Yi Tu Ming Bian (易圖明辨)

予初讀易，惟知朱子《本義》而已。年垂三十，始集漢魏以後諸家傳注，與裡中同志者講習，乃頗涉其津涯。因嘆朱子篤信邵子之過，而《本義》卷首之九圖為可已也。友人德清胡朏明先生，精於明學，庚辰仲夏，示予以《易圖明辨》十卷，則《本義》之九圖咸為駁正，而謂朱子不當冠於篇首。予讀之大喜，躍然曰：至哉言乎，何其先得我心乎！

I used to read the Zhou Changes, knowing only Zhu Xi's The Original Meaning of the Zhou Changes during my early years. When I was about to turn thirty, I began collecting commentaries from the Han and Wei dynasties onwards, and studied with like-minded friends in my hometown. Only then did I begin to understand the entrance to the study of the Zhou Changes. Then I felt that Zhu Xi had placed too much trust in Shao Yong's learning from the Northern Song Dynasty. The nine diagrams listed at the beginning of The Original Meaning of the Zhou Changes are actually entirely unnecessary. My friend, Mr. Hu Wei from Deqing (with the courtesy name Feiming), had a very profound understanding of this subject. In the summer of Gengchen year (the thirty-ninth year of the reign of Emperor Kangxi), he showed me his ten-volume work, The Clear Discrimination of the Diagrams of the Zhou Changes. In this book, he critically examined the nine diagrams at the beginning of The Original Meaning of the Zhou Changes, arguing that Zhu Xi should not have placed them at the beginning of the entire text. After reading this, I was very pleased and jumped up exclaiming: How accurate this is! It seems to have exactly hit what I was thinking.

予嘗謂河圖洛書、先天後天、羲文八卦、六十四卦方圓諸圖，乃邵子一家之學，以此為邵子之易則可，直以此為羲、文之易，則大不可。乃朱子恪遵之，反若羲文作易本此諸圖，不亦異乎？夫河圖見於《顧命》《繫辭》《論語》，古固有之，而後世亡之矣。今之自一至十之圖，本出陳希夷，古人未嘗語及，非真河圖也。戴九履一之圖，今之所謂洛書者，見於《漢書·張衡傳》及緯書《乾鑿度》，乃太乙下行九宮圖，非洛書也。後世術家配以一白二黑之數，至今遵用不變，豈果真洛書乎。

I have always thought that the entire system of diagrams, including the River Chart and the Luo Square, the Earlier Heaven and Later Heaven diagrams, the Eight Trigrams of Fuxi and King Wen, and the sixty-four hexagrams in square and circular forms, are all the contributions of Shao Yong alone. It is acceptable to regard them as part of Shao Yong's study of the I Ching, but to directly consider them as the study of Fuxi and King Wen is most inappropriate. Yet Zhu Xi respectfully followed them, as if Fuxi and King Wen composed the I Ching based on these diagrams, which is very strange. The term "River Chart" appears in the "Book of Documents · Gu Ming," the "Great Treatise" of the I Ching, and the "Analects." In ancient times, there was indeed such a thing, but it has long since been lost. The diagram of black and white dots from one to ten that is currently passed down is actually transmitted by Chen Tuan, a Daoist of the Five Dynasties and early Song Dynasty, who was known as Master Xiyi. Ancient scholars never mentioned it, so it is not the true River Chart. The diagram known as "Daijiu" or "Wearing One on the Sole," which is what modern people call the Luo Square, appears in the "Biography of Zhang Heng" in the "Book of Han" and the esoteric text "Gan Zao Du." Originally, it was a diagram of the "Taiyi moving through the nine palaces," and it is not the true Luo Square. Later numerologists added the numbers of the nine stars, such as one white and two black, and this has been used continuously up to the present day. How can it be the true Luo Square?

卦止有出震齊巽之位，乃孔子之所繫，而文王周公之遺法也，安得有先天之位？此誰言之而誰傳之？「天地定位」一節，不過言八卦之相錯耳，何曾有東西南北之說，而欲以是為先天卦位乎？此不特先天二字可去，即後天二字亦必不可存。蓋卦位止一而無二，不得妄為穿鑿也。八卦之序，自當以父母六子為次，孔子《繫辭》屢言之，乃舍此不遵，以乾兌離震巽坎艮坤為次，此何理乎？

The directional arrangement of the Eight Trigrams is only explained in the "Shuo Gua Zhuan" as "The Emperor emerges from Zhen, and harmonizes with Xun," which is the text transmitted by Confucius, also passed down by King Wen and the Duke of Zhou. How could there be any notion of "Earlier Heaven" direction? Who said this and who passed it down? The section in the "Shuo Gua Zhuan" called "Heaven and Earth are positioned" merely discusses the mutual opposition of the Eight Trigrams and the intermingling of yin and yang. It never mentions the directions of southeast, northwest, etc. How can it be used to confirm the so-called Earlier Heaven positions? In this case, not only should the term "Earlier Heaven" be deleted, but the term "Later Heaven" should also be discarded, because there is only one set of trigram positions, and there is no second set. There should be no arbitrary fabrication. The order of the Eight Trigrams should naturally follow the sequence of Qian and Kun as parents giving birth to the six sons: Zhen, Kan, Gen, Xun, Li, and Dui. Confucius repeatedly mentions this in the "Xi Ci Zhuan." However, nowadays this order is abandoned, and instead the sequence of Qian, Dui, Li, Zhen, Xun, Kan, Gen, and Kun is used. What is the reason for this change?

太極生兩儀、兩儀生四象、四象生八卦，固出於《繫辭》，而實非生卦之謂也。乾坤生六子，其理顯然，而坤可置於最末乎？三男三女，可錯亂而無序乎？易但有三畫之卦，重之則為六畫，未嘗有二畫四畫五畫之卦也；但有八卦六十四卦，未聞八卦重為十六、十六重為三十二、三十二始重為六十四也。必曰一每生二，以次而加，試問易中曾有是說乎？

The saying "The Supreme Ultimate gives rise to the Two Principles, the Two Principles give rise to the Four Images, the Four Images give rise to the Eight Trigrams" is indeed from the Great Treatise, but it does not actually describe the process of generating the trigrams. The trigrams Qian and Kun produce six children, and the reasoning is clear, yet in the Earlier Heaven sequence, why is the trigram Kun placed last? How can the three male and three female trigrams be so disordered with no clear order? The Zhou Changes contains only three-line basic trigrams, and by overlapping them, they form the six-line composite trigrams. There are no two-line, four-line, or five-line trigrams in the Zhou Changes. There are only the Eight Trigrams and the sixty-four trigrams, and there is no mention of the Eight Trigrams first being overlapped to form sixteen, then sixteen overlapping to form thirty-two, and thirty-two overlapping to form sixty-four. If one insists that each generation doubles the number, then please ask, has the Zhou Changes ever mentioned such a concept?

至於卦變，惟程蘇二家為可信，古人十闢之說，予猶不敢從。若朱子之《本義》，益為支離。況與《啟蒙》之言不合，一人而持兩說，令學者何所適從？此予必不敢附會者也。凡此諸說，間與友人言之，或然或不然。讀先生此書，一一為之剖析，洵大暢予懷。而其採集之博，論難之正，即令予再讀書十年，必不能到。何先生之學大而能精如此！以此播於人間，易首之九圖即從此永廢可也。四明同學弟萬斯同纂

As for the concept of "guabian" (changing hexagrams), only Cheng Yi and Su Shi's interpretations are credible; the ancient idea that the ten derived hexagrams generate the miscellaneous hexagrams is something I still dare not follow. For instance, the hexagram changes listed in Zhu Xi's "The Original Meaning of the Zhou Changes" are even more fragmented and inconsistent with his own explanations in "The Awakening of the Study of the Changes." How can a single person hold two contradictory views? What should scholars follow? This is something I certainly dare not fabricate. These views, I have occasionally shared with my friends, and some agree while others do not. After reading Mr. Hu's book, I found that he thoroughly analyzed each issue, which truly made me feel relieved. His extensive collection of materials and precise arguments are so thorough that even if I studied for another ten years, I would not reach such a level. How could Mr. Hu's scholarship be so vast and profound? If this book were to be circulated among people, the nine diagrams at the beginning of the "Zhou Changes" would eventually be discarded forever. Wansong, a fellow student from Mingsheng (Ningbo), compiled this.

古者有書必有圖，圖以佐書之所不能盡也。凡天文、地理、鳥獸、草木、宮室、車旗、服飾、器用、世系位著之類，非圖則無以示隠賾之形，明古今之制，故詩書禮樂春秋皆不可以無圖。唯易則無所用圖，六十四卦二體六爻之畫，即其圖矣。白黑之點、九十之數、方圓之體、復姤之變，何為哉？其卦之次序方位，則乾坤三索、出震齊巽二章盡之矣，圖可也，安得有先天後天之別？

In ancient times, whenever there was a book, there must have been a diagram to supplement what the text could not fully express. For matters such as astronomy, geography, birds and beasts, plants and trees, palaces and houses, chariots and banners, clothing and ornaments, utensils and objects, as well as genealogies and ranks, without diagrams, the hidden and obscure forms could not be shown, and the differences in systems through the ages could not be explained clearly. Therefore, the books of Poetry, Documents, Rites, Music, and Spring and Autumn Annals could not do without diagrams. Only the Zhou Changes (I Ching) did not need diagrams, because the sixty-four hexagrams, with their upper and lower parts and six lines, were themselves the diagrams. As for the black and white dots, the numbers nine and ten, the forms of square and circular diagrams, and the progression from the hexagram Fu to Guo, what are they for? When it comes to the order and position of the hexagrams, the chapters "Three searches of Qian and Kun" and "The Emperor arises from Zhen, harmonizes with Xun" in the Sayings on the Hexagrams have already explained everything thoroughly. According to these, one could draw a diagram, but where would there be a distinction between Earlier Heaven and Later Heaven?

河圖之象自古無傳，從何擬議？洛書之文見於《洪範》，奚闗卦爻？五行九宮初不為易而設，《參同契》先天太極，特借易以明丹道，而後人或指為河圗，或指為洛書，妄矣！妄之中又有妄焉，則劉牧所宗之《龍圖》、蔡元定所宗之《闗子明易》是也，此皆偽書，九十之是非，又何足校乎？故凡為易圖以附益經之所無者，皆可廢也。

The image of the Yellow River Chart has never been passed down since ancient times; how can later generations guess or discuss it? The text of the Luo Writing appears in the "Book of Documents · Hongfan," and how is it related to the hexagrams and lines of the Zhou Changes? The systems of the Five Phases and the Nine Palaces were never originally designed for the Zhou Changes; what Liu Mu refers to as the Earlier Heaven and the Taiji in his "Zhou Yi Cangtongqi" is merely using the Zhou Changes to explain alchemy, yet later people have some claiming it to be the Yellow River Chart and others claiming it to be the Luo Writing, which is truly absurd. Among these absurdities, there is even more absurd: the "Longtu" that Liu Mu takes as his basis and the "Guanziming Yixuan" that Cai Yuanping takes as his basis are all fake books. If this is the case, then whether the Yellow River Chart is nine numbers or ten numbers, and whether the Luo Writing is ten numbers or nine numbers, these distinctions are not worth arguing about. Therefore, all those who add diagrams to the Zhou Changes, using things that are not originally in the classics, can all be discarded.

就邵子四圖論之，則橫圖義不可通，而圓圖別有至理。何則？以其為丹道之所寓也。俞琰曰：先天圖雖易道之緒餘，亦君子養生之切務。人曰丹家之說雖出於易，不過依仿而托之者，初非易之本義，因作《易外別傳》以明之。故吾謂先天之圖與聖人之易，離之則雙美，合之則兩傷。伊川不列於經首，固所以尊聖人，亦所以全陳邵也。觀吾書者，如以為西山之戎首、紫陽之罪人，則五百年來有先我而當之者矣，吾其可末減也夫。康熙丙戌上已，七十四叟東樵胡渭書於顒溪客舍。

Taking Shao Yong's four diagrams into consideration: the horizontal diagram, which presents the order of the Eight Trigrams and the order of the sixty-four Trigrams, does not make sense in terms of meaning. However, the circular diagram has another deeper meaning. Why? Because the circular diagram embodies the principles of alchemy. Yuan dynasty scholar Yu Yan once said: the Earlier Heaven diagram, although merely a continuation of the Way of the Zhou Changes, is also a crucial practice for the cultivation of gentlemen. He also said that the Daoist alchemists' interpretations, although derived from the Zhou Changes, were merely imitations of the Zhou Changes, falsely attributed to them. They were not originally the true meaning of the Zhou Changes, so he wrote "The Transmission Outside the Zhou Changes" to clarify this. Therefore, I believe: the Earlier Heaven diagram and the sage's Zhou Changes, when separated, each has its own beauty, but when combined, they harm each other. Cheng Yi did not include these diagrams at the beginning of the text, not only to honor the sages, but also to protect Chen Tuan and Shao Yong. Those who read this book, if they think I am the one who attacked Cai Yuan Ding (Xishan) and offended Zhu Xi (Ziyang), then five hundred years ago, someone else has already taken on this blame before me, so I may be leniently treated. Written by Hu Wei, an old man of seventy-four, on the Upper Fourth Day of the Third Month in the 45th year of the Kangxi era, at the Yongyang Guest House by the Yongxi Stream.

元幼學易，心疑先後天諸圖之說。庚子得毛西河先生全集中《河圖洛書原舛篇》，讀之豁然，得其原委。友人歙凌次仲廷堪謂元曰：子知西河之辨易，未見德清朏明先生《易圖明辨》，尤詳備也。元識之，求其書不可得。繼在京師見四庫館書目錄之，曰其書一卷辨河圖洛書，二卷辨五行九宮，三卷辨《參同契》先天圖太極圖，四卷辨《龍圖》《易數鉤隱圖》，五卷辨《啟蒙》圖表，六卷七卷辨先天古易，八卷辨後天之學，九卷辨卦變，十卷辨象數流弊，並引據經典，原原本本，於易學深為有功，元鄉注益切。

When I was young and studied the I Ching, I had doubts about the various diagrams of Earlier Heaven and Later Heaven. In the Gengzi year of the Qianlong era (the forty-fifth year), I obtained the complete works of Master Mao Qiling (whose courtesy name was Xihex), particularly the essay "Original Errors of the Yellow River Chart and the Luo Writing," which clarified for me the origins and development of these diagrams. A friend from Xishan, Ling Tingkan (whose name was Cizhong), told me that although I knew Mao Xihex's interpretation of the I Ching, I had not yet seen the work of Master Hu Feiming from Deqing, "Clear Discrimination of the I Ching Diagrams." He said that this book provided especially detailed and comprehensive analysis. I noted his words but could not find the book anywhere. Later, when I saw the catalog of the Four Treasuries Collection in the capital, I recorded its entry, which stated that the book had ten chapters: the first chapter discussed the Yellow River Chart and the Luo Writing, the second the Five Phases and the Nine Palaces, the third the "Threefold Concordance" of the I Ching and the Earlier Heaven Diagram and the Taiji Diagram, the fourth the "Dragon Diagram" and the "Hidden Numbers of the I Ching," the fifth the diagrams in the "I Ching Enlightenment," the sixth and seventh the ancient Earlier Heaven I Ching, the eighth the Later Heaven studies, the ninth the changes of the hexagrams, and the tenth the drawbacks of the use of images and numbers. Everywhere, it cited classical texts and explained the origins and development thoroughly, making a great contribution to the study of the I Ching. My desire to study it became even more intense.

丙辰視學至吳興，始求得讀之，蓋距昔已十六年矣。愧聞道之甚遲，喜斯篇之未泯，亟命其家修板刷印，廣為流傳，以貽學者，因並識其事於篇首。至其圖辨大略，則萬季野先生序言之已盡，茲不贅論。嘉慶元年八月二十八日，浙江督學使者、內閣學士兼禮部侍郎、儀徵後學阮元謹序。

In the third year of the Jiaqing era (the first year of the Jiaqing reign), I, serving as a scholar-official in charge of examinations, arrived at Wuxing and only then obtained this book to read, having heard of it sixteen years earlier. I felt ashamed that I had learned about the Way so late, yet I was delighted that this book had not been lost. I hurriedly instructed the descendants of Hu to repair the old edition and print it again, so that it could be widely circulated and passed on to future scholars. Therefore, I recorded this incident at the beginning of the book. As for the main principles of the book's discussion of diagrams, Mr. Wan Siting (whose courtesy name was Jiyě) has already explained them thoroughly in his preface, so I will not elaborate further. On the 28th day of the eighth lunar month of the first year of Jiaqing, Ruan Yuan, the imperial examiner of Zhejiang, a scholar of the Yizheng school, and a minister of the cabinet and deputy minister of the Ministry of Rites, respectfully presents this preface.

右《易圖明辨》十卷，國朝胡渭撰。按渭原名渭生，字朏明，一字東樵，德清人。事蹟著撰具見江鄭堂《漢學師承記》，稱先生嘗謂：詩書禮春秋皆不可無圖，惟易無所用圖。六十四卦二體六爻之畫即圖也，八卦之次序方位，乾坤三索、出震齊巽二章盡之矣，安得有先後天之別哉？河圖之象自古無傳，何從擬議？洛書之文見於《洪範》，五行九宮初不為易而設，乃作是書云云。

The above is a ten-volume work entitled "Yitu Mingbian" written by Hu Wei of the present dynasty. According to Hu Wei's original name was Weisheng, with the courtesy name Feiming, and also the name Dongqiao, from Deqing, Zhejiang. His life and writings are recorded in Jiang Fan's "Hanxue Shicheng Ji" (Record of the Transmission of Han Learning), where it is stated that Mr. Hu once said: The "Book of Poetry," "Book of Documents," "Book of Rites," and "Spring and Autumn Annals" cannot exist without diagrams, but the "Zhou Yi" (Book of Changes) does not need diagrams. The diagram of the sixty-four hexagrams, with their upper and lower trigrams and six lines, is itself a diagram. The order and direction of the eight trigrams have already been fully explained in the "Shuogua Zhuan" (Commentary on the Trigrams) in the sections "Qian and Kun Three Times" and "The Emperor Emerges from Zhen, Aligns with Xun," so how could there be a distinction between Earlier Heaven and Later Heaven? The image of the River Chart has never been passed down since ancient times, so how can we guess it? The text of the Luo Book appears in the "Shangshu · Hongfan" (Book of Documents · Hongfan). The Five Phases and the Nine Palaces were originally not designed for the "Zhou Yi"—thus he wrote this book, and so on.

又云：洪範古聖所傳，如日月之麗天，有目所共覩，而間有晦盲否塞者，先儒曲說為之害也。漢儒五行傳專主災異，以瞽史矯誣之說，亂彝倫攸敘之經，其害一也；洛書之本文具在《洪範》，宋儒創為黑白之點、方圓之體、九十之位，書也，而變為圖矣，且謂洪範之理通於易，劉牧以九為河圖、十為洛書，蔡元定兩易其名，其害二也；《洪範》原無錯簡，而宋儒任意改竄，移「庶徵王省惟歲」以下為五紀之傳，移「皇斂時五福」至「作汝甲咎」及「三德惟闢作福」以下併為五福六極之傳，其害三也。作《洪範正論》五卷雲雲。其言有足與是書相發明者。

Jiang Fan also recorded that he said: The "Hongfan" (The Mandate of Heaven) was passed down by ancient sages, like the sun and moon hanging in the sky, visible to all who have eyes. Occasionally, there are obscure and difficult-to-understand parts, which are the result of misunderstandings by earlier scholars. The Han dynasty scholars' "Hongfan Wuxing Zhuan" (Commentary on the Five Phases of Hongfan) focused solely on calamities and portents, using superstitious and deceptive language of diviners and historians, which disturbed this classic text that speaks of "the orderly arrangement of the principles of conduct." This is the first kind of harm. The original text of the Luo Book was fully preserved in the "Hongfan," but Song dynasty scholars invented black and white dots, square and circular forms, and the arrangement of numbers nine and ten, turning what was originally a text into a diagram. They also claimed that the principles of the "Hongfan" are connected to the "Zhou Yi" (I Ching). Liu Mu regarded the number nine as the He Tu (Yellow River Chart) and ten as the Luo Shu (Luo Writing), while Cai Yuan Ding reversed the names of the two. This is the second kind of harm. The original "Hongfan" had no misplaced passages, but Song scholars arbitrarily altered and confused the text, moving "Shuying: Wang sheng wei su" and following sections to become the commentary on "Wujì" (Five Celestial Objects), and moving "Huang lian shi wufu" to "Zuo ru jia jiu" and "Sandé: Wei bi zuofu" and following sections to become the commentary on "Wufu Liují" (Five Blessings and Six Curses). This is the third kind of harm. Therefore, he also wrote five volumes of "Hongfan Zhenglun" (Correct Discussion on Hongfan), and so on. These remarks can be very helpful in complementing this book.

先生篤志經學，著述甚夥，所撰《禹貢錐指》一書，曾呈聖祖御覽，賜「耆年篤學」扁，稽古之榮，至今豔稱之。顧四庫提要著錄是書，與阮文達《國朝儒林傳稿》，均稱視《禹貢錐指》尤為有功經學，則其推崇也至矣。咸豐壬子冬至前一日，南海伍崇曜謹跋。

Mr. Hu devoted himself entirely to studying the classics and wrote many works. His book "Yugong Zhenzhi" was presented to Emperor Kangxi for his inspection, and he was awarded a plaque inscribed with "Qinian Duxue" (meaning "advanced age and devoted learning"). This honor of studying ancient texts has been admired by people ever since. Both the "Siku Quanshu Zongmu Tiyao" and the "Guochao Rulin Zhuan Gao" edited by Ruan Yuan (posthumously honored as Wen Da) noted that this book made greater contributions to the study of classics than "Yugong Zhenzhi," indicating the highest level of praise. This inscription was made by Wu Chongyao of Nanhai on the day before the winter solstice of the second year of the Nengzi year of the Xianfeng era.

卷一　河圗洛書。卷二　五行、九宮。卷三　周易參同契、先天太極。卷四　龍圗、易數鉤隠圗。卷五　啟蒙圗書。卷六　先天古易上。卷七　先天古易下。卷八　後天之學。卷九　卦變。卷十　象數流弊。

The entire book consists of ten volumes with the following contents: Volume one discusses the 'Yellow River Chart' and 'Luo Writing'; Volume two discusses the 'Five Phases' and 'Nine Palaces'; Volume three discusses Wei Boyang's 'Zhou Changes Comprehensive Concordance' and the 'Earlier Heaven Diagram' and 'Taiji Diagram'; Volume four discusses the 'Dragon Diagram' and Liu Mu's 'Yi Numbers Hidden Diagram'; Volume five discusses the diagrams and texts recorded in Zhu Xi's 'Yi Learning Enlightenment'; Volume six discusses the upper part of the 'Earlier Heaven Ancient Yi'; Volume seven discusses the lower part of the 'Earlier Heaven Ancient Yi'; Volume eight discusses the 'Later Heaven Studies'; Volume nine discusses the 'Hexagram Transformations'; Volume ten discusses the various evils arising from the transmission of the study of symbolic representations and numbers.

《易圖明辨》十卷，國朝胡渭撰。渭原名渭生，字朏明，號東樵，徳清人。是書專為辨定圖書而作。初，陳摶惟闡易理，衍為諸圖，其圖本凖易而生，故以卦爻反覆研求，無不符合。傳者務神其說，遂歸其圖於伏羲，謂易反由圖而作；又因繫詞河圖洛書之文，取大衍算數作五十五點之圖，以當河圖；取《乾鑿度》太乙九宮法造四十五點之圖，以當洛書。其陰陽竒偶，亦一一與易相應，傳者益神其說，又真以為龍馬神龜之所負，謂伏羲由此而有先天之圖。

The book "Yitu Mingbian" consists of ten volumes and was written by Hu Wei of this dynasty. Originally named Wei Sheng, with the courtesy name Feiming and the style name Dongqiao, Hu was from Deqing, Zhejiang. This book was specifically written to clarify the theories concerning the "Heavenly Chart" and "Luo Writing." Initially, Chen Tuan of the Five Dynasties and early Song Dynasty merely expounded the principles of the "Zhou Changes" and developed them into a series of diagrams; these diagrams were originally derived from the "Zhou Changes," so when comparing the hexagrams and lines repeatedly, they naturally matched. However, those who transmitted the teachings became overly mystical, attributing these diagrams to Fuxi. They claimed that the "Zhou Changes" were actually based on these diagrams. Moreover, since the "Xici Zhuan" mentions "the river produced the chart, the Luo produced the book," they used the large derivation method of divination to create a diagram with fifty-five points, which they used as the "Heavenly Chart." They also took the method of the Taiyi Nine Palaces from the esoteric text "Qian Zao Du" to create a diagram with forty-five points, which they used as the "Luo Writing." The odd and even numbers of points in these diagrams correspond with the "Zhou Changes" in every aspect. The transmitters further exaggerated their significance, even claiming that they were brought forth by the dragon horse and the divine turtle, and that Fuxi thus created the "Earlier Heaven" diagram.

實則唐以前書絶無一字之符驗，而突出於北宋之初。夫測中星而造儀器，以驗中星無不合，然不可謂中星生於儀器也；候交食而作算經，以驗交食無不合，然不可謂交食生於算經也。由邵子以及朱子，亦但取其數之巧合，而未暇究其太古以來從誰授受，故《易學啟蒙》及《易本義》前九圖皆沿其說，同時袁樞、薛季宣皆有異論。

In fact, there is no single character in the classical texts before the Tang dynasty that can confirm these diagrams. Yet they suddenly appeared in the early Song dynasty. For example, instruments were made by observing the position of the central star, and these instruments were used to verify the central star's position without any discrepancy, but one cannot say the central star was created by the instrument. Similarly, calculations were compiled by predicting solar and lunar eclipses, and these calculations were used to verify the eclipses without any discrepancy, but one cannot say the eclipses were created by the calculations. From Shao Yong to Zhu Xi, they only took these diagrams as coincidental in numbers, without investigating who passed them down from ancient times. Therefore, the nine diagrams at the beginning of "Yixue Qimeng" and "Zhouyi Benyi" all followed this tradition. Contemporary scholars of Zhu Xi, such as Yuan Shu and Xue Jixian, proposed different opinions.

然考《宋史·儒林傳》，《易學啟蒙》朱子本屬蔡元定創稿，非所自撰。《晦庵大全集》中載《答劉君房書》曰：啟蒙本欲學者且就大傳所言卦畫蓍數推尋，不須過為浮說。而自今觀之，如河圖洛書，亦不免尚有剰語。至於《本義》卷首九圖，王懋竑《白田雜著》以文集、語類鉤稽參考，多相矛盾，信其為門人所依附，其說尤明。則朱子當日亦未嘗堅主其說也。元陳應潤作《爻變易蘊》，始指先天諸圖為道家假借易理以為修煉之術，呉澄、歸有光諸人亦相繼排擊，各有論述。國朝毛竒齡作《圖書原舛編》，黃宗羲作《易學象數論》，黃宗炎作《圖書辨惑》，爭之尤力。然皆各據所見抵其罅隙，尚未能窮溯本末，一一抉所自來。

But examining the "Biographies of Literati" section in the "Song History," we know that Zhu Xi originally entrusted Cai Yuan ding to draft the book "Yixue Qimeng," and did not himself write it. In the "Wuhu Xiansheng Zhu Wengong Wenji," there is an entry titled "Dapeng Liu Junfang Shu," which says: writing "Yixue Qimeng" was originally intended for scholars to explore the hexagram diagrams and the method of using the yarrow stalks as explained in the "Great Treatise," without making excessive and superficial discussions. Now, looking back, even content related to the Yellow River Chart and the Luo Writing still contains some superfluous remarks. As for the nine diagrams at the beginning of the "Zhouyi Benyi," Wang Maosheng of the Qing dynasty, in his "Baitian Za Zhu," compared Zhu Xi's collected writings with the "Zhu Zi Yulu," and found many contradictions, concluding that these diagrams were later added by Zhu Xi's disciples. This view is especially clear. Thus, Zhu Xi himself did not firmly advocate the theory of the diagrams. In the Yuan dynasty, Chen Yingrun wrote "Yao Bian Yiyun," first pointing out that the diagrams of the Earlier Heaven were fabricated by Daoists to explain alchemical practices through the principles of the I Ching. Wu Cheng and later figures such as Guo Youguang in the Ming dynasty successively criticized and discussed these views. In our dynasty, Mao Qilin wrote "Hetu Luoshu Yuan Chuan Bian," and Huang Zongxi wrote "Yixue Xiangshu Lun," while Huang Zongyan wrote "Tushu Bianhuo," making particularly strong arguments against these theories. However, they only attacked the flaws from their own perspectives, and could not thoroughly trace the origin and development of this theory, revealing the source of each point.

渭此書，卷一辨河圖洛書，卷二辨五行九宮，卷三辨周易參同、先天太極，卷四辨龍圖、易數鉤隠圖，卷五辨啟蒙圖書，卷六卷七辨先天古易，卷八辨後天之學，卷九辨卦變，卷十辨象數流弊，皆引據舊文，互相參證，以箝依託者之口，使學者知圖書之說，雖言之有故、執之成理，乃修煉術數二家旁分易學之支流，而非作易之根柢。視所作《禹貢錐指》，尤為有功於經學矣。

Hu Wei's book is divided into ten volumes. The first volume discusses the Yellow River Chart and the Luo Writing. The second volume examines the Five Phases and the Nine Palaces. The third volume differentiates between the "Threefold Concordance" of the Zhou Changes and the Earlier Heaven Diagram and the Taiji Diagram. The fourth volume distinguishes between the "Dragon Diagram" and Liu Mu's "Diagram of the Hidden Numbers in the Changes." The fifth volume analyzes the diagrams appended to the "Introduction to the Study of the Changes." Volumes six and seven discuss the ancient Changes of the Earlier Heaven. Volume eight examines the Later Heaven studies. Volume nine deals with the changes of the hexagrams. Volume ten addresses the drawbacks of the study of imagery and numbers in the Changes. All these volumes cite existing texts to cross-reference and verify each other, aiming to block the mouths of those who falsely claim to be inspired by ancient sages. This enables scholars to understand that although the theories of diagrams and books may seem to have a historical origin and form a coherent system, they are actually only offshoots of alchemists and numerologists who branched off from the study of the Changes, and not the fundamental basis of the sages in composing the Changes. Compared to his work "Concise Guide to the Yu Gong," this book has made greater contributions to the study of classical texts.

《繫辭傳》曰：古者包犧氏之王天下也，仰則觀象於天，俯則觀法於地，觀鳥獸之文與地之宜，近取諸身，逺取諸物，於是始作八卦，以通神明之德，以類萬物之情。

The *Zhou Yi* *Xi Ci Xia Zhuan* says: In ancient times, when Fu Xi ruled over the world, he looked up to observe the celestial phenomena and looked down to study the principles of the earth. He observed the patterns on birds and animals and the products of the land according to its natural conditions. He took inspiration from the human body nearby and from all things in the world afar. Thus he began to draw the Eight Trigrams, using them to connect with the virtue of the divine and to classify and compare the forms and conditions of all things. Hu Wei placed this passage at the beginning of his entire work precisely to indicate that Fu Xi's creation of the *Yi* was based on observing the heavens and studying the earth, not on the *He Tu* or * Luo Shu*.

朱子曰：俯仰逺近，所取不一，然不過以驗陰陽消息兩端而已。草廬吳氏澄曰：氣之有文者曰象，形之有理者曰法。天有雷風日月，雷風氣也，日月象也，言象可以兼氣；地有水火山澤，水火質也，山澤形也，言形可以兼質。鳥獸之文謂動物，地之宜謂植物。身就人而言，物該服食器用而言。神明，天地之氣象形質，妙而可測、顯而可見者也。德若健順動入陷麗止說，及鼔之散之潤之晅之之屬。萬物，凡動植人器皆是。情，猶言其意義也。

Zhu Xi said: Observing upwards and examining downwards, taking distant and near objects, the objects taken are different, yet they are all used to verify the waxing and waning of yin and yang. Wu Cheng, the master of the Yuan dynasty, said: Among the qi there are those with patterns called 'xiang', and among forms there are those with order called 'fa'. In the sky there are thunder, wind, sun, and moon; thunder and wind belong to qi, while sun and moon belong to xiang. Saying 'xiang' includes qi as well. On the ground there are water, fire, mountains, and marshes; water and fire are substances, while mountains and marshes are forms. Saying 'form' includes substances as well. 'Bird and beast patterns' refer to animals, and 'the suitability of the land' refers to plants. 'Body' refers to human beings themselves, while 'things' include clothing, food, and utensils. 'Shenming' refers to the subtle and inferable principles and the evident and visible aspects of the qi, xiang, form, and substance in heaven and earth. 'De' is like the virtues of the eight trigrams, such as strength, compliance, movement, entering, sinking, adhesion, stopping, and speech, as well as actions such as stirring, spreading, moistening, and scorching. 'All things' include all animals, plants, humans, and objects. 'Qing' is equivalent to the meaning of them.

渭按：易之為書，八卦焉而已。卦各具三畫，上畫為天，下畫為地，中畫為人，三才之道也。羲皇仰觀而得天道，俯觀而得地道，中觀於兩間之萬物而得人道，三才之道黙成於心，故立八卦以象之，因而重之，遂為六十四，所謂兼三才而兩之也。言八卦則六十四卦在其中矣，觀下文所舉離、益、噬嗑等皆因重之卦可知也。夫子言羲皇作易之由，莫備於此。

Hu Wei commented: The book of The Zhou Changes is essentially the Eight Trigrams. Each trigram consists of three lines, with the upper line representing Heaven, the lower line representing Earth, and the middle line representing Humanity. This is the way of the Three Powers of Heaven, Earth, and Humanity. Fuxi observed the celestial phenomena to understand the way of Heaven, examined the geography to understand the way of Earth, and observed the myriad things between Heaven and Earth to understand the way of Humanity. The way of the Three Powers formed silently in his mind, so he established the Eight Trigrams to symbolize it. Then he combined the Eight Trigrams two by two, resulting in the sixty-four trigrams. This is what the "Say of the Trigrams" refers to as "combining the Three Powers and doubling them." When discussing the Eight Trigrams, the sixty-four trigrams are already included within them. Looking at the examples in the "Great Treatise" below, such as the trigrams Li, Yi, and Shihe, which are all examples of creating objects based on observations, they all use combined trigrams, which can be understood clearly. Confucius' explanation of why Fuxi composed the Book of Changes is nowhere more complete than this passage.

河圗洛書乃仰觀俯察中之一事，後世專以圗書為作易之由，非也。河圗之象不傳，故周易古經及註疏未有列圗書於其前者，有之自朱子《本義》始。《易學啟蒙》屬蔡季通起藁（見《宋史·儒林傳》），則又首本圗書，次原卦畫，遂覺易之作全由圗書，而舍圗書無以見易矣。學者溺於所聞，不務觀象玩辭，而唯汲汲於圗書，豈非易道之一厄乎？

The Yellow River Chart and the Luo Writing are merely one aspect of observing the heavens and examining the earth. Later generations mistakenly regarded the charts as the sole reason for Fuxi composing the Zhou Changes, which is incorrect. The image of the Yellow River Chart has not been passed down, so the ancient texts of the Zhou Changes and the commentaries through the ages have never placed the charts before the main text. This practice began only with Zhu Xi's The Original Meaning of the Zhou Changes. The book Yi Xue Qimeng (启蒙 of the Study of Changes) was commissioned by Zhu Xi to be drafted by Cai Yuan ding (whose name was Jitong) (see the Song Shi, the Biography of the Literati). In this book, "The Origin of the Charts" is listed as the first section, and "The Origin of the Hexagrams" follows. This leads people to believe that the origin of the Zhou Changes entirely comes from the charts, and without the charts, the Zhou Changes cannot be understood. Scholars are addicted to the commonly heard views and are unwilling to put in effort to observe the hexagrams and study the line statements. Instead, they rush to pursue the charts. Is this not a calamity for the Way of the Changes?

右論伏羲作易之本不專在圗書。

In the previous section, it was argued that the fundamental basis for Fuxi's creation of the Zhou Changes lies in observing the heavens above and examining the earth below, rather than specifically relying on the Yellow River Chart and the Luo Writing.

天一，地二；天三，地四；天五，地六；天七，地八；天九，地十。

The Great Treatise says: "Heavenly numbers are one, three, five, seven, and nine; earthly numbers are two, four, six, eight, and ten." Among these ten numbers, the odd numbers one, three, five, seven, and nine belong to heaven, while the even numbers two, four, six, eight, and ten belong to earth. The Song dynasty Confucian scholars precisely grasped this passage and regarded it as the Yellow River Chart.

朱子曰：此簡本在第十章之首，程子云宜在此，今從之。此言天地之數，陽奇陰偶，即所謂河圗者也。

Zhu Xi said: This passage originally appeared at the beginning of the tenth chapter of the Upper Great Treatise. Cheng Yi thought it should be moved here, and now we follow Cheng's suggestion. This passage discusses the numbers of heaven and earth, with yang being odd numbers and yin being even numbers, which is referred to as the Yellow River Chart.

天數五，地數五，五位相得而各有合。天數二十有五，地數三十，凡天地之數五十有五，此所以成變化而行鬼神也。（伊川先生曰：變化言功，鬼神言用。白雲郭氏曰：變化見於萬物者也，鬼神運於四時者也。）

The Great Treatise says: Heaven has five numbers, Earth has five numbers. The five positions are paired two by two and each has its union. The total of Heaven's numbers is twenty-five, the total of Earth's numbers is thirty. The combined numbers of Heaven and Earth total fifty-five, which is used to accomplish transformation and the movement of ghosts and spirits. (Cheng Yi said: 'Transformation' refers to the workings of creation and transformation, and 'ghosts and spirits' refer to the functions of creation and transformation. Master Guo Yong said: transformation is manifested in all things, and ghosts and spirits operate within the four seasons.)

朱子曰：此簡本在大衍之後，今案宜在此。

Zhu Xi said: This passage originally appeared after the chapter on "The Great Derivation Number," but now it has been determined to be moved here.

平庵項氏安世曰：姚大老云，「天一地二」至「天九地十」，班固《律歴志》及衛元嵩《元包·運蓍篇》皆在「天數五、地數五」之上。今按新安朱先生《易傳》亦用此說，與「天數五」至「行鬼神也」合為一節，置在大衍之首，今從之。

Ping'an Sir Xiang Anshi said: Yao Dalao (Song dynasty Yao Kuan) mentioned that from "tian yi di er" to "tian jiu di shi" is placed before "tian shu wu, di shu wu" in Ban Gu's "Hanshu · Lüli Zhì" and Wei Yuansong's "Yuanbao · Yunshi pian" from the Northern Zhou dynasty. Now, examining Xin'an Zhu Xi's "Zhouyi Benyi", it also adopts this approach, combining it with "tian shu wu" up to "xing gui shen ye" into one section, placing it at the beginning of the chapter on "dayan zhi shu". Now we also follow this arrangement.

渭按：卦者，易之體，所以立；蓍者，易之用，所以行。韓康伯云：卦，象也；蓍，數也。蓍極數以定象，卦備象以盡數。四語劃然分曉。葢象中雖有數，而終以象為主；數中亦有象，而終以數為主。故夫子言數皆主蓍：曰「極數知來之謂占」，曰「參伍以變，錯綜其數」，曰「極其數遂定天下之象」，曰「幽贊於神明而生蓍，參天兩地而倚數」，曰「數往者順，知來者逆，是故易逆數也」，凡此類無一不以蓍言。

Hu Wei commented: The trigrams are the essence of the Book of Changes, used to establish the principles of images; the divining stalks are the function of the Book of Changes, used to carry out divination. A Jin dynasty scholar named Han Kangbo said: the trigrams belong to "images," and the divining stalks belong to "numbers"; the divining stalks must exhaust numbers in order to determine images, and the trigrams must be complete in images in order to exhaust numbers. These four sentences clearly distinguish the two. Generally speaking, although images contain numbers, they ultimately take images as the main aspect; and although numbers contain images, they ultimately take numbers as the main aspect. Therefore, whenever Confucius spoke about "numbers," he was referring to the method of using the divining stalks: he said, "To know the future by exhausting numbers is called divination," he said, "By combining three and two, numbers change and intermingle," he said, "By exhausting numbers, the images of the world are determined," he said, "To consult the divine and generate the divining stalks, to take heaven as three and earth as two, and rely on numbers," he said, "To follow the past is to follow numbers, to know the future is to reverse numbers, thus the Book of Changes is about reversing numbers." All these statements are about the method of using the divining stalks.

而此章尤為明白，舉天地之數正為大衍之數張本。其曰五位者，即五奇五偶，非指天數之中五。一、三、五、七、九同為奇，二、四、六、八、十同為偶，是謂五位相得；一與二、三與四、五與六、七與八、九與十，一奇一偶兩兩為配，是謂各有合。於五行五方曷與焉？於天地生成曷與焉？於河圗洛書又曷與焉？

This chapter explains this very clearly: listing the numbers of heaven and earth is precisely to set the stage for the following discussion of "the great derivation number." It refers to "five positions" as meaning the five odd numbers and the five even numbers, not the central "five" in the heavenly numbers. One, three, five, seven, and nine are all odd numbers; two, four, six, eight, and ten are all even numbers. This is called "five positions interacting with each other." One pairs with two, three with four, five with six, seven with eight, and nine with ten, with one odd and one even in each pair. This is called "each having a corresponding partner." How does this relate to the Five Phases and the five directions? How does it relate to the so-called "heavenly generation numbers" of "heaven produces and earth forms"? How does it relate to the Yellow River Chart and the Luo Writing?

又按：章中言數者三：一曰天地之數，二曰大衍之數，三曰萬物之數。葢天地之數為大衍之法所自出，而萬物之數乃二篇之策適相當耳，於畫卦全無交涉。使五位相得而各有合，果為伏羲所則河圗之象，夫子何難一言以明之，曰「此河圗也」，而顧廋辭隠語，使天下後世之人百端推測邪？至其後章雖言河圗，而與洛書並舉，且與神物、變化、垂象比類而陳，文勢語脈遙遙隔絶，又安見此河圗者即前五十有五之數邪？

Again, it is noted that in this chapter, the term "number" appears three times: first, the numbers of heaven and earth; second, the numbers of the Great Derivation method; and third, the numbers of all things. The numbers of heaven and earth are the source from which the Great Derivation method originates, while the numbers of all things are merely the fact that the sixty-four hexagrams in the upper and lower chapters correspond exactly in their counts, having nothing to do with drawing the hexagrams. If "the five positions are in harmony and each has its counterpart" is indeed the image of the Yellow River Chart that Fuxi followed, then why is Confucius adding the statement "this is the Yellow River Chart"? What difficulty is there in this? Why would he deliberately use a cryptic expression, causing later generations to make endless guesses? As for the following chapter, although it mentions the Yellow River Chart, it is mentioned alongside the Luo Writing, and is presented in parallel with the statements about "the heavens producing divine objects," "the transformation of heaven and earth," and "the heavens displaying omens." The flow of the text and the connection of the words are far removed from the previous passage. How can we then determine that the Yellow River Chart mentioned here is the same as the one with the number fifty-five?

或問：五位以蓍法言之，其相得有合之實，亦有可見者乎？曰：有。一變所餘之策，左一則右必三，左二則右亦二，左三則右必一，左四則右亦四，非奇與奇相得、偶與偶相得乎？二變三變所餘之策，左一則右必二，左二則右必一，左三則右必四，左四則右必三，非一奇一偶兩兩為配而各有合乎？若夫一六、二七、三八、四九、五十之相合，而為天地生成之數、水火木金之象，此後世五行家言，豈易之所有哉？

Someone asked: When referring to the concept of "five positions," if we consider the method of divining with yarrow stalks, is there a visible manifestation of "mutual compatibility" and "mutual pairing"? The answer is yes. In the first change, the remaining number of stalks in the left hand, if one remains, the right hand must have three left; if two remain, the right hand also has two left; if three remain, the right hand must have one left; if four remain, the right hand also has four left. This is not precisely the mutual pairing of odd numbers with odd numbers and even numbers with even numbers, known as "mutual compatibility"? In the second and third changes, the remaining numbers of stalks in the left hand, if one remains, the right hand must have two left; if two remain, the right hand must have one left; if three remain, the right hand must have four left; if four remain, the right hand must have three left. This is not precisely the pairing of one odd and one even, forming pairs, known as "mutual pairing"? As for pairing one with six, two with seven, three with eight, four with nine, and five with ten, and interpreting them as the numbers of heaven and earth generating the world, and the images of water, fire, wood, and metal, this is the interpretation of later Five Phases scholars. The Zhou Changes does not contain such things.

右論天地之數不得為河圗。

The above section argues that the numbers of heaven and earth discussed in the Great Treatise cannot be regarded as the Yellow River Chart.

大衍之數五十，其用四十有九。（兼山郭氏曰：凡數有母、有法、有實。蓍之母，四十九是也；蓍之法，四是也；蓍之實，三十六、二十四、二十八、三十二是也。數有是母，必有法以用之，然後得是實，三者闕一，則蓍道絶矣，此聖人幽贊神明之道也。白雲郭氏曰：是三者之數，莫知所立之後先。謂四十九為先乎，則非法之四，亦不用四十九矣；謂法之四為先乎，則非三十六、二十四、二十八、三十二，亦不用法之四矣。故三者之數，一有一無則蓍之道不立，一先一後則蓍之用不成，惟同冇同立，莫知先後，故其數一本於自然，如環之無端，雖聖人不能加毫末於是矣。）

The Great Treatise of the Upper Classic says: The number of the Great Derivation is fifty, but only forty-nine is actually used. (Master Jiusan Guo Zhongxiao said: All numbers have a "mother," a "method," and a "realization." The mother of the divination method with the yarrow stalks is forty-nine; the method is four; and the realization consists of the numbers thirty-six, twenty-four, twenty-eight, and thirty-two, which are the numbers obtained through the process of counting the stalks. With the mother, one must use the method to apply it, and only then can the realizations be obtained. If any of these three is missing, the way of divination with yarrow stalks is cut off. This is precisely the reason why the sage secretly supports the divine. Master Baiyun Guo Yong said: The numbers of these three elements cannot be known which comes first or which comes later. If one says forty-nine comes first, but without the method of four, forty-nine cannot be used. If one says the method of four comes first, but without the realizations of thirty-six, twenty-four, twenty-eight, and thirty-two, the method of four has nowhere to be applied. Therefore, if one of these three is present and the other is absent, the way of divination with yarrow stalks cannot be established. If one comes first and the other comes later, the function of divination cannot be realized. Only when all three are present at the same time and established together, without distinguishing order, can the numbers be entirely based on nature, like a circular ring with no beginning or end. Even the sage cannot add or subtract anything in this regard.)

分而為二以象兩，掛一以象三，揲之以四以象四時，歸奇於扐以象閏，五歲再閏，故再扐而後掛。（朱子曰：兩，謂天地也。掛，懸其一於左手小指之間也。三，三才也。揲，間而數之也。奇，所揲四數之餘也。扐，勒於左手中三指之兩間也。閏，積月之餘日而成月者也。五歲之間，再積日而再成月，故五歲中凡有再閏，然後別起積分；如一掛之後，左右各一揲而一扐，故五者之中凡冇再扐，然後別起一掛也。又曰：掛一歲，右揲二歲，扐三歲，一閏也；左揲四歲，扐五歲，再閔也。）

The Great Treatise says: divide the yarrow stalks into two parts to symbolize the two principles of heaven and earth; take one stalk to hold between the fingers to symbolize the three elements of heaven, earth, and humanity; count the stalks in groups of four to symbolize the four seasons; place the remaining stalks between the fingers to symbolize the leap month; there are two leap months in five years, so after two times of handling and placing the remaining stalks, one should again hang a stalk. Zhu Xi explains: 'two' refers to heaven and earth; 'hang' means to suspend one stalk between the index finger and the little finger of the left hand; 'three' refers to the three elements; 'discern' means to count in groups; 'odd' refers to the remaining stalks after counting in groups of four; 'place' means to hold the remaining stalks between the fingers of the left hand; 'leap' refers to accumulating the extra days of each month into a month. In five years, two such accumulations form a leap month, so there are two leap months in five years, and then a new cycle begins; just as after hanging one stalk, one discerns and places on both sides, so there are two times of placing in the five steps, and then a new hanging begins. Zhu Xi also says: hanging one stalk corresponds to the first year, discerning on the right corresponds to the second year, placing corresponds to the third year, which is the first leap; discerning on the left corresponds to the fourth year, placing corresponds to the fifth year, which is the second leap.

乾之策二百一十有六，坤之策百四十有四。（韓氏曰：陽爻六，一爻三十六策，六爻二百一十六策；陰爻六，一爻二十四策，六爻百四十四策。白雲郭氏曰：九六，天地之數也，乾坤之策也；七八出於九六者也，六子之策也，乾坤相索而成者也。）凡三百有六十，當期之日。（朱子曰：少陰退而未極乎虛，少陽進而未極乎盈，故此獨以老陽老陰計乾坤六爻之策數，餘可推而知也。期，周一歲也，凡三百六十五日四分日之一，此特舉成數而槩言之耳。）

The Great Treatise says: The number of strategies for the Qian hexagram is 216, and for the Kun hexagram is 144. Han Kangbo said: Qian has six yang lines, each line has 36 strategies, so six lines total 216 strategies; Kun has six yin lines, each line has 24 strategies, so six lines total 144 strategies. Bai Yun Guo Yong said: Nine and six are the numbers of heaven and earth, which are the numbers of strategies for the Qian and Kun hexagrams; seven and eight are derived from nine and six, which are the numbers of strategies for the six subsidiary hexagrams, generated by mutual inquiry between Qian and Kun. Together, they total 360, which exactly corresponds to the number of days in a year. Zhu Xi said: The lesser yin is retreating but has not yet reached the extreme emptiness, and the lesser yang is advancing but has not yet reached the extreme fullness, so here only the old yang and old yin are used to calculate the six lines of Qian and Kun. The rest can be inferred accordingly. "Period" refers to a whole year, which is actually 365 and 1/4 days. Here it is just a rough approximation using an integer.

二篇之策，萬有一千五百二十，當萬物之數也。（二篇謂上下經。凡陽爻百九十二，得六千九百一十二策；陰爻百九十二，得四千六百八策，合之得此數。）是故四營而成易，十有八變而成卦。（四營謂分二、掛一、揲四、歸奇也。易，變易也，謂一變也。三變成爻，十八變則成六爻也。）八卦而小成。（謂九變而成三畫，得內卦也。）引而伸之，觸類而長之，天下之能事畢矣。（引伸觸類，謂已成六爻而視其爻之變與不變以為動靜，則一卦可變而為六十四卦，以定吉凶，凡四千九十六卦也。）

The Great Treatise of the Upper Transmission says: The total number of divination sticks used in the upper and lower parts is eleven thousand five hundred and twenty, exactly corresponding to the number of all things. (The term 'two chapters' refers to the upper and lower sections of The Zhou Changes. All the yang lines total one hundred and ninety-two, which equals six thousand nine hundred and twelve sticks; all the yin lines total one hundred and ninety-two, which equals four thousand six hundred and eight sticks. Adding these two numbers together gives the total number mentioned.) Therefore, after four steps of divination, one change is completed; after eighteen changes, one hexagram is formed. (The four steps refer to dividing into two, hanging one, counting by fours, and placing the remaining sticks in the palm. 'Change' (yi) refers to one change. Three changes form one line, so eighteen changes form six lines.) The eight trigrams form a small completion. (This refers to nine changes producing three lines, forming the inner trigram.) By extending and applying this principle widely, all things that can be done in the world are fully covered. (Extending and applying this principle refers to after the six lines are formed, determining whether each line changes or remains the same to judge its movement or stillness. Thus, one hexagram can transform into sixty-four hexagrams, used to determine fortune and misfortune, totaling four thousand and nine十六 hexagrams.)

朱子曰：大衍之數五十，葢以河圗中宮天五乘地十而得之。至用以筮，則又止用四十有九，葢皆出於理勢之自然，而非人之知力所能損益也。

Zhu Xi said: The number of great transformation is fifty, which is roughly obtained by multiplying the five heavenly numbers from the Yellow River Chart with the ten earthly numbers. However, when actually used for divination, only forty-nine are used. This is all due to the natural course of things and circumstances, and not something that human intelligence can add to or subtract from.

按：大衍之解，康節云：五者，蓍之小衍也，故五十為大衍。漢上云：小衍之五，參兩也；大衍之五十，則小衍在其中矣。此說近是。五十非以河圗中宮天五乘地十而得之，葢古之立數者，凡畸零不用，故於五十五數去其五，亦猶期三百六十五日四分日之一，而去其畸零以為三百有六十也。且蓍草之生，一本百莖，中分之得五十，彼此參會，皆由自然。

Hu Wei remarked: Regarding the explanation of "da yan zhi shu" (the great derivation number), Shao Yong (posthumous name Kangjie) said: "Wu" (five) is the "xiao yan" (small derivation) of the number of the yarrow stalks, so fifty is called "da yan" (great derivation). Zhu Zhen, the master from Han Shang, said: the "five" of "xiao yan" is the number of heaven and earth, taking two from heaven and two from earth. The "fifty" of "da yan" already includes the "xiao yan." This explanation is closer to the truth. Fifty is not obtained by multiplying the heavenly five of the river chart's central palace with the earthly ten. Instead, in ancient numbering, any remainder was discarded, so five was subtracted from fifty-five. Just as a year actually consists of three hundred sixty-five and one fourth of a day, the ancients discarded the remainder and only took three hundred sixty. Moreover, the growth of the yarrow stalks, one root producing one hundred stalks, when divided exactly gives fifty. The two sides correspond and verify each other, all arising naturally.

及其用也，則又止四十有九。王弼云一不用以象太極，妄也，諸家穿鑿附會尤無理。唯鄭康成云：以五十之數，不可以為七八九六卜筮之占，更減其一，故四十有九。是為正義，而李泰伯、郭子和宗之。

In actual use, only forty-nine strands are used. Wang Bi said that the one strand not used was to symbolize the Taiji, which is a baseless claim; the elaborate interpretations of other schools are even more unreasonable. Only Zheng Xuan said: the number fifty cannot derive the numbers seven, eight, nine, and six, which are used in divination, so one strand is subtracted to make forty-nine. This is the correct explanation. Song dynasty scholars Li Gou (style name Taibo) and Guo Yong (style name Zihe) both followed this view.

（子和曰：世俗皆以三多三少定卦象，如是則不必四十九數，以四十五、四十一皆初揲非五則九，再揲三揲非四則八矣，豈獨四十五、四十一為然哉？自三十以上論之，則三十三、三十七、五十三、五十七、六十一、六十五、六十九、七十三、七十七、八十一、八十五、八十九、九十三、九十七，皆可得五九四八多少之象，與四十九數為母者無以異，獨不可得三十六、二十四、二十八、三十二之策數，故蓍數四十九為不可易之道，可易者非聖人之法也。）此正所謂出於理勢之自然，而非人之智力所能損益者，又何必以河圗太極之五一為蓍法之所自出乎？

Guo Yong said: The common practice is to use the "three more, three less" method to determine the hexagram. If we follow this method, it is not necessarily required to use forty-nine stalks. One could use forty-five or forty-one stalks, and the remainder of the first change would be either five or nine, while the remainders of the second and third changes would be either four or eight. Moreover, why only forty-five and forty-one? Starting from thirty upwards, numbers such as thirty-three, thirty-seven, fifty-three, fifty-seven, sixty-one, sixty-five, sixty-nine, seventy-three, seventy-seven, eighty-one, eighty-five, eighty-nine, ninety-three, and ninety-seven can also produce remainders of five, nine, four, and eight, which are similar to those obtained using forty-nine stalks. Therefore, using forty-nine stalks as the base number is not fundamentally different. The only numbers that cannot be obtained are thirty-six, twenty-four, twenty-eight, and thirty-two, which are the excess numbers in the divination process. Hence, using forty-nine stalks is an unchangeable method, for anything that can be changed is not the method of the sage. This is precisely what is meant by something arising naturally from the circumstances and principles, not something that can be altered by human intellect. Then why must we necessarily regard the number 'five' from the Yellow River Chart's Central Palace and the number 'one' from the Taiji as the origin of the divination method?

蕭山毛太史奇齡《河洛原舛編》曰：間嘗學易淮西，見鄭康成所注太衍之數，起而曰：此非河圗乎？則又思曰：焉有康成所注圗，而漢代迄今不一引之為據者？則又思大衍所注見於李民《易解》者，干寶、崔憬言人人殊，何以皆並無河圗之言？則又思康成所注大傳，其於「河出圗」句既有成注，何以翻引入春秋緯文（河圗九篇，洛書六篇），而不實指之為大衍之數？於是怳然曰：圗哉圗哉，吾今而知圗之所來矣。摶之所為圗，即大衍之所為注也。

Xiao Shan Mao Qilin, a historian, wrote in his work "Original Compilation of Errors in the River Chart and the Luo Writing" that when I was studying the I Ching in the western part of Huai River region, I saw Zheng Xuan's commentary on the Great Derivation Number, and I jumped up saying: "This is not the River Chart?" Then I thought again: How could there be a chart commented on by Zheng Xuan from the Han dynasty to the present day, yet no one has ever cited it as a reference? Then I thought again: Zheng Xuan's commentary on the Great Derivation Number is preserved in Li Dingzuo's "Collected Explanations of the Zhou Changes," and in the same book, the interpretations of Gan Bao and Cui Jing are all different, yet no one has mentioned the River Chart. Then I thought again: Zheng Xuan commented on the "Great Treatise" passage about "the River produced the Chart," and since there was already a commentary available, why did he instead introduce the text from the "Spring and Autumn Writings" saying that the River Chart has nine chapters and the Luo Writing has six chapters, without clearly identifying it as the Great Derivation Number? Then I suddenly realized: Chart, chart, today I have finally understood where the chart comes from! The chart created by Chen Tuan is actually the commentary that Zheng Xuan gave to the Great Derivation Number.

然而大衍之注之斷非河圗者，則以河圗之注之別有在也。大衍之注曰：天地之數五十有五，天一生水在北，地二生火在南，天三生木在東，地四生金在西，天五生土在中。然而陽無耦，陰無妃，未相成也，於是地六成水於北，與天一併（一六在北）；天七成火於南，與地二並（二七在南）；地八成木於東，與天三並（三八在東）；天九成金於西，與地四並（四九在西）；地十成土於中，與天五並（五十在中），而大衍之數成焉。

However, Zheng Xuan's commentary on the "Da Yan" is certainly not the "Heavenly River Chart," because he has another interpretation of "Heavenly River Chart." He explains the "Da Yan" as follows: the numbers of heaven and earth total fifty-five. Heaven begins with one and produces water, located in the north; Earth begins with two and produces fire, located in the south; Heaven begins with three and produces wood, located in the east; Earth begins with four and produces metal, located in the west; Heaven begins with five and produces earth, located in the center. However, the yang numbers have no counterparts, and the yin numbers have no matches, so they cannot be paired to achieve completeness. Therefore, Earth six completes water in the north, paired with Heaven one (one and six reside in the north); Heaven seven completes fire in the south, paired with Earth two (two and seven reside in the south); Earth eight completes wood in the east, paired with Heaven three (three and eight reside in the east); Heaven nine completes metal in the west, paired with Earth four (four and nine reside in the west); Earth ten completes earth in the center, paired with Heaven five (five and ten reside in the center). In this way, the numbers of Da Yan are completed.

則此所為注，非即摶之所為圗乎？康成但有注而無圗，而摶竊之以為圗；康成之注即可圗，亦非河圗，而摶竊之以為河圗。其根其柢，其曲其裡，明白顯著，可謂極快。然而趙宋元明千年長夜，而及今而始得之，其說有二：

Then Zheng Xuan's annotation is precisely the same as the diagram drawn by Chen Tuan. Zheng Xuan only provided the annotation but not the diagram, while Chen Tuan stole it and turned it into a diagram. Even if Zheng Xuan's annotation could be turned into a diagram, it would not be the Yellow River Chart, yet Chen Tuan stole it and falsely claimed it as the Yellow River Chart. The fundamental nature and internal and external intricacies of this diagram are now clearly revealed, which can be called a most satisfying revelation. However, through the thousand-year darkness of the Song, Yuan, and Ming dynasties, it was not until today that this was uncovered. The reasons for this are two-fold:

一則世之言河圗者亦皆知大衍之數，然第以為河圗之陽二十五點、河圗之陰三十點，與大衍之數一三五七九、二四六八十共成五十有五者，其數相合已耳。而其天生地成、地生天成，或北或南，為水為火，能方能圎，有單有復，按之可為形，指之可為象，則河圗有之，大衍不得而有之也。而孰知大衍之數其為形為象原自如此，而人初不知，其長夜一。

First, people who talk about the Yellow River Chart all know the number of the great derivation, but they think that the Yellow River Chart has twenty-five yang points and thirty yin points, which together with the numbers one, three, five, seven, nine, and two, four, six, eight, ten in the great derivation number add up to fifty-five, and this is merely a numerical coincidence. As for the idea that 'heaven is born and earth is formed, earth is born and heaven is formed,' or that they are located in the north or the south, representing water or fire, which can be arranged in a square or a circle, with single and double forms, and through which one can see the shape and the numbers and the symbolic meanings—these are features unique to the Yellow River Chart, which the great derivation number cannot have. Who would have thought that the great derivation number originally possesses such forms and symbolic representations, yet people were completely unaware of them at first? This is the first long night.

一則魏晉以後俗尚王學（謂王弼），而鄭學稍廢，其所遺注第散見於易、詩、書、三禮、春秋疏義及釋文、漢書、文選諸所引注，而迄無成書。故唐惟李鼎祚略採其注於《易解》中，而其在他書，則惟王氏應麟復為彚輯而補於其後。此在劉、邵言易時皆未之見，今摶得其說而不言所自，或亦轉得之他人，而並其所自而亦不之知，皆未可定，則冥冥矣，其長夜二。

Second, after the Wei and Jin dynasties, the scholarly trend favored Wang Bi's interpretations, and Zheng Xuan's studies gradually fell into neglect. His remaining annotations were only sporadically found in the commentaries on the Book of Changes, the Book of Poetry, the Book of Documents, the three Rituals, the Spring and Autumn Annals, as well as in the Classic Interpretations, the annotations to the Han Shu, and the annotations to the Wen Xuan. They were never compiled into a complete work. Therefore, during the Tang dynasty, only Li Dingzuo slightly included Zheng Xuan's annotations in his Collected Explanations of the Zhou Changes. As for those scattered in other texts, only Wang Yinglin of the Song dynasty recompiled them and appended them to the end of the books. These materials were not known to Liu Mu and Shao Yong when they discussed the Book of Changes. Now Chen Tuan has obtained Zheng Xuan's views but does not cite the source; perhaps he obtained them from others, and even the origin is unclear. All these cannot be determined, leaving only confusion. This is the second long night.

乃幸而得白，顯有從來，但當名之為大衍圗，非然則名天地生成圗，非然則名五行生成圗，而斷斷不得名之為河圗。浸假河圗即此圗，則此圗固康成所注者也，其於大傳「河出圗」下，何難直注之曰：所謂河圗，即揲蓍所稱大衍之數，天一地二、天三地四、天五地六、天七地八、天九地十者？而乃又曰：河龍圗發，其書九篇。則豈非衍數河圗截然兩分，數不得為圗，衍不得為畫乎？

Now that the truth has been revealed, the origin is clear: this diagram should be called the "Great Derivation Diagram," or alternatively the "Heaven and Earth Generating Diagram," or the "Five Phases Generating Diagram." It must not be called the "Yellow River Chart." Even if we suppose that the Yellow River Chart is indeed this diagram, then this diagram was originally explained by Zheng Xuan. He directly noted under the phrase "the river produced the chart" in the "Great Treatise" that "the so-called Yellow River Chart is the great derivation numbers used in divination with yarrow stalks, namely, heavenly one and earthly two, heavenly three and earthly four, heavenly five and earthly six, heavenly seven and earthly eight, heavenly nine and earthly ten." What difficulty is there in that? Yet he deliberately added another note saying "the dragon chart appeared in the river, consisting of nine chapters." This clearly shows that the great derivation numbers and the Yellow River Chart are entirely separate matters: numbers cannot be regarded as diagrams, and the derivation numbers from yarrow stalks cannot be regarded as hexagram figures.

《原舛》云數不得為圗、衍不得為畫二句，真千古格言，顧其說猶有不盡然者，餘不可以無辨。謹案：大衍者，揲蓍求卦之法也，大衍之數出於天地之數，而非即天地之數。葢天地之數，易與範共之，凡天下之言數者未有外於此者也；大衍之數，則唯易有之，範不得而有之也。

Hu Wei said: The two sentences "Numbers cannot be taken as diagrams, and the numbers of divination with yarrow stalks cannot be taken as hexagram figures" in the book "Original Errors of the River and Luo" are truly famous sayings of all time. However, Mao Qiling's view still has some inappropriate aspects, which I cannot help but analyze. It is stated: The method of "Da Yan" is the way of divining hexagrams by using yarrow stalks. The numbers of Da Yan come from the numbers of heaven and earth, but they are not equal to the numbers of heaven and earth. This is because the numbers of heaven and earth are shared by the "Zhou Yi" and the "Shang Shu · Hong Fan", and all numbers discussed in the world do not go beyond this scope; while the numbers of Da Yan exist only in the "Zhou Yi" and are not found in the "Hong Fan".

康成注大衍與四象，皆本漢書五行志。志據劉向父子洪範五行傳以推災異，其所引左氏陳災傳說，葢劉歆取大傳之六七八九十，以續洪範之一二三四五，而為生成妃牡之數，意主洪範，初不為易而設。即其末舉坎離二卦，亦以證水為火牡、火為水妃云爾，終於大衍無涉也。

Zheng Xuan's commentary on the Great Derivation and the Four Images is based on the "Five Phases Chapter" of the "Book of Han." The "Five Phases Chapter" derives its reasoning from the "Huang Fan Five Phases Commentary" by Liu Xiang and his son Liu Xin, which interprets calamities and anomalies. Among the passages cited from the "Zuo Zhuan," the story about the fire in the state of Chen is actually a fabrication by Liu Xin, who connected the sixth, seventh, eighth, ninth, and tenth sections of the "Great Treatise" with the first, second, third, fourth, and fifth sections of the "Huang Fan," to form the so-called generation and mutual generation numbers. His intention was to explain the "Huang Fan," not for the "Zhou Yi." Even though the passage at the end mentions the Kan and Li trigrams, they were only used to demonstrate that water is the male of fire and fire is the female of water. In the end, they have nothing to do with the Great Derivation.

唯律歴志言備數則引易大衍之數五十，言鐘律則引參天兩地而倚數，言歴法則引大衍之數四營之象，而以天地之數終焉。大抵五行主洪範，則附以春秋而不及大衍；律歴主大衍，則附以春秋而不及洪範。考厥源流，區以別矣。

Only the "Lüli Zhì" (Chronology and Music Chapter) of the "Hàn Shū" (Book of Han) cites the "Zhou Yi" (I Ching) when discussing "bèi shù" (complete numbers), quoting "dà yǎn zhī shù wǔ shí" (the great derivation number is fifty). When discussing the tuning of bells, it cites "cān tiān liǎng dì ér yǐ shù" (three heavens and two earths to rely on numbers). When discussing the calendar, it cites "dà yǎn zhī shù sì yíng zhī xiàng" (the great derivation number and the four operations of the compass). Finally, it concludes with the "tiān dì zhī shù" (numbers of heaven and earth). In general, the "Wuxing Zhì" (Five Elements Chapter) mainly relies on the "Hóngfàn" (Huang Fan), with a mention of the "Chūnqiū" (Spring and Autumn Annals) but does not involve the great derivation. The "Lüli Zhì" mainly relies on the great derivation, with a mention of the "Chūnqiū" but does not involve the "Hóngfàn". When examining their origins and boundaries, the distinctions are clearly defined.

故劉說雖未嘗有圗，而圗實在其中，藉令繪以為圗，亦但可名天地生成圗，或五行生成圗，而斷斷不得名之曰大衍圗。何也？蓍無五行，無方位，無生成，無配耦也。今試就筮法而按之，自四營成易以至十八變而成卦，格中之所陳，版上之所畫，孰為天生而地成、地生而天成邪？孰居北而為水、居南而為火邪？方者圎者、單者復者皆安在邪？而《原舛》云大衍之數其形其象原自如此，吾所不解。

Therefore, although Liu Xin's explanation did not draw a diagram, the diagram was already contained within his explanation; even if it were drawn, it could only be called the "Heaven and Earth Generating Diagram" or the "Five Phases Generating Diagram," and could never be called the "Great Derivation Diagram." Why is that? Because the method of using the yarrow stalks does not include the Five Phases, directions, generation, or pairing. Now let us check according to the method of divination: from the four preparations forming one change until eighteen changes form a hexagram, what in the compartments of the stalks or the lines drawn on the board corresponds to "Heaven generates and Earth completes, Earth generates and Heaven completes"? What corresponds to the north being water and the south being fire? Where are the round and square, the single and double? The "Original Errors Collection" claims that the number of the Great Derivation inherently possesses such forms, but I cannot understand this.

若乃竊之為河圗，則固有其形其象矣，生成南北、方圎單復，一一不爽，如宋人之所說矣。幸彼不見鄭注，苟見之，則援以相證，更増一重金湯之固矣。然而天地之數終不得為河圗者，則以大傳無明文，而五十有五但可以生蓍，不可以畫卦也。毛公惟知數不得為圗，而不知大衍之數與天地之數不可混而為一；惟知衍不得為畫，而不知鄭注乃劉氏洪範五行之數，非伏羲大衍四營之數也。長夜始旦，明尚未融，此餘之所以不能無辨也。

As for the case where the diagram was stolen and used as the Yellow River Chart, naturally it would have form and image: generation, north and south, square and circle, single and double, each part precise without error, just as the Song people said. Fortunately, the Song people did not see Zheng Xuan's commentary; if they had, they would have verified it with each other, thus adding another layer of protection to this claim. However, the numbers of heaven and earth cannot be regarded as the Yellow River Chart, because the Great Treatise does not explicitly state it, and the number fifty-five can only be used to deduce the method of divination with yarrow stalks, not to draw the hexagrams. Mao Qiling knew only that "numbers cannot be regarded as diagrams," but did not know that the numbers of Da Yan are not the same as the numbers of heaven and earth; he knew only that "the numbers of Da Yan cannot be regarded as hexagram images," but did not know that Zheng Xuan's commentary is actually the numbers from Liu Xiu's "Huang Fan Wu Xing Zhuan," not the numbers of Fuxi's Da Yan four operations. The long night has just begun to dawn, and the light has not yet penetrated thoroughly, which is why I cannot help but clarify this.

總之康成以九篇為河圗，久已認賊作子，而復據生成配耦之數以注易，遂為偽闗易之嚆矢，此所謂藉寇兵而齎盜糧者也，於摶乎何尤？毛公惡宋太過，故其立言往往刻於宋而寛於漢，夫豈平心之論與？

In summary, Zheng Xuan regarded the nine chapters from the writings of the "Wujing" as the Yellow River Chart, which was already treating the enemy as a son; he also used the numbers of generation and pairing to interpret the Zhou Changes, thus becoming the precursor of the false school of "Guan Lang Yi Zhuan." This is exactly what is meant by lending weapons to the enemy and giving food to thieves. If this is the case, how can we blame Chen Tuan alone? Mao Qilin detested the Song scholars too much, so his arguments are often harsh towards the Song people and lenient towards the Han people. Is this considered a balanced view?

右論五行生成之數非河圗並非大衍。

In the previous section, it was argued that the numbers generating the Five Phases are neither the Yellow River Chart nor the Great Derivation Numbers.

易有太極，是生兩儀，兩儀生四象，四象生八卦，八卦定吉凶，吉凶生大業。

The Great Treatise of the Upper Transmission says: The Book of Changes contains the Taiji, from which the two principles arise, from the two principles the four images arise, from the four images the eight trigrams arise, and the eight trigrams are used to determine fortune and misfortune. Once fortune and misfortune are determined, great undertakings can be accomplished. This passage is the main classical basis for the Song Confucian scholars' establishment of the Earlier Heaven sequence diagram (a doubling method of one producing two, two producing four, four producing eight). Therefore, Hu Wei wanted to specifically clarify its original meaning.

劉氏禹錫《辨易九六論》曰：一行《大衍論》云，三變皆剛，太陽之象；三變皆柔，太陰之象；一剛二柔，少陽之象；一柔二剛，少陰之象。

Tang dynasty scholar Liu Yuxi in his "Discourse on the Six Yin and Six Yang of the Book of Changes" said that Buddhist monk Yixing's "Great Derivation Treatise" explained that when three divination steps using the yarrow stalks result in all yang (odd numbers), it represents the image of the sun; when all are yin (even numbers), it represents the image of the moon; when one is yang and two are yin, it represents the image of the lesser yang; and when one is yin and two are yang, it represents the image of the lesser yin.

東坡蘇氏《易論》曰：老者，陰陽之純也；少者，陰陽之雜而不純者也。陽數皆奇而陰數皆偶，故乾以一為之爻，而坤以二。天下之物以少（上聲）為主，故乾之男皆二陰，而坤之女皆二陽。老陽老陰者，乾坤是也；少陰少陽者，乾坤之子是也。

Su Shi, known as Dongpo, wrote in his "Yi Lun" that "old" represents the purity of yin and yang, while "young" represents the mixture and impurity of yin and yang. The numbers of yang are all odd, and the numbers of yin are all even. Therefore, Qian uses one line as a yao, and Kun uses two lines as a yao. The world's things are governed by the side with fewer numbers, so the three male trigrams born from Qian are each composed of two yin lines and one yang line, and the three female trigrams born from Kun are each composed of two yang lines and one yin line. Old yang and old yin are the two trigrams Qian and Kun; young yin and young yang are the six trigrams born from Qian and Kun.

漢上朱氏曰：乾，老陽也；震坎艮，少陽也；坤，老陰也；巽離兊，少陰也。故四象生八卦。

Han Shang Master Zhu Zhen said: Qian is old yang, Zhen, Kan, and Gen are young yang, Kun is old yin, Xun, Li, and Dui are young yin, so the classic text says "the four images give birth to the eight trigrams."

平庵項氏曰：凡繫辭之稱八卦者，即六十四卦也。八卦更相上下，變為六十四卦，故例以八卦稱之。

Ping'an Xiang Anshi said: All the "Eight Trigrams" mentioned in the Great Treatise refer to the sixty-four hexagrams. The eight trigrams are combined one above the other to form the sixty-four hexagrams, so they are still usually called "Eight Trigrams."

虛齋蔡氏清曰：四象生八卦，此八卦該六十四卦者也，故繼之以八卦定吉凶。

Master Xuzhai Cai Qing said: "The four yin-yang pairs give rise to the Eight Trigrams." The term "Eight Trigrams" here includes all sixty-four trigrams. Therefore, the text immediately follows with "The Eight Trigrams determine fortune and misfortune."

《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 An Guo 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 An Guo 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 An Guo 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?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

右論古河圗之器。

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

右論古洛書之文。

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

《書·洪範》曰：「一、五行：一曰水，二曰火，三曰木，四曰金，五曰土。」

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

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

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

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

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

右論古五行之序。

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

右論洪範五行傳生成之數。

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

《禮記·月令》：孟春，天子居青陽左個（注云：太寢東堂北偏也。《正義》云：是明堂北偏，而云太寢者，明堂與太廟、太寢制同；北偏者，近北也；四面旁室謂之個）；仲春居青陽太廟（東堂當太室）；季春居青陽右個（東堂南偏）；孟夏居明堂左個（太寢南堂東偏）；仲夏居明堂太室（南堂當太室）；季夏居明堂右個（南堂西偏）；中央土居太廟太室（中央之室也。土寄旺四時各十八日，共七十二日，除此則木火金水亦各七十二日矣。土無專氣，無定位，寄旺於辰戌丑未之末。未月在火金之間，又居一歲之中，故特揭中央土於此，以成五行之序焉）；孟秋居總章左個（太寢西堂南偏）；仲秋居總章太廟（西堂當太室）；季秋居總章右個（西堂北偏）；孟冬居玄堂左個（太寢北堂西偏）；仲冬居玄堂太廟（北堂當太室）；季冬居玄堂右個（北堂東偏）。

The Book of Rites, Monthly Orders records the system by which the Son of Heaven resided in different rooms of the Bright Hall according to the months: In the first month of spring, he stayed in the left room of Qingyang (Zheng Xuan's commentary says this is the room to the north of the eastern hall of the Great Hall. The Commentary says it is actually the room to the north of the Bright Hall. It is called "Great Hall" because the Bright Hall, the Great Temple, and the Great Hall have the same construction; "to the north" means close to the north. The side rooms on the four sides are called "ge"). In the second month of spring, he stayed in the central room of Qingyang (the central room of the eastern hall, facing the Great Hall). In the third month of spring, he stayed in the right room of Qingyang (the southern part of the eastern hall). In the first month of summer, he stayed in the left room of the Bright Hall (the eastern part of the southern hall). In the second month of summer, he stayed in the central room of the Bright Hall (the central room of the southern hall). In the third month of summer, he stayed in the right room of the Bright Hall (the western part of the southern hall). When the central earth element is in command, he stays in the central room of the Great Temple (the central room). The earth element is temporarily strong in the four months of the seasons, each for eighteen days, totaling seventy-two days. Excluding these seventy-two days, the wood, fire, metal, and water elements each also have seventy-two days. The earth element has no specific element or fixed direction, and it temporarily resides in the last days of the months of Chen, Xu, Chou, and Wei. The month of Wei is between fire and metal, and it is also the middle of the year, so it is specially marked as "central earth" to complete the order of the Five Phases. In the first month of autumn, he stays in the left room of Zongzhang (the southern part of the western hall). In the second month of autumn, he stays in the central room of Zongzhang (the central room of the western hall). In the third month of autumn, he stays in the right room of Zongzhang (the northern part of the western hall). In the first month of winter, he stays in the left room of Xuantang (the western part of the northern hall). In the second month of winter, he stays in the central room of Xuantang (the central room of the northern hall). In the third month of winter, he stays in the right room of Xuantang (the eastern part of the northern hall).

朱子曰：「論明堂之制者非一，竊意當有九室，如井田之制。東之中為青陽太廟，東之南為青陽右個，東之北為青陽左個；南之中為明堂太廟，南之東即東之南為明堂左個，南之西即西之南為明堂右個；西之中為總章太廟，西之南即南之西為總章左個，西之北即北之西為總章右個；北之中為玄堂太廟，北之東即東之北為玄堂右個，北之西即西之北為玄堂左個；中為太廟太室。

Zhu Xi said: There are many different accounts regarding the form of the Bright Hall. In my private opinion, it should be nine rooms arranged in three rows and three columns, like the well-field system. The central room on the east is the Qingyang Taomiao, the room to the southeast of the east is Qingyang Youge, and the room to the northeast of the east is Qingyang Zige. The central room on the south is the Mingtang Taomiao, the room to the southeast of the south (which is also the room to the northeast of the east) is Mingtang Zige, and the room to the southwest of the south (which is also the room to the northwest of the west) is Mingtang Youge. The central room on the west is the Zongzhang Taomiao, the room to the southwest of the west (which is also the room to the southeast of the south) is Zongzhang Zige, and the room to the northwest of the west (which is also the room to the northeast of the north) is Zongzhang Youge. The central room on the north is the Xuantang Taomiao, the room to the northeast of the north (which is also the room to the northwest of the west) is Xuantang Youge, and the room to the northwest of the north (which is also the room to the northeast of the east) is Xuantang Zige. The central room is the Taomiao Taishi.

凡四方之太廟異方所，其左右個則青陽左個即玄堂之右個，青陽右個即明堂之左個，明堂右個即總章之左個，總章右個乃玄堂之左個也，但隨其時之方位開門耳。太廟太室，則每季十八日天子居之歟。古人制事多用井田遺意，此恐然也。」

The four cardinal temples each occupy different directions; as for left and right, the left of Qingyang is the right of Xuantang, and the right of Qingyang is the left of Mingtang, the right of Mingtang is the left of Zongzhang, and the right of Zongzhang is the left of Xuantang— the rooms at the four corners are shared by two sides, but the door is opened on which side corresponds to the current direction. The central temple, Tai Shi, is probably where the Son of Heaven resides for the last eighteen days of each season. Ancient people established systems often following the idea of well-field land division, and the nine chambers of Mingtang may be exactly like that.

