" (Commentaries) and "Hou Shu" (Later Books) emerged openly, attaching themselves to the Six Arts without hesitation. Wang Mang fabricated omens to seize power, and Emperor Guangwu especially believed in omens. Zheng Xing and Jia Kui rose to prominence by supporting the omens and commentaries, while Han Tan and Yin Min fell into disgrace for opposing them. From then on, studying omens and commentaries became known as "inner learning" (because these matters were secret, they were called "inner"). Zheng Xuan, known as a leading scholar of Confucianism in his generation, could not go against the crowd and hold his own views, so he used these commentaries to explain the "Zhou Yi" (I Ching).

信如所言，則伏羲畫卦之本變為錄紀興亡之數，而河圗亦是文字，洛書且非九疇矣，妖妄不經莫甚於此。故參同契之流得乘隙而起，以九宮之數縱橫十五者冒河圗之名，而稍近於理，世莫能辨。向使東漢諸儒不為緯候所惑，紹先正之傳而更為之發明，彼方技家言安得竄入於吾易而亂聖真、欺來學也哉？噫，是康成之過也。

If it is indeed as Zheng Xuan said, then the basis for Fuxi's drawing of the trigrams would have become a record of the rise and fall of emperors, the numerological signs of imperial destiny. The Yellow River Chart would have become text, and the Luo Writing would no longer be the Nine Categories of the Hongfan. There is no more absurd and baseless claim than this. Precisely because of this, the school of the "Zhou Yi Cang Tong Qi" was able to take advantage of the situation, using the system of adding numbers in the nine-square grid to always arrive at fifteen, and pass it off as the Yellow River Chart. It appears somewhat reasonable, and thus the world has no way of distinguishing it. If the scholars of the Eastern Han dynasty had not been misled by the prophecies and omens in the "Wei Shu" and "Hou Shu," and had instead inherited the correct tradition of the earlier scholars and further elaborated upon it, how could the doctrines of the alchemists have entered our study of the "Zhou Yi," disturbing the true meaning of the sages and deceiving later scholars? Alas, this is Zheng Xuan's fault.

河洛九六之說，至今猶有為彼所惑而遷就其間者。黃氏《象數論》曰：天垂象見吉凶聖人象之者，仰觀於天也；河出圗洛出書聖人則之者，俯察於地也。謂之圗者，山川險易、南北髙深，如後世之圗經是也；謂之書者，風土剛柔、戶口阨塞，如夏之禹貢、周之職方是也；謂之河洛者，河洛為天下之中，凡四方所上圗書皆以河洛繫其名也。愚竊謂伏羲之世風俗淳厚，豈有山川險易之圗？結繩而治，豈有戶口阨塞之書？且舉河洛以該四方，未免曲說，改「出」為「上」尤覺難通矣。

Regarding the question of whether the Yellow River Chart and the Luo Writing consist of nine chapters or six, people even today are still confused by Zheng Xuan's views and attempt to reconcile the two. Huang Zongxi's "Commentary on the Imagery and Numerical Calculations of the Book of Changes" says: "Heaven displays omens to show auspicious and ominous events; sages imitate these omens." This refers to observing the heavens. "The Yellow River produces a chart, and the Luo River produces a writing; sages follow these." This refers to examining the earth. The term "chart" refers to the difficulties and ease of mountains and rivers, and the depth and height of north and south, just like later map records. The term "writing" refers to the toughness and softness of the land and the key points of population, similar to the Xia Dynasty's "Yu Gong" and the Zhou Dynasty's "Zhi Fang." The term "He Luo" is used because the Yellow and Luo Rivers are the center of the world, and all the documents presented from the four directions are named after He Luo. I (Hu Wei) privately believe that in the time of Fuxi, the customs were simple and honest; how could there be charts recording the difficulties and ease of mountains and rivers? At that time, they governed by tying knots, how could there be writings recording the key points of population? Moreover, using He Luo to summarize the four directions is certainly a forced interpretation. Changing the character "sheng" (to emerge) in the text to "shang" (to present) is even more illogical.