《大戴禮記·明堂》篇曰：「明堂者，古有之也，凡九室。」（句。）「二九四」（句），「七五三」（句），「六一八」（句）。

The "Great Dai Li Ji · Bright Hall" chapter says: The system of the Bright Hall existed in ancient times, consisting of nine rooms. (This is one sentence.) Next are three sentences: "Two nine four" (one sentence), "Seven five three" (one sentence), "Six one eight" (one sentence). These three lines of nine numbers are the earliest textual record of the later "Nine Palaces," where the sum of the numbers in each row and column equals fifteen. This is also the source that Hu Wei sought to trace back to the true origin of the Nine Palaces.

按：後世以九宮為河圗，實造端於明堂《月令》之說。今考小戴言天子居明堂九室，依四時十二月之序，而大戴則分九室為三條而言之。南曰明堂，其本名。古者以西為上，故從西南起。或曰：《封禪書》公玉帶上黃帝時明堂圗，有樓從西南入，命曰崑崙，天子從之入以拜祠上帝，故九室起自西南也。

Hu Wei says: Later generations regarded the nine palaces as derived from the Yellow River Chart, but the origin actually comes from the Bright Hall and the concept in the "Monthly Orders." Now examining this: The "Small Dai Li Ji" states that the Son of Heaven resided in the nine rooms of the Bright Hall in sequence according to the four seasons and twelve months; the "Great Dai Li Ji" divides the nine rooms into three groups. The room facing south is called "Bright Hall," which is the proper name of the entire building. Ancients considered the west to be the direction of respect, so they counted from the southwest corner. Some also say: The "Records of the Grand Historian: Book of the Rites of the Imperial Sacrifices" records that Gong Yu Dai presented a diagram of the Bright Hall from the Yellow Emperor's time. The diagram shows a building entering from the southwest, named Kunlun, through which the Son of Heaven entered to worship the Supreme Deity. Therefore, the nine rooms were counted starting from the southwest.

「二九四」者，二為總章左個與明堂右個，九為明堂太室，四為明堂左個與青陽右個也；「七五三」者，七為總章太廟，五為太廟太室，三為青陽太廟也；「六一八」者，六為總章右個與玄堂左個，一為玄堂太廟，八為玄堂右個與青陽左個也。二九四共為十五，七五三共為十五，六一八亦共為十五，縱橫十五，妙合自然，後世九宮之數實權輿於此。其以某室當某數者，葢取九九算術所設乘除之位以定明堂九室之數也。（詳見於後。）

The so-called "two nine four" refers to two being the total hall on the left and the bright hall on the right (southwest corner), nine being the bright hall's main chamber (due south), and four being the bright hall on the left and the qingyang on the right (southeast corner). The so-called "seven five three" refers to seven being the total hall's main chamber (due west), five being the main chamber of the main hall (center), and three being the qingyang's main chamber (due east). The so-called "six one eight" refers to six being the total hall on the right and the xuantang on the left (northwest corner), one being the xuantang's main chamber (due north), and eight being the xuantang on the right and the qingyang on the left (northeast corner). Two plus nine plus four equals fifteen, seven plus five plus three also equals fifteen, and six plus one plus eight equals fifteen as well. Whether adding horizontally or vertically, the total is fifteen, a harmonious natural number. The later nine palace numbers really originated from here. As for which room should be assigned which number, it was probably determined by the multiplication and division positions of the nine by nine multiplication table, used to number the nine chambers of the bright hall. (Details are provided later.)

《漢蓺文志》禮十三家有《明堂陰陽》三十三篇，又《明堂陰陽說》五篇，此必戴記所自出。故宣帝時魏相表採《易陰陽》及《明堂月令》奏之，言五帝所司各有時，東方之卦不可以治西方，南方之卦不可以治北方，則以八卦之方位配明堂之九室可知矣。坎之為一以至離之為九，則又據明堂九室之數而定之也。

The Book of Han, in its section on rites, mentions under the category of thirteen schools of rites a text called "Bright Hall Yin and Yang" with thirty-three chapters, and another called "Explanations of Bright Hall Yin and Yang" with five chapters. This particular chapter from the Dai Dai Li Ji must have originated from these texts. Therefore, during the reign of Emperor Xuandi of the Han dynasty, the chancellor Wei Xiang submitted a memorial, adopting the "Yi Yin and Yang" and "Bright Hall Monthly Command" to present to the court. He stated that the five celestial emperors each preside over a season, and that the trigrams of the East cannot be used to govern the West, nor can the trigrams of the South be used to govern the North—this shows that at that time the trigrams had already been associated with the nine chambers of the Bright Hall. As for the system of matching Kan to Li as nine, this arrangement was also determined based on the number of the nine chambers of the Bright Hall.

古之制度，大而分州，小而井田，莫不以九為則，明堂亦然，其制皆起於黃帝，在伏羲畫卦之後。八卦之方位已定，並其中數之則為九，九州島、井田、明堂皆黃帝所以法八卦也。九宮葢即明堂之九室，故《隋志》有《九宮經》，依託黃帝。然自歆、固以前，未有直指為河圗者，唯《後漢·劉瑜傳》桓帝延熹八年上書，言「河圗授嗣，正在九房」，九房即九室也。（《考工記》云「內有九室，九嬪居之」，葢王者路寢聽朝時，則九嬪在此共聽事也。）

Ancient systems, whether large as the division of the Nine Provinces or small as the well-field system, all followed the number nine as a standard, and the Bright Hall was the same. These systems originated with the Yellow Emperor, after Fuxi had drawn the Eight Trigrams. Once the directions of the Eight Trigrams were fixed, including the center, the total became nine. Therefore, the Nine Provinces, the well-field system, and the Bright Hall were all products of the Yellow Emperor imitating the Eight Trigrams. The Nine Palaces might be the nine rooms of the Bright Hall, so the "Nine Palace Classic" recorded in the "Book of Sui, Catalogue of Books" is attributed to the Yellow Emperor. However, before Liu Xin and Ban Gu, no one directly referred to it as the Yellow River Chart. Only in the "Biography of Liu Yu" in the "Book of the Later Han" is there a record that in the eighth year of Huan Di's Yanshi period, Liu Yu submitted a memorial saying, "The Yellow River Chart is passed down to the successor, in the nine rooms." The "nine rooms" here refer to the nine rooms. ("The Rites of Zhou, Records of the Master of Works" states, "Inside there are nine rooms, where the nine concubines reside." Perhaps when the king held court in the main hall, the nine concubines would be here to attend to affairs together.)

葢其時已有據《乾鑿度》「河圗八文」一章而直指九宮為河圗者，此即偽《龍圗》三變之粉本矣。（《龍圗》第三變，劉牧謂之「太皥授龍馬負圗」。）然河圗乃天成卦畫之象，伏羲因之以作《易》，數因象而見，象不由數以生。縱橫十五之數，雖非人私智所能為，亦出畫卦之後，終不可指以為河圗也。

It is evident that by the Eastern Han dynasty there were already people who, based on the chapter "The Eight Characters of the River Chart" in the "Gan Zao Du," directly identified the nine palaces as the River Chart, which became the basis for the later false "Longtu" "Three Transformations." (The third transformation of the "Longtu," Liu Mu called "Tai Hao was given the dragon horse carrying the chart.") However, the River Chart was originally the image of the heavenly patterns used by Fuxi to create the Zhou Yi; numbers emerged along with the images, and the images were not produced by numbers. The system of adding numbers vertically and horizontally to total fifteen, although not something humans could fabricate on their own, also appeared after the drawing of the hexagrams, and therefore cannot be regarded as the River Chart. This sentence is Hu Wei's conclusive statement that the nine palaces are not the River Chart.

《後漢書·張衡傳》：自中興之後，儒者爭學圗緯，兼復附以妖言。衡以圗緯虛妄，非聖人之法，乃上疏曰：「聖人明審律歴以定吉凶，重之以卜筮，雜之以九宮，經天驗道，本盡於此。圗讖成於哀、平之際，皆欺世罔俗，以昧埶位，情偽較然。且律歴、卦候、九宮、風角，數有徵效，世莫肎學，而競稱不占之書，譬猶畫工惡圗犬馬而好作鬼魅，誠以實事難形而虛偽不窮也。宜收藏圗讖，一禁絶之，則朱紫無所眩，典籍無瑕玷矣。」

The Book of the Later Han, Biography of Zhang Heng, records that since the middle period of the Eastern Han dynasty, scholars of Confucianism had been competing to study diagrams, prophecies, and the writings of the School of the Mandate of Heaven, and they had also attached various superstitious and false statements. Zhang Heng believed that these diagrams and prophecies were baseless and inconsistent with the principles of the sages. Therefore, he submitted a memorial stating that the sages had carefully examined the laws of music, calendars, and astronomy to determine auspicious and inauspicious signs, and they had supplemented this with divination and the Nine Palaces system, observing celestial phenomena and verifying the heavenly way, and all these fundamental aspects were already included. Diagrams and prophecies were fabricated during the reigns of Emperor Ai and Emperor Ping of the Han dynasty, and they were all meant to deceive the world and confuse the people, in order to gain power. The truth or falsehood of these is obvious. Moreover, the studies of laws and calendars, the correspondence of hexagrams with climate, the Nine Palaces system, and wind divination all have verifiable results, yet people do not wish to learn them, but instead compete in citing those books that cannot predict events. It is like a painter who dislikes painting dogs and horses but prefers to paint ghosts and monsters—this is because real things are hard to depict, while false things can be easily fabricated. The diagrams and prophecies should be confiscated and sealed away, and completely prohibited, so that truth and falsehood will no longer be confused, and the classics will no longer be tainted.

按：九宮不見於《漢書》，至張衡始兩言之，上與律歴、卜筮並稱，下與卦候、風角相埓，非圗緯妖妄不經者比。九宮之數縱橫十五，不知起於何時。按《管子·輕重戊》篇曰：「宓戲作，造六峜以迎陰陽（方以智《通雅》云：舊以「峜」字未詳，一切字書皆不收入。智按《宛委編》以「六計」解之，升庵之說也，則當為「計」音，以「企」本是「跂」音也。又辛子文號計研，漢碑作「峜研」。王若谷曰：六峜其如《周髀》算法乎），作九九之數以合天道，而天下化之。」

Hu Wei said: The Nine Palaces are not mentioned in the "Book of Han," but Zhang Heng mentioned them twice. The above text refers to them together with the laws and calendars, and divination, while the following text compares them with the weather and wind divination, indicating that the Nine Palaces do not belong to the class of superstitious and baseless diagrams and writings. The numbers of the Nine Palaces, both in rows and columns, add up to fifteen. It is unknown when this system began. Checking the "Light and Weight" chapter of the "Guanzi," it says: When Fuxi rose to power, he created the "six jie" to conform to yin and yang. (Fang Yizhi's "Tongya" says: The character "jie" was not understood in the past, and it is not included in any dictionary. Fang Yizhi, following the "Wanwei Collection," interpreted it as "six ji," which is the view of Yang Shen. Therefore, it should be read as "ji" sound, since "qi" is originally read as "qi." Also, there was a scholar in the Warring States period named Xin Zi, whose courtesy name was Jiyan, and in Han dynasty inscriptions, it was written as "jieyan." Wang Ruogu said: "The six jie" probably correspond to the calculation system in the "Zhou Bi Suan Jing.") He also created the nine-by-nine multiplication table to conform to the heavenly way, and thus the world received education.

《世本》曰「隸首作數」，宋忠云「隸首，黃帝史也」。魏劉徽《九章算經》序曰：「包犧氏始畫八卦，作九九之術，以合六八之變，黃帝引而伸之。」（邵子《觀物外篇》曰：天圎而地方，圎之數起一而積六，方之數起一而積八，變之則起四而積十二也。六者常以六變，八者常以八變，十二者亦以八變，自然之道也。此所謂「六八之變」，疑即是此數。）

The Shiben says, "Li Shou first created arithmetic." Han dynasty's Song Zhong's commentary says, "Li Shou was the historian of the Yellow Emperor." In the preface to the Jiuzhang Suanshu, Liu Hui of the Three Kingdoms period Wei dynasty said: Fuxi first drew the eight trigrams and created the nine-nine multiplication table to correspond with the "six and eight changes." The Yellow Emperor then further developed and expanded it. (Shao Yong's Guanwu Wai pian says: Heaven is round and Earth is square. The numbers of the round start from one and accumulate to six, while the numbers of the square start from one and accumulate to eight. When they change, they start from four and accumulate to twelve. Six always changes according to six, eight always changes according to eight, and twelve also changes according to eight. This is the natural principle. The "six and eight changes" mentioned by Liu Hui probably refers to this set of numbers.)

夏侯陽《算經》序曰：「算數起自伏羲，而黃帝定三數為十等，隸首因以著《九章》。」《韓詩外傳》曰：「齊桓公設庭燎，東野人有以九九見者。」《吳書》：趙達治九宮一算之術。《隋志》有楊淑《九九算術》一卷。葢九宮一算即九九算術，伏羲始作之，黃帝使隸首引而伸之，以為《九章》之數者也。據劉徽之言，則伏羲先畫八卦，後作九九，班固云「伏羲畫八卦由數起」，非也。（漢儒據《說卦》第一章先言生蓍倚數，後言立卦生爻，故謂畫卦由數起，而傳意實不然，葢錯解也。）

Xiahou Yang's preface to the "Suanjing" says: arithmetic originated from Fuxi, and the Yellow Emperor established ten levels of numbers called "san shu." Li Shou wrote the "Jiu Zhang" based on this. The "Han Shu Wai Zhuan" says: when Duke Huan of Qi lit torches in the courtyard to attract talented people, a man from the east suburb requested an audience by demonstrating the "jiujiu" method. The "Wu Shu" records Zhao Da's mastery of the "jiu gong yi suan" technique. The "Sui Shu Jing Ji Zhi" lists Yang Shu's "Jiu Jiu Suan Shu" as a single volume. This shows that "jiu gong yi suan" is the same as "jiujiu suan," which was first created by Fuxi and later developed and expanded by the Yellow Emperor's minister Li Shou into the arithmetic system of the "Jiu Zhang." According to Liu Hui's view, Fuxi first drew the Eight Trigrams and then invented the "jiujiu" method. Therefore, Ban Gu's statement that "Fuxi drew the Eight Trigrams based on numbers" is incorrect. (Han dynasty scholars, based on the first chapter of the "Shuo Gua," first mentioned "sheng zhi yi shu" and then "li gua sheng yao," so they thought the drawing of the trigrams originated from numbers. In reality, the original intention of the "Shuo Gua" was not this, but they misunderstood it.)

今九九八十一乘除之算，疑即隸首遺制。《算經》每以物設為乘除法（《觀物外篇》曰：乘數，生數也；除數，消數也。算去雖多，不出乎此），有九數列為三條書之者，與《大戴·明堂》篇所列正相似。術家取九室之數配以八卦五行，名之曰九宮。後漢黃香有《九宮賦》，《隋志》有《黃帝九宮經》一卷、《九宮行棊經》三卷，並鄭玄注，又《九宮八卦式圗》一卷；《唐志》有《太一九宮雜占》一卷、《遁甲九宮八門圗》一卷。其曰「黃帝九宮」，葢以數成於隸首，而明堂之制亦創自黃帝，故依託之也。

Today's multiplication and division calculations involving the number 81, which is nine times nine, are suspected to be the old system left by Li Shou. Arithmetic texts often use physical objects to set up multiplication and division problems. The "Observations Beyond Objects" states that multiplication is "the generating number" and division is "the consuming number." Although there are many names for arithmetic methods, they all originate from these two concepts. Among them, there are problems that arrange nine numbers into three rows, which is exactly similar to the "two nines four, seven five three, six one eight" listed in the "Great Dai Li Ji · Bright Hall" chapter. Numerologists take the numbers of the nine rooms in the Bright Hall and combine them with the eight trigrams and the five phases, calling this arrangement the "Nine Palace." During the Eastern Han dynasty, Huang Xiang wrote the "Nine Palace Assignment." The "Sui Shu · Jing Ji Zhi" records "The Yellow Emperor's Nine Palace Classic" in one volume and "Nine Palace Chess Classic" in three volumes, both with Zheng Xuan's annotations, as well as "Nine Palace Eight Trigrams Diagram" in one volume. The term "Yellow Emperor's Nine Palace" is probably because this system was created by Li Shou, the official of the Yellow Emperor, and the construction of the Bright Hall also originated from the Yellow Emperor, so it was attributed to him.

右論古九宮之數。

The above section examines the origin of the ancient nine-square grid numbers.

王氏應麟《玉海》引《易·乾鑿度》曰：「河圗八文，《易》變而為一，一變而為七，七變而為九，九者氣之究也，乃復變而為一。」（語本《列子》。彼注云：太極本一而生陰陽五行則為七，其變為九，則又以七之少陽而進為老陽。陽主進，陰主退，八退為六，七進為九也。）

Wang Yinglin cites in his "Yu Hai" the "Yi Wei Gan Zao Du" which says: the River Chart consists of eight sections of text. The "Yi" originates from Tai Yi, which transforms into one, then one transforms into seven, and seven transforms into nine; nine is the ultimate of qi numbers, so it returns again to one. (This passage is based on the "Liezi." Zhang Zhan's commentary on the "Liezi" says: Tai Ji originally is one; when it produces yin and yang and the Five Phases, it becomes seven; it transforms into nine because the minor yang seven becomes old yang. Yang is active and progresses, while yin is passive and regresses, so eight regresses to six, and seven progresses to nine.) Hu Wei cites this passage to indicate that the "He Tu" referred to in the "Gan Zao Du" is eight sections of esoteric text, and is not the same as the nine palace diagram or the diagram with fifty-five points.

東坡蘇氏曰：「世之通於數者，論參伍錯綜，則以九宮言之。九宮不經見，見於《乾鑿度》，曰『太乙行九宮』。九宮之數，以九一三七為四方，以二四六八為四隅，而五為中宮，經緯四隅，交絡相值，無不得十五者。陰陽老少皆分取於十五：老陽取九，餘六以為老陰；少陽取七，餘八以為少陰。此與一行之學不同，然吾以為相表裡者。二者雖不經見，而其說皆不可廢也。」

Su Shi said: Those who are skilled in divination often talk about "San Wu Cuo Zhong" when discussing the Nine Palaces. The Nine Palaces are not found in the classics, but only in the "Qian Zao Du," which says "Taiyi moves through the Nine Palaces." The numbers of the Nine Palaces are arranged with nine, one, three, and seven in the four cardinal directions, and two, four, six, and eight in the four corners, with five in the Central Palace. When adding numbers horizontally, vertically, or along the diagonals crossing the corners, each combination adds up to fifteen. The four yin-yang trigrams of old and young are derived from fifteen: old yang takes nine, and the remaining six is old yin; young yang takes seven, and the remaining eight is young yin. This differs from the theory of Yixing of the Tang dynasty, but I believe they complement each other. Although neither school is found in the classics, their theories should not be discarded.

程氏大昌《易原》曰：「晉張湛傳《列子》，至『七變為九』，曰『此章全是《周易乾鑿度》』，則漢魏已降，凡言《易》《老》者皆已宗而用之，非後世托為也。然則圗書也者，《乾鑿度》實能得之，而孔、劉反不得見，何邪？所可言者，其四正四維皆為十五，正符陳摶所傳，則其來已古，篤可信爾。」

In the Southern Song dynasty, Cheng Dachang (styled Tai zhi) in his work "The Origins of the Changes" said: When Zhang Zhan of the Jin dynasty annotated the "Liezi," he came to the sentence "seven changes become nine" and said, "This entire chapter is entirely from the "Qian Zao Du" of the Zhou Changes." This shows that since the Han and Wei dynasties, anyone discussing the Changes and the Laozi has already followed and used it, and it is not a fabrication of later generations. If this is the case, then the Yellow River Chart and the Luo Writing, which the author of the "Qian Zao Du" actually saw, while Kong Anguo and Liu Xin did not, why is this so? It can be concluded that the sum of the four cardinal directions and the four intermediate directions adds up to fifteen, which exactly matches the diagram passed down by Chen Tuan. This shows that its origin is very ancient and entirely credible.

緯書多出於哀、平之世，而《後漢·律歴志》順帝時邊韶上言「太初改元易朔，以《乾鑿度》八十分之四十三為日法」，則似武帝時已有《乾鑿度》矣。是殆不然，葢作者以《太初》歴法竄入其中，暗與之合，非武帝果用此書為日法也。圗緯至唐時已多殘缺，宋世別有《乾鑿度》二卷，題云「蒼頡修」，乃贗書，《玉海》所載，不知是殘缺本文否。據晉張湛注《列子》「太易」一章云全是《乾鑿度》，而孔穎達《易正義》引《乾鑿度》有太易、太初、太始、太素，正與張湛所言合，其為本文無疑矣。河圗之形象久已無傳，自田何軰不能贊一辭，況撰《乾鑿度》者乎？程泰之謂作者親見河圗，葢為其所愚也。

Hu Wei argued that the writings of the 'Wai Shu' mostly originated during the reigns of Emperor Ai and Emperor Ping of the Han dynasty. However, the 'Book of the Later Han, Volume on the Calendar and Music' records that during the reign of Emperor Shun, Bian Shao submitted a memorial stating that during the Tai Chu period, the calendar was changed and the 'Qian Zao Du' used forty-three parts out of eighty as the 'ri fa' (daily standard). According to this, it seems that the 'Qian Zao Du' existed as early as the time of Emperor Wu of Han. In reality, this was the author of the 'Qian Zao Du' who secretly inserted the calendar system of the Tai Chu calendar into his book, making it appear to align with it, but Emperor Wu did not actually use this book as the basis for the 'ri fa'. By the Tang dynasty, the diagrams and writings had already become fragmented. In the Song dynasty, another two-volume version of the 'Qian Zao Du' was compiled, attributed to 'Cang Jie', which was a forgery. The citations from the 'Yu Hai' are unclear whether they are remnants of the original text. According to Zhang Zhan of the Jin dynasty, who annotated the 'Lie Zi' on the chapter 'Tai Yi', the entire chapter was derived from the 'Qian Zao Du'. The 'Zhou Yi Zhen Yi' by Kong Yingda also cites the 'Qian Zao Du' and mentions 'Tai Yi', 'Tai Chu', 'Tai Shi', and 'Tai Su', which exactly match what Zhang Zhan said. This shows that the text is indeed original. As for the image of the 'He Tu', it has long been lost. Even the early Han dynasty scholars who transmitted the 'Yi Jing', such as Tian He, could not say a word about it, let alone the person who fabricated the 'Qian Zao Du'. Cheng Dachang claimed that the author of the 'Qian Zao Du' had personally seen the 'He Tu', but he was deceived by this book.

《後漢書·張衡傳》注引《易·乾鑿度》曰「太一取其數以行九宮」，鄭玄注云：「太一者，北辰神名也，下行八卦之宮，每四乃還於中央。中央者，地神之所居（《日知錄》云：「地神」疑作「北辰」），故謂之九宮。天數大分，以陽出，以陰入，陽起於子，陰起於午，是以太一下九宮，從坎宮始。自此而坤而震而巽，所行者半矣，還息於中央之宮；既又自此而乾而兊而艮而離，行則周矣。上游息於太一之星，而反紫宮也。」

The "Hou Han Shu · Zhang Heng Zhuan" cites Li Xian's annotation which refers to the "Yi Wei Gan Zao Du" saying, "The Taiyi takes this set of numbers to tour the nine palaces." Zheng Xuan explains that Taiyi is the name of the star god at the North Pole, moving through the palace positions governed by the Eight Trigrams. Every time it moves through four palaces, it returns to the center. The center is where the earth god resides (Gu Yanwu's "Ri Zhi Lu" says, "earth god" is likely "beichi"), so it is called the nine palaces. The division of heavenly numbers is based on yang energy emerging and yin energy entering; yang begins at the Zi position, and yin begins at the Wu position. Therefore, Taiyi moves through the nine palaces starting from the Kan palace, proceeding to the Kun, Zhen, and Xun palaces, completing half the journey and resting in the central palace. Then it continues from there to the Qian, Dui, Gen, and Li palaces, completing one full circle. After that, it ascends to rest at the Taiyi star and returns to the Ziwei palace.

（《史記·天官書》：中宮天極星，其一明者為太一常居。《封禪書》：亳人謬忌奏祠太一方，曰「天神貴者太一，太一佐曰五帝。古者天子以春秋祭太一東南郊，用太牢七日，為壇開八通之鬼道」。於是天子令太祝立其祠長安東南郊，常奉祠如忌方。鄭康成《周禮注》云：昊天上帝又名太一。）

(Notes: The "Records of the Grand Historian: Celestial Officials" says that the brightest star in the Central Palace, Tianjiu Star, is where Taiyi resides permanently. The "Records of the Grand Historian: Rituals of Propitiation" says that a man from Bo County, Miu Ji, proposed the method of worshiping Taiyi, saying "Among the heavenly deities, Taiyi is the most exalted, and Taiyi's assistants are the Five Emperors; in ancient times, the Son of Heaven would worship Taiyi at the southeast outskirts in spring and autumn, using the grand sacrifice of ox, sheep, and pig for seven days, building a temple and opening eight paths leading to all directions." Thus, the Son of Heaven ordered the Grand Priest to establish a temple for Taiyi in the southeast outskirts of Chang'an, and to worship it permanently according to Miu Ji's method. Zheng Kangcheng's commentary on the "Rites of Zhou" says: "Hu Tian Shangdi is also called Taiyi.")

《南齊書·髙帝紀》：案太一九宮占歴，推自漢髙帝五年至宋順帝升明元年太一所在。《易·乾鑿度》曰「太一取其數以行九宮」。九宮者，一為天蓬，以制冀州之野；二為天內，以制荊州之野；三為天沖，其應在青；四為天輔，其應在徐；五為天禽，其應在豫；六為天心，七為天柱，八為天任，九為天英，其應在雍、在梁、在揚、在兗。天沖者木也，天輔者亦木也，故木行太過不及，其眚在青、在徐；天柱金也，天心亦金也，故金行太過不及，其眚在梁、在雍。惟水無應宮也。

The "Nan Qi Shu · Gao Di Ji" records that according to the divination method of the Taiyi Nine Palaces, one calculates the position of Taiyi in the nine palaces from the fifth year of Han Gao Di to the first year of Liu Song Shun Di Shengming. The "Yi Wei Qian Zao Du" says, "Taiyi takes that set of numbers to move through the nine palaces." The nine palaces are as follows: the first is Tianpeng, governing the Ji State; the second is Tiannei, governing the Jing State; the third is Tianchong, affecting the Qing State; the fourth is Tianfu, affecting the Xu State; the fifth is Tianqin, affecting the Yu State; the sixth is Tianxin, the seventh is Tianzhu, the eighth is Tianren, and the ninth is Tianying, each affecting the Yong State, Liang State, Yangzhou, and Yan State respectively. Tianchong belongs to wood, and Tianfu also belongs to wood, so when the movement of wood is excessive or insufficient, calamities occur in Qing and Xu States. Tianzhu belongs to metal, and Tianxin also belongs to metal, so when the movement of metal is excessive or insufficient, calamities occur in Liang and Yong States. Only water does not have a corresponding palace.

《唐書·玄宗紀》：天寶三載十二月癸丑，祠九宮貴神於東郊。

The Xintangshu · Xuanzong Benji records that on the tenth day of the twelfth month in the third year of Tianbao, Emperor Xuanzong performed worship at the eastern outskirts to the Nine Palaces Noble Deities. This marks the beginning of the Nine Palaces, as explained by numerological scholars, being formally included in the state rituals.

《唐會要》：玄宗天寶三載十月，術士蘇嘉慶上言，請於京城置九宮壇，壇一成，其上依位置小壇：東南曰招搖，正東曰軒轅，東北曰太陰，正南曰天一，中央曰天符，正北曰太一，西南曰攝提，正西曰咸池，西北曰青龍。五數為中，戴九履一，左三右七，二四為上，六八為下，符於遁甲。（晁氏曰：遁甲之書見於《隋志》凡十三家，則其學之來亦不在近世矣。以休、生、傷、杜、景、死、驚、開八門推國家之吉凶，通其學者以為冇驗，未之嘗試也。）肅宗至德三年六月，置太一神壇於南郊東。九宮以四孟隨歲改位行棊，謂之飛位，乾元後遂不易位。

The Tang Huiyao records that in the third year of Tianbao of Emperor Xuanzong, the astrologer Su Jiaqing submitted a memorial requesting the establishment of a nine palace altar in the capital. The altar was built in one layer, and on top of it, nine small altars were set up according to the directions: the southeast was called Zhao Yao, the due east was called Xuanyuan, the northeast was called Tai Yin, the due south was called Tian Yi, the center was called Tian Fu, the due north was called Tai Yi, the southwest was called She Ti, the due west was called Xian Chi, and the northwest was called Qing Long. Five occupied the center, with nine on top, one beneath, three on the left, seven on the right, two and four above (the shoulders), and six and eight below (the feet), matching the method of Dun Jia. (Chao Gongwu said: books on Dun Jia were recorded in thirteen families in the Sui Shu Jingji Zhi, indicating that this discipline is not a recent development. It uses the eight gates of Xiu, Sheng, Shang, Du, Jing, Si, Jing, and Kai to calculate the auspiciousness and misfortune of the state. Those who are skilled in this discipline say it is very effective, but I have not tried it myself.) In the sixth month of Zhongde third year of Emperor Suzong, a Tai Yi deity altar was set up to the east of the southern altar. The nine palaces changed positions according to the four beginning months of the year, moving like playing chess, a practice called "fei wei"; however, after the reign of Ganyuan, the positions no longer changed.

武宗會昌二年正月，左僕射王起等奏：按《黃帝九宮經》及蕭吉《五行大義》，一宮其神太一，星天蓬，卦坎，行水，方白；二宮其神攝提，星天內，卦坤，行土，方黑；三宮其神軒轅，星天沖，卦震，行木，方碧；四宮其神招搖，星天輔，卦巽，行木，方綠；五宮其神天符，星天禽，卦坤，行土，方黃；六宮其神青龍，星天心，卦乾，行金，方白；七宮其神咸池，星天柱，卦兊，行金，方赤；八宮其神太陰，星天任，卦艮，行土，方白；九宮其神天一，星天英，卦離，行火，方紫。統八卦，運五行，土飛於中，數轉於極。（章俊卿《山堂考索》云：漢立太一祠，即甘泉泰畤也，唐謂之太清紫極宮，宋謂之太一宮，尤重其祠。以太一飛在九宮，每四十餘年而一徒，所臨之地則兵疫不興，水旱不作。）

In the second year of Wu Zong's reign during the period of the Kai Cheng era, Left Chancellor Wang Qi and others submitted a memorial stating: According to the "Yellow Emperor's Nine Palaces Classic" and Xiao Ji's "The Great Meaning of the Five Phases," the deity of the first palace is Taiyi, whose star is Tianpeng, associated with the Kan trigram, governing water, with the color white. The deity of the second palace is SheTi, whose star is Tiannei, associated with the Kun trigram, governing earth, with the color black. The deity of the third palace is Xuanyuan, whose star is Tianchong, associated with the Zhen trigram, governing wood, with the color green. The deity of the fourth palace is Zhaoyao, whose star is Tianfu, associated with the Xun trigram, governing wood, with the color green. The deity of the fifth palace is Tianfu, whose star is Tianqin, associated with the Kun trigram, governing earth, with the color yellow. The deity of the sixth palace is Qinglong, whose star is Tianxin, associated with the Qian trigram, governing metal, with the color white. The deity of the seventh palace is Xianchi, whose star is Tianzhu, associated with the Dui trigram, governing metal, with the color red. The deity of the eighth palace is Taiyin, whose star is Tianren, associated with the Gen trigram, governing earth, with the color white. The deity of the ninth palace is Tianyi, whose star is Tianying, associated with the Li trigram, governing fire, with the color purple. These deities oversee the eight trigrams and the five phases, with earth flying in the center, and the numbers cycling back when they reach the end. (Zhang Junqing's "Shangtang Kao Suo" states: The Taiyi temple established during the Han dynasty was the Taizhi Palace at Ganquan; during the Tang dynasty it was called the Taqing Zijie Palace, and during the Song dynasty it was called the Taiyi Palace, and the worship of Taiyi was especially emphasized. Because Taiyi moves through the nine palaces, shifting every forty years or so, the places it arrives at are free from war, plague, and drought or flood.)

按：張衡所稱九宮，不過如明堂《月令》之說，而《易緯·乾鑿度》則以為太一下行之數，涉於誕矣。衡方斥圗緯為非聖之書，九宮必不取諸《乾鑿度》，章懷不當引以為注。蘇嘉慶、王起等所奏神號、星名、方色，則又其穿鑿傅會之甚者也。

Hu Wei said: Zhang Heng's nine palaces are merely the explanation of the Bright Hall in the "Monthly Orders"; however, the "Yi Wei Qian Zao Du" describes it as the number of the Supreme Ruler moving downward, which becomes absurd. Zhang Heng was actually condemning the diagrams and writings of the classics as non-sacred books, so the nine palaces he mentioned must not have come from the "Qian Zao Du". Prince Li Xian of Zhanghua should not have cited the "Qian Zao Du" to annotate him. As for the divine names, star names, and directional colors mentioned in the memorials by Su Jiaqing and Wang Qi, they are even more fabricated and forced.

九宮非河圗也。自《乾鑿度》有「河圗八文」之語，劉瑜有「河圗九房」之稱，而世遂以九宮為河圗矣。又有指此為洛書者，葢以九疇之故。然九疇有次第，無方位也，強配八卦以附會之數，豈理也哉！

The Nine Palaces are not the Yellow River Chart. It is only because the "Qian Zao Du" mentions "eight characters of the Yellow River Chart" and Liu Yu refers to "nine rooms of the Yellow River Chart" that people have come to associate the Nine Palaces with the Yellow River Chart. Similarly, some people claim the Nine Palaces correspond to the Luo Writing, because the Luo Writing relates to the nine categories. However, the nine categories only have a sequence of order, not a directional aspect. To force them into the Eight Trigrams and create this system is clearly not reasonable.

右論乾鑿度太一九宮之數。

In the above section, the discussion examines the numerical system of the Great One (Taiyi) moving through the nine palaces as described in the "Danzuode."

《舊唐書·經籍志》丙部五行類：《周易參同契》二卷，魏伯陽撰；《周易五相類》一卷，魏伯陽撰。

The *Old Book of Tang* *Catalogue of the Classics* under the category of the Five Phases records: *The Threefold Concordance of the Zhou Changes* in two volumes, written by Wei Boyang; and *The Five Categories of the Zhou Changes* in one volume, also written by Wei Boyang. Wei Boyang was a native of Shangyu, Huizhou, in the Eastern Han dynasty. Daoist alchemists regard his *Threefold Concordance* as the "King of Ten Thousand Ancient Alchemical Classics." Hu Wei devoted a special section, volume three, to *The Threefold Concordance* because the diagrammatic forms known as the "Earlier Heaven Diagram" and the "Taiji Diagram" mentioned by Song dynasty scholars actually originated from this alchemical text.

《唐書·藝文志》五行類：魏伯陽《周易參同契》二卷，又《五相類》一卷。（《古文參同契》本云「三相類」，淳于叔通撰，未知孰是。）

The "Five Phases" category in the "Art and Literature Catalogue" of the "New Book of Tang" lists Wei Boyang's "Threefold Concordance of the Zhou Changes" in two volumes, and another volume titled "Five Categories." ("Ancient Texts of the Threefold Concordance" refers to it as "Three Categories," attributed to Chunyu Shutong. It is unclear which account is correct.)

真一子彭曉《參同契解義序》曰：「魏伯陽，會稽上虞人，修真潛黙，養志虛無，博贍文詞，通諸緯候，得《古文龍虎經》，盡獲妙旨，乃約《周易》譔《參同契》三篇，復作《補塞遺脫》一篇，密授青州徐從事（名景休），徐乃隠名而注之。桓帝時復授同郡淳于叔通，遂行於世。」

In the preface of his work "Explanation of the Meaning of the Great Ultimate" (参同契解义), Peng Xiao, a person from the Shu state during the Five Dynasties period (道号真一子), said that Wei Boyang was from Shangyu, Kuaiji. He practiced the true Dao, remained silent and self-restrained, cultivated his mind in the void, had rich and eloquent writings, and understood various books of omens and prophecies. He obtained the "Classic of the Dragon and Tiger in Ancient Texts" (古文龙虎经), fully grasped its profound meanings, and then modeled his work on the "Zhou Changes" (周易) to compose the "Great Ultimate" (参同契) in three chapters. He also wrote another chapter called "Supplementing the Missing and Removing the Deficient" (补塞遗脱). He secretly passed it on to Xu Chengshi (徐从事), a person from Qingzhou named Jingxiu. Xu Jingxiu then concealed his name and made annotations on it. Later, during the reign of Emperor Huan of Han, it was passed on to Chunyu Shutong, a person from the same county, and the book then became well known in the world.

《雲笈七籤·神仙傳》曰：「魏伯陽作《參同契》，似解釋《周易》，其實假借爻象以論作丹之意。而儒者不知神仙之事，多作陰陽注之，失其奧旨矣。」

The "Yun Ji Qi Jian" includes a passage from the "Shen Xian Zhuan" which says: Wei Boyang wrote the "Cen Tong Qi", which on the surface seems to be explaining the "Zhou Yi", but in reality uses the trigrams to discuss the principles of alchemy. However, Confucian scholars do not understand the practices of immortality, and mostly interpret it according to the meanings of yin and yang, thus losing its profound meaning. This very point shows that the "Cen Tong Qi" was not originally a book for interpreting the "Zhou Yi". Hu Wei cited it in order to clearly distinguish alchemical diagrams from the study of the "Zhou Yi".

鼂氏公武《讀書志》曰：「《周易參同契》三卷，漢魏伯陽撰，彭曉為之解，隋、唐書皆不載。（唐新舊二史皆有。）按陸德明解『易』字雲『虞翻作《參同契》，言字從日下月』，今此書有『日月為易』之文，其為古書明矣。」

In the Southern Song dynasty, Zhao Gongwu's "Juzhai Reading Notes" says: "The "Zhou Yi Cangtongqi" (The Supreme Concord of the Zhou Yi) in three volumes was written by Han dynasty Wei Boyang, and Peng Xiao wrote an explanation for it. The "Sui Shu" and "Tang Shu" did not record it. (Hu Wei's marginal note points out that both the old and new versions of the "Tang Shu" actually did record it.) Zhao Gongwu also says: Lu Deming explained the character "Yi" by saying "Yu Fan wrote the "Cangtongqi", explaining that this character is composed of "sun" on top and "moon" below." Now this book actually contains the phrase "the sun and moon are called Yi", which shows that it is indeed an ancient text.

陳氏振孫《書錄解題》曰：「《參同契分章通真義》三卷、《明鏡圗訣》一卷，真一子彭曉秀川撰，蜀永康人也。《參同契》因《易》以言養生，後世言修煉者祖之。序稱廣政丁未（蜀孟昶廣政十年歲在丁未，漢髙祖之天福十二年也），以《參同契》分十九章而為之注，且為圗八環，謂之《明鏡圗》。」

In the Southern Song dynasty, Chen Zhenzun of the "Zhai Zhai Shu Lu Jie Ti" said: "The book 'Fen Zhang Tong Zhen Yi' of the 'Cantongqi' in three volumes and 'Ming Jing Tu Jue' in one volume were written by Zhenyi Zi Peng Xiao (whose name was Xiu Chuan), who was from Yongkang in Sichuan. The 'Cantongqi' uses the 'Zhou Yi' to discuss health preservation, and later generations of those who practiced cultivation regarded it as the ancestor. Peng Xiao's preface is titled 'Guangzheng Dingwei' (the tenth year of Guangzheng of Meng Chang, the ruler of the Later Shu, which coincided with the year Dingwei, also known as the twelfth year of Tianfu of the Later Han High Ancestry). He divided the 'Cantongqi' into nineteen chapters and provided annotations, and also drew eight circular diagrams, called 'Ming Jing Tu'."

升庵楊氏慎《古文參同契序》曰：「《參同契》為丹經之祖，然考隋、唐經籍志皆不載（承鼂氏之誤），惟《神仙傳》云魏伯陽上虞人，通貫詩律，文詞贍博，修真養志，約《周易》作《參同契》，徐氏景休箋註，桓帝時以授同郡淳于叔通，因行於世。五代之時，蜀永康道士彭曉分為九十章，以應火候之九轉，餘《鼎歌》一篇，以應真鉛之得一，其說穿鑿，且非魏公之本意也。其書散亂橫決，後之讀者不知孰為經，孰為注，亦不知孰為魏，孰為徐與淳于，自彭始矣。朱子作《考異》及解，亦據彭本；元俞玉吾所注，又據朱本。」

In the Ming dynasty, Yang Shen (styled Sheng'an) wrote in his "Preface to the Ancient 'Canyongqi'": The "Canyongqi" is regarded as the ancestor of alchemical texts, but it is not recorded in the "Classic Catalogue" of the "Sui Shu" or the "Tang Shu". This is following the mistake of Zhao Gongwu. Only the "Shenxian Zhuan" mentions that Wei Boyang was from Shuyu, skilled in poetry and prose, knowledgeable in literature, and devoted to cultivating his spirit and virtue. He studied the "Zhou Yi" and composed the "Canyongqi", which was annotated by Xu Jingxiu. It was passed down to Chen Yushutong of the same county during the reign of Emperor Huan, thus becoming well known. In the Five Dynasties period, the Daoist priest Peng Xiao from Yongkang in Shu divided the text into ninety chapters, corresponding to the "nine transformations" of alchemical fire. The remaining chapter, "Dingge", corresponds to the concept of "getting one" in true lead. This division is artificial and inconsistent with Wei Boyang's original intention. The text is disordered and mixed, making it difficult for later readers to distinguish between the original text, annotations, and contributions from Wei Boyang, Xu Jingxiu, and Chen Yushutong. The confusion began with Peng Xiao. Zhu Xi's "Examination and Commentary on the 'Zhou Yi Canyongqi'" and his commentary were based on Peng Xiao's version. Later, Yuan dynasty scholar Yu Yan (styled Yiwu) also based his commentary on Zhu Xi's version.

復陽子蔣一彪《古文參同契集解序》曰：「昨偶檢先大夫雲龍公遺籍，得《古文參同契》一帙，魏伯陽所著上中下三篇、序一篇，徐景休箋註亦三篇、序一篇，淳于叔通補遺《三相類》上下二篇、後序一篇，合為十一篇，惟白文無注，是未經後人妄紊者，為成都升庵楊慎氏所序本。覽之始知往年所閱者，乃以魏君序及景休、叔通二家之注序竄入於魏君經文中，大相混亂。

A Ming dynasty scholar named Jiang Yibiao, who took the Daoist name Fuyangzi, wrote in the preface to his collected interpretations of the "Ancient Texts of the Perfect Union" that some time ago he accidentally came across some old books left by his father, Yunlong Gong, and found a copy of the "Ancient Texts of the Perfect Union." It contained the upper, middle, and lower chapters written by Wei Boyang, as well as an introduction, and three chapters plus an introduction by Xu Jingxiu's annotations, and two chapters plus a postscript by Chunyu Shutong's supplements, making a total of eleven chapters. This version had only the main text and no marginal notes, and had not been disturbed by later commentators. It was exactly the edition that Chengdu Yang Shen wrote a preface for. Only after reading this version did he realize that the commonly circulated edition had mixed Wei Boyang's introduction and the annotations and prefaces by Xu Jingxiu and Chunyu Shutong into the main text of Wei Boyang's work, causing great confusion.

後人注者不知所自，訛以因訛，經注莫辨，皆緣飾以成文，則不無牽引附會之誤。又無怪乎最後之觀者，見其重文復義，不達所指，咸即成說而一切草草錯會焉。不知亂肇自何人，而升庵謂於彭始。予今釐正其訛，一以古文為準，別出魏君經文，取彭曉、陳顯微、陳致虛、俞琰四子之注節集於各段之下，以顯明其義。」（一彪餘姚人，萬歴甲寅序。）

Later commentators did not know the origins of these words, and they passed on errors, making it difficult to distinguish between the original text and the annotations. They simply embellished everything to form coherent passages, inevitably leading to forced and incorrect interpretations. It is therefore not surprising that later readers found the text repetitive and its meanings overlapping, unable to understand what it actually meant, and thus followed old interpretations without proper understanding. Who started this confusion is unknown, but Yang Shen claimed it began with Peng Xiao. Now I am correcting these errors, using the ancient text as the standard. I have separately extracted Wei Boyang's original text and selected excerpts from the annotations of Peng Xiao, Chen Xianwei, Chen Zhi Xu, and Yu Yan, placing them beneath each section to clarify the meaning. (Jiang Yibiao was from Yuyao; this preface was written in the year Jiayin of the Wanan era.)

《朱子語類》曰：「《易》只是個陰陽，莊生曰『《易》以道陰陽』，亦不為無見。等而下之，如醫技、養生家之說，皆不離陰陽二者。魏伯陽《參同契》，恐希夷之學有些是其源流。」又曰：「先天圗傳自希夷，希夷又自有所傳，葢方士技術用以修煉，《參同契》所言是也。」

The Zhu Zi Yu Leiu records Zhu Xi's words saying: The Zhou Yi talks about nothing but yin and yang. The Zhuangzi says, "The Yi is used to explain yin and yang," which cannot be considered without insight. Going further, the doctrines of medicine and those of the practitioners of health preservation all depend on these two aspects of yin and yang. Wei Boyang's Cang Tong Qi, perhaps part of Chen Tuan's learning (who was known as Master Xiyi) came from it. Zhu Xi also said: The Earlier Heaven diagram was passed down by Chen Tuan, and Chen Tuan had another lineage - that was originally a technique of alchemists used for cultivation. The Cang Tong Qi talks about exactly that. Hu Wei cites Zhu Xi's two statements, using Zhu Xi's own words to prove that the Earlier Heaven diagram originated from alchemy, not from Fuxi.

「參，雜也；同，通也；契，合也。」謂與《周易》理通而義合也。其書假借君臣以彰內外，敘其離坎；直指汞鉛，列以乾坤；奠量鼎器，明之父母；保以始終，合以夫妻；拘其交媾，譬諸男女；顯以化生，材以陰陽；導之反覆，示之晦朔；通以降騰，配以卦爻；形於變化，隨之斗柄；取以周星，分以晨昏，昭諸刻漏：莫不託《易》象而論之，故名《周易參同契》云。

The explanation of the book's title is: "San" means mixture, "Tong" means communication, and "Qie" means conformity. It means that it is in harmony with the principles of the Zhou Changes and its meanings are consistent. This book uses the relationship between sovereign and minister to illustrate internal and external distinctions, discussing the trigrams Li and Kan; it directly points to mercury and lead, combined with Qian and Kun; it arranges the vessels for measurement, likening them to parents; it uses beginning and end to preserve, and husband and wife to coordinate; it restrains their interaction, comparing it to male and female; it shows generation and transformation, drawing from yin and yang; it guides the cycle of movement and stillness, using the waxing and waning of the moon to indicate; it connects ascending and descending, combined with trigrams and lines; it demonstrates change, following the movement of the Big Dipper's handle; it takes the celestial phenomena of the entire year as a model, dividing day and night, using water clocks to demonstrate—all these are based on the trigrams of the Zhou Changes, hence the name "The Zhou Changes Combined with the Three Principles."

合沙鄭氏東卿曰：「伯陽之《參同契》意在鍛鍊，而入於術，於聖人之道為異端。」

A scholar from the Southern Song dynasty named Zheng Dongqing from Heshā said that Wei Boyang's "Cantong Qi" was intended for the alchemy of elixirs, falling into the category of esoteric practices, and thus regarded as heretical in relation to the teachings of the sages.

黃氏震《日抄》曰：「《參同契》者，漢世魏伯陽所造，其說出於《神仙傳》，不足憑。為之註釋者五代末彭曉，則此書必出於五代之前也。此方士煉丹之書，然必冒《周易》為稱者，煉丹取子午時為火候，是坎離，因用乾坤坎離四正卦於槖鑰之外。

In the Southern Song dynasty, Huang Zhen's "Huang Shi Ri Chao" said: The "Cantong Qi" was created by Wei Boyang of the Han dynasty, but this claim comes from the "Shen Xian Zhuan" and is not reliable. The person who made annotations on it was Peng Xiao from the late Five Dynasties period, which shows that the book must have existed before the Five Dynasties. Originally, it was a book used by alchemists for the practice of elixir making. It was forced to take the name of the "Zhou Changes" because in the process of elixir making, they used the time of the "zi" and "wu" hours as the fire timing, which corresponded to the trigrams Kan and Li. Therefore, in addition to the "tuoyue" (furnace and bellows), they also used the four trigrams Qian, Kun, Kan, and Li.

其次言屯蒙六十卦，以見一日用功之早晚；又次言納甲六卦，以見一日用功之進退；又次言十二闢卦，以分納甲六卦而兩之：要皆附會《周易》以張大粉飾之。其實煉丹無藉於《易》，《易》本無預於煉丹。而今世言火候者，因以三百八十四爻為一周天，以一爻直一日，而爻多日少，終不相合，其妄可知。近世蔡季通學博而不免於雜，嘗留意此書，而晦庵與之遊，因為校正，其書頗行，然求其義則終無之。」

Then he explained the sixty hexagrams following Zhun and Meng, using them to represent the early and late times of effort in a day; next he explained the six hexagrams of Najia, using them to represent the advance and retreat in effort during the day; then he explained the twelve great hexagrams, which were formed by doubling the six Najia hexagrams. In summary, all these are artificial interpretations of the Zhou Changes to embellish and decorate their own practices. In reality, alchemy does not need to rely on the Zhou Changes, and the Zhou Changes were originally unrelated to alchemy. Now, those who talk about fire timing take the 384 lines as one cycle of the heavens, with each line corresponding to one day. However, since there are more lines than days, they do not match up, and their absurdity is evident. In recent times, Cai Yuan ding (whose name is Jitong) had broad knowledge but was not free from confusion, and he once paid attention to this book. Zhu Xi, having communicated with him, corrected it, and thus the book became quite popular. However, there is no real meaning to be found in it.

河津薛氏瑄曰：「《參同契》假《易》論長生之術，若指諸掌，然終是方技之書。」

In the Ming dynasty, Xue Xuan, a famous Confucian scholar from Hejin, said: The "Canyongqi" uses the "Zhou Yi" to explain the method of long life, explaining it as clearly as pointing to one's own palm. However, it is ultimately a book about magical techniques.

京山郝氏敬《學易枝言》曰：「《周易參同契》作自魏伯陽，大旨宗老氏《道德經》者，老子之《易》也。門戶、轂軸、槖鑰、牝牡，稽數探賾，不一而足，有無玄妙悉本其中。故知此書宗老氏，於《易》則《參同契》云爾。」

In the "Xue Yi Zhi Yan" by Hao Jing of Jingshan in the Ming dynasty, it is said that the "Zhou Yi San Tong Qi" was written by Wei Boyang, and its main purpose is based on the "Dao De Jing" by Laozi -- the "Dao De Jing" is Laozi's "Yi." The book contains many terms such as "men hu," "gu zhou," "tuo yao," and "pi mu," which explore numerical principles and delve into subtle mysteries. All the profound and subtle ideas in the book are rooted in the "Dao De Jing." Therefore, it can be known that this book follows the teachings of Laozi. As for the "Zhou Yi," it is merely a matter of "participating in harmony and unity" with it.

河右毛氏奇齡曰：「《參同契》諸圗，自朱子注後則學者多刪之。徐氏注本已亡，他本厖雜不足據，惟彭本有《水火匡廓圗》《三五至精圗》《斗建子午圗》《將指天罡圗》《昬見圗》《晨見圗》《九宮八卦圗》《八卦納甲圗》《含元播精三五歸一圗》，然或並《至精》《歸一》圗，或並《斗建》《將指》圗，故或九或七，今藏書家與道家多有之。以其書本丹灶家抽坎填離之術，故隋、唐志以其書入道家類（渭按：唐志入五行類，隋志無）。相傳漢桓帝時淳于叔通受其學，始以行世，故張平叔《悟真詩》云『叔通受學魏伯陽，留為萬古丹經王』也。」（見《太極圗說遺議》。）

In the early Qing dynasty, Mao Qiling, who was from He You, said: The various diagrams attached to the "Cantong Qi" have, since Zhu Xi's commentary, mostly been deleted by scholars. Xu Jingxiu's commentary has long been lost, and other versions are disorderly and unreliable. Only Peng Xiao's edition preserves the "Water and Fire Enclosure Diagram," "Three and Five Ultimate Essence Diagram," "Celestial Stem and Earthly Branches Diagram," "Heavenly Gang Diagram," "Dusk Appearance Diagram," "Dawn Appearance Diagram," "Nine Palaces and Eight Trigrams Diagram," "Eight Trigrams and Heavenly Stems Assignment Diagram," and "Inclusion of Essence and Distribution of Vitality, Three and Five Return to One Diagram." However, some editions combine the "Ultimate Essence" and "Return to One" into one diagram, and others combine the "Celestial Stem and Earthly Branches" and "Heavenly Gang" into one diagram, so the number of diagrams varies, either nine or seven. Now, these diagrams are mostly preserved in the collections of bibliophiles and Daoists. Since this book is essentially a method of alchemical practice known as "drawing the Yin into the Yang," the "Sui Shu" and "Tang Shu" classified it under the Daoist category. (Hu Wei remarked: In fact, the "Tang Shu" classified it under the Five Phases category, and the "Sui Shu" did not even record it.) It is said that this book began to circulate in the world after Chun Yu Shutong received this teaching during the reign of Emperor Huan of Han. Therefore, Zhang Boshan (Zhang Pingshu) in his "Wuzhen Pian" wrote, "Chun Yu Shutong received the teachings from Wei Boyang, leaving it as the supreme alchemical classic for all ages." (See Mao Qiling's "Yitiku Shuyi.") Hu Wei's key point is that the predecessors of the Song dynasty's "Taiji Diagram," namely the "Water and Fire Enclosure Diagram" and the "Three and Five Ultimate Essence Diagram," are preserved in the diagrams of this alchemical text.

《書錄解題》言彭本《明鏡圗》有八環，今其存者非九則七，葢《斗建》《將指》不當併合，而《至精》《歸一》本係一圗，是為八環耳。

Chen Zhenzun in "Zhai Zhai Shu Lu Jie Ti" says that Peng Xiao's "Ming Jing Tu" originally had eight rings, but the version passed down today is either nine or seven. Probably the two pictures "Dou Jian" and "Jiang Zhi" should not have been combined, while "Zhi Jing" and "Gui Yi" were originally a single picture; thus, adding them up, they make exactly eight rings.

《易外別傳》校正彭真一《明鏡圖》，畧加增損而成九環。《易》曰：「至哉坤元，萬物資生，乃順承天。」《參同契》曰：「恆順地理，承天布宣。」石澗俞氏琰曰：「人之元氣藏於腹，猶萬物藏於坤；神入氣中，猶天氣降而至於地；氣與神合，猶地道之承天。天地以此而生物，吾身以此而產藥。《太玄經》云『藏心於淵，美厥靈根』，與此同旨。」

In the Yuan dynasty, Yu Yan of the Shih Chien school edited Peng Zhenyi, a scholar from the Shu state of the Five Dynasties period, who wrote the "Ming Jing Tu" (Diagram of the Clear Mirror). Yu Yan made slight additions and deletions to the original diagram, transforming it into nine circular rings. The first ring cites the "Commentary on the Judgment" from the "Zhou Yi" (I Ching): "How great is the primordial power of the Earth! All things depend on it for their growth, and it follows and supports the heavenly way." It also cites the "Chen Tong Qi" from the "Zhou Yi": "Forever following the order of the earth, receiving the gifts of heaven and spreading them forth." Master Shi Jian, Yu Yan, explains that human vital energy is stored within the abdomen, just as all things are stored within the earth; the "spirit" enters the "vital energy," just as the heavenly qi descends to the earth; the "vital energy" and "spirit" unite, just as the earth's way supports the heavenly way. Heaven and earth use this principle to nurture all things, and the human body uses this principle to produce the elixir. Yang Xiong's "Classic of Supreme Mystery" says, "Keep the mind in the deep abyss, nurturing one's spiritual root," which is the same meaning as here.

邵子曰：「月體本黑，受日之光而白。」俞氏曰：「日為太陽，月為太陰。月本無光，月之光乃日之光也。陽明陰暗，陽稟陰受，故太陰受太陽之光以為明。人之心為太陽，氣海猶太陰。心定則神凝，神凝則氣聚。人能凝神入於氣中，則氣與神合，與太陰受太陽之光無異。」

The second ring cites Shao Yong's words: "The essence of the moon is originally black, and it appears white only after receiving the light of the sun." Yu Yan explains that the sun belongs to "Taiyang" and the moon belongs to "Taiyin." The moon itself does not emit light; its light is actually the light of the sun. Yang represents brightness, while Yin represents darkness. Yang is responsible for giving, and Yin is responsible for receiving. Therefore, Taiyin must receive the light of Taiyang to become bright. In the human body, the heart corresponds to Taiyang, and the "Qihai" in the lower abdomen corresponds to Taiyin. When the heart becomes calm, the spirit gathers, and when the spirit gathers, the qi accumulates. If a person can hold the spirit and send it into the qi, the qi and spirit will merge into one, which is the same as Taiyin receiving the light of Taiyang.

邵子曰：「神統於心，氣統於腎，形統於首。形氣交而神主乎其中，三才之道也。」俞氏曰：「人之一身，首乾腹坤，而心居其中，其位猶三才也。氣統於腎，形統於首，一上一下本不相交，所以使之交者神也。神運乎中，則上下渾融，與天地同運，此非三才之道歟？夫神守於腎則靜而藏伏，坤之道也；守於首則動而運行，乾之道也。藏伏則妙合而凝，運行則周流不息。妙合而凝者藥也，用流不息者火也。」

The third ring cites Shao Yong's words: "The spirit is governed by the mind, the vital energy by the kidney, and the form by the head. When form and vital energy interact, the spirit acts as the central authority, which is the principle of heaven, earth, and humanity." Yu Yanyan explains that in the human body, the head belongs to Qian (Heaven), the abdomen to Kun (Earth), and the heart is in the middle, a position analogous to the three principles. Vital energy is governed by the kidney below, and form by the head above; naturally, they do not interact. The spirit enables their interaction. The spirit moves in the center, uniting the upper and lower parts, harmonizing with the rhythm of heaven and earth. Is this not the way of the three principles? When the spirit resides in the kidney, it is quiet and hidden, embodying the principle of Kun; when it resides in the head, it is active and in motion, embodying the principle of Qian. Being hidden allows for "wonderful union and coagulation," while being active allows for continuous circulation. The "wonderful union and coagulation" forms the "drug," and the continuous circulation is the "fire," that is, the fire timing.

《陰符經》曰：「機在目。」邵子曰：「天之神發乎日，人之神發乎目。」俞氏曰：「目之所至，心亦至焉，故內煉之法，以目視鼻，以鼻對臍，降心火入於氣海，葢不過片餉工夫而已。」《易》曰：「乾為天，坤為地，離為日，坎為月。」又曰：「乾為首，坤為腹。」《太玄經》曰：「陽氣潛萌於黃宮。」《黃庭經》曰：「子欲不死修崑崙。」又曰：「出日入月呼吸存。」

The fourth ring cites the "Classic of Hidden符" saying, "The key lies in the eyes." It also cites Shao Yong saying, "The divine manifestations of heaven are revealed in the sun, and the divine manifestations of man are revealed in the eyes." Yu Yan explains that wherever the eyes look, the mind follows, so the method of internal alchemy involves looking from the eyes to the nose, aligning the nose with the navel, and bringing the heart fire down into the qihai. This is actually only a brief moment. The next ring cites the "Commentary on the Hexagrams" from the "Zhou Changes" saying, "Qian represents heaven, Kun represents earth, Li represents the sun, and Kan represents the moon." It also says, "Qian represents the head, and Kun represents the abdomen." It cites Yang Xiong's "Classic of Supreme Mystery" saying, "Yang energy quietly emerges from the yellow central palace." It also cites the Taoist "Classic of the Yellow Court" saying, "If you wish to avoid death, cultivate the 'Kunlun' (referring to the top of the head)." It also says, "The sun rises and the moon enters, all within the breath and mental visualization."

俞氏曰：「首居上而圎，諸陽之所會，乾天之象也，故《易》以乾為首；崑崙在西北乾位，故《黃庭經》以乾為崑崙。腹居下而中虛，八脈之所歸，坤地之象也，故《易》以坤為腹；天玄而地黃，故《太玄》以坤為黃宮。日生於東，月生於西，故《易》以離為日、坎為月；呼吸出入，升降上下，往來無窮，故《黃庭》以呼吸為日月。或以兩目為日月，非也，兩目僅有日月之形，無日月之用。」

Yu Yan explains that the head is the highest part of the human body and has a round shape, being the place where all the yang meridians converge. This corresponds to the image of Heaven, so the Zhou Changes use Qian to represent the head. The Kunlun Mountains are located in the northwest, which is the position of Qian, so the Huangting Jing refers to Qian as "Kunlun," meaning the top of the head. The abdomen is located below the body and is hollow in the center, being the place where the eight extraordinary meridians converge. This corresponds to the image of Earth, so the Zhou Changes use Kun to represent the abdomen. The sky is dark and the earth is yellow, so the Tai Xuan Jing refers to Kun as "the Yellow Palace." The sun rises in the east and the moon appears in the west, so the Zhou Changes use Li to represent the sun and Kan to represent the moon. Human breathing has both exhalation and inhalation, rising and falling, moving up and down endlessly, so the Huangting Jing compares breathing to the sun and moon. Some people take the two eyes as representing the sun and moon, which is incorrect: the two eyes only have the shape of the sun and moon, but not the function of the sun and moon moving and circulating endlessly.

《參同契》曰：「九還七返，八歸六居。」又曰：「七八數十五，九六亦相應。」又曰：「金水合處，木火為侶，四者渾沌，列為龍虎。」俞氏曰：「六七八九乃水火木金之成數。木數八屬東，火數七屬南，木自東而升，則與火為侶於南矣；金數九屬西，水數六屬北，金自西而降，則與水合處於北矣。丹家有所謂赤龍、黑虎者，東方蒼龍七宿運而之南則為赤龍，西方白虎七宿運而之北則為黑虎，無非譬喻身中之呼吸。究而言之，何龍虎之有？何金水木火之有？何七八九六之有？皆譬喻耳。或疑九、七、八言還、返、歸，六獨言居，得無異乎？曰：六居北不動，三方之還、返、歸皆聚於北，故言居也。」

The *Zhou Yi San Tong Qi* says: "Nine returns, seven reverses, eight returns, six resides." It also says: "Seven plus eight equals fifteen; nine plus six also equals fifteen." It further says: "Gold and water meet together, wood and fire become companions; the four elements blend and are indistinct, arranged as dragon and tiger." Yu Yan explains that six, seven, eight, and nine are the 'completed numbers' of water, fire, wood, and metal. The number for wood is eight, belonging to the east; the number for fire is seven, belonging to the south; wood rises from the east and meets fire in the south. The number for metal is nine, belonging to the west; the number for water is six, belonging to the north; metal descends from the west and meets water in the north. The alchemists' "red dragon" and "black tiger" refer to the seven stars of the eastern dragon constellation moving to the south becoming the red dragon, and the seven stars of the western white tiger constellation moving to the north becoming the black tiger. This is merely a metaphor for the breathing within the body. In the end, where are there really dragons and tigers? Where are there really gold, water, wood, and fire? Where are there really nine, seven, eight, and six? They are all metaphors. Some people question: nine, seven, and eight respectively refer to 'return,' 'reverse,' and 'return,' but six refers to 'reside,' is this not inconsistent? The answer is: six resides in the north and does not move; the returns, reverses, and returns from the other three directions eventually converge to the north, so six is only said to 'reside.'

俞氏曰：「乾上坤下，吾身之天地也；泰左否右，吾身天地之升降也。復非十一月，亦非夜半子時，乃身中之子也；姤非五月，亦非日中午時，乃身中之午也。張悟真雲『否泰交，則陰陽或升或降』，葢謂身中之泰否。」俞氏曰：「坎北離南，吾身之水火也；既濟東，未濟西，吾身水火之升降也。屯居寅，蒙居戌，吾身之火候也。寅非平旦寅，乃身中之寅；戌非黃昏戌，乃身中之戌。張悟真雲『屯蒙作動靜，在朝在昏』，葢謂身中之屯蒙。」

Yu Yanyin explains the other two circles: Qian is above and Kun is below, representing the heaven and earth within my body; Tai is on the left and Po is on the right, representing the rising and falling of the heavenly and earthly energies within my body. The Fu hexagram in the diagram does not refer to the eleventh lunar month or the midnight Zi hour, but rather the internal "Zi" within the body; the Gou hexagram does not refer to the fifth month or the noon Wu hour, but rather the internal "Wu" within the body. Zhang Bodaan's "Wuzhen Pian" says "the alternation of Po and Tai leads to the rising and falling of yin and yang," referring precisely to the Tai and Po within the body. Yu Yanyin also says: Kan is in the north and Li is in the south, representing the water and fire within my body; Ji Ji is in the east and Wei Ji is in the west, representing the rising and falling of water and fire within my body. The Tun hexagram corresponds to Yin and the Meng hexagram corresponds to Xu, representing the "fire timing" within the body. Yin is not the寅 hour of morning, but the internal Yin within the body; Xu is not the evening Xu hour, but the internal Xu within the body. Zhang Bodaan says "Tun and Meng differentiate between active and still states, one in the morning and one in the evening," referring also to the internal Tun and Meng within the body.

《參同契》曰：「朔旦屯直事，至暮蒙當受。晝夜各一卦，用之依次序。既未至昧爽，終則復更始。日辰為期度，動靜有早晚。春夏據內體，從子到辰巳；秋冬當外用，自午訖戌亥。」俞氏曰：「《參同契》以乾坤為鼎，坎離為藥物，因以其餘六十卦為火候。一日有十二時，兩卦計十二爻，故日用兩卦：朝屯則暮蒙，朝需則暮訟，以至於既濟未濟一也。屯倒轉則為蒙，有一升一降之象。屯自內而升，為朝、為晝、為春夏；蒙自外而降，為暮、為夜、為秋冬，諸卦皆然。夫以六十卦分佈為三十日以象一月，然遇小盡則當如之何？葢比喻耳，非真謂三十日也。或以此為閉目數息之法，則不勝其煩且勞矣，豈至簡至易之道哉！」

The Shangong Qishi says: "On the first day of the month, the Zun trigram is in charge in the morning, and the Meng trigram takes over in the evening. Day and night each use one trigram, following the order. From Ji Ji to Wei Ji until dawn, one cycle is completed and then it starts again. Using the day branch as the measure, movement and stillness each have their own time. In spring and summer, the trigrams are based on the inner trigram, from Zi to Chen and Si hours; in autumn and winter, the trigrams are based on the outer trigram, from Wu to Xu and Hai hours." Yu Yan explains that the Shangong Qishi uses Qian and Kun as the 'cauldron,' and Kan and Li as the 'medicinal ingredients,' and uses the remaining sixty trigrams as the 'fire timing.' A day has twelve hours, and two trigrams together make twelve lines, so each day uses two trigrams: Zun in the morning and Meng in the evening, Xu in the morning and Song in the evening, continuing until Ji Ji and Wei Ji, the reasoning is the same. Zun reversed is Meng, symbolizing an ascent and descent. Zun rises from within, matching morning, day, spring and summer; Meng descends from outside, matching evening, night, autumn and winter, and the rest of the trigrams follow the same pattern. However, if the sixty trigrams are divided into thirty days to symbolize a month, what about months with only twenty-nine days, called 'small full'? This shows that it is only a metaphor, not actually referring to thirty days. Some people take it as a method of counting breaths with closed eyes, which would be too complicated and exhausting, how could it be called the simple and easy great way?"

《周易參同契》金丹鼎器藥物火候萬殊一本之圗。惟斯之妙術兮，審諦不誑語；傳於億世後兮，昭然而可考；煥若星經漢兮，昺如水宗海；思之務令熟兮，反覆眂上下。千秋燦彬彬兮，萬遍將可覩；神明或告人兮，心靈忽自悟；探端索其緒兮，必得其門戶；天道無適莫兮，當傳與賢者。

This is the title and inscription of the diagram titled 「Diagram of the Single Root of the Golden Elixir Cauldron, Medicinal Substances, Fire, and Timing」 from the book Zhou Yi Can Tong Qi. The inscription says: This marvelous art, when carefully examined, is certainly not empty talk; it will still be clearly understandable even after countless generations. It shines brightly like stars across the Milky Way, and is clear as countless rivers flowing into the sea. To contemplate it, one must thoroughly understand it, repeatedly examining it from top to bottom. Even thousands of years later, it will still shine brilliantly; reading it ten thousand times will eventually make it clear. Perhaps the divine will enlighten people, and the mind will suddenly become enlightened. Grasping the thread to trace its origins, one will surely find the way in. The heavenly way has no favor or neglect for people; it should be passed on to the virtuous.

右論《參同契》指要十七。

The above is a discussion of the essential principles of the Zhou Changes (I Ching) with seventeen points.

《參同契》曰：「乾坤者，易之門戶，眾卦之父母。坎離匡廓（朱子《考異》作「匡郭」，雲其象如垣郭之形），運轂正軸，牝牡四卦，以為槖鑰。」（空同道士鄒欣曰：以宇內言之，則乾天在上，坤地在下，而陰陽變化在其間；以人身言之，則乾陽在上，坤陰在下，而一身之陰陽變化在其間。此乾坤所以為易之門戶、眾卦之父母也。凡言易皆指陰陽變化而言，在人身則所謂金丹大藥者也。然則乾坤其爐鼎歟？乾坤位乎上下，而坎離升降於其間，如車軸之貫轂以運輪，□下而□上也。牝牡謂配合之四卦，震、艮、巽、兊是也。槖，鞴囊；鑰，其管也。）

The *Zhou Yi San Tong Qi* says: "Qian and Kun are the gateways of the *I Ching* and the parents of all hexagrams; Kan and Li are like city walls surrounding the outside, driving the wheel hub and supporting the axle; the four hexagrams of male and female pairing serve as the bellows and the blowing tube." The Taoist monk Kong Tong explains that in the universe, Qian (Heaven) is above and Kun (Earth) is below, with yin and yang transformations occurring in between; in the human body, Qian yang is above and Kun yin is below, with the body's yin and yang transformations also occurring in between. This is why Qian and Kun are called the gateways of the *I Ching* and the parents of all hexagrams. Whenever the term "easy" is mentioned, it refers to the transformation of yin and yang. When applied to the human body, this is called the "golden elixir." Therefore, are Qian and Kun not the furnace and cauldron for alchemy? Qian and Kun are fixed at the top and bottom, while Kan and Li rise and fall in the middle, like the axle passing through the hub to drive the wheel, one moving down and the other up (the original text has two missing characters here). "Pine and male" refer to the four paired hexagrams, namely Zhen, Gen, Xun, and Dui. "Tuo" is a leather bag for blowing air, and "yue" is the air duct of the bag.

（上陽子陳致虛曰：何謂坎離匡廓？葢陽乘陰則乾中虛而為離，陰乘陽則坤腹實而為坎，故坎離繼乾坤之體而為陰陽之匡廓。比乾坤之於坎離，猶車輻之於轂軸，乾坤正坎離之輻，坎離輳乾坤之轂。老子曰「三十輻共一轂」，此大小徐君之旨同也。）

Shangyangzi Chen Zhi Xu continued to explain: What does "Kan Li Kuang Kuo" mean? Basically, when yang is above yin, the Qian hexagram in the middle becomes empty and transforms into the Li hexagram; when yin is above yang, the Kun hexagram in the middle becomes full and transforms into the Kan hexagram. Therefore, Kan and Li take on the form of Qian and Kun, serving as the outer boundaries of yin and yang. Comparing Qian and Kun with Kan and Li is like comparing the spokes of a wheel to the hub and axle: Qian and Kun are the spokes, while Kan and Li are the hub formed by the gathering of all the spokes. Laozi said, "Thirty spokes share a single hub," which is consistent with the meaning of the two masters, Da Xu Jun and Xiao Xu Jun.

「天地設位，而易行乎其中矣。天地者，乾坤之象也；設位者，列陰陽配合之位也。易謂坎離，坎離者乾坤二用。二用無爻位，周流行六虛，往來既不定，上下亦無常，幽潛淪匿，升降於中，包囊萬物，為道紀綱。」（全陽子俞琰曰：乾天坤地，吾身之鼎器也；離日坎月，吾身之藥物也。先天八卦乾南坤北，列天地配合之位；離東坎西，分日月出入之門。反求吾身，其致□也。乾坤為體，坎離為用。坎離二者周流升降於六虛，往來上下木無爻位；吾身坎離運行乎鼎器之內，潛天潛地，豈有爻位哉！）

The "Supplement to the Great Ultimate" also says: "Heaven and Earth have established positions of above and below, and the 'Book of Changes' operates within them. Heaven and Earth represent the images of Qian and Kun; 'setting positions' refers to arranging the positions of yin and yang. Here, the 'Book of Changes' refers to Kan and Li, which are the two functions of Qian and Kun. These two functions do not have fixed lines, but circulate through the six directions above and below, coming and going without fixed positions, moving up and down without constant place, hidden deep within, rising and falling in the middle, encompassing all things, becoming the principles of the great way." Master Qu Yanyin explains that Qian Heaven and Kun Earth are the 'vessel' within my body; Li Sun and Kan Moon are the 'medicinal substances' within my body. In the Earlier Heaven Trigrams, Qian is in the south and Kun in the north, arranging the positions of Heaven and Earth; Li is in the east and Kan in the west, distinguishing the gates of the rising and setting of the sun and moon. Reversing this to seek within oneself, the principle is the same. Qian and Kun are the essence, while Kan and Li are the functions. Kan and Li circulate and rise and fall within the six voids, moving up and down without fixed lines; the Kan and Li within my body operate within the vessel, able to rise to Heaven and descend to Earth, where could there be any fixed lines!"

河右毛氏曰：「水火匡廓圗者，以章首有『坎離匡廓，運轂正軸』二語，所云水火即坎離也。丹家以坎離為用，故輪而象之，又名水火二用圗，則又取『天地者乾坤之象，坎離者乾坤之用』二語。葢其圖正作坎離二卦而運為一軸，非所謂兩儀也，亦非所謂陽動生陰、陰靜復生陽也。其中一○則坎離之胎也，左((為離，白黑白即□—□也；右))為坎，黑白黑即—□—也。」（見《太極圗說遺議》）

Heavenly Stems: Jia, Yi, Bing, Ding, Wu, Ji, Geng, Xin, Ren, Gui Earthly Branches: Zi, Chou, Yin, Mao, Chen, Si, Wu, Wei, Shen, You, Xu, Hai Trigrams: Qian (Heaven), Dui (Lake), Li (Fire), Zhen (Thunder), Xun (Wind), Kan (Water), Gen (Mountain), Kun (Earth) Mao Qiling, a person from He You, said: The so-called "Water and Fire Enclosure Diagram" is because the beginning of the "Cantongqi" mentions "Kan and Li enclose, the wheel moves along the axis." The water and fire referred to here are Kan and Li. The alchemists regard Kan and Li as functions, so they draw them in a wheel-like form to symbolize them. This diagram is also called the "Diagram of the Two Functions of Water and Fire," taking the phrase "Heaven and Earth are the images of Qian and Kun, while Kan and Li are their functions." In reality, this diagram merely draws the two trigrams Kan and Li and makes them rotate like a wheel axis. It is not the "Two Principles" mentioned by Zhou Dunyi, nor does it refer to "Yang moves to produce Yin, and Yin is still to produce Yang." The circle in the middle of the diagram is the embryo of Kan and Li. The left half is the trigram Li, with white, black, and white alternating, which is exactly the way Li is drawn: Yang, Yin, Yang. The right half is the trigram Kan, with black, white, and black alternating, which is exactly the way Kan is drawn: Yin, Yang, Yin. This view is presented in Mao Qiling's "Discourses on the Diagram of the Supreme Ultimate."

《參同契》曰：「物無陰陽，違天背元。牝雞自卵，其雛不全。夫何故乎？配合未連，三五不交，剛柔離分。」（陳顯微曰：張紫陽詩云「莫把孤陰謂有陽，獨修一物轉羸尩」，鍾離先生詩云「莫謂此身亡是道，獨修一物是孤陰」。須知一陰一陽之謂遒，男女構精，萬物化生，而後可語還丹矣。苟二物不合，三五不交，水火未濟，剛柔離分，則陰陽隔絶，天地閉塞，所謂偏陰偏陽謂之疾也。）

The Zhou Changes (I Ching) says: "If things lack the union of yin and yang, they violate the heavenly way and depart from their origin. A hen hatching its own egg will not produce complete chicks. Why is this? Because there is no connection, the 'three and five' do not meet, and the strong and the soft are separated." Chen Xianwei explains that Zhang Ziyang's poem says, "Do not call a solitary yin as having yang; single cultivation leads to becoming weaker and weaker." Zhong Li Master's poem says, "Do not say that discarding this body is the way; single cultivation is a solitary yin." One must know that the alternation of yin and yang is called the great Dao. The union of male and female, the generation of vital energy, and the transformation of all things are prerequisites for the concept of 'returning to the red pill.' If two substances do not combine, the 'three and five' do not meet, water and fire do not achieve the state of mutual overcoming, and the strong and the soft are separated, then yin and yang are cut off, heaven and earth become blocked, which is precisely what is meant by 'being biased toward yin or yang is called illness.'

又曰：「三五與一，天地至精，可以口訣，難以書傳。子當右轉，午乃東旋，夘酉界隔，主客二名。金水合處，木火為侶，四者混沌，列為龍虎。龍陽數奇，虎陰數偶。肝青為父，肺白為母，腎黑為子，心赤為女，脾黃為祖，子五行始。三物一家，都歸戊巳。」（彭曉曰：子水數一，為五行始；金火木三物同功，首尾造化俱歸戊巳者，是故脾黃為藥之祖也。）

The "Cantong Qi" also says: "Three, five, and one are the most subtle principles in the universe. They can be passed down orally but are difficult to express in writing. The position of Zi should rotate to the right, while the position of Wu should turn eastward. The positions of Mao and You set boundaries, distinguishing between host and guest. Metal and water meet together, wood and fire become companions. The four elements blend together without distinction, forming the arrangement of dragon and tiger. Dragon belongs to yang and its number is odd; tiger belongs to yin and its number is even. The liver, which is green, is the father; the lung, which is white, is the mother; the kidney, which is black, is the son; the heart, which is red, is the daughter; the spleen, which is yellow, is the ancestor. The son is the beginning of the Five Phases. The three substances return to one family and all converge on Wu Ji soil." Peng Xiao explains that Zi belongs to water and has the number one, being the beginning of the Five Phases. The functions of metal, fire, and wood are the same, and the beginning and end of the transformations all converge on Wu Ji soil, so the yellow spleen becomes the ancestor of the elixir.

「剛柔迭興，更歴分佈，龍西虎東，建緯夘酉，刑德並會，相見歡喜，刑主伏殺，德主生起。」（陳致虛曰：青龍屬東，白虎屬西，此其正也。更歴分佈者，青龍建緯於酉，白虎建緯於夘，是刑德並會而龍虎歡喜顛倒相見。）「子南午北，互為綱紀，一九之數，終而復始，含元虛危，播精於子。」

The Treatise on the Union of the Three Principles continues: "Yang and Yin alternate in rising, taking turns to experience and being arranged separately; the Dragon moves to the west, the Tiger moves to the east, establishing the meridians at the卯 and酉 positions; punishment and virtue meet together, meeting each other with joy; punishment governs concealment and severity, while virtue governs growth and emergence." Chen Zhi Xu explains that the Blue Dragon belongs to the east and the White Tiger belongs to the west, which are their proper positions. The phrase "taking turns to be arranged" means that the Blue Dragon sets the meridian at the酉 position, while the White Tiger sets the meridian at the卯 position, which is why punishment and virtue meet together, the Dragon and Tiger reverse and meet with joy. The Treatise on the Union of the Three Principles also says: "The position of Zi moves to the south, the position of Wu moves to the north, becoming the main framework; the numbers from one to nine, when reaching the end, begin again; the vital energy is contained between the mansion of Emptiness and the mansion of Rooftop, scattering the true essence at the position of Zi."

（陳致虛曰：子南午北者，顛倒五行也。仙聖云「五行順行，法界火坑；五行顛倒，大地七寶」，所以水火互為綱紀，方能既濟也。陽生於一，成於九，陽數至九則極，極則復於一，此謂一九之數終而復始。「含元虛危，播精於子」者，丹之神功在此兩句。葢虛危之次，日月合璧之地，一陽初生之方，龜蛇蟠結之所，故太一所含先天之元氣，其真精遇子則播施，此復應前文「子五行始」之義也。俞琰曰：子午即南北水火，夘酉即東西金木。右轉左旋，一伏一起，則水火相交，金木自然不間隔矣。然東西夘酉皆金木異名，非天地方位，亦非人身左右。）

Chen Zhi Xu explained that "zi to the south, wu to the north" reverses the Five Phases. The immortal sages said, "If the Five Phases proceed in order, the world becomes a fire pit; if the Five Phases are reversed, the earth becomes the seven treasures." Thus, water and fire serve as the main principles, forming the image of completion. Yang begins from one and reaches nine to complete, and when yang's number reaches nine, it reaches its peak, then returns to one, which is called "the number one and nine completes and begins again." As for "containing the original emptiness and danger, spreading the essence at zi," the mysterious practice of alchemy lies entirely in these two sentences: the star positions of xu xiu and wei xiu are where the sun and moon meet, the direction where the first yang begins, and where the turtle and snake coil. Therefore, the true essence of the original qi contained in Taiyi returns to the position of zi, spreading out, which also responds to the previous statement that "zi is the beginning of the Five Phases." Yu Yan explained that zi and wu represent the south and north, water and fire;卯 and酉 represent the east and west, metal and wood. One turns right, the other turns left; one is hidden, the other rises, so water and fire meet, and metal and wood naturally are not separated. However, the east and west,卯 and酉, are merely alternative names for metal and wood, neither the actual directions of heaven and earth nor the left and right of the human body.

張氏伯端《悟真篇》曰：「三五一都三個字，古今明者實然稀。東三南二同成五，北一西方四共之，戊巳自居生數五，三家相見結嬰兒。嬰兒是一含真氣，十月胎圎入聖機。」

Zhang Boduan's "Wuzhen Pan" says: "The three characters 'san wu yi' (three five one) altogether make three characters. Throughout history, truly understanding people are indeed rare. The three from the East and the two from the South combine to form a five, and the one from the North and the four from the West also combine to form a five. The Wu Ji earth itself occupies the number five of the generating numbers. When these three families meet, they form an infant. The infant is the 'one,' containing true energy, and after being fully developed for ten months, it enters the crucial point of attaining sainthood."

毛氏曰：「三五至精圗者，取『三五與一，天地至精』語，而分五行為三五。中央土一五也，天五生土也；左火與木共一五也，地二生火，天三生木也，二三五也；右水與金又共一五也，天一生水，地四生金也，一四亦五也。故其為生序，則水承坎下，火承離下；其為行序，則金盛為水，木盛為火，而合而復歸於一元也（合三五而皆鉤連於下之一）。則此一○者，三五之合，非二五之合；三五之精，非二五之精。葢丹家水火必還一元，故其後復有含元播精、三五歸一之語。」（見《太極圖說遺議》）

Maos Qilin said: The so-called "San Wu Zhi Jing Tu" (Diagram of the Three and Five to the Essence) is derived from the phrase "San Wu yu Yi, Tian Di Zhi Jing" (Three and Five with One, the Supreme Essence of Heaven and Earth). It divides the Five Phases into three "fives." The central earth is one five, because "Tian Wu Sheng Tu" (Heaven Five produces Earth). On the left, fire and wood combine into one five, because "Di Er Sheng Huo, Tian San Sheng Mu" (Earth Two produces Fire, Heaven Three produces Wood), and two plus three equals five. On the right, water and metal also combine into one five, because "Tian Yi Sheng Shui, Di Si Sheng Jin" (Heaven One produces Water, Earth Four produces Metal), and one plus four also equals five. According to the order of generation, water is beneath the Kan trigram, and fire is beneath the Li trigram. According to the order of operation, metal becomes water when it is full, and wood becomes fire when it is full, finally converging and returning to the original unity (the three fives are all connected by lines to the single "one" below). Thus, the single circle in the diagram represents the convergence of the three fives, not two fives; it represents the essence of the three fives, not two fives. Generally, Daoist alchemists emphasize that water and fire must return to the original unity, so later texts also mention expressions such as "Hanyuan Bosheng" (Contain the Original and Spread the Essence) and "San Wu Gui Yi" (Three and Five Return to One). This statement is found in Maos Qilin's "Yi Tu Shuo Wei Yi Yi."

按：三輪肖坎離二卦，五行即天地之生數。然伯陽專心修煉，特藉此以明作丹之意，初非為易而設。葢三輪不可以為兩儀，五行不可以為四象，其所謂易，專指坎離水火，非聖人生生之易也。唐《真元妙經品》有太極先天圗，合三輪五行為一，而以三輪中一○、五行下一○為太極，又加以陰靜、陽動、男女、萬物之象，凡四大○。陰靜在三輪之上，陽動在三輪之下（三輪左離右坎者，水火既濟之象；二○上陰下陽者，天地交泰之象。《鼎器歌》云「陰在上，陽下奔」，即此義也）。

Hu Wei commented: The three circular rings imitate the Kan and Li trigrams, and the Five Phases use the generating numbers of heaven and earth. However, Wei Boyang was focused on cultivation, using these elements merely to explain the concept of forming the elixir pill. Originally, these were not intended to interpret the Yi Classic. The three circular rings should not be regarded as the Two Principles, and the Five Phases should not be regarded as the Four Symbols. The "Yi" he referred to specifically meant the water and fire of Kan and Li, not the ever-renewing Yi of the sage. In the Tang Dynasty's "Zhenyuan Miaojing Pin," there is an illustration called "Taiji Qianxian Tu," which combines the three wheels with the Five Phases into one. It also treats the central circle of the three wheels and the circle below the Five Phases as the Taiji. Additionally, it adds four large circles representing yin stillness, yang movement, male and female, and the myriad things. Yin stillness is drawn above the three wheels, and yang movement is drawn below the three wheels (the left side of the three wheels is Li, and the right side is Kan, symbolizing the harmony of water and fire; the upper and lower circles have yin above and yang below, symbolizing the union of heaven and earth. The "Dingqi Ge" from the "Cantongqi" says "yin is above, yang flows downward," which refers to this meaning).

男女萬物皆在五行之下，與宋紹興甲寅朱震在經筵所進周子太極圗正同。今《性理大全》所載者，以三輪之左為陽動、右為陰靜，而虛其上下之二○以為太極，乃後人所改，非其舊也。此不在《本義》九圗之列。或曰陳摶傳穆修，穆修傳周子；或曰周子所自作，而道家竊之以入藏。疑不能明，存而弗論雲。

All things, both male and female, are ranked beneath the Five Phases. This is exactly the same as the Taiji Diagram presented by Zhu Zhen at the court during the Jia Yin year of the Shaoxing era in the Southern Song dynasty, based on the work of Zhou Dunyi. The version currently recorded in the Xingli Dquan, which depicts the left side of the three circles as yang movement and the right side as yin stillness, and leaves the upper and lower circles empty as the Taiji, has been altered by later people and is not the original form. This diagram is not included in the nine diagrams at the beginning of Zhu Xi's Zhouyi Benyi. Some say it was passed down from Chen Tuan to Mu Xiu, and then from Mu Xiu to Zhou Dunyi; others claim it was created by Zhou Dunyi himself, and that the Daoist sects later took it and included it in the Daozang. This matter is doubtful and unclear, so it is left unjudged for now.

右論二用三五。

The above is a discussion on the "Two Uses" and "Three and Five" diagrams from the "Cantong Qi" (The Concordance of the Three).

《參同契》曰：「言不苟造，論不虛生，引驗見效，校度神明，推類結字，原理為徵。坎戊月精，離己日光，日月為易，剛柔相當。土旺四季，羅絡始終，青赤白黑，各居一方，皆稟中宮戊己之功。」（彭曉曰：「坎戊月精」者，月陰也，戊陽也，乃陰中有陽，象水中生金虎也；「離己日先」者，日陽也，己陰也，乃陽中有陰，象虎中生柔龍也。）

The Zhou Changes (I Ching) says: "Words are not fabricated at will, and discussions are not generated out of nowhere. They are all cited and verified, seen to be effective, checked and measured to align with the divine. Using analogy to combine words, with the original principles as evidence. The Wu earth in the Kan trigram is the essence of the moon, and the Ji earth in the Li trigram is the brilliance of the sun. The characters 'sun' and 'moon' combined form the character 'easy' (易), with the yang and yin perfectly corresponding. Earth is strong in the last months of the four seasons, encompassing the beginning and the end; the colors green, red, white, and black each occupy their respective directions, all receiving the function of the central palace's Wu and Ji earth." Peng Xiao explains that "Wu in Kan is the essence of the moon": the moon belongs to yin and Wu belongs to yang, which is yang within yin, symbolizing gold tiger born from water; "Ji in Li is the light of the sun" (the original text says "sun first"), the sun belongs to yang and Ji belongs to yin, which is yin within yang, symbolizing a soft dragon born from the tiger.

（陳顯微曰：《易》卦納甲法，坎納六戊，離納六己，坎為月，離為日，故曰「坎戊月精，離已日光」。「日月」二字合為「易」字，故曰「推類結字」，是皆原理為證，而非虛造言論也。易既不外乎日月，丹豈不本乎坎離？然坎之與離皆存戊巳，古人云「都綠彼此懷真土，遂使金丹有返還」。況土旺四季，羅絡始終，水火木金雖各居一方，而皆稟中宮土徳也。張紫陽詩云「四象五行全藉土」，土德之功大矣哉！葢土者金母也，知五行之俱歸於土，則知五行之俱變為金，然後能會造化於中宮，種黃芽於后土矣。）

Chen Xianwei explained that in the method of Najia for the hexagrams of the Yi, the Kan hexagram is assigned six Wu stems, and the Li hexagram is assigned six Ji stems. Kan symbolizes the moon, and Li symbolizes the sun, so it is said that "the Wu earth in the center of Kan is the essence of the moon, and the Ji earth in the center of Li is the brilliance of the sun." The characters "sun" and "moon" combined form the character "Yi," so it is said "deducing by analogy and forming characters." These statements are all based on the original principles, not fabricated words. Since "Yi" is not outside the sun and moon, how could alchemy not take Kan and Li as its foundation? Both Kan and Li contain Wu and Ji earth. Ancients said, "It is precisely because they both contain true earth that the golden elixir can return." Moreover, earth is strong in the last months of the four seasons, and it runs through all seasons. Although metal, wood, water, and fire each occupy their own position, they all receive the virtue of the Central Palace earth. Zhang Ziyang's poem says, "The four elements and five phases rely entirely on earth." The function of the earth virtue is indeed great! Earth is the mother of metal. Understanding that all five phases return to earth means understanding that all five phases can become metal, and then one can meet the transformations in the Central Palace and plant the "yellow sprout" on the earth.

「晦朔之間，合符行中，混沌鴻蒙，牝牡相從，滋液潤澤，施化流通，天地神明，不可度量，利用安身，隠形而藏。始於東北，箕斗之鄉，旋而右轉，嘔輪吐萌，潛潭見象，發散清光，昴畢之上，震出為徵。」（陳顯微曰：晦朔之間，當合符行中，如混沌鴻蒙不可度量，葢牝牡相從、滋液潤澤、施化流通之時也，豈可用功乎？故利用安身，隠形而藏，卻自箕斗之鄉嘔輪吐萌、發散輝光可也。寒山子詩云「不得露其根，根虛則子墜」，葢體用不同，施功亦異故也。）

The *Cantong Qi* says: "At the time of the new moon and full moon meeting, the sun and moon align and move along the central path, the world is in a state of chaos and primordial unity, yin and yang follow each other, the essence is moist and nourishing, and the transformation flows smoothly; the workings of heaven and earth are beyond measure, at this time one should settle down, hide one's form and retreat into concealment. It begins in the northeastern region of the mansion of the Winnowing Basket and the Dipper, then turns to the right, and the moon's wheel sprouts like a wheel, the deep pool first shows the form of things, and emits a clear light; when it reaches the mansion of the Hairy Head and the Net, the trigram Zhen (Thunder) with one yang appears, which is a sign." Chen Xianwei explains that at the time of the new moon and full moon meeting, the sun and moon align and move along the central path, just like the chaotic and primordial state that is beyond measure, which is the time when yin and yang follow each other, the essence is moist and nourishing, and the transformation flows smoothly; how can one talk about effort at this time? Therefore, one should settle down, hide one's form, and retreat into concealment, waiting until the moon's wheel sprouts and emits light from the mansion of the Winnowing Basket and the Dipper before beginning to act. Han Shanzi's poem says, 'Do not let the root be exposed, for if the root is empty, the fruit will fall,' because the body and its function are different, and the timing for effort is also different."

「聖人不虛生，上觀顯天符。天符有進退，詘伸以應時，故易統天心。復卦建始萌，長子繼父體，因母立兆丌（音其，薦物之具），消息應鍾律，升降據斗樞。三日出為爽，震庚受西方；八日兊受丁，上弦平如繩；十五乾體就，盛滿甲東方。蟾蜍與兔魄，日月氣雙明，蟾蜍視卦節，兔者吐生光。七八道已訖，屈折低下降，十六轉就綂，巽辛見平明；艮直於丙南，下弦二十三；坤乙三十日，東北喪其朋。節盡相禪與，繼體復生龍，壬癸配甲乙，乾坤括始終。七八數十五，九六亦相應，四者合三十，陽氣索滅藏。」

The "Supplement to the Book of Changes" says: "The sage does not appear without purpose; he observes the heavenly phenomena to manifest the heavenly signs. The heavenly talisman advances and retreats, bending and stretching in accordance with the seasons, so the "Book of Changes" encompasses the heart of heaven. The hexagram of Fu represents the beginning of a single yang line, the eldest son Zhen inherits the form of his father Qian, and relies on his mother Kun to establish the vessel for offerings (the character "丌" is read as "qi", the vessel for sacrificial items). The waxing and waning, fullness and emptiness correspond to the tones of the bell, and the rising and falling follow the pivot of the Big Dipper. On the third day, when the moon's light first appears, it is called "shuang", and Zhen hexagram receives it from the western position of Geng. On the eighth day, the hexagram Dui receives it from the southern position of Ding, and the waxing moon is straight like a rope. On the fifteenth day, the hexagram Qian is complete, and the moon's light is full at the eastern position of Jia. The toad and the rabbit's shadow represent the manifestation of the qi of the sun and moon; the toad reflects the measure of the hexagrams, and the rabbit exhales new light. When the paths of seven and eight are completed, they bend and descend; on the sixteenth day, it transitions to the governing hexagram, and the hexagram Xun is visible at the western position of Xin during early morning. The hexagram Gen is in charge of the southern position of Bing, and the waning moon occurs on the twenty-third day; the hexagram Kun is at the position of Yi, and on the thirtieth day, it loses its companion in the northeast. When one section is completed, they pass on to each other, and the successor gives rise to the dragon; the combinations of Ren and Gui with Jia and Yi, and Qian and Kun encompass the beginning and the end. Seven plus eight equals fifteen, nine plus six also corresponds, and the four together make thirty, the yang energy is exhausted and hidden here."

（陳顯微曰：魏君以一月之間月形圎缺喻卦象進退：自初三日為一陽，初八日為二陽，十五則三陽全而乾體就；十六則一陰生，二十三則二陰生，三十日則三陰全而坤體成。）

Chen Xianwei explained that Wei Boyang used the waxing and waning of the moon in a month to illustrate the progression and retreat of hexagrams: on the third day, one yang is counted; on the eighth day, two yangs; on the fifteenth day, three yangs are complete, forming the hexagram Qian (Heaven). On the sixteenth day, one yin begins to arise; on the twenty-third day, two yins arise; on the thirtieth day, three yins are complete, forming the hexagram Kun (Earth).

（昴畢在西方庚位，每月初三日月現微明於西方庚位，應震之一陽初生，而《周易》納甲法震卦納六庚，其造化之理參合如此。初八日月現上弦於南方丁位，應兊卦二陽生，而納甲法則兊納六丁。以至十五日月滿於東方甲位，則乾卦又納六甲，其時卦備三陽，三五之道已終，則滿者虧而伸者屈，髙者低而升者降。至十六日一陰生而當陰用事，月於平旦現在西方辛位，以應巽卦納辛；至二十三日月於平旦現南方丙位，應艮卦納丙；至三十日月沒東方乙位，應坤卦納乙。節盡則又相禪與，陽復用事。）

Chen Xianwei continued saying: The constellations Hairy Head mansion and Net mansion are located in the western position of Geng. On the third day of each month, the moon appears faintly bright in the western Geng position, corresponding to the Zhen trigram with the first yang line emerging. In the Najia method of the Zhou Changes, the Zhen trigram is assigned the six Geng stems. Thus, the principles of heaven and earth are in harmony. On the eighth day, the moon appears as a waxing crescent in the southern Ding position, corresponding to the Dui trigram with two yang lines emerging. In the Najia method, the Dui trigram is assigned the six Ding stems. On the fifteenth day, the moon is full in the eastern Jia position, corresponding to the Qian trigram which is assigned the six Jia stems. At this time, the trigram has three yang lines complete, and the 'three and five' principle has been fulfilled. Thus, the full moon begins to wane, the extended begins to bend, the high turns low, and the rising turns descending. On the sixteenth day, the first yin line emerges and yin takes control. The moon appears in the western Xin position in the morning, corresponding to the Xun trigram which is assigned the six Xin stems. On the twenty-third day, the moon appears in the southern Bing position in the morning, corresponding to the Gen trigram which is assigned the six Bing stems. On the thirtieth day, the moon disappears in the eastern Yi position, corresponding to the Kun trigram which is assigned the six Yi stems. After one section is completed, they take turns and alternate, and the yang energy regains control.

（俞琰曰：火候之妙，有未易明言者，於是古之至人觀天之道，設為法象以示人：以天地喻鼎器，以日月喻藥物，以日月往來喻火候。月行於天，一月一度與日交合，故謂天符。應時者，十二時也。月自初一以後光漸進，魂長魄消，陰屈陽伸，象一日之子至已；十六日以後光漸退，魄長魂消，陰伸陽屈，象一日之午至亥。火候進退屈伸，猶是也。）

Yu Yanyin explained that the subtlety of the fire timing is sometimes difficult to explain clearly. Therefore, ancient sages observed the heavenly way and established a system of diagrams based on celestial phenomena to guide future generations. They used heaven and earth to symbolize the furnace of alchemy, and the sun and moon to symbolize the medicinal substances. They used the movement of the sun and moon to represent the fire timing. The moon moves in the sky, meeting the sun once a month, so it is called "Heavenly Talisman." The term "responding to the right time" refers to the twelve hours. After the first day of the month, the moon's light gradually increases, with the spirit growing and the shadow decreasing, yin retreating and yang advancing, symbolizing the time from Zi to Si in a day. After the sixteenth day, the moon's light gradually wanes, with the shadow growing and the spirit decreasing, yin advancing and yang retreating, symbolizing the time from Wu to Hai in a day. The advance and retreat, bending and stretching of the fire timing are exactly like this.

「謬誤失事緒，言還自敗傷。別序斯四象（謂七八九六），以曉後生盲。八卦佈列曜，運移不失中，元精眇難睹，推度效符徵。上觀天河（今本作「河圗」，非）文，下序地形流，中稽於人心，參合考三才。」

The Classic of Mutual Generation says: "If you make mistakes, you will lose the thread of things, and your words will only lead to self-harm. Additionally, arranging these four images (referring to seven, eight, nine, and six) is meant to enlighten the blind of later generations. The Eight Trigrams are arranged like shining stars, rotating and shifting without losing their center; the original essence is subtle and invisible, and can only be verified through calculation and inference. Look upward to observe the patterns of the Milky Way (the current text mistakenly changes 'Milky Way' to 'Yellow River Chart'), look downward to describe the terrain and the flow of water, and in the middle examine human hearts. Refer to these three aspects for verification, seeking the triple principles of heaven, earth, and humanity."

（陳顯微曰：上察天文，下察潮候，中稽人心。俞琰曰：古之修丹者，仰觀天文，俯察地理，中稽人心，於是虛吾心，運吾神，迴天闗，轉地軸，上應河漢昭回，下應海潮升降。天地雖大，而其日月星辰、五行八卦皆掇入於吾身，或為爐鼎，或為藥物，或為火候，一反觀而三才皆備於我，未嘗外身而他求也。）「動則觀卦節，靜則因彖辭，乾坤用施行，天地然後治。」

Chen Xianwei explained that this involves looking upward to observe the heavenly phenomena, looking downward to observe the tides and seasonal changes, and examining the human mind in between. Yu Yan explained that ancient practitioners of the golden elixir would look upward to observe the heavenly phenomena, look downward to examine the geographical features, and examine the human mind in between. Thus they would empty their minds, circulate their spirit, turn the heavenly pivot and rotate the earth's axis. Upward, they would correspond with the revolving and reflecting of the Milky Way; downward, they would correspond with the rising and falling of the sea tides. Though the heavens and earth are vast, the sun, moon, stars, the Five Phases, and the Eight Trigrams are all taken into oneself. Some serve as the furnace and cauldron, some as the medicinal substances, and some as the timing of the fire. As long as one turns inward and observes oneself, the three elements of heaven, earth, and humanity are all complete within oneself, and one need never seek outside the body. The final passage of the "Cantong Qi" says: "When moving, observe the measures of the hexagrams; when still, follow the meaning of the彖 (tuan) words. The functions of the heavens and earth are thus carried out, and only then can the heavens and earth be properly governed."

鄒欣曰：「《參同》之說見一日之間有晦朔弦望。上弦者，氣之方息，自上而下也；下弦者，氣之方消，自下而上也；望者，氣之盈，日沈於下而月圎於上也；晦朔之間者，日月之合乎上下，所謂『舉水以滅火，金來歸性初』之類是也。」又曰：「《參同》本不為明易，借納甲之法以寓行持進退之候雲。甲乙丙丁庚辛者，乃以月之昬旦出沒言之，非以分六卦之方也。」

Zou Xin said: The view expressed in the "Cantong Qi" can be seen from the fact that within a single day there are also the phases of waning, new moon, first quarter, and full moon. "Upper quarter" is when the energy is growing, moving from top to bottom; "lower quarter" is when the energy is retreating, moving from bottom to top; "full moon" is when the energy is complete, with the sun setting below and the moon full above; "between new and full moon" is when the sun and moon meet above and below, which is referred to as "pouring water to extinguish fire, and gold returning to its original nature at the beginning." Zou Xin also said: The "Cantong Qi" was not originally written to explain the "Yi," but rather used the method of Najia to indicate the timing for advancing and retreating in the practice of cultivation. The heavenly stems of Jia, Yi, Bing, Ding, Geng, and Xin mentioned in the text refer to the positions where the moon appears in the evening or disappears in the morning, not to divide the positions of the six hexagrams.

朱子答袁機仲書曰：「《參同契》所言納甲之法，則今所傳京房占法見於《火珠林》者是其遺說。此雖非為明易而設，然易中無所不有，苟其言自成一說，可推而通，則亦無害於易，恐不必輕肆詆排也。」

Zhu Xi said in his letter "Answer to Yuan Jizhong" that the method of Najia in the "Zhou Yi San Tong Qi" is the remnants of the system found in the book "Hu Zhu Lin" today known as Jing Fang divination. Although it was not originally intended to explain the Yi, since the Yi encompasses everything, if its approach can form its own school of thought and be logically extended and connected, it would not be harmful to the Yi, and perhaps should not be hastily criticized or rejected.

漢上朱氏《周易卦圖說》曰：「納甲何也？曰：舉甲以該十日也。乾納甲壬，坤納乙癸，震巽納庚辛，坎離納戊巳，艮兊納丙丁，皆自下生。聖人仰觀日月之運，配之以坎離之象，而八卦十日之義著矣。」

Han Shang Xiansheng Zhu Zhen said in "Zhou Yi Gu Tu Shuo" that what is meant by "Najia" is to use "Jia" to represent the ten heavenly stems. The Qian trigram takes Jia and Ren, the Kun trigram takes Yi and Gui, the Zhen trigram and Xun trigram take Geng and Xin, the Kan trigram and Li trigram take Wu and Ji, the Gen trigram and Dui trigram take Bing and Ding. All these are generated from the bottom up. The sage observed the movement of the sun and moon, using the images of Kan and Li to match them, thus making clear the significance of the eight trigrams being paired with the ten heavenly stems.

《繫辭傳》「懸象著明莫大乎日月」，虞翻曰：「謂日月懸天成八卦象：三日暮震象月出庚，八日兊象月見丁，十五日乾象月盈甲壬，十六日旦巽象月退辛，二十三日艮象月消丙，三十日坤象月滅乙。晦夕朔旦則坎，坎象水流戊；日中則離，離象火就己。戊巳土位象見於中，日月相推而明生焉。」《坤·彖》「西南得朋」，虞曰：「陽喪滅坤，坤終復生，此指說易道陰陽之大要也。」又曰：「消乙入坤，滅藏於癸。」

The Great Treatise of the Zhou Changes says, "Hanging the images of things to make them clear, nothing is greater than the sun and moon." Yu Fan explains: This refers to the sun and moon hanging in the sky forming the images of the Eight Trigrams. On the third day of the month, in the evening, the image of Zhen (Thunder) appears, with the moon appearing in the position of Geng; on the eighth day, the image of Dui (Lake) appears, with the moon appearing in the position of Ding; on the fifteenth day, the image of Qian (Heaven) appears, with the moon full in the positions of Jia and Ren; on the sixteenth day in the morning, the image of Xun (Wind) appears, with the moon waning in the position of Xin; on the twenty-third day, the image of Gen (Mountain) appears, with the moon waning in the position of Bing; on the thirtieth day, the image of Kun (Earth) appears, with the moon disappearing in the position of Yi. From the night of the last day of the month to the morning of the first day of the next month, it belongs to Kan (Water), which symbolizes flowing water, paired with Wu. At noon, it belongs to Li (Fire), which symbolizes fire, paired with Ji. Wu and Ji are the earth positions, their image appearing in the center. The sun and moon move in succession, and light is thus produced. The Commentary on the Judgment of the Kun Hexagram says, 'In the southwest, friends are gained.' Yu Fan explains: When yang energy is lost and disappears in Kun, Kun reaches its end and regenerates yang, indicating the main principle of the Way of the Book of Changes, which is the interplay of yin and yang. Yu Fan also says: Yang energy disappears in the position of Yi and enters Kun, finally disappearing and being hidden in the position of Gui.

按：鄒欣注本圗悉刪去，唯存納甲一環，葢以彭本之昏見、晨見合而為一圗也。甲乙丙丁庚辛指月昏旦出沒之方，而圗移六卦於月體之下，悖矣。漢上圗較勝，然坎離寄納戊巳、乾坤兼納壬癸之義，皆不能有所發揮，因更定附列於左而為之說焉。

Hu Wei's commentary: Zou Xin's annotated version deleted all the original diagrams in the "Cantong Qi," retaining only the Najia stem assignment. This is probably because he merged the "Hun Jian Tu" (Diagram of the Moon's Appearance at Dusk) and "Chen Jian Tu" (Diagram of the Moon's Appearance at Dawn) from Peng Xiao's version into one diagram. Originally, Jia, Yi, Bing, Ding, Geng, and Xin referred to the positions where the moon rose at dusk or set at dawn. However, the diagram placed the six trigrams beneath the moon, which does not make sense. Zhu Zhen's diagram is somewhat better, but he failed to explain the principle that Kan and Li incorporate Wu and Ji, and Qian and Kun include Ren and Gui. Therefore, I have devised a new diagram to be listed on the left and provided an explanation for it.

按：納甲者，始於京房之積算，以甲為十干之首，舉一干以該其餘，故謂之納甲。魏伯陽以月象附會之，以寓丹家行持進退之候，葢以月之明魄多少取象於卦畫，而以所見之方為所納之甲。震一陽始生，於月為生明□，三日夕出於庚，故曰震納庚，謂一陽之氣納於西方之庚也；兊二陽為上弦□，八日夕見於丁，故曰兊納丁，謂二陽之氣納於南方之丁也；乾純陽為望○，十五夕盈於甲，故曰乾納甲，謂三陽之氣納於東方之甲也。此望前三候陽息陰消之月象也（月分六候，每五日為一候）。

Hu Wei commented: The method of Najia originated from Jing Fang's calculation. Since Jia is the first of the ten heavenly stems, using one stem to represent the rest, it is called "Najia." Wei Boyang compared it with the lunar phases to indicate the timing of progression and retreat in the practice of alchemy. Basically, the brightness and darkness of the moon are used to symbolize the hexagram lines, and the position where the moon appears is considered as the heavenly stem it contains. The Zhen hexagram has one yang line, which corresponds to the initial brightness of the moon, appearing in the Geng position at the end of the third day, so it is said "Zhen contains Geng," meaning the yang energy is contained in the western Geng. The Dui hexagram has two yang lines, corresponding to the waxing moon, appearing in the Ding position at the end of the eighth day, so it is said "Dui contains Ding," meaning the two yang energies are contained in the southern Ding. The Qian hexagram has three yang lines, corresponding to the full moon, appearing in the Jia position at the end of the fifteenth day, so it is said "Qian contains Jia," meaning the three yang energies are contained in the eastern Jia. This refers to the three periods before the full moon when yang increases and yin decreases, with a month divided into six periods, each lasting five days.

巽一陰始生，於月為生魄□，十六旦明初退於辛，故曰巽納辛，渭以一陰之氣納於西方之辛也；退二陰為下弦□，二十三旦明半消於丙，故曰艮納丙，謂二陰之氣納於南方之丙也；坤純陰為晦●，三十旦明盡滅於乙，故曰坤納乙，謂三陰之氣納於東方之乙也。此望後三候陽消陰息之月象也。

The Trigram Xun represents the initial emergence of one yin, corresponding to the new moon phase when the dark moon first appears. On the sixteenth day of the month, in the early morning, the moonlight begins to retreat from the Xin position, hence it is said "Xun includes Xin," meaning the energy of one yin is included in the west at Xin. The Trigram Gen represents two yins, corresponding to the waning gibbous moon. On the twenty-third day of the month, in the early morning, the moonlight diminishes halfway at the Bing position, hence it is said "Gen includes Bing," meaning the energy of two yins is included in the south at Bing. The Trigram Kun represents pure yin, corresponding to the new moon with no moon visible. On the thirtieth day of the month, in the early morning, the moonlight completely disappears at the Yi position, hence it is said "Kun includes Yi," meaning the energy of three yins is included in the east at Yi. This describes the three phases after the full moon when yang wanes and yin increases according to the lunar phases. (The original text "Wei yi yin qi" should be "Wei yi yin qi," and "tu er yin wei xia xian" should be "Gen er yin wei xia xian.")

離為日，日生於東，故離位乎東；坎為月，月生於西，故坎位乎西。至望夕，則日西月東，坎離易位，其離中一陰即是月魄，坎中一陽即是日光，東西正對，交注於中，此二用之氣所以納戊巳也。故曰「坎戊月精，離己日光，日月為易，剛柔相當」，「蟾蜍與兔魄，日月氣雙明」也。

The trigram Li represents the sun, which rises in the east, so Li is located in the east. The trigram Kan represents the moon, which rises in the west, so Kan is located in the west. On the evening of the full moon, the sun is in the west and the moon is in the east, so Li and Kan exchange their positions. The yao in the center of Li that is yin represents the dark part of the moon; the yao in the center of Kan that is yang represents the bright part of the sun. East and west are exactly opposite, and their energies meet and flow into the center. This is why the energies of Li and Kan, known as the 'two uses' (二用), are said to incorporate Wu and Ji earth. Therefore, the "Cantong Qi" states, "The Wu earth in the center of Kan is the essence of the moon, and the Ji earth in the center of Li is the brilliance of the sun. The sun and moon together form the character 'yi,' with yin and yang perfectly balanced." It also says, "The toad and the rabbit's shadow, the energies of the sun and moon appear together."

乾納甲而又納壬，坤納乙而又納癸者，何也？謂乾之中畫即太陰之精，望夕夜半，月當乾，納其氣於壬方地中對月之日；坤之中畫即太陽之精，晦朔之間，日在坤，納其氣於癸方地中合日之月也。

The trigram Qian (Heaven) both receives the stem Jia and the stem Ren, while the trigram Kun (Earth) both receives the stem Yi and the stem Gui. This is because the central line of the Qian trigram represents the essence of Taiyin (the Yin Sun): during the full moon at midnight, the moon is directly in the position of Qian, and it channels its energy to the direction of Ren, which is the sun beneath the earth directly opposite the moon. The central line of the Kun trigram represents the essence of Taiyang (the Yang Sun): at the transition between the new moon and the full moon, the sun is directly in the position of Kun, and it channels its energy to the direction of Gui, which is the moon beneath the earth that corresponds with the sun.

徐敬可云：「望夕之陽既盈於甲矣，其夜半日行至壬而月與為衡。日中原有陰魄，所謂離中一陰者，平時含蘊而不出，至是則盛陽將革，又感正對之陰，乃充溢流滋而為生陰之本，故其象為□，即望夕夜半壬方之日也。晦旦之陽既盡於乙矣，其夜半日行至癸而月與同躔。月中原有陽精，所謂坎中一陽者，平時胚渾而不分，至是則盛陰將革，又感摩戛之陽，乃剖發迸洩而為生陽之本，故其象為□，即晦朔間癸方之月也。」故曰「壬癸配甲乙，乾坤括始終」，此尤易象之要樞也。

Xu Jingke said: On the full moon evening, the yang energy has already filled the Jia position. On that night half, the sun moves to the Ren position, while the moon is opposite to it like the two ends of a balance scale. The sun originally contains the yin essence, which is referred to as the yin line in the center of the Li trigram. Usually it is contained and not revealed, but at this time, the yang is about to change, and it responds to the yin opposite, thus overflowing and spreading, becoming the root of the initial yin energy. Therefore, its image is that of the initial emergence of yin, which is the sun at the Ren position on the night of the full moon. On the new moon morning, the yang energy has already exhausted at the Yi position. On that night half, the sun moves to the Gui position, while the moon is at the same degree. The moon originally contains the yang essence, which is referred to as the yang line in the center of the Kan trigram. Usually it is chaotic and unified without separation, but at this time, the yin is about to change, and it responds to the yang that is in contact, thus splitting and bursting forth, becoming the root of the initial yang energy. Therefore, its image is that of the initial emergence of yang, which is the moon at the Gui position during the transition from new moon to full moon. Therefore, the "Cantong Qi" says, "Ren and Gui pair with Jia and Yi, and Qian and Kun encompass the beginning and the end," which is especially the key point of the "Yi" images.

「七八數十五，九六亦相應，四者合三十，陽氣索滅藏」，葢即明堂九室縱橫十五之數。雖不言九宮，而九宮在其中矣。橫言之，二四為六之與九也，三五為八之與七也，一八為九之與六也，七八九六皆十五也；縱言之，三四為七之與八也，一五為六之與九也，二六為八之與七也，七八九六皆十五也；四維斜對言之，二五為七之與八也，四五為九之與六也，七八九六皆十五也。

"Seven and eight add up to fifteen, nine and six also add up accordingly, and the four numbers together make thirty, at which point the yang energy is exhausted and hidden." This is actually referring to the number fifteen obtained by adding the numbers in the rows and columns of the Bright Hall's nine rooms. Although the term "nine palace" is not mentioned, it is already included. In terms of the horizontal rows: two plus four equals six, which pairs with nine; three plus five equals eight, which pairs with seven; one plus eight equals nine, which pairs with six—seven, eight, nine, and six all add up to fifteen. In terms of the vertical columns: three plus four equals seven, which pairs with eight; one plus five equals six, which pairs with nine; two plus six equals eight, which pairs with seven—seven, eight, nine, and six again all add up to fifteen. In terms of the diagonal corners: two plus five equals seven, which pairs with eight; four plus five equals nine, which pairs with six—seven, eight, nine, and six once more all add up to fifteen.

七八數十五，九六數亦十五，合之為三十，當一月之日數。陽氣謂目光也，月本無光，感日之明以為光。明，陽也；魄，陰也。三日生明，十五而望，十六生魄，三十而晦，故曰「四者合三十，陽氣索滅藏」。索者，盡也，謂月所感日之光至是盡滅，全體皆魄也。

The numbers seven and eight add up to fifteen, and nine and six also add up to fifteen. Together they make thirty, which corresponds to the number of days in a month. Here, "yang qi" refers to sunlight (the original text says "guang" which should be "ri guang"). The moon itself does not emit light; it shines by reflecting the brightness of the sun. "Ming" belongs to yang, while "po" belongs to yin. On the third day of the month, the moon's light begins to appear, and on the fifteenth day, it is full, called "wang." On the sixteenth day, the dark "po" starts to grow, and on the thirtieth day, it is completely dark, called "hui." Therefore, it is said that "the four aspects together make thirty, and the yang qi is exhausted and hidden." "Suo" means to reach the end, indicating that the sunlight the moon receives is completely gone at this point, and the entire moon becomes dark "po."

此雖言月體之消長，而未嘗不合於九宮之數。然其卦則以子午為綱，夘酉為緯，所謂「乾坤定上下之位，離坎列左右之門」者是也，與明堂九室之卦位不同。觀漢上納甲圗用乾南坤北、離東坎西之位，則可知矣。彭本有九宮八卦圗，舉二者合而為一，殊覺齟齬。

This discusses the waxing and waning of the moon, yet it is not inconsistent with the numbers of the nine palaces. However, in terms of trigram positions, it takes the Zi and Wu as the main axes, and the Mao and You as the cross lines, which is said to be "the Heaven and Earth trigrams determining the vertical positions, and the Fire and Water trigrams arranging the left and right gates." This is different from the trigram positions of the Bright Hall with nine chambers. Looking at Zhu Zhen's Najia diagram, which places Qian in the south, Kun in the north, Li in the east, and Kan in the west, one can understand this. In Peng Xiao's version, there is a diagram called "Nine Palaces and Eight Trigrams," which combines these two systems into one, but they contradict each other and are incompatible.

「上觀天河文，下察地形流」，注家皆以「天河文」為雲漢，「地形流」為海潮。今本云「上觀河圗文」，葢後人妄改，以應九為河圗之說。河圗非天象，安得云「上觀」？其為俗子點竄可知。且淳于叔通《五相類》曰：「法象莫大乎天地兮，玄溝數萬里；河鼓臨星紀兮，人民皆驚駭。」

The original text of the "Cantong Qi" says, "Look up to observe the heavenly river text, and look down to examine the terrain flow." Historically, commentators have interpreted "heavenly river text" as the Milky Way and "terrain flow" as tidal movements. However, the current standard edition reads "Look up to observe the river chart text," which is a later alteration made to conform to the idea that "the number of wearing nine and bearing one comes from the Yellow River Chart." The Yellow River Chart is not a celestial phenomenon, so how can it be "looked up to observe"? This clearly shows that it is a fabrication by the unlearned. Moreover, Chun Yu Shu Tong's "Wu Xiang Lei" states: "There is no greater model to follow than the heavens and earth; the dark ditch extends for tens of thousands of miles; the river drum star is near the Xing Ji constellation, causing people to be greatly alarmed."

俞琰注云：「玄溝者，天河也，自箕尾之間至栁星之分，介斷天盤，不知幾萬里。修丹者法天象地，反身而求，則身中自有一壺天也。河鼓星位在天河邊斗牛之間，星紀，天盤之丑位也。丹法火臨於丑，則驅回尾穴連雲焰，趕入天衢直上奔（其氣自尾閭升於泥丸也），正當斬闗出路之時，一身之人民豈不竦然驚駭乎？」觀此文及注，則天河正有精義，不得作河圗。以是知七八九六，伯陽特以為晦朔弦望之候，雖有「別序斯四象」句，而實於河圗之四象絶無交涉也。

Yu Yan's commentary says: "Xuanguo" refers to the Milky Way, running from between the Tail Mansion and the Winnowing Basket Mansion all the way to the Willow Mansion and the Star Mansion, cutting across the entire Heaven Plate, without knowing how many thousands of miles it spans. Those practicing alchemy take inspiration from heaven and take form from earth, then turn inward to seek within themselves, so that within the body there naturally exists another world. The position of the River Drum Star is on the edge of the Milky Way, between the Dipper Mansion and the Ox Mansion; "Xingji" refers to the position of the Ox in the Heaven Plate. When the fire timing in alchemy reaches the Ox position, it drives back the tail闾穴, ignites a flame that connects to the sky, and sends it up along the celestial path (meaning the energy rises from the tail闾 to the mud ball), which is precisely the time when one cuts through the barriers and takes the direct path. How could the "people" within the body not be startled and frightened? By looking at this passage and its commentary, we can see that the term "Milky Way" indeed has profound meaning and cannot be changed to "Yellow River Chart." From this we can understand that the numbers seven, eight, nine, and six, which Wei Boyang refers to, are merely indicating the times of new moon, full moon, waxing moon, and waning moon. Although there is a sentence saying "another arrangement of these four images," in reality, it has nothing to do with the four images of the Yellow River Chart.

右論月體納甲。

The above is a discussion about the diagram of "Monthly Body Stem Assignment."

呂純陽《沁園春》丹詞（按《宋史·陳摶傳》：闗西逸人呂洞賓，世以為神仙，數來摶齊中。希夷丹道，豈即純陽所授邪？詞云「不因師指，此事爭知」，葢雖有希夷之風骨，不遇神仙終難成就金丹，歲晚無消息，能不重嘆乎）：「七返還丹，在人先須煉已待時。」

Heavenly Stems: Jia, Yi, Bing, Ding, Wu, Ji, Geng, Xin, Ren, Gui Earthly Branches: Zi, Chou, Yin, Mao, Chen, Si, Wu, Wei, Shen, You, Xu, Hai Trigrams: Qian (Heaven), Dui (Lake), Li (Fire), Zhen (Thunder), Xun (Wind), Kan (Water), Gen (Mountain), Kun (Earth) Hu Wei remarked: The "Chen Tuan Biography" in the "Song History" records that Lü Dongbin, a reclusive hermit from Guanxi, was regarded by everyone as a deity. He often visited Chen Tuan's residence. Could Chen Tuan's alchemical practices, known as the Xiyi School, have been passed down by Lü Chunyang? The poem says, "Without a master's guidance, how could one know about this matter?" This shows that even with the noble character of Xiyi, without encountering a divine being, one would still find it difficult to successfully refine the golden elixir. If one reaches old age without any progress, how could one not lament repeatedly? The poem begins by saying, "To return the seven essences and refine the elixir, one must first cultivate oneself and wait for the right time."

石澗俞氏曰：「七，火數也。煉丹之法，其先以紅投黑而生藥，既有藥，然後進火，煉黑入紅而成丹，故曰七返還丹，即非自寅至申之七時也。張紫陽《悟真篇》云『金公本是東家子，送在西鄰寄體生，認得喚來歸舍養，配將奼女作親情』，是此義也。」

Shi Jian Xiansheng Yu Yan explained that seven is the number of fire. The method of alchemy involves first putting red into black to produce the medicine, then using fire to transform black into red and form the elixir, hence called "seven return elixir," not referring to the seven hours from寅 to申. Zhang Ziyang's "Wuzhen Pian" says "Jin Gong is originally the son of the eastern family, sent to be raised by the western neighbor, recognized later and called back to be raised, then paired with Chajun to form a marriage," which explains the same meaning.

《離騷·逺遊》篇云：「毋滑而魂兮，彼將自然；一氣孔神兮，於中夜存；虛以待之兮，無為之先。」即「煉已待時」之謂也。要在收視返聽，寂然不動，凝神於太虛，無一毫雜想，少焉神入氣中，氣與神合，則真息自定，神明自來，不過片晌間耳。邵康節《先天吟》云：「若問先天一字無，後天方要著工夫。」丹法亦然：採藥於先天則無為，進火於後天則有為，不可以一律齊也。

The "Yu You" section of the "Chu Ci" says: "Do not disturb your spirit, let it follow its natural course; the vital energy is extremely profound, cultivating it in the middle of the night; remain quiet and wait for it, do not act prematurely before non-action." This is precisely the meaning of "refining oneself and waiting for the right time." The key lies in withdrawing the senses and turning inward, remaining still and unmoving, gathering the spirit into the great void, with no trace of scattered thoughts; after a while, the spirit enters the qi, and the spirit and qi unite, thus the true breath becomes naturally calm, and the spirit becomes naturally present, which is merely a matter of a moment. Shao Yong's "Earlier Heaven Ode" says: "If you ask about the Earlier Heaven, it is nothing at all; only when reaching the Later Heaven, effort is needed." Alchemical methods are the same: refining the elixir in the Earlier Heaven is "non-action," while advancing the fire in the Later Heaven is "action," and they cannot be treated as the same.

「正一陽初動，中宵漏永，溫溫鉛鼎，光透簾帷。」俞氏曰：「白紫清《珠玉集·丹髓歌》云『煉丹不用尋冬至，身中自有一陽生』，然吾何以知身中之一陽生也？葢彈指聲中巽門豁開，而心覺恍忽之時是也。吾於此時鼓之以槖鑰，煅之以猛火，則真鉛出坎，而河車不敢暫停，直運入崑崙峰頂，乃可以為還丹。邵康節《恍忽吟》云『恍忽陰陽初變化，絪縕天地乍迴旋，中間些子好光景，安得功夫入語言』，非洞曉陰陽造化，疇克知此。」

The text continues: "At the moment when the first yang begins to move, the long sound of the midnight drum echoes, and the lead cauldron in the dantian warms up gently, with light passing through the curtain-like eyelids." Yu Yan explains that Bai Ziqing (Bai Yuchan) in his "Zhu Yu Ji · Dan Sui Ge" says, "One does not need to look for the day of winter solstice to cultivate the elixir; there is already a first yang within the body." Then he asks, how can I know that the yang within my body has already arisen? Generally, it is at the moment when, with a single finger snap, the "Xun gate" suddenly opens and one feels a vague and indistinct sensation. At this time, I use breathing like a bellows to stir it, and use fierce fire to refine it. The true lead comes forth from Kan, and the "He Che" does not stop for a moment, directly transporting it to the summit of Kunlun Mountain. Only then can it be called the return of the elixir. Shao Yong's "Huang Hu Yin" says, "In the vague and indistinct state, yin and yang begin to change; in the misty and ethereal atmosphere, the heavens and earth suddenly rotate. This brief moment of clarity is beyond words." Unless one thoroughly understands the transformation of yin and yang, who could comprehend this.

中宵即半夜子時也。《參同契》云「含元虛危，播精於子」是也。又云「晦朔之間，合符行中」，謂三十日半夜子時之前介乎晦朔之間也。若蹙之於一日，則每夜子時之前即晦朔之間，初不拘於三十日之半夜也。《悟真篇》云「日月三旬一遍逢，以時易日法神功」，其說明矣。鉛即藥也，鼎謂下丹田也。子時將至而陽氣潛萌於其下，所以溫溫也。簾帷者，眼也，垂眼下視有垂簾之象，故曰簾帷。惟丹田有藥而陽氣上升，透於兩睂之間，是以有光也。

"Zhongxiao" refers to the middle of the night, specifically the Zi hour. The "Cantongqi" states, "The original qi is contained within the mansion of Xuxu and Weixu, and the true essence is scattered at the Zi position," which refers to this. It also says, "At the meeting of the waning moon and the new moon, they align and move along the central path," meaning that before the Zi hour in the middle of the night, one is situated between the waning and new moon. If we compress a month into a single day, then the time before the Zi hour each night is considered the "meeting of the waning and new moon," and this is not limited to the middle of the night on the thirtieth day. The "Wuzhenpian" says, "The sun and moon meet once every thirty days, using hours to replace days, a profound method," which explains this principle. "Lead" refers to the medicine, and "ding" refers to the lower dantian. As the Zi hour approaches and yang qi begins to quietly rise in the lower part, it is said to be "wen wen," meaning warm. "Lianwei" refers to the eyes; lowering the eyelids and looking downward is like hanging a curtain, hence the term "Lianwei." Because there is medicine in the dantian and yang qi rises, reaching between the eyebrows, there is thus a glow.

「造化爭馳，虎龍交媾，進火工夫牛斗危。」俞氏曰：「造化爭馳，謂坤之末、復之初也。《參同契》云『龍呼於虎，虎吸龍精，兩相飲食，俱相吞併』，作丹之時，要在心息相依，然後神凝氣聚，交媾而為藥。陳朝元《玉芝書》云『玄黃若也無交媾，爭得陽從坎下飛』，故必陰陽交媾，丹田有藥，乃可以進火也。」

The text continues: "The vital energy of creation is in constant motion; the tiger and dragon meet, and the fire must be applied in the directions of the constellations Cow, Dou, and Wei." Yu Yan explains that "the vital energy of creation is in constant motion" refers to the moment at the end of the Kun hexagram and the beginning of the Fu hexagram. The "Shentingqi" says, "The dragon calls to the tiger, the tiger absorbs the dragon's essence, and they mutually consume each other, each devouring the other." When forming the elixir, the key is for the mind and breathing to be in harmony, then the spirit gathers and the energy accumulates, merging to form the elixir. Chen Chao Yuan's "Yuzhi Book" states, "If the dark and the yellow have not yet merged, how can the yang energy rise from beneath the Kan position?" Therefore, it is necessary for yin and yang to merge and for the dantian to have the elixir before proceeding with the fire.

牛斗危，乃身中火候之方位，謂進火工夫至寅而般運，如天之生物胚胎於子，至寅而出也。《參同契》云「始於東北，箕斗之鄉，旋而右轉，嘔輪吐萌」，《翠虛篇》云「有一子母分胎路，妙在尾箕斗牛女」，與此同旨。

"The positions of 'Ox, Dipper, and Hazard' refer to the internal fire energy within the body. It means that the practice of entering the fire should begin at the position of 'Yin' before the movement of energy can commence. This is analogous to how heaven and earth nurture all things; at the position of 'Zi', the embryo is formed, and at the position of 'Yin', it begins to sprout. The 'Compendium of the Supreme Harmony' states, 'It begins in the Northeast, in the mansions of 'Winnowing Basket' and 'Dipper', then turns right and exhales a sprout like a wheel.' The 'Green Void Chapter' says, 'There is a path of mother and child differentiation in the womb, its subtlety lies between the mansions of 'Tail', 'Winnowing Basket', 'Dipper', 'Ox', and 'Woman.' This is the same meaning."

「曲江上，見月華瑩淨，有個烏飛。」俞氏曰：「《翠虛篇》云『西南路上月華明，大藥還從此處生』，記得古人詩一句『曲江之上鵲橋橫』。古仙本以小腸有九盤十二曲，是為曲江，而《翠虛》又以西南路上發明其說，可謂深切著明矣。葢西南屬坤，坤為腹，藥生於丹田之時，陽氣上達麗於目而有光，故自目至臍一路皆虛白晃耀，如月華之明也。有個烏飛者，身中之天地交、坎離合，二氣絪縕，結成一滴露珠而飛落丹田中也。陳希夷《指玄篇》云『有個烏飛入桂宮』，《翠虛篇》云『紅蓮含蕊露珠凝碧，飛落華池滴滴』。」

The text also says: "On the curve of the river, one sees the moonlight clear and bright, with a crow flying by." Yu Yan explains that the "Cui Xu Chapter" says, "On the road to the southwest, the moonlight is bright, and the great elixir arises from here." He also recalls an old poem that says, "On the curve of the river, the magpie bridge is stretched across." Ancient immortal masters originally called the small intestine, which has nine twists and twelve bends, the "curve river," and the "Cui Xu Chapter" uses "on the road to the southwest" to elaborate on this idea, which can be said to be very clear and thorough. Generally speaking, the southwest belongs to the Earth, which corresponds to the abdomen; when the elixir is generated in the dantian, the yang energy rises and attaches to the eyes, thus producing light. Therefore, the path from the eyes to the navel is bright and clear, shining like moonlight. The phrase "there is a crow flying" refers to the union of heaven and earth within the body, the meeting of the kan and li energies, with the two kinds of qi mingling and colliding, condensing into a drop of dew that flies down to the dantian. Chen Tuan's "Zhi Xuan Chapter" says, "A crow flies into the osmanthus palace," and the "Cui Xu Chapter" says, "Red lotus holds its flower bud, dewdrops condense into green, dripping drop by drop into the huachi."

「當時自飲刀圭（謂但以服食為事），又誰信無中養就兒（即所謂三家相見結嬰兒也）。」俞氏曰：「金丹大道，至簡至易，於無中生有，養就嬰兒。如涕唾精津氣血液之類，止可按助以為階梯，非丹質也。學者局於管見，往往以先入之說為主，更不肻參究丹書，雖有道者欲與開發，孰為之信？《翠虛篇》云『怪事敎人笑幾回，男兒今也會懷胎，自家精血自交結，身裡夫妻是妙哉』。葢夫婦即陰陽之異名，非真有所謂夫婦也。或者偏執竹破竹補之說，遂謂以人補人，而專意於三峰邪術，又安信金丹乃清淨無為之道，而專於無中生有哉！」

The text also says: "At that time, I drank the knife and jade (meaning I regarded taking the elixir as the main pursuit), but who would believe that an infant was born from 'nothingness' (referring to the earlier mention of the meeting of three families to form the infant)." Yu Yan explains that the great way of the golden elixir is extremely simple and easy, it is to produce 'being' from 'nothingness,' and to nurture the infant. As for things like snot, saliva, semen, body fluids, breath, blood, and body fluids, they can only be used as auxiliary means, as the initial steps for beginners, but they are not the essence of the elixir. Those who practice the Dao are often confined by narrow views, and are often dominated by previous notions, unwilling to investigate the alchemical texts. Even if there are those who have attained the Dao and wish to guide them, who would believe them? The "Cui Xu Chapter" says, "Strange things have made people laugh many times, now men can also become pregnant, their own semen and blood unite on their own, the true couple within the body is indeed wonderful." Here, the term 'couple' is merely another name for yin and yang, and there is no real couple. Some people cling to the saying 'when bamboo breaks, use bamboo to mend it,' thinking that 'using human to mend human' is possible, and focus solely on perverse practices like the three peaks. How could they believe that the golden elixir is actually a path of purity and non-action, focusing on producing 'being' from 'nothingness'?

「辨水源清濁，木金間隔，不因師指，此事爭知。」俞氏曰：「人身有一物，分而為二，其浮者為木，沈者為金，一東一西，故謂之間隔。若得斗柄之機斡運，使之上下循環，如天河之流轉，則木性愛金，金情戀木，而刑德並會，不間隔矣。」

The text also says: "To distinguish the clarity and turbidity of water, wood and metal are separated from each other; without the guidance of a master, how could one know about this matter?" Yu Yanyi explains that a single thing in the human body splits into two parts: the light one is wood, the heavy one is metal, one located in the east and the other in the west, hence called 'separation.' If one can obtain the pivot of the Big Dipper's handle to regulate and coordinate them, making them circulate up and down like the Milky Way, then the nature of wood will love metal, and the affection of metal will cherish wood, with punishment and virtue coming together, thus eliminating separation.

（按：人身之水有清有濁，東坡《天慶觀乳泉賦》謂若汗、血、涕、洟、涎、沬之類，皆水之外騖者，一出而不復返；唯華池之真液，下湧於舌底而上流於牙頰，甘而不壞，白而不濁，宜古之仙者以是為金丹之祖、長生不死之藥也。故水源之清濁不可以不辨。木金間隔，即東家西鄰之謂。）

Hu Wei commented: The water in the human body is either clear or turbid. Su Shi's "Tianqingguan Ruyuan Fu" says that things like sweat, blood, tears, nasal mucus, saliva, and spittle are all waters that flow outward, once they flow out, they never return. Only the true liquid in the "Huachi" rises from beneath the tongue root and ascends between the teeth and cheeks, sweet and not spoiled, white in color and not turbid. That is why ancient immortals regarded it as the ancestor of the golden elixir and the elixir for eternal life. Therefore, it is essential to distinguish the clarity and turbidity of the water source. As for "mu jin ganjie," it refers to the meaning of "the eastern neighbor" and "the western neighbor" mentioned earlier.

《悟真篇》云：「饒君聰慧過顏閔，不遇真人莫強猜。」葢丹經所陳，或假物以明理，或設象以寓意，名義不同，學者卒然讀之，莫不有望洋之嘆。且以五行言之，或曰金木，或曰水土，或曰水火，或曰金火，或曰金水，或曰木火，或曰水土，使人心目俱眩，誠不易知也。

The "Wuzhen Pan" says: "Even if your wisdom surpasses Yan Hui and Min Ziqian, without meeting a true master, do not force your guesses." Generally speaking, the Daoist scriptures often explain their teachings by using external things or setting up symbols to convey profound meanings. The names and meanings vary, and scholars, upon first reading them, feel overwhelmed, as if looking at the sea from the shore. Take the Five Phases for example. Sometimes they talk about metal and wood, sometimes about water and soil, sometimes about water and fire, sometimes about metal and fire, sometimes about metal and water, sometimes about wood and fire, and sometimes about water and soil. This makes it very confusing and difficult to understand.

「道要玄微，天機深逺，下手速修猶太遲。」俞氏曰：「丹道之要有二：曰交媾，曰進火。雖有先後次序，要皆一片功夫。天機謂半夜子陽初動之時也。天機將至，人能動吾之機以應之，則天人合發，內外相符，結而為丹矣。雖曰一日十二時，凡相交處亦皆可為，而古仙必用半夜子陽初動之時者，其時太陽正在北方，而人身氣到尾閭闗，葢與天時相應，所謂盜天地、奪造化，惟此時為然。乃若丑時則太陽已偏，人身之氣已過尾閭矣；寅時則太陽已出地，人身之氣已過腎堂矣，皆不可用也。《玉芝書》云『凡煉丹隨子時陽氣而起火，其火方全；餘外別時起火，其火不全』，斯言盡之矣。」

The text also says: "The essence of the great way is profound and subtle, and the heavenly mechanism is deep and remote. Even if one starts practicing immediately, it would still be too late." Yu Yan explains that the key points of the alchemical path are two: one is "union," and the other is "furnace fire." Although there is a sequence, in reality they are one continuous practice. "Heavenly mechanism" refers to the moment at the beginning of the Zi hour when the first yang energy begins to stir. When the heavenly mechanism approaches, a person can start their own mechanism to correspond with it, which means that heaven and humanity act together, and internal and external aspects align, thus forming the elixir. Although there are twelve hours in a day, and any time when yin and yang intersect can be used, ancient immortals always chose the moment of the first yang stirring at the Zi hour, because at that time the sun was in the north, and the person's qi was exactly passing through the tail闾 gate, corresponding with the heavenly timing. This is called "stealing from heaven and earth, seizing the process of creation," which can only be done at this time. As for the Chou hour, the sun has already moved away, and the person's qi has passed the tail闾 gate; at the Yin hour, the sun has already risen above the horizon, and the person's qi has passed the kidney hall, so they cannot be used. The "Yuzhi Book" says, "Whenever one practices alchemy, one must start the fire according to the yang energy of the Zi hour; only then can the fire be complete. If one starts the fire at other hours, the fire will not be complete." These words fully explain the principle.

「蓬萊路，仗三千行滿，獨步雲歸。」（尸解則能輕舉，然只成地仙，故歸名山洞府也。）俞氏曰：「三千行滿，謂九年三千日也。三千日內，務要積功累行，十二時中不可須臾離道。劉虛谷《還丹篇》云『大功欲就三千日，妙用無虧十二時』是也。丹法片晌結胎，百日而功靈，週年而胎圎，九年而行滿，皆有程度，決無今日遇師、明日便能成仙之理。當知一年而小成，九年而大變：始而易氣，次而易血，次而易脈，次而易肉，次而易髓，次而易筋，次而易骨，次而易髮，次而易形，積九年而閱九變，煉盡純陰，變成純陽，然後可以遺世獨立，羽化而登仙也。」

The passage concludes by saying: "The path to Penglai is only possible through the completion of three thousand days of meritorious deeds, allowing one to return alone upon clouds." (Hu Wei notes: "Although the body can be lightened and one can fly, this only results in becoming a terrestrial immortal, so the final resting place is in a famous mountain cave dwelling.") Yu Yan explains that "three thousand days" refers to nine years of three thousand days. Within these three thousand days, one must accumulate merit and cultivate diligently, without leaving the Dao for even a moment in the twelve hours of each day. Liu Xugü's "Huan Dan Chapter" states, "Great achievements require three thousand days, and the wonderful application is not lost in the twelve hours," which is precisely this meaning. In alchemy, the fetus is formed in an instant, becomes effective after one hundred days, is fully mature after one year, and is completed after nine years, with a clear progression. There is no such thing as becoming an immortal simply by meeting a master today and achieving immortality tomorrow. One must understand that one year represents a small achievement, while nine years is a great transformation: first changing the breath, then the blood, then the pulse, then the flesh, then the marrow, then the sinews, then the bones, then the hair, and finally the body. After nine years of experiencing nine transformations, all the pure yin is refined into pure yang, and then one can transcend the worldly realm, stand independently, and ascend to immortality.

渭按：丹家之煉已，一曰交媾，亦曰生藥、採藥，又曰作丹，此其事在亥子之交，《參同契》云「晦朔之間，合符行中，混沌洪蒙，牝牡相從」是也；進火一曰起火，此其事在子丑之會，《參同契》云「始於東北，箕斗之鄉，旋而右轉，嘔輪吐萌」是也。陳致虛云「人先須養性，乃可修命，臨爐一差百錯，總由煉已無功」，言生藥不可不早也；俞琰云「丹法火臨於丑，則驅回尾穴連雲焰，趕入天衢直上奔」，言進火不可不力也。

Hu Wei comments: The Daoist alchemists refer to "refining oneself" as "coitus," also called "producing medicine," "collecting medicine," and "making the elixir." This process occurs at the time between the亥 and子 hours. The "Chen Tong Qi" says, "At the meeting of the waning moon and the new moon, the symbols meet and proceed along the middle path, in a state of chaos and primordial unity, with yin and yang following each other," which refers to this. "Advancing the fire" is also called "starting the fire," and this occurs at the time between the子 and丑 hours. The "Chen Tong Qi" says, "It begins in the northeast region of Ji and Dou, then turns right, exhaling a sprout like a wheel," which refers to this. Chen Zhi Xu says, "One must first cultivate virtue before one can cultivate destiny; if one starts at the furnace with even a slight error, it will lead to a great mistake, entirely because refining oneself is not done thoroughly," which means that collecting the medicine must not be delayed. Yu Yan says, "In alchemy, when the fire reaches the position of丑, it drives back the single hole of the tail闾, ignites a continuous flame, and rushes up the celestial path," which means that advancing the fire must not be done with weak effort.

其於天地之撰、陰陽之義、水火之情、日月之運，亦可謂探其微而抉其奧矣。惜乎其以聖人之大道而小試之也！惜乎其以聖人之公心而私用之也！聖人能盡其性則能盡人物之性，贊天地之化育，何其大也；丹家之功效止於一身，小之至矣。孔子曰「死生有命」，又曰「朝聞道，夕死可矣」；孟子曰「夭壽不貳，修身以俟之」；張子曰「存吾順事，沒吾寧也」。聖人於死生之際如是而已，何其公也；丹家日孳孳唯以長生久視為念，私亦甚矣。故謂丹道出於易則可，謂聖人之作易意在明丹道則不可也。

The alchemists have also explored the structure of heaven and earth, the principles of yin and yang, the nature of water and fire, and the movement of the sun and moon. They can be said to have reached the subtle and uncovered the profound mysteries. Unfortunately, they took the great way of the sages and used it for minor experiments. They took the public spirit of the sages and used it for private purposes. A sage who fully understands his own nature can fully understand the nature of others and all things, participating in and assisting the transformation of heaven and earth. How grand this is! The achievements of the alchemists are limited to their own bodies, which is truly insignificant. Confucius said, "Death and life are determined by destiny," and also said, "If I hear the great way in the morning, I can die at night." Mencius said, "Whether one lives a short or long life, one does not change his aspirations; he cultivates himself and waits for destiny." Zhang Zai said, "When I am alive, I follow the course of things; when I die, I find peace." The attitude of the sages toward life and death is like this, how just it is! The alchemists, however, constantly strive day and night, always thinking only of longevity and immortality, which is too selfish. Therefore, it is acceptable to say that the alchemy comes from the Book of Changes, but it is not acceptable to say that the sage composed the Book of Changes with the intention of explaining alchemy.

右論煉已進火。

The above is a discussion on the two alchemical techniques known as "refining the self" and "advancing the fire."

清容袁氏桷《謝仲直易三圗序》曰：「上饒謝先生遯於建安，番昜吳生蟾往受易，而後出其圗焉。建安之學為彭翁，彭翁之傳為武夷君，而莫知所受，或曰托以隠秘，故謂之武夷君焉。始晁以道紀傳易統緒，截立疆理，俾後無以偽。至荊州袁溉道潔，始受於薛翁而易復傳，袁乃以授永嘉薛季宣士龍。始薛授袁時，嘗言河洛遺學多在蜀漢間，故士大夫聞是說者爭陰購之。」

Qingrong Ju Shi Yuan Jue wrote in "Xie Zhongzhi Yi San Tu Xu" that in Shangrao, the scholar Xie Sir lived in Jian'an. A man named Wu Chan from Poyang went to study the Book of Changes with him, and later Xie Sir revealed the three diagrams. The scholarly tradition of Jian'an came from Peng翁, who learned from the Master of Wuyi, but no one knows who the Master of Wuyi's teacher was. Some say it was a pseudonym to keep it secret, hence the name "Master of Wuyi." At first, Chao Shuozhi (styled Yidao) recorded the transmission of the Book of Changes, setting boundaries so later people could not fabricate. Later, Yuan Gai (styled Daojie) from Jingzhou learned from Xue翁, and thus the study of the Book of Changes was revived. Yuan Gai then passed it on to Xue Jixuan (styled Shilong) from Yongjia. When Xue翁 taught Yuan Gai, he said that the remaining teachings of the Yellow River Chart and the Luo Writing were mostly preserved in Sichuan and Shu Han regions. Therefore, when scholars heard this, they all competed to secretly spend money to acquire them.

「後有二張，曰行成，精象數；曰演，通於玄。最後朱文公屬其友蔡季通如荊州，復入峽，始得其三圗焉。或言洛書之傳，文公不得而見。今蔡氏所傳書訖不著圗，藏其孫抗，秘不復出。臨卭魏了翁氏嘗疑之，欲經緯而卒不可得。季通宋武夷，今彭翁所圗疑出蔡氏，惜彭不具本始。謝先生名字今不著，其終也世能道之。」

Yuan Jue continued to say: Later there were two men surnamed Zhang. One was Zhang Xingcheng, who was proficient in the principles of figures and numbers. The other was Zhang Yan, who understood the profound meanings. Finally, Zhu Xi entrusted his friend Cai Yuan ding (whose name was Jitong) to go to Jingzhou and further into the Three Gorges, only then obtaining those three diagrams. Some people say that Zhu Xi did not see the transmitted version of the Luo Writing. Now the book passed down by the Cai family does not include the diagrams, which are kept by Cai Kang, his grandson, and are not shown to others. Wei Le翁 from Linqiong once doubted this, wanting to systematically organize the diagrams and their explanations, but ultimately failed to do so. Cai Yuan ding was a person from the Wuyi area in the Song Dynasty. Now the diagram drawn by Peng翁 is suspected to have come from the Cai family, but unfortunately Peng翁 did not explain its origin. The name of Xie先生 is not written now, and his final fate is something that people can still talk about.

渭按：清容博雅君子也，君子之言信而有徵，故首著之。季通所得三圗，一為先天太極圗無疑矣，其二葢九宮圗與五行生成圗，而希夷未嘗名之曰洛書，故「或言洛書朱子不得見」也。（謝枋得字君直，信州弋陽人，宋末以江西招諭使知信州事，國亡變姓名遯入建陽，其後人稍識之，被徵不就。福建行省參政魏天佑送至大都，遂不食而死，事具《宋史》本傳。仲直即君直也。清容以謝拒元命為時所忌，故隠其名，復更其字。）

Hu Wei's commentary: Yuan Jue was a learned and refined gentleman. A gentleman speaks with credibility and evidence, so he first recorded Yuan Jue's words here. Cai Yuanding obtained three diagrams, one of which was the "Earlier Heaven Taiji Diagram," which is without doubt; the other two were probably the "Nine Palace Diagram" and the "Five Phases Generation Diagram." Chen Tuan himself did not call them the "Luo Writing," so Yuan Jue said, "Some people say that the transmission of the Luo Writing was not seen by Zhu Xi." (Xie Fangde, whose name was Junzhi, was from Xinyang in Xingzhou, and in the late Southern Song dynasty, he served as an envoy to pacify Jiangxi and administered the affairs of Xingzhou. After the fall of the Song, he changed his name and surname and fled to Jianyang. Later, the local people gradually recognized him, and the Yuan court summoned him, but he refused to take office. The provincial governor of Fujian, Wei Tianyou, sent him to Dadu, where he starved himself to death. His deeds are recorded in the "Biography of the Song History." The term "Zhongzhi" in the text refers to "Junzhi." Yuan Jue concealed Xie Fangde's name because he refused to accept the Yuan court's summons, and he also altered his given name.)

趙氏撝謙《六書本義》曰：「天地自然之圗，虙戲氏龍馬負圗出於榮河，八卦所由以畫也。《易》曰『河出圗，聖人則之』，《書》曰『河圗在東序』是也。此圗世傳蔡元定得於蜀之隠者，秘而不傳，雖朱子亦莫之見，今得之陳伯敷氏。嘗熟玩之，有太極函陰陽、陰陽函八卦之妙。」（撝謙字古則，餘姚人，宋宗室，別號老古先生。《名山藏》作趙謙，雲洪武初聘修《正韻》。）

Zhao Huiqian in his work "The Original Meaning of the Six Scripts" says: this "Diagram of Heaven and Earth in Nature" is the same diagram that appeared when the dragon horse carried it out of the Xing River during the time of Fuxi, upon which the Eight Trigrams were drawn. The "Great Treatise" of the "Zhou Changes" says "the diagram appeared from the Yellow River, and the sage took it as a model." The "Book of Documents, Gu Meng" says "the diagram was placed in the eastern hall," referring to this very diagram. This diagram is said to have been obtained by Cai Yuanding from a hermit in Sichuan, and it was kept secret and not passed on outside. Even Zhu Xi did not see it. Now I have obtained it from Chen Boyufu. I have pondered it repeatedly, and found the subtle aspect of the Taiji containing yin and yang, and yin and yang containing the Eight Trigrams. (Hu Wei's note: Zhao Huiqian, whose courtesy name was Guzhe, was from Yuyao, a descendant of the royal family of the Song dynasty, and was also known as Old Master Gugong. The "Name Mountains Collection" writes his name as Zhao Qian, stating that he was summoned in the early years of Hongwu to participate in compiling the "Hongwu Correct Pronunciation." )

楊氏時喬《周易全書》曰：「趙氏圗書，世競傳之為真圗書，靈寶許公誥、郴陽何公孟春尤篤信之。獨季彭山本云：朱子與蔡氏無書不講明，豈有秘不與言之理？」渭按：蔡氏所得之三圗，清容不言其形象，未知何如。據古則所傳以為蔡氏之所得，葢三圗之中此居其一，名曰先天圗，亦曰太極圗，取《參同契》之月體納甲、二用三五與九宮八卦混而一之者也。朱子發云「陳摶以先天圗授种放，三傳而至邵雍」，則康節之學實出於希夷，其所演以為先天古易者悉本此圗，可知也。

Yang Shi Qiao said in "The Complete Book of the Zhou Yi": Zhao Huiqian's diagram has been widely circulated among people, who claim it to be the true River Chart and Luo Writing. Xu Guo, a person from Lingbao, and He Mengchun, a person from Chenyang, especially believe in it wholeheartedly. Only Ji Ben, who was known as Pengshan, based on the original version said: Zhu Xi and Cai Yuan ding had discussions on every book, so how could there be any secret knowledge that they did not share with each other? Hu Wei's commentary: The three diagrams that Cai Yuan ding obtained, Yuan Jue did not describe their shapes, so we cannot know what they looked like. If we take Zhao Huiqian's diagram as one of the three diagrams that Cai Yuan ding obtained, then this diagram would be one of the three, called the "Earlier Heaven Diagram," also called the "Taiji Diagram." In reality, it is a combination of the "Cantongqi" moon body stem assignment, the two uses of three and five, and the nine palace trigrams. Zhu Zhen said, "Chen Tuan passed down the Earlier Heaven Diagram to Zhongfang, and it passed through three generations to Shao Yong." This shows that Shao Yong's learning indeed came from Chen Tuan. All the system he developed and called the "Earlier Heaven Ancient Yi" was based on this diagram, which can be definitely concluded.

後人謂之天地自然之圗，又謂之太極真圗。其環中為太極，兩邊白黑回互，白為陽，黑為陰。陰盛於北而陽起薄之，故邵子曰「震始交陰而陽生」，自震而離而兊以至於乾，而陽斯盛焉。震東北，白一分黑二分，是為一奇二偶；兊東南，白二分黑一分，是為二奇一偶；乾正南全白，是為三奇純陽；離正東，取西之白中黑點為二奇含一偶，故云「對過陰在中」也。

Later people called it the "Diagram of Heaven and Earth in Their Natural State," also known as the "True Diagram of the Taiji." In the center of the diagram is the Taiji, with black and white swirling around it, white representing Yang and black representing Yin. Yin energy is strong in the north, and Yang energy rises to approach it, so Shao Yong said, "The Zhen hexagram begins to interact with Yin, and Yang energy arises." From Zhen to Li to Dui up to Qian, Yang energy becomes increasingly strong. Zhen is in the northeast, with white taking one part and black taking two parts, which is one odd and two even; Dui is in the southeast, with white taking two parts and black taking one part, which is two odds and one even; Qian is in the due south, entirely white, which is three odds representing pure Yang; Li is in the due east, taking the black dot in the western white as two odds containing one even, so it is said, "the single point of Yin is in the center."

陽盛於南而陰來迎之，故邵子曰「巽始消陽而陰生」，自巽而坎而艮以至於坤，而陰斯盛焉。巽西南，黑一分白二分，是為一偶二奇；艮西北，黑二分白一分，是為二偶一奇；坤正北全黑，是為三偶純陰；坎正西，取東之黑中白點為二偶含一奇，故云「對過陽在中」也。

Yang energy is strong in the south, and yin energy comes to meet it, so Shao Yong said, "The Xun trigram begins to diminish yang energy and yin energy arises." From Xun to Kan to Gen and finally to Kun, yin energy becomes more powerful. Xun is in the southwest, with black occupying one part and white occupying two parts, which is one even and two odd; Gen is in the northwest, with black occupying two parts and white occupying one part, which is two even and one odd; Kun is in the due north, entirely black, which is three even and pure yin; Kan is in the due west, taking the white dot from the eastern black as two even containing one odd, so it is said, "the yang dot is in the middle opposite."

坎離為日月，升降於乾坤之間而無定位，納甲寄中宮之戊巳，故東西交易，與六卦異也。八方三畫之奇偶與白黑之質次第相應，天工乎？人巧乎？其自然而然之妙，非竊窺造化陰陽之秘者亦不能為也，但不可指以為伏羲之河圗耳。

The trigrams Kan and Li symbolize the sun and moon, rising and falling between Qian and Kun, without fixed positions. When applying the Najia stem assignment, they are寄托ed on the Central Palace's Wu Ji earth. Thus, they alternate between east and west, differing from the other six trigrams. The odd and even lines of the three-line trigrams correspond in order to the black and white dots on the chart; is this the work of heaven's skill or human ingenuity? This natural and subtle artistry could not be achieved without secretly understanding the secret of yin and yang from the creation. Yet we cannot simply call it the River Chart of Fuxi.

或問：「朱子謂希夷之學源出《參同契》，何以知其然乎？」曰：即其陰陽盛衰之數以推晦朔弦望之氣，而知其理有若合符節者矣。陽氣生於東北而盛於正南，震、離、兊、乾在焉，即望前三候陽息陰消之月象也；陰氣生於西南而盛於正北，巽、坎、艮、坤在焉，即望後三候陽消陰息之月象也。

Someone asked: How do we know that Chen Tuan's learning indeed comes from the "Zhou Yi Cang Tong Qi"? The answer is: By examining the proportions of yin and yang in the diagram and using them to deduce the climatic changes of new moon, full moon, waxing moon, and waning moon, one will find that the principles align perfectly like a matching seal. Yang energy originates in the northeast and reaches its peak in due south, with the four trigrams Qian, Dui, Li, and Zhen arranged on this side, corresponding exactly to the three days before the full moon when yang increases and yin decreases. Yin energy originates in the southwest and reaches its peak in due north, with the four trigrams Xun, Kan, Gen, and Kun arranged on this side, corresponding exactly to the three days after the full moon when yang decreases and yin increases.

陰極於北而陽起薄之，陰避陽，故回入中宮而黑中復有一點之白；陽極於南而陰來迎之，陽避陰，故回入中宮而白中復有一點之黑。葢望夕月東日西，坎離易位，其黑中白點即是陽光，白中黑點即是陰魄，東西正對，交注於中，此二用之氣所以納戊巳也。舉《參同》千言萬語之玄妙而括之以一圗，微而著，約而賅，丹家安得不私之為秘寶而肯輕出示人耶？

When yin reaches the north and becomes most vigorous, yang energy arises and approaches it, so yin retreats from yang, thus turning back into the Central Palace, resulting in a small white spot within the black. When yang reaches the south and becomes most vigorous, yin energy comes to meet it, so yang retreats from yin, thus turning back into the Central Palace, resulting in a small black spot within the white. Generally, on the full moon evening, the moon is in the east and the sun is in the west, with the trigrams Kan and Li exchanging positions. The white spot in the black is the sunlight, and the black spot in the white is the moon's essence. East and west are directly opposite, and their energies intersect and flow into the center, which is why the energies of Kan and Li are said to include the earth elements Wu and Ji. The myriad profound meanings of the "Supplement to the Secret Teachings" are all summarized in a single diagram, being both subtle and clear, concise and comprehensive. How could the alchemists not regard it as a closely guarded treasure, and be willing to easily reveal it to others?

自种放之後，儒者受此圗皆有所變通恢廓，而非復希夷之舊，唯蜀之隠者得其本真，私相授受以為丹家之要訣，篾叟、醬翁之徒是也。故雖朱子之博洽亦不得見，而必屬季通入峽求之，葢即酷愛《參同契》之意，以為坐談龍肉不如吃豬肉而飽也。其終不以為河圗而列諸經首者，葢以圗出希夷，源自伯陽，不若根柢《大傳》五十有五之數為得其正耳，非季通秘之而不與言也。

Since Zhong Fang, the figure who first introduced the diagram, scholars of the Confucian tradition who accepted it each interpreted it in their own way, so it was no longer in its original form as presented by Chen Tuan. Only those hermits in Sichuan province retained the original version, passing it on secretly among themselves as a key secret of alchemy. Even people like the old man selling bamboo strips or the old man selling sauce would possess it. Therefore, even a person as knowledgeable as Zhu Xi was unable to see it, and he had to entrust Cai Yuan Ding to search for it deep in the Three Gorges. This was actually due to his deep affection for the "Compendium of the Supreme Ultimate," thinking that merely talking about dragon meat was not as satisfying as actually tasting a piece of pork. In the end, Zhu Xi did not include this diagram among the Yellow River Chart in the beginning of his "Original Meaning of the Zhou Changes," because the diagram originated from Chen Tuan and was rooted in Wei Boyang, which was not as pure as basing his argument on the "Great Treatise" saying "the numbers of heaven and earth total fifty-five." It was not because Cai Yuan Ding concealed the secret from him.