毛氏《原舛編》曰：大抵圗為規畫，書為簡冊，無非典籍之類。鄭康成注大傳，引春秋緯云河圗有九篇、洛書有六篇，則直指為簡冊之物，此漢代近古，似乎可案者。夫緯書，六經之稂莠也，康成引以釋經，侮聖已甚，後儒不能鋤而去之，而反為之灌溉滋長焉，其何以息邪而閒道乎？

Ma Qilin's "Original Compilation on the Errors of the Yellow River Chart and the Luo Writing" says: generally speaking, "tu" refers to a drawn diagram, while "shu" refers to a set of bamboo slips bound into a book, both belonging to the category of classical texts. Zheng Xuan, in his commentary on the "Great Treatise," cites the "Spring Annals Commentary" to say that the Yellow River Chart has nine chapters and the Luo Writing has six, directly referring to them as bamboo slip books. This is the view of the Han dynasty, which is closer in time to antiquity and seems still worth relying upon. As for the "Commentaries on the Six Classics," they are like weeds among the six classics. Zheng Xuan used them to explain the classics, which was already a great disrespect to the sages. Later Confucian scholars failed to remove these weeds, instead watering and fertilizing them to make them grow even more. How then could they suppress heretical doctrines and uphold the orthodox path?

揚雄《核靈賦》曰：大易之始，河序龍馬，洛貢龜書。（見李善文選注。）禮緯《含文嘉》曰：伏羲德合上下，天應以鳥獸文章，地應以河圗洛書。

In the Western Han dynasty, Yang Xiong's "He Ling Fu" states: When the Great Easy (Yi) began, the Yellow River successively presented a dragon horse, and the Luo River contributed a tortoise book. (As cited in Li Shàn's "Wen Xuan Zhu.") The Li Wei "Hán Wén Jiā" says: Fuxi's virtue harmonized with heaven above and earth below. Heaven responded with the patterns of birds and beasts, while the earth responded with the Yellow River Chart and the Luo Writing.

按：此謂圗書並出伏羲之世。揚雄與劉歆同時，而其說之互異如此。葢伏羲受河圗，經無明文，即無以驗洛書之果不出也，故諸儒各據所見以為言。然夫子云「上古結繩而治，後世聖人易之以書契」，上古謂包犧神農，後世聖人則黃帝也。許慎說文序曰：神農氏結繩而治，黃帝之史倉頡見鳥獸蹏迒之跡，乃造書契。

Hu Wei's commentary: Both accounts state that the Yellow River Chart and the Luo Writing appeared together in the time of Fuxi. Yang Xiong and Liu Xin were contemporaries, yet their accounts contradict each other so greatly. Since there is no clear record in the classics about Fuxi receiving the Yellow River Chart, there is no way to verify whether the Luo Writing was present at that time or not. Therefore, various scholars have each formed their own theories based on their own opinions. However, Confucius said, "In the ancient past, people used knots to govern, but later sages changed to using written characters." The "ancient past" refers to Fuxi and Shen Nong, and the "later sages" refers to the Yellow Emperor. Xu Shen's "Shuo Wen Jie Zi · Xu" says that Shen Nong used knots to govern, and it was the historian Cang Jie of the Yellow Emperor who saw the tracks of birds and beasts that led to the invention of written characters.

又河圗玉版曰：倉頡為帝，南巡登陽虛之山，臨於玄扈洛汭之水，靈龜負書，丹甲青文以授之。孝經援神契曰：奎主文章，倉頡效象，洛龜曜書，垂萌畫字。則書契興於黃帝之世，倉頡感洛書而作明矣。（孔安國尚書序雲伏羲造書契以代結繩之政，顯背大傳，不可從。）伏羲時未有書名，洛之所出，安得稱書？子云亦未深考耳。

The Yellow River Chart's Jade Edition says: When Cangjie was emperor, he traveled south and climbed Mount Yangxu, arriving at the waters of Xuanhu and Luorui. A divine turtle carried a book, and presented it to him with red stems and blue characters. The Xiaojing Yunsenchui says: The star Kui governs literature, and Cangjie imitated the stars. The turtle from Luo River revealed the book, showing signs and drawing characters. This shows that the use of written records began in the time of the Yellow Emperor, and Cangjie created characters by observing the Luo Chart. This is clear. (Kong Anguo's "Shangshu Xu" says Fuxi invented written records to replace the system of knotted cords, which clearly contradicts the Great Treatise, and should not be followed.) In the time of Fuxi, there was no term "book," so what came from the Luo River could not be called "book." Yang Xiong (whose courtesy name was Ziyun) did not examine this deeply.

漢書五行志劉歆曰：虙犧氏繼天而王，受河圗，則而畫之，八卦是也；禹治洪水，賜雒書，法而陳之，洪範是也。

The Han Shu's Five Elements Chronicle records Liu Xin's statement: Fuxi received the mandate of heaven and became king, accepted the Yellow River Chart, and based on it created the Eight Trigrams; Yu the Great controlled the floods, and heaven bestowed the Luo Writing upon him, which he used to elaborate the Nine Categories of the Hongfan.

張衡東京賦曰：龍圗授羲，龜書畀姒。

In the Eastern Han dynasty, Zhang Heng's "Eastern Capital Assignment" says: the dragon carried a diagram and gave it to Fuxi, and the turtle carried a book and gave it to the姒 surname Xia Yu.

按：禹受洛書，不可謂無其事，然不自禹始也。據河圗玉版、挺輔佐，黃帝堯舜時洛已出龜書矣；亦不自禹止也，據沈約宋書符瑞志，成王周公時洛又出龜書矣。河圗不止羲受，洛書亦不止禹受，故夫子並舉以贊易。

Hu Wei remarked: The story that Great Yu received the Luo Writing cannot be said to be entirely false; but it was not started with Great Yu. According to the Hu Tu Yu Ban and Hu Tu Ting Zuo Fu, the Luo River had already produced turtle scripts during the time of the Yellow Emperor, Yao, and Shun. It was not ended with Great Yu either, as the Shen Yue Song Shu Fu Rui Zhi records that the Luo River again produced turtle scripts during the time of Cheng Wang and the Duke of Zhou. This shows that the Hu Tu was not received only by Fuxi, and the Luo Writing was not received only by Great Yu. Therefore, Confucius mentioned both to praise the Way of the Changes.

吳草廬云：大抵周後漢初，儒家專門之學率是口耳授受，故凡有文辭可記誦者有傳，無文辭不可記誦者無傳。五經皆存而獨樂之一經亡，三百五篇詩皆存而獨笙詩六篇亡，葢以無文辭可記誦故也。若先天古易止有卦畫，河圗洛書止有圗象，則儒家亦不傳，是以魏晉唐宋初之儒不見圗書。

Wu Cheng, a scholar of the Yuan dynasty (also known as Cao Lu), said: In general, during the late Zhou dynasty and early Han dynasty, the specialized studies of Confucianism were passed down orally, so any texts that could be memorized were preserved, while those without written texts that could not be memorized were lost. The Five Classics were all preserved, but the Classic of Music was lost; the 305 poems of the Classic of Poetry were all preserved, but the six笙 poems such as Nan Gai were lost, because they had no written texts to be memorized. If the Earlier Heaven Yi had only trigrams, and the Yellow River Chart and Luo Writing had only diagrams, then Confucianism would not have been passed down. Therefore, scholars of Confucianism from the Wei and Jin dynasties up to the early Tang and Song dynasties had never seen the diagrams and charts.

渭按：自秦禁學，口說流行，漢初挾書之律未除，凡無文字可記誦者，儒家或逸而不傳，亦未可知。然易又與它經不同，秦以為卜筮之書，獨不在禁中，使果有先天古易、河圗洛書，不妨公行於世，何竟無一人知之？

Hu Wei remarked: Since the Qin dynasty banned private schools and knowledge was passed down orally, the "Book of Documents" had not yet been abolished at the beginning of the Han dynasty. Any doctrine without written records to be memorized might have been lost and not transmitted, which is uncertain. However, the Zhou Yi is different from other classics: the Qin people regarded it as a book for divination, and thus it was not included in the list of forbidden books. If there really were the ancient Zhou Yi of the Earlier Heaven, the Yellow River Chart, and the Luo Writing, they could have been openly circulated throughout the world. Why then has no one ever known about them?

且草廬謂儒家無傳，其意以為獨養生家傳之耳。漢蓺文志道家之外，又有房中、神仙、方技諸家，皆不以記誦為事，能傳河圗洛書者也。彼縱私為養生之術，豈遂不知為包犧作易之由也者？孝文好黃老而創置博士，孝武慕神仙而表章六經，儒道二流皆其所尚，真千載一時也。苟出所藏以為人主長生久視之助，且明指為河圗洛書，以附四聖人之易而立於學官，其道將由是大光，奚為終秘而不出乎？宋世之所傳，其非古之河圗洛書也明矣。

Moreover, Wu Cheng said that Confucianism had no transmission, implying that only the practitioners of alchemy and longevity had passed it down. The "Book of Han · Catalogue of Arts and Literature" lists, in addition to the School of Tao, the schools of Housekeeping, Immortality, and Techniques, which do not rely on memorization, precisely those capable of transmitting the Yellow River Chart and the Luo Writing. Even if they privately regarded it as a method for longevity, could they not know that it was the basis for Fuxi's "Book of Changes"? Emperor Wen of Han favored the Yellow and Black doctrines and established the position of Doctor, while Emperor Wu of Han admired immortality and honored the Six Classics. Both Confucianism and Taoism were esteemed by the court, making it a rare opportunity in a thousand years. If they had presented their secret teachings to help the sovereign achieve longevity, and clearly identified it as the Yellow River Chart and the Luo Writing, attaching it to the "Book of Changes" of Fuxi, King Wen, the Duke of Zhou, and Confucius, and placing it in the official schools, this school of learning would have gained great prominence. Why then have they always kept it secret and not presented it? It is clear that the diagrams passed down in the Song dynasty are not the ancient Yellow River Chart and Luo Writing.