趙氏仲全《道學正宗》曰：「古太極圗，陽生於東而盛於南，陰生於西而盛於北，陽中有陰，陰中有陽，而兩儀、而四象、而八卦，皆自然而然者也。」按：潛溪宋氏濂曰：「新安羅端良願（羅願字端良）作陰陽相含之象，就其中八分之以為八卦，謂之河圗；用井文界分九宮，謂之洛書。言出於青城山隠者，然不寫為象。」今觀趙氏此圗，正所謂陰陽相含、就中八分之以為八卦者，青城隠者之所授當亦如此，然不著陰陽分數，視古則為疎略。其不曰河圗而謂之古太極圗，何也？葢其時既從《啟蒙》以五十五數為河圗，而濂溪又自有所為太極圗者，故不名河圗，曰太極圗而加「古」以別之。

Zhao Zhongquan said in "Dao Xue Zheng Zhong": This "ancient Taiji diagram" shows that yang is born in the east and reaches its peak in the south, while yin is born in the west and reaches its peak in the north. Yang contains yin and yin contains yang, thus giving rise to the two principles, the four images, and the eight trigrams, all naturally formed. Hu Wei's commentary: Qianxi Xian Shen (Song Lian) said that Luo Yuan (Luo Yuan, whose courtesy name was Duanliang) created an image called "yin and yang containing each other." He divided it into eight parts as the eight trigrams, calling it the Yellow River Chart; then he divided it into nine sections with a grid pattern, calling it the Luo Writing. It is said that this came from a hermit in Qingcheng Mountain, but Luo Yuan did not draw it as a diagram. Now looking at Zhao Zhongquan's diagram, it is exactly the kind of image called "yin and yang containing each other," dividing it into eight parts as the eight trigrams. The hermit in Qingcheng Mountain must have also used this method, but he did not indicate how much yin and yang each occupied. Compared to Zhao Huiqian's diagram, it is more rough and simplified. It is not called the Yellow River Chart but "ancient Taiji diagram." Why is that? Probably because at that time, people had already followed Zhu Xi's "Yi Xue Ming Lun" to regard the number fifty-five as the Yellow River Chart, and Zhou Dunyi had his own "Taiji Diagram." Therefore, it is not called the Yellow River Chart, but instead called the Taiji Diagram, and adding the word "ancient" to distinguish it.

先天圗雖丹家修煉之訣，然亦必得其人而傳之，非其人則不傳也，故宋初唯种放、穆修受希夷之學，而他無聞焉。其後穆修授李之才，之才授邵雍，而天下始知有象數之學，即上所列二圗是也，亦曰太極圗，或謂之河圗。（有蔣公順字得之者，魏鶴山之門人也，著論以先天圗為河圗，五行生成數為洛書，戴九履一為太一下行九宮圗，鶴山云「此亦是一說」。）

The Earlier Heaven diagram is although a secret teaching for alchemists' cultivation, it must be transmitted only to suitable persons; it is not passed on to unsuitable ones. Therefore, at the beginning of the Song dynasty, only Zong Fang and Mu Xiu received Chen Tuan's learning, and there is no record of others. Later, Mu Xiu passed it on to Li Zhi Cai, who passed it on to Shao Yong. Thus, the world became aware of what is called the study of figures and numbers, referring to the two diagrams mentioned above, also called the Taiji diagram. Some people call it the Yellow River Chart. There was a Master Jiang Shun, whose name was De Zhi, a disciple of Wei Le翁 He Shan Master. He wrote articles advocating that the Earlier Heaven diagram should be regarded as the Yellow River Chart, the Five Phases generation numbers as the Luo Writing, and the "Wearing Nine and Wearing One" as the diagram of the Supreme Ultimate descending into the nine palaces. Wei Le翁 said, "This is also a kind of interpretation."

希夷之所授受盡於此矣，而說者謂此外別有河圗洛書，种放得之以傳李溉及許堅，不亦謾乎？溉惟有卦氣圗（見漢上《周易卦圗》，雲其說源於易緯《類是謀》），而堅無所著，不知其說云何。今觀范諤昌、劉牧之言，則皆祖述偽龍圗者也，與希夷之學相去徑庭矣。

Chen Tuan's lineage of transmission ends here, but some scholars say there are also the Yellow River Chart and the Luo Writing. Zheng Zong obtained them and passed them on to Li Gai and Xu Jian. Is this not a lie? Li Gai only had one "Diagram of Hexagram Qi" (see Zhu Zhen's "Zhou Yi Gu Tu," which says its theory comes from the Yi Wai text "Lei Shi Miao"). Xu Jian had no writings, so we do not know what his theory was. Now looking at the words of Fan Echang and Liu Mu, they all trace back to that forged "Longtu," which differs from Chen Tuan's learning by ten thousand eight thousand miles at least.

葢自种放既沒，天禧以後龍圗託名希夷，當世翕然宗之。邵子之書雖得真傳，而變通恢廓多所自得，良工不示人以樸，人莫測其所從來；其流傳蜀漢間者，又不過二三隠淪私為養生之訣，儒者無過而問焉，非若劉牧之徒造作文字、更相標榜以簧鼔天下也。故朱子雖力辨劉牧之非，而終不能脫龍圗之窠臼，逮乎晚年始覺其妄，遂令季通入峽購得三圗耳。蔡氏秘不肻出，及元末明初復見於世，雖無當於聖人之易，而源出《參同》，猶勝龍圗之怪誕。彼疑清容、二趙之言為不足信者，得吾說而思之，夫亦可渙然釋矣。

In general, since Zhongfang passed away, after the Tianxi period, the "Longtu" (Dragon Diagram) was falsely attributed to Chen Tuan. At that time, people universally regarded it as the standard. Although Shao Yong's writings received the true transmission, he made many variations and interpretations, expressing his own insights, like a master craftsman who does not show his unprocessed raw materials to others, so others could not understand its origin. As for the branch that spread in Sichuan and Hanzhong regions, it was merely a few reclusive scholars who used it as a method for health preservation, and Confucian scholars did not even pay attention to it, unlike Liu Mu and his group who fabricated texts and boasted to deceive the world. Therefore, although Zhu Xi strongly refuted Liu Mu's errors, he could not escape the framework of the "Longtu," and only in his later years did he realize its absurdity, so he sent Cai Yuanding to go to the Three Gorges to purchase the three diagrams. The Cai family kept them secret and did not reveal them, until they reappeared again in the Yuan and early Ming dynasties. Although these diagrams have nothing to do with the sages' "Yi," they originate from the "Cantongqi" (The Secret of the Supreme Ultimate), which is still better than the absurdity of the "Longtu." Those who doubt the reliability of Yuan Jue and Zhao Huiqian, Zhao Zhongquan, should think again after reading my discussion, and then they will understand clearly.

右論希夷先天圗。

The above is a discussion on Master Chen Tuan Xiyi's "Earlier Heaven Diagram."

希夷陳先生《龍圗序》曰：「且夫龍馬始負圗，出於羲皇之代，在太古之先也。今存已合之位尚疑之，況更陳其未合之數邪？然則何以知之？答曰：於夫子三陳九卦之義探其旨，所以知之也。況夫天之垂象，的如貫珠，少有差則不成次序矣，故自一至於盈萬，皆累累然如繫之於縷也。且若龍圗便合，則聖人不得見其象；所以天意先未合而形其象，聖人觀象而明其用。是龍圗者，天散而示之，伏羲合而用之，仲尼黙而形之。」

Chen Tuan, the Master Xiyi, in his "Preface to the Dragon Chart," said: The dragon horse first appeared carrying the chart in the time of Fuxi, even before the ancient times. Now the "already combined positions" that are preserved are still doubted by people, how much more so the "uncombined numbers"? Then how can we know it? The answer is: by exploring its meaning from Confucius' three explanations of the nine trigrams. Therefore, we come to know it. Moreover, the celestial phenomena shown by heaven are orderly like a string of pearls, and any slight error would disrupt the sequence. Therefore, from one to ten thousand, they are connected one after another like beads strung with a thread. Furthermore, if the Dragon Chart was originally combined, the sages would not have seen its image. Therefore, heaven first shows its image in an uncombined form so that the sages can observe it and understand its use. Thus, the Dragon Chart is something that heaven first breaks apart to show people, Fuxi combines it and applies it, while Confucius does not explicitly state it but reveals its meaning.

「始龍圗之未合也，惟五十五數。上二十五，天數也，中貫三五九，外包之十五，盡天三、天五、天九，並十五之位，後形一六無位，又顯二十四之為用也，茲所謂天垂象矣。」

The Dragon Diagram sequence continues to say: At first, when the Dragon Diagram had not yet been completed, there was only the number fifty-five. Above was the number twenty-five, representing the heavenly number; in the middle ran through three, five, and nine, while outside was surrounded by fifteen, thus occupying all the positions of three, five, nine, and fifteen in the heavens; afterwards, the numbers one and six were found to have no place, and then the number twenty-four appeared as a function — this is what is called "the heavens revealing the star patterns."

「下三十，地數也，亦分五位，皆明五之用也。十分而為六，形地之象焉；六分而成四象，地六不配。在上則一不配，形二十四；在下則六不用，亦形二十四。」

The *Longtu Xu* also says: The number thirty below refers to the earth numbers, which are also divided into five positions, all showing the function of the number 'five'. Dividing ten into six parts forms the image of the earth; six is then divided again into four images, and the earth number six has no corresponding match. Above is the number 'one' without a match, showing twenty-four; below is the number 'six' that is not used, also showing twenty-four.

「後既合也，天一居上為道之宗，地六居下為器之本，三乾地二地四為之用（本注：參一三乂天數合九，乾元用九也；兩二四地數合六，坤元用六也）。三若在陽則避孤陰，在陰則避寡陽（本注：成八卦者三位也。上則一三五為三位，二四無中正，不能成卦，為孤陰；下則六八十為三位，七九無中正，不能成卦，為寡陽。三皆不處，若避之也）。大矣哉，龍圗之變，岐分萬塗，今畧述其梗槩焉。」

The Dragon Diagram sequence also says: later, when combined, the number one of the heavenly numbers resides above, becoming the master of the "Dao"; the number six of the earthly numbers resides below, becoming the foundation of the "objects" (things). The number three, together with the second and fourth earthly numbers, fulfills their functions (original note: one and three combine to form nine, which is the "use of all nines" in the Qian trigram; two and four combine to form six, which is the "use of all sixes" in the Kun trigram). The number three, if it is on the yang side, avoids isolated yin; if it is on the yin side, it avoids isolated yang (original note: the three positions that can form the eight trigrams are as follows. The top positions one, three, and five are the three positions; the positions two and four lack the proper central and upright positions, and cannot form trigrams, called "isolated yin." The bottom positions six, eight, and ten are the three positions; the positions seven and nine lack the proper central and upright positions, and cannot form trigrams, called "isolated yang." The number three does not stay on either side, as if avoiding them). How great! The transformation of the Dragon Diagram branches out into countless paths; now we can only roughly outline its main points.

仲尼黙示三陳九卦：履，德之基（《序卦》次十，明用十，示人以辨上下）；謙，德之柄（次十五，明用十五，示人以裒多益寡）；復，德之本（次二十四卦，示氣變之始）；恆，德之固（下經次二卦，示形化之始）。

Confucius' secret revelation of the "Three Presentations and Nine Trigrams" includes: the Guan trigram represents the foundation of virtue (it is the tenth trigram in the "Sequence of Trigrams," indicating the number 'ten,' which guides people to discern the distinction between above and below); the Qian trigram represents the handle of virtue (it is the fifteenth trigram, indicating the number 'fifteen,' which guides people to reduce excess and increase deficiency); the Fu trigram represents the root of virtue (it is the twenty-fourth trigram, showing the beginning of the transformation of qi); the Heng trigram represents the stability of virtue (it is the second trigram in the lower section, showing the beginning of the generation and nurturing of form).

損，德之修；益，德之裕（此二卦示人以盛衰之端）。困，德之辨；井，德之地（此二卦示人以遷通之義）。巽，德之制（巽以行權，權者聖人之大用也，因事制宜、隨時變易之義備矣）。

The hexagram Sun indicates the cultivation of virtue, and the hexagram Yi indicates the abundance of virtue (these two hexagrams indicate the signs of prosperity and decline). The hexagram Gun indicates the discernment of virtue, and the hexagram Jing indicates the place of virtue (these two hexagrams indicate the principles of movement and adaptability). The hexagram Xun indicates the judgment of virtue (Xun is used for flexible action, "flexibility" is the greatest function of the sage, and the meaning of adapting to circumstances and changing with time is fully contained here).

按：李邯鄲淑《書目》有《易龍圗》一卷，陳摶撰，朱子以為假書，其序則錄於《宋文鑑》。劉靜修云：「龍圗之說未必出於劉牧之前。」（牧受能圗於范諤昌，諤昌傳自李溉、許堅，則其書固先牧而出。）呂伯恭從而誤信之，猶張敬夫為戴師愈所欺也。希夷未聞有書。（《宋史·隠逸傳》：陳摶好讀易，著《指玄篇》，言導養及還丹之事，而無所謂龍圗者。）

Hu Wei's commentary: The book "Book Catalogue" by Li Shu of Handan records a one-volume work titled "Yi Longtu," attributed to Chen Tuan. Zhu Xi considered it a forgery, and its preface is included in the "Song Wenjian." Liu Yin (Jingxiu) said: "The idea of 'Longtu' may not have appeared before Liu Mu." (Liu Mu received the Yellow River Chart from Fan Echang, who in turn received it from Li Gai and Xu Jian, so the book "Longtu" originally appeared before Liu Mu.) Lü Zuguan (Bogong) therefore mistakenly believed in it, just like Zhang Xi (Jingfu) was deceived by Dai Shiyu. Chen Tuan was not known to have written any books. (The "Song Shi · Yinyeti Zhuan" records that Chen Tuan liked to read the "Yi," and wrote "Zhi Xuan Pan," which discusses guiding breathing and alchemy, but there was no "Longtu.")

今觀其序之荒謬，則有不可勝言者。未合之數以為探三陳九卦之旨而得之，夫三陳九卦於「河出圗」之義有何干涉？比儗不倫，殊為可笑。

Now looking at the absurdity of that preface, it is simply beyond words. It claims that "the number of uncombined elements" is derived from the meaning of the three teachings and nine trigrams, but how does the three teachings and nine trigrams relate to the meaning of the Yellow River producing a map? This comparison is completely inappropriate and truly laughable.

又云「若龍圗本合，則聖人不得其象，故天必先散而示之」。夫以聖人之智，天即合而示之，聖人豈不能見其所分？且使天合而聖人果不能見其所分，當其散也，聖人又豈能合而用之邪？狂瞽之談，不足深辨。而宋景濂謂「序非圗南不能作」，甚矣儒者之易愚，非獨一呂伯恭也。餘姚黃先生云：「河出未合之圗，聖人合而用之，是伏羲畫卦又畫圗也。」一言破的，此書之偽妄灼然可覩矣。

The preface also says, "If the Dragon Chart was originally closed, the sage would not be able to perceive its image, so heaven must have first scattered it to show people." With the wisdom of a sage, even if heaven had closed it for him to see, could the sage not see how it could be separated? Moreover, if heaven had closed it and the sage truly could not see how to separate it, then when it was scattered, how could the sage use it again? Such reckless and foolish words are not worth discussing in detail. Yet Song Lian (Jinglian) even said, "This preface could not have been written by Chen Tuan (Tunan)." This shows how easily scholars are deceived; not only Lu Zuxian was deceived. Master Huang Zongxi from Yuyao said, "The Yellow River produced an open chart, and the sage later used it to close it again. That would mean Fuxi both drew the trigrams and the chart." With one sentence, he exposed the core issue, making the falseness and absurdity of this book clearly evident.

三陳九卦之義，其有合於龍圗者不可曉。雖然，彼既妄言之，吾不妨妄解之：葢天地未合之數、已合之位，一陳也；龍馬負圗，二陳也，所謂「散而示之」者也；伏羲復位五行生成之數、地上八卦之體，三陳也，所謂「合而用之」者也（詳見後）。仲尼不明言，而於《大傳》三陳九卦以微示其意，故曰「黙而形之」。作偽者之肺腸，容或如此。舊注泥九卦立解，則穿鑿無理甚矣。

The meaning of "San Chen Ji Guà" (Three Arrangements of Nine Trigrams) in relation to the "Longtu" (Dragon Chart) is really unclear. However, since the forgers have said it this way carelessly, I will also explain it carelessly: perhaps the "uncombined numbers" of heaven and earth and the "combined positions" are the first arrangement; the dragon horse carrying the chart out is the second arrangement, which is called "breaking it down to show to people"; and Fuxi reordering the numbers of the Five Phases and the forms of the eight trigrams on earth is the third arrangement, which is called "combining them for application" (see details later). Confucius did not clearly state this, but he mentioned the nine trigrams three times in the "Great Treatise" and subtly revealed this meaning, hence saying "silently shaping it." The forgers' thoughts may be like this. Old interpretations that fixate on the nine trigrams to make their theories are completely forced and meaningless.

《東都事略·儒學傳》：陳摶讀《易》，以數學授穆修，以象學授种放，放授許堅，堅授范諤昌。

The Dongdu Shi Lue: Ru Xu Transmission records that Chen Tuan studied the Zhou Changes, passing on the branch of knowledge concerning numbers to Mu Xiu, and the branch concerning images to Zhong Fang. Zhong Fang then passed it on to Xu Jian, and Xu Jian to Fan Echang. This is the transmission lineage of the scholarly study of the Zhou Changes in the Song dynasty.

按：馬令《南唐書》，許堅不知其家世，或曰晉長史穆之裔。形陋而怪，或寓廬阜白鹿洞，幘巾芒屩，短襴至骭，亦無齎裝，唯自負布囊，常括不解。每沐浴不脫衣，就澗浴，出而暵之。癖嗜魚，得大魚則全體而烹，不加酰鹽，熟而啖之。後或居茅山，或居九華，適意往返，人不能測。舊與錢若水善，若水後因轉挽江南，遇堅於簡寂觀，勉之以仕，則顰蹙不答。堅嘗至陽羨，人不之識。一日涉西津，臨波闊步若平地然，眾始神之，不知其所往雲。此亦是神仙面目，絶無儒者氣象，其自托於希夷之徒，有以也。

Hu Wei said: Ma Ling's "Southern Tang Book" says that Xu Jian's family background is unknown, and some people say he was a descendant of Xu Mu Zhi, a chief of the Eastern Jin Dynasty. He had an ugly and strange appearance. He once lived in the White Deer Cave on Mount Lu, wearing a cloth headscarf and straw shoes, wearing a short robe that only reached his knees, and had no luggage, only carrying a single cloth bag on his back, which was always tied tightly and never untied. Every time he bathed, he would not take off his clothes and go directly to the mountain stream to wash, and after washing, he would let it dry naturally. He had a strong fondness for fish, and when he caught a big fish, he would cook it whole, without adding vinegar or salt, and eat it when it was cooked. Later, he sometimes lived in Mao Mountain and sometimes in Jiuhua Mountain, wandering freely, and others could not understand his whereabouts. In his early years, he was friendly with Qian Ruoshui. Later, Qian Ruoshui was sent to Jiangnan to supervise the transportation of grain, and met Xu Jian at Jianji Guan, and advised him to take up an official post, but Xu Jian only frowned and did not answer. Xu Jian once went to Yangxian, where the local people did not recognize him. One day, he crossed the Xijin River, walking on the waves with large steps, as if walking on flat ground. Everyone then realized that he was extraordinary, and after that, his whereabouts were unknown. This was entirely the appearance of a immortal, with no trace of a Confucian scholar; he claimed to be a disciple of Chen Tuan (Xiyi), which was not without reason.

《宋史·儒林傳》：朱震有《漢上易解》，云：种放以河圗、洛書授李溉，溉傳許堅，堅傳范諤昌，諤昌傳劉牧，牧陳天地五十有五之數。其論圗書授受源委如此，葢莫知其所自雲。

The "Song History · Confucian Scholars Biography" records that Zhu Zhen wrote "Han Shang Yi Jie," in which he says that Zhong Fang passed on the Yellow River Chart and Luo Writing to Li Gai, who passed them on to Xu Jian, who passed them on to Fan Echao, who passed them on to Liu Mu. Liu Mu then deduced the fifty-five numbers of heaven and earth from them. Zhu Zhen's account of the transmission of the Yellow River Chart and Luo Writing is like this, but perhaps even he did not know where this account originally came from.

晁氏《讀書志》：《易證墜簡》一卷，天禧中毘陵從事范諤昌撰，自謂其學出於湓浦李處約、廬陵許堅。（陳氏《書錄解題》又有《易源流圖》一卷。）

Chao Gongwu's "Juzhai Reading Notes" records: "Yizheng Zuijian" in one volume, written by Fan Echang, an official in Piling during the Tianxi period of the Song Zhenzong emperor. He claimed his learning came from Li Chuyue of Penu, and Xu Jian of Luling. (Chen Zhenzun's "Zhaizhai Shulü Jieti" also records Fan Echang's "Yiyuanliutu" in one volume.)

按：《東都事略》言陳摶以象學授种放，放授許堅，象學者，河圗、洛書也。而朱震云：放以圗書授李溉，溉傳許堅，堅傳范諤昌，諤昌傳劉牧。晁公武云：諤昌自謂其學出於李處約、許堅。其說互異。溉與處約不知是一是二，諤昌又不言處約傳自誰氏，中間授受不甚分明，識者疑之。昔孟喜得《易》家候陰陽災變書，詐言師田生且死時枕喜厀，獨傳喜。又蜀人趙賓為《易》，持論巧慧，非古法，雲受孟喜，喜為名之。賓死，喜因不肻仞。（見《漢書·儒林傳》。）葢曲學授受之際，往往多依託隠諱，不可考究。李、許之學自附於种放，其亦田生獨傳孟喜不仞之類乎？

Hu Wei said: The "Eastern Capital Affairs" states that Chen Tuan passed on the "Xiangxue" to Zhong Fang, who passed it on to Xu Jian. The so-called Xiangxue refers to the Yellow River Chart and the Luo Writing. However, Zhu Zhen said that Zhong Fang passed the books to Li Gai, who passed them on to Xu Jian, then to Fan Echang, and finally to Liu Mu. Chao Gongwu also said that Fan Echang claimed his learning came from Li Chuyue and Xu Jian. These three accounts are contradictory. It is unclear whether Li Gai and Li Chuyue are the same person or two different individuals. Furthermore, Fan Echang does not mention from whom Li Chuyue learned his knowledge, so the transmission between generations is not clear. Even discerning people have long been suspicious. In the past, Meng Xi obtained a book on divination and yin-yang omens from the School of Changes, and he falsely claimed that his teacher Tian Wangsun had placed his head on his knee as he was dying, and passed the knowledge solely to him. There was also a man from Shu, Zhao Bin, who studied the School of Changes and presented his arguments in a clever and novel way, which did not conform to ancient methods. He claimed to have learned it from Meng Xi, and Meng Xi even supported him. But after Zhao Bin died, Meng Xi refused to acknowledge this. (See "The Book of Han: The School of Scholars." ) Generally speaking, in the transmission of esoteric learning, there are often fabrications and concealments, making it difficult to investigate. The learning of Li Gai and Xu Jian, who claimed to have inherited from Zhong Fang, might also be a trick similar to Meng Xi's claim of being the sole inheritor of knowledge from Tian Wangsun, which he later denied.

空山雷氏思齊《易圗通變》曰：由漢而唐，《易經》行世，凡經傳疏釋之外，未有及於圗書之文刋列經首者。迨故宋之初，陳摶圗南始創意推明象數，自謂因玩索孔子三陳九卦之義，得其逺旨，新有書述，特稱《龍圗》。離合變通，圗第一為龍馬圗，餘二十是全用《大傳》天地五十有五之數，雜以納甲，貫穿《易》理。內一圗謂形九宮，附一圗謂形洛書者，則盡去其五生數，秖起地六至地十，自釋十為用、十為成形，故《洪範》陳五行之用數語而已。及終其書，再出兩圗：其一形九宮者，元無改異，標為河圗；其一不過盡置列《大傳》五十有五之數於四方及中，而自標異謂為洛書，並無傳例言說。

Lei Siqi, the Dao Ren of Empty Mountain, in his work "The Communication of the Diagrams and Changes of the Book of Changes," said: From the Han dynasty to the Tang dynasty, the Book of Changes was popular in the world, and besides the classic text, the commentary and annotations, there was never any arrangement of the diagrams and writings in the beginning of the text. It was not until the early Song dynasty that Chen Tuan, who was called Tu Nan, began to create a new approach in explaining the images and numbers. He claimed that he had understood the meaning of the three times that Confucius mentioned the nine trigrams in the Great Treatise, and thus grasped the profound meaning. He then wrote a new work, and specially named it "Longtu." In the book, he discussed the combination, separation, and transformation of diagrams. The first diagram was the Dragon Horse Diagram, and the remaining twenty diagrams all used the number fifty-five of heaven and earth mentioned in the Great Treatise, combined with the method of assigning stems, to connect the meaning of the Zhou Changes. One of the diagrams was said to be a depiction of the Nine Palaces, and another was said to be a depiction of the Luo Writing, but he removed all five generating numbers, and only used the numbers from the earth six to the earth ten. He explained that ten was "use" and ten was "taking shape," so the "Discourses of the Duke of Yu" in the Book of Documents only briefly mentioned the use of the Five Phases. At the end of the whole book, there were two more diagrams: one was a depiction of the Nine Palaces, exactly as it was, but labeled as the Yellow River Chart; the other was simply arranging the fifty-five numbers from the Great Treatise in the four directions and the center, but he gave it a new name, the Luo Writing, without any explanation of the traditional system.

圗南之後，种放、許堅、李溉未及見其它有著述。若劉長民所親授之師如范諤昌，所著《大易源流》，其稱龍馬負圗出河，羲皇窮天人之際，復位五行生成之數、地上八卦之體，故老子自西周傳授孔子造《易》之原。天一正北，地二正南，天三正東，地四正西，天五正中央，地六配子，天七配午，地八配卯，天九配酉，地十配中寄於未，乃天地之數五十有五矣。因考其既以圗之前五數置於北南東西之正及中，復以後五數配子午卯酉及中，何也？夫子午卯酉非四方之正邪？地十配中雲寄於未，夫中抑有未邪？諦詳所置之數，正今圗所傳有四方而無四維者。是諤昌元不識圗南所以標異，特因《太玄》準《易》，取於《洪範》一水、二火、三木、四金、五土而然，鑿空無故，造端老子，増立怪論，以實圗南易置二七四九之位耳。

After Chen Tuan, Zhong Fang, Xu Jian, and Li Gai did not leave any other writings. As for Liu Mu (whose courtesy name was Changmin), who directly followed his teacher Fan Echang, in his book "The Origin of the Great Changes," he said: the dragon horse carried a diagram out of the Yellow River, and Fuxi thoroughly examined the relationship between heaven and humanity, reorganized the numbers of the Five Phases' generation and the structure of the eight trigrams on earth. Therefore, Laozi passed on the original principles of the "Zhou Yi" from the Western Zhou dynasty to Confucius. He also said that Tianyi (Heavenly One) is located in the due north, Di'er (Earthly Two) in the due south, Tian San (Heavenly Three) in the due east, Di Si (Earthly Four) in the due west, and Tian Wu (Heavenly Five) in the center. Di Liu (Earthly Six) corresponds to Zi (the rat), Tian Qi (Heavenly Seven) corresponds to Wu (the horse), Di Ba (Earthly Eight) corresponds to Mao (the rabbit), Tian Jiú (Heavenly Nine) corresponds to You (the rooster), and Di Shí (Earthly Ten) corresponds to the center but is assigned to Wei (the sheep). Altogether, these make up fifty-five numbers of heaven and earth. I therefore examined this: since he placed the first five numbers in the four cardinal directions and the center, why did he assign the remaining five numbers to Zi, Wu, Mao, You, and the center again? Are Zi, Wu, Mao, and You not the four cardinal directions? If he says Di Shí corresponds to the center but is "assigned to Wei," does the center have another position called Wei? Upon careful examination of his arrangement, it is exactly the same as the current diagram that has four cardinal directions but no four corners. This shows that Fan Echang completely misunderstood Chen Tuan's original intention. He merely followed Yang Xiong's "Tai Xuan" which compared the "Zhou Yi" and used the "Hong Fan" concept of one water, two fire, three wood, four metal, and five earth. He thus arranged them in the same way. He fabricated a baseless origin, traced the source back to Laozi, and added strange interpretations, merely to confirm Chen Tuan's change of the positions of Erqi (two seven) and Sijiu (four nine).

按：雷氏所言，則似親見《龍圗》之書者，然不著其形象，唯清江張氏《易象圗說》載之頗詳，謹列如左。

Hu Wei said: According to what Lei Siqi said, it seems he had personally seen the original book of the Longtu, but unfortunately he did not draw the shape of the diagram. Only Qingjiang Zhang Li's "Yi Xiang Tu Shuo" provides a fairly detailed account. Here follows a careful listing of it.

右龍圗天地未合之數。張氏曰：上位天數也。天數中於五，分為五位，五五二十有五；積一、三、五、七、九，亦得二十五焉。五位縱橫見三，縱橫見五；三位縱橫見九，縱橫見十五。序言「中貫三五九，外包之十五」者，此也。下位地數也。地數中於六，亦分為五位，五六凡三十；積二、四、六、八、十，亦得三十焉。序言「十分而為六，形地之象」者，此也。

The above is the "Number of Heaven and Earth Not Yet Combined" from the Dragon Diagram. Zhang Li says: The figure above represents the heavenly number. The heavenly number takes five as its center, divided into five positions. Five multiplied by five gives twenty-five; adding one, three, five, seven, and nine together also results in twenty-five. Five positions arranged in rows and columns show three, and arranged in rows and columns show five. Three positions arranged in rows and columns show nine, and arranged in rows and columns show fifteen. The "middle passes through three, five, and nine, and the outer encompasses fifteen" mentioned in the "Preface to the Dragon Diagram" refers to this. The figure below represents the earthly number. The earthly number takes six as its center, also divided into five positions. Five multiplied by six gives thirty; adding two, four, six, eight, and ten together also results in thirty. The "ten parts into six, forming the shape of the earth" mentioned in the "Preface to the Dragon Diagram" refers to this.

古龍圗天地已合之位。張氏曰：上位象也。合一、三、五為參天，偶二、四為兩地，積之凡十五，五行之生數也。即前象上五位：上五去四得一，下五去三得二，右五去二得三，左五去一得四，惟中□不動。序言「天一居上，為道之宗」者，此也。案《律歴志》云「合二始以定剛柔」，一者陽之始，二者陰之始。今則此圗，其上天○者，一之象也；其下地□者，之象也；其中天□者，四象五行也。左上一○太陽，為火之象；左上一○少陰，為金之象；左下一○少陽，為木之象；右下一○太陰，為水之象。土者，沖氣居中，以運四方，暢始施生，亦陰亦陽。右旁□三才之象，卦之所以畫三；左旁□四時之象，蓍之所以揲四。是故上象一二三四者，蓍數卦爻之體也。

This is the Dragon Diagram "the position where heaven and earth are united." Zhang Li says: the figure above refers to "the image." Combining the three odd numbers one, three, and five is called "ascending to heaven," while combining the two even numbers two and four is called "united earth." Adding them together gives fifteen, which is the generating numbers of the Five Phases. This corresponds to the five positions above the previous diagram: the five at the top minus four gives one, the five at the bottom minus three gives two, the five on the right minus two gives three, the five on the left minus one gives four, and only the center remains unchanged. The "heavenly one resides above, as the origin of the Dao" mentioned in the "Preface to the Dragon Diagram" refers to this. According to the "Book of Han · Laws and Calendars," it says "combine the two beginnings to determine hardness and softness." One is the beginning of yang, and two is the beginning of yin. Now looking at this diagram, the circle above belongs to heaven and represents the image of one; the square below belongs to earth and represents the image of two; the center square belongs to heaven and represents the four images and five phases. The circle above on the left represents the sun, symbolizing fire; the circle above on the left represents the lesser yin, symbolizing metal; the circle below on the left represents the lesser yang, symbolizing wood; the circle below on the right represents the great yin, symbolizing water. Earth is the harmonious qi in the center, used to transform the four directions, promote vitality, and distribute nourishment. It is both yin and yang. The square on the right represents the three elements, so the hexagram is drawn with three lines; the square on the left represents the four seasons, so divination with yarrow stalks counts four stalks at a time. Therefore, the numbers one, two, three, and four above represent the "body" of the yarrow stalks and the lines of the hexagram.

下位形也。九、八、七、六，金木水火之成數，中見地十土之成數也。即前象下五位，以中六分開，置一在上六而成七，置二在左六而成八，置三在右六而成九，惟下六不配而自為六。序言「六分而成四象，地六不配」者，此也。案七者蓍之圎，七七而四十有九；八者卦之方，八八而六十有四；九者陽之用，陽爻百九十二；六者陰之用，陰爻亦百九十二；十者大衍之數，以五乘十，以十乘五，而亦皆得五十焉。是故下形六七八九者，蓍數卦爻之用也。上體而下用，上象而下形，象動形靜，體立用行，而造化不可勝既矣。

The next part discusses "form." The numbers nine, eight, seven, and six represent the completed numbers of metal, wood, water, and fire respectively. In the middle, the number ten appears, which is the completed number of earth. This refers to the five positions below the previous diagram: by separating the six in the center, placing one on top of the six makes seven, placing two on the left of the six makes eight, placing three on the right of the six makes nine. Only the six at the bottom does not combine with other numbers and remains as six on its own. The "Dragon Diagram Preface" says, "Six divides into the four images, and the earth six does not combine," referring to this. Note: Seven is the circular number of the divining stalks; seven times seven equals forty-nine. Eight is the square number of the hexagram; eight times eight equals sixty-four. Nine is the function of yang; the total number of yang lines is one hundred ninety-two. Six is the function of yin; the total number of yin lines is also one hundred ninety-two. Ten is the number of the great derivation; five times ten and ten times five both result in fifty. Therefore, the six, seven, eight, and nine below represent the "function" of the divining stalks and the lines of the hexagram. The upper part is the body and the lower part is the function; the upper part is the image and the lower part is the form. The image initiates action while the form is static. Once the body is established, the function operates, thus the subtlety of creation is endless.

案：一二三四，天之象，象變於上；六七八九，地之形，形成於下。上下相重而為五行，則左右前後生成之位是也；上下相交而為八卦，則四正四隅九宮之位是也。今以前後圗參考，當如太乙遁甲陰陽二局圗：一二三四猶遁甲天盤在上，隨時運轉；六七八九猶遁甲地盤在下，布定不易。法明天動地靜之義，而前此諸儒未有能發其旨。

Zhang Li also explained: one, two, three, and four are the images of heaven, changing above; six, seven, eight, and nine are the forms of earth, solidifying below. The upper and lower layers combined form the Five Phases, which correspond to the positions where the generating numbers and the productive numbers are paired left, right, front, and back. The upper and lower layers interwoven form the Eight Trigrams, which correspond to the positions of the four cardinal directions and four intermediate directions in the nine palaces. Now, by comparing the front and back diagrams, it should be like the diagram of Taiyi Dunjia with yin and yang: one, two, three, and four are like the Heaven Plate of Dunjia above, moving with the sequence of time; six, seven, eight, and nine are like the Earth Plate of Dunjia below, fixed and unmoving. This method explains the principle of heaven moving and earth still, and none of the previous scholars among the Confucianists could grasp its meaning.

是故一在南，起法天象，動而右轉。初交，一居東南，二居西北，三居西南，四居東北，四陽班布居上右，四陰班布居下左，分陰分陽而天地設位。再交，一居東北，二居西南，三居東南，四居西北，則牝牡相銜而六子卦生。合是二變，而成先天八卦自然之象也。然後重為生成之位，則一六、二七、三八、四九陰陽各相配合，即邵子、朱子所述之圗也。三交，一居西北，二居東南，三居東北，四居西南，則剛柔相錯而為坎離震兊。四交，一居西南，二居東北，三居西北，四居東南，則右陽左陰而乾坤成列。合是二變，而成後天八卦裁成之位也。再轉則一復於南矣。《大傳》所謂「參伍以變，錯綜其數」，劉歆云「河圗洛書相為經緯，八卦九章相為表裡」，此其義也。

Therefore, the trigrams begin in the south, following the celestial patterns, moving and rotating to the right. The first transformation leads one to the southeast, two to the northwest, three to the southwest, and four to the northeast. The four yang numbers are arranged above and to the right, while the four yin numbers are placed below and to the left. Yin and yang are thus divided, and heaven and earth each take their proper positions. The second transformation leads one to the northeast, two to the southwest, three to the southeast, and four to the northwest. Thus, the male and female elements connect, and the six trigrams of Zhen, Kan, Gen, Xun, Li, and Dui are formed. Combining these two transformations, the natural appearance of the Earlier Heaven Trigrams is established. Then, by stacking them into the positions of generation, one and six, two and seven, three and eight, four and nine, yin and yang are paired accordingly, as described by Shao Yong and Zhu Xi in their diagram. The third transformation leads one to the northwest, two to the southeast, three to the northeast, and four to the southwest, resulting in the intermingling of firm and yielding elements to form Kan, Li, Zhen, and Dui. The fourth transformation leads one to the southwest, two to the northeast, three to the northwest, and four to the southeast, resulting in right yang and left yin, and the trigrams Qian and Kun being arranged in order. Combining these two transformations, the positions of the Later Heaven Trigrams are established. If the rotation continues, one returns again to the south. The "Great Treatise" says, "By combining three and five, transformations occur, and numbers are interwoven." Liu Xin says, "The Yellow River Chart and the Luo Writing form the meridians and parallels, while the Eight Trigrams and the Nine Chapters form the inside and outside." This is precisely the meaning.

右龍圗天地生成之數。張氏曰：此即前圗一二三四，天之象也，動而右旋；六七八九，地之形也，靜而正位。是故一轉居北而與六合，二轉居南而與七合，三轉居東而與八合，四轉居西而與九合，五十居中而為天地運行之樞紐。《大傳》言「錯綜其數」者，葢指此而言。錯者，交而互之，一左一右，三四往來是也；綜者，總而挈之，一低一昂，一二上下是也。分作二層看之，則天動地靜上下之義昭然矣。

The above is the Dragon Figure "The Number of Heaven and Earth Generating Each Other." Zhang Li says: This represents the numbers one, two, three, and four from the previous diagram, which belong to the heavenly aspect, moving and rotating to the right. The numbers six, seven, eight, and nine belong to the earthly aspect, being still and each occupying its proper position. Therefore, one moves to the north and combines with six, two moves to the south and combines with seven, three moves to the east and combines with eight, and four moves to the west and combines with nine. Five and ten are in the center, becoming the pivot of the movement of heaven and earth. The "错综其数" mentioned in the Great Treatise probably refers to this. "错" means crossing and exchanging; one on the left and one on the right, with three and four exchanging places. "综" means comprehending and lifting up; one low and one high, with one and two stacked vertically. If we divide it into upper and lower layers, the meaning of heaven moving and earth still, with the upper part representing the principle and the lower part the application, becomes clear at a glance.

右河洛縱橫十五之象。張氏曰：《洪範》「初一曰五行，次二曰敬用五事，次三曰農用八政，次四曰協用五紀，次五曰建用皇極，次六曰又用三德，次七曰明用稽疑，次八曰念用庶徵，次九曰向用五福、威用六極」，漢儒以此六十五字為洛書本文。而希夷所傳，則以此為龍圗三變，以生成圗為洛書本文，葢疑傳寫之誤而啟圗九書十之辨。今以二象兩易其名，則龍圗龜書不煩擬議而自明矣。

The above is the "cross and vertical fifteen forms" of the River Chart and the Lo Book. Zhang Li said: "The first of the nine sections in the 'Book of Documents: Hongfan' is the Five Phases, the second is the use of five things with reverence, the third is the use of eight administrative measures in agriculture, the fourth is the coordination with five celestial phenomena, the fifth is the establishment of the supreme principle, the sixth is the use of three virtues again, the seventh is the use of inquiry to resolve doubts, the eighth is the use of various signs with careful consideration, and the ninth is the use of five blessings and the use of six calamities." These sixty-five characters were considered by Han dynasty Confucian scholars to be the original text of the Lo Book. However, Chen Tuan (Xiyi) passed down a different interpretation, treating this diagram as the third transformation of the Dragon Chart, and instead regarded the diagram of generation as the original text of the Lo Book. This was probably due to his suspicion that there were errors in transmission, thus giving rise to the debate over "the River Chart has nine and the Lo Book has ten." Now, if we simply exchange the names of these two diagrams, then the Dragon Chart and the Tortoise Book no longer need to be discussed at length, and their distinctions will become clear naturally.

按：以上四圗並見《易象圗說》內篇，清江張理仲純所著也。其第一為天地未合之數，上位以五五為天數二十有五，下位以五六為地數三十，葢漢《律歴志》云「天之中數五，地之中數六」，故依託為此圗也。第二為天地已合之位，上位一上、二下、四左、三右、五居其中，即劉牧所謂上下未交之象也。及其已交，則天一下生地六，地二上生天七，天三左生（天地未合之數，一變也；已合之位，二變也；龍馬負圗，三變也）地八，地四右生天九，故下位六七八九十皆以生數乘中五而得之，即劉牧之洛書五行成數也。其縱橫十五之象，本龍圗三變，劉牧所謂龍馬負圗是也，雷氏以為河圗，張氏易其名曰洛書；天地生成之數，即范諤昌所謂羲皇復位五行生成之數、地上八卦之體者也，雷氏以為洛書，張氏易其名曰河圗。

Hu Wei said: The above four diagrams are all found in the Inner Part of "Yi Xiang Tu Shuo," written by Zhang Li, a man from Qingjiang, whose name is Zhongchun. The first diagram is called "the number before heaven and earth are combined." The upper part uses five fives to represent the heavenly number, totaling twenty-five, while the lower part uses five sixes to represent the earthly number, totaling thirty. This is probably based on the statement in the "Hanshu · Lüli Zhì" that "the central number of heaven is five, and the central number of earth is six," and thus this diagram was created by relying on these two sentences. The second diagram is called "the position after heaven and earth have combined." The upper part has one at the top, two at the bottom, four on the left, three on the right, and five in the center, which is the image of "heaven and earth not yet intersecting" as Liu Mu described. When they have intersected, heaven one gives birth to earth six, earth two gives birth to heaven seven, heaven three gives birth to earth eight, and earth four gives birth to heaven nine. Therefore, the numbers six, seven, eight, nine, and ten in the lower part are obtained by multiplying the generating numbers by the central number five. This is the five generating numbers of the Five Phases as described by Liu Mu in the Luo Shu. As for the "image of fifteen in both horizontal and vertical directions," it originally is the third transformation of the Longtu, that is, the Longma Fu Tu described by Liu Mu. Lei Siqi considered it to be the Hetu, but Zhang Li changed its name to Luo Shu. The "number of heaven and earth generating each other" is the diagram that Fan Ech Chang mentioned as "Fu Xi reordering the numbers of the Five Phases and the forms of the eight trigrams on the earth." Lei Siqi considered it to be the Luo Shu, but Zhang Li changed its name to the He Tu.

今考之本書，縱橫十五之象，九數各居一位，故序曰「天散而示之」；天地生成之數，一六、二七、三八、四九、五十皆耦居一方，故序曰「伏羲合而用之」。河圗之數四十有五，洛書五十有五，本象元自如此。張氏宗《啟蒙》，恐啟圗九書十之辨，故疑為傳寫之誤而兩易其名。然劉牧師范諤昌，諤昌師李溉、許堅，三傳弟子，一脈相承，使圗書果如張氏所列，而牧輒兩易之，是入室而操戈也，其何以取信於當世而學者翕然宗之乎？西山謂圗九書十出於劉牧之意見，非也，而張氏宗之亦過矣。

Now examining the book of the Dragon Chart: the image consists of fifteen rows and columns, with nine numbers each occupying a position, so the "Preface to the Dragon Chart" says "Heaven scatters and reveals it." The numbers of heaven and earth generating the numbers one and six, two and seven, three and eight, four and nine, five and ten are paired and reside in the same area, so the "Preface to the Dragon Chart" says "Fuxi combined and used them." The numbers of the Yellow River Chart total forty-five, and the numbers of the Luo Writing total fifty-five, and these two images have always been like this. Zhang Li respects Zhu Xi's "Awakening to the Study of Changes," fearing the controversy of "the Yellow River Chart has nine numbers, the Luo Writing has ten numbers," so he suspects it is a mistake in copying and swaps the names of the two. However, Liu Mu studied under Fan Echang, who studied under Li Gai and Xu Jian, and the disciples passed down through three generations in a continuous line. If the Yellow River Chart and Luo Writing were indeed arranged as Zhang Li proposed, and Liu Mu still swapped them, then he would be reversing the order and using the teacher's weapons against the teacher. Then on what basis could he gain the trust of the contemporary world and have scholars universally follow him? Cai Yuanding (Xishan) said that "the Yellow River Chart has nine numbers, the Luo Writing has ten numbers" comes from Liu Mu's personal speculation, which is incorrect; and Zhang Li following this view is also excessive.

易圗以白為陽、黑為陰，自《參同》水火匡廓始，其後先天太極圗亦然。而《龍圗》則獨用奇白偶黑之點，序曰「天之垂象，的如貫珠」，自一至於盈萬，皆累累然如繫之於縷也。因於點間為墨絲以聮絡之，使若貫珠然，思之可發一笑。前此未有此狀，圗出希夷之後，是亦一證也。雷氏不知《龍圗》源出湓廬，非華山道士所作，故以為希夷必不如此，而歸其罪於諤昌，此亦莫須有之獄。至以復位五行生成之數為老子自西周傳孔子，不知出何典記，鑿空造端，増立怪論，誠有如雷氏所譏者，諤昌直一妄人耳。語曰「不知其形視其景」，景曲則形必曲，觀諤昌之言，則李、許之為人從可知矣。

The diagram of the I Ching uses white dots for yang and black dots for yin, a practice that began with the Water and Fire Enclosure Diagram from the "Zhou Yi Cang Tong Qi" and continued in the Earlier Heaven Taiji Diagram. However, the "Longtu" uses only odd numbers of white dots and even numbers of black dots. The "Longtu Xu" says, "The heavens manifest their signs, clear as beads strung on a thread," from one end to the other, densely arranged as if strung on a single thread. Therefore, lines were drawn between the dots with ink to connect them, making them look like a string of beads. This is truly amusing. Before this, there was no such style, indicating that this diagram came after Chen Tuan. This is another piece of evidence. Lei Siqi did not know that the "Longtu" originated from the lineage of Pengpu and Luling, not from Chen Tuan, a Taoist priest from Huashan. Therefore, he concluded that Chen Tuan would never have done such a thing, and blamed Fan Echang entirely. This is another case of an unjust accusation without evidence. As for claiming that "rearranging the numbers of the Five Phases" was passed down from Laozi to Confucius from the Western Zhou dynasty, there is no source in any classic to support this. This is indeed, as Lei Siqi mocked, a fabrication by a foolish person. As the saying goes, "If you don't know the shape, look at its shadow." If the shadow is curved, the shape must be curved. Looking at Fan Echang's remarks, one can easily imagine the character of Li Gai and Xu Jian.

右論龍圗。

The above is part of the examination and verification of the authenticity of the book "Longtu."

三衢劉氏牧《鉤隠圗序》曰：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。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。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《繫辭》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，點之成圗，於逐圗下各釋其義，庶覽之者易曉耳。夫《易》道淵邈，雖往哲難窺於至賾，牧也蕞生祖述，誠媿其狂簡，然象有定位，變有定數，不能妄為之穿鑿耳，博雅君子試為詳焉。

Three衢 person Liu Mu, in his "Preface to the Diagrams of the Numbers in the Book of Changes," says: The so-called "Book of Changes" discusses the mutual interaction of yin and yang energies. If yin and yang do not interact, the four images cannot be established; if the eight trigrams are not differentiated, how could all things come into being? Therefore, the two principles (yin and yang) change to produce the four images, the four images change to produce the eight trigrams, and the eight trigrams overlap to form the sixty-four trigrams, thus encompassing all things and principles under heaven. The trigrams are established by the sages, derived from observing physical phenomena; the images are the responses of the transcendent. Tracing back to its origin, form arises from the images, and the images are determined by numbers. Without numbers, one cannot see the origin of the four images. Therefore, Confucius praised the "Book of Changes," necessarily citing the extreme numbers of heaven and earth to explain the principle of "producing change and acting like ghosts and spirits." This shows that the "Book of Changes" must be thoroughly studied in terms of numbers to understand its fundamental nature. Looking closely at the commentaries and annotations by scholars throughout history, they are indeed detailed and precise in distinguishing the text and analyzing the meaning; but when it comes to explaining the numbers of heaven and earth, they are vague and do not match the "Great Treatise," making it difficult for scholars to grasp the meaning. Now I have collected the odd and even numbers of heaven and earth, starting from the generation of the Taiji into the two principles, down to the Fu trigram, totaling fifty-five positions. I have drawn diagrams, and for each diagram, I have explained its meaning, hoping that readers will find it easy to understand. The way of the "Book of Changes" is profound; even the sages of previous generations found it difficult to reach its deepest aspects. I, Liu Mu, a humble person, dare to trace back and follow in the footsteps of the ancients, and I feel deeply ashamed of my own simplicity and lack of caution. However, the images have fixed directions, and changes have fixed numbers; I have not fabricated or invented them at will. I humbly request that learned and refined gentlemen examine and verify my work carefully.

晁氏《讀書志》曰：《易解》十五卷，劉牧長民撰。仁宗時，言數者皆宗之。慶歴初，吳秘獻其書於朝，優詔奬之，田況為序。又有《鉤隠圗》三卷，皆《易》之數也，凡五十五圗，並《遺事》九，有歐陽永叔序，而其文殊不類。

Chao Gongwu in "Juzhai Reading Notes" says: "The "Yi Xie" consists of fifteen volumes, written by Liu Mu (style name Changmin). During the reign of Emperor Renzong of the Song dynasty, those who discussed the principles of figures and numbers all held him in high esteem. In the early years of the Qingle era, Wu Mi presented this book to the court, and Emperor Renzong issued a commendatory edict. Tian Kuang wrote a preface for it. Liu Mu also wrote "Yi Shu Gou Yin Tu" in three volumes, which discusses the numbers of the "Zhou Yi", containing fifty-five diagrams, plus "Yi Wei Shi" with nine sections. The beginning of the volume has a preface by Ouyang Xiu (style name Yongshu), but the style of the text does not resemble Ouyang Xiu's handwriting."

渭按：歐公與劉牧同時，位尊望重，不信圗書，乃祖述《鉤隠》者之所憂，故其序託名歐公以欺世。千載而下，黨同作偽者之肺肝，猶如見之也。

Hu Wei said: Ouyang Xiu and Liu Mu were contemporaries, holding high positions and enjoying great prestige, yet they did not believe in the Yellow River Chart and the Luo Writing. This was precisely what those who followed the "Yi Shu Gou Yin Tu" were worried about. Therefore, that preface falsely attributed to Ouyang Xiu in order to deceive the world. A thousand years later, the hearts and minds of those who formed factions, fabricated texts, and conspired still appear as clearly as if seen with one's own eyes.

三百年來，學者唯知有《本義》卷首所列之圗書，而不復問其原委，故餘詳考《龍圗》及《鉤隠》，以著謬種所自出，使學者參觀而猛省焉，非為其有當於聖人之《易》而錄之也。

For three hundred years, scholars have only known the two diagrams of the Yellow River Chart and the Luo Writing listed at the beginning of Zhu Xi's The Original Meaning of the Zhou Changes, but they no longer inquire into their origins. Therefore, I have carefully examined The Dragon Diagram and The Hidden Numbers of the Zhou Changes to reveal the source of this absurd origin, so that scholars may compare and see it suddenly with clarity; it is not because they conform to the sage's Zhou Changes that they are included.

劉氏曰：昔虙犧氏之有天下，感龍馬之瑞，負天地之數出於河，是為龍圗者也。戴九履一，左三右七，二與四為肩，六與八為足，五為腹心，縱橫數之皆十五，葢《易繫》所謂「參伍以變，錯綜其數」者也。太皥乃則而象之，遂因四正定五行之數。以陽氣肇於建子，為發生之源；陰氣萌於建午，為肅殺之基。二氣交通，然後變化，所以生萬物焉、殺萬物焉。且天一生坎，地二生離，天三處震，地四居兊，天五由中，此五行之生數也。且孤陰不生，獨陽不發，故子配地六，午配天七，卯配地八，酉配天九，中配地十。既極五行之成數，遂定八卦之象，因而重之，以成六十四卦、三百八十四爻，此聖人設卦觀象之奧旨也。

Liu Mu said: In ancient times, when Fuxi ruled the world, he was inspired by the auspicious omen of the dragon horse. The dragon horse emerged from the Yellow River bearing the numbers of heaven and earth, which is called the Dragon Diagram. Its head was adorned with nine, its feet with one, its left side with three, and its right side with seven. The numbers two and four were on its shoulders, six and eight on its feet, and five in the center of its body. When added vertically and horizontally, they all totaled fifteen. This is what the Great Treatise refers to as "three and five intermingling to produce change, and their numbers being interwoven." Fuxi then took inspiration from it and established the numbers of the Five Phases according to the four cardinal directions. Because yang energy begins in the first month of the rat (Jian Zi), which is the source of all things; and yin energy begins in the seventh month of the horse (Jian Wu), which is the basis for the withering of all things. The interaction of these two energies leads to transformation, thus enabling the generation and nurturing of all things, as well as their destruction. Furthermore, the first heavenly number is Kan (Water), the second earthly number is Li (Fire), the third heavenly number is Zhen (Thunder), the fourth earthly number is Dui (Lake), and the fifth heavenly number is in the center. These are the generating numbers of the Five Phases. Moreover, isolated yin cannot produce life, and isolated yang cannot develop. Therefore, the hour of Zi (rat) is paired with the number six on earth, the hour of Wu (horse) with seven on heaven, the hour of Mao (rabbit) with eight on earth, the hour of You (rooster) with nine on heaven, and the center is paired with ten on earth. Once the numbers of the Five Phases are fully established, the images of the Eight Trigrams are determined. These trigrams are then overlapped to form the sixty-four hexagrams and the 384 lines, which is the profound meaning of the sages' method of setting up hexagrams and observing their images.

今龍圗其位有九，四象八卦皆所包蘊，且其圗縱橫皆合天地自然之數，則非後人能假偽而設之也。

Now this dragon diagram has nine positions, encompassing the four symbols and the eight trigrams. Moreover, both its horizontal and vertical additions conform to the natural numbers of heaven and earth. Clearly, it could not have been fabricated by later people.

河圖兩儀（此即龍圖天地已合之上位而虛其中也）。河圖四象（此即龍圖天地已合之下位而虛其中也）。河圖八卦（關子明則圖畫卦之說與此無異）。

The Yellow River Chart two principles diagram (this is the upper part of the Dragon Diagram "the position where heaven and earth have already joined," but with the middle left empty). The Yellow River Chart four images diagram (this is the lower part of the Dragon Diagram "the position where heaven and earth have already joined," also with the middle left empty). The Yellow River Chart Eight Trigrams diagram (Guan Lang, whose courtesy name is Ziming, followed the method of drawing trigrams based on the Yellow River Chart, and this diagram is essentially the same as this one).

劉氏曰：原夫八卦之宗，起於四象。四象者，五行之成數也。水數六，除三畫為坎，餘三畫布於亥上成乾；金數九，除三畫為兊，餘六畫布於申上成坤；火數七，除三畫為離，餘四畫布於已上成巽；木數八，除三畫為震，餘五畫布於寅上成艮。此所謂四象生八卦也。

Liu Mu said: Investigating the origin of the Eight Trigrams, they arise from the Four Symbols. The Four Symbols refer to the completed numbers of the Five Phases. The number for water is six; subtracting three lines for the Kan trigram, the remaining three lines are arranged at the亥 position to form the Qian trigram; the number for metal is nine; subtracting three lines for the Dui trigram, the remaining six lines are arranged at the申 position to form the Kun trigram; the number for fire is seven; subtracting three lines for the Li trigram, the remaining four lines are arranged at the巳 position to form the Xun trigram; the number for wood is eight; subtracting three lines for the Zhen trigram, the remaining five lines are arranged at the寅 position to form the Gen trigram. This is what is called "the Four Symbols give birth to the Eight Trigrams."

雷氏《易圗通變》曰：究核諤昌之取用，不過循納甲之緒餘，及五子歸庚之殊向，又謂天上八卦，坎離對中之外，移置乾兊坤於東，艮震巽於西。不謂五行之說多起於《易》後，而反引五行以為定卦之原，此又其敢於創異之大端也。是宜長民不獨増以五十五圗，又因諤昌坎離震兊四正之外，而以四成數同於四方，謂坎六退本卦三數，以餘三數三畫為乾；離七退本卦三數，以餘四數四畫為巽；震八退本卦三數，以餘五數五畫為艮；兊九退本卦三數，以餘六數六畫為坤，皆以數為畫，標為河圗，是不揣本而齊末。夫八卦各三畫，以剛柔生爻，未聞本卦止用三畫，而以其餘畫之多反分為別卦也。所陳之數抑配偶然，且以坎離震兊為四象，則尤非也。象本在未成卦之先，故曰四象生八卦也。

Lei Siqi in his book "Yitu Tongbian" says: Upon careful examination, what Fan Echang used was merely following the remnants of the Najia system and another peculiar approach called "Wu Zi Gui Geng." He also spoke of heavenly trigrams, placing Kan and Li in the center facing each other, while moving Qian and Dui to the east and Gen, Zhen, and Xun to the west. He did not consider that the theory of the Five Phases mostly emerged after the Zhou Yi, yet he used the Five Phases as the fundamental principle for determining the hexagrams, which was one of his bold innovations. It's no wonder Liu Mu not only added fifty-five diagrams but also followed Fan Echang's idea of placing Kan, Li, Zhen, and Dui in the four cardinal directions, assigning the four completed numbers to the four directions. He said that Kan six subtracts the three numbers from the original hexagram, using the remaining three numbers and three lines to form Qian; Li seven subtracts the three numbers from the original hexagram, using the remaining four numbers and four lines to form Xun; Zhen eight subtracts the three numbers from the original hexagram, using the remaining five numbers and five lines to form Gen; Dui nine subtracts the three numbers from the original hexagram, using the remaining six numbers and six lines to form Kun. He used numbers to represent lines and called it the Yellow River Chart, which was not considering the fundamental principles but only seeking to make the details neat. Each trigram has three lines, which are generated by the combination of yin and yang. There is no record of using only three lines for the original hexagram, yet he separated the extra lines into other hexagrams. The numbers he presented were merely forced together. Moreover, by treating Kan, Li, Zhen, and Dui as the Four Symbols, he made an even greater mistake. The images originally existed before the hexagrams were formed, so the Great Treatise says, "The Four Symbols give rise to the Eight Trigrams."

按：希夷天地自然之圗宗《參同契》，用乾南坤北、離東坎西之位，而《鉤隠》仍以坎離震兊居四正，乾坤艮巽居四隅，即此一端，亦足以證《龍圗》之本不出於希夷矣。

Hu Wei remarked: Chen Tuan (Xiyi) 's "Diagram of Heaven and Earth in their Natural State" followed the "Threefold Concordance" of the Zhou Changes, adopting the orientation of Qian in the south, Kun in the north, Li in the east, and Kan in the west. However, the "Diagram of Hidden Calculations of the Changes" still placed Kan, Li, Zhen, and Dui in the four cardinal directions, and Qian, Kun, Gen, and Xun in the four corners. Based on this alone, it is sufficient to prove that the "Dragon Diagram" was not originally created by Chen Tuan.

洛書五行生數。洛書五行成數（以上二圖合之，即是羲皇復位五行生成之數）。

The Luo Writing Five Phases Generating Numbers Diagram. The Luo Writing Five Phases Forming Numbers Diagram (the above two diagrams together are the Five Phases Generating Numbers as reorganized by Fuxi according to Fan Echanghai's account).

劉氏曰：或問：洛書一曰水，二曰火，三曰木，四曰金，五曰土，則與龍圗五行之數之位不偶者何也？答曰：此謂陳其生數也。雖則陳其生數，乃是已交之數，下篇分土王四季，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。

Liu Mu said: Someone asked: The Luo Writing says "one is water, two is fire, three is wood, four is metal, five is earth," but this does not match the positions of the five elements' numbers in the Dragon Figure. Why is that? The answer is: Here it refers to the arrangement of the initial numbers. Although these are initial numbers, they are already numbers after yin and yang have combined; in the next section, which discusses the rule of earth over the four seasons, the completed numbers are supplemented. Moreover, the nine categories of the Luo Writing are derived from the numbers of the five elements, so first arranging the initial numbers that have already combined yin and yang, and then supplementing with the numbers of earth, allows one to see the completed numbers.

《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，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「鯀無聖德，汨陳五行，是以彝倫攸斁」，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，猶龍圗止負四象八純之卦，餘重卦六十四皆伏羲仰觀俯察，象其物宜，伸之以爻象也。或曰：既云龍圗兼五行，則五行已具於龍圗矣，不應更用龜書也。答曰：雖兼五行，有中位而無土數，惟四十有五，是有其象而未著其形也，唯四象八卦之義耳；龜書乃具生成之數五十有五矣。《易》者包象與數，故聖人資圗書而作之也。

Liu Mu also said: The nine categories in the "Nine Categories" of the "Book of Documents: Hongfan" only the category of the Five Phases contains the natural numbers of heaven and earth. The other eight categories were classified and developed by Da Yu according to the heavenly timing and human affairs, and they were not originally on the turtle's back. Looking closely at the "Hongfan Wu Xing Zhuan," whenever it discusses calamities and anomalies, it always traces back to the Five Phases. For example, "Gun lacked virtue and recklessly manipulated the Five Phases, thus causing the constant decline of the way." This shows that the Five Phases are the natural numbers revealed by heaven. This passage is what the divine turtle carried, while the other eight categories were elaborated by Da Yu. This is like the Dragon Chart which only carries 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, imitating the suitability of all things, and using the yao symbols to elaborate further. Someone asked: If the Dragon Chart includes the Five Phases, then the Five Phases are already contained within the Dragon Chart, so why use the turtle script? The answer is: Although the Dragon Chart includes the Five Phases, it only has the central position and lacks the earth numbers, making the total number forty-five. This is having the image but not the form, possessing only the meaning of the Four Symbols and the Eight Trigrams. The turtle script fully contains the generating numbers, fifty-five in total. The "Zhou Yi" includes both the images and numbers, so the sages created it based on the Yellow River Chart and the Luo Writing.

雷氏《易圗通變》曰：書之九疇，各疇自有成數，如一五行、二五事，猶或得以其數從而強推引之；至於五皇極，則已不可指實之為何物何事，而甚則九五福而附以六極，則將計九乎？計五福而兼計六極乎？皇極謂大中，而六極者，其極又可謂中乎？皇極本非物非事，故可指之為中，今徒實以五點，而五點者乃遂得為中乎？疇自一至九，界界然各存本有之數，不知何自而可以合於五十有五之數，強謂合者，葢其人之妄也。若其後而至於以書謂圗、以圗謂書者，又妄人中之妄人也。此餘特謂圗則有數可通，而書則有疇類可數，而不可布之以為圗也。

Lei Siqi in "Yi Tu Tong Bian" says: The nine categories of the "Hong Fan" each have their own fixed numbers. For example, the first category is the Five Phases, the second is the Five Affairs, and perhaps one can roughly infer them by their numbers. However, the fifth category, the Great Center, is already unclear as to what it refers to, whether it is an object or an event. Even more serious is the ninth category, which talks about the Five Blessings and adds the Six Extremes. Should this be counted as nine, or as five blessings plus six extremes? The meaning of "Great Center" is "Great Center," but the "extreme" in "Six Extremes," can it also be called "Center"? Originally, the Great Center was neither an object nor an event, so it could be called "Center." Now, however, people force it to be represented by five points. Can five points be called "Center"? The nine categories, from one to nine, each have clear original numbers. But how can they be combined to make fifty-five? To say they can be combined is the delusion of the person. Even worse, later people have confused the Luo Book with the Yellow River Chart and the Yellow River Chart with the Luo Book. These are the delusions of deluded people. Therefore, I specially say: the Yellow River Chart has numbers that can be connected, but the Luo Book can only be counted in categories, and cannot be arranged into a diagram.

按：劉牧謂洛書與河圗並出於伏羲之世，兼則之以畫卦，而五行之數未顯，故禹復法之以陳九疇。然一為五行，二為五事，以至九十為福極，禹何以知之？故又為之說曰「惟五行是天垂自然之數，餘八者皆禹自類之」，意謂五事以下禹從五行推演而得之也。然五事、皇極、庶徵、五福、六極，劉向嘗以此附會於五行，猶可通也，其餘則絶無交涉矣。六十四卦不離乎八卦，河圗具八卦之象，則六十四卦包在其中；若九疇五事以下，未見五行中具有此義也。禹乃鑿空而増之，以綴於五行之後，則幾同駢拇枝指矣，是亦不可以已乎？且經云「天錫禹九疇」，不言「錫禹五行」，九疇皆天之所設，非人之所為，謂八者禹自類之，妄也。

Hu Wei said: Liu Mu believed that the Luo Writing and the Yellow River Chart both originated in the time of Fuxi, and Fuxi combined both to draw the trigrams. However, the numbers of the Five Phases were not yet clear, so Yu the Great later took the Luo Writing as a model and explained the nine categories. But the first category was the Five Phases, the second was the Five Actions, and the ninth dealt with blessings and extremes. How did Yu the Great know to divide it this way? Therefore, Liu Mu tried to explain that "only the Five Phases are the natural numbers revealed by Heaven, while the other eight categories were classified by Yu the Great himself." This meant that the Five Actions and below were derived by Yu the Great from the Five Phases. However, Liu Xiang once connected these five items to the Five Phases, and this could bewith difficulty explained. The rest, however, had nothing to do with the Five Phases. The sixty-four trigrams are based on the eight trigrams, and the Yellow River Chart contains the images of the eight trigrams, so the sixty-four trigrams must be included within it. But the nine categories, from the Five Actions onwards, do not seem to be contained within the Five Phases. Yu the Great added them out of nowhere and attached them after the Five Phases, which is like having extra toes on the feet or extra fingers on the hands. Such a claim should be abandoned. Moreover, the classic text says "Heaven bestowed the nine categories upon Yu the Great," not "the Five Phases." The nine categories were all set by Heaven, not by human effort. To say that eight of them were classified by Yu the Great himself is pure fabrication.

《易乾鑿度》曰：陽起而進，陰動而退，故陽以七、陰以八為彖。《易》一陰一陽，合而為十五之謂道，陽變七之九，陰變八之六，亦合於十五，則彖變之數若一。陽動而進，變七之九，象其氣之息也；陰動而退，變八之六，象其氣之消也。故太一取其數以行九宮，四正四維皆合於十五。五音、六律、七始，由此作焉。

The Yi Wei · Qian Zao Du says: When the yang energy begins to rise and move forward, and the yin energy begins to move and retreat, therefore seven is used to represent yang and eight to represent yin as the彖 numbers. The Zhou Yi speaks of one yin and one yang, combining to make fifteen, which is called "the Dao." Yang changes from seven to nine, and yin changes from eight to six, combining also to make fifteen, showing that the彖 numbers and the changing numbers are consistent. When yang energy moves forward and increases, changing from seven to nine, it symbolizes its energy growing; when yin energy moves backward and decreases, changing from eight to six, it symbolizes its energy diminishing. Therefore, the Taiyi uses these numbers to move through the nine palaces, with the four cardinal directions and the four corners adding up to fifteen. The five tones, six laws, and seven beginnings are all made based on this.

《隋經籍志》：宋大明中始禁圗讖，梁天監以後又重其制，及髙祖受禪，禁之愈切。煬帝即位，乃發使四出，搜天下書籍與讖緯相涉者皆焚之，為吏所糾者至死，自是無復其學，秘府之內亦多散亡。今按志有鄭氏注《易緯》七卷，而無《乾鑿度》；唐《藝文志》有宋均注《易緯》九卷，亦無《乾鑿度》。孔穎達義疏、章懷《後漢書注》所引《乾鑿度》，葢即秘府散亡之餘，僅存於《易緯》九卷中者也，是為可信。宋時復有《乾鑿度》二卷，晁氏云「舊題蒼頡修古籀文，鄭氏注」。案唐四庫書目有鄭玄注《詩》《書》緯及宋均注《易緯》，而無此書，其中有不可曉者，獨九宮之法頗明。

The Sui Shu · Jing Ji Zhi records that during the reign of Emperor Ming of the Southern Song Dynasty, the government began to ban diagrams and prophecies. After the reign of Emperor Wen of Liang, the ban was intensified, and by the time Emperor Gaozu of Sui took the throne, the prohibition became even stricter. When Emperor Yang of Sui ascended the throne, he sent envoys to search everywhere for any books connected with prophecies and had them all burned. Those accused by officials were even executed. From then on, this field of study ceased to be passed down. The books kept in the imperial library were mostly lost. Now, checking the entries in the Sui Zhi, there is a record of Zheng Xuan's commentary on the Yi Wei with seven volumes, but there is no entry for the Qian Zao Du. The Xin Tang Shu · Yi Wen Zhi records that there were nine volumes of the Yi Wei with commentary by Song Jun, but again there is no entry for the Qian Zao Du. The commentary on the Yi by Kong Yingda in the Zhou Yi Zhengyi and the annotations by Prince Li Xian of Changhui on the Later Han Shu both cite the Qian Zao Du. These are probably the remaining parts of the nine volumes of the Yi Wei after the imperial library's collection was dispersed. These are considered reliable. Later, in the Song Dynasty, another version of the Qian Zao Du with two volumes appeared. Zhao Gongwu said that it was "originally attributed to Cang Jie, written in ancient cursive script, with commentary by Zheng Xuan." Checking the catalog of the four libraries of the Tang Dynasty, there are entries for Zheng Xuan's commentaries on the Shi Wei and Shu Wei, and for Song Jun's commentary on the Yi Wei, but there is no entry for this book. The text has some parts that are unclear, but the section on the nine palace method is quite clear.

愚謂此贗書無疑。圗緯興於哀平之際，《乾鑿度》縱出其先，亦當在漢世，而題曰蒼頡修，將誰欺乎？「太一取其數以行九宮」，章懷所引鄭注盡之矣，無七八九六進退消息、彖易彖變之說也，是必蒼頡二卷中語。葢其時《洞極經》出，十圗九書早已萌芽，故劉牧之徒偽造《乾鑿度》二卷，以《參同契》七八九六之文竄入於其中，以見此河圗之象出自西漢，逺有端緒，使人不敢動搖。陳氏所云「殘闕不完，於偽之中又有偽焉」者也。而昧者更題云蒼頡修，若此書為黃帝繼伏羲而作，適以自獻其偽，可不謂大愚乎？

I am certain that this must be a forgery. Diagrams, prophecies, and esoteric writings emerged during the reigns of Emperor Ai and Emperor Ping of the Han dynasty. Although "The Qian Zao Du" appeared even earlier, it should have originated in the Han dynasty, yet it is attributed to "Cang Jie," which is meant to deceive whom? The statement "The Taiyi uses these numbers to operate within the nine palaces" has already been fully explained by Li Xian's quotation of Zheng Xuan's commentary. There is no mention of the concepts of seven, eight, nine, and six advancing and retreating, nor the ideas of "tuan shu" and "tuan bian" in his explanation. This indicates that these statements must have been added later in the two-volume forgery attributed to Cang Jie. Probably at the time when "The Dong Ji Jing" was published, the idea of "the River Chart has ten numbers, the Luo Writing has nine numbers" had already begun to take shape. Therefore, the school of Liu Mu fabricated "The Qian Zao Du" in two volumes, inserting the words about seven, eight, nine, and six from "The Zhou Yi Cang Tong Qi" into it, in order to show that the image of the River Chart originated in the Western Han dynasty, thus appearing to have a long and continuous source, making people hesitate to doubt it. This is exactly what Chen Zhenzun referred to as "incomplete and further forged within the realm of forgeries." Furthermore, the ignorant ones even further attributed it to "Cang Jie's revision," as if the book was composed in the Yellow Emperor's era, following Fuxi. This is precisely how they expose their own forgery, which is not a great stupidity?

《子華子》曰：二與四抱九而上躋也，六與八蹈一而下沈也。戴九而履一，據三而持七，五居中宮，數之所由生；一從一橫，數之所由成。胃之實也，神氣之守也。故曰：天地之數，莫中於五，莫過於五。

The Zhihua Zi says: Two and four embrace nine and rise upward, while six and eight step on one and descend downward. The head bears nine, the feet rest on one, the left holds three, the right holds seven, and five resides in the Central Palace. This is where numbers originate. One vertical and one horizontal intersect, which is the method by which numbers are formed. It is like the fullness within the abdomen, the dwelling place guarded by spirit and energy. Therefore, it is said that the numbers of heaven and earth have none more central than five, nor any more transcendent than five.

晁氏《讀書志》曰：《子華子》十卷，其傳云子華子程氏名本，晉人也，劉向校定其書。按《莊子》稱子華子見韓昭侯，陸德明以為魏人，既不合；又《蓺文志》不錄，且多用字說，謬誤淺陋，殆元豐以後舉子所為耳。

Chao Gongwu in "Junzai Dushu Zhi" says: "The book "Zihua Zi" has ten volumes. The preface states that Zihua Zi was a man surnamed Cheng, named Ben, from the state of Jin. Liu Xiang once corrected this book. However, according to the "Zhuangzi," Zihua Zi visited Han Zhaohou, and Lu Deming thought he was from the state of Wei, which conflicts with the statement that he was from Jin. Moreover, the "Han Shu · Yiwen Zhi" did not record this book, and the book often uses the method of interpreting characters as in Wang Anshi's "Zishuo," which is erroneous and superficial. Therefore, it is likely that this book was written by candidates taking the imperial examinations after the Yuanfeng period of Emperor Shenzong of the Song dynasty."

朱子《偶讀漫記》曰：會稽官書版本有《子華子》，雲是程本字子華者所作，孔子所與傾葢而語者。以予觀之，其詞故為艱澀而理實淺近，其體務為髙古而氣實輕浮，但如近年後生巧於摹擬變換者所為，不惟決非先秦古書，亦非百十年前文字也。如論河圗，巧亦甚矣，惟其巧甚，所以知其非古書也。或云王銍性之、姚寛令威多作贗書，二人皆居越，恐出其手。又曰：但觀其書數篇與前後三序皆一手文字，其前一篇托為劉向，而殊不類向它書。

Zhu Xi wrote in his "Evening Notes on Reading": In the official printed editions of books from Kuaiji, there is a text called "Zi Hua Zi", which is said to have been written by Cheng Ben (whose courtesy name was Zi Hua), the person with whom Confucius once stopped his carriage to talk. In my opinion, its language is deliberately written in a difficult and obscure style, yet its meaning is shallow. Its style strives to be ancient and refined, but its character is actually light and superficial. It is merely like the works of recent young men who are good at imitating and changing styles. It is not at all an ancient text from the Pre-Qin period, nor is it from a hundred years ago. For example, the text's discussion on the Yellow River Chart is very clever; precisely because it is too clever, we know it is not an ancient text. Some people say that Wang Zhi (whose courtesy name was Xingzhi) and Yao Kuan (whose courtesy name was Lingwei) often fabricated false texts. Both of them lived in the region of Yue. This text is probably the work of one of them. Zhu Xi also said: Just look at the main body of this text and the three prefaces before and after, all written by the same person. Among them, the first preface falsely attributes it to Liu Xiang, but it does not resemble Liu Xiang's other works.

周氏《涉筆》曰：其書多解字義，吾嘗疑其三經後此書方出，故信《字說》而主老莊。

The Zhou氏's "Ink Brush" says: This book contains much content explaining the meanings of characters. I once suspected that it appeared after Wang Anshi's "Three Classics New Interpretations," so I came to believe in the "Character Explanation" and took the teachings of Laozi and Zhuangzi as my main principles.

陳氏《書錄解題》曰：《家語》有孔子遇程子傾葢事，而莊生亦載子華子見昭僖侯一則。莊生固寓言，而《家語》亦未可考信，班固《古今人表》亦無之。

In the Southern Song dynasty, Chen Zhenwen's "Zhai Zhai Shu Lu Jie Ti" says: The "Analects of Confucius" records an incident where Confucius met Master Cheng on the road and stopped his carriage to talk with him. The "Zhuangzi" also mentions a passage about Zi Huazi visiting Han Zhaoxi Hou. The "Zhuangzi" book itself is mostly made up of parables and not reliable. The book "Analects of Confucius" is also not verifiable. As for Ban Gu's "Book of Han: Table of Ancient and Modern People," there is no mention of Zi Huazi at all.

王氏《困學紀聞》曰：《子華子》後序謂鬼谷子之師，水心銘鞏仲至所謂程子即此書也。朱文公謂詞艱而理淺，近世巧於模擬者所為，決非先秦古書。

In the Southern Song dynasty, Wang Yinglin in his work "Kunxue Jiwen" said that the postscript of the book "Zihua Zi" claims that Zihua Zi was the teacher of Guiguzi. The "Chengzi" mentioned in the inscription written by Ye Xie (also known as Shuixin) for Gong Zhongzhi refers to this book. Zhu Xi criticized it for having obscure language and shallow meaning, saying it was the work of modern people who were good at imitating ancient texts, and not an ancient book from the Warring States period.

劉牧之徒偽撰《乾鑿度》以自固其學，而猶未已也。葢緯書出於西漢，恐不足以厭服天下之心，故又造《子華子》，其人為與孔子傾葢而語者，以「戴九履一，據三持七」為河圗，始可以屈《洞極經》而伸吾之說。然格致凡近，辭義淺陋，序雲劉向作，而《漢蓺文志》無之。人皆知其出於元豐後《三經》《字說》盛行之時，竟何益哉？故曰：作偽心勞日拙。

Liu Mu's school forged the "Qian Zao Du" to strengthen their own doctrine, yet they were not satisfied. Probably because the writings of the Western Han dynasty were not enough to silence the doubts of the people, they then created another work called "Zi Hua Zi", claiming that the person named Zi Hua in the book was someone who had a deep conversation with Confucius when they stopped their carriage and talked heart to heart. By using this person's mouth, they attributed the "nine palace numbers" of "dai jiu lu yi, ju san chi qi" to the Yellow River Chart. In this way, they could surpass the "Dong Ji Jing" and promote their own views. However, the book's discussion on the study of things and the attainment of knowledge is extremely ordinary, and its language and reasoning are very shallow. The preface claims that it was written by Liu Xiang of the Western Han dynasty, but the "Han Shu · Yi Wen Zhi" did not record it. Everyone can see that it was written in the period after the Yuanfeng era of Emperor Shenzong of Song, when Wang Anshi's "San Jing Xin Yi" and "Zi Shuo" were popular. So what use is there in forging such a work? Therefore, the more effort a forger puts into his deception, the more obvious the flaws become.

旴江李氏覯《刪定易圗論序》曰：世有治易根於劉牧者，其說日不同。因購牧所為《易圗》五十有五觀之，則甚復重，乃刪其圗而存之者三，所謂河圗也、洛書也、八卦也。於其序解之中撮舉而是正之，諸所觸類亦復詳說，成六論。別有一冊黃黎獻為之序者，頗増多誕謾，自鄶以下無譏焉。[論作於仁宗景佑三年。王湜《易學》曰：吳秘之《通神》、黃黎獻之《畧例》《隠訣》、徐庸之《易縕》皆本劉氏。逮鮮于侁稍辨其非，其後論易者交攻之，而九圗十書宋之群儒恆主其說。]

In the "Preface to the Revised Diagrams of the Book of Changes" written by Li Gou, a native of Xujiang during the Northern Song Dynasty, he said: Those who study the Book of Changes based on Liu Mu's teachings have varying interpretations each day. I therefore bought Liu Mu's fifty-five diagrams of the Book of Changes and examined them carefully, finding them repetitive and redundant. I deleted the superfluous parts and retained only three diagrams: the Yellow River Chart, the Luo Writing, and the Eight Trigrams Diagram. I also summarized and corrected his original preface and explanations, elaborating further wherever analogical reasoning could be applied, and wrote six essays. Additionally, there is another version with a preface by Huang Lixian, which contains even more absurd elements. That would be like the fifteen states of the Book of Songs starting from the state of Hui, which is not worth commenting on. (This essay was written in the third year of Jingyou of Emperor Renzong of Song. Wang Shi's "Studies on the Book of Changes" states: Works such as Wu Mi's "Communicating with the Divine," Huang Lixian's "General Principles" and "Secret Methods," and Xu Yong's "Essence of the Book of Changes" all base themselves on Liu Mu's teachings. It was only until Xian Yu Shen that someone began to slightly clarify his errors. After that, those who discussed the Book of Changes started to criticize him. However, the idea that "nine refers to diagrams and ten refers to writings" remained a common view among scholars of the Song Dynasty.)

谷水林氏至《易裨傳·極數篇》曰：夫子於《繫辭》言數者三：曰「天地之數五十有五」，曰「天一終於地十」，曰「參天兩地」而已。雖曰「河出圗，洛出書」，初未嘗曰某為圗、某為書也。至劉牧出《鉤隠圗》，始以四十五為河圗而五十五為洛書，且以為出於希夷之所傳授，始有「戴九履一，左三右七，二四為肩，六八為足，縱橫十五，總四十有五」之說，前此未之見也。孔穎達曰：「龜負洛書，先無此事，見之緯候之書。」牧不信聖人之言而主緯候之說，何邪？大抵聖人闡易，有象則有數，有數則有變。象則太極生兩儀、四象、八卦者也；數則五十有五奇耦之生成者也；變則揲蓍倚數生爻者也。要不出於三者而已。如牧之為圗，巧則巧矣，於易何取焉？且其數曰縱橫十五而已，所以生卦成卦無聞焉，不知何與於易哉？

In the Southern Song dynasty, Lin Zhi (also known as Huashui) wrote in his "Yi Bi Zhuan · Ji Shu Pian" that Confucius mentioned "number" three times in the "Great Treatise." The first was "the number of heaven and earth is fifty-five," the second was "the beginning is heaven one... ending with earth ten," and the third was "three for heaven, two for earth." Although it was said that "the Yellow River produced the chart and the Luo River produced the book," there was never a specific mention of which one was the chart and which was the book. It was only when Liu Mu wrote "Gou Yin Tu" that he fixed forty-five as the Yellow River Chart and fifty-five as the Luo River Book, claiming that this knowledge was passed down by Chen Tuan. Thus, the idea of "nine at the top, one at the bottom, three on the left, seven on the right, two and four as shoulders, six and eight as feet, with the vertical and horizontal sums all being fifteen, and the total number forty-five" came into being. This was not seen before. Kong Yingda said, "The tortoise did not carry the Luo Book before, it was only mentioned in the writings of the 'waihou' class." Why did Liu Mu not believe the words of the sages but instead follow the 'waihou' theory? In general, the sages explained the Way of the Book of Changes, with images, numbers, and transformation. Images are the generation of the Taiji into two principles, four images, and eight trigrams. Numbers are the odd and even numbers that form fifty-five. Transformation is the process of divination with yarrow stalks, which produce the lines according to numbers. These three aspects are the main points. Liu Mu's making of diagrams was indeed skillful, but how does it help with the Book of Changes? Moreover, his numbers only discussed the vertical and horizontal sums being fifteen, but he gave no explanation of how the hexagrams were generated or formed. It is unclear how this relates to the Book of Changes.

又曰：緯候之家不過借河圗洛書之說以神其事，至牧反覆言之，而世之論易者多宗其說，易之本原愈以不明。本朝惟歐陽公以圗書為怪妄之甚，為說以黜之，然一人之言不能勝久習之溺也，特學易者不深察之耳。今所謂極數者，本之天地五十有五之數而黜圗書之妄，雖得罪於君子不辭也。

Lin Zhi also said: The school of Weihou merely uses the terminology of the Yellow River Chart and the Luo Writing to make their own theories seem mysterious and supernatural; when Liu Mu took up this idea and elaborated on it repeatedly, most scholars who discussed the Book of Changes followed him as their master, and thus the original nature of the Book of Changes became increasingly obscure and unclear. In our dynasty, only Ouyang Xiu considered the theories of the Yellow River Chart and the Luo Writing to be utterly absurd, and he specifically wrote treatises to oppose them; however, the words of one person cannot overcome the long-standing habits of the scholarly community. It is merely that those who study the Book of Changes are unwilling to examine deeply. Now, what I am explaining as 'ji shu' (extreme numbers) is based on the number fifty-five of heaven and earth, and I discard the false claims of the Yellow River Chart and the Luo Writing. Even if this leads me to be condemned by the virtuous, I would not hesitate.

按：五十有五即自一至十之數，林氏因錯簡而誤析為二耳。《繫辭》言數者三：天地之數一也，參伍錯綜二也，參天兩地三也。此皆主蓍而言，於圗書無涉。宋人不知此義，而以數為圗書，易道之榛蕪至此而極。雖命世大儒如伊川，不能廢五行之說，而郭子和非之，以為歴數之學；如考亭，不能廢圗書之說，而林德久斥之，以為緯候之流。嗚呼，之二子者，豈非豪傑之士哉！

Hu Wei said: "Fifty-five" is originally the total sum from one to ten, and Lin Zhi mistakenly split it into two parts because the text of the Great Treatise was disordered. The Great Treatise discusses "number" in three places: the number of heaven and earth, "three and two intermingled to produce change, and the numbers interwoven," and "three for heaven, two for earth." These three instances all refer to the method of divination using the yarrow stalks, and have nothing to do with the Yellow River Chart or the Luo Writing. The Song scholars did not understand this, and they took these numbers as part of the diagrams. The confusion in the study of the Book of Changes has reached its peak here. Even among the great scholars of their time, Cheng Yi did not abandon the theory of the Five Phases combined with the Book of Changes, but Guo Yong (whose name was Zihe) criticized him, saying that it was the study of astronomy and mathematics. Zhu Xi did not abandon the Yellow River Chart and the Luo Writing, but Lin Zhi (whose name was Dejiu) criticized him, saying that it belonged to the category of esoteric doctrines. Alas, these two men who dared to correct the great scholars, are they not truly heroic men!

雷氏《易圗通變》曰：龍圗流傳未逺，知者亦鮮，至劉牧乃増至五十五圗，名以《鉤隠》，師友自相推許，更為倡述，各於易有註釋：曰《卦德論》，曰《室中語》，曰《記師說》，曰《指歸》，曰《通微》，亦總謂之《周易新注》。每欲自神其事，及跡而究之，未見其真能有所神奇也。時則有李覯泰伯者，著六論以駁之，刪其復重，止存三圗。自後愈傳愈失，甚者反以五十五數為河圗，而圗南所傳者為洛書，顛倒迷謬，靡所底止。

In the Yuan dynasty, Lei Siqi in his work "Yitu Tongbian" said that Chen Tuan's "Longtu" did not circulate for a long time and few people understood it. When it came to Liu Mu, it was expanded to fifty-five diagrams, named "Gouyin Tu." They and their disciples and friends praised each other, continuously wrote, and each annotated the "Yi," producing works such as "Gude Lun," "Shizhong Yu," "Jishi Yue," "Zhiui," and "Tongwei," collectively called "Zhouyi Xin Zhu." They tried everywhere to make their works seem very mysterious, but when tracing their origins, there was nothing really miraculous. At that time, Li Gou (whose name was Taibai) wrote six essays to refute them, deleting repeated diagrams and keeping only three. Later, the transmission became more distorted, even reversing the number fifty-five as the Yellow River Chart, and taking Chen Tuan's transmission as the Luo Writing, causing confusion and disorder without end.

按：劉牧之學，當時皆謂其源出於希夷，而不知希夷所傳者乃天地自然之圗、白黑回互之狀[見第三卷]，康節之所受而演之者也，於《龍圗》曷與焉？於《鉤隠》又曷與焉？葢自天禧之後，偽書盛行，而天地自然之圗隠矣。說者以劉牧之學為希夷之傳，是猶呂之代嬴、牛之易馬，世仍以秦、晉目之，而不知其血脈之已非也。李泰伯存其三圗，雷齊賢歸咎後人，亦尋常之見耳。《鉤隠》支離破碎，繳繞窒塞，真無一可取。譬諸田功，聖人之易，五穀也；希夷之易，荑稗也；牧之易，進不可窮理以盡性，退不可養生以盡年，徒為稂莠而已矣。

Hu Wei said: Liu Mu's learning, at that time, was said by everyone to have come from Chen Tuan (who was called Xiyi), but no one knew that what Chen Tuan passed down was actually the 'Diagram of Heaven and Earth in their Natural State', which is the one with black and white dots interconnecting in a circular manner (see Volume Three of this book). That was actually what Shao Yong inherited and further developed, so what connection does it have with the 'Dragon Diagram'? What connection does it have with the 'Hooked Hidden Diagram'? Probably since the time of Emperor Zhenzong of the Song Dynasty's Tianxi period, fake books became widespread, and the Diagram of Heaven and Earth in their Natural State gradually disappeared. Those who discussed Liu Mu's learning as being the direct transmission from Chen Tuan were like the Liu family replacing the Ying family, or the Niu family taking over the Sima family. The world still called them Qin and Jin, but they no longer had the original lineage. Li Gou only preserved three diagrams, and Lei Siqi (whose name was Qixian) blamed the later generations, which was just common opinion. The Hooked Hidden Diagram was fragmented and confused, with no part worth taking. Taking farming as an analogy: the sage's Book of Changes is the five grains, Chen Tuan's Book of Changes is the稗草, Liu Mu's Book of Changes could not reach the ultimate understanding of principles and human nature, nor could it help people live a long and healthy life, it was just weeds in the field.

右論易數鉤隠圗。

The previous section examines the origin and authenticity of Liu Mu's "Yishu Gouyun Tu."

西山蔡氏元定曰：古今傳記，自孔安國、劉向父子、班固，皆以為河圗授羲、洛書錫禹；闗子明、邵康節皆以十為河圗、九為洛書。葢大傳既陳天地五十有五之數，《洪範》又明言「天乃錫禹洪範九疇」，而九宮之數戴九履一、左三右七、二四為肩、六八為足，正龜背之象也。惟劉牧意見以九為河圗、十為洛書，託言出於希夷，既與諸儒舊說不合，又引大傳以為二者皆出於伏羲之世，其易置圗書並無明驗。但謂伏羲兼取圗書，則易、範之數誠相表裡，為可疑耳。其實天地之理一而已矣，雖時有古今先後之不同，而其理則不容於有二也。故伏羲但據河圗以作易，則不必豫見洛書，而已逆與之合矣；大禹但據洛書以作範，則亦不必追考河圗，而已暗與之符矣。其所以然者何哉？誠以此理之外無復他理故也。

In the Southern Song dynasty, Cai Yuan ding, who was known as Xishan, said: The biographies of ancient and modern times, from Kong An guo, Liu Xiang and his son Liu Xin to Ban Gu, all believed that the Yellow River Chart was given to Fuxi and the Luo Writing was bestowed upon Da Yu. Guan Ziming and Shao Yong both regarded the number ten as belonging to the Yellow River Chart and the number nine as belonging to the Luo Writing. Since the Great Treatise has already listed the numbers of heaven and earth as fifty-five, and the Book of Documents, the Hongfan chapter clearly states that "Heaven thus bestowed upon Da Yu the Hongfan Nine Categories," and the nine palace numbers "with nine on top, one beneath, three on the left, seven on the right, two and four as shoulders, six and eight as feet," exactly resemble the pattern of a tortoise's shell. Only Liu Mu, based on his own speculation, took the number nine as the Yellow River Chart and the number ten as the Luo Writing, and falsely attributed this view to Chen Tuan. This contradicts the previous views of the scholars of earlier generations, and he also cited the Great Treatise to claim that both the Yellow River Chart and the Luo Writing originated in the time of Fuxi. His reversal of the association between the charts and writings lacks any solid evidence. However, his statement that Fuxi used both the charts and writings together does point out that the numbers of the Book of Changes and the Hongfan indeed complement each other, and this is something worth considering. In reality, the principles of heaven and earth are one, and although times have different sequences of ancient and modern, the principles cannot be divided into two different systems. Therefore, Fuxi only used the Yellow River Chart to draw the hexagrams and did not need to see the Luo Writing beforehand, yet naturally aligned with it; Da Yu only used the Luo Writing to compose the Hongfan and did not need to investigate the Yellow River Chart, yet naturally corresponded with it. This is because there is no other principle beyond this one.

右見《易學啟蒙》注。季通為朱子起藳，故不敢列已說為正文。然朱子河圗洛書之象數實由季通而定。初劉牧以四十有五為河圗、五十有五為洛書，實龍圗之本象，而季通以為牧之所易置，至此乃復其舊，且引闗、邵以相證。今按闗《易》明繫偽書，不可以為據；而邵子圎星方土之論，其意別有所在，未嘗以五十有五為河圗也。謹列其說如左，明者幸垂察焉。

The above passage appears in the annotations of the "Yixue Qimeng" (Introduction to the Study of the Changes). Cai Yuanding, who was given the courtesy name Jitong, was the one who drafted the "Qimeng" for Zhu Xi, so he did not dare to present his own opinions as the main text; however, the figures and numbers of the Yellow River Chart and the Luo Writing in Zhu Xi's book were actually determined by Cai Yuanding. Originally, Liu Mu had taken forty-five as the Yellow River Chart and fifty-five as the Luo Writing, which was already the original form of the "Longtu" (Dragon Chart). Cai Yuanding, however, believed that Liu Mu had reversed the two, and only here did it become "restored to its original appearance," and he cited the views of Guan Ziming and Shao Yong as evidence. Now, upon examination: Guan Ziming's "Yi Zhuan" (Commentary on the Changes) is clearly a forgery and cannot be used as evidence; and Shao Yong's statement "the round is the star, the square is the earth" originally had a different meaning and did not take fifty-five as the Yellow River Chart. I now list the views of various scholars below, and I hope discerning readers will carefully examine them.

《闗子明易傳》曰：河圗之文，七前六後，八左九右，聖人觀之以畫卦。是故全七之三以為離，竒以為巽；全八之三以為震，奇以為艮；全六之三以為坎，奇以為乾；全九之三以為兊，奇以為坤。正者全其位，隅者盡其畫。[此與《鉤隠》四象生八卦同。]洛書之文，九前一後，三左七右，四前左，二前右，八後左，六後右。後聖稽之為三象：一四七為天生之數，二五八為地育之數，三六九為人資之數。

The Guanzi Ming Yi Zhuan says: The diagram of the Yellow River Chart has seven in front, six behind, eight on the left, and nine on the right. The sage observed it to draw the trigrams. Therefore, taking the number seven, filling three strokes to form the trigram Li (Fire), and using the remaining odd number to form Xun (Wind); taking the number eight, filling three strokes to form Zhen (Thunder), and using the remaining number to form Gen (Mountain); taking the number six, filling three strokes to form Kan (Water), and using the remaining number to form Qian (Heaven); taking the number nine, filling three strokes to form Dui (Lake), and using the remaining number to form Kun (Earth). The trigrams in the four cardinal directions occupy their proper positions, while those in the four corners use up the remaining strokes. (This is consistent with Liu Mu's Gou Yin Tu, which says 'the four basic trigrams give rise to the eight trigrams.') The diagram of the Luo Writing has nine in front, one behind, three on the left, and seven on the right, four in the upper left, two in the upper right, eight in the lower left, and six in the lower right. Later sages examined it, dividing it into three groups of numbers: one, four, and seven are the numbers generated by Heaven; two, five, and eight are the numbers nurtured by Earth; three, six, and nine are the numbers relied upon by humans.

《邯鄲書目》[宋皇佑中李淑撰]：《闗子明易傳》一卷，唐趙蕤注。魏孝文使幷州刺史王虯與子明著《疑筮論》數十篇，蕤雲亡篇過半，今無能詮次，但隨文解義，庶學者觸類而長。阮逸詮次刋正《洞極元經傳》五卷[逸字天隠，宋仁宗時人]。闗子明以生、育、資為傳以釋其蘊，為經論十一篇[《玉海》云：子明《易傳》卜百年義第一，次以統言易義、大衍、乾坤策、盈虛、闔闢、理性、時變、動靜、神義，終於雜義第十一]，又為圗以序其象。《文中子》錄子明事：太和末，穆公與談易，言於孝文帝，帝曰：「且與卿就成筮論。」子明曰：「乾坤之策，陰陽之數，推而行之不過三百六十六，引而伸之不過三百八十四，天之道也。象生有定數，吉凶有前期，變而能通，故治亂有可易之理。」

The "Handan Book Catalogue" (compiled by Li Shu during the Huangyou period of Emperor Renzong of the Song dynasty) records: "The Commentary on the Changes by Guan Ziming" in one volume, with annotations by Tang dynasty person Zhao Rui. In the Northern Wei dynasty, Emperor Xiaowen sent the governor of Pingzhou, Wang Qiu, to collaborate with Guan Ziming in writing "Discourses on Divination" in dozens of chapters. Zhao Rui said that the lost chapters were more than half, and now it is impossible to compile them in order, so only the meaning of the text can be explained, hoping that scholars can understand the principles by analogy. Ruan Yi compiled and edited "The Transmission of the Transmission of the Deep Origin Classic" in five volumes (Ruan Yi, whose name was Tianyin, was a person of the Song dynasty during Emperor Renzong's reign). Guan Ziming explained the meaning of the book by using the three concepts of "birth, nurture, and support," composing eleven commentaries on the Classic (The "Zhyouzi" records Guan Ziming's deeds, saying: in the late Tahe period, Mu Gong talked about the Changes with him and recommended him to Emperor Xiaowen. Emperor Xiaowen said: "Let us first write the Discourses on Divination together." Guan Ziming replied: "The numbers of the two trigrams, Qian and Kun, and the numbers of yin and yang, when calculated, amount to no more than 366, and when extended, no more than 384. This is the way of heaven. The generation of things has a fixed number, and the fortune and misfortune have a predictable limit. Change can lead to understanding, so there is a principle for transforming between peace and chaos.")

晁氏《讀書志》曰：《闗子明易傳》一卷，魏闗朗撰，李邯鄲始著之目，王通贊易葢宗此也。

In the Southern Song dynasty, Zhao Gongwu's "Juzhai Reading Notes" states: "The "Gu Ziming Yijie" is one volume, written by Guan Lang of the Northern Wei dynasty. It was first included in the "Hendan Book Catalogue" by Li Shu. In the Sui dynasty, Wang Tong promoted the principles of the Book of Changes, probably taking this work as his main reference."

《後山叢談》曰：世傳王氏《元經》、薛氏傳、《闗子明易傳》、《李衛公問對》，皆阮逸所著。逸以草示蘇明允，而子瞻言之。

In the Northern Song dynasty, Chen Shidao of the Houshan Congtan said that the works circulating in the world, such as Wang Tong's "Yuan Jing," Xue Shou's biographies, the "Gu Ziming Yi Zhuan," and the "Li Weigong Wen Dui," were all fabricated by Ruan Yi. Ruan Yi had shown the original manuscript to Su Xun, who was known by his courtesy name Mingyun. This statement was made by Su Shi, who was known by his courtesy name Zizhan.

《朱子語類》：鄒浩問李壽翁椿最好《闗子明易》。先生曰：是阮逸偽作，陳無已集說得分明。

The Shu Li Lu records that Zou Hao asked about Li Chun, who most highly praised the Guan Ziming Commentary on the Yi Jing. Zhu Xi replied that it was forged by Ruan Yi, and that Chen Shidao's collected writings clearly explain this.

姚氏曰：世所傳闗子明《洞極經》亦言河圗洛書如劉氏說，而兩易之，以五方者為圗、九宮者為書。按唐李鼎祚《易解》盡備前世諸儒之說，獨無闗氏；至本朝阮逸始偽作《洞極經》，見於《後山叢談》，則闗亦不足為證矣。[見《周易玩辭》]

Yao said: The world has been passing on Guan Ziming's "Dongji Jing," which discusses the He Tu and Luo Shu in the same way as Liu Mu's account, but reverses the two, taking the five directions' generating numbers as the He Tu and the nine palace numbers as the Luo Shu. Upon examination, during the Tang dynasty, Li Dingzuo's "Collected Explanations of the Zhou Changes" collected the views of previous scholars almost entirely, but omitted Guan Lang; it was only in this dynasty that Ruan Yi fabricated the "Dongji Jing," as recorded in "Houshan Congtan." Therefore, Guan Ziming's view is not sufficient as evidence. (This entry is found in "Zhou Yi Wan Ci")

雷氏《易圗通變》曰：楊次公自著《洞極經》，託名於闗子明[渭按：楊傑字次公，元豐中與范鎮論樂。《洞極經》果為傑所撰，則又出阮逸之後，恐非]。如其敘本篇稱「子曰：河圗之文，七前六後，八左九右，聖人觀之以畫八卦。是故全七之三以為離，奇以為巽；全八之三以為震，奇以為艮；全六之三以為坎，奇以為乾；全九之三以為兊，奇以為坤。正者全其位，隅者盡其畫」，而謂四象生八卦，此謬之尤者。乾坤相索而生六子，今為男女者反能生父母之卦邪？

In the Yuan dynasty, Lei Siqi's "Yi Tu Tong Bian" says: "The 'Dong Ji Jing' was written by Yang Cigong himself, but it was falsely attributed to Guan Ziming. (Hu Wei notes: Yang Jie, who was called Cigong, once discussed music theory with Fan Zhen during the Yuanfeng period of Emperor Shenzong of the Song dynasty. If the 'Dong Ji Jing' was indeed written by Yang Jie, it would be later than Ruan Yi, which seems unlikely.) For example, the text describes the origin of this chapter as: 'Confucius said: The diagram of the Yellow River Chart has seven in front, six behind, eight on the left, and nine on the right. The sage observed it to draw the Eight Trigrams. Therefore, taking the number seven, filling three strokes to form Li (Fire), and the remaining number forms Xun (Wind); taking the number eight, filling three strokes to form Zhen (Thunder), and the remaining number forms Gen (Mountain); taking the number six, filling three strokes to form Kan (Water), and the remaining number forms Qian (Heaven); taking the number nine, filling three strokes to form Dui (Lake), and the remaining number forms Kun (Earth). The ones in the central position occupy their own position, while those in the corner positions use up the remaining strokes.' According to this, the Four Symbols can generate the Eight Trigrams, which is the most absurd mistake. According to 'Shuo Gua,' the two trigrams Qian and Kun interact to produce the six subsidiary trigrams. Now it is claimed that the six subsidiary trigrams, which are the male and female trigrams, can generate the parents trigrams, which is illogical."

《文中子中說》三卷，隋王通之門人共集其語為是書，而晁氏擿其三事以為可疑。其一則闗朗在太和中見魏孝文，自太和丁巳至通生之年甲辰，葢一百七十年矣，而其書有問禮於闗子明，是以知其妄也。程子謂王通隠君子，當時有些少言語，後來為人傅會，不可謂全書，續經之類皆非其作，朱子亦以為然。王氏《揮麈錄》直以為阮逸偽作。今按《中說》宋有阮逸、龔鼎臣二本，其文多異，闗子明事葢逸所傅會，與《洞極經》論總出一手，彼此扶同，以欺天下後世也。

The *Zhong Shuo* in three volumes was compiled by Bao Tong's disciples, collecting his sayings. However, Chao Gongwu pointed out three things in it as doubtful. One of them is that Guan Lang visited Emperor Xiaowen of the Northern Wei during the Taihe period, from the Taihe Dingsi year to the Jiachen year when Wang Tong was born, spanning about 170 years. Yet the book records Wang Tong consulting Guan Ziming on rites, which shows it is fabricated. Cheng Yi said that Wang Tong was a reclusive gentleman, who left some sayings, but later they were fabricated and added to, so it cannot be considered a complete and reliable work; he called it "continuation of classics," which were not written by Wang Tong. Zhu Xi also agreed with this view. Wang Mingqing's *Hui Chu Lu* directly claimed that *Zhong Shuo* was forged by Ruan Yi. Now we examine that in the Song dynasty there were two versions of *Zhong Shuo*, by Ruan Yi and Gong Dingchen, with many differences in wording. The story of Guan Ziming is probably fabricated by Ruan Yi, and the arguments in *Dong Ji Jing* seem to come from the same person, connected together to deceive future generations.

宋仁宗朝，劉牧著《易數鉤隠》，以九宮為河圗、五合為洛書，其學盛行於世。同時有阮逸者，陰欲排之，乃撰《闗子明易傳》而兩易其名。季通不察，以為真古書也，遂引為圗十書九之證。季通無論已，獨怪朱子素斥《龍圗》為假書，又據《後山叢談》深信闗《易》為阮逸所造，而於此則曲從季通之說，何也？

During the reign of Emperor Renzong of Song, Liu Mu wrote the "Yishu Gouyun Tu," treating the nine-square grid numbers as the Yellow River Chart and the Five Phases generation numbers as the Luo Writing. This system became popular at that time. At the same time, there was a person named Ruan Yi who secretly wanted to surpass it, so he fabricated the "Guanziming Yixuan," swapping the names of the charts and writings. Cai Yuanping did not realize this and thought it was indeed an ancient text, thus using it to support the idea that the Yellow River Chart has ten numbers and the Luo Writing has nine numbers. Cai Yuanping was not a problem, but it is strange that Zhu Xi, who usually condemned the "Longtu" as a fake text, and who was convinced by the "Houshan Congtan" that the "Guanziming Yixuan" was written by Ruan Yi, yet here he deliberately followed Cai Yuanping's view. Why was that?

葢自漢魏以來，言河圗者皆主《乾鑿度》《參同契》，而此獨根柢大傳五十有五之數，其據地尊而取義正也。然河圗久已無傳，不知其形象若何，而強以五十五數當之，大傳既無明文，古注亦無可考。「七前六後，八左九右」之位不見於經，「天生地成，奇白偶黑」之點非易所有。至其所以則之者，謂伏羲分四正之餘數以成四隅之卦畫，支離舛錯，全無義理。藉令此書真出於古，猶不可據以說經，而況明明為阮逸之偽作乎？且此數但可以生蓍而不可以畫卦，九與十何擇焉？

Since the Han and Wei dynasties, those who have discussed the River Chart have mostly relied on the "Yi Wei Gan Zuo Du" and the "Zhou Yi San Tong Qi," but this book alone bases itself on the "Xì Cí" passage "the numbers of heaven and earth total fifty-five," thus occupying a lofty position and presenting a proper meaning. However, the River Chart has long been lost, and no one knows what its actual form was. Now, forcing the number fifty-five upon it is arbitrary, as the "Xì Cí" does not clearly state this, and ancient commentaries offer no reference. Statements such as "seven is in front, six is behind, eight is on the left, nine is on the right" are not found in the text; similarly, the idea that odd numbers are represented by white dots and even numbers by black dots is not original to the "Yi." As for its claim that sages derived the hexagrams from the River Chart, saying that Fuxi separated the remainders of the four cardinal numbers to form the four corner hexagrams, this is fragmented and confused, with no logical basis. Even if this book were indeed an ancient text, it could not be used to explain the "Yi," let alone the fact that it is clearly a forgery by Ruan Yi. Moreover, these numbers are only suitable for divination with the yarrow stalks, not for drawing hexagrams. So whether it is nine or ten, what difference does it make?

范諤昌《大易源流》言：龍馬負圗出河，羲皇窮天人之際，復位五行生成之數，地上八卦之體：天一正北，地二正南，天三正東，地四正西，天五正中央，地六配子，天七配午，地八配夘，天九配酉，地十配中寄於未，乃天地之數五十有五矣。雷氏云：正今圗所傳有四方而無四維者也，闗子明之河圗實本諸此。然諤昌但謂伏羲據龍圗以復位五行之數、八卦之體有如此者，未嘗直指此為河出之圗也。故劉牧《鉤隠》仍以九為圗而十為書，偽闗《易》竊其義，遂以「七前六後，八左九右」為河圗之文。人皆知其書之出於阮逸，而不知其數之本乎諤昌也。

Fan Echáng's "Great Origins of the Changes" says: The dragon horse carried a diagram emerging from the Yellow River, and Fuxi investigated the connection between heaven and humanity, using it to determine the numbers of the Five Phases and the positions of the eight trigrams on the earth. Heaven one resides in the due north, earth two in the due south, heaven three in the due east, earth four in the due west, heaven five in the center, earth six is paired with the position of the rat, heaven seven is paired with the position of the horse, earth eight is paired with the position of the rabbit, heaven nine is paired with the position of the rooster, and earth ten resides in the center and is assigned to the position of the sheep. Together they make up the total number of heaven and earth, which is fifty-five. Lei Siqi says: This is exactly the diagram that is passed down today, which only includes the four cardinal directions and not the four intermediate directions. The river chart mentioned by Guan Ziming actually originates from this. However, Fan Echáng only said that Fuxi used the dragon diagram to determine the numbers of the Five Phases and the positions of the eight trigrams in this way, without directly stating that this was the diagram that emerged from the Yellow River. Therefore, Liu Mu's "Hooking the Hidden Diagram" still regarded the nine numbers as the river chart and the ten numbers as the Luo writing. The forged "Yi Transmission by Guan Ziming" stole Fan's meaning, and thus claimed that "seven in front, six behind, eight on the left, nine on the right" was the diagram of the river chart. Everyone knows that this book was written by Ruan Yi, but few know that these numbers originated from Fan Echáng.

邵子《觀物外篇》曰：圎者星也，歴紀之數其肇於此乎[《易學啟蒙》注云：歴法合二始以定剛柔，二中以定律歴，二終以紀閏餘，是所謂歴紀也。按此說出唐一行《歴本議》]？方者土也，畫州井地之法其放於此乎[《啟蒙》注云：州有九，井九百畝，是所以畫州井地也]？葢圎者河圗之數，方者洛書之文，故羲文因之而造易，禹箕敘之而作範也[《啟蒙》引此段遺後四句，殊為疎謬]。

Shao Yong's "Outer Chapter of Observing Things" says: "The round shape refers to stars, and the numbers used in the calendar and year reckoning probably originated from this (the commentary in "Awakening to the Yi" says: The calendar combines the two beginnings to determine the yin and yang, combines the two middles to determine the musical scales and calendar numbers, and combines the two endings to record the leap years, which is called 'calendar record'. Note: This statement comes from Yixing's "Discussions on the Calendar"). The square shape refers to earth, and the methods of dividing states and managing the well-field system probably imitate this (the commentary in "Awakening to the Yi" says: There are nine states in total, and one well-field is nine hundred mu, which is the origin of dividing states and the well-field system). Generally speaking, the round shape belongs to the numbers of the Yellow River Chart, and the square shape belongs to the writings of the Luo Writing. Therefore, Fuxi and King Wen based the Yi on them, and Da Yu and Ji Zi used them to compose the "Hong Fan". (The commentary in "Awakening to the Yi" omitted the following four sentences, which is a serious omission and error)."

《朱子語類》曰：二始者，一二也，一奇故為剛，二偶故為柔；二中者，五六也，五者十干，六者十二辰也；二終者，九與十也，閏餘之法以十九歲為一章。姑借其說以明十數之為河圗耳。又曰：「圎者星也」，圎者河圗之數，言無那四角底，其形便圎。又曰：河圗既無那四隅，則比之洛書固亦為圎矣。「方者土也」，方者洛書之文，言畫州井地之所依仿而作者也。《書·禹貢》禹別九州島，冀北、揚南、青東、梁西、兗東北、雍西北、徐東南、荊西南、豫中也。孟子言周家井地之制，井九百畝，其中為公田，八家皆私百畝，同養公田，是皆法洛書之九數也。

Master Zhu Xi said: The term "two beginnings" refers to one and two. One is an odd number and thus belongs to the category of yang, while two is an even number and thus belongs to the category of yin. The term "two middles" refers to five and six. Five corresponds to the ten heavenly stems, and six corresponds to the twelve earthly branches. The term "two endings" refers to nine and ten. The method of intercalation uses nineteen years as a cycle. This is merely using this terminology temporarily to explain that the number ten is from the Yellow River Chart. He also said: "A circle represents the stars." A circular shape belongs to the numbers of the Yellow River Chart, because it has no four corners, and thus naturally appears round. He further said: since the Yellow River Chart does not have four corners, it is naturally round compared to the Luo Writing. "A square represents the earth." A square shape belongs to the text of the Luo Writing, because dividing the regions and planning the well-field system were based on it. In the "Book of Documents: Yu Gong," Yu the Great divided the nine states: Ji in the north, Yang in the south, Qing in the east, Liang in the west, Yan in the northeast, Yong in the northwest, Xu in the southeast, Jing in the southwest, and Yu in the center. Mencius discussed the well-field system of the Zhou dynasty, which was one well with nine hundred mu, with the central part being public land and each of the eight families having one hundred mu of private land, all working together on the public land. These were all based on the nine numbers of the Luo Writing.

鶴山魏氏了翁《題司馬子已易圗》曰：涑水司馬叔原覃思易理之學，著《已易》。朱文公以十為河圗、九為洛書，引邵子說辨析甚詳，叔原從之。乃邵子不過曰「圎者河圗之數，方者洛書之文」，今戴九履一之圗其象圎，五行生成之圗其象方，是九圎而十方也，安知邵子不以九為圗、十為書乎？故朱子雖力攻劉氏，而猶曰「易範之數誠相表裡」，又曰「安知圗之不為書、書之不為圗」，則朱子尚有疑乎此也。近世朱子發、張文饒精通邵學，而皆以九為圗、十為書，朱以《列子》為證，張以邵子為主。予嘗以《乾鑿度》及張平子傳所載太一下行九宮法考之，即所謂戴九履一者，則是圗相傳已久，安知非河圗也？紹定四年書。

In the Southern Song dynasty, Wei Liaoong (also known as He Shan) wrote in his "Commentary on the Diagram of the Book of Changes by Sima Ziyi" that Sima Shuyuan, a man from Sushui, devoted himself to the study of the principles of the Book of Changes, and wrote a work called "Yi" (the Book of Changes). Zhu Xi regarded ten as the numbers of the Yellow River Chart and nine as the numbers of the Luo Writing, and he cited Shao Yong's statements to explain them in detail, and Sima Shuyuan followed Zhu Xi's view. However, Shao Yong merely said, "The circular form represents the numbers of the Yellow River Chart, and the square form represents the text of the Luo Writing." Now, the diagram called "Daijiu Lüyi" (the diagram with nine at the top and one at the bottom) has a circular form, while the diagram of the Five Phases has a square form. This shows that nine is circular and ten is square. How can we be sure that Shao Yong did not mean that nine is the diagram and ten is the writing? Therefore, although Zhu Xi strongly criticized Liu Mu, he still said, "The numbers of the Book of Changes and the numbers of the Hongfan (the Nine Chapters) are indeed complementary." He also said, "How can we know that the diagram cannot be the writing or the writing cannot be the diagram?" This shows that Zhu Xi still had doubts about this point. In recent times, Zhu Zhen (also known as Zifā) and Zhang Xingcheng (also known as Wenrao) both were well-versed in Shao's teachings, yet they both regarded nine as the diagram and ten as the writing. Zhu Zhen cited the "Liezi" as evidence, while Zhang Xingcheng mainly followed Shao Yong. I once examined this using the "Qian Zao Du" and the account in the "Later Han Book" about "Taiyi moving through the nine palaces," which clearly shows the "Daijiu Lüyi" diagram. This indicates that this diagram has been passed down for a long time. How can we be sure it is not the Yellow River Chart? Recorded in the fourth year of Shao Ding.

靜修劉氏因《河圗洛書辨》曰：邵子但言方圎之象，而不指九十之數。若以象觀之，則九又圎於十矣。且其所謂方圎而前後乎此者，不過指陰陽剛柔奇偶而已。在此則星少陽而土少柔，其偶者固當為方而為陰，奇者固宜為圎而為陽矣。

In his work "Discernment of the Yellow River Chart and the Luo Writing" (He Tu Luo Shu Bian), Liu Yin of the Yuan dynasty (styled Jingshu) said that Shao Yong only discussed the images of square and circle, but did not specify whether it was nine numbers or ten numbers. If we look solely at the forms, nine numbers appear more circular than ten numbers. Moreover, the square and circle mentioned by him before were merely referring to yin and yang, hardness and softness, odd and even. In this context, stars belong to the category of less yang, while earth belongs to the category of less softness. Even numbers should be paired with square and yin, while odd numbers should be paired with circle and yang.

邵子之於圗書，言方圎而不言九十。蔡季通以圎星為十為圗、方土為九為書，而朱子從之，謂河圗無四隅，比洛書便圎；魏華父則以為九圎而十方，劉夢吉亦云九圎於十，葢皆以九為圗。說者以為物有八隅必作圎形，九宮是也；物止四面必成方形，五合是也。魏說較長，以理言之誠有然者。若摹寫為奇白偶黑、累累貫珠之狀，則九亦可觚稜之以為方，十亦可彎環之以為圎，安見九必圎而十必方乎？方圎之或九或十終無定論，而邵子埓之以星土，固有所自來，其數可考而知也。

Shao Yong discussed the Yellow River Chart and the Luo Writing, referring only to square and circle, without mentioning nine and ten. Cai Yuanping designated "the round as stars" as the number ten, assigning it to the Yellow River Chart, and "the square as earth" as the number nine, assigning it to the Luo Writing. Zhu Xi followed this approach, saying that the Yellow River Chart has no four corners, so it is naturally round compared to the Luo Writing. However, Wei Leiweng (whose name was Huafu) argued that nine is round and ten is square, while Liu Yin (whose name was Mengji) also said that nine is more round than ten. Generally, they all tended to associate nine with the Yellow River Chart. The reasoning given by the commentators was that an object with eight corners must be round, like the nine-square diagram; and an object with four sides must be square, like the Five Phases generation diagram. Wei Leiweng's view seems more reasonable, as it makes sense in terms of logic. However, if they are drawn with odd numbers represented by white dots and even numbers by black dots, arranged in a chain-like pattern, then nine can also be drawn with sharp angles to form a square, and ten can be curved to form a circle. How can we be certain that nine is always round and ten is always square? Whether square and circle belong to nine or ten remains undetermined. Shao Yong's pairing of stars with earth has its own origin, and the numbers involved can be examined and clarified.

友人徐敬可嘗謂余曰：《觀物外篇》所謂圎星方土，乃論積數自然之理，非論圗書也，連上文讀之即明。朱子斷章取義，載之《啟蒙》，遂不可解，而引一行二始二中二終之說以釋歴數肇於圎星之義，殊為牽強。今按此之上文曰：「天圎而地方，圎之數起一而積六，方之數起一而積八，變之則起四而積十二也。六者常以六變，八者常以八變，而十二者亦以八變，自然之道也。」又曰：「圎者六變，六六而進之，故六十變而三百六十矣；方者八變，故八八而成六十四矣。陽主進，是以進之為六十矣。」

My friend Xu Shan (style name Jingke) once told me that in the "Outer Chapter of Observing Things" it says, "Round things are stars, square things are earth," which refers to the natural principle of the accumulation of numbers, not the Yellow River Chart or the Luo Writing. As long as one reads the preceding text, it becomes clear. Zhu Xi took this passage out of context and included it in his "Introduction to the Study of the Changes," which makes no sense. He also used Yixing's idea of "two beginnings, two middles, and two ends" to explain "the numbers of the calendar begin with the round stars," which is forced. Now, examining the preceding text, it says: "The sky is round and the earth is square; the numbers of the round start from one and accumulate to six, while the numbers of the square start from one and accumulate to eight. When changes occur, they start from four and accumulate to twelve. Six always changes in multiples of six, eight always changes in multiples of eight, and twelve also changes in multiples of eight, which is a natural principle." It also says: "The round undergoes six changes, and six multiplied by six and then progresses, so it reaches sixty and then three hundred and sixty. The square undergoes eight changes, so eight multiplied by eight becomes sixty-four. Yang is dominant in advancement, so it progresses to sixty."

然後繼以圎星方土之說，玩其辭旨，葢積數自然之理。凡以七圎物相聚，必以一為心而環之以六□，此形是起一而積六也；凡以九方物相聚，必以一為心而圍之以八□，此形是起一而積八也；凡以十二方物相聚，必以四為心而圍之以十二□，此形是起四而積十二也。

Then it goes on to say, "A circle represents a star, and a square represents earth." Delving into its meaning, it is speaking of the natural principle of accumulation of numbers. Whenever seven circular objects are gathered together, one must be in the center with six surrounding it (as shown in the diagram), which is "accumulating from one to six"; whenever nine square objects are gathered together, one must be in the center with eight surrounding it (as shown in the diagram), which is "accumulating from one to eight"; whenever twelve square objects are gathered together, four must be in the center with twelve surrounding them (as shown in the diagram), which is "accumulating from four to twelve."

圎者聚七之形，如眾星之麗乎天，以六變而為三十六，進之極於三百六十，當期之日，得氣朔盈虛之中，而星於是乎一周，是為治歴之本，故曰歴紀之數肇於此，二始二終曷與乎？方者聚九之形，象九州島，亦八家同井、中為公田象也。變之則為聚十六之形，象四邑為丘，丘容十六井；又加兩圍共六十四，乃四丘為甸之象，甸容六十四井；更進而四甸為縣，縣容六十四邑；更進而四縣為都，都容六十四丘，皆所謂八八而成六十四也，故曰畫州井地之法放於此也。

The round shape represents the form of gathering seven, just like countless stars attached to the sky: after six transformations it becomes thirty-six, and when pushed to the extreme it reaches three hundred and sixty, exactly matching the number of days in a year. Within this number are the average figures of the twenty-four solar terms, new and full moons, and the waxing and waning of the moon. Thus the stars complete one cycle, which is the fundamental principle of establishing a calendar. Therefore, it is said, "The numbers of the calendar originate here." Now, what connection does the concept of "two beginnings" and "two endings" mentioned by Yixing have with this? The square shape represents the form of gathering nine, symbolizing the nine provinces. It also represents the image of eight families sharing one well-field, with the central part being the public field. When this form expands, it becomes the shape of gathering sixteen, symbolizing four towns forming one hill, with one hill containing sixteen well-fields; adding two more layers around it makes sixty-four, representing four hills forming one town, with one town containing sixty-four well-fields; further expansion leads to four towns forming one county, with one county containing sixty-four hills; and further expansion leads to four counties forming one capital, with one capital containing sixty-four hills. These are all referred to as "eight eights forming sixty-four." Therefore, it is said, "The methods of dividing states and well-fields are modeled after this."

更推而廣之，古有河圗亦圎體也，羲文因之以造易，則圎星之類也；古有洛書亦方體也，禹箕敘之以作範，則方土之類也。此不過因論方圎之積數而牽綴及之，不專為圗書而發。方九猶可言，彼圎則何以知其為九與十也哉？

When extending this further, in ancient times there was the Yellow River Chart, which was round in form, and Fuxi and King Wen based the Book of Changes on it, which would fall under the category of "round stars"; in ancient times there was also the Luo Writing, which was square in form, and Yu the Great and Ji Zi based the Classic of Documents on it, which would fall under the category of "square land". This is merely a passing mention due to the discussion of the accumulation of numbers in square and round forms, and not specifically about the Yellow River Chart and the Luo Writing. The square form is determined by nine numbers, which can be somewhat explained, but how can we determine the round form as either nine or ten?

其下文則曰：「蓍數不以六而以七，何也？並其餘分也。去其餘分則六，故策數三十六也。是以五十者，六十四卦閏歲之策也；其用四十有九，六十四卦一歲之策也；歸奇掛一，猶一歲之閏也。卦直去四者何也？天變而地效之，是以蓍去一則卦去四也。」又曰：「蓍德圎以況天之數，故七七四十九也，五十者存一而言之也；卦德方以況地之數，故八八六十四也，六十者去四而言之也。」

Continuing the text: "The number of the divining stalks uses seven instead of six, why? Because the remainder is also counted in; if the remainder is removed, it becomes six, so the number of stalks for each line is thirty-six. Therefore, the number fifty is the number of the sixty-four hexagrams in a leap year; actually using forty-nine is the number of the sixty-four hexagrams in a regular year; the remainder is set aside, just like the leap month in a year. As for the hexagram numbers being reduced by four, why is that? Because heaven changes first and earth follows, so the number of stalks is reduced by one, and the number of hexagrams is reduced by four." It also says: "The nature of the divining stalks is round, used to compare with the number of heaven, so it is seven times seven, forty-nine, saying fifty includes the one that is kept but not used; the nature of the hexagrams is square, used to compare with the number of earth, so it is eight times eight, sixty-four, saying sixty is the number after removing the four."

然則天圎主蓍、地方主卦，蓍數以七相乘則為四十九，以六相乘則為三十六，無九位四十有五之數；卦數以八相乘為六十四，去其四則為六十，亦無十位五十有五之數。竊意邵子所指為河圗者，即希夷先天太極一圈之形，故謂之圎，與闗朗之河圗全無交涉；其所指為洛書者，即九宮之形，中起一而外積八，故謂之方，此則與闗朗闇合，而其所以為方之意，季通亦未之識也，故漫引以為圗十書九之證。從來憒憒，茲特為一闡明之。

Thus, it appears that the circular form represents the yarrow stalks and the square form represents the trigrams: the number of yarrow stalks, when multiplied by seven, gives forty-nine, and when multiplied by six, gives thirty-six, with no mention of the forty-five number of the nine squares; the number of trigrams, when multiplied by eight, gives sixty-four, and subtracting four gives sixty, with no mention of the fifty-five number of the ten positions. I privately infer that the river chart referred to by Shao Yong is the circular shape of Chen Tuan's Earlier Heaven Taiji, hence called "circular," and has nothing to do with the river chart mentioned by Guan Lang; the Luo Writing he refers to is the shape of the nine squares, with one at the center and eight surrounding it, hence called "square," which coincides with Guan Lang's view, though the reason for calling it "square" was not understood by Cai Yuanping, so he mistakenly used it as evidence for the "chart ten, writing nine" theory. Throughout history, this has been confused, and here I specially clarify it.

朱子《答劉君房書》曰：「《啟蒙》本欲學者且就大傳所言卦畫蓍數推尋，不須過為浮說，而自今觀之，如河圗洛書亦未免有剩語。」觀此言，知季通代斵不中繩墨，文公晚年亦深悔之，但未及改削耳。而近代諸儒奉《啟蒙》為不刋之書，不亦過乎！

Zhu Xi in his letter to Liu Junfang said: "The original intention of the 'Easy Enlightenment' was to have scholars investigate the diagrams of the hexagrams and the method of divination with yarrow stalks as explained in the Great Treatise, without engaging in excessive and superficial discussions; looking back now, contents such as the Yellow River Chart and the Luo Writing are also unnecessary. From this statement, we can see that Cai Yuanding, acting on behalf of others, wielded the axe without following the correct pattern; Zhu Xi himself deeply regretted this in his later years, but it was too late to make revisions. However, modern scholars have regarded the 'Easy Enlightenment' as an unchangeable definitive text, which is surely excessive."

《本義圗說》：《繫辭傳》曰「河出圗，洛出書，聖人則之」，又曰「天一地二，天三地四，天五地六，天七地八，天九地十。天數五，地數五，五位相得而各有合。天數二十有五，地數三十，凡天地之數五十有五，此所以成變化而行鬼神也」，此河圗之數也。洛書葢取龜象，故其數戴九履一，左三右七，二四為肩，六八為足。

The Original Meaning of the Zhou Changes states in its preface that the Great Treatise says, "The Yellow River produced the chart, and the Luo River produced the writing; the sage took them as models." It also says, "Heaven has one, Earth has two; Heaven has three, Earth has four; Heaven has five, Earth has six; Heaven has seven, Earth has eight; Heaven has nine, Earth has ten. The numbers of Heaven are five in total, and the numbers of Earth are five in total. Each of the five directions corresponds and is matched accordingly. The total of the Heaven numbers is twenty-five, and the total of the Earth numbers is thirty. The total numbers of Heaven and Earth together are fifty-five, which is used to accomplish changes and the movement of ghosts and spirits." This is the numerical pattern of the Yellow River Chart. The Luo Writing is probably modeled after the pattern of a turtle's back, so its numbers are arranged with nine at the head, one at the feet, three on the left, seven on the right, two and four as the shoulders, and six and eight as the feet.

《易學啟蒙》曰：河圗之位，一與六共宗而居乎北，二與七為朋而居乎南，三與八同道而居乎東，四與九為友而居乎西，五與十相守而居乎中。葢其所以為數者，不過一陰一陽、一奇一偶，以兩其五行而已。所謂天者，陽之輕清而位乎上者也；所謂地者，陰之重濁而位乎下者也。陽數奇，故一三五七九皆屬乎天，所謂天數五也；陰數偶，故二四六八十皆屬乎地，所謂地數五也。天數地數各以類而相求，所謂五位之相得者然也。

The *Yixue Qimeng* says: In the Yellow River Chart, the number one and six share the same origin and are located in the north; the number two and seven are companions and are located in the south; the number three and eight are on the same path and are located in the east; the number four and nine are friends and are located in the west; the number five and ten are companions and are located in the center. Basically, the principle of the formed numbers is simply the combination of one yin and one yang, one odd and one even, to pair each of the Five Phases with two numbers. The term "heaven" refers to yang energy, which is light and clear and resides in the upper position; the term "earth" refers to yin energy, which is heavy and turbid and resides in the lower position. Yang numbers are odd, so one, three, five, seven, and nine belong to heaven, which is called "five heavenly numbers"; yin numbers are even, so two, four, six, eight, and ten belong to earth, which is called "five earthly numbers." Heavenly and earthly numbers each seek their own kind, and the phrase "five positions correspond" refers to this.

天以一生水而地以六成之，地以二生火而天以七成之，天以三生木而地以八成之，地以四生金而天以九成之，天以五生土而地以十成之，此又其所謂各有合焉者也。積五奇而為二十五，積五偶而為三十，合是二者而為五十有五，此河圗之全數，皆夫子之意而諸儒之說也。至於洛書，則雖夫子之所未言，然其象其說已具於前，有以通之，則劉歆所謂經緯表裡者可見矣。

Heaven produces water with the number one and Earth completes it with six; Earth produces fire with the number two and Heaven completes it with seven; Earth produces wood with the number three and Heaven completes it with eight; Earth produces metal with the number four and Heaven completes it with nine; Earth produces earth with the number five and Heaven completes it with ten. This is what is called 'each has its corresponding number.' The sum of the five odd numbers is twenty-five, and the sum of the five even numbers is thirty. Together they make fifty-five, which is the total number of the Yellow River Chart. This is the meaning intended by Confucius and the views of the various scholars. As for the Luo Writing, although Confucius did not mention it, its image and its meaning are already presented earlier. If one can connect them together, then the statement by Liu Xin that 'the Yellow River Chart and the Luo Writing are like the meridians and the parallels, one inside and one outside' can be clearly understood.

天地之數五十有五，專為大衍之數五十張本，此蓍策之原，非畫卦之法。《易雅》云：九六七八為揲蓍策數，乃先有卦而後揲蓍，非先得數而後畫卦，夫子未嘗以是明河圗也。李泰伯云：天一至地十乃天地之氣降出之次第，而曰五十有五者，葢聖人假其積數以起算法，非實數也。譬如兄弟行第一至第十者乃十人耳，今《鉤隠》河圗有白黑四十五點，是九人而化為四十五人也；《啟蒙》河圗有白黑五十五點，是十人而化為五十五人也。以積數為實數，以算法為卦原，而寫之以成象，九圗十書、十圗九書，總無是處。

Hu Wei said: "The number fifty-five of heaven and earth" is specifically intended to set up the foundation for "the fifty numbers of the great derivation," which is the origin of the divination with yarrow stalks, not the method of drawing hexagrams. The "Yi Ya" says that nine, six, seven, and eight are the numbers of stalks obtained by divination, indicating that hexagrams come first and then the divination with yarrow stalks, not that numbers are obtained first and then hexagrams are drawn. Confucius never used these numbers to explain the Yellow River Chart. Li Gou said: from heavenly one to earthly ten, it is merely the order of the birth of the qi of heaven and earth; calling it fifty-five is the way of the sage to use this cumulative number to start the calculation, not that there are actually fifty-five numbers. For example, the order of brothers from first to tenth refers to ten people, but now the "Gou Yin Tu" draws the Yellow River Chart with forty-five black and white dots, equivalent to turning nine people into forty-five; the "Ming Gong" draws the Yellow River Chart with fifty-five black and white dots, equivalent to turning ten people into fifty-five. Taking the cumulative number as an actual number and taking the calculation method as the origin of drawing hexagrams, then drawing the figure accordingly—whether saying nine is the diagram and ten is the text or ten is the diagram and nine is the text, all of them make no sense.

然九宮猶存八卦之位，而五合缺其四隅，則與八卦一毫不相似矣。易有八卦而無五行，以《洪範》五行附會於翼傳，自漢儒始。《五行志》曰：天一生水，地二生火，天三生木，地四生金，天五生土。又曰：水之大數六，火七，木八，金九，土十。大數即成數，此以天地之數配五行也。坎水、離火、巽木見於夫子之大象，而坤艮不言土，乾為金惟見於《說卦》。據《左傳》莊二十二年周史曰「坤，土也」，《周語》太子晉曰「山，土之聚也」，是坤艮亦可言土矣，而震木兊金無聞焉。《五行志》曰：震在東方為木，兊在西方為金。震木兊金始見於此。《漢上易傳》云：京房以乾兊為金。然則震巽同為木，葢亦始於房。此以八卦方位配五行也，皆非夫子之意。

However, the Nine-square Diagram still retains the directional positions of the Eight Trigrams, while the Five Elements Generating Diagram lacks four corners, making it completely unlike the Eight Trigrams. The Book of Changes contains only the Eight Trigrams and not the Five Elements; attaching the Five Elements from the Hongfan (The Mandate of Heaven) to the Ten Wings of the Book of Changes began from the Han dynasty scholars. The "Book of Han · Five Elements Chapter" says: "Heaven produces water with the number one, Earth produces fire with the number two, Heaven produces wood with the number three, Earth produces metal with the number four, Heaven produces earth with the number five." It also says: "The great number of water is six, fire is seven, wood is eight, metal is nine, and earth is ten." "Great number" is the same as "completed number," which is matching the numbers of heaven and earth with the Five Elements. The associations of Kan with water, Li with fire, and Xun with wood are found in the Great Image Commentary written by Confucius, but Kun and Gen are not stated as earth. The association of Qian with metal is only mentioned in the "Sayings on the Trigrams." According to the "Zuo Zhuan" from the 22nd year of Duke Zhuang, the Zhou dynasty historian said, "Kun is earth." The "Zhou Yu" from the "Guoyu" says, "Mountains are the accumulation of earth." This shows that Kun and Gen can also be interpreted as earth. As for Zhen being wood and Dui being metal, there is no evidence in the classic text. The "Book of Han · Five Elements Chapter" says: "Zhen is in the east and belongs to wood, Dui is in the west and belongs to metal"—this is the first time the idea of Zhen as wood and Dui as metal appears. Zhu Zhen's "Han Shang Yijie" says: "Jingfang associated Qian and Dui with metal." Therefore, the association of Zhen and Xun with wood probably began with Jingfang. This method of matching the Eight Trigrams with the Five Elements is not in line with Confucius's original intention.

劉牧云：洛書之數五十有五，演五行而不述四象，謂禹則之以陳範，故專主五行也。今既以五十有五為河圗，而羲則之以畫卦，即與五行全無交涉，奚為拾漢儒之餘瀋而以五行生成之數附會於其間乎？劉歆言羲則圗、禹則書，而繼之曰「河圗洛書相為經緯，八卦九章相為表裡」，此真所謂畫蛇添足者，而《啟蒙》欲有以通之，吾未見其有可通之理也。

Liu Mu said: The number of the Luo Shu is fifty-five, and it only deduces the Five Phases without mentioning the Four Symbols, because Da Yu took it as a model to explain the Hong Fan, so it is exclusively about the Five Phases. Now, if we take fifty-five as the He Tu, and Fuxi took it as a model to draw the trigrams, then it has nothing to do with the Five Phases. Why should we pick up the leftovers of Han scholars and force the numbers of the generation of the Five Phases into it? Liu Xin said Fuxi took the He Tu as a model and Da Yu took the Luo Shu as a model, and then he said "the He Tu and Luo Shu are like the meridians and parallels, the Eight Trigrams and the Nine Categories are like the inside and outside," which is truly adding legs to a snake. The启蒙 also wants to integrate them, but I don't see any reason to integrate them.

然則聖人之則之也奈何？曰：則河圗者虛其中，則洛書者總其實也。河圗之虛五與十者，太極也；奇數二十、偶數二十者，兩儀也；以一二三四為六七八九者，四象也；析四方之合以為乾坤離坎，補四隅之空以為兊震巽艮者，八卦也。洛書之實：其一為五行，其二為五事，其三為八政，其四[四庫本此至「五十合」闕]為五紀，其五為皇極，其六為三德，其七為稽疑，其八為庶徵，其九為福極，其位與數尤曉然矣。

So how did the sage derive from them? The answer is: to derive from the Yellow River Chart, one should take the central part as empty; to derive from the Luo Writing, one should summarize the actual numbers. In the Yellow River Chart, removing the five and ten from the center, that is the Taiji; the odd numbers total twenty, and the even numbers also total twenty, that is the two principles; pairing one, two, three, and four with six, seven, eight, and nine, that is the four images; dividing the four cardinal directions to determine Qian, Kun, Li, and Kan, and filling in the four intercardinal directions to determine Dui, Zhen, Xun, and Gen, that is the eight trigrams. The actual numbers of the Luo Writing: the first is the Five Phases, the second is the Five Affairs, the third is the Eight Policies, the fourth (the Complete Library of the Four Treasuries edition begins here and continues to the section "fifty combined" below) is the Five Records, the fifth is the Imperial Center, the sixth is the Three Virtues, the seventh is the Inquiry into Doubt, the eighth is the Various Signs, the ninth is the Ultimate Blessing—its positions and numbers are even clearer.

又曰：洛書而虛其中，則亦太極也；奇偶各居二十，則亦兩儀；一二三四而含九八七六，縱橫十五而互為七八九六，則亦四象也；四方之正以為乾坤離坎，四隅之偏以為兌震巽艮，則亦八卦也。河圖之一六為水，二七為火，三八為木，四九為金，五十為土，則固洪範之五行，而五十有五者又九疇之子目也。是則洛書固可以為易，而河圖亦可以為範矣，且又安知圖之不為書、書之不為圖也耶？

It is also said that if the center of the Luo Writing is removed, it is also the Taiji; the odd and even numbers each total twenty, which is also the two principles; within the numbers one, two, three, and four there are nine, eight, seven, and six, and when added vertically and horizontally they all total fifteen, and they correspond to each other as seven, eight, nine, and six, which is also the four images; the four cardinal directions are assigned to Qian, Kun, Li, and Kan, while the four intermediate directions are assigned to Dui, Zhen, Xun, and Gen, which is also the eight trigrams. In the He Tu, one and six represent water, two and seven represent fire, three and eight represent wood, four and nine represent metal, and five and ten represent earth, which is originally the Five Phases of the Hongfan chapter. Moreover, the total number fifty-five is exactly the sum of the details of the nine categories. Thus, the Luo Writing can be used as the Yi, and the He Tu can be used as the Hongfan; and how can we be certain that the diagram cannot be the book, or the book cannot be the diagram?

玉齋胡氏方平《啟蒙通釋》曰：四方為乾坤離坎、四隅為兌震巽艮者，蓋一六老陰之數而畫卦為艮坤，反居六、坤居一也；三八少陰之數而畫卦為離震，離居三、震居八也；四九老陽之數而畫卦為乾兌，乾居九、兌居四也；二七少陽之數而畫卦為巽坎，巽居二、坎居七也，此洛書亦可以為八卦也。九疇子目者：五行五，五事五，八政八，五紀五，皇極一，三德三，稽疑七，庶徵十，福極十一，總五十五。

In the Yuan dynasty, Hu Fangping (styled Yu Zhai) wrote in "Yixue Qimeng Tongshi" that the four cardinal directions are Qian (Heaven), Kun (Earth), Li (Fire), and Kan (Water), while the four intermediate directions are Dui (Lake), Zhen (Thunder), Xun (Wind), and Gen (Mountain). This is because one and six are the numbers of old yin, and using them to draw the trigrams results in Gen and Kun, which are placed at the sixth and first positions respectively; three and eight are the numbers of young yin, and using them to draw the trigrams results in Li and Zhen, which are placed at the third and eighth positions respectively; four and nine are the numbers of old yang, and using them to draw the trigrams results in Qian and Dui, which are placed at the ninth and fourth positions respectively; two and seven are the numbers of young yang, and using them to draw the trigrams results in Xun and Kan, which are placed at the second and seventh positions respectively. This means that the Luo Writing can also be used to match the eight trigrams. As for the details of the nine categories: five for the Five Phases, five for the Five Affairs, eight for the Eight Policies, five for the Five Records, one for the Imperial Center, three for the Three Virtues, seven for the Deliberation of Doubts, ten for the Various Signs, eleven for the Ultimate Blessings, totaling exactly fifty-five.

黃氏《象數論》曰：就二數通之於易，則十者有天一至地十之數可據，九者並無明文，此朱子爭十為河圖之意長於長民也。雖然，自一至十之數，易之所有也；自一至十之方位，易之所無也。一三五七九之合於天、二四六八十之合於地，易之所有也；一六合、二七合、三八合、四九合、五十合，易之所無也。天地之數，易之所有也；水火木金土之生成，易之所無也。試盡去後人之添入，依經為說，則此數仍於易無與，而況名之為河圗乎？

Huang Zongxi's "Discussion on the Images and Numbers of the Book of Changes" says: Using the numbers nine and ten to correspond with the Book of Changes, the number ten still has the classic text "Heaven one to Earth ten" to support it, but the number nine has no clear text. This is why Zhu Xi advocated that the number ten corresponds to the Yellow River Chart, and his reasoning is more convincing than Liu Mu's (whose courtesy name was Changmin). Nevertheless, the numbers from one to ten are originally present in the Book of Changes; however, the arrangement of these numbers in directions is not found in the Book of Changes. The odd numbers one, three, five, seven, and nine correspond to Heaven, while the even numbers two, four, six, eight, and ten correspond to Earth, and these are originally present in the Book of Changes. However, the pairing of one with six, two with seven, three with eight, four with nine, and five with ten is not found in the Book of Changes. The numbers of Heaven and Earth are originally present in the Book of Changes, but the generating numbers and completing numbers of water, fire, wood, metal, and earth are not found in the Book of Changes. If we try to remove all the additions made by later scholars and base our discussion solely on the classic texts, then these numbers still have nothing to do with the Book of Changes, let alone attaching the name "Yellow River Chart" to them.

天一至地十之數，儒者必欲言聖人則之以畫卦。崔憬曰：參天者，謂從三始順數而至五七九，不取於一；兩地者，謂從二起逆數而至十八六，不取於四。艮為少陽其數三，坎為中陽其數五，震為長陽其數七，乾為老陽其數九，兊為少陰其數二，離為中陰其數十，巽為長陰其數八，坤為老陰其數六。劉長民水六金九火七木八而生八卦[以坎離震兊為四正]：六居坎而生乾，謂三為坎、三為乾也；九居兊而生坤，謂三為兊、六為坤也；七居離而生巽，謂三為離、四為巽也；八居震而生艮，謂三為震、五為艮也。朱子曰：河圗之虛五與十者，太極也；奇數二十、偶數二十者，兩儀也；以一二三四為六七八九者，四象也；析四方之合以為乾坤離坎，補四隅之空以為兊震巽艮者，八卦也。同此一數，而三家所指不同如此。

The number system of "Heavenly One to Earthly Ten" has always been interpreted by Confucian scholars as the basis for the sage's drawing of the trigrams. Tang dynasty scholar Cui Jing said: the term "ascending to Heaven" refers to counting upward from three to five, seven, and nine, excluding one; the term "descending to Earth" refers to counting downward from two to ten, eight, and six, excluding four. Gen represents the Lesser Yang and is numbered three; Kan represents the Middle Yang and is numbered five; Zhen represents the Greater Yang and is numbered seven; Qian represents the Old Yang and is numbered nine; Dui represents the Lesser Yin and is numbered two; Li represents the Middle Yin and is numbered ten; Xun represents the Greater Yin and is numbered eight; Kun represents the Old Yin and is numbered six. Liu Mu said: water is six, metal is nine, fire is seven, wood is eight, and from these come the eight trigrams (with Kan, Li, Zhen, and Dui as the four cardinal trigrams). Six is in the position of Kan and gives rise to Qian, meaning three lines for Kan and three lines for Qian; nine is in the position of Dui and gives rise to Kun, meaning three lines for Dui and six lines for Kun; seven is in the position of Li and gives rise to Xun, meaning three lines for Li and four lines for Xun; eight is in the position of Zhen and gives rise to Gen, meaning three lines for Zhen and five lines for Gen. Zhu Xi said: in the Yellow River Chart, the numbers five and ten are removed, which is the Taiji; the odd numbers total twenty and the even numbers total twenty, which are the two principles; pairing one, two, three, and four into six, seven, eight, and nine, which are the four images; splitting the numbers of the four cardinal trigrams to determine Qian, Kun, Li, and Kan, and filling in the empty corners to determine Dui, Zhen, Xun, and Gen, which are the eight trigrams. It is the same number system, yet the interpretations of the three scholars differ greatly.

配卦之論始於崔憬。憬但言其數不言其位，乾坤震巽數有可據，其附會者坎離艮兊耳。長民兼位數而言，六為水而坎屬之，七為火而離屬之，八為木而震屬之，九為金而兊屬之，以四卦之五行遷就其位數，未為不可，至於乾坤艮巽則不可通矣。朱子祖先天之說，以乾南坤北者宓羲之卦位也，離南坎北者文王之卦位也，河圗出於宓羲，其時尚無離南坎北之位，硬以乾南坤北配之，則更無一合者矣。天下之物，一人以為然，千萬人以為然，其為物也不逺矣；一人可指之為此，又一人可指之為彼，其為物也無定名矣。故以天地之數配八卦者，皆非定名也。

The discussion of matching numbers with trigrams began with Cui Jing. Cui Jing only discussed numbers and not directions. Among the trigrams, the numbers for Qian, Kun, Zhen, and Xun have some basis, but the reasoning for Kan, Li, Gen, and Dui is forced. Liu Mu combined both numbers and directions: six is water and matches Kan, seven is fire and matches Li, eight is wood and matches Zhen, nine is metal and matches Dui. Using the Five Phases of these four trigrams to fit their directions and numbers makes some sense, but when it comes to Qian, Kun, Gen, and Xun, the reasoning fails. Zhu Xi followed the Earlier Heaven theory: Qian is in the south and Kun is in the north, which is the position of trigrams from Fuxi; Li is in the south and Kan is in the north, which is the position from King Wen. Since the Yellow River Chart originated in Fuxi's time, there was no concept of Li in the south and Kan in the north then. Forcing Qian to the south and Kun to the north to match the chart is even more inconsistent. In the world, if one person thinks something is so and a thousand others also think so, then that thing is close to the truth. But if one person calls it Jia and another calls it Yi, then that thing has no fixed name. Therefore, all the theories of matching the numbers of heaven and earth with the eight trigrams do not have fixed names.

毛氏《原舛編》曰：夫圗書非他，神聖之事也，豈有神聖之事而一人授之、一二人受之哉？授者無憑，受之者無據，而或四或五，或方或圎，或羲或禹，或卦或範，彼此可以爭先後，可以易，一室兩家，茫無定準，其為不足道亦可見矣。

Mo Shi's "Original Compilation of Errors" says: The Yellow River Chart and the Luo Writing are not anything else, but sacred matters; how could sacred matters be transmitted by only one person and accepted by just one or two people? The transmitter has no evidence, and the receiver has no basis. As for the accounts, some say four, some say five, some say square, some say round, some attribute them to Fuxi, some to the great Yu, some use them for drawing the trigrams, some for composing the "Hongan Fan" (the Nine Codes). They can argue about the sequence, they can interchange with each other; even within the same room there are two conflicting views, and there is no definite standard—this shows clearly that they are not reliable.

按：季通據先天八卦之方位，而附會以太極兩儀四象之名，曰「析四方之合以為乾坤離坎，補四隅之空以為兊震巽艮」[即闗《易》所云「正者全其位，隅者盡其畫」，然彼用後天卦位，此用先天卦位]。噫！伏羲上聖，其則河圗以畫卦，乃煩割裂補綴，費如許經營邪？雖至愚者亦知其無是理矣。劉歆所云相為經緯表裡者，不過以五行生成言之耳，季通發明其義，以為易之太極兩儀四象皆通於洛書，而洪範之五行、九疇之子目則又通於河圗，任意牽合，無所不可。然十圗九書本無定理，故結之曰「安知圗之不為書、書之不為圗」，終歸於鶻突無據而已矣。

Hu Wei said: Cai Yuan Ding based on the positions of the Earlier Heaven Trigrams, and attached the names of Taiji, two principles, and four images. He said, "Split the numbers of the four cardinal directions to determine the positions of Qian and Kun, Li and Kan, and supplement the empty corners to determine Dui, Zhen, Xun, and Gen." (This is what the fake "Guanzimi Yi Zhuan" said: "Those in the central positions occupy their proper places, and those in the corners use up the remaining lines," but there they used the Later Heaven Trigram positions, while here they used the Earlier Heaven Trigram positions.) Alas! Fuxi was an ancient sage, who took the form of the Yellow River Chart to draw the trigrams. Could he have needed to cut and patch things up, going through so much trouble? Even the most foolish person would know that there is no such reasoning. Liu Xin's statement of "mutual interweaving of meridians and moxibustion, inside and outside" was merely referring to the numbers of the Five Phases' generation. Cai Yuan Ding extended this meaning, believing that the Taiji, two principles, and four images of the Yi Classic could all be connected to the Luo Writing, and that the Five Phases and the nine categories of the Hongfan Classic could all be connected to the Yellow River Chart. He arbitrarily connected them, believing anything was possible. However, since "ten is the chart and nine is the writing" originally had no fixed meaning, in the end he could only say, "How do we know the chart cannot be the writing, or the writing cannot be the chart?" Eventually, he ended up with a vague and unsupported conclusion.

朱子《書河圗洛書後》曰：世傳一至九數者為河圗、一至十數者為洛書，考之於古，正是反而置之，予於《啟蒙》辨之詳矣。近讀《大戴禮》，又得一證：其《明堂篇》有「二九四七五三六一八」之語，而鄭氏注云「法龜文也」。然則漢人固以此九數者為洛書矣。

Zhu Xi said in his "Commentary on the Yellow River Chart and the Luo Writing": The commonly circulated views take numbers from one to nine as the Yellow River Chart and numbers from one to ten as the Luo Writing. But when we examine ancient texts, it is exactly the opposite. I have already analyzed this thoroughly in my "Awakening to the Yi Classic." Recently, while reading the "Da Dai Li Ji," I found further evidence: its "Bright Hall Chapter" mentions "two nine four, seven five three, six one eight," and Zheng Xuan's commentary says "this is based on the patterns on the turtle's back." Thus, it appears that the Han dynasty people originally regarded these nine numbers as the Luo Writing.

《大戴禮·明堂篇》注云：「記用九室，謂法龜文，故取此數以明其制也。」朱子以為鄭氏語。餘姚黃先生云：鄭玄注小戴禮，未嘗注《大戴禮》，在《藝文志》可考，今之所傳亦後人假託為之也，甚疎略，不出於鄭氏明矣；況鄭氏明言河圗九篇、洛書六篇，豈又以九宮為洛書自背其說哉？今按《後漢書·鄭玄傳》，康成無《大戴禮》注；而《周書·盧辯傳》云：辯字景宣，以《大戴禮》未有訓詁，乃注之。《儒林傳》云：魏永熙三年，敕中書舍人盧景宣解《大載禮·夏小正》篇。然則「九室法龜文」乃景宣語，非康成語也。今之所傳葢出景宣，亦非假託。以洛書為龜文有數至於九，實始於晚出孔安國《書傳》，而景宣襲之。揚雄、張衡但言龜書，無九數之說。

The annotations to the "Mingtang Chapter" in the "Da Dai Li Ji" say: "This chapter records the use of nine rooms in the Bright Hall, which refers to taking the pattern of the tortoise's shell as a model, so using this number system to explain its system." Zhu Xi thought this was Zheng Xuan's view. Master Huang Zongxi of Yuyao said: Zheng Xuan annotated the "Xiao Dai Li Ji," not the "Da Dai Li Ji," which can be seen in the "Hanshu · Yiwen Zhi"; the annotations passed down today are also attributed to later people, and their content is very brief and obviously not from Zheng Xuan; moreover, Zheng Xuan clearly said that the He Tu had nine chapters and the Luo Shu had six chapters, so how could he again take the nine palace system as the Luo Shu and contradict himself? Now examining the "Hou Hanshu · Zheng Xuan Zhuan," Zheng Xuan (styled Kangcheng) did not annotate the "Da Dai Li." The "Rulin Zhuan" says: In the third year of Yongxi of the Eastern Wei, an imperial edict was issued ordering the middle secretary Lu Jingxuan to explain the "Xia Xiaozheng" chapter of the "Da Dai Li." Thus, it appears that the statement "nine rooms take the pattern of the tortoise's shell" is Lu Jingxuan's view, not Zheng Xuan's; the annotations passed down today are probably from Lu Jingxuan, and thus not a forgery. The idea of equating the Luo Shu with the tortoise's pattern and having numbers up to nine actually began with Kong Anguo's "Shangshu Zhuan" in later times, and Lu Jingxuan followed this idea. Yang Xiong and Zhang Heng only mentioned the tortoise script, without mentioning the number nine.

西山兩易圗書，援孔、劉、闗、邵以證已之說，其實唯孔安國以洛書為九數，而闗朗之圗書與所反悉同，劉不言其數，邵亦但以九為書而未嘗以十為圗也。《本義》雖列此二圗，終不能厭服天下之心。故呂伯恭與朱子友善而信劉牧龍圗之學，魏華父私淑朱子亦以戴九履一者為河圗，他如朱元升、葛同叟、李簡、胡一中皆生於朱子之後而不從《啟蒙》。宋末元初朱學盛行，始有從《啟蒙》者，而郝經、劉因、雷思齊猶以為非。迨明之中葉，士子舍《程傳》而專宗《本義》，天下於是惟知有卷首之圗書，而不復問其所從來矣。

Cai Yuanding reversed the River Chart and the Lo Shu, citing Kong Anguo, Liu Mu, Guan Lang, and Shao Yong to support his view. In reality, only Kong Anguo regarded the Lo Shu as the nine numbers, while the diagrams and texts in Guan Lang's writings completely reversed what he opposed. Liu Mu did not discuss that system, and Shao Yong only regarded nine as the Lo Shu, never taking ten as the River Chart. Although The Original Meaning of the Zhou Changes listed these two diagrams at the beginning, it could not convince the people. Therefore, Lu Zuguan, who was close to Zhu Xi, believed in Liu Mu's study of the Dragon Diagram; Wei Leoweng, who privately followed Zhu Xi, also regarded the diagram with "nine on top and one below" as the River Chart. Others like Zhu Yuansheng, Ge Tongshou, Li Jian, and Hu Yizhong, who were born after Zhu Xi, did not follow the启蒙. Only when Zhu Xi's learning became popular in the late Song and early Yuan dynasties did people begin to follow the启蒙. However, Hao Jing, Liu Yin, and Lei Siqi still thought it wrong. By the mid-Ming dynasty, scholars abandoned the Cheng氏 Commentary on the Zhou Changes and focused solely on The Original Meaning of the Zhou Changes. Thus, the world only knew about the two diagrams at the beginning of the book and no longer questioned their origins.

震川歸氏有光《易圗論》曰：或曰：子以易圗為非伏羲之舊，固已明矣，若夫「河以通乾出天苞，洛以流坤出地符」，所謂河圗洛書可廢耶？葢宋儒朱子之說甚詳：揭中五之要，明主客君臣之位，順五行生剋之序，辨體用常變之殊，合卦範兼通之妙，縱橫曲直無不相值，可謂精矣。曰：此愚所以恐其說之過於精也。夫事有出於聖人而在學者有不必精求者，河圗洛書是也。聖人聰明睿智，德通於天，符瑞之生出於世之所創見，而奇偶法象之妙足以為作易之本，理亦有然者。然曰「河圗洛書聖人則之」者，此大傳之所有也；「通乾流坤、天苞地符」之文，「五行生成、戴九履一」之數，非大傳之所有也。

In the "Commentary on the Diagrams of the Book of Changes" by Gu Yi Guang (styled Zhenchuan) of the Ming dynasty, someone asked: You have already clearly explained that you do not consider the diagrams of the Book of Changes to be original to Fuxi. As for the statements in the apocryphal texts that "the river water flows into Heaven and produces the heavenly bundle, and the Luo river flows into Earth and produces the earthly symbol," can the Yellow River Chart and the Luo Writing be discarded? Zhu Xi, a Song dynasty scholar, provided a very detailed explanation: He emphasized the central five numbers as the key, clarified the positions of host and guest, ruler and subject, followed the order of mutual generation and mutual control among the Five Phases, distinguished between essence and function, constancy and change, and combined the hexagrams of the Book of Changes with the nine categories of the "Huang Fan" to reveal their profound unity. In every direction, straight or curved, the correspondence is complete. This is indeed very precise. The reply was: This is exactly the point I am worried about, that his theory is "too refined." Some things are from the sage, but scholars need not pursue them in excessive detail. The Yellow River Chart and the Luo Writing are like that. The sage is wise and intelligent, with virtue reaching the heavens. The appearance of auspicious signs is rare. The subtlety of odd and even numbers as symbols is sufficient to serve as the foundation for the Book of Changes. This reasoning is reasonable. However, the statement "the sage took the Yellow River Chart and Luo Writing as models" is found in the "Great Treatise." As for the phrases "the river flows into Heaven and the Luo flows into Earth, heavenly bundle and earthly symbol" and the numbers "the number nine is on top and one is beneath," these are not found in the "Great Treatise."

以彼之名合此之跡，以此之跡符彼之名，不與大易同行，不藏於博士學官，而千載之下，山人野士持盈尺之書而曰「古之圗書者如是」，此其付受固已沈淪詭秘，而為學者之所疑矣。雖其說自以為無所不通，然此理在人，仁者知者皆能見之，龍虎之經、金石草木之卜、軌菥占算之術，隨其所自為說而亦無不合，豈必皆聖人之為之乎？大傳曰：「包羲氏之王天下也，仰則觀象於天，俯則觀法於地。」夫天地之間，何往非圗而何物非書也哉？揭其圗而示之曰「孰為上下，孰為左右，孰為乾兊離震，孰為巽坎艮坤」，天之告人也何其瀆；因其上下以為上下，因其左右以為左右，因其乾兊離震以為乾兊離震，因其巽坎艮坤以為巽坎艮坤，聖人之效天也何其拘。且彼所謂效變化則垂象者，毫而析之，又何所當也？

Using the names from one side to match the traces on the other, and using the traces on the other side to confirm the names from one side; this set of things neither circulated together with the Book of Changes nor was kept in the official schools of the scholars, yet after more than a thousand years, a person from the mountains and woods held a square foot of a diagram and said, "Ancient books were like this." Its transmission and reception have always been obscure and mysterious, and have long been doubted by scholars. Although this claim claims to be comprehensive, this point is clear in everyone's mind, and both the benevolent and the wise can see it: the alchemical text called the Dragon and Tiger Classic, the divination methods using metals, stones, herbs, and trees, and various systems of calculation and prediction, each set up their own theories at will, and none of them are without their own consistency. Could they all have been made by the sages? The Great Treatise says: "When Fu Xi ruled the world, he looked up to observe the patterns of heaven and looked down to study the principles of earth." Between heaven and earth, where is there not a diagram, and what is not a book? If one says that heaven raised a diagram to show people, pointing out where up and down, left and right, and where Qian, Dui, Li, and Zhen are, and where Xun, Kan, Gen, and Kun are, then the way heaven communicates with mankind is too careless; if one says that the sages followed its up and down to determine up and down, followed its left and right to determine left and right, followed its Qian, Dui, Li, and Zhen to determine Qian, Dui, Li, and Zhen, and followed its Xun, Kan, Gen, and Kun to determine Xun, Kan, Gen, and Kun, then the way the sages imitate heaven is too rigid. Moreover, their so-called "imitating change and revealing the images of things" requires every detail to be analyzed, which is not understandable at all.

使二圗者果在如今所傳，然其所謂精蘊者，聖人固已取而歸之易矣，求圗書之說於易可也。子產曰：「天道逺，人道邇。」天者，聖人之所獨得，而人者，聖人之所以告人者也。告人以天，人則駭而惑；告人以人，人則樂而從。故聖人之作易，凡所謂深微悠忽之理，舉皆推之於庸言庸行之間，而卦爻之象、吉凶悔吝之辭，不亦深切而著明也哉！聖人見轉蓬而造車，觀鳥跡而制字，世之人求為車之說與夫書之義則有矣，而必轉蓬鳥跡之求，愚未見其然也。

Even if these two diagrams were indeed as they are today, the profound meanings contained within them have already been incorporated by the sages into the Book of Changes. Therefore, seeking the meaning of the diagrams within the Book of Changes is sufficient. Zichan said, "The way of Heaven is distant, the way of humanity is near." The way of Heaven is understood solely by the sages, while the way of humanity is what the sages use to enlighten the people. To explain the way of Heaven to people would cause them confusion and fear; but to explain the way of humanity to people would make them willing to listen. Thus, the sages composed the Book of Changes, transferring all subtle and indistinct principles into everyday speech and actions. Therefore, the images of the hexagrams and the terms expressing fortune, regret, and hardship are both profound and clear. The sages observed the rotating thistle and invented the cart, and saw the tracks of birds and beasts and created writing. It is proper for people to seek the principles behind the cart and the meaning of writing, but if they insist on delving deeply into the thistle and the tracks, I do not see the necessity.