昔張平子言緯候虛妄，譬猶畫工惡圗犬馬而好作鬼魅。彼謂龍銜一片之甲、龜負一卷之書者，固不足信；而宋以後圗書之說，亦復與畫鬼魅無異。葢東序之河圗、天錫之洛書，世無其器，任意寫之，無所不可，故或云九圗而十書，或云十圗而九書，或刓方而使之圎，或引圎而使之方；

Zhang Heng, whose name was Pingzi, once said that the writings of the纬书 and the books of the候书 were baseless and false, just like a painter who dislikes painting dogs and horses but prefers to paint ghosts and monsters. Those who said that a dragon was holding a piece of Jia or a turtle was carrying a scroll were already not credible; and the theories about books from the Song dynasty onwards were no different from painting ghosts and monsters. Because the Yellow River Chart displayed in the East Hall and the Luo Writing bestowed by heaven did not exist as physical objects in the world, people could draw them however they wanted. Therefore, some said the Yellow River Chart had nine numbers and the Luo Writing had ten numbers, while others said the Yellow River Chart had ten numbers and the Luo Writing had nine numbers; some cut squares into circles, while others stretched circles into squares.

或作陰陽相含之象（羅願以一圈為河圗，陰陽相含，言出於青城山隠者，見宋文憲集。蔣公順雲當以先天圗為河圗，即此）；或為白黑相間之形（郝經盡廢先儒之說，自畫一圗，為白圈黒圈，與五相間而為十，以白為天奇，以黑為地偶，取三奇為乾、三偶為坤，其餘卦取之亦然，見劉因河圗辨）；

Some people draw it as a circle with yin and yang interwoven (in the Southern Song dynasty, Luo Yuan depicted a circle as the Yellow River Chart, symbolizing the mutual inclusion of yin and yang. He claimed it came from a hermit in the Qingcheng Mountains, as mentioned in Song Lian's "Song Wenxian Gong Ji." Master Jiang Shun supported the view that the Earlier Heaven Diagram should be regarded as the Yellow River Chart, referring to this). Others draw it as a pattern of black and white alternating (in the Yuan dynasty, Hao Jing completely abandoned the previous scholars' interpretations and created his own diagram, arranging ten circles with white and black circles alternating with the number 'five.' He used white circles to represent the odd numbers of heaven and black circles for the even numbers of earth. He took three odd numbers as Qian (Heaven) and three even numbers as Kun (Earth), and the other trigrams were also determined in this way, as discussed in Liu Yin's "River Chart Differentiation.")

或言蜀隠者之秘授（趙撝謙六書本義云：天地自然之圗，世傳蔡元定得於蜀之隠者，秘而不傳。毛氏原舛編云：蜀山隠者、青城隠者及篾叟醬翁之徒，總闇昧不可考，從來無名氏皆是寓言，不必有人者。君平季主皆蜀隠君子，亦皆言易，何必無名也）；或稱武夷君之真傳（謝枋得有一圗，髣髴八卦，作坎離中畫交流，謂之真河圗。袁清容曰：謝先生遯於建安，得圗書於彭翁，彭得之武夷君。原舛編云：此即魏伯陽諸家抽坎填離之術）。

Some say it was secretly passed down by a hermit in the Shu region (Ming dynasty scholar Zhao Huiqian in his work "Original Meaning of the Six Scripts" says: "The diagram of heaven and earth in their natural state," which is traditionally said to have been obtained by Cai Yuanding from a hermit in Shu, and was kept secret. Mao Qilin in his "Original Compilation of Errors" says: what about the hermits of Sichuan mountains, Qingcheng, and figures like Mei Sou and Jiang Wang, they are all indistinct and unverifiable; such nameless figures have always been part of allegory, and may not have actually existed; Yan Junping and Sima Jizhu are both hermits from Shu who also discussed the Book of Changes, so why must we attribute it to nameless people?). Others claim to have received it from the true transmission of the Wuyi Lord (At the end of the Song dynasty, Xie Fangde had a diagram that seemed like the Eight Trigrams, with the middle lines of the Kan and Li trigrams drawn in a cross-like form, which he called the true Yellow River Chart. Yuan Jue (who went by the name Qingrong) said: Mr. Xie retreated to Jian'an and obtained the diagrams from Peng翁, who in turn obtained them from the Wuyi Lord. "Original Compilation of Errors" says: this is actually the same as the "drawing the Kan into the Li" alchemical practice of Wei Boyang's school).