孔子贊易，刪《連山》《歸藏》而取《周易》，始於乾而終於未濟，則圗書之列粲然者莫是過矣。今夫冶之所貴者範，而用者不求範而求器也；耕之所資者耒，而食者不求耒而求粟也。有圗書而後有易，有易無圗書可也。故《論語》「河不出圗」，與鳳鳥同瑞而已；《顧命》「河圗在東序」，與兊弓和矢同寶而已。是故圗書不可以精，精於易者精於圗書者也。惟其不知其不可精而欲精之，是以測度摹擬無所不至，故有九宮之法，有八分井文之畫，有坎離交流之卦，與夫孔安國、向、歆、揚雄、班固、劉牧、魏華父、朱子發、張文饒諸儒之論，或九或十，或合或分，紛紛不定，亦何足辨也。

Confucius explained the principles of the I Ching, omitting the Lianshan and Guicang and choosing only the Zhouyi. He began with the Qian hexagram and ended with the Weijì hexagram. Therefore, the truly clear and visible parts in the theory of the River Chart and the Book of Changes are no more than this. For example, in metal casting, the most important thing is the mold, but those who use it do not seek the mold but the finished object; in farming, the plow is essential, but those who eat do not seek the plow but the grain. First there was the River Chart and the Book of Changes, but now that the Book of Changes exists, the River Chart is not necessary. Therefore, the saying in the Analects that "the Yellow River does not produce a chart" is merely another kind of auspicious omen, like the phoenix; and the statement in the Shangshu Guiming that "the River Chart is displayed in the eastern hall" is just another kind of treasure, like the bow and arrows of the earth. Therefore, the River Chart and the Book of Changes do not need to be pursued for perfection. Those who seek perfection in the Book of Changes are also seeking perfection in the River Chart. Because people do not understand that it is not necessary to pursue perfection, they go to great lengths in conjecture and imitation: thus arose the method of the nine palaces, the method of drawing the eight-part grid pattern, the theory of the mutual exchange of Kan and Li, and the discussions of various scholars such as Kong An Guo, Liu Xiang, Liu Xin, Yang Xiong, Ban Gu, Liu Mu, Wei Le翁, Zhu Zhen, and Zhang Xingcheng, who hold different views, some advocating nine, some advocating ten, some combining, some separating, resulting in endless disputes without a definite conclusion. So why bother to argue about it?

自《本義》之圗書盛行，學者捲舌而不敢議，震川先生獨能昌言以正之，引繩批根，不遺餘力，真三百年來有數文字。

Since the theory of the Book and Diagram in the preface of The Original Meaning of the Zhou Changes became popular, scholars have all kept silent and dared not comment. Only Mr. Gui Youguang was able to speak out and correct it directly, straightening the measuring rope and uprooting the error completely, without any hesitation. This is truly an outstanding article among the three hundred years of writings.

秀水徐善敬可博覽精思，無所不通，而尤深於易，晚著書以發其蘊，有《天易》《羲易》《商易》《周易》。天易者，河圗洛書也；羲易者，先天古易也；商易者，《歸藏》首坤也；周易者，文王所演也。連山無傳，故不著夏易。同縣朱太史彝尊名其書曰《徐氏四易》而為之序。敬可與餘厚，向在京師出以示余，其言河圗洛書以劉牧得希夷之傳，而西山兩易殊可疑，餘深以為然，僭作題辭，要不出此意。

Xu Shanjie, a man from Xiushui, was well-read and deeply thoughtful, with profound understanding in all fields, but especially skilled in the study of the I Ching. In his later years, he wrote four books to explain his insights: The Heavenly I Ching, The Xia I Ching, The Shang I Ching, and The Zhou I Ching. The Heavenly I Ching discusses the Yellow River Chart and the Luo Writing. The Xia I Ching refers to the ancient Earlier Heaven I Ching. The Shang I Ching discusses the Guicang, with the Earth Trigram as the first. The Zhou I Ching refers to the I Ching developed by King Wen. The Lianshan has no surviving texts, so there is no separate section for the Xia I Ching. A historian from the same county, Zhu Yizun, named this collection The Four I Chings of Xu and wrote an introduction. Xu Jingke and I had a close friendship. When we were in the capital together, he showed me his books. He discussed the Yellow River Chart and the Luo Writing, believing that Liu Mu was the true inheritor of Chen Tuan's teachings, while Cai Yuanding's reversal of the charts was suspicious. I strongly agreed with him, so I wrote an introduction, which mainly expressed this view.

既而思之，河圗洛書自秦漢以來未有能言其狀者，至五季而始出，何可遽信？學者不能痛絶圗書之謬種，而徒辨劉蔡之是非，無為也。歲庚午，與敬可讀書莫釐峰下，方且效一得之慮，相與更定是書，而敬可尋以病歸，卒於家，吾欲言之無以為質矣。因復窮究其義，知圗書之形象自古無傳，當姑從漢孔劉之言而闕其疑，至於宋人之所傳，一槩難信。越七歲，為今丁丑，始成此五卷。追念舊好，歔欷者久之。嗟乎！郢人逝矣，誰與盡言？此嵇生所以致慨也。

Later, upon further reflection, I thought: since the Han dynasty, no one has been able to describe the shape of the Yellow River Chart and the Luo Writing, until the Five Dynasties period when they suddenly appeared. How can we easily believe them? Scholars who cannot eliminate these false doctrines at their roots and instead argue over whether Liu Mu or Cai Yuanping was right are wasting their efforts. In the year Gengwu, I was studying with Xu Jingke on the Molei Peak, intending to present my own opinion and revise this book together; but unfortunately, Jingke soon returned home due to illness and died there. I had no one to discuss my thoughts with. Thus, I once again thoroughly examined the meaning and principles, realizing that the image of the Book of Changes has never been passed down since ancient times. Therefore, we should only follow the interpretations of Han dynasty scholars like Kong An Guo and Liu Xin, keeping doubts and not discussing them. As for the versions passed down by the Song dynasty, they are all difficult to believe. Seven years later, this year Dingchou, I have finally completed these five volumes. Thinking of my old friends, I have been sighing for a long time. Alas! The person who was matched with the master craftsman, Ying, has already passed away. Who else can I discuss this with freely? This is precisely the reason why Ji Kang felt deeply sorrowful over the loss of a true friend.

右論啟蒙圗書。

In the previous section, the discussion examines the interpretations of the Yellow River Chart and the Luo Writing as presented in the "Commentary on the Origins of the Book of Changes."

《繫辭傳》曰：「易有太極，是生兩儀，兩儀生四象，四象生八卦。」

The Great Treatise of the Zhou Changes says: The Book of Changes has a "Taiji" (Supreme Ultimate), from which arises "two yin and yang" (the Two Principles), from which arise the "Four Symbols," and from the Four Symbols arise the Eight Trigrams.

朱子曰：「一每生二，自然之理也。《易》者，陰陽之變；大極者，其理也。兩儀者，始為一畫以分陰陽；四象者，次為二畫以分太少；八卦者，次為三畫而三才之象始備。此數言者，實聖人作《易》自然之次第，有不假絲毫智力而成者。畫卦揲蓍，其序皆然。」

Zhu Xi explained that one must necessarily produce two, which is the natural principle. The "Book of Changes" discusses the transformation of yin and yang. The term "Great Ultimate" (i.e., "Taiji") refers to the principle behind these transformations. "Two Principles" (liang yi) are the first line drawn, used to distinguish yin and yang. "Four Symbols" (si xiang) are the second lines drawn, used to distinguish Taiyin, Taiyang, Xiaoyin, and Xiaoyang. "Eight Trigrams" (bagua) are the third lines drawn, and at this point, the images of heaven, earth, and humanity ("san cai") are fully complete. These statements truly reflect the natural order in which the sages created the "Book of Changes," without any artificial ingenuity. Whether drawing the trigrams or using the divination method with yarrow stalks, the sequence remains the same.

按：此節夫子本言揲蓍之序，與畫卦無涉，說見第一卷。

Hu Wei remarks: In this section of the Great Treatise, Confucius originally discussed the order of counting the yarrow stalks when seeking a hexagram, which has nothing to do with Fuxi drawing the trigrams. A detailed argument can be found in the first volume of this book.

《語類》曰：「某嘗聞季通：『康節之數，伏羲也曽理會否？』曰：『伏羲須理會過。』某以為不然。伏羲只是據他見得一個道理，恁他便畫出幾畫，他也那裡知得疉出來恁地巧。此伏羲所以為聖。若他也恁地逐一推排，便不是天然意思。《史記》曰伏羲至淳厚，作《易》八卦，那裡恁地巧推排。」（此葉賀孫所録也。劉砥録以「伏羲至淳厚」為季通述太史公語，以規朱子。）

The *Zhu Zi Yu Le* records Zhu Xi's words: I once asked Cai Jitong (Cai Yuan ding): "Did Fuxi also investigate the system of numbers that Shao Kangjie discussed?" He replied: "Fuxi certainly did." I did not think so. Fuxi merely drew those trigrams based on the principle he himself understood, without knowing that layering them in sequence could result in such a neat and complete system. It is precisely for this reason that Fuxi can be called a sage. If he had also calculated step by step as later people did, it would not have been natural and spontaneous. The *Records of the Grand Historian* says that Fuxi was extremely simple and sincere, and he composed the *Book of Changes* and drew the Eight Trigrams. How could he have arranged them so cleverly? (This entry is recorded by Ye Hesun. Liu Di's record, however, takes the phrase "Fuxi was extremely simple and sincere" as Cai Jitong quoting Sima Qian's words, used to advise Zhu Xi.)

又董銖問：「《程易》乾繇辭下解云：『聖人始畫八卦，三才之道備矣，因而重之，以盡天下之變，故六畫而成卦。』據此說，卻是聖人始書八卦，每卦便是三畫，因而重之為六畫，似與邵子說不同。」曰：「程子之意，只雲三畫上疉成六畫，八卦上疉成六十四耳，與邵子說異。蓋康節此意不曽說與程子，程子亦不曽問之，故一向只隨他所見去。但他說聖人始畫八卦，不知其時先畫甚卦，此處便曉他不得。」

There is another question raised by Dong Zhu: "In the Hexagram Statement of the Qian hexagram, Cheng Yi explains that 'the sage first drew the Eight Trigrams, and thus the principles of Heaven, Earth, and Humanity were all complete. Then he overlapped the Eight Trigrams to exhaust all changes in the world, hence forming a hexagram with six lines.' According to this explanation, the original Eight Trigrams each had three lines, and they were overlapped to form six lines, which seems different from Shao Yong's view." Zhu Xi replied: "Cheng's meaning is simply that three lines were overlapped to form six lines, and the Eight Trigrams were overlapped to form the sixty-four hexagrams. This is indeed different from Shao Yong's view. Perhaps Shao Yong's idea was never communicated to Cheng, and Cheng never asked him about it, so Cheng always explained according to his own understanding. However, when he says the sage first drew the Eight Trigrams, he does not explain which trigram was drawn first, which is illogical."

按：康節先天八卦次序，伊川不用，以為聖人始畫八卦，每卦便是三畫。其後精通邵學者莫如漢上，而《集傳》釋兩儀、四象、八卦亦不從康節，意可知矣。朱子初亦疑之，謂伏義至淳厚，未必如此巧推排，而蔡季通堅執不移，故《本義》屈伊川而伸康節。蓋牧堂（季通父，名發，字神與）嘗以《皇極經世》授季通曰：「此孔孟正脈。」故季通篤信邵學不啻如孔孟，朱子方以為老友，不在弟子之列，往往曲從其言。至《啟蒙》則屬季通起藁，其《原卦畫》一篇敷暢邵學尤為詳備，而其說遂牢不可破矣。

Hu Wei said: Shao Kangjie's arrangement of the Earlier Heaven Trigrams was not adopted by Cheng Yi. He believed that when the sage originally drew the eight trigrams, each trigram was directly composed of three lines. Later scholars who thoroughly understood Shao Yong's teachings did not surpass Zhu Zhen (the Master of Han Shang). His Han Shang Commentary on the Zhou Changes did not follow Shao Kangjie when explaining the two principles, four images, and eight trigrams. His attitude towards this issue is evident. Zhu Xi initially also doubted, saying that Fuxi was extremely simple and sincere, and would not have arranged things so cleverly. However, Cai Jitong refused to yield, so The Original Meaning of the Zhou Changes finally compromised Cheng Yi's view and supported Shao Kangjie's. Originally, Cai Muting (Jitong's father, named Fa, with the style name Shenyu) once passed on the Huang Ji Jing Shi to Jitong, saying, "This is the orthodox lineage of Confucius and Mencius." Therefore, Jitong believed in Shao's teachings no less than he did in Confucius and Mencius. Zhu Xi regarded him as an old friend, not as a disciple, and often yielded to his opinions. When compiling the Yi Xue Ming Tong, he even entrusted Jitong to draft it. Among the chapters, the "Original Trigram Diagram" elaborated and developed Shao's teachings in a particularly detailed and complete manner, thus making this theory firmly established and unshakable.

朱子又疑伊川不知康節之意。愚謂程、邵在洛中晨夕往來，豈有邵不言而程亦不問者？此必伊川灼見其非，故《易傳》不從耳。又疑八卦不知先畫何卦。萬季野云：「讀《大傳》『成象之謂乾，效法之謂坤』，便見是先畫乾，次畫坤，然後以乾坤相索成六子，有何難曉？」李剛主亦云。

Zhu Xi also doubted that Cheng Yi did not understand Shao Kangjie's intention. I Hu Wei think that Cheng Yi and Shao Yong were both in Luoyang, living together day and night, so there could not be a situation where Shao Yong never spoke and Cheng Yi never asked. This must be because Cheng Yi clearly saw something wrong with it, so the Book of Changes Commentary did not adopt it. Zhu Xi also doubted that Cheng Yi could not explain which hexagram was drawn first. Wan Siting (style name Jiyě) said, "As long as one reads the two sentences from the Great Treatise, 'Forming the image is called Qian, following the pattern is called Kun,' one can see that Qian was drawn first, then Kun, and then the six subordinate hexagrams were generated through the mutual inquiry between Qian and Kun. What is there difficult to understand about it?" Li Nen (style name Gangzhu) also said the same thing.

邵子《觀物外篇》曰：「太極既分，兩儀立矣。陽下交於陰，陰上交於陽，四象生矣。陽交於陰，陰交於陽，而生天之四象；剛交於柔，柔交於剛，而生地之四象。於是八卦成矣。八卦相錯，然後萬物生焉。是故一分為二，二分為四，四分為八，八分為十六，十六分為三十二，三十二分為六十四。故曰：『分陰分陽，迭用柔剛，易六位而成章也。』」

Shao Yong said in "Guangwu Wai Pian" that after the Taiji is divided, the two principles are established. Yang goes down to meet Yin, and Yin goes up to meet Yang, thus the four images are generated. The meeting of Yang and Yin, and the meeting of Yin and Yang, produce the four celestial images; the meeting of hardness and softness, and the meeting of softness and hardness, produce the four terrestrial images. At this point, the eight trigrams are formed. The eight trigrams intermingle and combine, and then all things are generated from this. Therefore, it is said: one divides into two, two divides into four, four divides into eight, eight divides into sixteen, sixteen divides into thirty-two, thirty-two divides into sixty-four. Therefore, the "Shu Guan Zhuan" says: "Separating Yin and separating Yang, alternating the use of softness and hardness, the Book of Changes is completed through six lines."

「十分為百，百分為千，千分為萬，猶根之有乾，乾之有枝，枝之有葉，愈大則愈小，愈細則愈繁。合之斯為一，衍之斯為萬。是故乾以分之，坤以翕之，震以長之，巽以消之。長則分，分則消，消則翕也。」

Ten is divided into a hundred, a hundred into a thousand, a thousand into ten thousand, just as tree roots produce the trunk, the trunk produces branches, and branches produce leaves: the larger the whole, the smaller the units divided from it; the more detailed the division, the greater the number. When combined, it becomes one; when extended, it becomes myriad. Therefore, Qian is used for differentiation, Kun for convergence, Zhen for growth, and Xun for retreat; growth leads to differentiation, differentiation leads to retreat, and retreat leads to convergence.

《本義》圖說：右《繫辭傳》曰「易有太極，是生兩儀，兩儀生四象，四象生八卦」，邵子曰「一分為二，二分為四，四分為八也」。《說卦傳》曰「易逆數也」，邵子曰「乾一、兌二、離三、震四、巽五、坎六、艮七、坤八，自乾至坤皆得未生之卦，若逆推四時之比也」。後六十四卦次序仿此。（黒白之位本非古法，但今欲易曉，且為此以寓之耳。後六十四卦次序仿此。）

The diagram attached to The Original Meaning of the Zhou Changes is said to come from the Great Treatise, which states, "The Book of Changes has the Taiji, from which the two principles arise, from the two principles the four images, and from the four images the eight trigrams." Shao Yong explains this as "one divides into two, two divides into four, four divides into eight." The Sayings on the Trigrams also say, "The Book of Changes proceeds in reverse order." Shao Yong explains that Qian is one, Dui is two, Li is three, Zhen is four, Xun is five, Kan is six, Gen is seven, and Kun is eight. Counting from Qian to Kun, all the trigrams are those that have not yet been generated, like counting the seasons in reverse. The order of the sixty-four trigrams is also arranged in this way. (The diagram uses black and white to indicate the positions of odd and even numbers, which is not the ancient method, but is used here to make it easier for modern people to understand, serving merely as a way to represent the trigram figures. The order of the sixty-four trigrams is also arranged in this way.)

李剛主《學易》曰：「先天圖杜撰乾一、兌二、離三、震四、巽五、坎六、艮七、坤八之數，毛河右闢之是矣。若宗康成，以天地生成之數配八卦，則乾天也乃得地六數，坤地也乃得天九數，且中遺五數亦可疑也。蓋必分八卦次序之數，則畫卦自乾而終兌可為數，卦位自震而終艮可為數，然總不必也。何者？用九用六，爻有數；用四十有九，大衍有數，即卦數也。若乾一至坤八之數，聖人所不言，何為為渾敦畫眉乎？」

Li Neng said in his "Learning the Book of Changes": The Earlier Heaven diagram arbitrarily assigns the trigrams with numbers, starting with Qian as one, Dui as two, Li as three, Zhen as four, Xun as five, Kan as six, Gen as seven, and Kun as eight. Mao Qiling (He Yu) correctly refuted this. If we follow Zheng Xuan's (Kangcheng) method of matching the trigrams with the numbers of heaven and earth, then Qian, which is heaven, is assigned the number six of earth, and Kun, which is earth, is assigned the number nine of heaven. Moreover, the number five is missing in between, which is also suspicious. If we must assign numbers to the trigrams in order, then according to the method of drawing the trigrams, counting from Qian to Dui is one way of numbering; according to the positions of the trigrams, counting from Zhen to Gen is another way. However, these are actually unnecessary. Why? "Yong Ji" and "Yong Liu" already have numbers inherent in the lines. "The Great Derivation has a number of forty-nine," and the process of divination with yarrow stalks already has numbers, which are the numbers of the trigrams. As for the numbers from Qian to Kun eight, the sages never mentioned them. Why should we go out of our way to draw eyebrows on a chaos?

《易學啟蒙》曰：「盈天地之間莫非太極陰陽之妙，聖人於此仰觀俯察，逺求近取，固有以超然而黙契其心矣。故自兩儀之未分也，渾然太極，而兩儀、四象、六十四卦之理已粲然於其中。自太極而分兩儀，則太極固太極也，兩儀固兩儀也；自兩儀而分四象，則兩儀又為太極，而四象又為兩儀矣。自是而推之，由四而八，由八而十六，由十六而三十二，由三十二而六十四，以至於百千萬億之無窮，雖其見於摹畫者若有先後而出於人為，然其已定之形、已成之勢，則固已具於渾然之中，而不容毫髮思慮作為於其間也。」

The "Yixue Qimeng" says: Everything that fills the space between heaven and earth is nothing but the subtlety of the Taiji and the yin and yang. The sage observed the heavens above and examined the earth below, taking images from all things in the distance and from his own body in the near. Thus, he could naturally comprehend and have a silent harmony in his mind. Therefore, when the two principles had not yet separated, it was a single Taiji. But the principles of the two, the four images, and the sixty-four hexagrams were already clearly contained within it. When the Taiji splits into the two principles, the Taiji remains the Taiji, and the two principles remain the two principles. When the two principles split into the four images, then the two principles become the Taiji again, and the four images become the two principles. Continuing in this way, from four to eight, from eight to sixteen, from sixteen to thirty-two, from thirty-two to sixty-four, and so on endlessly. Although the diagram seems to show a sequence and an artificial order, the determined form and the established trend were already present in the unity of the whole, leaving no room for human thought or artificial creation.

「程子所謂『加一倍法』者，可謂一言以蔽之；而邵子所謂『畫前有易』者，又可見其真不妄矣。世儒於此或不知察，往往以為聖人作《易》蓋極其心思探索之巧而得之，甚者至謂凡卦之畫必由蓍而後得，其誤益以甚矣。」

Cheng Hao's "add one more" method can be summarized in one sentence the entire principle of generating hexagrams. Similarly, Shao Yong's statement "before drawing, there is the easy" can be seen as not mere empty talk. Later Confucian scholars sometimes fail to understand this point, often thinking that the sage composed the Book of Changes by exhausting his mind and achieving it through clever exploration. Worse still, some even claim that all hexagram diagrams must first be obtained through divination with yarrow stalks, which is an even greater mistake.

又曰：「太極者，象數未形而其理已具之稱，形器已具而其理無朕之目，在《河圖》《洛書》皆虛中之象也。周子曰『無極而太極』，邵子曰『道為太極』，又曰『心為太極』，此之謂也。」

The "Book of Changes: Awakening to the Teachings" also says: The term "Taiji" refers to a state where the image and numbers have not yet taken form, but its principle is already complete; it also refers to a state where the physical forms are already present, but the principle is not evident at all. In the "Yellow River Chart" and the "Luo Writing," it is represented by the image of the center being empty. Zhou Dunyi said "from non-polarity comes Taiji," Shao Yong said "the Dao is Taiji," and also said "the mind is Taiji," referring to this very concept.

「太極之判，始生一竒一偶而為一畫者二，是為兩儀，其數則陽一而陰二，在《河圖》《洛書》則竒偶是也。周子所謂『太極動而生陽，動極而靜，靜而生陰，靜極復動，一動一靜，互為其根，分陰分陽，兩儀立焉』，邵子所謂『一分為二』者，皆謂此也。」

The Taiji splits into two, producing two kinds of symbols, one odd and one even, which are called "the Two Principles" or "two yi." In terms of numbers, yang is represented by one and yin by two, corresponding to odd and even numbers in the Yellow River Chart and the Luo Writing. The "Taiji Diagram Explanation" by Zhou Dunyi describes how the Taiji, when it moves, gives rise to yang; when it moves to its extreme, it becomes still, and from stillness comes yin; when stillness reaches its extreme, it returns to movement. The alternation of movement and stillness forms the basis for distinguishing yin and yang, thus establishing the Two Principles. Similarly, Shao Yong's concept of "dividing one into two" refers to this same principle.

「兩儀之上各生一竒一偶而為二畫者四，是謂四象。其位則太陽一、少陰二、少陽三、太陰四，其數則太陽九、少陰八、少陽七、太陰六。以《河圖》言之，則六者一而得於五者也，七者二而得於五者也，八者三而得於五者也，九者四而得於五者也；以《洛書》言之，則九者十分一之餘也，八者十分二之餘也，七者十分三之餘也，六者十分四之餘也。周子所謂『水火木金』，邵子所謂『二分為四』者，皆謂此也。」

The *Yixue Qimeng* continues to say: Above the two principles, each generates one odd and one even, resulting in four symbols composed of two lines, which is called the "Four Images." In terms of position, the Sun is first, the Lesser Yin is second, the Lesser Yang is third, and the Great Yin is fourth. In terms of numbers, the Sun corresponds to nine, the Lesser Yin to eight, the Lesser Yang to seven, and the Great Yin to six. Using the *He Tu* (Yellow River Chart), these four numbers are each the base number plus the central five: six is one plus five, seven is two plus five, eight is three plus five, and nine is four plus five. Using the *Luoshu* (Luo Writing), these four numbers are derived by subtracting the base number from ten: nine is what remains after subtracting one from ten, eight is what remains after subtracting two from ten, seven is what remains after subtracting three from ten, and six is what remains after subtracting four from ten. What Zhou Dunyi discusses in his *Taiji Tu Shuo* as "water, fire, wood, metal," and what Shao Yong refers to as "dividing two into four," all refer to this level.

「四象之上各生一竒一偶而為三畫者八，於是三才略具而有八卦之名矣。其位則乾一、兌二、離三、震四、巽五、坎六、艮七、坤八。在《河圖》則乾坤離坎分居四實，兌震巽艮分居四虛；在《洛書》則乾坤離坎分居四方，兌震巽艮分居四隅。《周禮》所謂『三易經卦各八』，《大傳》所謂『八卦成列』，邵子所謂『四分為八』者，皆指此而言也。」

Above the Four Symbols, each generates one odd and one even, forming eight trigrams of three lines. At this point, the principles of heaven, earth, and humanity are largely complete, thus giving rise to the name of the Eight Trigrams. In terms of their positions, Qian is one, Dui two, Li three, Zhen four, Xun five, Kan six, Gen seven, and Kun eight. In the Yellow River Chart, Qian, Kun, Li, and Kan occupy four solid positions, while Dui, Zhen, Xun, and Gen occupy four empty positions. In the Luo Writing, Qian, Kun, Li, and Kan occupy the four cardinal directions, while Dui, Zhen, Xun, and Gen occupy the four corners. The "three books of Change" mentioned in the Zhou Li each have eight trigrams, the "Eight Trigrams in order" mentioned in the Great Treatise, and Shao Yong's "four divided into eight" all refer to this.

《語類》曰：「康節之書固自是好，而季通推得來又甚縝宻（觀此語則《啟蒙》仍季通之藁無所更定可知），若見於用，不知果如何，恐絶勝諸家也。」

The "Shuzi Yilu" records Master Zhu's words saying: Shao Kangjie's book was originally good, and Cai Jitong elaborated on it with great detail (from this statement alone, it can be seen that "Yixue Qimeng" is still Cai Jitong's original manuscript, and Master Zhu did not make any revisions). If applied in practice, it is uncertain how it would turn out, but it is likely to be far superior to other schools.

康節之學似揚子雲。《太玄》擬《易》，方、州、部、家皆自三數推之。玄之為首，一以生三為三方，三生九為九州島，九生二十七為二十七部，九九乘之斯為八十一家。首之以八十一，所以準六十四卦；贊之以七百二十有九，所以準三百八十四爻，無非以三數推之。康節之數，則是加倍之法。

Zhu Xi also said that Shao Kangjie's learning is somewhat similar to Yang Xiong. Yang Xiong's "Tai Xuan" was modeled after the "Yi Jing," where the four levels of "fang," "zhou," "bu," and "jia" were all derived according to the number three. "Tai Xuan" established "shou," beginning with one and generating three to form three fang, three generating nine to form nine zhou, nine generating twenty-seven to form twenty-seven bu, and then multiplying nine by nine to obtain eighty-one jia. It used eighty-one shou to correspond to the sixty-four hexagrams of the "Yi Jing," and seven hundred twenty-nine zan to correspond to the three hundred eighty-four lines of the "Yi Jing," with no part not derived by the number three. As for the numbers used by Shao Kangjie, he employed a method of doubling and adding.

程先生有一柬說先天圖甚有理，可試往聴他說看。觀其意甚不把當事，然自有《易》以來，只有康節說一個物事如此齊整。如揚子雲《太玄》便零星補湊得可笑，若不補又卻欠四分之一，補得來又卻多四分之三。如《潛虛》之數用五，只似如今算位一般，其直一畫則五也，下橫一畫則為六，橫二畫則為七，蓋亦補湊之書。

Zhu Xi also said that Cheng Yi once wrote a short letter saying that the Earlier Heaven diagram makes a lot of sense, and one could try to listen to his explanation. From his tone, it seems he did not take the matter very seriously. However, since the Book of Changes came into being, only Shao Kangjie (Shao Yong) has presented such a complete system. In contrast, Yang Xiong's Tai Xuan is a haphazard patchwork, which is laughable. If one does not supplement it, it is missing a quarter; if one does supplement it, it exceeds three quarters. Similarly, Sima Guang's Qian Xu uses five as the base number, which is like the way counting rods are arranged today: a vertical line represents five, adding a horizontal line below it represents six, adding two horizontal lines represents seven. In the end, it is also a book put together by patching things together.

按：《太玄》方、州、部、家表贊皆自三數推之，全從「三生萬物」得來，不待清靜寂寞等語而始知其為老氏之學也。《易》之為書，廣大悉備，天象厯數之理皆包括其中，然伏羲作《易》之本，夫子仰觀俯察數語盡之，天象厯數非其本也。雄因覃思渾天而作《太玄》以擬之，與《太初厯》相應。

Hu Wei said: The sections of "Tai Xuan" such as Fang, Zhou, Bu, Jia, as well as the Biao and Zan, are all derived according to the number three. They completely originate from Laozi's statement "three gives rise to all things." One does not need to see the words like "quiet and solitary" in the text to know that it comes from the school of Laozi. The Book of Changes is vast and comprehensive, containing the principles of celestial phenomena and calendar systems; but the fundamental idea of Fuxi's creation of the Book of Changes was fully explained by Confucius in the few words "looking up to observe the heavens and looking down to examine the earth." Celestial phenomena and calendrical calculations are not its fundamental basis. Yang Xiong composed the "Tai Xuan" to parallel the Book of Changes, based on his deep contemplation of the theory of the浑天 (hun tian, a cosmological theory). Therefore, it corresponds exactly with the Han dynasty's "Tai Chu Li" (Great Initial Calendar).

《易》太極生兩，兩生四，四生八；《玄》太極函三為一，一生二，二生三，三生萬物：其所據者固老氏之《易》，而非聖人之《易》矣。列子言太易自一而七而九，亦皆竒數，卻不言三。夫子所言自一而兩而四而八皆偶數，故康節用加一倍法。子云之乘法以參，康節之倍數以兩，故蔡季通云：「使康節為之，定是四公、八辟、十六侯、三十二卿、六十四大夫，都是加倍法也。」

The Book of Changes arises from the Taiji generating two principles, the two principles generating four images, and the four images generating the Eight Trigrams; the Tai Xuan, however, originates from the Taiji containing three as one, one generating two, two generating three, and three generating all things. This shows that it is based on the Book of Changes of Laozi's tradition, not the Book of Changes of the sages. Liezi speaks of "Taiyi" originating from one, then seven, then nine, using only odd numbers, but does not mention three. Confucius, on the other hand, speaks of originating from one, then two, then four, then eight, using only even numbers, so Shao Kangjie adopted the method of doubling. Yang Zhonglin's method involves multiplying by three, while Shao Kangjie's method involves doubling, hence Cai Jitong said, "If Kangjie were to compose the Tai Xuan, he would certainly arrange it as four publics, eight divisions, sixteen peers, thirty-two ministers, and sixty-four scholars, all following the method of doubling."

子云草《玄》，自丑至午得七百二十九而止，《玄》其所自造，任意可也。康節著先天圖，自兩至八，《易》之所有也；自八而為十六、三十二、六十四，以至於百千萬億而無窮，又豈《易》之所有乎？是亦邵子之數學，而非古聖人之《易》矣。

Yang Zi Yun composed the "Tai Xuan" starting from the Chou position up to the Wu position, obtaining seven hundred and twenty-nine zan and then stopping; since the "Tai Xuan" was a book he himself created, the arrangement was entirely up to his own will. Shao Kangjie composed the Earlier Heaven diagram, deriving the Eight Trigrams from the Two Principles, which is something already present in the "Yi"; but starting from the Eight Trigrams and proceeding to sixteen, thirty-two, sixty-four, and so on infinitely, is this also something originally present in the "Yi"? This is also merely Shao Yong's own mathematics, not the "Yi" of the ancient sages.

朱子嘗云「康節之學似揚子雲」，又云「康節數學源流於陳希夷」。希夷，老氏之徒也，不啻若子云之小疵。朱子斥《太玄》學本老氏，而顧以出自希夷者為聖人之《易》，獨何與？

Zhu Xi once said that Shao Kangjie's learning was like Yang Xiong's, and also said that Kangjie's mathematical origins came from Chen Tuan (Xiyi). Chen Tuan was originally a figure from the Daoist Laoshang school, and his faults were far more serious than just the minor flaws of Yang Xiong. Zhu Xi on one hand criticized the study of Tai Xuan as being based on Laoshang, yet on the other hand regarded things originating from Chen Tuan as the sacred Book of Changes. Why was this so?

嗟乎！仲尼沒而微言絶，七十子喪而大義乖。漢世崇尚黃老，至謂《老子》兩篇過於五經，子云擬《易》，所以墮其玄中也。魏晉諸人皆以老、易混稱，歴唐宋而未艾。伊川始闢異端，専宗十翼，《易》道昌明如日月之中天矣，而希夷之徒以象數自鳴，復從而亂之。蓋自孔子贊《易》之後二千年間，其不以老氏之《易》為聖人之《易》者無幾。迨宋末元初，《啟蒙》之說盛行，以至於今，則反謂文王、周公、孔子之《易》非伏羲之《易》，而老、列、希夷、康節之《易》乃真伏羲之《易》矣。晦盲否塞五百餘年，非屏絶先天諸圖而専宗程氏《易》，不可得而明也。

Alas! After Confucius' death, the subtle teachings were cut off, and the seventy disciples declined, distorting the great principles. During the Han dynasty, the doctrines of the Yellow Emperor and Laozi were esteemed, even claiming that the Upper and Lower Chapters of the Dao De Jing surpassed the Five Classics. Yang Xiong imitated the Yi Jing to compose the Tai Xuan, thus falling into the Daoist path of mysticism. The scholars of the Wei and Jin dynasties further confused Laozi's teachings with the Yi Jing, and this trend continued through the Tang and Song dynasties without ceasing. It was only Cheng Yi who began to reject heresies and focused solely on the ten wings of Confucius, making the Yi Jing's principles as clear as the sun and moon. However, the school of Chen Tuan once again claimed the image and number methods as their own, causing further confusion. In general, for two thousand years since Confucius praised the Yi Jing, few people regarded the Yi Jing of Laozi as the true Yi Jing of the sage. By the late Song and early Yuan dynasties, the teachings of the "Yi Xue Ming Cong" became popular and have continued to the present day. People now claim that the Yi Jing of King Wen, the Duke of Zhou, and Confucius is not the Yi Jing of Fuxi, but rather the Yi Jing of Laozi, Liezi, Chen Tuan, and Shao Yong is truly the Yi Jing of Fuxi. This darkness and confusion has lasted for more than five hundred years. Without completely rejecting the earlier heaven diagrams and focusing solely on Cheng Yi's "Yi Zhuan," the principles of the Yi Jing cannot be clarified again.

鯤溟黃氏曰中曰：「卦之短長闊狹彼此如一，若依橫圖畫法，下畫一竒一偶，以視四象，每竒偶當截為二段，八卦當截為四段，十六當截為八段，三十二當截為十六段，六十四當截為三十二段。其四象、八卦、十六、三十二亦各各當截。若不截下，以一竒一偶牽連上之六十四，竒偶長短不倫，且圓圖如何抝轉？方圖如何堆疉？」

Huang Yu Zhong, who goes by the name Hao Kunming, said: The length and width of the trigrams are originally all the same. If we follow the method of drawing the horizontal diagram, the lowest line is divided into one odd and one even. When compared with the four trigrams, each odd or even line must be divided into two parts; when compared with the eight trigrams, divided into four parts; when compared with sixteen, divided into eight parts; when compared with thirty-two, divided into sixteen parts; and when compared with sixty-four, divided into thirty-two parts. Among the layers of four trigrams, eight trigrams, sixteen, and thirty-two, each also needs to be divided. If the lowest line is not divided, then one odd or even line would have to connect to the upper sixty-four trigrams. In this case, the odd and even lines would be of uneven length, making it impossible for the circular diagram to bend smoothly or for the square diagram to be stacked properly.

「若依六十四截之，截竒則竒仍是竒，截偶則偶已非偶矣。何也？偶之為畫，中斷者也，自兩儀一截而後，偶固蚤化而為竒矣。今觀橫圖，亦自知其法不可通，不得已而以黒白分竒偶，大失畫竒偶之本色矣。」

If the sixty-four hexagrams are divided according to their structure, when a yī (odd line) is cut, it remains an odd line. But when an è (even line) is cut, the even line is no longer an even line. Why is this? Because the even line was originally a single broken line in the middle. After being divided from the two principles (yīn and yáng) at the level of the two trigrams, the even line has already been transformed into two short odd lines. Now, looking at the horizontal diagram, the person drawing the diagram himself realizes that this method does not make sense. Therefore, he is forced to use black and white colors to distinguish between odd and even lines. This greatly distorts the original appearance of odd and even lines.

按：橫圖逐爻漸生之法，唯揲蓍三變而成爻、十八變而成卦，自初而二、而三、而四、而五、而上，六爻次第得之，誠有然者。然兩儀主一變言，但分竒偶；而初畫則兼三變，三變之餘或老或少，各視其所得之九六七八以為名，則初畫便當為四象，不可謂兩儀。四象三畫皆有，獨以中畫為四象，尤不可也。然則就揲蓍言之，其義亦有難通者矣。

Hu Wei said: The method of generating lines one by one in a horizontal diagram only makes sense when using the divination with yarrow stalks: three changes produce one line, eighteen changes produce one hexagram. From the first line to the second, third, fourth, fifth, and top line, the six lines are obtained in order, and this is indeed the case. However, the concept of "two principles" refers only to one change, distinguishing between odd and even. But the first line requires three changes, and the remaining number of stalks after three changes, whether old or young, is named according to nine, six, seven, or eight. Therefore, the first line should be considered as "four principles," not "two principles." Moreover, the four principles are present in each of the three lines of the trigram, yet only the middle line is regarded as the four principles, which is even more unreasonable. Thus, even when considering the method of divination with yarrow stalks, this theory has inconsistencies.

若夫畫卦之法，三才一時俱備，豈有先畫一竒一偶，其上覆為一竒一偶之理？康節以揲蓍之序為畫卦之序，又何怪乎世儒謂凡卦之畫必由蓍而後得也哉！《儀禮》注云「卦者主畫地識（音志）爻，爻備以方寫之」，方即牘也。伏羲時書契未興，其始作八卦不知畫在何處，然亦必有一物焉以載此八卦之象可知也。

As for the method of drawing the trigrams, the three elements of heaven, earth, and humanity are all present at the same time, so how could there be a method of first drawing one odd and one even, and then adding another odd and even on top of it? Shao Kangjie took the sequence of divining with yarrow stalks as the sequence of drawing the trigrams, which is why later Confucian scholars claimed that all trigram diagrams must be obtained through the process of divining with yarrow stalks. Zheng Xuan's commentary on the "Rites of Zhou" says, "A trigram is used to record the lines on the ground, and after the six lines are complete, they are copied down on a square board" (the character "识" is read as "zhì", meaning "to record"). Here, the term "方" refers to a wooden tablet. In the time of Fuxi, written characters and records had not yet emerged, so we do not know exactly where Fuxi originally drew the eight trigrams. However, it is certain that there must have been some medium used to carry the imagery of the trigrams.

信如康節所圖，則初畫最長，巾畫半之，終畫又半之。吾不知伏羲既作此象，將截為八段以示人乎？將連者仍連而聴人之自為識別乎？抑亦殫其智力以為之初，如今人之起藁，繼乃更定，劃然分列為八乎？揆諸事情，決無是理。鯤溟之辯良足解頤。吾不知季通何以極贊其妙，而朱子舍己從之也。

If it is indeed as Shao Kangjie depicted, then the lowest line is the longest, the middle line is only half of it, and the top line is only half of the middle line. I really do not know: since Fuxi created such a diagram, was it intended to be divided into eight parts for people to see? Or was it meant to keep the connected lines as they are, leaving it to others to distinguish on their own? Or perhaps he first used his full intellect to draw a rough draft, like modern people do when sketching, and then revised it later, making the Eight Trigrams clearly separated? By common sense, there is no such thing. Huang Kunming's argument is truly amusing. I do not understand why Cai Jitong praised this method so highly, while Zhu Xi abandoned his own view and followed it instead.

林黃中栗與朱子論《易》，以一卦之全體為太極，內外為兩儀，內外及互體為四象，又顛倒取為八卦。朱子曰：「如此則不是生，卻是包也。」林曰：「惟其包之，所以生之。」朱子曰：「包如母之懷子，子在母中；生如母之產子，子在母外。」此特據康節之圖以為言耳。

Lin Li (style name Huangzhong) discussed the Book of Changes with Zhu Xi, advocating that the whole hexagram should be considered as the Taiji, the inner and outer trigrams as the two principles, and the inner trigram, outer trigram, and mutual trigrams together as the four images. He also suggested taking the hexagram in reverse order to form the eight trigrams. Zhu Xi said, "If it is explained this way, it is not 'birth' but 'containment.'" Lin Li replied, "Exactly because it contains, it can give birth." Zhu Xi said, "Containment is like a mother carrying a fetus, where the child is within the mother's body; birth is like a mother giving birth, where the child is outside the mother's body." In fact, Zhu Xi's remarks were based solely on Shao Kangjie's diagram.

若希夷太極圖作白黒回互之狀，函兩儀、四象、八卦，皆子在母中。譬諸歲時，一歲本一氣耳，析之而為寒暑則二氣矣，又析之而為春夏秋冬則四氣矣，又析之而為分至啟閉則八節矣，皆一分為二、子在母中者也。

If we talk about Chen Tuan's Taiji diagram, which is drawn in a black and white interlocking pattern, containing the Two Principles, the Four Symbols, and the Eight Trigrams, all of these belong to the situation of "a child within the mother's body." Taking the twelve months of the year as an analogy: originally, a year is just one kind of energy. When it is divided, it becomes the cold and hot energies; further divided, it becomes the four seasons: spring, summer, autumn, and winter; and further divided, it becomes the eight solar terms: spring equinox and autumn equinox, summer solstice and winter solstice, and the beginning of spring, summer, autumn, and winter. All of these are cases of division into two, which belong to the situation of "a child within the mother's body."

至康節變為橫圖，則兩儀、四象、八卦皆子在母外：初畫為儀，中畫為象，終畫為卦，而太極一畫更居其先，是猶一歲之外別有寒暑，寒暑之外別有四時，四時之外別有八節也，其謬不已甚乎？雖名為先天，而實失希夷之意矣。

When Shao Kangjie changed it into a horizontal diagram, then the two principles, four images, and eight trigrams all became "a child outside the mother's body": the lowest line represents the two principles, the middle line represents the four images, and the top line represents the eight trigrams, while the single line representing the Taiji is placed before them. This is like saying there is another cold and heat beyond a year, another four seasons beyond cold and heat, and another eight solar terms beyond the four seasons; how absurd is that! Although it carries the name "Earlier Heaven," it has actually lost the original meaning intended by Chen Tuan.

《仲氏易》曰：「趙宋専襲陳摶先天圖，謂老陽、少陽、老陰、少陰為四象，而世共遵之。考陰陽老少仍是揲蓍所用，與畫卦不同。惟卦有動靜，爻有貞變，老動少靜，老變少不變，故立此數。」

Ma Qiying's "Zhong Shi Yi" says: The Song dynasty specifically inherited Chen Tuan's Earlier Heaven diagram, treating old yang, young yang, old yin, and young yin as the four trigrams. Everyone followed this tradition. However, upon examination, the terms old and young yin and yang were originally names used in the process of divining with yarrow stalks, and were separate from the act of drawing the hexagrams. It was only because the hexagrams have movement and stillness, and the lines have unchanging and changing ones, that old yang and old yin were considered active, while young yang and young yin were considered still. Old ones are meant to change, while young ones remain unchanged, hence these numbers were established.

「今繪圖者先以兩儀為一重，則自兩畫始，非一畫也；若又加一虛中夾畫於兩儀之前以為太極，則又別一畫，非卦畫也。乃以兩陰兩陽作四象而以為二重。夫老之與少並從已成之卦所推，故乾為老陽，非老陽而後乾也。當庖羲作乾畫時，雖有二畫，然尚未知所成為何等，而乃先曰此當為純陽之卦、此畫為老陽，有是理乎？此說之必不可通者也。」

Nowadays, those who draw diagrams first consider the two principles as one layer, starting from two lines rather than one; if they add another intermediate broken line before the two principles to represent the Taiji, that would form another line, but that is not a trigram. Then they take two yin and two yang as the four images, considering them as the second layer. One must know that the distinction between old and young is derived from the already formed trigrams, so it is only after the Qian trigram is formed that it is called old yang, not that old yang exists first and then the Qian trigram comes into being. When Fuxi was drawing the Qian trigram and reached the second line, although there were already two lines, he still did not know what trigram it would eventually become. How could he possibly say in advance, "This will become a pure yang trigram" or "This line belongs to old yang"? This is a fundamental flaw in this theory.

「乃作三重畫而並以乾、兌、離、震、巽、坎、艮、坤一齊出之為八卦，是一畫之後不必成乾，已先作兌離諸卦之畫；及成乾之後，又不必繼坤，而反以六子之卦成之坤前。將夫子《大傳》所云『成象乎乾，效法乎坤』，與『乾坤成列』『因而重之』『一索再索』『得男得女』諸語顯然抵梧（去聲），是敢於悖聖，而以此解經，真鹵莽之甚者也。」

So he then drew the third layer, arranging Qian, Dui, Li, Zhen, Xun, Kan, Gen, and Kun all together as the Eight Trigrams. In this way, after completing the first line, one did not necessarily have to start with the Qian trigram first; instead, the Dui, Li, and others were drawn first. Moreover, after the Qian trigram was formed, one did not immediately proceed to the Kun trigram, but instead placed the six subsidiary trigrams before the Kun trigram. This directly contradicts what Confucius said in the Great Treatise, such as "forming the image is called Qian, following the pattern is called Kun," and phrases like "Qian and Kun are arranged in order," "thereby doubling them," "one inquiry, then another," and "receiving a male or female." ("Contradict" is written as "抵梧," where "梧" is pronounced in the falling tone.) This is daringly opposing the sage, yet using it to explain the classics, which is extremely crude and reckless.

按：卦，象也；蓍，數也。《左傳》韓簡曰：「物生而後有象，象而後有滋，滋而後有數。」蓋數即象之分限節度處，生於象而不可以生象。康節加一倍法欲以數生卦，非也。四象唯揲蓍三變成爻後有之，乾坤男女即是八卦，不得稱四象，専屬第二畫尤無理，說見上文。

Hu Wei said: The trigrams belong to the category of "xiang" (image), while the yarrow stalks belong to the category of "shu" (number). In the "Zuo Zhuan", Han Jian said: "Things first come into being, then there is an image; with the image, there is growth; with growth, there is number." Number is merely the boundary and measure of the image, originating from the image, and not the other way around. Shao Kangjie's method of doubling aims to generate trigrams through number, which is incorrect. The four trigrams only come into being after the yarrow stalks are divided three times to form a line; the trigrams Qian and Kun and the six subsidiary trigrams are themselves the eight trigrams, and cannot be called the four trigrams. To specifically assign the four trigrams to the second line is even more unreasonable, as explained in the previous text.

《說卦傳》曰：「雷以動之，風以散之，雨以潤之，日以晅之，艮以止之，兌以說之，乾以君之，坤以藏之。」

The Sayings on the Trigrams states: Thunder is used to move all things, wind is used to scatter all things, rain is used to nourish all things, the sun is used to dry all things, mountain is used to stop all things, lake is used to make all things joyful, heaven is used to govern all things, and earth is used to store all things.

石門梁氏寅曰：「『天地定位』一節首乾坤，此一節則先六子者，蓋前乃先天八卦之體也，故先言不用者而後言用；此乃先天八卦之用也，故先言其用者而後言不用。如文王八卦専以用言之，亦始於震巽，而退乾於西北，退坤於西南。於此見八卦之體用固當不同也。」

Shi Men person Liang Yin said: The section "Heaven and Earth are positioned" in "Shuo Gua" begins with Qian and Kun, but this section starts with the six subordinate trigrams. The reason is that the previous section discusses the "body" of the Earlier Heaven Trigrams, so it first mentions Qian and Kun, which do not directly function, and then the six subordinate trigrams, which do function. This section discusses the "function" of the Earlier Heaven Trigrams, so it first mentions the six subordinate trigrams, which do function, and then Qian and Kun, which do not directly function. As for the King Wen Trigrams, which are based specifically on "function," they also begin with Zhen and Xun, and place Qian in the northwest and Kun in the southwest. This shows that the "body" and "function" of the Trigrams should inherently be different.

「神也者，妙萬物而為言者也。動萬物者莫疾乎雷，撓萬物者莫疾乎風，燥萬物者莫熯乎火，說萬物者莫說乎澤，潤萬物者莫潤乎水，終萬物始萬物者莫盛乎艮。故水火相逮，雷風不相悖，山澤通氣，然後能變化，既成萬物也。」

The "Commentary on the Hexagrams" continues by saying: The term "spirit" refers to its subtle ability to transform all things. Nothing is more swift in stirring up all things than thunder; nothing is more swift in gently moving all things than wind; nothing is more intense in drying out all things than fire; nothing is more capable of bringing joy to all things than the marsh; nothing is more effective in nourishing all things than water; and nothing is more powerful in ending and beginning all things than mountain. Therefore, water and fire influence each other, thunder and wind do not contradict each other, and the energies of mountain and marsh are interconnected, only then can transformation and movement take place, leading to the generation of all things.

平庵項氏曰：「動、撓、燥、說、潤、盛皆據後天分治之序，而相逮、不相悖、通氣、變化復據先天相合之位者，明五氣順布、四季分王之時，無極之真、二五之精所以妙合而凝者，未始有戾於先天之學也。苟無此章，則文王為無體，伏羲為無用矣。」

Ping'an Master Xiang Anshi said: "Motion, disturbance, dryness, speech, moisture, and prosperity" these phrases are all explaining the order of the Later Heaven Trigrams governing the four seasons; while "mutual assistance," "not conflicting," "communication," and "change" these phrases return to the position of the Earlier Heaven Trigrams where each pair combines with another. This is to show that when the five phases' energies proceed in order and each of the four seasons takes its turn, the "true essence of the boundless void" and the "essence of yin and yang and the five phases" can miraculously combine, never violating the teachings of the Earlier Heaven. If there were no this chapter, then the Later Heaven Trigrams of Wen Wang would have no origin, and the Earlier Heaven Trigrams of Fuxi would have no function.

又曰：「先天之首以天地、山澤、雷風、水火為序，後天之末乃自水火、雷風、山澤、天地倒而言之，彼言乾坤之用成於坎離，此推坎離之功歸於乾坤也。」

Xiang Anshi also said: In the beginning of the Earlier Heaven section, the order is arranged as Heaven and Earth, Mountains and Marshes, Thunder and Wind, Water and Fire; but at the end of the Later Heaven section, it starts from Water and Fire, Thunder and Wind, Mountains and Marshes, Heaven and Earth, and goes back in reverse order. The former explains that the functions of Heaven and Earth depend on Kan and Li, while the latter attributes the achievements of Kan and Li back to Heaven and Earth.

按：「天地定位」「雷以動之」二章皆以對待之體言，一首乾坤明六子所自出，一先六子而歸功於乾坤，未見其為先天之方位也。「帝出乎震」章以流行之用言，故順四時以為序而各著其方位。「神也者」章兼流行、對待言之：動、撓、燥、說、潤、盛，流行之用也；水火、雷風、山澤，對待之體也。雖不言乾坤，而六子之功用莫非乾坤之所為，「神」與「變化」正指乾坤而言，與「雷以動之」章略同，亦無以見上六句為後天之位而下三句為先天之位也。

Hu Wei remarked: "The chapters 'Heaven and Earth are positioned' and 'Thunder moves it' both discuss the two opposing 'bodies' in pairs. The first chapter begins with Qian and Kun, explaining from which six sub-trigrams arise. The second chapter first discusses the six sub-trigrams and attributes the credit to Qian and Kun. From these two chapters, one cannot see that they refer to the earlier heaven arrangement. The chapter 'The Emperor arises from Zhen' discusses the popular 'use' and thus arranges the order according to the four seasons, and each is marked with its own position. The chapter 'What is the spirit' discusses both the popular and the opposing aspects: the six phrases 'movement, disturbance, dryness, speech, moisture, and prosperity' belong to the popular use; the three phrases 'water and fire, thunder and wind, mountain and marsh' belong to the opposing body. Although the text does not explicitly mention Qian and Kun, the functions of the six sub-trigrams are all attributable to Qian and Kun. The term 'spirit' and the word 'change' refer precisely to Qian and Kun, similar to the chapter 'Thunder moves it'. Therefore, one cannot see that the six phrases above refer to the later heaven positions and the three phrases below refer to the earlier heaven positions.

橫圖、方圖從中起者為震、巽，人皆謂根柢於此。自余觀之，「三索」章先父母而後六子，此兩章先六子而後父母，要皆歸重於乾坤，豈有六子居母前之理？此天地之大經、古今之通義，而邵圖紊亂如此，尚可信乎？

The positions in the horizontal diagram and square diagram that are counted from the middle are Zhen and Xun. People often say that the root of the Earlier Heaven theory lies here. In my opinion, the chapter in "Shuo Gu" that talks about "one inquiry, two inquiries, three inquiries" first discusses the parents and then the six sons. However, these two chapters first discuss the six sons and then return to the parents. In the end, they all place emphasis on Qian and Kun. How can the six subsidiary trigrams come before the parents? This is a great principle in the universe and a principle that has been consistent throughout ancient and modern times. Yet Shao Yong's diagram has become so disordered, how can we still believe in it?

右論邵子伏羲八卦次序。

The above discussions concern Shao Yong's diagram of the "Fuxi Eight Trigrams Sequence."

《說卦傳》曰：「天地定位，山澤通氣，雷風相薄，水火不相射，八卦相錯。數往者順，知來者逆，是故《易》逆數也。」（「數往」，色主反；「逆數」，色具反。）

The Sayings on the Trigrams states: Heaven and Earth established their positions above and below, the energies of Mountain and Marsh interconnect, Thunder and Wind interact with each other, and Water and Fire do not mutually dislike each other. Thus the Eight Trigrams are interrelated. Counting past events follows the order, while predicting future events involves reversing the order. Therefore, the Book of Changes is about reversing numbers. (The "数" in "数往" is pronounced "se3 zhu3 fan3" using reverse phonetic annotation; the "数" in "逆数" is pronounced "se3 ju4 fan3.")

韓氏康伯注曰：「《易》八卦相錯，變化理備，於往則順而知之，於來則逆而數之。」又曰：「作《易》以逆覩來事，以前民用。」

Han Kangbo explained that the Book of Changes uses the eight trigrams to interconnect and pair, thus encompassing all the principles of change; for past events, one can follow the sequence to understand them, and for future events, one can work backwards to calculate them. He also said that the sages composed the Book of Changes precisely to foresee future events, thereby guiding the people's actions.

孔氏穎達《正義》曰：「此一節就卦象明重卦之意。《易》以乾坤象天地，艮兌象山澤，震巽象雷風，坎離象水火。若使天地不交、水火異處，則庶類無生成之用，品物無變化之理，所以因而重之，令八卦相錯，則天地人事莫不備矣。故云天地定位而合徳，山澤異體而通氣，雷風各動而相薄，水火不相入而相資。」

Kong Yingda in The Correct Meaning of the Zhou Changes says: This section explains the purpose of the compound hexagrams by referring to the trigrams. The Zhou Changes use Qian and Kun to symbolize Heaven and Earth, Gen and Dui to symbolize Mountain and Lake, Zhen and Xun to symbolize Thunder and Wind, and Kan and Li to symbolize Water and Fire. If Heaven and Earth do not interact, and Water and Fire remain separate, then myriad things would not have the function of generation, and the principle of change would not exist. Therefore, the eight trigrams are overlapped to make compound hexagrams, so that the eight trigrams are intermingled and paired. Thus, the ways of Heaven, Earth, and human affairs are all complete. Therefore, Heaven and Earth each occupy their proper position yet their virtues are harmonized, Mountains and Lakes have different forms yet their energies are connected, Thunder and Wind each move independently yet they interact and generate movement, and Water and Fire which naturally do not mix yet they support each other.

「既八卦之用變化如此，故聖人重卦，令八卦相錯，乾坤震巽坎離艮兌莫不交互而相重，以象天地雷風水火山澤莫不交錯，則《易》之爻卦與天地等，成性命之理、吉凶之數，既往之事、將來之幾備在爻卦之中矣。故《易》之為用，人慾數知既往之事者，《易》則順後而知之；人慾數知將來之事者，《易》則逆前而數之。是故聖人用此《易》道以逆數知來事也。」

Since the functions and transformations of the Eight Trigrams have reached this level, the sage combined them to form hexagrams, making the Eight Trigrams intermingle and pair with each other. Thus, Qian (Heaven), Kun (Earth), Zhen (Thunder), Xun (Wind), Kan (Water), Li (Fire), Gen (Mountain), and Dui (Lake) all interact and overlap with one another, symbolizing the interconnection of heaven and earth, thunder and wind, water and fire, and mountains and marshes. In this way, the lines and hexagrams of the Book of Changes are equivalent to heaven and earth. The principles of life and death, the numbers of good fortune and misfortune, past events and the signs of future occurrences are all contained within the lines and hexagrams. Therefore, in terms of the function of the Book of Changes: when people wish to calculate and know past events, the Book of Changes follows the past to understand them; when people wish to calculate and know future events, the Book of Changes goes against the future to predict them. Thus, the sage used this system of the Book of Changes, relying on reverse calculation to foresee future events.

平庵項氏曰：「數往者順，即卦以藏往也；知來者逆，即蓍以知來也。」

Xiang Anshi said: "Knowing the past is following the trend," refers to using hexagrams to conceal past events; "Knowing the future is going against the trend," refers to using the yarrow stalks to foresee future events.

丘氏程曰：「《易》言『藏徃知來』『彰徃察來』，又言『數往知來』，則方來已往之事《易》皆有以知之。然往者已過而易知，來者未形而難見，《易》之占筮為知來設，故曰『《易》逆數也』。正如所謂『占事知來』、所謂『遂知來物』、所謂『前民用』，皆逆數之謂也。」

Qu Cheng said: The Yi Classic speaks of "concealing the past to know the future" and "making clear the past to observe the future," and also mentions "using numbers of the past to know the future." This shows that both what is about to come and what has already passed can be known through the Yi. However, past events have already occurred and are therefore easy to know, while future events have not yet taken shape and are therefore difficult to see. The divination of the Yi is specifically designed to foresee the future, hence it is said "the Yi is inverse in its numbers." As the Yi also states "divining matters to know the future" and "thus knowing the coming things," and "guiding the people's daily use," all of these refer to the inverse calculation of numbers.

亭林顧氏炎武《日知錄》曰：「數往者順，造化人事之跡有常而可驗，順以考之於前也；知來者逆，變化云為之動日新而無窮，逆以推之於後也。聖人神以知來，知以藏往，作為《易》書以前民用，所設者未然之占，所期者未至之事，是以謂之逆數。雖然，若不本於八卦已成之跡，亦安所觀其會通而繫之爻象乎？是以『天下之言性也，則故而已矣』。」

Gu Yanwu (Tinglin) in his "Rizhilu" says: "To understand the past is to follow the pattern," because the signs of nature and human affairs have regularities that can be verified, so one follows them to investigate the past; "To know the future is to reverse the process," because changes and human actions are constantly renewed day by day and have no end, so one reverses to predict the future. The sage, with his divine knowledge, foresees the future, and with his wise knowledge, retains the past, and composed the Book of Changes to guide the people's conduct. The Book of Changes deals with divination about things that have not yet occurred, and aims at events that have not yet arrived, hence it is called "reversing the count." Nevertheless, if one does not take the existing signs of the Eight Trigrams as the foundation, on what basis can one observe their interconnections and attach the line statements and hexagram images? Therefore, the "Mengzi" says: "The world discusses human nature, only based on the already manifested signs."

劉汝佳云：「天地間一理也。聖人因其理而畫為卦以象之，因其象而著為變以占之。象者體也，象其已然者也；占者用也，占其未然者也。已然者為往，往則有順之之義焉；未然者為來，來則有逆之之義焉。」

Liu Ruji says: Between heaven and earth there is only one principle. The sages based on this principle to draw the trigrams to symbolize it, and further based on these trigrams to deduce changes in order to predict them. "Xiang" (image) belongs to the body, it is a simulation of things that have already happened; "Zhan" (divination) belongs to the application, it is used to predict things that have not yet happened. Things that have already happened are called "Wang" (past), and "Wang" contains the meaning of counting in order; things that have not yet happened are called "Lai" (future), and "Lai" contains the meaning of reasoning backwards.

「如象天而畫為乾，象地而畫為坤，象雷風而畫為震巽，象水火而畫為坎離，象山澤而畫為艮兌，此皆觀變於陰陽而立卦、發揮於剛柔而生爻者也，不謂之數往者順乎？」

For example, taking the image of heaven to form the trigram Qian, taking the image of earth to form the trigram Kun, taking the images of thunder and wind to form the trigrams Zhen and Xun, taking the images of water and fire to form the trigrams Kan and Li, and taking the images of mountain and marsh to form the trigrams Gen and Dui. These all belong to what the "Sayings on the Trigrams" (Sayi) discusses, namely "observing the changes of yin and yang to establish the trigrams, and expressing the function of firmness and flexibility to generate the lines (yao)." This is not precisely "understanding the past in order to follow the trend" ("shu wang zhe shun")?

「如筮得乾而知『乾元亨利貞』，筮得坤而知『坤元亨，利牝馬之貞』，筮得震而知『震亨，震來虩虩，笑言啞啞』，筮得巽而知『巽小亨，利有攸往，利見大人』，筮得坎而知『習坎，有孚維心亨，行有尚』，筮得離而知『離利貞亨，畜牝牛吉』，筮得艮而知『艮其背，不獲其身，行其庭，不見其人』，筮得兌而知『兌亨利貞』，此皆通神明之徳、類萬物之情者也，不謂之知來者逆乎？」

For example, if one obtains the Qian hexagram through divination, one knows that its hexagram statement is "Yuan, Heng, Li, Zhen"; if one obtains the Kun hexagram, one knows its hexagram statement is "Yuan, Heng, beneficial to the virtuous mare's constancy"; if one obtains the Zhen hexagram, one knows "Zhen Heng, Zhen comes with fear, laughter and joy follow"; if one obtains the Xun hexagram, one knows "Xun small Heng, beneficial to go somewhere, beneficial to see a great person"; if one obtains the Kan hexagram, one knows "Practice Kan, with sincerity in the heart, the path is smooth, action is commendable"; if one obtains the Li hexagram, one knows "Li, beneficial to constancy and smoothness, keeping the virtuous bull is auspicious"; if one obtains the Gen hexagram, one knows "Gen its back, not obtaining its body, walking in the courtyard, not seeing the person"; if one obtains the Dui hexagram, one knows "Dui, smooth, beneficial to constancy." All these belong to what the Great Treatise says, "penetrating the virtue of the divine, comparing the forms of myriad things"; is this not exactly "knowing the future by reversing the present"?

「夫其順數已往，正所以逆推將來也。孔子曰『殷因於夏禮，所損益可知也；周因於殷禮，所損益可知也』，數往者順也；『其或繼周者，雖百世可知也』，知來者逆也。故曰『《易》逆數也』。」

Counting the past in order is done in order to reverse and predict the future. Confucius said, "The Shang dynasty followed the rites of the Xia dynasty; what was reduced and what was added can be known. The Zhou dynasty followed the rites of the Shang dynasty; what was reduced and what was added can also be known," which is called "numbering the past in sequence." He also said, "If there is a successor to the Zhou dynasty, even after a hundred generations, it can be foreknown," which is called "knowing the future in reverse." Therefore, it is said, "The Book of Changes is about reversing numbers."

「若如邵子之說，則是羲、文之《易》已判而為二，而又以震、離、兌、乾為數已生之卦，巽、坎、艮、坤為推未生之卦，殆不免強孔子之書以就已之說矣。」

If we follow Shao Yong's view, then Fuxi's Book of Changes and King Wen's Book of Changes would be split into two separate parts. Moreover, he treats Zhen, Li, Dui, and Qian as already formed trigrams, while Xun, Kan, Gen, and Kun are regarded as trigrams yet to be formed. This inevitably forces Confucius' writings to fit his own theory.

按：此章與八方之位無涉。「天地定位」，言乾坤自為匹也；「山澤通氣」，言艮兌自為匹也；「雷風相薄」，言震巽自為匹也；「水火不相射」，言坎離自為匹也。至於「八卦相錯」，則天或位乎下、地或位乎上，而且與六子之位同列矣；山澤之氣不但二者自相通，而且與天地、雷風、水火之氣互相通矣，雷風水火亦然。

Hu Wei remarked: The chapter "Say on the Trigrams" has nothing to do with the eight cardinal directions. "Heaven and earth are positioned" means that the trigrams Qian (Heaven) and Kun (Earth) form a pair by themselves; "Mountains and marshes communicate with each other" means that the trigrams Gen (Mountain) and Dui (Lake) form a pair by themselves; "Thunder and wind contend with each other" means that the trigrams Zhen (Thunder) and Xun (Wind) form a pair by themselves; "Water and fire do not oppose each other" means that the trigrams Kan (Water) and Li (Fire) form a pair by themselves. When it comes to "the eight trigrams interconnect," then heaven may be below and earth may be above, and they also need to be arranged together with the six subordinate trigrams; the qi of mountains and marshes is not only mutual communication between them, but also interconnected with the qi of heaven, earth, thunder, wind, water, and fire. The situation is similar for the trigrams of thunder, wind, water, and fire.

上四句即所謂「八卦成列，象在其中」，下一句即所謂「因而重之，爻在其中」也，意重下句。孔疏云「就卦象明重卦之意」，深得經旨。夫子《大象》皆以二體八物發明其義，此節正其註腳。八卦相錯是為六十四卦，而占筮之法生焉。

The four sentences above correspond to what is said in the "Great Treatise" that "When the eight trigrams are arranged in order, the images are already contained within them." The next sentence refers to "stacking them together, the lines are then included." The emphasis of the meaning lies in the latter sentence. Kong Yingda's commentary explains that this is "using the trigram images to explain the purpose of stacking trigrams," which thoroughly captures the original meaning of the text. The "Great Image Commentary" composed by Confucius all use the upper and lower parts and eight kinds of physical images to explain the meanings of the trigrams. This section serves as a commentary on the "Great Image Commentary." "The eight trigrams interacting with each other" becomes the sixty-four trigrams, and the method of divination is thus established.

卦之徳方以知，知以藏往，所謂數往者順也，君子居則觀其象而玩其辭，藏往之學也；蓍之徳圓而神，神以知來，所謂知來者逆也，君子動則觀其變而玩其占，知來之道也。雖往來並舉，卻重在知來。知來乃揲蓍求卦之事，《繫辭傳》云「極數知來之謂占」，又云「無有逺近幽深，遂知來物」，又云「占事知來」，有一不以蓍言者乎？於卦何與焉？

The virtue of the hexagram is upright and wise, and wisdom allows it to contain the past, which is called "knowing the past in order to follow the trend." A gentleman, when at ease, observes the hexagram and reflects on its line statements, which is the study of containing the past. The virtue of the yarrow stalks is round and profound, and their profundity allows them to foresee the future, which is called "knowing the future in reverse." A gentleman, when acting, observes the changing lines and reflects on the divination, which is the way of foreseeing the future. Although "past" and "future" are mentioned together, the emphasis is on "knowing the future." And "knowing the future" is precisely what the yarrow stalk divination entails. The "Great Treatise" says, "Exhausting the yarrow stalks' numbers to know the future is called divination," and also says, "No matter how distant or deep, one can know the future," and again says, "Divining a matter and foreseeing the future." Which of these is not speaking about the yarrow stalks? Then what is the connection with the hexagram?

卦主象，蓍主數，雖象中亦有數、數中亦有象，然其間有賓主之辨。韓康伯曰：「蓍極數以定象，卦備象以盡數。」賓主極其分明。希夷之圖，象學也，而康節則専精於數，故往往以蓍數為卦象，與經旨背。

Hexagrams are primarily based on "images" while the yarrow stalks are primarily based on "numbers"; although images contain numbers and numbers contain images, there is a distinction between the main and the auxiliary. Han Kangbo said, "The yarrow stalks exhaust numbers to determine the images, while the hexagrams possess images to exhaust numbers." The distinction between main and auxiliary is very clear. Chen Tuan's diagram belongs to the school of image studies, while Shao Kangjie specialized in the study of numbers, so he often took the numbers of the yarrow stalks as the images of the hexagrams, which goes against the original meaning of the classic.

至於據橫圖從中折取，以自震至乾為順數已生之卦、自巽至坤為逆推未生之卦，然則「《易》逆數也」，豈専用巽坎艮坤而不用乾兌離震乎？就其言解之，已有不可得通者矣。

As for the method of taking the diagram by splitting it in the middle, taking the section from Zhen to Qian as proceeding in order to indicate already formed hexagrams, and the section from Xun to Kun as proceeding in reverse to indicate hexagrams yet to be formed, then the statement "The Book of Changes is about reverse counting" — could this be referring only to the four hexagrams of Xun, Kan, Gen, and Kun, and not to the four of Qian, Dui, Li, and Zhen? Even if we follow his own words for explanation, there are already inconsistencies.

《本義》圖說：《說卦傳》曰「天地定位，山澤通氣，雷風相薄，水火不相射，八卦相錯，數往者順，知來者逆」，邵子曰「乾南坤北，離東坎西，震東北，兌東南，巽西南，艮西北，自震至乾為順，自巽至坤為逆」。後六十四卦方位仿此。

The Original Meaning of the Zhou Changes includes a diagrammatic explanation which states: The Sayings on the Trigrams say, "Heaven and Earth are positioned, mountains and marshes communicate, thunder and wind interact, water and fire do not oppose each other, and the Eight Trigrams interconnect; to understand the past is to follow the sequence, to foresee the future is to reverse the sequence." Shao Yong based his theory on this, stating that Qian is located in the due south, Kun in the due north, Li in the due east, Kan in the due west, Zhen in the northeast, Dui in the southeast, Xun in the southwest, and Gen in the northwest; counting from Zhen to Qian is in the order of progression, while counting from Kun to Qun is in the order of regression. After this, the arrangement of the sixty-four hexagrams also follows this method.

《易學啟蒙》邵子曰：「此一節明伏羲八卦也。八卦相錯者，明交相錯而成六十四也。數往者順，若順天而行是左旋也，皆已生之卦也，故曰數往也；知來者逆，若逆天而行是右行也，皆未生之卦也，故云知來也。夫《易》之數由逆而成矣。」此一節直解圖意，若逆知四時之謂也。

The "Yixue Qimeng" cites Shao Yong's words: this section explains the Eight Trigrams of Fuxi. The phrase "the eight trigrams are intermingled" means that the eight trigrams are combined in pairs to form the sixty-four hexagrams. The phrase "counting the past in the direction of movement" is like following the direction of the celestial movement, which is left rotation, and the counted are all the already existing hexagrams, hence called "counting the past"; the phrase "knowing the future in the opposite direction" is like going against the direction of the celestial movement, which is right rotation, and the deduced are all the hexagrams that have not yet been formed, hence called "knowing the future." The numbers of the "Yi" are indeed formed by reverse deduction. The "Qimeng" says: this section directly explains the meaning of the diagram, just like going against to foresee the four seasons.

（以橫圖觀之，有乾一而後有兌二，有兌二而後有離三，有離三而後有震四，有震四而巽五、坎六、艮七、坤八亦以次而生焉，此《易》之所以成也。而圓圖之左方，自震之初為冬至，離兌之中為春分，以至於乾之末而交夏至焉，皆進而得其已生之卦，猶自今日而追數昨日也，故曰數往者順；其右方自巽之初為夏至，坎艮之中為秋分，以至於坤之末而交冬至焉，皆進而得其未生之卦，猶自今日而逆計來日也，故曰知來者逆。然本《易》之所以成，則其先後始終如橫圖及圓圖右方之序而已，故曰《易》逆數也。）

Zhu Xi's own commentary: Looking at the horizontal diagram, there is first Qian one, then Dui two, then Li three, then Zhen four; after Zhen four, Xun five, Kan six, Gen seven, and Kun eight follow in sequence, which is the entire process by which the Book of Changes comes into being. Now looking at the circular diagram: its left half starts from Zhen as the winter solstice, passes through Li and Dui as the spring equinox, and reaches Qian's end as the summer solstice; the sequence along this path consists of already formed trigrams, like counting backwards from today to yesterday, which is called "knowing the past in a forward direction." Its right half starts from Xun as the summer solstice, passes through Kan and Gen as the autumn equinox, and reaches Kun's end as the winter solstice; the sequence along this path consists of trigrams yet to be formed, like calculating backwards from today to tomorrow, which is called "knowing the future in a reverse direction." However, tracing back to the origin, the formation of the Book of Changes follows the order of the horizontal diagram and the right half of the circular diagram. Therefore, it is said, "The Book of Changes is counted in reverse."

邵子《觀物外篇》曰：「震始交陰而陽生，巽始消陽而陰生。兌，陽長也；艮，陰長也。震兌在天之陰也，巽艮在地之陽也，故震兌上陰而下陽，巽艮上陽而下陰。天以始生言之，故陰上而陽下，交泰之義也；地以既成言之，故陽上而陰下，尊卑之義也。乾坤定上下之位，離坎列左右之門，天地之所闔闢，日月之所出入，是以春夏秋冬、晦朔弦望、晝夜長短、行度盈縮莫不由乎此矣。」

Shao Yong said in "Guangwu Wai pian" that Zhen is when the yin energy begins to meet and yang energy arises, Xun is when yang energy begins to decline and yin energy arises; Dui is when yang energy gradually increases; Gen is when yin energy gradually increases. Zhen and Dui belong to the yin on the heavenly side, while Xun and Gen belong to the yang on the earthly side. Therefore, the top line of Zhen and Dui is yin while the bottom line is yang, and the top line of Xun and Gen is yang while the bottom line is yin. From the perspective of the beginning of heaven, yin is above and yang is below, which represents the meaning of "jiao tai" (mutual generation). From the perspective of the completion of earth, yang is above and yin is below, which represents the meaning of "zun bi" (respect and hierarchy). Qian and Kun determine the positions of above and below, Li and Kan arrange the positions of left and right, which are the places where heaven and earth open and close, and where the sun and moon rise and set. Therefore, the shifting of the four seasons, the changing of the new moon, full moon, and the waxing and waning of the moon, the changes in the length of day and night, and the expansion and contraction of celestial movements all originate from this.

朱子《語類》曰：「先天圖直是精微，不起於邵子。希夷以前元有，只是秘而不傳，次第是方士輩所相傳授。《參同契》中所言亦有些意思。」

The Zhu Zi Yu Leiu records Zhu Xi's words saying: The Earlier Heaven diagram is indeed profound and subtle, and was not first created by Shao Yong. There was already such a diagram before Chen Tuan, but it was kept secret and not passed on, probably transmitted through generations of alchemists. What is discussed in the Threefold Concordance on the Zhou Changes also shares some similar meanings.

按：「震始交陰而陽生」，謂震與坤按而一陽生於下，三日夕月出庚，納震一陽之氣也，即《參同契》所謂「三日出為爽，震庚受西方」也；「巽始消陽而陰生」，謂巽與乾接而一陰生於下，十六日旦月退卒，納巽一陰之氣也，即《參同契》所謂「十六轉就緒，巽辛見平明」也。自震一陽進而納兌之二陽，至乾三陽而滿，此望前三候明生魄死之月象也；自巽一陰退而納艮之二陰，至坤三陰而滅，此望後三候魄生明死之月象也。

Hu Wei explains: The statement "Zhen begins to meet Yin and Yang is born" means that the Zhen trigram connects with Kun, and one Yang is generated at the lower trigram; on the third day of the month, the moon appears in the Geng direction in the evening, which is receiving the Yang energy of the Zhen trigram, as mentioned in the "Cantong Qi" as "on the third day, the moon appears as Shuang, Zhen receives Geng and is seen in the west." The statement "Xun begins to eliminate Yang and Yin is born" means that the Xun trigram connects with Qian, and one Yin is generated at the lower trigram; on the sixteenth day of the month, the moon gradually retreats in the morning, which is receiving the Yin energy of the Xun trigram, as mentioned in the "Cantong Qi" as "on the sixteenth day, the moon completes its cycle, Xun receives Xin and is seen at dawn." From the one Yang of Zhen advancing to receive the two Yang of Dui, reaching the three Yang of Qian and the full moon, this is the first three phases before the full moon "ming is born and魄 is dead" in the lunar cycle; from the one Yin of Xun retreating to receive the two Yin of Gen, reaching the three Yin of Kun and the moonlight fading away, this is the last three phases after the full moon "魄 is born and ming is dead" in the lunar cycle.

《禮運》曰「播五行於四時，和而後月生也，是以三五而盈，三五而闕」，正合此意。「播五行於四時」，以一歲中四氣之流行言之，「出震齊巽」之方位是也；「三五而盈，三五而闕」，以一月中月體之消長言之，「乾南坤北」之方位是也。

The Li Ji · Li Yun says, "Distributing the Five Phases among the four seasons, harmony is achieved and then the moon begins to shine; thus, after fifteen days it is full, and after another fifteen days it wanes," which precisely matches the meaning discussed above. "Distributing the Five Phases among the four seasons" refers to the flow of the four seasonal energies throughout the year, which corresponds to the Later Heaven arrangement of "The Emperor arises from Zhen, and harmonizes with Xun." "After fifteen days it is full, and after another fifteen days it wanes" refers to the waxing and waning of the moon's body within a month, which corresponds to the Earlier Heaven arrangement of "Qian in the south and Kun in the north."

熊氏朋來《五經說》曰：「《參同契》云『易謂坎離』，又云『日月為易』『乾坤門戶，坎離匡廓，牝牡四卦』。先天以乾坤坎離牝牡，兌震巽艮四卦。又云『坎離者乾坤二用，老陽變陰用九，老陰變陽用六』，其牝牡之體、九六之用皆坎離也。」

Xiong Penglai's "Commentary on the Five Classics" says: "The "Zhou Yi Cang Tong Qi" says 'the "Yi" is the Kan and Li,' and also says 'the sun and moon combined make the character "Yi." 'The Qian and Kun are the gateways, and the Kan and Li are the outer walls, with the male and female principles together forming four trigrams.' The Earlier Heaven diagram precisely pairs the Qian and Kun with the male and female principles, and the Dui, Zhen, Xun, and Gen as the other four trigrams. The "Zhou Yi Cang Tong Qi" also says 'the Kan and Li are the two functions of the Qian and Kun; the old yang transforms into yin and is called 'use nine,' and the old yin transforms into yang and is called 'use six.' ' It is evident that the substance of the male and female principles and the functions of nine and six ultimately all rest upon the Kan and Li.

「姑就《參同契》言之，則先後天圖已在其中。乾坤爐鼎，坎離水火，故後天坎離居先天乾坤之位，以坎中陽實離中陰虛仍為乾坤，故丹經謂之還元。乾専於陽，坤専於陰，曰爐鼎者，器之。惟夫離已日光，坎戊月精，互相根依，在納甲則主中宮戊巳之功，在先天則為日東月西之象，在後天則正火南水北之位。」

Taking the "Cantongqi" as an example, both the Earlier Heaven diagram and the Later Heaven diagram are already included within it. Qian and Kun are regarded as the furnace and cauldron, while Kan and Li represent water and fire. Therefore, in the Later Heaven diagram, Kan and Li occupy the positions of Qian and Kun in the Earlier Heaven diagram. Using the yang element of the middle line of the Zan卦 (Kan) to fill the yin vacancy of the middle line of the Li卦, it reverts back to Qian and Kun, hence the alchemical texts refer to this as "returning to the original state" (huan yuan). Qian is entirely yang and Kun is entirely yin, and they are called "furnace and cauldron" because they are regarded as vessels. As for Li paired with Ji to form the light of the sun and Kan paired with Wu to form the essence of the moon, they depend on each other. In the Najia method, they oversee the functions of the central palace (zhonggong) governed by Wu and Ji. In the Earlier Heaven diagram, they form the image of the sun in the east and the moon in the west. In the Later Heaven diagram, they are positioned at the south for fire and the north for water.

「八卦中乾兌二金，坤艮二土，震巽二木，皆陰陽和順；惟坎離水陰根陽、火陽根陰，不同他卦。天降而地升，陽倡而陰和，坎離者天地之交也。」

Among the Eight Trigrams, Qian and Dui belong to metal, Kun and Gen belong to earth, Zhen and Xun belong to wood, and all are harmonious within yin and yang. Only Kan and Li are different: Kan represents water, which is yin with yang as its root; Li represents fire, which is yang with yin as its root, differing from the other trigrams. When heavenly energy descends and earthly energy ascends, yang initiates and yin follows in response. Kan and Li are precisely where heaven and earth meet.

「故日為太陽精，離者日之象，何不三爻純陽而中有陰爻？才說太陽，其間便有少陰，所以日納月之烏，認得日中有月則可以知離卦。月為太陰精，坎者月之象，何不三爻純陰而中有陽爻？才說太陰，其間便有少陽，所以月納日之兔，認得月中有日可以知坎卦。」

Therefore, the sun is the essence of extreme yang, and the Li hexagram represents the image of the sun; yet why is it not composed of three yang lines with one yin line in the center? Because when we speak of the sun, it already contains a trace of yin, so the sun contains the black bird, which belongs to the moon. Understanding that the sun contains the moon allows one to understand the Li hexagram. The moon is the essence of extreme yin, and the Kan hexagram represents the image of the moon; yet why is it not composed of three yin lines with one yang line in the center? Because when we speak of the great yin, it already contains a trace of yang, so the moon contains the rabbit, which belongs to the sun. Understanding that the moon contains the sun allows one to understand the Kan hexagram.

「乾與離同受太極之陽，而離者中虛之乾；坤與坎同受太極之陰，而坎者中滿之坤。乾坤，太極之兩儀；坎離，太極之四象。是以坎離二卦常為陰陽造化之樞紐也。」

Qian and Li both receive the Taiji yang, but Li is merely Qian with a hollow center; Kun and Kan both receive the Taiji yin, but Kan is merely Kun with a filled center. Qian and Kun are the two yin and yang produced by Taiji, while Kan and Li are the four images produced by Taiji. Therefore, the two trigrams Kan and Li often serve as the pivot of yin and yang transformation.

「乾南坤北，離東坎西」之圖，朱子雖知其出於《參同契》而不欲盡言，至熊與可始發其隠。崑山吳先輩喬著《他石錄》，其外篇《儒辨》曰：「六經多被混亂，尤甚者《易》，《易》中尤甚者先天八卦。夫卦之方位，『帝出乎震』章八方有明文，『天地定位』章不言八方，蓋謂有天上地下之《否》而亦有地上天下之《泰》，八卦相蕩而成六十四卦也。逆數者，卜筮而前知吉凶也。先天之文見於乾卦，『先』讀去聲，非邵子之所謂也。」

The diagram "Qian in the south, Kun in the north, Li in the east, Kan in the west" was known by Zhu Xi to come from the "Zhou Yi Cang Tong Qi," but he did not fully explain it. It was not until Xiong Penglai (whose name was Yu Ke) that the hidden meaning was revealed. The elder scholar from Kunshan, Wu Qiao, wrote a book called "He Shi Lu," whose outer part, "Ru Bian," says: the Six Classics have been greatly confused, and the "Zhou Yi" is the most disturbed. Among the "Zhou Yi," the Earlier Heaven Trigrams are the most significant. Regarding the directions of the trigrams, the chapter "Di Chu Hu Zhen" in "Shuo Gua" clearly states the directions of the eight trigrams, but the chapter "Tian Di Ding Wei" does not mention directions. That passage merely refers to the "Pu" hexagram which has heaven below and earth above, and the "Tai" hexagram which has earth below and heaven above. The eight trigrams interact with each other to form the sixty-four hexagrams. The term "ni shu" refers to divination where the outcome is known in advance. As for the term "xiangan," its origin is found in the "Wenyan" of the Qian hexagram, "xiangan er tian fei wei," where the character "xian" is pronounced in the falling tone, and is not the "xiangan" as explained by Shao Yong.

「愚嘗得張平叔《悟真篇》之傳於方外士（宋天台張伯端，字平叔，一名用成，撰《通玄秘要悟真篇》一卷），其意與邵子之圖適合：離東者，移火於木位，東三南二同成五也；坎西者，移水於金位，北一西將四共之也；乾南坤北者，移坎之中實以填離之中虛，而成金丹三家相見結嬰兒也。」

I once received the transmission of Zhang Pingshu's "Wuzhen Pan" from a hermit (Zhang Bodaon, a person from Tiantai during the Song dynasty, also known as Zhang Yongcheng, who wrote a single volume called "Tongxuan Miya Wuzhen Pan"), and found that its meaning coincided exactly with Shao Yong's diagram. The statement that "Li is in the east" refers to moving fire to the position of wood, combining the number three of the east with the number two of the south to make five; the statement that "Kan is in the west" refers to moving water to the position of metal, combining the number one of the north with the number four of the west to be together; the statement that "Qian is in the south and Kun is in the north" refers to removing the yang element from the middle line of Kan hexagram to fill the yin vacancy in the middle line of Li hexagram, which is what the alchemists call "three families meeting" to form an infant.

「巽居西南坤位，以長女合老陰，黃婆也；艮居西北乾位，以少男合老陽，築基也；兌居東南巽位，以少女合長女，隠寓三七於其中，鼎器也；震居東北艮位，以長男合少男，隠寓二八於其中，藥物也。其於數往知來，遙寓順則成人、逆則仙也。」

The Trigram Xun occupies the Southwest, which originally belongs to Kun, thus combining the Elder Sister with the old yin, referring to the "Yellow Wife" mentioned by the alchemists. The Trigram Gen occupies the Northwest, which originally belongs to Qian, thus combining the Young Son with the old yang, referring to "building the foundation." The Trigram Dui occupies the Southeast, which originally belongs to Xun, thus combining the Young Girl with the Elder Sister, implicitly indicating the number "three and seven," referring to the "cauldron." The Trigram Zhen occupies the Northeast, which originally belongs to Gen, thus combining the Elder Son with the Young Son, implicitly indicating the number "two and eight," referring to the "medicine." As for the phrase "knowing the future from the past," it remotely embodies the alchemists' principle of achieving human longevity through progressive cultivation and immortality through reverse cultivation.

「《易》道無所不包，何獨丹法？凡醫藥、相地、三命等無不倚之以立言，而離於文王處憂患、孔子無大過，即非吾儒之《易》。希夷，仙也，不妨以外道說《易》；邵子交於二程，何可出此？考亭于丹道有所見，是以手注魏伯陽之《參同契》，見邵子之圖欣然會心，入之《本義》，而不計丹道可以倚《易》、《易》不為丹道作也。《本義》之混濫者多矣，以『天地定位』章為第一。」

The principles of the I Ching encompass everything, not merely the art of alchemy. All fields such as medicine, geomancy, and the three destinies rely on the I Ching to establish their theories. However, if one departs from the fundamental idea that King Wen composed the I Ching in times of distress and Confucius studied it to avoid great mistakes, then it is no longer the Confucian I Ching. Chen Tuan was originally a person of the Daoist tradition, so it is acceptable for him to use external doctrines to explain the I Ching. Shao Yong, having interacted with the two Cheng brothers, how could he produce such things? Zhu Xi (from the Kao Ting school) had some understanding of alchemy, so he personally annotated Wei Boyang's Treatise on the Concordance of the Three. When he saw Shao Yong's diagrams, he was delighted and included them in his The Original Meaning of the Zhou Changes, without realizing that while alchemy can be related to the I Ching, the I Ching was not created for alchemy. There are many mixed and confused parts in The Original Meaning of the Zhou Changes, with the chapter on "Heaven and Earth Positioned" being the first.

渭按：「丹道可以倚《易》，《易》不為丹道作」，又云「《易》道無所不包，而離於文王處憂患、孔子無大過，即非吾儒之《易》」，此真千古格言。方技家既借「天地定位」四句撰為此圖，下文順逆亦自有其說，邵子「已生未生」之解大非。「順則成人，逆則仙」，修齡義亦有所未盡，說在《參同契》「坎離之為易」也。

Hu Wei remarked: Wu Qiao said, "The Dao of alchemy can be based on the Book of Changes, but the Book of Changes was not written for alchemy." He also said, "The Dao of the Book of Changes encompasses everything, but once it departs from King Wen's concern with calamities and Confucius' pursuit of avoiding great mistakes, it is no longer the Book of Changes of the Confucian school." This is indeed a timeless and unchanging saying. Since the practitioners of techniques have used the four lines "Heaven and Earth are positioned" to fabricate this diagram, the subsequent terms "ascending" and "descending" must have their own interpretations in their view. Shao Yong's explanation using "already born" and "not yet born" is entirely wrong. As for the statement that "ascending leads to human life and descending leads to immortality," in terms of the meaning of cultivating longevity and health, there are still aspects not fully explained. This point will be discussed again when we talk about the "Kan and Li as the Book of Changes" in the "Cantongqi."

《周易參同契》曰：「天地設位，而易行乎其中矣。天地乾坤也，易謂坎離。坎離者，乾坤二用；二用無爻位，周流行六虛，往來既不定，上下亦無常。」又曰：「坎戊月精，離己日光，日月為易，剛柔相當。」又曰：「人所稟軀，體本一元，元精雲布，因氣托初。陰陽為度，魂魄所居。陽神日魂，陰神月魄，魂之與魄，互為室宅。」

The "Zhou Yi San Tong Qi" says: Heaven and Earth have established positions of above and below, and "Yi" operates within them. By "Heaven and Earth" it refers to Qian and Kun; by "Yi" it refers to Kan and Li. Kan and Li are the two functions of Qian and Kun; these two functions have no fixed lines, but pervade the six voids in all directions. Their movement has no fixed place, and their up and down have no regular pattern. It also says: Kan belongs to Wu and is the essence of the moon, while Li belongs to Ji and is the light of the sun. The sun and moon together form the character "Yi," with the firm and the yielding precisely matching each other. It also says: the body humans receive is originally derived from the single source. The original essence spreads like clouds, and takes form by relying on the original qi. Yin and Yang serve as the standards, being the dwelling places of the soul and spirit. The yang spirit is the sun's soul, and the yin spirit is the moon's body, with the soul and spirit mutually serving as each other's dwelling.

朱子《語類》曰：「《參同契》所言坎離水火龍虎鉛汞之屬，只是互換其名，其實則精氣二者而已。精，水也，坎也，龍也，汞也；氣，火也，離也，虎也，鉛也。其法以神運精氣，結而為丹。陽氣在下初成水，以火煉之則凝，神丹內外異色，如鴨子卵。」又曰：「水一也，火二也，以魂載魄，以二守一，則水火相濟而不相離，所以能永年也。養生家千言萬語，說龍說虎，說鉛說汞，說坎說離，其術只如此而已。」

The *Zhu Zi Yu Le* records Zhu Xi's words: The *Cantongqi* speaks of Kan and Li, water and fire, dragon and tiger, lead and mercury, but these are merely different names for the same things. In reality, they are only "essence" and "vital energy." Essence is water, Kan, dragon, and mercury; vital energy is fire, Li, tiger, and lead. Its method is to use the "useful god" to transform essence and energy, and to condense them into the elixir. When yang energy is at the bottom, it first becomes water. By using fire to refine it, it can condense. The inner and outer colors of the elixir are different, like a duck egg. He also said: The number of water is one, and the number of fire is two. Using the soul to carry the body, and using two to guard one, water and fire can assist each other without separation, thus achieving longevity. The words of the alchemists, speaking of dragon and tiger, lead and mercury, Kan and Li, are all just this.

先天八卦方位，丹家用之最親切而有味。其所謂「易」者，坎離也，與儒學不同，故解此章之順逆亦自有其義。孔子之意在蓍卦，丹家之意在水火。

The directional arrangement of the Earlier Heaven Trigrams is most fitting and meaningful for the Daoist alchemists. They refer to "Yi" as meaning Kan and Li, which differs from the Confucian approach. Therefore, their interpretation of the terms "shun" and "ni" in this chapter has their own set of principles. Confucius focused on the use of the yarrow stalks and the hexagrams, while the Daoist alchemists focused on water and fire.

人之一身，乾為首，坤為腹。自首以下有心，心屬火而為氣之總會；自腹以下有腎，腎屬水而為精之所藏。火炎上，水潤下，自有生而已然，所謂數往者順也。及加以修煉之功，以乾坤為爐鼎，坎離為鉛汞，務使火降而下、水升而上，所謂知來者逆也。

In the human body, Qian corresponds to the head and Kun corresponds to the abdomen. From the head downward is the heart, which belongs to fire and is the gathering place of qi; from the abdomen downward is the kidney, which belongs to water and is the storage of essence. Fire tends to rise upward, while water tends to descend and moisten, and this is the way it is from the moment a person is born, which is what the Daoist alchemists refer to as "knowing the past in a natural way." When cultivation is added, one uses Qian and Kun as the furnace and cauldron, and Kan and Li as lead and mercury. One must necessarily make the fire descend and the water ascend, which is what they call "knowing the future in a reverse way."

《鼎器歌》云「陰在上，陽下奔」，陰謂水，陽謂火。丹家以坎離為易，水下而反上，火上而反下，故曰「易逆數也」。《說卦》離南而坎北，丹家抽坎之中實以填離之中虛，故乾南而坤北。《參同契》云「子南午北，互為綱紀，一九之數，終而復始」，亦此義也。

The "Ding Qi Ge" from the "Cantong Qi" says, "Yin is above, Yang rushes downward," where "Yin" refers to water and "Yang" refers to fire. Alchemists associate Kan and Li with the "Yi" (Change). Water naturally resides below but rises upward, while fire naturally resides above but descends downward, hence the saying "the Yi reverses the order." The Later Heaven directions in "Shu Gua" place Li in the south and Kan in the north. Alchemists extract the Yang element from the middle line of Kan and use it to fill the Yin deficiency in the middle line of Li, resulting in Qian in the south and Kun in the north. The "Cantong Qi" states, "The position of Zi is in the south, the position of Wu is in the north, they mutually form the framework; the numbers one and nine, cycle and repeat," which explains the same principle.

人之生也，火在水上，未濟之象也；神丹既成，則水在火上為既濟。以魂守魄，使陰陽不相離，可以長生而久視。仙訣云「五行順行，法界火坑；五行顛倒，大地七寳」，是為順則成人、逆則仙也。

When a person is born, fire is on water, which corresponds to the image of the hexagram "Not Yet Completed." Once the divine elixir is successfully prepared, it becomes water on fire, forming the hexagram "Already Completed." By using the soul to control the body, and keeping yin and yang from separating, one can achieve long life and prolonged vision. The secret words of the immortal masters say, "If the Five Phases proceed in order, the entire realm becomes a fire pit; if the Five Phases reverse, the whole world is filled with treasures." This is what is meant by following the natural order to be a human being, and reversing the order to become an immortal.

邵子小橫圖用加一倍法以為伏羲八卦之次序，誤矣；而又推之於方位，以自震至乾為順、自巽至坤為逆，且喻之以左旋右行。夫天之與日月五星也，左則俱左，右則俱右，豈有左右各半之理乎？既失丹家之旨，又非孔子之義，無一而可者也。

Shao Yong's small horizontal diagram arranges the trigrams by doubling, treating them as the order of Fuxi's eight trigrams, which is already incorrect. He further applied this method to directions, claiming that from Zhen to Qian is clockwise and from Xun to Kun is counterclockwise, using left rotation and right movement as metaphors. However, the movement of heaven and the sun, moon, and five planets either all move left or all move right; there is no logic to having half moving left and half moving right. In this way, it loses the essence of the Daoist alchemists' teachings and contradicts Confucius's original meaning, and there is nothing that stands up to scrutiny.

或問：「子以希夷先天圖為康節之學所自出，其詳可得聞乎？」曰：「康節受《易》於李之才，以先天古《易》衍其旨，蓍書十餘萬言（謂《皇極經世》《觀物內外篇》《漁樵問對》）以發希夷之蘊。史稱『探賾索隠，妙悟神契，洞徹蘊奧，汪洋浩博，德其所自得者』，此實録也。」

Someone asked, "Do you think Chen Tuan's Earlier Heaven Diagram is the source of Shao Kangjie's learning? Could you explain in detail?" The answer was: Shao Yong learned the study of the Book of Changes from Li Zhicai, using the ancient Earlier Heaven version of the Book of Changes to explore its meaning, and wrote more than ten thousand words of works, including The Huangji Jingshi, The Guanwu Neiwaipian, and The Yuqiao Wen Dui, to elaborate on the profound insights of Chen Tuan's school. Historical records say he "explored the profound, searched for the hidden, had a wonderful insight that harmonized with the divine principles, thoroughly understood its depth, and his vast and profound knowledge was all his own," and these words are accurately recorded.

今以八卦次序、方位圖考之：太極即希夷先天圖之環中也；初畫為兩儀，即圈之白黒各半左右回互者；中畫為四象，即白中之黒、黒中之白與半白半黒而為四也；終畫為八卦，即一圈界分為八，而八卦竒偶之畫與白黒之質相應者也。從中折取，則乾南坤北、離東坎西、震東北、兌東南、巽西南、艮西北，八卦有方位而九宮具焉也。

Now examining the sequence diagram of the Eight Trigrams and the directional diagram of the Eight Trigrams: the so-called "Taiji" is the central circle in Chen Tuan's Earlier Heaven diagram. The two principles at the lowest line are represented by the black and white each occupying half of the circle, interlocking and embracing left and right. The four images at the middle line are formed by the black within white, the white within black, and the half-black and half-white, making a total of four. The Eight Trigrams at the top line are formed by dividing the circle into eight parts, and the odd and even lines of the Eight Trigrams correspond exactly with the black and white qualities. By folding the diagram from the center, the directions of the Eight Trigrams are determined: Qian in the South, Kun in the North, Li in the East, Kan in the West, Zhen in the Northeast, Dui in the Southeast, Xun in the Southwest, and Gen in the Northwest. The Eight Trigrams now have directions, and the nine-square grid numbers are included within this structure.

圓者引之使長，合者攡之使分，而圖遂化為畫矣。然兩儀、四象、八卦皆子在母外，既失希夷之本意；而又以白代單、以黒代拆，則乾之三連變為三白□，坤之六斷變為三黒□，六子皆然（坎離即水火匡廓之形）。表畫以色，有竒無偶，大非三代以來相傳之卦象，瀆經侮聖與劉牧無異，何為其從之也？

To stretch the circle into a straight line to make it longer, and to separate what was joined to make it dispersed, thus the circular diagram became the hexagram diagram. However, in this way, the two principles, four images, and eight trigrams all became like "a child outside the mother's body," having lost Chen Tuan's original meaning. Moreover, using white to represent the odd lines and black to represent the even lines, the three continuous lines of Qian became three white squares, and the three broken lines of Kun became three black squares, and all six sub-trigrams were treated in the same way (the trigrams Kan and Li are the shape described in the "Compendium of the Three" as water and fire encircling each other). Using colors to indicate the trigrams results in only odd lines and no even lines, which greatly contradicts the trigrams' forms passed down since the Three Dynasties. This disrespectful treatment of the classics and contempt for the sages is no different from Liu Mu's approach, so why follow him?

右論邵子伏羲八卦方位。

The above points discuss the "Fuxi Eight Trigrams Diagram" as determined by Shao Yong.

《繫辭傳》曰：「八卦成列，象在其中矣；因而重之，爻在其中矣。」又曰：「《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。」《說卦傳》曰：「昔者聖人之作《易》也，將以順性命之理。是以立天之道曰陰與陽，立地之道曰柔與剛，立人之道曰仁與義，兼三才而兩之，故《易》六畫而成卦。分陰分陽，迭用柔剛，故《易》六位而成章。」

The Great Treatise of the Zhou Changes says: "The eight trigrams are arranged in rows, and all the myriad phenomena of heaven and earth are already contained within them; when the eight trigrams are combined two by two, the six lines are already contained within them." It also says: "The Book of Changes encompasses vastness and is complete in all things: it contains the way of heaven, the way of humanity, and the way of earth. By doubling the three principles of heaven, earth, and humanity, one trigram consists of six lines. This 'six' is not anything else but the way of the three principles." The Sayings on the Trigrams says: "In ancient times, the sage created the Book of Changes to follow the principles of life and destiny, so he established the way of heaven as 'yin' and 'yang,' the way of earth as 'flexibility' and 'firmness,' and the way of humanity as 'benevolence' and 'righteousness.' By doubling the three principles, the Book of Changes is composed of six lines. By distinguishing the positions of yin and yang, and alternately using flexible and firm lines, the Book of Changes forms its textual structure through six lines."

按：夫子曰「重」、曰「兼」，明是倍三為六，非逐爻漸生之謂。《本義》猶從舊解，云「因而重之」謂各因一卦而以八卦次第加之為六十四，又云三畫已具三才，重之故六。至《圖說》則與邵義並存，而以邵為善；及蔡氏草《啟蒙》，則専主《觀物外篇》，而顯背經文亦有所不顧矣。

Hu Wei's commentary: Confucius said "repetition" and "comprehensiveness," clearly indicating that the three lines are doubled to form six lines, not that the six lines are generated layer by layer one by one. Zhu Xi's "The Original Meaning of the Zhou Changes" still followed the old interpretations, explaining "thereby repeating" as each trigram serving as the lower part, and then successively adding the eight trigrams above to form the sixty-four trigrams. He also said that the three lines already contain the three elements of heaven, earth, and humanity, and that by repeating them, they become six lines. However, in the diagram section of "The Awakening of the Study of the Changes," he presented both the old interpretations and Shao Yong's view side by side, and even considered Shao's view better. When Cai Yuanping drafted "The Awakening of the Study of the Changes," he focused mainly on Shao Yong's "Outer Chapters of Observing Things," clearly disregarding the classical texts of "The Great Treatise" and "The Explanation of the Trigrams."

《大傳》但云包犧氏始作八卦，其因而重之以為六十四者不言其人。先儒或以為神農，或以為大禹，或以為文王，總無確證。然吾觀夫子所陳十三卦制器尚象之事，唯網罟創自包犧，取諸《離》之純卦，而耒耨之利取諸《益》，日中為市取諸《噬嗑》，皆神農之所為也，則謂神農重卦者庶幾得之。蓋伏羲雖有因重之意，而八卦成列之後未嘗復加之畫；至神農則始一一演之，以為六十四卦、三百八十四爻，而重卦之名至黃帝乃備耳。子曰：「聖人立象以盡意，設卦以盡情偽。」蓋立象即八卦成列，設卦即因而重之，伏羲略而神農詳也。

The Great Treatise mentions only that Fuxi first drew the Eight Trigrams, but does not say who first overlapped them and derived the sixty-four trigrams. Previous scholars have suggested different people: some say Shennong, others say Yu the Great, and others say King Wen. There has never been conclusive evidence. However, when Confucius lists in the Great Treatise the thirteen trigrams related to "making tools and taking images as models," only the part about tying knots and making nets comes from Fuxi, taking its image from the pure trigram Li, which is composed of two identical lines. The invention of the plow and hoe, taking its image from the Yì trigram, and the establishment of markets at noon, taking its image from the Shìkè trigram, are all attributed to Shennong. Therefore, it is probably correct to say that the overlapping of trigrams originated with Shennong. Although Fuxi had the idea of "overlapping," after the Eight Trigrams were arranged, he did not add more lines. It was Shennong who developed each trigram step by step, forming the sixty-four trigrams and the 384 lines. The term "overlapping trigrams" was only fully established during the time of the Yellow Emperor. Confucius said, "The sage establishes images to express meaning, and sets trigrams to reveal human nature and falsehood." What is meant by "establishing images" is the arrangement of the Eight Trigrams, and what is meant by "setting trigrams" is overlapping them. Fuxi did it simply, while Shennong did it in detail.

若夫重卦之次序，絶無可考。《連山》首《艮》，《歸藏》首《坤》，先儒雖有是說，而其書已亡，自《艮》《坤》以後六十三卦其次序不知如何，今可言者獨文王所演之易象耳。或云烈山氏之易，文王因之，烈山氏即神農也。首《乾》《坤》，終二《濟》，兩兩反對，皆有至理，安得於此外更造一圖以為伏羲六十四卦之次序哉？智者之鑿，孟子之所惡也。

After the creation of the sixty-four hexagrams, the order in which they are arranged is completely unattainable through historical verification. The book "Lianshan" began with the hexagram "Gen," while "Guicang" began with "Kun." Although previous scholars have mentioned these arrangements, both books have long since been lost. Therefore, no one knows how the remaining sixty-three hexagrams were ordered after "Gen" and "Kun." Today, the only hexagram sequence that can be clearly explained is the one developed by King Wen. Some people claim that Liushanshi had a book of "Yi," which King Wen used. Liushanshi is said to be Shennong. King Wen's hexagram sequence starts with "Qian" and "Kun," and ends with "Ji Ji" and "Wei Ji." The sixty-four hexagrams are paired in opposition, and each pair contains profound meaning. How can one create another diagram outside of this sequence and claim it to be the original order of the sixty-four hexagrams from Fuxi? This kind of artificial and clever fabrication is exactly what Mencius despised.

《本義圖說》曰：前《八卦次序圖》即《繫辭傳》所謂「八卦成列」者，此圖即其所謂「因而重之」者也。故下三畫即前圖之八卦，上三畫則各以其序重之，而下卦因亦各衍而為八也。若逐爻漸生，則邵子所謂「八分為十六，十六分為三十二，三十二分為六十四」者，尤見法象自然之妙也。《易學啟蒙》曰：八卦之上各生一竒一偶而為四畫者十六，於經無見，邵子所謂「八分為十六」者是也，又為兩儀之上各加八卦，又為八卦之上各加兩儀也。四畫之上各生一竒一偶而為五畫者三十二，邵子所謂「分為三十二」者是也，又為四象之上各加八卦，又為八卦之上各加四象也。

In Zhu Xi's "The Original Meaning of the Zhou Changes," the diagram explanation states: the previous diagram of the "Order of the Eight Trigrams" is what the "Great Treatise" refers to as "the eight trigrams arranged in order." This diagram, however, is what it calls "thereby stacking them again." Therefore, the three lines below each trigram correspond to the eight trigrams in the previous diagram, while the three lines above each trigram are stacked in the order of the eight trigrams, thus allowing each lower trigram to generate the eight trigrams again. If we follow the gradual generation of each line, this is what Shao Yong refers to as "eight divided into sixteen, sixteen divided into thirty-two, thirty-two divided into sixty-four," which more clearly reveals the natural elegance of the generation of trigrams. "The Awakening of the Study of the Changes" says: adding one odd and one even line above each of the eight trigrams results in sixteen figures of four lines—this is not supported by the text, which is exactly what Shao Yong refers to as "eight divided into sixteen." From another perspective, this is equivalent to adding the eight trigrams to the two principles, or adding the two principles to the eight trigrams. Adding one odd and one even line to each of the four-line figures results in thirty-two figures of five lines, which is exactly what Shao Yong refers to as "divided into thirty-two." From another perspective, this is equivalent to adding the eight trigrams to the four principles, or adding the four principles to the eight trigrams.

五畫之上各生一竒一偶而為六畫者六十四，則兼三才而兩之，而八卦之乘八卦亦周，於是六十四卦之名立，而易道大成矣。《周禮》所謂「三易之別皆六十有四」，《大傳》所謂「因而重之，爻在其中矣」，邵子所謂「三十二分為六十四」者是也。若於其上各卦又各生一竒一偶，則為七畫者百二十八矣；七畫之上又各生一竒一偶，則為八畫者二百五十六矣；八畫之上又各生一竒一偶，則為九畫者五百十二矣；九畫之上又各生一竒一偶，則為十畫者千二十四矣；十畫之上又各生一竒一偶，則為十一畫者二千四十八矣；十一畫之上又各生一竒一偶，則為十二畫者四千九十六矣。

Above the five lines, each one generates one odd and one even line, resulting in six lines with a total of sixty-four hexagrams. This is what the "Sayings on the Trigrams" refers to as "combining the three elements and doubling them." The multiplication of the eight trigrams with each other covers all possibilities completely, thus establishing the names of the sixty-four hexagrams. The Way of the Book of Changes is thus fully realized. The "Rites of Zhou" states, "There are three kinds of the Book of Changes, each different, but all have sixty-four hexagrams." The "Great Treatise" says, "By doubling the trigrams, the lines are included within." Shao Yong says, "Thirty-two divided into sixty-four." All these statements refer to the same concept. The "启蒙" continues with the same method of "doubling": if each hexagram is further doubled by adding one odd and one even line above the six lines, it results in seven lines with a total of one hundred and twenty-eight; doubling again above the seven lines results in eight lines with two hundred and fifty-six; doubling again above the eight lines results in nine lines with five hundred and twelve; doubling again above the nine lines results in ten lines with one thousand and twenty-four; doubling again above the ten lines results in eleven lines with two thousand and forty-eight; doubling again above the eleven lines results in twelve lines with four thousand and ninety-six. Each time a line is added, the number doubles.

此焦贛《易林》變卦之數，蓋以六十四乘六十四也，今不復為圖於此，而略見第四篇中。若自十二畫上又各生一竒一偶，累至二十四畫，則成千六百七十七萬七千二百一十六變，以四千九十六自相乘，其數亦與此合，引而伸之，蓋未知其所終極也。雖未見其用處，然亦足以見易道之無窮矣。

This is the number of changing hexagrams in Jiao Yanshou's "Yi Lin," which is the product of sixty-four multiplied by sixty-four. Here, no separate diagram is drawn, but a general account can be found in the fourth chapter. If one continues to add one odd and one even line above the twelve lines, and keeps adding them up to twenty-four lines, it would result in sixteen million seven hundred seventy-seven thousand two hundred and sixteen changes; multiplying four thousand and nine十六 by itself also gives the same number. If this process is extended further, it is impossible to know where it would end. Although it seems to have no practical use, it sufficiently demonstrates the boundless nature of the Way of the Book of Changes.

康節先天之學，其病根全在小橫圖。蓋八卦之次序既乖，則其論方位亦誤，六十四卦之次序方位更不待言矣。而吾竊有怪於《啟蒙》之說也。數用加一倍法，可以推之百千萬億而無窮；若《易》卦則六畫而止，其變而之他亦不過六畫。

The root of the problem in Shao Yong's Earlier Heaven theory lies entirely in that small horizontal diagram of the Eight Trigrams. Since the order of the Eight Trigrams is wrong, the directions he talks about are also incorrect; the order and directions of the sixty-four Trigrams are even worse. What puzzles me most privately is a passage from his "Introduction to the Study of the Changes." Although using the "doubling method" can calculate numbers to infinity, the hexagrams in the Book of Changes only have six lines, and when one hexagram transforms into another, it still remains with six lines.

即如焦氏《易林》，每一卦變為六十四，至四千九十六，其本卦仍自為本卦，之卦別自為之卦，曷嘗屋上架屋，於六畫之上覆自七畫遞加至十二畫乎？而且云「自十二畫上又累至二十四畫，引而伸之，未知其所終極，足以見易道之無窮」也。夫易道無窮而卦畫則有窮，季通之藁荒謬至此，朱子曽不一是正，何歟？

Take Jiao Yanshou's "Yi Lin" for example. Each hexagram can transform into sixty-four hexagrams, resulting in a total of four thousand and ninety-six. However, the original hexagram remains a hexagram with six lines, and the transformed hexagram is also a hexagram with six lines. How could it be that they build upon six lines by adding seven lines up to twelve lines? The "Ming Guan" even says, "From twelve lines, they add up to twenty-four lines, and so on without end, showing that the Way of the Book of Changes is boundless." But we must know that although the Way of the Book of Changes is indeed boundless, the hexagrams themselves are limited. Cai Yuanping's (Zi Jitong) draft is so absurd, yet Zhu Xi did not correct a single word. Why is that?

《仲氏易》曰：夫兩儀四象者，生卦之序，非畫卦之序也。因而重之者，以三重三，非謂二可重一、四可重二、八可重四也。故就其成卦而觀之，則由兩而四，由四而八，由八而至六十四，未為不可；而就其畫卦而觀之則不然。夫伏羲但畫八卦耳，何曽畫六十四卦乎？《繫辭傳》曰「乾坤成列，易立其中」，則先畫乾坤；又曰「八卦成列，象在其中」，則次畫八卦；又曰「因而重之，爻在其中」，則於是不再畫也，第因其所畫而復配之為六十四卦，而易象終焉。故《周禮》經卦皆八，揚雄謂宓羲經以八卦，孔安國曰「伏羲氏之王天下也，始畫八卦」，皆以畫八卦為一截，未嘗一及重卦。

Ma Qilin's "Zhong Shi Yi" says that the concept of two principles and four images refers to the order in which trigrams were generated, not the order in which Fuxi drew the trigrams. The phrase "thereby stacking them" means using a three-line trigram to stack another three-line trigram, not that two principles can be stacked into one line, or four images can be stacked into two principles, or eight trigrams can be stacked into four images. Therefore, in terms of the generation of trigrams, it is possible to say that it proceeds from two principles to four images, from four images to eight trigrams, and from eight trigrams to the sixty-four trigrams. However, in terms of the actual order in which Fuxi drew the trigrams, it was not like that. Fuxi only drew the eight trigrams; he never drew the sixty-four trigrams. The "Xici Zhuan" says, "When Qian and Kun are arranged in order, the Book of Changes is established in the middle," indicating that Qian and Kun were drawn first. It also says, "When the eight trigrams are arranged in order, the images are contained within them," showing that the eight trigrams were drawn next. Furthermore, it says, "By stacking them, the lines are contained within them," indicating that at this point, no further drawing was done. Instead, the already drawn eight trigrams were combined with each other to form the sixty-four trigrams, and the images of the Book of Changes were thus complete. Therefore, the "Zhou Li" says that all the basic trigrams are eight, Yang Xiong says that Fuxi's fundamental trigrams were only the eight trigrams, and Kong An Guo says, "Fuxi ruled the world and began to draw the eight trigrams," all of them regard drawing the eight trigrams as a single stage, and none of them ever mention stacking trigrams.

而重卦之起，舊有歸之神農者（京房引孔子之言曰「神農重乎八純」，謂取伏羲八純卦而重之為六十四卦。《史記》亦云神農始作重卦），有歸之大禹者（《周禮》三易，一曰《連山》，即夏易，謂以重艮為連山也。晉孫盛曰「夏禹修用《連山》」，以艮之重卦為夏易首）。雖其說不可深信，然亦以見八卦與六十四卦縱成自伏羲，亦必不連次而加畫之，斷可識矣。故先天之圖其誤有八。一、畫繁（自一畫為陽，二畫為陰，三一為乾，三二為坤，而其畫已畢，未有畫至六十四卦者。今圖取巧便，但以黒為陰、白為陽耳，此非羲畫法也。若羲畫原法則黒皆兩畫，是六十四卦在陽有一百九十二畫、在陰有三百八十四畫，太不憚煩矣，此非自然因重之數也。其誤一也）。

As for the origin of the sixty-four hexagrams, old accounts attribute it to the Yellow Emperor (Shennong). Jing Fang cited Confucius' words saying, "Shennong repeated the eight pure trigrams," meaning that he combined the eight trigrams of Fuxi into hexagrams. The "Records of the Grand Historian" also states that Shennong first created the repeated trigrams. Others attribute it to the Great Yu. The "Rites of Zhou" mentions three types of the Book of Changes, the first being "Lianshan," which is the Book of Changes of the Xia dynasty. It says that "Lianshan" starts with the repeated trigram of Ken. Jin dynasty's Sun Sheng said, "Great Yu revised and used Lianshan," meaning that the repeated trigram of Ken was the first hexagram of the Xia Book of Changes. Although these accounts are not entirely reliable, they do show that even if both the eight trigrams and the sixty-four hexagrams were created by Fuxi, they could not have been drawn one after another, layer by layer. This can be definitely concluded. Therefore, the Earlier Heaven diagram has eight errors. The first is that the method is complicated. One line represents yang, two lines represent yin, three ones make Qian, three twos make Kun, and the drawing stops there, never continuing to the sixty-four hexagrams. The current diagram, for convenience, uses black to represent yin and white to represent yang, which is not the method of Fuxi. If we follow Fuxi's original method, each yin line would need to be drawn with two strokes. Then, in the sixty-four hexagrams, there would be 192 strokes for yang lines and 384 strokes for yin lines, which is too complicated. This is not the natural number that should result from "repeating" them. This is the first error.

二、四五無名（四象分四畫為太陽、少陰、少陽、太陰，今増至十六畫，又増至三十二畫，則可名十六象、三十二象乎？抑仍名四象乎？若仍名四象，則八卦又生四象矣。其誤二也）。三、三六無住法（惟只有三畫，並無四畫五畫之加，故三畫而止便可名之為八卦。如連翩加畫，則何以三畫有名，四畫五畫秖空畫更無名也？且何以見畫之當止於三、止於六也？其誤三也）。四、不因（乾坤成列畫八卦，八卦成列始作重卦，故曰「因而重之」。因者，因成列之卦也，若一連畫去，何所因乎？其誤四也）。五、父子母女並生（乾父坤母合生六子，此《繋辭》明言次第也，今八卦並生。其誤五也）。

Second, there is no name for the figures with four or five lines (the four trigrams are divided into four types of figures called Sun, Xiao Yin, Xiao Yang, and Tai Yin; now they have increased to sixteen figures and then to thirty-two figures. Can they be called "sixteen figures" or "thirty-two figures"? Or should they still be called the four trigrams? If they are still called the four trigrams, then the eight trigrams would have generated the four trigrams again. This is the second error). Third, there is no reason to stop at three or six lines (since there are only three lines, there is no level of four or five lines. Therefore, once the three lines are drawn, they can be called the eight trigrams. If one keeps adding lines layer by layer, then why do the three lines have names while the four and five lines are just empty lines without names? And on what basis can we decide to stop at three lines and not go further? This is the third error). Fourth, it does not conform to the word "because" (after the trigrams Kan and Qian are arranged, the eight trigrams are drawn; after the eight trigrams are arranged, the compound trigrams are made. Therefore, it is said "because they are repeated." The term "because" means to follow the already arranged trigrams. If one draws the lines continuously, then what is there to "because"? This is the fourth error). Fifth, the parents and children are born at the same time (Qian is the father and Kun is the mother, and together they produce six children, which is clearly stated in the Great Treatise. Now the eight trigrams are all born at the same time. This is the fifth error).

六、子先母，女先男，少先長（六子俱先坤，兌離先震，巽先坎，兌又先離，離又先巽，於一索再索之敘俱失盡矣。羲畫次第必不如是。其誤六也）。七、卦位不合（《說卦》卦位千古不蔑，今以第加之畫而環圖之，乾一右轉，巽五左旋，以乾南坤北離東坎西為象，此實本魏氏《參同契》乾坤運軸、坎離匡廓之圖而妄名先天，致邵子以「雷風相薄」「水火不相射」為證。其誤七也）。八、卦數杜撰無據（卦原無數，但以大衍之數推之，則乾西北卦正當地六相成之數，故曰乾六；坤西南卦正當天九相成之數，故曰坤九。今無故而為乾一、兌二、離三、震四之數，此何據乎？其誤八也）。具此八誤而以為伏羲畫卦次第如是，不可通矣。

Sixth, the children come before the mother, the daughter before the son, and the young before the elder (all six children trigrams are placed before the trigram of Earth, the trigrams Dui and Li are placed before Zhen, Xun before Kan, and Dui before Li, which in turn is before Xun. The order of the first, second, and third draws in the "Say on the Trigrams" is completely disrupted. The order in which Fuxi arranged the trigrams would not be like this. This is the sixth error). Seventh, the positions of the trigrams do not match the text of the classics (the positions of the eight trigrams as recorded in the "Say on the Trigrams" have been unchangeable since ancient times. Now, however, they are arranged in a circular diagram according to the order of successive additions. The trigram Qian one starts from the right and proceeds clockwise, while Xun five starts from the left and moves counterclockwise, forming a diagram in which Qian is in the south, Kun in the north, Li in the east, and Kan in the west. This is actually based on Wei Boyang's "Complementary Treatise," which uses Qian and Kun as the axis and Kan and Li as the frame, as found in alchemical diagrams. Yet it is mistakenly labeled as "Earlier Heaven." This has led Shao Yong to use the phrases "Thunder and Wind contend" and "Water and Fire do not oppose" from the "Say on the Trigrams" as evidence. This is the seventh error). Eighth, the numbers assigned to the trigrams are entirely fabricated without basis (the trigrams originally had no numbers. If we use the number of the Great Derivation, Qian is located in the northwest, which corresponds to the number of the earth's sixfold formation, thus Qian is six; Kun is located in the southwest, which corresponds to the number of the sky's ninefold formation, thus Kun is nine. Now, however, they arbitrarily assign the numbers Qian one, Dui two, Li three, Zhen four. Why is this done? This is the eighth error). With these eight errors, it is still claimed that this is the order in which Fuxi arranged the trigrams, which is not logical.

按：仲氏八誤之辯，剖析無遺，總由伏羲六十四卦次序元無可考而任意為之，所以來後人之彈射也。冠諸經首，不愈彰邵子之過乎？

Hu Wei commented: Mao Qiling's eight refutations are thorough and leave nothing out. Ultimately, it is because the order of the sixty-four hexagrams by Fuxi originally cannot be verified, yet someone made up a fabricated sequence, which led to later criticism. To place such a diagram at the very beginning of the Zhou Changes text would not only be inappropriate but also further highlight Shao Yong's mistake.

右論邵子伏羲六十四卦次序。

The above section examines the diagram of the "Fuxi Sixty-Four Trigrams Order" transmitted by Shao Yong.

《本義圖說》曰：右伏羲四圖，其說皆出於邵氏。蓋邵氏得之李之才挺之，挺之得之穆修伯長，伯長得之華山希夷先生陳摶圖南者，所謂先天之學也。此圖圓布者，乾盡牛中，坤盡子中，離盡卯中，坎盡酉中，陽生於子中，極於午中，陰生於午中，極於子中，其陽在南，其陰在北。方布者，乾始於西北，坤盡於東南，其陽在北，其陰在南。此二者陰陽對待之數。圓於外者為陽，方於中者為陰；圓者動而為天，方者靜而為地者也。

Zhu Xi's "The Original Meaning of the Zhou Changes · Diagram Explanation" says: The four diagrams of Fuxi mentioned above all originate from Shao Yong. Shao Yong learned from Li Zhici (whose courtesy name was Tengzhi), who in turn learned from Mu Xiu (whose courtesy name was Boyang), who learned from Master Chen Tuan of Huashan (whose courtesy name was Tunan). This is what is called "Earlier Heaven Learning." When this diagram is arranged in a circular form, the Qian trigram ends at the midpoint of the southern direction's midpoint (the original text's "Niu Zhong" should be "Wu Zhong"), the Kun trigram ends at the midpoint of the northern direction's midpoint, the Li trigram ends at the midpoint of the eastern direction's midpoint, and the Kan trigram ends at the midpoint of the western direction's midpoint. Yang energy originates from the midpoint of the Zi position and reaches its peak at the midpoint of the Wu position, while Yin energy originates from the midpoint of the Wu position and reaches its peak at the midpoint of the Zi position. Therefore, Yang is in the south and Yin is in the north. When arranged in a square form, the Qian trigram begins at the northwest corner, and the Kun trigram ends at the southeast corner. Yang is in the north and Yin is in the south. These two forms illustrate the mutual relationship between Yin and Yang. The circular diagram is external and belongs to Yang, while the square diagram is internal and belongs to Yin. The circle is active and represents Heaven, while the square is still and represents Earth.

邵子《觀物外篇》曰：夫易根於乾坤而生於姤復，蓋剛交柔而為復，柔交剛而為姤，自茲而無窮矣。又曰：復至乾凡百一十有二陽，姤至坤凡八十陽；姤至坤凡百一十有二陰，復至乾凡八十陰。邵氏伯溫曰：先君云，乾坤大父母也，故能生八卦；復姤小父母也，故能生六十四卦。

Shao Yong's "Outer Chapter of Observing Things" says: The Book of Changes takes Qian and Kun as its fundamental elements, from which the hexagrams of Gou and Fu arise. When a yang line enters the yin center, it forms the hexagram Fu; when a yin line enters the yang center, it forms the hexagram Gou. From this, changes are endless. He also says: From Fu to Qian, there are a total of 112 yang lines; from Gou to Kun, there are 80 yang lines. From Gou to Kun, there are a total of 112 yin lines; from Fu to Qian, there are 80 yin lines. Shao Bowen says: My father once explained that Qian and Kun are the "great parents," thus able to generate the Eight Trigrams; Fu and Gou are the "small parents," thus able to generate the 64 hexagrams.

《朱子語類》：董銖問：「先天圖有自然之象數，伏羲當初亦知其然否？」曰：「也不見得如何。但橫圖據現在底畫較自然，圓圖便是就這中間抝做兩截，恁地轉來者是竒，恁地轉去厎是偶，有些造作，不甚依他元初畫厎。」

The Shu Leiclass of Zhu Xi records: Dong Zhu asked, "The Earlier Heaven diagram contains naturally occurring images and numbers. Did Fuxi know it was like this originally?" Zhu Xi answered, "This cannot be seen clearly. The horizontal diagram arranged according to existing methods still appears natural. However, the circular diagram cuts the horizontal diagram in half down the middle, then turns one half clockwise representing odd (yang) and the other counterclockwise representing even (yin). This seems somewhat artificial and does not fully conform to the original way Fuxi drew the hexagrams."

黃氏宗炎曰：圖南本黃冠師，此圖不過仙家養生之所寓，故牽節候以配合，毫無義理。再三傳而堯夫受之，指為性天窟宅，千古不發之精蘊盡在此圖。《本義》崇而奉焉，證是羲皇心傳，置夫大易之首。以言乎數，則不逮京房、焦贛之可征；以言乎理，則逺遜輔嗣、正叔之可據。且曲為之說曰：此圖失自秦火，流於方外，自相授受，不入人間。夫《易》為卜筮之書，不在禁例，宜並其圖而不禁，豈有止許民間藏卦爻而獨不許藏圖之事？朱元晦與王子合書云：「邵氏言伏義卦位近於穿鑿附會，且當闕之。」乃《易學啟蒙》《本義》又如此其敬信，不可解也。

Huang Zongyan said: Chen Tuan originally came from a Daoist background, and this diagram was merely a symbolic representation of Daoist techniques for cultivating life. Therefore, forcing the connection between the twenty-four solar terms and the natural phenomena is completely meaningless. After passing through a couple of generations, Shao Yong (style name Yaofu) accepted it and regarded it as the dwelling place of the principles of life and death and the heavenly way, claiming that the profound and subtle secrets that no one in history had ever uncovered were all contained in this diagram. The "Original Meaning of the Zhou Changes" also praised and believed in it, claiming that it was the secret teaching passed down directly from Fuxi, and placed it at the beginning of the Zhou Changes text. However, in terms of numbers, it is not as verifiable as that of Jing Fang and Jiao Yanshou; in terms of principles, it is even far less coherent than that of Wang Bi (style name Fusi) and Cheng Yi (style name Zhengshu). Yet they still went out of their way to defend it, saying that this diagram was lost during the burning of books in the Qin dynasty, and fell into the hands of the Daoist sects, passed down secretly among them, and never entered the common people's hands. But we should know that the "Zhou Changes" is originally a book of divination, and was not among the books burned by the Qin dynasty, so the diagram should not have been banned either. How could it be that the common people were allowed to keep the hexagrams and lines, but not the diagram? Zhu Xi (style name Yuanhui) wrote in his letter to Wang Zihe: "Shao's explanation of the positions of the hexagrams of Fuxi is close to fabrication and forced interpretation; we may temporarily hold it in doubt." However, in his "Awakening of the Study of the Changes" and "Original Meaning of the Zhou Changes," he treated it with such reverence and belief, which is really confusing.

按：夫子云「八卦成列，象在其中矣；因而重之，爻在其中矣」，又云「八卦相蕩」「八卦相錯」，六十四卦皆三畫八卦之所生也。姤、復同在六十四卦中，豈能生諸卦乎？康節受學於李挺之，挺之《六十四卦相生圖》，凡五陰一陽、五陽一陰之卦皆自姤復而來，凡四陰二陽、四陽二陰之卦皆自臨遯而來，凡三陰三陽、三陽三陰之卦皆自泰否而來，此即姤復小父母之意。

Hu Wei commented: Confucius said, "When the eight trigrams are arranged in order, the images are already contained within them; by adding lines to them, the yao are also contained within them." He also said, "The eight trigrams interact with each other" and "The eight trigrams are in opposition to each other." This shows that the sixty-four hexagrams are all generated by the mutual generation of pairs of the three-line trigrams. The hexagrams of Gou and Fu are themselves among the sixty-four hexagrams; how can they then generate the other hexagrams? Shao Yong learned from Li Zhichai, who had a diagram called "The Diagram of the Generation of the Sixty-Four Hexagrams." According to this diagram, all hexagrams with five yin lines and one yang line, or five yang lines and one yin line, are generated from Fu, the hexagram of one yang line returning, and Gou, the hexagram of one yin line beginning. All hexagrams with four yin lines and two yang lines, or four yang lines and two yin lines, are generated from Lin, the hexagram of two yang lines, and Duan, the hexagram of two yin lines. All hexagrams with three yin lines and three yang lines, or three yang lines and three yin lines, are generated from Tai, the hexagram of three yang lines, and Po, the hexagram of three yin lines. This is the origin of what Shao Bowen called "Fu and Gou as the small parents."

蓋推乾坤三索之說，施之於六畫卦，故有是圖。然姤復所生止十卦，而康節舉臨遯否泰之所生悉歸之姤復，則又與挺之異。就今六十四卦觀之，逐爻變遷，義亦可通，伏羲作易之初實不爾也。其中間抝為兩截，左陽右陰，則又極其造作，而非法象自然之妙矣。

This diagram extends the idea from the "Three Searches" of the trigrams Qian and Kun in the "Shuo Gua" to the six-line hexagrams. However, according to Li Zhichai's diagram, the hexagrams generated by Guo and Fu are only ten, while Shao Yong included the hexagrams generated by Lin, Duan, Pi, and Tai under the names of Guo and Fu, which differs from Li Zhichai's approach. Considering the existing sixty-four hexagrams, it is reasonable to say they evolved line by line. But this was not the original method when Fuxi first created the Book of Changes. As for splitting the horizontal diagram into two parts, with the left side entirely yang and the right side entirely yin, this is clearly artificial and far from the "method of following nature" that is supposed to be its essence.

《擊壤集》詩曰：「耳目聰明男子身，洪鈞賦予不為貧。須探月窟方知物，未躡天根豈識人。乾遇巽時觀月窟，地逢雷處見天根。天根月窟閒來往，三十六宮都是春。」

Shao Yong's "Yichuan Jiyang Ji" contains a poem that says: "Heaven and earth have given me a body with keen hearing and sight, and their grant is not meager. Without exploring the 'Moon Cave,' one cannot understand all things; without stepping on the 'Heaven's Root,' one cannot know oneself. At the intersection of the Qian hexagram and the Xun hexagram, one can observe the Moon Cave; at the meeting of the Earth (Kun) hexagram and the Thunder (Zhen) hexagram, one can see the Heaven's Root. Moving freely between Heaven's Root and Moon Cave, every place among the thirty-six palaces is filled with spring."

石澗俞氏曰：月窟在上，天根在下，往來乎月窟天根之間者，心也。何謂三十六宮？乾一、兌二、離三、震四、巽五、坎六、艮七、坤八是也。「三十六宮都是春」，謂和氣周流乎一身也。如此則三十六宮不在紙上，而在吾身中矣。

Shi Jian Xiansheng Yu Yan said: The Moon Cave is above, and the Heaven Root is below. Those who can travel between the Moon Cave and the Heaven Root are the human heart. What is meant by 'thirty-six palaces'? It refers to Qian one, Dui two, Li three, Zhen four, Xun five, Kan six, Gen seven, Kun eight. When these eight numbers are added together, they total thirty-six. The phrase 'all thirty-six palaces are spring' means that harmonious energy circulates throughout the body. In this way, the thirty-six palaces are not confined to the diagram on paper, but are present on my own body.

黃氏《象數論》曰：康節因先天圖而創為天根月窟，即《參同契》乾坤門戸牝牡之論也。故以八卦言者，指坤震二卦之間為天根，以其為一陽所生之處也；指乾巽二卦之間為月窟，以其為一陰所生之處也。程前村直方謂天根在卯，離兌之中是也；月窟在酉，坎艮之中是也，引《爾雅》「天根，氐也」、《長楊賦》「西壓月窟」證之，然與「乾遇巽」「地逢雷」之義背矣。以六十四卦言者，朱子曰天根月窟指復姤二卦。有以十二闢卦言者，十一月為天根，五月為月窟。

Huang Zongxi's "Yixue Xiangshu Lun" says that Shao Yong created the concept of "tian gen" and "yue ku" based on the Earlier Heaven diagram. This is essentially the same as the ideas in the "Cantongqi" regarding the乾 and坤 as gateways, and the坎 and离 as male and female. Therefore, in the context of the Eight Trigrams, the relationship between the坤 and震 trigrams is called "tian gen," because it is where the first yang begins; and the relationship between the乾 and巽 trigrams is called "yue ku," because it is where the first yin begins. Cheng Zifang (who was called Qiancun) said that "tian gen" is located at the卯 position, that is, between the离 and兑 trigrams, and "yue ku" is located at the酉 position, that is, between the坎 and艮 trigrams. He also cited the "Erya" saying "tian gen is the Root Mansion" and Yang Xiong's "Changyang Fu" saying "the moon's cave is pressed westward" as evidence. However, this contradicts the meaning in Shao Yong's poem "When Qian meets Xun" and "When the earth meets Thunder." In the context of the sixty-four hexagrams, Zhu Xi believed that "tian gen" and "yue ku" refer to the hexagrams "Fu" and "Gou." There is also an interpretation based on the twelve great trigrams, taking the hexagram "Fu" in the eleventh month as "tian gen" and the hexagram "Gou" in the fifth month as "yue ku."

其三十六宮凡有六說。以八卦言者三：乾一、兌二、離三、震四、巽五、坎六、艮七、坤八之次第，積數為三十六；乾一對坤八為九，兌二對艮七為九，離三對坎六為九，震四對巽五為九，四九亦三十六；乾畫三，坤畫六，震坎艮畫各五，巽離兌畫各四，積數亦三十六。以六十四卦言者二：朱子曰卦之不易者有八（乾、坤、坎、離、頥、中孚、大過、小過），反易者二十八，合之為三十六；方虛谷回曰復起子左得一百八十日，姤起午右得一百八十日，一旬為一宮，三百六十日為三十六宮。

As for the "Thirty-six Palaces," there are six interpretations. In terms of the Eight Trigrams, there are three: first, adding the sequence of numbers assigned to the trigrams, which are Qian one, Dui two, Li three, Zhen four, Xun five, Kan six, Gen seven, and Kun eight, the total is thirty-six; second, pairing Qian one with Kun eight to make nine, Dui two with Gen seven to make nine, Li three with Kan six to make nine, and Zhen four with Xun five to make nine, four nines total thirty-six; third, Qian has three lines, Kun has six lines, Zhen, Kan, and Gen each have five lines, and Xun, Li, and Dui each have four lines, adding up to thirty-six. In terms of the sixty-four hexagrams, there are two: first, Zhu Xi said that eight hexagrams remain unchanged when reversed (Qian, Kun, Kan, Li, Yi, Zhongfú, Daguò, Xiaoguò), and twenty-eight pairs of hexagrams change when reversed, totaling thirty-six; second, Fang Hui (who took the号虚谷) said the hexagram Fu starts at the Zi position and moves left for one hundred eighty days, while Guo starts at the Wu position and moves right for one hundred eighty days, counting ten days as one palace, making three hundred sixty days equal to thirty-six palaces.

以十二闢卦言者一：鮑魯齋恂曰，自復至乾六卦，陽爻二十一、陰爻十五，合之則三十六；自姤至坤六卦，陰爻二十一、陽爻十五，合之亦三十六，陽爻陰爻總七十二，以配合言，故云三十六。按諸說雖異，其以陽生為天根、陰生為月窟無不同也。蓋康節之意，所謂天根者性也，所謂月窟者命也，性命雙修，老氏之學也（愚謂煉己是修性，進火是修命），其理為《易》所無，故其數與《易》無渉也。

With regard to the twelve trigrams of the Great Trigrams,鲍恂 (numbered as Lu Zhai) said that from the trigram 复 (Fu) to 乾 (Qian), there are six trigrams with twenty-one yang lines and fifteen yin lines, totaling thirty-six; from 姤 (Gou) to 坤 (Kun), there are six trigrams with twenty-one yin lines and fifteen yang lines, also totaling thirty-six. In total, there are seventy-two lines, yin and yang combined, hence called thirty-six, because they are calculated in pairs of yin and yang. Note: Although these statements differ, they all agree that the initial emergence of yang energy is called 天根 (heaven's root), and the initial emergence of yin energy is called 月窟 (moon's cave). This point is consistent. Shao Yong's original meaning is that 天根 refers to 性 (nature), and 月窟 refers to 命 (destiny). Cultivating both 性 and 命 is the practice of Daoist philosophy (I believe that 炼己 (refining oneself) is cultivating 性, and 进火 (advancing fire) is cultivating 命). This principle is not found in the Book of Changes, so its numbers have nothing to do with the Book of Changes.

按：天根月窟即《參同》納甲之說。天，陽也；月，陰也。以八卦言之，月三日生明於庚，納震一陽之氣，庚當乾終巽始，故曰「乾遇巽時觀月窟」；震一陽始交於甲，納乾初九之氣，甲當坤終震始，故曰「地逢雷處見天根」也。以六十四卦言之，純乾遇巽之一陰是為姤，於月為生魄，陽消陰息自此始，故謂之月窟，即乾盡午中而陰生之謂也；純坤遇震之一陽是謂復，於月為合朔，陰消陽息自此始，故謂之天根，即坤盡子中而陽生之謂也（《參同契》云「晦至朔旦，震來受符，當斯之時，天地媾其精，日月相撢持，雄陽播玄施，雌陰化黃包，混沌相交接，權輿樹根基」，邵子所謂「地逢雷處見天根」者是）。

Hu Wei commented: The concept of "tian gen" and "yue ku" is essentially the Najia stem assignment theory in the "Cantong Qi". Heaven belongs to yang, and the moon belongs to yin. In the eight trigrams, on the third day of the lunar month, the moon appears in the western position of Geng, receiving the yang energy of the Zhen trigram. Geng is exactly where the Qian trigram ends and the Xun trigram begins, so it is said "When Qian meets Xun, observe the yue ku". The Zhen trigram's initial yang energy first meets at the eastern position of Jia, receiving the initial yang energy of the first line of Qian. Jia is exactly where the Kun trigram ends and the Zhen trigram begins, so it is said "When earth meets thunder, see the tian gen". In the sixty-four trigrams, when the pure yang Qian meets the pure yin Xun, it forms the Guo trigram, which corresponds to the beginning of the moon's waxing phase, the start of yin growing and yang declining, so it is called yue ku, meaning the yang energy begins at the center of the noon position where Qian ends. When the pure yin Kun meets the pure yang Zhen, it forms the Fu trigram, which corresponds to the new moon, the start of yang growing and yin declining, so it is called tian gen, meaning the yang energy begins at the center of the midnight position where Kun ends. The "Cantong Qi" says: On the last day of the lunar month and the early morning of the first day, the Zhen trigram comes to receive the mandate, at this time, the heavens and earth meet and their vital energy combines, the sun and moon mutually attract and support each other, the yang of the male spreads out mysteriously, and the yin of the female nurtures the yellow placenta. In the chaos, they meet and exchange, thus the foundation of all things is established. Shao Yong's statement "When earth meets thunder, see the tian gen" refers exactly to this.

三十六宮，朱子之義較長。蓋人身之天根在尾閭，月窟在泥丸。修煉之法，夜子以心神注氣海，謂之生藥；子後則自尾閭進火以達於泥丸，午中則自泥丸還元以訖於尾閭。從復姤用功而諸卦皆到，上下往來，終而復始，和氣滿腔，盎然流溢，故曰「三十六宮都是春」也。邵子雖不事修煉，而其理固已洞徹，丹家秘寳和盤托出矣。

Discussing the "Thirty-six Palaces" is more coherent with Zhu Xi's explanation. The heavenly root on the human body is located at the tail闾 (the end of the spine), and the moon cave is at the mud ball (the top of the head, the brain palace). The method of cultivation is: at the moment of the midnight Zi hour, to concentrate the mind and spirit into the Qi sea, called "producing medicine"; after the Zi hour, to start a fire from the tail闾 and ascend it up to the mud ball, and at the noon Wu hour, to return from the mud ball back to its origin and descend down to the tail闾. Focusing on the hexagrams of "Reversal" and "Meeting," the sixty-four hexagrams are all covered, with movement up and down in a cycle, continuously returning to the beginning, thus harmonious energy fills the chest and abdomen, overflowing outward, so it is said "All thirty-six palaces are spring." Although Shao Yong himself did not practice cultivation, he had already thoroughly understood this principle, revealing the secret teachings of the alchemists completely.

或問：邵子既知此理，何不事修煉？曰：修煉亦是苦功，頗妨人作樂。邵子襟懷疎放，得蒙莊逍遙之趣，可以養生，可以盡年，無所待於修煉，故知而不為。其詩曰「不佞禪伯，不諛方士」，自是真實語，非因與二程遊而有所揜飾也。

Someone asked: Since Shao Yong understood this principle, why didn't he practice cultivation? The answer is: Cultivation is also a hard task, which greatly interferes with enjoying life's pleasures. Shao Yong had a broad and open mind, deeply understanding the carefree and effortless way of Zhuangzi. This in itself was sufficient for maintaining health and living out his natural lifespan, so he did not need to rely on cultivation. Therefore, he knew the truth but did not practice it. In his poetry, he said, "I do not flatter Buddhist masters, nor do I pay homage to those who practice esoteric arts," which is a straightforward statement, not something he intentionally concealed because of his interactions with Cheng Hui and Cheng Yi, his brothers.

《朱子語類》：周謨問：先天卦氣相接皆是左旋，蓋乾接以巽初姤卦，便是一陰生；坤接以震初復卦，便是一陽生。自復卦一陽生（十一月），盡震四、離三一十六卦，然後得臨卦（十二月）；又盡兌二凡八卦，然後得泰卦（正月）；又隔四卦得大壯（二月）；又隔大有一卦得夬（三月）；夬接乾（四月），乾接姤。自姤卦一陰生（五月），盡巽五、坎六一十六卦，然後得遯卦（六月）；又盡艮七凡八卦，然後得否卦（七月）；又隔四卦得觀（八月）；又隔比一卦得剝（九月）；剝接坤（十月），坤接復，周而復始，循環無端。

The Shu Leiclass records: Zhou Mo asked: In the Earlier Heaven diagram, the connection of the trigrams proceeds to the left. After the trigram Qian, it connects to the first trigram of the Xun palace, which is Guo, indicating the initial emergence of yin; after the trigram Kun, it connects to the first trigram of the Zhen palace, which is Fu, indicating the initial emergence of yang. Starting from Fu, which marks the initial emergence of yang in the eleventh month, after traversing four trigrams in the Zhen palace and three in the Li palace, totaling sixteen trigrams, we arrive at Lin in the twelfth month; then after traversing two trigrams in the Dui palace, we arrive at Tai in the first month of the year; then after four more trigrams, we arrive at Da Zhuang in the second month; then after one more trigram, Da You, we arrive at Guai in the third month; Guai connects to Qian in the fourth month, and Qian connects back to Guo. Starting from Guo, which marks the initial emergence of yin in the fifth month, after traversing five trigrams in the Xun palace and six in the Kan palace, totaling sixteen trigrams, we arrive at Dun in the sixth month; then after traversing seven trigrams in the Gen palace, we arrive at Po in the seventh month; then after four more trigrams, we arrive at Guan in the eighth month; then after one more trigram, Bi, we arrive at Po in the ninth month; Po connects to Kun in the tenth month, and Kun connects back to Fu, thus forming a cycle that continues endlessly.

卦氣左旋，而一歲十二月之卦皆得其序。但陰陽初生各歴十六卦而得一月，又歴八卦再得一月，至陰陽將極處只歴四卦為一月，又歴一卦遂一併三卦相接，其初如此之疎，其末如此之密，此陰陽盈縮當然之理歟？然此圖於復卦之下書曰「冬至子中」，於姤卦之下書曰「夏至午中」，此固無可疑者；獨於臨卦之下書曰「春分卯中」，則臨卦本為十二月之卦，而春分合在泰卦之下；於遯卦之下書曰「秋分酉中」，則遯卦本為六月之卦，而秋分合在否卦之下，是固不可曉者。答曰：伏羲易自是伏羲說話，文王易自是文王說話，固不可交互求合。所看先天卦氣盈縮子細，某亦嘗如此理會來，而未得其說。

The trigram energies rotate to the left, and the twelve months of the year each have their proper position in the trigrams. However, when yin and yang first begin to arise, each requires passing through sixteen trigrams to complete a month, then passing through the eight trigrams again to complete another month. When yin and yang are about to reach their peak, they only require passing through four trigrams to complete a month, and then passing through one trigram followed by three trigrams in succession. At the beginning, the trigrams are sparse, but at the end, they are dense. Is this not the natural way of yin and yang waxing and waning? Also, this diagram notes under the hexagram "Fu" (Return) "Winter Solstice at the midpoint of the Zi hour," and under "Gou" (Meeting) "Summer Solstice at the midpoint of the Wu hour," which is without doubt. However, it notes under "Lin" (Approaching) "Spring Equinox at the midpoint of the Mao hour"—but "Lin" is actually the hexagram of the twelfth month, and the Spring Equinox should be noted under "Tai" (Great). Similarly, it notes under "Dun" (Retreating) "Autumn Equinox at the midpoint of the You hour"—but "Dun" is the hexagram of the sixth month, and the Autumn Equinox should be noted under "Pǐ" (Obstruction). This is truly confusing. Zhu Xi replied: The "Book of Changes" of Fuxi is Fuxi's own interpretation, and the "Book of Changes" of King Wen is King Wen's own interpretation. They are fundamentally different and cannot be forced to fit together. If you look carefully at the expansion and contraction of the earlier heaven trigrams, I have also considered this, but have never been able to find a satisfactory explanation.

黃氏《象數論》曰：《易緯》有卦氣之法，京房精於其學。以坎、震、離、兌主二十四氣，其餘六十卦起自中孚。卦有六爻，爻主一日，凡主三百六十日，餘五日四分日之一。每日分為八十分，五日得四百分，四分日之一得二十分，積四百二十分，均於六十卦，六七四十二，每卦得六日七分。又於六十卦之中別置復、臨、泰、大壯、夬、乾、姤、遯、否、觀、剝、坤十二以為闢卦，每爻各主一候。自復至乾為息卦曰太陽，自姤至坤為消卦曰太陰，息卦所屬者曰少陽，消卦所屬者曰少陰。

Huang Zongxi in his "Discussion on the Imagery and Numerical Calculations of the Book of Changes" says that the "Book of Changes' Writings" contains a method called "Hexagram Qi" (卦气). Jing Fang was particularly skilled in this discipline. It uses the four cardinal hexagrams, Kan (Water), Zhen (Thunder), Li (Fire), and Dui (Lake), to govern the twenty-four solar terms. The remaining sixty hexagrams are arranged starting from Zhongfou (Middle Trust). Each hexagram has six lines, with each line governing one day, thus governing a total of three hundred and sixty days, leaving five and one fourth days remaining. A day is divided into eighty parts. Five days make four hundred parts, and one fourth of a day is twenty parts, totaling four hundred and twenty parts. These are evenly distributed among the sixty hexagrams. Six multiplied by seven gives forty-two, so each hexagram governs six days and seven parts. In addition, among the sixty hexagrams, twelve hexagrams, namely Fu (Return), Lin (Approach), Tai (Great Benefit), Da Zhuang (Great Strength), Guai (Approaching), Qian (Heaven), Gou (Meeting), Duan (Retreat), Pǒ (Obstruction), Guan (Observation), Po (Decrease), and Kun (Earth), are established as "Bi Hexagrams" (sovereign hexagrams). Each line of these hexagrams governs one "hou" (a period of five days). From Fu to Qian are the hexagrams of yang qi growth, called "Taiyang" (Great Yang); from Gou to Kun are the hexagrams of yang qi decline, called "Taiyin" (Great Yin). Those belonging to the growth hexagrams are called "Shaoyang" (Less Yang), and those belonging to the decline hexagrams are called "Shaoyin" (Less Yin).

故孔穎達《復·彖》「反復其道，七日來復」之疏，謂剝卦陽氣之盡在於九月之末，十月純坤用事，坤卦之盡則復卦陽來，坤卦有六日七分，舉成數故言七日。王昭素駁之曰：坤卦之盡復卦陽來，則十月之節終一陽便來，不得到冬至之日矣；據其節終尚去冬至十五日，則卦七日之義難用《易緯》之數。某以為昭素駁之是矣，然昭素未悉卦氣之法，不能針其錮疾也。

Therefore, Kong Yingda, in his commentary on the "Fu" hexagram's zhuangci, "Reversing its path, the yang returns after seven days," explained that the yang energy of the "Bo" hexagram ends by the end of the ninth lunar month, and in the tenth month, the pure Kun hexagram prevails. Once the Kun hexagram is completed, the "Fu" hexagram's single yang returns. Since the Kun hexagram lasts six days and seven parts, taking an integer, it is said "seven days." Wang Zhaozu refuted this, saying: if the yang of the "Fu" hexagram returns immediately after the Kun hexagram is completed, then the yang would return on the day the tenth lunar month ends, which would be before the winter solstice. According to the solar terms, there are still fifteen days until the winter solstice, showing that the idea of "seven days" for the hexagram is not applicable to the system of the "Yi Wei." I (Huang Zongxi) think Wang Zhaozu's refutation is correct, but he did not fully understand the method of hexagram energies, so his criticism did not address the core issue.

以十二闢卦言之，剝之至復所隔唯坤六爻，其一爻當一候，一候得五日五十六分分之五，六爻得三十日三十五分，非七日也。以六十卦言之，一卦六日七分，剝之至復中隔艮、既濟、噬嗑、大過、坤、未濟、蹇、頤、中孚九卦，計五十四日六十三分，非一卦也。孔氏牽合兩者，故其說不能合。《易》之「七日來復」，取卦之反易為義，反剝為復，所歴七爻，以一日為一爻，故曰「反復其道」，反覆即反覆也，與卦氣何與？即使孔氏之疏能合卦氣，則《易》之辭無乃為卦氣圖說乎？為卦氣之法者，宓戲耶？文王耶？

If calculated according to the twelve trigrams of the heavenly stem, from the trigram "Bao" to "Fu" there are only six lines of the trigram "Kun" in between. Each line corresponds to one period, and one period is five days and five parts, so six lines total thirty days and thirty-five parts, which is not seven days. If calculated according to the sixty trigrams, each trigram corresponds to six days and seven parts. From "Bao" to "Fu" there are nine trigrams in between: Gen, Ji Ji, Shi He, Da Guo, Kun, Wei Ji, Jian, Yi, Zhong Fu. The total is fifty-four days and sixty-three parts, which is more than one trigram. Kong Yingda combined the two calculation methods, so his explanation does not match. The "Yi" says "seven days to return," which refers to the meaning of reversing and turning over the trigrams: turning the trigram "Bao" upside down gives the trigram "Fu," and in between there are seven lines. Taking one line as one day, it is said "reversing its path." "Reversing" means turning over, so how is this related to the trigram qi? Even if Kong Yingda's commentary matches the trigram qi, can the trigram line statements really be explanations of the trigram qi diagram? Moreover, who established the method of trigram qi, Fuxi or King Wen?

先儒之議卦氣者，謂卦氣不起於中孚而起於復，中孚為大雪之終氣，至冬至而始盡，故繫於冬至之下，中孚之於冬至，於象於名兩無當也。然觀《太玄》之辭曰「陽氣藏於黃宮，信無不在其中」，則中孚之直冬至者，顧以其名耳。《太玄》之釋卦序，自闢卦之外，無不以其名為義也，又何獨疑於中孚乎？所謂六日七分者，六日既盡，七分便為來日之始，非必取足八十分而自為一日也。趙汝楳乃以餘算歸之一卦，於是有一卦直七日者，失其意矣。葉氏則以七分為之氣盈，六十卦餘五日二十分，若積餘以置閏者，是一卦直六日，且並京、焦之學失其傳也。

Earlier scholars discussed the concept of "gu qi" (卦气), arguing that the sequence should start from the hexagram "Fu" (复) rather than "Zhongfu" (中孚). This is because "Zhongfu" corresponds to the end of the "Daxue" (大雪) solar term, and it would not be completed until the "Dongzhi" (冬至) solar term. Therefore, it was placed under "Dongzhi," but "Zhongfu" neither matches the symbolic meaning nor the name of "Dongzhi." However, according to Yang Xiong's "Tai Xuan," which says, "Yang qi is hidden in the Yellow Palace, and sincerity is present throughout," it shows that "Zhongfu" is appropriate for "Dongzhi" because of its name. The "Tai Xuan" explains the order of hexagrams, using the names of the hexagrams to derive meaning, except for the "bi gua" (辟卦). So why should we doubt "Zhongfu" alone? The term "liu ri qi fen" (六日七分) means that six days are completed, and the remaining seven parts are considered the beginning of the next day. It does not mean that one must complete eighty parts to form a day. Zhao Ru Mei, however, assigned all the remaining parts to a single hexagram, leading to the idea that one hexagram corresponds to seven days, which deviates from the original meaning. Ye Shi, on the other hand, treated the seven parts as surplus of the solar terms, saying that the sixty hexagrams exceed five days and twenty parts, similar to accumulating surplus to perform intercalation. This led to the idea that one hexagram corresponds to six days, and thus the teachings of Jing Fang and Jiao Yanshou were also lost.

六日七分之說相傳最久，其餘卦氣皆自後起。有自乾至未濟並依《易》書本序，以一卦直一日，乾直甲子，坤直乙丑，至未濟直癸亥，乃盡六十日，六周而三百六十日；四正卦則直二分二至，坎冬至、離夏至、震春分、兌秋分，不在六十卦輪直之列者，焦氏之法也。有以乾坤坎離四卦為槖鑰，餘六十卦依序卦，一爻直一時，一月有三百六十時足其數者，又以十二闢卦每卦管領一時，魏伯陽之法也。

The idea of "six days and seven parts" has been around the longest, while other methods of卦气 are later developments. One method follows the original order of the sixty hexagrams in the Zhou Changes, assigning each hexagram to one day: Qian (Heaven) corresponds to Jiazi, Kun (Earth) to Yichou, and so on until Wei Ji (Completion) corresponds to Guihai, making exactly sixty days. Six cycles of this make up three hundred and sixty days. The four main hexagrams, Kan (Water), Zhen (Thunder), Li (Fire), and Dui (Lake), each correspond to two solstices and two equinoxes—Kan governs the winter solstice, Li the summer solstice, Zhen the spring equinox, and Dui the autumn equinox, and they do not participate in the sixty-hexagram cycle. This is Jiao Yanshou's method. Another method treats Qian, Kun, Kan, and Li as the windbox (tuo yue), with the remaining sixty hexagrams arranged according to the "Sequence of Hexagrams." Each trigram corresponds to an hour, and a month of three hundred and sixty hours fits perfectly. Then the twelve great hexagrams each govern an hour. This is Wei Boyang's method.

至宋而後有所謂先天圖者，於是邵子以六日七分之法施於其圖，黜卦起中孚之說，以復起冬至、姤起夏至，其以坎離震兌四正卦主二十四氣者，改為乾坤坎離，此圓圖之卦氣也。張理以方圖覆背置之，泰處於東北，乾處於東南，否處於西南，坤處於西北，亦以冬至起復，至泰而正月，至乾而四月；夏至起姤，至否而七月，至坤而十月，此方圖之卦氣也。張氏又以一陰一陽至六陰六陽類而並列，六陽處南，六陰處北，陽自下而升，陰自上而降，廣闢卦之法也。

The concept of the "Earlier Heaven Diagram" appeared only after the Song Dynasty. Shao Yong applied the method of six days and seven parts to this diagram, abandoning the old idea that the hexagram qi began with the hexagram Zhongfou, and instead changed it so that the hexagram Fu began at the winter solstice and the hexagram Gou began at the summer solstice. Originally, the four cardinal hexagrams Kan, Li, Zhen, and Dui were used to correspond to the twenty-four solar terms, but this was changed to the four cardinal hexagrams Qian, Kun, Kan, and Li, forming the circular diagram of hexagram qi. Zhang Li further rotated the square diagram and placed the hexagram Tai in the Northeast, the hexagram Qian in the Southeast, the hexagram Pǒ in the Southwest, and the hexagram Kun in the Northwest. Similarly, starting from the winter solstice with Fu, reaching Tai in January and Qian in April; starting from the summer solstice with Gou, reaching Pǒ in July and Kun in October, forming the square diagram of hexagram qi. Zhang Li also arranged the hexagrams in groups of one yin and one yang up to six yin and six yang, placing the six yang hexagrams to the south and the six yin hexagrams to the north. Yang qi rose from below to above, while yin qi descended from above to below, which is an extension of the method of dividing hexagrams.

邵子又以方圖乾兌離震各重之為六十四卦，共二百五十六卦，以之算大運，亦以算小運，二十四氣每氣六十四爻，積一千五百六十二爻，合乾兌離震掛一之數，謂之掛一圖，所謂皇極之學也。諸家之不同如此。蓋初無一定之理，各以意之所見為之，是故六日七分之外，有一卦直一日者，兩卦直一日者，有一爻直一日者，四爻三分強直一日者，總卦與日之大數而後分配其小數，或多或少，不顧其果否如是也。

Shao Yong then took the four palaces of Qian, Dui, Li, and Zhen in the square diagram and each of them was repeated six times to form sixty-four hexagrams, totaling two hundred and fifty-six hexagrams, which were used to calculate great destiny and small destiny. Each of the twenty-four solar terms was paired with sixty-four lines, accumulating a total of fifteen hundred and sixty-two lines, exactly matching the number of "one hexagram" in the four palaces of Qian, Dui, Li, and Zhen, known as the "One Hexagram Diagram." This is referred to as the study of the "Huang Ji Jing Shi." The differences among various schools are like this. Originally, there is no fixed and unchanging principle; each person arranges according to their own opinion, so besides the six days and seven parts, there are also cases where one hexagram corresponds to one day, two hexagrams correspond to one day, one line corresponds to one day, and four lines plus three parts and more correspond to one day. In general, one first determines the approximate number of hexagrams and days, then distributes the remaining small numbers, more or less, without considering whether it actually corresponds to reality.

其卦之排比，惟《序卦》可據，《序卦》之義於時日不可強通，故漢儒別求其義於卦名，而有中孚之起。然揚雄氏所傳之卦義未免穿鑿附會，未嘗為《易》之篤論也。宋儒始一變其說，以竒偶之升降消長為言，而於經文可據之方位一切反之。然則宋儒之畫、漢儒之義，猶二五之為十也，孰分其優劣哉？

As for how the sixty-four hexagrams are arranged, only the "Sequence of Hexagrams" can be relied upon; however, the principles in the "Sequence of Hexagrams" cannot be forced to correspond with time and days. Therefore, Han scholars sought justification from the names of the hexagrams, leading to the idea that the hexagram qi originates from Zhongfou. However, the interpretation of hexagrams passed down by Yang Xiong is overly speculative and cannot be considered an accurate explanation of the Book of Changes. Starting from the Song dynasty, scholars changed the old approach, focusing exclusively on the rise and fall of odd and even lines, yet they completely reversed the established positions of the eight trigrams as recorded in the text. In this light, the method of the Song scholars and the interpretation of the Han scholars are like two times five and five times two, both resulting in ten. Who can determine which is superior or inferior?