而其所載之以出者，則曰馬之旋毛如星點，龜之甲坼如字畫；或又云馬毛似連錢之文，龜甲有瑇瑁之點。至近世豐坊謂龍駰之革燼於武庫，其象傳於石經（坊偽撰石經正音，有一圈為河圗，其說云：包羲之世，龍駰出於榮河，背上旋毛有此圗象，歴世相傳，至晉元康五年武庫火，駰革燼焉，其象傳於石經，宋藏之秘府，而清敏公手摹之。清敏，坊逺祖稷也。晉書五行志：元康五年武庫火，王莽頭、孔子履、漢髙祖斷白蛇劍一時蕩盡，坊因而附會，以為駰革之燼亦在此年也）。

As for the origins of the diagrams and texts, some say that the dragon's spiral hair resembles stars, and the cracks on the turtle shell resemble characters and patterns. Others claim that the horse's hair resembles the patterns of a horse with a coat of spots, and the turtle shell has spots like those of a tortoiseshell. In more recent times, Feng Fang claimed that the dragon horse's skin was burned in the great fire at the Jin Dynasty's military storehouse, yet its image was passed down through the stone classics. Feng Fang forged the "Stone Classics Correct Pronunciation," in which a circle was used as the Yellow River Chart. He claimed that during the time of Fuxi, the dragon horse emerged from the Xing River, and the spiral hair on its back formed this diagram. It was passed down through the generations until the year 315 of the Western Jin Dynasty, when the military storehouse caught fire, and the dragon horse's skin was reduced to ashes, but its image was preserved in the stone classics. These were collected in the secret treasury during the Song Dynasty and were personally copied by Qingmin Gong. Qingmin Gong was actually Feng Jis, the distant ancestor of Feng Fang. According to the "Book of Jin, Five Elements Chronicle," in the year 315 of the Western Jin Dynasty, the military storehouse caught fire, and the head of Wang Mang, the shoes of Confucius, and the sword of Han Gaozu that cut the white snake were all burned to ashes. Feng Fang took this opportunity to fabricate, claiming that the dragon horse's skin was also burned in that same year.

朱謀<土韋>謂河圗世藏秘府，宋徽宗始出示中外傳寫（謀<土韋>著易象通，有衍河圗一太極、二兩儀、三四象、四八卦，俱作圎圈，葢解剝希夷古太極體而為之。其說曰：三代以來，厥圗世蔵秘府，學者莫得而窺，逮宋徽宗考古搜奇，始出示中外傳寫，迄今寖失其舊，以故學者舍河圗而造太極，昧四象而贅五行，位置顛冥，方物舛謬）。

Zhu Mouzhuo also said that the Yellow River Chart has been kept in the imperial secret treasury throughout the ages, and was only presented for copying both inside and outside the country during the time of Emperor Huizong of Song (In his work "Yi Xiang Tong", Zhu Mouzhuo proposed a set of diagrams for interpreting the Yellow River Chart: one Taiji, two Liyi, three Sanxiang, and four Bagua, all drawn as circles. In reality, this was a dissection of Chen Tuan's ancient Taiji diagram. His claim was that since the Three Dynasties, this diagram has been kept in the secret treasury, and scholars have had no opportunity to see it. It was only when Emperor Huizong sought ancient objects and collected rare things that it was taken out for copying both inside and outside the country. Until now, it has gradually lost its original form. Therefore, scholars have abandoned the Yellow River Chart to create the Taiji diagram, failed to understand the Four Symbols, yet added the Five Phases, resulting in reversed positions and confused directions and things).

而誕謾斯極矣。夫畫工之寫鬼神，雖天容道貌，吾猶不敢信以為真，而況夔魖罔象變相迭出者乎？易道至此，亦陽九之阸、百六之會也。迂談僻論愈出愈奇，矯誣上天，蕪穢聖經，何怪乎歐陽永叔、司馬君實、姚小彭、項平甫、袁機仲、林德久、趙汝楳、王子充、歸熙甫、郝仲輿諸人之慾屏絶圗書也哉！雖然，河圗洛書古實有其事，後之君子不信河洛五九之篇、方圎九十之數可也，並夫子所謂河出圗洛出書者而疑之，則過矣。

It has become absurd and deceptive to this extent. Painters depicting ghosts and spirits, even if they portray the appearance of the heavenly emperor or the style of Daoist sages, I still dare not believe them to be true. How much more so for those strange creatures of mountains and waters, and the ever-changing forms that appear? The principles of the Book of Changes have reached this point, and indeed have encountered the calamity of "Yangjiu" and the meeting of "Bailu." The strange and eccentric discussions have become increasingly peculiar, falsely claiming to represent heaven and deceiving people, thus making the classics of the sages chaotic and corrupt. It is not surprising that figures like Ouyang Xiu (style name Yongshu), Sima Guang (style name Junshi), Yao Xiaopeng, Xiang Anshi (style name Pingfu), Yuan Shu (style name Jizhong), Lin Zhi (style name Dejiu), Zhao Ruyi, Wang Yi (style name Zichong), and Guo Jing (style name Zhongyu) would advocate for completely abandoning the study of books! However, the Yellow River Chart and the Luo Writing did indeed exist in ancient times. Later scholars may reasonably doubt the writings of the River and Luo, as well as the theories of square and circular diagrams and the numbers of nine and ten, but to doubt even Confucius' statement that "the river produced the chart and the Luo produced the book" would be excessive.

右論圗書不過為易興先至之祥。

In the previous section, it was argued that the Yellow River Chart and the Luo Writing were merely auspicious signs preceding the rise of the Yi doctrine, and not the original sources upon which Fuxi based his hexagrams.

《書·顧命》曰：「赤刀、大訓、弘璧、琬琰在西序，大玉、夷玉、天球、河圗在東序。」

The Shangshu · Gu Ming records the situation of the items left by King Cheng of Zhou after his death, stating that the red knife, great instruction, broad jade, and琬琰 were placed in the western hall (west wing), while the great jade, Yi jade, heavenly sphere, and the Yellow River Chart were placed in the eastern hall (east wing). This is the only instance in the pre-Qin classics that treats the "Yellow River Chart" as a physical object, indicating that it was collected and displayed by the royal house of Zhou, thus becoming the most crucial evidence for later debates over what the Yellow River Chart actually was and whether it actually existed. Hu Wei's examination of the Yellow River Chart controversy began with this single reference.

孔氏安國曰：「大訓，虞書典謨。河圗，八卦。伏犧王天下，龍馬出河，遂則其文以畫八卦，謂之河圗。及典謨皆歴代傳寶之。」

An old attribution says that Kong Anguo of the Western Han dynasty (a descendant of Confucius, traditionally regarded as the author of the Commentary on the Book of Documents) explained this passage as follows: "Da Xun" refers to the classic texts such as the "Yao Dian," "Shun Dian," "Da Yu Mu," and "Gao Yao Mu" from the "Yushu"; "He Tu" refers to the Eight Trigrams. During the time when Fuxi ruled the world, a dragon horse emerged from the Yellow River, and Fuxi took the patterns on the dragon's body to create the Eight Trigrams, which was called "He Tu." Together with the classic texts, the He Tu was regarded as a valuable treasure passed down through generations of dynasties.

《論語》：子曰：「鳳鳥不至，河不出圗，吾已矣夫！」

The Analects of Confucius, in the section Zihan, records that Confucius said: "The phoenix will not come again, and the Yellow River will not produce the River Chart again; perhaps my life is coming to an end." Confucius regarded both "the appearance of the phoenix" and "the emergence of the River Chart" as omens of a sage king's rule and heavenly signs. This statement is the most frequently cited classical reference by later scholars discussing the River Chart. It also served as the key justification for Song dynasty scholars who interpreted the River Chart as a diagram of numbers.

何晏《集解》：孔曰：「聖人受命則河出圗，今無此瑞。」「河圗，八卦。」

The annotations by Kong AnGuo cited in the "Collected Explanations of the Analects" by He Yan of the Three Kingdoms Wei dynasty state that when a sage receives the mandate of heaven and ascends the throne, the Yellow River will produce the Yellow River Chart. Now there is no such auspicious omen. Kong AnGuo also notes that the Yellow River Chart is the Eight Trigrams. This shows that the old annotations from the Han to the Wei dynasties all equated the Yellow River Chart directly with the Eight Trigrams, without saying that it was a diagrammatic form composed of black and white dots arranged in numbers.

《禮記·禮運》曰：「天不愛其地，道不愛其寶，人不愛其情，故天降膏露，地出醴泉，山出器車，河出馬圗。」

The Book of Rites, Volume of the Transmission of Rites says: Heaven does not spare its great way, Earth does not spare its treasures, and people do not spare their sincere feelings. Therefore, Heaven sends down sweet dew, Earth produces sweet spring water, and in the mountains natural vehicles appear. In the Yellow River, a "horse figure" appears. (The common edition of the Transmission of Rites has this sentence as "Heaven does not spare its way, Earth does not spare its treasures," with the words "way" and "Earth" reversed in this version.) Hu Wei cites this passage to illustrate that in pre-Qin texts, the River Chart was regarded as a miraculous phenomenon, listed alongside sweet dew, spring water, and natural vehicles, rather than as a system of numerical patterns.

鄭氏玄曰：「馬圗，龍馬負圗而出也。」

Eastern Han dynasty Confucian scholar Zheng Xuan explained that the term "Ma Tu" refers to a dragon horse carrying a diagram emerging from the Yellow River. Zheng Xuan regarded the "Ma Tu" mentioned in the "Li Yun" and the "He Tu" in the "Zhou Yi" and "Lun Yu" as the same thing. The notion of "a dragon horse carrying a diagram" thus became established, and became the standard explanation for the origin of the He Tu in later generations.

孔氏穎達曰：「按《中候·握河紀》注云：『龍馬，龍而形象馬，故云馬圗。』」（或云：《周禮》馬八尺以上曰龍，出於河，猶漢武時天馬出渥窪水也。）

Tang dynasty scholar Kong Yingda, the compiler of the "Five Classics with Correct Interpretations," said that according to the annotations of "Shangshu Zhonghou · Wuhe Ji," the term "longma" refers to a dragon-like creature that resembles a horse, hence called "matu" (horse pattern). There is another interpretation: according to the "Rites of Zhou," a horse over eight chi in height is called "long," and such a horse comes from the Yellow River, similar to the heavenly horse that emerged from the Wuwa water during the Han Wudi period. These two interpretations view "longma" either as a divine creature or as a noble horse originating from the riverbank.

東坡蘇氏曰：「夫河圗、洛書，其詳不可得而聞矣，然著於《易》，見於《論語》，不可誣也。而今學者或疑焉。山川之出圗書，有時而然也。魏晉之間，張掖出石圗，文字粲然，時無聖人，莫識其義耳。河圗、洛書，豈足怪哉！」

Song Dynasty's Su Shi, who was known as Dongpo, said: The detailed accounts of the Yellow River Chart and the Luo Writing are no longer known, but since they are mentioned in the Great Treatise of the Zhou Changes and also appear in the Analects, they cannot be falsely claimed as fabricated. However, nowadays some scholars doubt them. The emergence of books and charts in the mountains and rivers is something that occasionally happens. During the Wei and Jin periods, a stone chart was found in Zhangye Prefecture, with clear writing, but at that time there were no sages to recognize its meaning. How remarkable is it to be surprised about the Yellow River Chart and the Luo Writing!

（《魏志·管寧傳》：青龍四年辛亥詔書：「張掖玄川湧溢，激波奮蕩，寶石負圗，狀象靈龜，宅於川西，嶷然盤峙，倉質素章，麟、鳳、龍、馬煥炳成形，文字告命，粲然著明。」太史令髙堂隆上言：「古王聖帝所未嘗蒙，實有魏之禎命，東序之世寶。」葢隆亦以此石為河圗之類也。）

(According to the "Records of the Three Kingdoms: Wei Records: Guan Ning Biography," in the fourth year of Qinglong during the reign of Wei Mingdi, on the Xinhai day, an imperial edict stated that in the Xuanchuan spring of Zhangye commandery, a spring overflowed, creating waves that surged and erupted, bringing forth a piece of stone bearing a pattern, shaped like a spiritual turtle, located on the west bank of the spring, towering and rising, with a dark green stone surface and white patterns, displaying clear images of qilin, phoenixes, dragons, and horses, and the text on it resembled a heavenly mandate, clearly visible. The Grand Astronomer Gao Tanglong submitted a memorial stating that this was a miraculous omen never before seen by ancient sage kings, truly a favorable omen for the Cao Wei dynasty, and it could be placed in the Eastern Hall as a treasured relic. This shows that Gao Tanglong also regarded this stone as something akin to the Yellow River Chart—this is exactly the basis upon which Hu Wei later inferred that the Yellow River Chart should be classified as a stone.)

厚齋王氏應麟曰：「歐陽公以河圗、洛書為怪妄，東坡曰：『見於《易》，著於《論語》，不可誣也。』南豐曰：『以非所習見，則果於以為不然，是以天地萬物之變為可盡於耳目之所及，亦可謂過矣。』蘇、曽皆歐陽公門人，而論議不苟同如此。」

Wang Yinglin of the Southern Song dynasty (also known as Housh斋, author of "Kunxue Jiwen" and "Yuhai") said: Ouyang Xiu regarded the Yellow River Chart and the Luo Writing as absurd and baseless, while Su Dongpo said, "It is mentioned in the Zhou Changes and recorded in the Analects, so it cannot be falsely fabricated." Also, Zeng Gong (known as Nanfeng Master) said, "It is merely because something is not commonly seen that one hastily concludes it cannot exist, which is equivalent to considering all changes in heaven and earth as things that can be fully known through one's own senses, which is certainly excessive." Both Su Shi and Zeng Gong were disciples of Ouyang Xiu, yet they did not agree with their teacher's views in their discussions.

一卷之書，亦必有師。尊所聞，行所知者，弟子之職也。然自非聖人，不能無過，故語云「智者千慮，必有一失」。夫入室操戈，固非師之所望於弟子，而義苟未安，則為弟子者虛心平氣以待公論之自定，未為不可。彼一聞異議輙疾之如讎，欲執兵而掊其後者，亦非君子之道也。蘇、曽不阿所好，其與世之黨同門、妬道真、挾恐見破之私意而無從善服義之公心者，相去逺矣。

Hu Wei remarked that even if one reads only one volume of books, there must be a teacher. To respect the principles one has learned from a teacher and to practice the knowledge one has understood is the duty of a disciple. However, except for the sages, no one is without faults, so there is a common saying: "Even a wise person, when he considers a thousand things, will surely have one mistake." To use the knowledge passed down by the teacher to attack the teacher himself is certainly not what the teacher expects from his disciple. But if there are indeed flaws in the principles, the disciple should remain humble and calm, waiting for the public opinion to form naturally, which is also acceptable. Those who, upon hearing different opinions, hate them as enemies and wish to take up weapons to strike from behind are equally inconsistent with the way of the gentleman. Su Shi and Cheng Gong did not bend to the teacher's preferences, which is far removed from those in the world who form cliques to protect their fellow students, envy truth, and harbor private fears of being exposed, while having no public spirit of seeking goodness and upholding righteousness.

山陽閻徵君若璩曰：「鳳鳥、河圗皆為帝王盛世之應，故《禮》以天之膏露、地之醴泉、山之器車與馬圗並言，《書》與兊之戈、和之弓、垂之竹矢一時而並陳，原不必定伏羲時出。秖緣《集註》如是，加以世多歐公之徒不信祥異，一似夫子思此不再見之物也者。不知河圗黃帝時亦出，堯、舜、禹時疉出，成王、周公時又出，載諸史志。即下至晚宋，朱子表章四書，有龍駒生於九峰山下，龍首馬身，狀若負河圗者，父老來致賀於元晦，以為與麟至同符，誰謂天人相與之際不有冥通者邪！」

Yan Jue of Shanyang (a scholar of the early Qing dynasty known for his extensive learning and called "the recluse scholar" because he was recommended but declined official posts; he wrote "Commentary on the Ancient Text of the Book of Documents") said: The phoenix bird and the Yellow River Chart are both omens that appear during the flourishing reigns of emperors. Therefore, the "Book of Rites" lists heavenly dew, sweet springs on earth, chariots in the mountains, and the horse pattern in the river together. The "Book of Documents · Gu Ming" also places the Yellow River Chart alongside the spear made by Dui, the bow made by He, and the bamboo arrows made by Chui in the same context. Originally, there was no need to claim that the Yellow River Chart appeared only during the time of Fuxi. It is only because Zhu Xi's "Collected Commentaries on the Analects" mentioned it in that way, and because many people follow Ouyang Xiu's school who do not believe in auspicious signs or portents, that it seems as if Confucius lamented something that would never appear again. They do not know that the Yellow River Chart also appeared during the time of the Yellow Emperor, and appeared repeatedly during the reigns of Yao, Shun, and Yu. It also appeared again during the time of Cheng Wang and the Duke of Zhou, and these events are recorded in the historical annals of successive dynasties. Even in the late Southern Song dynasty, when Zhu Xi promoted the "Four Books," there was a dragon horse born beneath the Jiufeng Mountains, with a dragon head and horse body, appearing to carry the Yellow River Chart on its back. Local elders came to Zhu Yuanhui (Zhu Xi) to congratulate him, believing this to be a similar auspicious omen to the appearance of the qilin during Confucius's time. Who can say that there is no hidden connection between heaven and humanity in such times ofsympathetic response?