按：《說卦傳》有經卦之方位，而無別卦之方位。蓋文王所演六十四卦，其八卦之貞錯綜而敘，不以其卦為類，故無方位之可言。京房六日七分法，卦氣起於中孚，亦不過取卦名之義以為當直冬至，非謂中孚方位在子之半也。自魏伯陽以乾坤坎離牝牡、震艮巽兌，先天八卦之方位端倪始見，而邵子演之曰：「乾坤定上下之位，離坎列左右之門，天地之所闔闢，日月之所出入。」於是有乾南坤北、離東坎西之圖，又推之於六十四卦為大橫圖以定其次序，又規夫橫圖而圓之以為六十四卦之方位，更有方圖居其中。

Hu Wei commented: The "Sayings on the Trigrams" only discusses the orientation of the three-line primary trigrams, but does not mention the orientation of the six-line composite trigrams. The sixty-four trigrams derived by King Wen have their lower trigrams (Zhen trigrams) arranged in a crosswise and intersecting manner, not grouped according to the same eight trigrams, so there is no mention of orientation. Jing Fang's method of six days and seven parts starts the trigram qi from Zhongfu, but this is merely taking the meaning of the trigram name Zhongfu, believing it should correspond to the winter solstice, not meaning that the trigram Zhongfu is located in the position of Zi. Since Wei Boyang used Qian, Kun, Kan, and Li as male and female, and paired them with Zhen, Gen, Xun, and Dui to explain the stem assignment, the beginning of the orientation of the Earlier Heaven trigrams started to appear; Shao Yong further developed this, saying: "Qian and Kun determine the upper and lower positions, Li and Kan form the left and right gates, the heavens and earth thus open and close, the sun and moon thus rise and set." Thus, a diagram was formed with Qian in the south, Kun in the north, Li in the east, and Kan in the west, and this was extended to the sixty-four trigrams to form the Great Horizontal Diagram to determine the order, then the horizontal diagram was bent into a circle as the orientation of the sixty-four trigrams, with a square diagram placed in the center.

於是經卦既非乾坤三索之序，別卦又失文王所演之舊。雖用京、焦分卦直日之遺法，而次序方位參錯不齊，其卦氣所自起，不得不黜中孚而用復姤；坎離震兌四正卦之主二十四氣者，亦改為乾坤坎離，固其所矣。然京房分卦直日以候災異，實有其用；而邵子大圓圖則但如《參同契》以六十卦象一月升降往來之氣，非真有分卦直日之事也。故闢卦相去之疎密前後不同，而二分卯酉之中乃繋之臨遯，蓋此圖惟明丹道，不主占候，固不必一一求合於卦氣也。

This way, the three-line trigrams no longer follow the order of the six sons generated by the trigrams Qian and Kun as described in the "Shuo Gua" text, and the six-line composite trigrams lose the original appearance as presented by King Wen. Although the method of assigning trigrams to days, inherited from Jing Fang and Jiao Yanshou, is still used, the sequence and positions are disordered, so the starting point of the trigram qi must be abandoned from Zhongfou and changed to Fu and Gu. Originally, the twenty-four solar terms were governed by the four main trigrams Kan, Li, Zhen, and Dui, but now they are replaced by Qian, Kun, Kan, and Li. This is naturally inevitable. However, Jing Fang's method of assigning trigrams to days was used for predicting disasters and anomalies, and indeed had practical use. Shao Yong's great circle diagram, on the other hand, is similar to the "Cantongqi" text, using the sixty trigrams to symbolize the rising and falling of yin and yang qi throughout the month, and did not actually intend to assign trigrams to days. Therefore, the spacing and order between the trigrams on the diagram are inconsistent, and the positions of Mao and You, corresponding to the spring and autumn equinoxes, are instead associated with the trigrams Lin and Dun. This shows that this diagram was intended to explain the Dao of alchemy and not for divination, and thus it was not necessary to align it with the trigram qi in every detail.

其極數知來之學全在加一倍法，與此圖無涉。至於方圖，則內外疉作四層，意在明十六卦兩隅尖射之巧妙，難用分卦直日法，而張仲純亦仿圓圖之例，起復姤，終乾坤，以定十二闢之卦氣，其舛謬不更甚乎？

As for Shao Yong's system of divination which aims to exhaust all numbers and predict the future, it entirely depends on the "Doubling Method," and has nothing to do with this circular diagram. As for the square diagram, it is composed of four layers overlapping from the inside out, intended to show the ingenious way in which the sixteen hexagrams shoot out from two opposite corners, and it is inherently difficult to apply the method of assigning daily values to hexagrams. Moreover, Zhang Li (style name Zhongchun) also followed the precedent of the circular diagram, arranging the twelve great hexagrams from the hexagram of "Returning" (Fu) and "Meeting" (Gou) to the hexagram of "Heaven" (Qian) and "Earth" (Kun), but this is not only incorrect but even more so than before.

「冬至子之半，天心無改移。一陽初動處，萬物未生時。玄酒味方淡，太音聲正希。此言如不信，更請問庖犧。」又曰：「何者謂之機？天根理極微。今年初盡處，明日起頭時。此際易得意，其間難下辭。人能知此義，何事不能知？」

Shao Yong wrote a poem saying: "At the midpoint of the Zi hour on the winter solstice, the heart of heaven and earth remains unchanged. This is the beginning of the first yang, and also the time when all things have not yet begun to sprout. It is like the taste of the dark wine, which is very mild, and like the sound of the highest music, which is almost imperceptible. If you do not believe this, then go and ask Fuxi again." In another poem he said: "What is called 'the mechanism'? It is the principle of the beginning of heaven, extremely subtle. It is at the moment when this year is about to end, and the next day is about to begin. This is the easiest to understand intuitively, yet the hardest to explain in words. If a person can understand this, then what else could he not understand?"

石澗俞氏曰：朱紫陽云「子之半是未成子，方離於亥之時」，又云「一陽初動處，在貞元之間」。愚謂此處正是造化之真機。程伊川云「若非竊造化之機，安能長生」，至哉言乎！

Master Shi Jian, Yu Yan said: Zhu Xi, who was known as Ziyang, explained "the half of Zi" as the moment when Zi had not yet fully formed and was just leaving the hour of Hai. He also spoke of "the beginning of the first yang" as occurring precisely at the junction between the last part of the old year and the beginning of the new year. I believe this is exactly where the true secret of nature lies. Cheng Yi, known as Master Yichuan, said, "If one is not stealing the key to the workings of nature, how could one attain longevity?" These words are truly profound!

《大易吟》曰：「天地定位，否泰反類；山澤通氣，損咸見義；風雷相薄，恆益起意；水火相射，既濟未濟。四象相交，成十六事；八卦相蕩，為六十四。」

Shao Yong's "Da Yi Yin" says: "Heaven and Earth are positioned above and below, and the hexagrams of 'Po' and 'Tai' are exactly opposite; mountains and marshes communicate their energies, and the hexagrams of 'Sun' and 'Xian' reveal this meaning; wind and thunder interact with each other, and the hexagrams of 'Heng' and 'Yi' elaborate on this idea; water and fire mutually shoot at each other, which is represented by the hexagrams of 'Ji Ji' and 'Wei Ji'. Four hexagram images interacting in pairs form sixteen matters; the eight trigrams interacting with each other become the sixty-four hexagrams."

《朱子語類》曰：此是說方圖中兩交股底。且如西北角乾、東南角坤，是天地定位，便對東北角泰、西南角否；次乾是兌，次坤是艮，便對次否之咸、次泰之損，後四卦亦如是，共十六卦。又曰：方圖自西北之東南，便是自乾以之坤；自東北之西南，便是由泰以之否。其間有咸恆損益、既濟未濟，所以又於此八卦見義，蓋為是自兩角尖射上與乾坤相對，不知怎生恁地巧。

Master Zhu Xi says: This refers to the situation where the two diagonals cross in the square diagram. For example, the northwest corner is the Trigram Qian (Heaven) and the southeast corner is the Trigram Kun (Earth), which represents 'Heaven and Earth are positioned.' This directly faces the northeast corner's Trigram Tai and the southwest corner's Trigram Po. Adjacent to Qian are the Dui trigrams, and adjacent to Kun are the Gen trigrams, which in turn face the trigrams adjacent to Po, namely Xian, and those adjacent to Tai, namely Shen. The following four trigrams are also arranged in this way, making a total of sixteen trigrams. He also says: The line from northwest to southeast in the square diagram is from Qian to Kun; the line from northeast to southwest is from Tai to Po. In between are Xian, Heng, Shen, Yi, Ji Ji, and Wei Ji, so the 'Great Yijing' also reveals meaning through these eight trigrams. It is probably because this is shot directly from the two corners, facing Qian and Kun, and it is truly amazing how this coincides.

天台董氏楷曰：愚因邵子《大易吟》，欲以方圖分作四層看。其第一層四隅乾坤否泰四卦，所謂「天地定位，否泰反類」也，然以周圍二十八卦橫直觀之，皆乾一坤八之卦，此見天地定位之不可易也。其第二層四隅兌艮咸損四卦，所謂「山澤通氣，損咸見義」也，然以周圍二十卦橫直觀之，亦皆兌二艮七之卦，此見山澤通氣之象也。

Heavenly Master Dong Kai of Tian Tai said: I read Shao Yong's "Great Yi Odes" and wanted to divide the diagram into four layers. The four corners of the outermost layer are the trigrams Qian, Kun, Po, and Tai, which is exactly what is said as "Heaven and Earth are positioned, Po and Tai are opposites"; and looking at the twenty-eight trigrams around this layer horizontally and vertically, they are all the trigrams from the first palace of Qian and the eighth palace of Kun, thus showing that the positioning of Heaven and Earth cannot be changed. The four corners of the second layer are the trigrams Dui, Gen, Xian, and Shen, which is exactly what is said as "Mountains and marshes communicate, the trigrams Xian and Shen illustrate this meaning"; and looking at the twenty trigrams around this layer horizontally and vertically, they are all the trigrams from the second palace of Dui and the seventh palace of Gen, thus showing the image of mountains and marshes communicating.

其第三層四隅為坎離既濟未濟四卦，所謂「水火相射，既濟未濟」是也，然以周圍十二卦橫直觀之，亦皆離三坎六之卦，此足以見水火不相射之象也。其最裡一層為震巽恆益四卦，所謂「雷風相薄，恆益起意」，其象亦可見矣。以此言之，邵子之詩曉然，足以見先天法象自然之妙。

The four corners of the third layer are the trigrams Kan, Li, Ji Ji, and Wei Ji, which are precisely referred to as "water and fire opposing each other, Ji Ji and Wei Ji"; when looking at the twelve trigrams surrounding this layer both horizontally and vertically, they are all trigrams from the three trigrams of Li and the six trigrams of Kan. This clearly demonstrates the image of water and fire not opposing each other. The innermost layer consists of the trigrams Zhen, Xun, Heng, and Yi, which are exactly called "thunder and wind colliding, Heng and Yi arising from intention," and their trigram images can also be seen. Thus, Shao Yong's poem is clear in meaning, sufficiently revealing the natural subtlety of the Earlier Heaven trigram arrangements.

按：方圖自西北至東南兩隅尖射為八純，自西南至東北兩隅尖射為否泰等卦，是為十六事。然後於四正各布十二卦，共四十八，合前十六為六十四，而八卦相錯徧焉。此亦邵子之巧推排，《易》無此卦位也。

Hu Wei remarked: The diagram shows eight pure trigrams radiating from the diagonal line running from northwest to southeast, namely Qian, Dui, Li, Zhen, Xun, Kan, Gen, and Kun. On the other diagonal from southwest to northeast, the trigrams such as 'Pu' and 'Tai' are arranged. Together they make up the 'sixteen trigrams'. Then, on each of the four cardinal directions, twelve trigrams are arranged, totaling forty-eight. Adding the sixteen trigrams mentioned earlier gives a total of sixty-four, thus covering all eight trigrams comprehensively. This is another clever arrangement by Shao Yong. The 'Book of Changes' originally did not have such positions for the trigrams.

《觀物外篇》曰：先天學，心法也，故圖皆從中起，萬化萬事生於心也（胡玉齋云：此明圖之所謂太極）。又曰：圖雖無文，吾終日言而未嘗離乎是，蓋天地萬物之理盡在其中矣。

Shao Yong's "Guānwù Wài Piān" says: The study of the Earlier Heaven is a system of "mental practice," so all the diagrams start from the center. All changes and transformations, all things and phenomena in the world arise from the mind. (Hu Yigui, who called himself Yu Zhai, said: Here the term "zhong" refers to the Taiji in the diagram.) It also says: Although there are no characters on the diagram, I have been talking about it all day long without ever leaving it, because the principles of heaven and earth and all things are contained within it.

前村程氏直方曰：邵子云「先天圖心法也，圖皆從中起」，曰「皆」者其故何也？兼方圓圖而言也。「天地定位」，圓圖之從中起也；「雷以動之，風以散之」，方圖之從中起也，皆五與十所寄之位也。故圓圖左旋起於六十四之坤，右轉起於一之乾，是中起於天地之定位也；方圖西北與東南之交也起於震巽，東北與西南之交也起於恆益，南北相直也則起於恆震巽益，東西相直也則起於震益恆巽，是中起於雷風之動散也。由此而論，圓者動，以定位為本；方者靜，以動散為用。故動而無動，靜而無靜，固先天之心法歟！是不可不皆求之圖也。

Master Cheng Zhifang of the Qiancun School said: Shao Yong said, "The Earlier Heaven Diagram is the heart method, and the diagram starts from the center." Why did he use the word "all" (都)? Because it refers to both the square diagram and the circular diagram. The sentence "Heaven and Earth are positioned" in the "Say on the Hexagrams" refers to the circular diagram starting from the center. The two sentences "Thunder moves it, Wind disperses it" refer to the square diagram starting from the center. These are all based on the central position of the number five and ten in the Yellow River Chart. Therefore, the circular diagram turns left, starting from the hexagram Kūn (Earth), which is the 64th; it turns right, starting from the hexagram Qián (Heaven), which is the first. This is starting from the center of the positioning of Heaven and Earth. For the square diagram, the intersection of the northwest and southeast corners starts from the two trigrams Zhen (Thunder) and Xun (Wind); the intersection of the northeast and southwest corners starts from the hexagrams Héng (Permanence) and Yì (Benefit). When looking along the north-south line, it starts from Héng, Zhen, Xun, and Yì; when looking along the east-west line, it starts from Zhen, Yì, Héng, and Xun. This is starting from the center of the movement and dispersion of Thunder and Wind. Thus, the circular diagram belongs to motion, with positioning as its foundation; the square diagram belongs to stillness, with movement and dispersion as its function. In motion there is no further motion, and in stillness there is no further stillness. This is probably the heart method of the Earlier Heaven. Therefore, both diagrams must not be neglected in seeking this meaning.

雙湖胡氏一桂曰：案程氏此論甚的。愚因推之：「天地定位」，起南北子午之中；「山澤通氣」，次西北東南之卦；「雷風相薄」，次東北西南之卦；「水火不相射」，又次東西之卦，圓圖自南北之中起也。「雷以動之，風以散之」，正居方圖中心；「雨以潤之，日以晅之」，則坎次巽、離次震；「艮以止之，兌以說之」，則艮次坎、兌次離；「乾以君之，坤以藏之」，則乾次兌、坤次艮，實由中而達乎西北東南，方圖亦自中起也。

Shuhu Xiansheng Hu Yigui said: Cheng Zhifang's remarks are very appropriate. I therefore proceeded to deduce further: The "Say on the Trigrams" states "Heaven and Earth are positioned," which begins from the central points of the north-south axis; "Mountains and marshes communicate with each other," which follows with the trigrams in the northwest and southeast corners; "Thunder and wind contend with each other," which comes next with the trigrams in the northeast and southwest corners; "Water and fire do not oppose each other," which follows with the trigrams in the due east and due west directions. This shows that the circular diagram originates from the center of the north-south axis. "Thunder moves it, wind disperses it," with Zhen and Xun located at the center of the square diagram; "Rain moistens it, sun brightens it," so Kan is adjacent to Xun, and Li is adjacent to Zhen; "Mountain stops it, Lake delights it," so Gen is adjacent to Kan, and Dui is adjacent to Li; "Heaven rules it, Earth conceals it," so Qian is adjacent to Dui, and Kun is adjacent to Gen. Thus, the path proceeds from the center to the northwest and southeast corners. This shows that the square diagram also originates from the center.

鄱陽董氏真卿曰：愚按畫卦之始，不過太極生兩儀，每一生二，以至於六十四卦，此說固不待贅矣。若夫邵子方圓圖，則又不過以六畫大橫圖中分，移右邊陽儀上生三十二卦自上而下居左，左邊陰儀上生三十二卦自上而下居右，規而圓之以象天而周其外，則自然有節氣之流行，而乾坤陰陽之極與復姤陰陽之始適居上下之中，而有以合乎「天地定位」之章。

A man from Poyang named Dong Zhenqing said: I think the beginning of drawing the hexagrams is simply the Taiji producing the two principles, and each principle producing two, continuing in this way until reaching the sixty-four hexagrams. This idea does not need to be explained further. As for Shao Yong's square diagram and circular diagram, they are merely taking the large horizontal hexagram diagram of six lines and cutting it in the middle. The thirty-two hexagrams generated by the yang principle on the right side are moved downward to the left, and the thirty-two hexagrams generated by the yin principle on the left side are moved downward to the right. Then they are bent into a circle to symbolize heaven, surrounding the outer circle. In this way, the movement of the twenty-four solar terms naturally appears. The hexagrams Qian and Kun, which represent the extreme of yin and yang, and Fu and Guo, which represent the beginning of yin and yang, are exactly placed in the middle of the top and bottom ends. This corresponds with the passage in "Shuo Gua" that says "Heaven and Earth are positioned."

又以六畫大橫圖從三畫乾至坤各上生八卦者，自右而左分割作八段，自下重起，矩而方之以象地，而居圓圖之內，以取地囿天中之象。而由中及外，自然有雷風雨日、山澤天地對待之象，且縱橫斜正，以三畫六畫卦數之，莫不有以合乎「雷動風散」之章。而十二闢卦皆左旋於圓圖之間，右轉於方圖之外，雖疎密之不均，莫不有自然之妙焉。以此觀之，邵子「皆從中起」之說，蓋指圓圖方圖而言，新安程氏最為得之。邵子只據已成之橫圖，或規而圓，或矩而方，以見卦畫之用耳，又何論乎卦畫之所由生哉？固不以橫圖畫卦之始例論也。

He then divided the part of the six-line large horizontal diagram from the three-line Qian to the three-line Kun, each generating the eight trigrams, into eight sections from right to left, and rearranged them starting from the bottom. He arranged them into a square with a measuring tool to symbolize the earth, placing it inside the circular diagram, representing the image of "the earth being embraced by the heaven in the center." Thus, looking outward from the center, there naturally appeared the images of thunder, wind, rain, sun, and mountain, marsh, heaven, and earth, each pair opposing each other. Moreover, whether looking vertically, horizontally, diagonally, or straight, counting according to the three-line trigrams and six-line hexagrams, everything aligned with the passage in "Shuo Gu" that says, "Thunder moves it, wind disperses it." The twelve trigrams of the twelve divisions are arranged in a counterclockwise direction within the circular diagram and in a clockwise direction outside the square diagram. Although the spacing is uneven, they all possess natural elegance. From this, we can see that Shao Yong's statement "all begin from the center" refers to both the circular and square diagrams. Cheng Zhi Fang's understanding is most accurate. Shao Yong merely used the already drawn horizontal diagram, either bent into a circle or arranged into a square, to demonstrate the function of the trigrams. He did not discuss how the trigrams were generated. It was never appropriate to use the principles of the initial drawing of the horizontal diagram to universally interpret it.

《觀物外篇》曰：圓數有一（一為心），方數有二（或以一為心，或以四為心），竒耦之義也。六即一也，十二即二也（兩其六為十二，以六視十二，猶之乎一與二也）。天圓而地方，圓之數起一而積六（眾圓簇聚，一外得六），方之數起一而積八（眾方簇聚，一外得八），變之則起四而積十二也（以四為心，四外得十二）。六者常以六變，八者常以八變，十二者亦以八變，自然之道也。八者天地之體也，六者天之用，十二者地之用也。天變方為圓而常存其一，地分一為四而常執其方；天變其體而不變其用也，地變其用而不變其體也。六者並其一而為七，十二者並其四而為十六也。

Shao Yong's "Outer Chapters of Observing Things" says: The number of a circle has only one center (this "one" is the center), while the number of a square has two methods of calculation (some take one as the center, others take four as the center). This is the distinction between odd and even. Six is equivalent to one, and twelve is equivalent to two (two sixes make twelve; comparing six and twelve is like comparing one and two). Heaven is round and Earth is square: the number of a circle begins with one and accumulates to six (when many circles are gathered together, with one center, exactly six can be arranged around it), while the number of a square begins with one and accumulates to eight (when many squares are gathered together, with one center, exactly eight can be arranged around it). If changed, it begins with four and accumulates to twelve (taking four as the center, exactly twelve can be arranged around it). Six always changes by six, eight always changes by eight, and twelve changes by eight. This is the natural principle. Eight is the essence of Heaven and Earth, six is the function of Heaven, and twelve is the function of Earth. Heaven transforms the square into a circle while always preserving the "one," and Earth divides one into four while always maintaining the square. Heaven changes its essence but does not change its function, and Earth changes its function but does not change its essence. Adding the center one to six makes seven, and adding the center four to twelve makes sixteen.

又曰：五十者，蓍之數也；六十者，卦數也。五者，蓍之小衍也，故五十為大衍也；八者，卦之小成，則六十四為大成也。蓍徳圓，以況天之數，故七七四十九也，五十者存一而言之也；卦徳方，以況地之數，故八八六十四也，六十者去四而言之也。蓍者用數也，卦者體數也；用以體為基，故存一也；體以用為本，故去四也。圓者本一，方者本四，故蓍存一而卦去四也。

It is also said that fifty refers to the number of the yarrow stalks, and sixty refers to the number of hexagrams. Five is the 'small development' of the yarrow stalks, so fifty is called 'great development'; eight is the 'small completion' of the hexagrams, so sixty-four is called 'great completion'. The yarrow stalks have a round nature, used to symbolize the heavenly numbers, so seventy times seven is forty-nine; saying fifty includes the one that is kept aside and not used. The hexagrams have a square nature, used to symbolize the earthly numbers, so eight times eight is sixty-four; saying sixty refers to removing the four that are not used. The yarrow stalks are the 'used' numbers, and the hexagrams are the 'substantial' numbers; the used numbers take the substantial numbers as their foundation, so one is kept aside; the substantial numbers take the used numbers as their basis, so the four are removed. Roundness is based on one, squareness is based on four, so the yarrow stalks keep one and the hexagrams remove four.

按：《書·洪範》「五皇極」傳云「極，中也」，《漢·律歴志》「太極元氣，函三為一。極，中也」，極皆訓中（不從此訓自朱子始）。邵子曰「先天學，心法也，故圖皆從中起」，又曰「心為太極」，可見極即中，中即心，從中起謂從太極起也（《觀物詩》云「天向一中分造化，人於心上起經綸」，亦即此意）。天地萬物之理有一不本於太極者乎？有一不具於人心者乎？故曰「吾終日言而未嘗離乎是」。先儒以「圖皆從中起」兼方圓圖言之，當矣，然其義猶有所未盡也。

Hu Wei's commentary: In the "Book of Documents · Hongfan," the section on "Five, the Supreme Principle" was traditionally interpreted as "the 'ji' means 'zhong' (center)." The "Book of Han · Laws and Measures Chapter" says "the Taiji original qi includes three and becomes one," also stating "the 'ji' means 'zhong'." This shows that "ji" has always been interpreted as "zhong." The use of this interpretation began from Zhu Xi. Shao Yong said, "The Earlier Heaven studies are based on the mind, so all diagrams start from the center," and also said, "the mind is the Taiji." This shows that "ji" is "zhong," and "zhong" is "xin," so "starting from the center" means starting from the Taiji. In his poem "Guanwu," he says, "Heaven differentiates creation from the single character 'zhong,' and humans unfold their governance from their own minds," which is exactly this meaning. The principles of heaven, earth, and all things, which one is not derived from the Taiji? Which one is not present in the human mind? Therefore, he said, "I have spoken all day long but have never departed from it." Previous scholars interpreted "all diagrams start from the center" to refer to both square and circular diagrams, which is correct, but the meaning is not fully explained.

蓋先天方圓之圖皆由一四之積數來也。天圓而地方，其在《易》則圓主蓍，方主卦。圓之數起一而積六，一在中，六在外也，蓍徳圓象之。六並一為七，六者常以六變，六七四十二，並初七為四十九，大衍之數五十而其一為太極不用，故曰「五十者存一而言之」，此蓍策也，與卦圖無涉。

In fact, both the square and circular diagrams of the Earlier Heaven are derived from the two numbers "one" and "four." The concept of "heaven round and earth square" applies to the Book of Changes, where the circular aspect relates to the number of stalks used in divination, and the square aspect relates to the number of lines in a hexagram. The circular numbers start from one and accumulate to six, with one at the center and six at the perimeter, symbolizing the circular nature of the stalks used in divination. Adding the central one to six gives seven, but six always remains six during the process. Multiplying six by seven gives forty-two, and adding the initial seven results in forty-nine. The number of stalks used in divination is fifty, with one representing the non-used part of the Taiji. Therefore, fifty includes the unused one. This discussion concerns the method of divination with stalks, and has nothing to do with the hexagram diagram.

方之數起一而積八，一在中，八在外也，卦徳方象之，小圓圖是也。八並一為九，中為太極，故一不用也。八者常以八變，積為八八六十四，太圓圖是也，乾坤坎離四正卦不用，故曰「六十者去四而言之」也。乾坤當南北之中，坎離當東西之中，圖從中起，中為太極，故不用而止於六十，猶小圓圖之虛其一也。

The number of the square starts from one and accumulates to eight, with one in the center and eight surrounding it. The virtue of the trigrams is square, which is symbolized in this way, hence the small circular diagram of the eight trigrams is formed. Adding the one in the center to eight gives nine, and the center is the Taiji. Therefore, that one is present but not used. The eight trigrams always change in groups of eight, accumulating to sixty-four, forming the large circular diagram of the sixty-four trigrams. Among these, the four trigrams of Qian, Kun, Kan, and Li are present but not used, so it is said that 'sixty' refers to the number after excluding these four. Qian and Kun are at the center of north and south, while Kan and Li are at the center of east and west. The diagram starts from the center, which is the Taiji, so these four trigrams are not used and only sixty are counted, just as the small circular diagram of the eight trigrams leaves the central one empty.

方之數變之則起四而積十二，四在中，十二在外也。十二者亦以八變，故四之外累加之，第一圍必十二，第二圍必二十，第三圍必二十八，併為六十四，方圖是也。圖從中起，中為太極，故震巽恆益四卦亦不用而止於六十，猶大圓圖之去其四也。卦徳本方，象地之體，而其中又有方圓之別。天變方為圓而常存其一者，謂大小圓圖也，地中之天，方中之圓也；地分一為四而常執其方者，謂方圖也，地中之地，方中之方也（邵子取渾天之象，天周地外，地在天中，故作方圓合一之圖。朱子謂圓圖中間虛者便是太極，不合方圖在中間塞卻，待挑出放外，如此恐失作者之意）。

The number of squares changes, starting from four and accumulating up to twelve, with four in the center and twelve on the outside. Twelve also changes in groups of eight, so adding layer by layer around the central four: the first layer must be twelve, the second twenty, the third twenty-eight, totaling exactly sixty-four hexagrams. This is how the figure of the sixty-four hexagrams is formed. The figure starts from the center, where the center represents the Taiji (Supreme Ultimate). Therefore, the four hexagrams at the center—Zhen (Thunder), Xun (Wind), Heng (Continuity), and Yi (Benefit)—are not counted, resulting in a total of sixty, just like the large circle diagram excludes the four cardinal hexagrams. The nature of the hexagrams belongs to the square, symbolizing the body of the earth, yet within the square there is a distinction between square and circle: "Heaven transforms the square into a circle while always preserving the one," referring to the two circular diagrams, which represent the sky within the earth and the circle within the square; "Earth divides one into four while always preserving the square," referring to the square diagram, which represents the earth within the earth and the square within the square. (Shao Yong's diagram is based on the concept of the浑天, where the sky surrounds the earth externally, and the earth is located within the sky, thus forming a diagram that combines square and circle. Zhu Xi said that the empty space in the circular diagram is the Taiji, and it should not be blocked by the square diagram in the center; instead, it should be removed and placed outside. However, this might have lost the original intention of the diagram's creator.)

推之於大小橫圖，兩儀四象八卦皆由太極而生，亦所謂從中起也。此邵子之數學，即邵子之心法，終日言而不離乎是，故托《易》以著為圖，不必與聖人之《易》盡同也（揚子《太玄》其圖亦由中而起，中為一元，自一元衍而為三方，自三方衍而為九州島，自九州島衍而為二十七部，自二十七部衍而為八十一家，故知先天與《太玄》均為老氏之學也）。邵子之心與太極為體，嘗作《無名公傳》以自寓，無名者，太極之謂也。贊曰：「借爾面貌，假爾形骸，弄丸餘暇（丸謂太極），閒往閒來。」則其所謂心法者可知矣。彼以圓圖為合乎「天地定位」之象、方圖為合乎「雷動風散」之次者，皆知其一而不知其它，得其皮毛而不得其骨髓者也。

Extending this to the large and small circular diagrams, the two principles, four images, and eight trigrams all originate from the Taiji, which is referred to as 'starting from the center.' This is Shao Yong's mathematics, or rather, his method of mind. He constantly spoke about it, so he used the name of the Book of Changes to create these diagrams. They need not be exactly the same as the sage's Book of Changes (Yang Xiong's Tai Xuan also starts from the center: the center is 'the original unit,' which evolves into three 'directions,' then into nine 'states' (the original text mistakenly says 'nine states'), then into twenty-seven 'regions,' and then into eighty-one 'families'; from this we can see that the learning of the Earlier Heaven is similar to the Tai Xuan, both being part of the Daoist tradition). Shao Yong's mind takes the Taiji as its fundamental principle. He once wrote an essay called "The Biography of the Nameless Gentleman" in which he compared himself to the Taiji. The term 'nameless' refers to the Taiji. The commentary following the biography says: 'Using your appearance and form, I move freely in the leisure of playing with balls (the 'balls' refer to the Taiji).' From this, we can understand his method of mind. Those who believe that the circular diagram corresponds to the 'positioning of heaven and earth' and the square diagram corresponds to the 'movement of thunder and dispersion of wind' are only aware of one aspect and not the rest, having only grasped the superficial without reaching the essence.

俞氏《易外別傳序》曰：《易外別傳》者，先天圖環中之秘，漢儒魏伯陽《參同契》之學也。人生天地間，首乾腹坤，呼日吸月，與天地同一陰陽。《易》以道陰陽，故伯陽借《易》以明其說，大要不出先天一圖。是雖《易》道之緒餘，然亦君子養生之切務，蓋不可不知也。圖之妙在乎終坤始復，循環無窮；其至妙則又在乎坤復之交，一動一靜之間。愚嘗學此矣，徧閱《雲笈》，略曉其一二，忽遇隱者授以讀《易》之法，乃盡得環中之秘。反而求之吾身，則康節邵子所謂太極、所謂天根月窟、所謂三十六宮，靡不備焉，是謂身中之易。

Yu Yan's "Preface" to "Yi Wai Bi Chuan" says: "Yi Wai Bi Chuan" discusses the secret of the Earlier Heaven diagram, known as "Huanzhong," which is the kind of learning found in the Han dynasty scholar Wei Boyang's "Cantong Qi." Human beings exist between heaven and earth, with their heads resembling Heaven (Qian) and their bellies resembling Earth (Kun). Their breathing corresponds with the sun and moon, and they share the same yin and yang principles as heaven and earth. The "Yi" discusses precisely the way of yin and yang, so Wei Boyang used the "Yi" to explain his alchemical methods. Basically, all of this does not go beyond this one diagram of the Earlier Heaven. Although this is only a continuation of the "Yi" tradition, it is also an essential matter for gentlemen to cultivate their health, and it is something that should not be unknown. The wonderful aspect of this diagram lies in its beginning with the hexagram "Fu" and ending with "Kun," forming an endless cycle. Its most wonderful aspect is the moment when "Kun" and "Fu" meet, the instant of one movement and one stillness. I once studied this subject, reading extensively works like "Yunji Qi Jian," and I understood a little. Later, I suddenly met a hermit who taught me the method of reading the "Yi," and only then did I fully grasp the secret of "Huanzhong." Looking back and seeking within myself, I found that what Shao Yong spoke of as the Taiji, the heavenly root and lunar cave, and the thirty-six palaces, were all present, which is called the "Yi within the body."

又書其後曰：先天圖環中之極玄，愚雖弗暇専志從事於斯，而丹之妙用非苟知之，蓋嘗試之者也，故敢直指方士之所靳，以破學者之惑。嘗慨夫世所傳丹家之書，廋辭隠語，使覽者無罅縫可入，往往目眩心碎而掩卷長嘆。如蔡季通、袁機仲嘗與朱子共訂正《參同契》矣，雖能考其字義，然不得其的傳，未免臆度而已。愚今既得所傳，又何忍緘黙以自私？乃述是書，附於《周易集說》之後，而名之曰《易外別傳》，蓋謂丹家之說雖出於《易》，不過依仿而托之者，初非《易》之本義也。

He also wrote in the colophon that the idea of the "circle in the center" in the Earlier Heaven diagram is extremely profound and subtle. Although I have no leisure to devote myself fully to this study, the subtle practices of alchemy are not something that can be heard casually, but rather something I have personally experienced. Therefore, I dare to directly reveal the secret teachings that alchemists have kept hidden, in order to dispel the doubts of scholars. I often feel sorrowful that the books passed down by alchemists are full of cryptic and obscure language, making it impossible for readers to find any entrance. They often read until they become confused and tired, closing the book with sighs of regret. For instance, Cai Yuan ding (whose name was Jitong), Yuan Shu (whose name was Jizhong) once collaborated with Zhu Xi in editing the "Cantongqi," although they were able to clarify the meanings of the words, they did not receive the accurate transmission, and thus their interpretations remained mere guesses. Now that I have received the transmission, how could I bear to remain silent and keep it for myself? Therefore, I have written this book and attached it to the end of "Zhouyi Jishuo," naming it "Yi Wai Bi Chuan." The meaning is that although the doctrines of alchemists come from the Book of Changes, they are merely dependent on the Book of Changes and寄托 upon it, and are not the original meaning of the Book of Changes.

《易外別傳》曰：《參同契》云「終坤始復，如循連環」，《皇極經世書》云「先天圖者，環中也」。愚謂人之一身即先天圖，心居人身之中，猶太極在先天圖之中，朱紫陽謂「中間空處」是也。圖自復而始，至坤而終，終始相連如環，故謂之環。環中者，六十四卦環於其外，即太極居其中也。在《易》為太極，在人為心，人知心為太極，則可以語道矣。

The *External Transmission of the Book of Changes* says: The *Supplement to the Supreme Concord* explains that "it ends with the *Kun* hexagram and begins with the *Fu* hexagram, resembling a continuous ring." The *Supreme Principles Governing the World* states that the *Earlier Heaven Diagram* is the "ring in the center." I believe that a person's body is like a *Earlier Heaven Diagram*: the heart is at the center of the body, just as the *Taiji* (Supreme Ultimate) is at the center of the *Earlier Heaven Diagram*. Zhu Xi's reference to "the empty space in the middle" refers to this. The diagram starts with the *Fu* hexagram and ends with the *Kun* hexagram, with the beginning and end connected like a circle, hence called "ring." The term "ring in the center" means that the sixty-four hexagrams are arranged around it, while the *Taiji* resides in the center. In the *Book of Changes*, this is called *Taiji*, but in the human body, it is called the heart. When a person understands that the heart is *Taiji*, he can then discuss the great Dao with him.

又云：冬至之後為呼，夏至之後為吸，此天地一歲之呼吸也。愚謂冬至後自復而乾，屬陽，故以為呼；夏至後自姤而坤，屬陰，故以為吸。呼乃氣之出，故屬冬至之後；吸乃氣之入，故屬夏至之後。大則為天地一歲之呼吸，小則為人身一息之呼吸。《參同契》曰「龍呼於虎，虎吸龍精」，又曰「呼吸相含育，佇息為夫婦」，蓋以呼吸為龍虎，為夫婦。千經萬論，譬諭紛紛，不過呼吸兩字而已矣。

It is also said that after the winter solstice, there is "hū" (exhalation), and after the summer solstice, there is "xí" (inhalation), representing the breath of heaven and earth over the course of a year. I believe that after the winter solstice, from the hexagram "Fù" (Return) to "Qián" (Heaven), it belongs to yang, so it is considered exhalation; after the summer solstice, from "Gòu" (Meeting) to "Kūn" (Earth), it belongs to yin, so it is considered inhalation. Exhalation is the movement of qi outward, hence it corresponds to after the winter solstice; inhalation is the movement of qi inward, hence it corresponds to after the summer solstice. Broadly speaking, this represents the breath of heaven and earth over a year; narrowly speaking, it is the breath of a person in a single inhalation and exhalation. The "Cāntongqì" says, "The dragon exhales to the tiger, and the tiger absorbs the dragon's essence," and also says, "Exhalation and inhalation mutually nurture each other, holding one's breath and focusing the mind is like the union of husband and wife." This compares breathing to dragon and tiger, and to husband and wife. Countless scriptures and discussions, with various analogies, all come down to the two words "breathing."

又曰：「一動一靜，天地之至妙者與；一動一靜之間，天地人之至妙至妙者與。」愚謂圖左自復至乾，陽之動也；圖右自姤至坤，陰之靜也。一動一靜之間，乃坤末復初陰陽之交，在一歲為冬至，在一月為晦朔之間，在一日則亥末子初是也。吾身之乾坤內交，靜極機發，而與天地之機相應，是誠天地人之至妙至妙者也。

It is also said: "One movement and one stillness are probably the most mysterious things in the universe; and the moment when one movement meets one stillness is probably the most mysterious thing among heaven, earth, and humanity." I believe the left half of the diagram, from the hexagram of "Return" to "Heaven," represents the movement of yang energy; the right half, from "Meeting" to "Earth," represents the stillness of yin energy. The point where movement and stillness meet is exactly where yin and yang converge at the end of "Earth" and the beginning of "Return": in a year, this is the winter solstice; in a month, it is between the last day and the first day; in a day, it is between the end of the亥 hour and the beginning of the子 hour. The yin and yang within my own body converge, reaching the utmost stillness and then the vital energy arises, thus resonating with the vital energy of heaven and earth. This is indeed the most mysterious thing among heaven, earth, and humanity.

又云：「無極之前，陰含陽也；有象之後，陽分陰也。」朱紫陽曰：邵子就圖上說循環之意，自姤至坤是陰含陽，自復至乾是陽分陰，坤復之間是無極。袁機仲曰：朱子謂坤復之間乃無極，其論察矣。又詩云：「忽然夜半一聲雷，萬戸千門次第開。若識無中含有象，許君親見伏羲來。」無中含有象，即是坤復之間無極而太極也。邵子之學，非朱子孰能明之？

He also said: "Before the state of Wuji, yin contained yang; after there was form, yang differentiated into yin." Zhu Xi said that Shao Yong was explaining the cyclical meaning in the diagram, from the hexagram Guo to Kun representing yin containing yang, and from Fu to Qian representing yang differentiating into yin. The space between Kun and Fu is Wuji. Yuan Shu said: Zhu Xi's view that the space between Kun and Fu is Wuji is very precise. Zhu Xi also wrote a poem saying: "Suddenly at midnight, a thunderclap echoes, and doors and windows open one after another. If you can recognize the image of 'having' within 'non-being,' you will be allowed to personally see Fuxi coming." The so-called "non-being containing image" is precisely the "Wuji giving rise to Taiji" between Kun and Fu. Who else besides Zhu Xi could explain Shao Yong's learning?

內煉之道，至簡至易，唯欲降心火入于丹田耳。丹田在臍之後、腎之前，正居腹中。丹家諱言心腎，謂心腎非坎離，蓋指呼吸為坎離，殊不思呼吸乃坎離之用，心腎乃坎離之體。人之一身，心為之主，故獨居中；腎為之基，故獨居下。丹家不言心腎而言身心，身即腹也，腎在其中矣，豈可舍腎哉？腎屬水，心屬火，火入水中，則水火交媾，如晦朔之間日月之合璧。

The principle of internal alchemy is extremely simple and easy; it is merely about bringing the fire of the heart down into the dantian. The dantian is located behind the navel and in front of the two kidneys, right in the center of the abdominal cavity. Internal alchemists avoid mentioning the heart and the kidneys, saying that the heart and kidney are not the坎 and 离, but instead take breathing as the坎 and 离. However, they fail to realize that breathing is only the 'use' of the坎 and 离, while the heart and kidney are the 'essence' of the坎 and 离. In the human body, the heart is the master, hence it is located in the center; the kidney is the foundation, hence it is located at the lower part. Internal alchemists do not speak of the heart and kidney but refer to 'body' and 'heart,' where 'body' means the abdomen, and since the kidney is originally within it, how can they ignore the kidney? The kidney belongs to water, and the heart belongs to fire. When fire enters water, water and fire unite, just like the conjunction of the new and full moon, where the sun and moon form a single circle.

《易》曰「山澤通氣」，又曰「二氣感應以相與」。愚按《參同契》云：「自然之所為兮，非有邪偽道；若山澤氣相烝兮，興雲而為雨。」蓋人身之陰陽絪縕交結于丹田，則升於泥丸，滃然如云，化為甘澤。陳希夷詩云「倏爾火輪煎地脈，愕然神瀵湧山椒」，與此同旨（神瀵出《列子》）。嘗謂山澤之氣相通，由其虛也，唯虛也故二氣感應以相與，不虛則窒而不通，安能相與？

The Book of Changes says, "Mountains and marshes communicate through their energies," and also says, "Yin and yang energies respond to each other and are mutually affectionate." I follow the Shentongqi in saying, "This is a natural occurrence, with no perverse or false methods; just like the energies of mountains and marshes rise and mingle, forming clouds that become rain." The yin and yang energies in the human body intertwine and condense in the dan田, then rise to the niwan, forming a dense cloud-like appearance, which then transforms into sweet bodily fluids. Chen Tuan's poem says, "Suddenly the fire wheel boils the earth's veins, and when startled, the divine spring surges up the mountain peak," which expresses exactly this meaning ("shenfou" is a term from the Liezi). I often say that mountains and marshes can communicate because there is emptiness between them; precisely because of this emptiness, the two energies can respond and interact. If there is no emptiness, there would be blockage, and how could they interact?

內煉之道貴乎心虛，心虛則神凝，神凝則氣聚，氣聚則興云為雨，與山澤相似。《離騷·逺遊篇》云：「道可受兮而不可傳，其小無內兮其大無垠，母滑而魂兮彼將自然，壹氣孔神兮於中夜存，虛以待之兮無為之先。」朱紫陽注云：「蓋廣成子之告黃帝，不過如此，實神仙之要訣也。」

The principle of internal cultivation lies in mental emptiness: mental emptiness allows the spirit to gather, the spirit's gathering leads to the accumulation of energy, and the accumulation of energy can summon clouds and cause rain, just as mountains and marshes communicate with each other. The "Chu Ci · Yuan You" says: "The Dao can be received but not transmitted through words; it is so small that it has no inner part, and so vast that it has no boundaries; do not disturb your soul and spirit, for it will naturally follow its course; concentrate your energy and reach its profound mystery, keeping it in mind at midnight; wait quietly for it, without rushing ahead before it begins." Zhu Xi explains in his commentary: "This is roughly what the broad-minded elder Guangcheng told the Yellow Emperor, and indeed, this is the essential secret of the immortal practices."

醫書云：人身有任、督二脈。任脈者，起於中極之下，以上毛際，循腹裡上闗元，至咽喉，屬陰脈之海；督脈者，起於下極之腀，並於脊裡，上至風府，入腦上顛，循額至鼻柱，屬陽脈之海。所以為任脈者，女子得之以姙養也；謂之督脈者，以其督領經脈之海也。鹿運尾閭，蓋能通其督脈者也；龜納鼻息，蓋能通其任脈者也。人能通此二脈，則百脈皆通。《黃庭經》云「皆在心內運天經，晝夜存之自長生」，天經乃吾身之黃道，呼吸往來於此，即任督二脈是也。

Medical texts say that the human body has two meridians, the Ren meridian and the Du meridian. The Ren meridian begins below the Zhongji acupoint, ascends along the edge of the pubic hair, runs along the inner side of the abdomen passing through the Guanyuan acupoint, and reaches the throat, serving as the convergence of all the yin meridians in the body. The Du meridian begins at the meeting point of the genitalia, runs alongside the inner side of the spine, ascends to the Fengfu acupoint, enters the brain, and continues upward to the top of the head, then follows the forehead down to the nose. It serves as the convergence of all the yang meridians in the body. It is called the Ren meridian because it is essential for women to conceive and nurture a fetus; it is called the Du meridian because it oversees and governs all the other meridians. Deer are good at moving their tail闾, which may be because they can open the Du meridian; turtles are good at breathing through their nose, which may be because they can open the Ren meridian. If a person can open these two meridians, all the hundred meridians in the body will become unblocked. The Huangting Jing says, "All things revolve within the heart according to the heavenly path, day and night one should maintain and guard naturally for long life." The so-called "heavenly path" refers to the Yellow Path on my body, through which breathing flows, which is precisely the Ren and Du meridians.

按：石澗，精於《參同契》者也，不徒心解之，且身試之，故知先天圖為老氏之易而非聖人之易，著書以闡其幽，名之曰《易外別傳》，以為丹家所依託，非《易》之本義。自有先天圖以來，知其妙而不使之混於《易》中者，唯石澗一人（明萬厯中有莆田林兆恩者，號三教先生，其徒述其說以成書，亦名《易外別傳》，而其指大異。石澗卻道家於《易》外，三教混釋老於《易》中，邪正相去懸絶）。

Hu Wei remarked: Yu Yan (with the courtesy name Shijian) was an expert in the "Supplement to the Supreme Ultimate," he did not only understand it in his mind, but also practiced it personally, so he knew that the Earlier Heaven diagram belonged to the Daoist school of thought, not to the Sage's "Book of Changes." He wrote a book to explain its subtle meanings, titled "An Extraordinary Transmission Outside the Book of Changes," believing that it was the Daoist alchemists who used the "Book of Changes" as a cover, and not the original meaning of the "Book of Changes." Since the emergence of the Earlier Heaven diagram, only Yu Yan was able to recognize its subtlety and prevent it from being mixed into the "Book of Changes." (In the Ming Dynasty, during the Wanli period, there was a person from Putian named Lin Zhaogeng, with the courtesy name Sanchiao, his disciples recorded his teachings and compiled them into a book, also named "An Extraordinary Transmission Outside the Book of Changes," but its doctrine was entirely different. Yu Yan placed Daoism outside the "Book of Changes," while the doctrine of the three teachings mixed Buddhism and Daoism into the "Book of Changes," thus being extremely different from the correct path.)

魏伯陽，丹經王也，希夷、康節乃其嫡派正傳，所言皆老氏之易也。康節橫圖以白代—、以黒代--，實本希夷。然《天地自然之圖》本謂龍馬授伏羲者如是，而伏羲則之以畫卦，變白黒為—、--耳；康節乃謂伏羲所作亦如是，然則伏羲之後更有何人變白黒為—、--如今卦首所列之六畫乎？

Feyi Yang is known as the king of alchemical texts. Chen Tuan and Shao Yong are his direct descendants and followers, and what they discussed was all based on the school of Laozi's "Book of Changes." Shao Yong's horizontal diagram used white to represent the yang line "—" and black to represent the yin line "--," which actually originated from Chen Tuan. However, the original "Diagram of Heaven and Earth Naturally" was said to be the pattern given to Fuxi by the dragon horse, and Fuxi took it as a model to draw the hexagrams, changing white and black into "—" and "--." Shao Yong, however, claimed that Fuxi's hexagrams were originally in white and black. Then, who after Fuxi changed white and black into "—" and "--," resulting in the six lines currently listed at the beginning of the hexagrams?

又兩儀四象八卦，希夷皆子在母中，康節卻子在母外，雖取法希夷，而實失先天之本意矣。希夷之圖止有八卦方位，而無其次序。康節既獨出臆見，於一竒一偶之上各加一竒一偶之三畫，而為乾一、兌二、離三、震四、巽五、坎六、艮七、坤八矣，又欲附會於希夷，乃以「天地定位」一章當希夷八卦方位，就中推出次序。

Now talking about the Two Principles, Four Symbols, and Eight Trigrams, Chen Tuan's diagram places the son within the mother, while Shao Yong places the son outside the mother. Though he took inspiration from Chen Tuan, he actually abandoned the original meaning of the Earlier Heaven diagram. Chen Tuan's diagram only includes the positions of the Eight Trigrams, without any sequence. Shao Yong, having formed his own independent view, added one odd and one even principle at each level, resulting in three lines and thus deriving the sequence: Qian one, Dui two, Li three, Zhen four, Xun five, Kan six, Gen seven, Kun eight. He also wanted to connect with Chen Tuan, so he compared the chapter "Heaven and Earth are positioned" from the "Shuo Gua" with Chen Tuan's diagram of the Eight Trigrams, and from there he established a sequence.

其左半乾兌離震適符橫圖之一二三四，遂以為「數往者順」；至右半坤艮坎巽，則與橫圖正相反，乃從中拗轉為巽五、坎六、艮七、坤八，以為「知來者逆」，斯不亦矯揉造作，失天地自然之妙乎？且次序與方位元不相謀，未聞乾坤三索之序由出震齊巽之位而定也，何獨於先天合之？故圓圖抽坎填離，猶是丹家之遺制，而橫圖則無謂甚矣。

The left half of the diagram, consisting of Qian, Dui, Li, and Zhen, exactly corresponds to the order of one, two, three, and four in the horizontal diagram. He therefore says this represents "following the numbers of the past." However, when it comes to the right half, consisting of Kun, Gen, Kan, and Xun, they are exactly opposite to the horizontal diagram. Therefore, they are reversed in the middle and arranged as Xun five, Kan six, Gen seven, and Kun eight, which he says represents "knowing the future in reverse." Is this not artificial and contrived, thereby losing the natural essence of heaven and earth? Moreover, the order and the direction are fundamentally different things. There has never been a mention that the order of the three sons generated by Qian and Kun is determined by the directional statements in the "Sayings on the Hexagrams" such as "The Emperor arises from Zhen and harmonizes with Xun." Why then, specifically in the Earlier Heaven diagram, are these two aspects forced together? Therefore, the circular diagram's "drawing out Kan and filling Li" is still a method left by alchemists, but the horizontal diagram is indeed without reason.

乃復引而伸之為六十四卦次序，遂至有四畫五畫之卦。夫此四畫五畫者，將名曰某卦乎？抑仍謂之兩儀四象乎？如以為兩儀四象，則八卦之後不應復有兩儀四象也。或曰此康節之數學，知來之道寓焉。然吾觀《皇極經世書》，其所推元會運世之數及天地萬物之變，恐別有方術，未必用加一倍法也。

He then extended and derived the horizontal diagram into the order of the sixty-four trigrams, thus producing trigrams with four and five lines. What should these four- and five-line figures be called? Should they still be called the two principles (two yi) and the four images (four xiang)? If they are considered as two yi and four xiang, then after the eight trigrams there should not be two yi and four xiang again. Some people say this is Shao Yong's mathematics, and the principle of foreknowledge is contained within it. But I think that in The Supreme Principles Governing the World, he calculated the numbers of the great cycle (yuan), great era (hui), great movement (yun), and great age (shi), as well as the changes of heaven and earth and all things, which probably involved another system of methods, not necessarily the 'doubling method'.

竒偶之上各加竒偶，只因錯解「易有太極」一節，遂以揲蓍生爻之次序為始作八卦之次序耳。然則大小橫圖，既戾於聖人之經，又絶非希夷之指，先天之贅肬也，安得冠諸經首以為伏羲不言之教乎？

Adding odd and even again upon odd and even was merely due to a misinterpretation of the passage in the Great Treatise "The Book of Changes has the Supreme Ultimate," which led to taking the sequence of divining with yarrow stalks as the original sequence for drawing the Eight Trigrams. In this view, both the large and small horizontal diagrams contradict the sages' texts and completely deviate from Chen Tuan's original intent. They are like a tumor on the body of the Earlier Heaven school, how can they be placed before the text of the Zhou Changes as the unspoken teaching of Fuxi?

右論邵子伏羲六十四卦方位。

The above section examines the diagram of the "Fuxi Sixty-Four Hexagram Directions" transmitted by Shao Yong.

《繋辭傳》曰：乾坤其易之縕邪？乾坤成列，而易立乎其中矣。乾坤毀，則無以見易；易不可見，則乾坤或幾乎息矣。

The Great Treatise says: The Qian and Kun hexagrams are probably the fundamental elements contained within the Book of Changes. Once Qian and Kun are arranged in sequence, the structure of the Book of Changes is thereby established. If Qian and Kun were destroyed, the Book of Changes would be invisible; and if the Book of Changes is invisible, then the functions of Qian and Kun would be nearly ceased.

南軒張氏曰：乾坤其易之門，言易出入於乾坤也；乾坤其易之縕，言易含蓄於乾坤也。

Nanxuan Zhang Shi said: The "Great Treatise" discusses "Qian and Kun are the gate of the Book of Changes," meaning the changes of the Book of Changes come in and out between the Qian and Kun hexagrams. It also discusses "Qian and Kun are the essence of the Book of Changes," meaning all the content of the Book of Changes is contained within the Qian and Kun hexagrams.

《本義》曰：縕，所包蓄者，猶衣之著（音灼）也。易之所有，陰陽而已。凡陽皆乾，凡陰皆坤，畫卦定位，則二者成列，而易之體立矣。乾坤毀，謂卦畫不立；乾坤息，謂變化不行。

Zhu Xi's "The Original Meaning of the Zhou Changes" says: "Wen" refers to the thing wrapped and contained, like the cotton stuffing in a piece of clothing (the character "zhuo" is read as "zhuo"). The content contained in the "Zhou Changes" is nothing but yin and yang. All yang aspects are categorized under Qian, and all yin aspects are categorized under Kun; by drawing the hexagrams and establishing their positions, yin and yang are arranged in order, and thus the essence of the "Zhou Changes" is established. What is meant by "the destruction of Qian and Kun" is that the hexagram forms cannot be established; what is meant by "the cessation of Qian and Kun" is that transformation cannot proceed.

《語類》曰：乾坤只是說二卦，此易只是說易之書，與「天地定位，易行乎其中」之易不同，行乎其中者卻是說易之道理。又曰：大抵易之言乾坤者多以卦言，易立乎其中，只是乾坤之卦既成而易立矣。又曰：乾坤只言卦，易只是陰陽卦畫。

The Zhu Zi Yu Leiu records: here, Qian and Kun refer only to the two trigrams, and the term "Yi" here refers only to the book of The Zhou Changes, which is different from the "Yi" in the sentence "Heaven and Earth are positioned, and Yi operates in the middle." The "Yi" in "operates in the middle" refers to the principle of change. It also says: generally speaking, the Yi discusses Qian and Kun mainly in terms of the trigrams; "Yi is established in the middle" merely means that once the trigrams Qian and Kun have been formed, the Yi is thereby established. It also says: Qian and Kun refer here only to the trigrams, and "Yi" refers only to the trigrams of yin and yang.

按：陰陽一畫，但可謂之剛柔，不可謂之乾坤。凡言乾坤者，皆純陽純陰之卦，非三畫則六畫，此經主三畫而言（《雜卦》「乾剛坤柔」主六畫）。《本義》云「凡陽皆乾，凡陰皆坤」，則似一畫亦可謂之乾坤，非經意也。易謂卦畫之交易而成變化者，乾坤成列，則六子及重卦皆在其中，故曰易之縕。乾坤毀無以見易，謂無乾坤二卦，則六十四卦無由而出；易不可見，乾坤或幾乎息，謂無易書，則天地變化之道不著，殆與滅息相似。此乾坤字義與上不同。

Hu Wei's commentary: The single line of yin or yang can only be called gāng (masculine) or róu (feminine), not Qian or Kun. Any reference to Qian and Kun refers to hexagrams that are entirely yang or entirely yin, which are either the three-line simple trigrams or the six-line compound hexagrams. This passage from the Great Treatise discusses the simple trigrams. The Miscellaneous Hexagram Transmission says "Qian is masculine, Kun is feminine," which refers to the compound hexagrams. The Original Meaning of the Zhou Changes states "all yang is Qian, all yin is Kun," which sounds as if a single line can be called Qian or Kun. This does not align with the original meaning of the text. "Yi" refers to the changing interactions of the hexagram lines that produce transformation. Once Qian and Kun are arranged in order, the six subsidiary trigrams—Zhen, Kan, Gen, Xun, Li, and Dui—as well as the sixty-four compound hexagrams are all included within them. Therefore, it is called "Yi's essence." "If Qian and Kun are destroyed, there would be no way to see Yi" means that without the hexagrams of Qian and Kun, the sixty-four hexagrams could not arise. "If Yi is not visible, then Qian and Kun might almost cease" means that without the Zhou Changes text, the way of transformation in heaven and earth would not be revealed, almost as if it were ceasing to exist. The meaning of the words "Qian and Kun" here is different from what was mentioned earlier.

乾坤其易之門邪？乾，陽物也；坤，陰物也。陰陽合徳而剛柔有體，以體天地之撰，以通神明之徳。

The Great Treatise also says: Qian and Kun are perhaps the gateways of the Book of Changes? Qian represents the Yang principle, and Kun represents the Yin principle. When the Yin and Yang principles combine, the qualities of firmness and flexibility take form, thus enabling the comprehension of the forms and conditions of all things in heaven and earth, and the harmonious union with the virtue of the divine.

南軒張氏曰：以卦言之，乾之三竒乃陽物也，坤之三耦乃陰物也。三竒三耦索而為六子，互體卦變積而為六十四，此陰陽合徳而剛柔有體也。

Nanxuan Zhang Shi said: In terms of the hexagrams, the three yang lines of the Qian hexagram represent yang substances, and the three even lines of the Kun hexagram represent yin substances. The three yang and three yin lines interact and generate the six subordinate hexagrams of Zhen, Kan, Gen, Xun, Li, and Dui. These are further developed through the concepts of 'mutual constitution' and 'hexagram transformation,' accumulating into the sixty-four hexagrams. This is what is called 'yin and yang combine in virtue and the firm and yielding have their forms.'

《本義》曰：諸卦剛柔之體，皆以乾坤合徳而成，故曰乾坤易之門。撰，猶事也。

Zhu Xi's "The Original Meaning of the Zhou Changes" says: The forms of yin and yang in each hexagram are all formed by the union of the virtues of the Qian and Kun trigrams. Therefore, Qian and Kun are the gateways of the Zhou Changes. The character "zhuàn" is equivalent in meaning to "shì", referring to the conditions and phenomena of the world.

按：陰陽合徳，謂一再三索；剛柔有體，謂六子成列也。因而重之為六十四，變化無窮，皆出於乾坤二卦，故曰易之門。自康節有伏羲先畫一竒一耦之說，世皆指乾坤為一畫，經旨鬱而不宣，茲特為正之。

Hu Wei remarked: "Yin and yang combine in virtue" refers to the generation of the six sons through the first, second, and third combinations of Qian and Kun. "Hard and soft have form" refers to each of the six sons forming their own sequence. By combining the eight trigrams two by two, sixty-four trigrams are formed, with infinite changes, all originating from Qian and Kun. Therefore, Qian and Kun are the gateways of the Book of Changes. Since Shao Yong proposed the idea that Fuxi first drew one odd and one even line, people have since regarded Qian and Kun as single lines, thus obscuring the original meaning of the classic text. Here, this is specially corrected.

《說卦傳》曰：乾，天也，故稱乎父；坤，地也，故稱乎母。震一索而得男，故謂之長男；巽一索而得女，故謂之長女；坎再索而得男，故謂之中男；離再索而得女，故謂之中女；艮三索而得男，故謂之少男；兌三索而得女，故謂之少女。

The *Sayings on the Trigrams* states: Qian represents Heaven, so it is called the father; Kun represents Earth, so it is called the mother. Zhen is the first to seek and obtain a male, so it is called the Eldest Son; Xun is the first to seek and obtain a female, so it is called the Eldest Daughter; Kan is the second to seek and obtain a male, so it is called the Middle Son; Li is the second to seek and obtain a female, so it is called the Middle Daughter; Gen is the third to seek and obtain a male, so it is called the Youngest Son; Dui is the third to seek and obtain a female, so it is called the Youngest Daughter.

南軒張氏栻曰：老陽為父，老陰為母。老陽能變，故自下而索震為長男，自中而索坎為中男，自上而索艮為少男；老陰能變，故自下而索巽為長女，自中而索離為中女，自上而索兌為少女。

Nanxuan Zhang Shi said: Old Yang is the father, old Yin is the mother. Old Yang can move, so from the lower line it forms Zhen, representing the eldest son; from the middle line it forms Kan, representing the middle son; and from the upper line it forms Gen, representing the youngest son. Old Yin can also move, so from the lower line it forms Xun, representing the eldest daughter; from the middle line it forms Li, representing the middle daughter; and from the upper line it forms Dui, representing the youngest daughter.

《本義》曰：索，求也，謂揲蓍以求爻也。男女指卦中一陰一陽之爻而言。

Zhu Xi's "The Original Meaning of the Zhou Changes" says: "Suo" means to seek or obtain, referring to the process of dividing the yarrow stalks to determine the lines. Here, the terms male and female refer to a single yin line or a single yang line within the hexagram.

《語類》曰：震一索而得男一段，看來不當専作揲蓍看，揲蓍有不依這序時便說不通。大概只是乾求於坤而得震坎艮，坤求於乾而得巽離兌，一二三者以其畫之次序言也。

Master Zhu says: "When the trigram Zhen is obtained by one count," this passage should not be understood solely in terms of divination with yarrow stalks, because in the practice of divination with yarrow stalks, such a sequence does not always occur, which would make the explanation inconsistent. Generally speaking, it refers to the trigrams Zhen, Kan, and Gen being obtained when Heaven seeks from Earth, and the trigrams Xun, Li, and Dui being obtained when Earth seeks from Heaven. The terms "one count," "two counts," and "three counts" refer to the order of the lines in the trigrams.

按：揲蓍之說本諸漢上，甚無理，故《語録》不從，而《本義》乃未及改正。李秀巖謂《本義》在前，《語録》在後，其間有十數條意義尤密者，此蓋其一也。

Hu Wei commented: interpreting "suo" as the process of divining lines by drawing stalks of chrysanthemum, this interpretation originally comes from Zhu Zhen's "The Transmission of the Zhou Changes from the Han River," which is very unreasonable. Therefore, Master Zhu's "Collected Sayings" did not adopt this view. However, since "The Original Meaning of the Zhou Changes" was written earlier, it could not be corrected. Li Xinzhuan (Xiuyan) said that "The Original Meaning" was written first and "The Collected Sayings" was recorded later. Among the dozens of sayings in "The Collected Sayings," several are more precise than those in "The Original Meaning." This is probably one of them.

朱子《荅袁機仲書》曰：自初未有畫時說到六畫滿處者，邵子所謂先天之學也；卦成之後各因一義推說，邵子所謂後天之學也。今來喻所引《繫辭》《說卦》三才六位之說，即所謂後天者也。先天後天既各自為一義，而後天說中取義又多不同，彼此自不相妨，不可執一而廢百也。若執此說，必謂聖人初畫卦時只見一個三才，便更不問事由，一連便埽出三畫以擬其象，畫成之後子細看來見使不得，又旋劃壁添出後一半截，此則全是私意杜撰補接，豈復更有易邪？

Zhu Xi in his letter "Answer to Yuan Jizhong" says: Starting from the beginning with no lines drawn, proceeding step by step until six lines are completed, this is what Shao Yong called "Earlier Heaven learning." After the hexagram structure is formed, interpreting and explaining it according to various meanings is what Shao Yong called "Later Heaven learning." The tripartite and six positions mentioned in the "Great Treatise" and "Explanations of the Hexagrams" in the present letter belong to the Later Heaven approach. Since Earlier Heaven and Later Heaven have each become their own principles, and the Later Heaven approach has various interpretations, they do not interfere with each other. One cannot fix on one interpretation and discard the rest. If one rigidly adheres to your interpretation, then one would have to say that the sage originally drew the hexagrams by seeing only the concept of the three elements, and without further consideration, drew three lines at once to imitate its image. After completing the hexagram, upon closer examination, it proved inadequate, so he hastily added the remaining half later. This would be entirely fabricated and pieced together, and there would be no "Book of Changes" left at all.

又曰：據邵氏說，先天者伏羲所畫之易也，後天者文王所演之易也。伏羲之易，初無文字，只有一圖以寓其象數，而天地萬物之理、陰陽始終之變具焉。文王之易，即今之《周易》，而孔子所為作傳者是也。孔子既因文王之易以作傳，則其所論固當專以文王之易為主，然不推本伏羲作易畫卦之所由，則學者必將誤認文王所演之易便為伏羲始畫之易，只從中半說起，不識向上根原矣。

Zhu Xi also said: According to Shao Yong's view, "Earlier Heaven" refers to the Book of Changes drawn by Fuxi, while "Later Heaven" refers to the Book of Changes interpreted by King Wen. Fuxi's Book of Changes originally had no written text, only a diagram used to express its images and numbers, and all the principles of heaven and earth, as well as the changes of yin and yang, were contained within it. King Wen's Book of Changes is the present Zhou Changes, which is the book that Confucius wrote the commentary for. Since Confucius based his commentary on King Wen's Book of Changes, what he discussed naturally should focus on King Wen's Book of Changes. However, if we do not trace back to the origin of Fuxi's drawing of the trigrams, scholars will inevitably mistake King Wen's interpretation of the Book of Changes for Fuxi's original drawing, starting only from the middle, and thus fail to recognize the fundamental source above.

故十翼之中，如「八卦成列，因而重之」，太極、兩儀、四象、八卦，與天地、山澤、雷風、水火之類，皆本伏羲畫卦之意；而今新書原卦畫一篇，亦分兩儀，伏羲在前，文王在後。必欲知聖人作易之本，則當考伏羲之畫；若只欲知今易書文義，則但求之文王之經、孔子之傳足矣。兩者初不相妨，而亦不可以相雜。來教乃謂専為邵氏解釋，而於易經無所折衷，則恐考之有未詳也。

Therefore, in the Ten Wings, statements such as "The eight trigrams are arranged in sequence, and then combined again" and concepts like the Taiji, two principles, four images, eight trigrams, as well as terms like heaven and earth, mountains and marshes, thunder and wind, water and fire, all originate from the intention behind Fuxi's drawing of the trigrams. In my newly written work, The Awakening of the Yi, the section titled "Original Meaning of the Trigrams" is divided into two parts, with the section on Fuxi coming first and the section on King Wen coming later. If one wishes to clarify the fundamental intent of the sages in composing the Yi, one should investigate the trigrams drawn by Fuxi. If one merely wants to understand the meaning of the present text of the Yi, then referring to King Wen's hexagrams and Confucius' commentaries would suffice. These two approaches do not interfere with each other, but they should not be confused. However, your letter says that I am merely explaining for the Shao school, and that my work does not provide a balanced interpretation of the Yi itself. Perhaps your examination has not been thorough enough.

按：伏羲胷羅造化，全體太極，仰觀俯察，近取逺取，三才之道了了於心目之間，便一連埽出三畫，有何不可，而必一生二、二生四、四生八，作巧推排計邪？一連埽出者為私意杜撰補接，然則逐爻生出者，豈反非杜撰補接邪？孔子之傳無一語推本伏羲者則已，既有推本伏羲者，則何以知兩儀四象為伏羲之所畫，而乾坤三索為文王之所演邪？先天後天強生分別，前第六卷中辨之已詳。知彼逐爻生出之為謬，則知一連埽出三畫而交易以成六子者，真伏羲之易而非文王之易矣。曉人自解，無庸辭費也。

Hu Wei commented: Fuxi's mind encompassed the creation of heaven and earth, fully possessing the whole of the Taiji. He looked up to observe the heavenly phenomena, looked down to examine the geographical features, drew near to study his own body, and looked far to observe all things. The principles of the three elements were clearly visible in his mind. Thus, he could draw the three lines in one breath. What is there that cannot be done? Why must there be a process of one giving birth to two, two giving birth to four, and four giving birth to eight, using that kind of clever and artificial reasoning? According to Zhu Xi's interpretation, drawing the three lines in one breath is considered an arbitrary fabrication. Then, if the lines are drawn one by one in sequence, is that not also an arbitrary fabrication? If Confucius' commentary does not trace back to Fuxi at all, that would be acceptable. But since there are indeed references to Fuxi, then on what basis can we determine that the two principles and four images were drawn by Fuxi, while the trigrams and their six sons were developed by King Wen? The distinction between the Earlier Heaven and Later Heaven is artificially divided into two parts, and this has already been thoroughly discussed in the sixth volume. Once we understand that the method of generating the lines one by one is wrong, we will realize that the true Yi of Fuxi is the one where the three lines are drawn in one breath and then interact and change to produce the six sons. This is not the Yi of King Wen. Those who understand naturally will comprehend, and there is no need to waste words.

右論邵子文王八卦次序。

The previous section examines the origin and the actual meaning of the name of the "King Wen's Eight Trigrams Sequence Diagram" transmitted by Shao Yong.

《說卦傳》曰：帝出乎震，齊乎巽，相見乎離，致役乎坤，說言乎兌，戰乎乾，勞乎坎，成言乎艮。萬物出乎震，震，東方也。齊乎巽，巽，東南也；齊也者，言萬物之潔齊也。離也者，明也，萬物皆相見，南方之卦也；聖人南面而聴天下，蓋取諸此也。坤也者，地也，萬物皆致養焉，故曰致役乎坤。兌，正秋也，萬物之所說也，故曰說言乎兌。戰乎乾，乾，西北之卦也，言陰陽相薄也。坎者，水也，正北方之卦也，勞卦也，萬物之所歸也，故曰勞乎坎。艮，東北之卦也，萬物之所以成終而所成始也，故曰成言乎艮。

The *Sayings on the Trigrams* says: The "Emperor" who governs all things originates from the trigram Zhen (Thunder), then reaches Xun (Wind) and becomes clean and orderly, then reaches Li (Fire) and things appear to each other, then reaches Kun (Earth) and nurtures all things, then reaches Dui (Lake) and things are joyful and speak, then reaches Qian (Heaven) and yin and yang contend, then reaches Kan (Water) and things are weary, then reaches Gen (Mountain) and the cycle of beginning and end is completed. All things sprout from Zhen, which is the trigram of the East. "Harmonized with Xun," Xun is located in the Southeast; "harmonized" means all things become clean and orderly. Li is "brightness," at which all things appear to each other, and it is the trigram of the South; sages face south to govern the world, probably taking this as a model. Kun is Earth, where all things are nurtured, so it is said "nurtured by Kun." Dui corresponds to autumn, the time when all things are joyful, so it is said "joyful speech is expressed in Dui." "Contending in Qian," Qian is the trigram of the Northwest, meaning yin and yang energies press against each other here. Kan is Water, the trigram of the North, also the trigram of weariness, where all things return, so it is said "weary in Kan." Gen is the trigram of the Northeast, where all things conclude one cycle and begin another, so it is said "completion is expressed in Gen."

白雲郭氏曰：自天地定位之後皆論八卦，此章獨異，復有重釋之辭。蓋上論八卦之位未明言其所，故下復明言之曰「震，東方也」「巽，東南也」，如是則無嫌於重釋之也。

White Cloud Guo Yong said: After the chapter "Heaven and Earth are positioned," the subsequent chapters of the "Commentary on the Hexagrams" all discuss the Eight Trigrams, but this chapter is different, as it is followed by a section of repeated explanation. Probably because the first part did not specify the directions of the trigrams, the second part clearly states "Zhen is in the East" and "Xun is in the Southeast." Thus, the repetition is not unnecessary.

石門梁氏曰：自東南至西，皆母與三女之位；自西北至東，皆父與三男之位。《本義》圖說：右見《說卦》。邵子曰：此文王八卦，乃入用之位，後天之學也。

Shi Men Liang Shi said: Going from the southeast to the west, all these positions belong to the mother (Kun) and the three female trigrams; going from the northwest to the east, all these positions belong to the father (Qian) and the three male trigrams. Zhu Xi's "The Original Meaning of the Zhou Changes" explains here that this is mentioned in the "Sayings on the Trigrams." Shao Yong said: This is the "Wen Wang Eight Trigrams," which belongs to the practical application of directions, that is, what is called "Later Heaven Learning."

按：以上二圖非古所傳，亦邵子作也。乾坤三索之次序、出震齊巽之方位，伏羲之易本是如此，而邵子獨以為文王之易，名之曰後天，以尊先天之學。序位皆是，而其名則非，九圖之中無一可存者也。

Hu Wei commented: The two diagrams mentioned above are not ancient ones, but both were made by Shao Yong. The order of the three trigrams of Qian and Kun producing the six sons, as well as the directional arrangement of "The Emperor arises from Zhen, and is harmonized with Xun," were originally the way they were in Fuxi's Book of Changes. However, Shao Yong deliberately called them King Wen's Book of Changes and named them "Later Heaven," in order to elevate his own "Earlier Heaven" theory. The order and direction themselves are correct, but the names given to them are wrong. Therefore, among the nine diagrams listed at the beginning of the "Yixue Guoming," none of them can be retained.

《觀物外篇》曰：至哉，文王之作易也！其得天地之用乎？故乾坤交而為泰，坎離交而為既濟也。乾生於子，坤生於午，坎終於寅，離終於申，以應天之時也。置乾於西北，退坤於西南，長子用事而長女代母，坎離得位，兌震為偶，應地之方，王者之法其盡於是矣。

Shao Yong said in his "Outer Chapters of Observing Things": What a great achievement, King Wen's creation of the Book of Changes! He must have grasped the functions of heaven and earth. Therefore, he arranged the trigrams Qian and Kun to form the Tai hexagram, and the trigrams Kan and Li to form the Ji Ji hexagram. Qian originates from the Zi position, Kun originates from the Wu position, Kan concludes at the Yin position, and Li concludes at the Shen position, corresponding to the heavenly sequence of time. He placed the Qian hexagram in the Northwest, and the Kun hexagram in the Southwest. The eldest son Zhen hexagram takes charge, while the eldest daughter Xun hexagram assumes the role of the mother. Kan and Li each occupy their proper positions, and Dui pairs with Zhen to form an even combination, corresponding to the directions of the earth. The principles of governance by a sovereign, perhaps, are all contained within this.

朱子《荅王伯豐書》曰：《說卦》「天地定位」至「坤以藏之」以前，伏羲所畫八卦之位也；「帝出乎震」以下，文王即伏羲已成之卦而推其義類之辭也。如卦變圖剛來柔進之類，亦是就卦已成後用意推說，以此為自彼卦而來耳，非真先有彼卦而後方有此卦也。

Zhu Xi in his letter to Wang Bo Feng says: The "Sayings on the Trigrams" from "Heaven and Earth are positioned" to "Kun conceals it" discusses the arrangement of the eight trigrams drawn by Fuxi. From "The Emperor arises from Zhen" onwards, it is King Wen's explanation of the meanings and categories of the trigrams already drawn by Fuxi. For example, terms like "Yang comes" and "Yin advances" in the trigram transformation diagram are interpretations developed after the trigram structure was already established. These explanations treat one trigram as derived from another, but they do not imply that one trigram existed before another.

林氏《易裨傳》法象篇曰：以造化之序論之，先天所以立體也，後天所以致用也。先天乾坤定上下之位，而天尊地卑之體立矣；坎離居左右之門，而日生乎東、月生乎西之象著矣；震巽對峙，而雷始於東北、風起於西南矣；兌艮角立，西北多山、東南多水之所鍾矣。後天震居東方，萬物出生之地；巽居東南，萬物潔齊之地；坤西南，萬物致養之地；兌正西，物之所說；乾西北，陰陽之相薄；坎正北，物之所歸；艮東北，所以成終成始者也。

Lin Zhi (Dejiu) in his "Yi Bi Zhuan · Fa Xiang Chapter" says: In terms of the order of creation, the Earlier Heaven diagram is used to establish the fundamental nature, while the Later Heaven diagram is used to carry out the functions. In the Earlier Heaven diagram, Qian and Kun determine the positions of upper and lower, thus establishing the fundamental principle that Heaven is exalted and Earth is humble; Kan and Li are positioned on both sides, making clear the phenomenon that the sun rises in the east and the moon appears in the west; Zhen and Xun face each other, thus causing thunder to arise in the northeast and wind to rise in the southwest; Dui and Gen stand at both corners, thus forming the situation where the northwest has many mountains and the southeast has much water, each accumulating in its own place. In the Later Heaven diagram, Zhen is located in the east, being the place where all things begin to sprout; Xun is located in the southeast, being the place where all things are purified and orderly; Kun is located in the southwest, being the place where all things receive nourishment; Dui is located in the west, being the place where all things are joyful; Qian is located in the northwest, being the place where yin and yang are in conflict; Kan is located in the north, being the place where all things return and hide; Gen is located in the northeast, being the place where all things complete and end, yet also begin anew.

以陰陽之體論之，巽離兌本陽體也，而陰來交之；震坎艮本陰體也，而陽來交之。伏羲之卦，得陽多者屬乎陽，得陰多者屬乎陰；後天之卦，得一陰者為三女，得一陽者為三男。先天之位，三女附乎乾，三男附乎坤，陰附陽、陽附陰也；後天之位，三男附乎乾，三女附乎坤者，陰附陰、陽附陽也。

If we consider the essence of yin and yang, Xun, Li, and Dui originally belong to the yang category (Heavenly category), but have a yin line coming to interact with them. Zhen, Kan, and Gen originally belong to the yin category (Earthly category), but have a yang line coming to interact with them. In Fuxi's trigrams, those with more yang lines are classified as yang, and those with more yin lines are classified as yin. In the Later Heaven arrangement, a single yin line is considered as three females, and a single yang line is considered as three males. In the Earlier Heaven arrangement, the three female trigrams are attached to Qian, and the three male trigrams are attached to Kun, which represents yin attaching to yang and yang attaching to yin. In the Later Heaven arrangement, the three male trigrams are attached to Qian, and the three female trigrams are attached to Kun, resulting in yang attaching to yang and yin attaching to yin.

黃氏《象數論》曰：離南坎北之位見於經文，而卦爻所指之方亦與之相合，是亦可以無疑矣。蓋畫卦之時即有此方位，易不始於文王，則方位亦不始於文王，故不當云文王八卦方位也。乃康節必欲言文王因先天乾南坤北之位改而為此，朱子則主張康節之說過當，反致疑於經文：曰曷言齊乎巽，不可曉；曰坤在西南，不成東北方無地；曰乾西北亦不可曉，如何陰陽來此相薄；曰西方肅殺之氣，如何言萬物之所說。

Huang Zongxi's "Discussion on the Imagery and Numerical Calculations of the Book of Changes" says: The orientation of Li in the south and Kan in the north is mentioned in the classic text of the "Transmission of the Commentary on the Hexagrams," and the directions indicated by each hexagram and its lines also correspond with it. This is originally not something to be doubted. Probably, this system of orientation was already established when the hexagrams were drawn. Since the Book of Changes was not started from King Wen, its orientation naturally also did not begin from King Wen, so it should not be called the "King Wen's Hexagram Orientation." However, Shao Yong insisted that this was King Wen who changed the original orientation of the Earlier Heaven diagram, with Qian in the south and Kun in the north, into this form. Zhu Xi further exaggerated Shao Yong's view, and even turned back to doubt the classic text: asking why it says "harmonized with Xun," which is hard to understand; questioning why Kun is in the southwest, as if there were no land in the northeast; questioning why Qian is in the northwest, as if yin and yang would be forced to meet there; and questioning why the west is associated with the cutting-off and withering energy, yet it is described as the place where all things rejoice.

凡此數說，有何不可曉？巽當春夏之交，萬物畢出，故謂之齊，觀北地少雨，得風則生氣鬱然可驗也。夏秋之交，土之所位，故坤位之，非言地也。若如此致難，則先天方位巽在西南，何不疑東北無風邪？其餘七卦莫不皆然。乾主立冬以後、冬至以前，故陰陽相薄，觀《說卦》乾之為寒為冰，非西北何以置之？萬物告成於秋，如何不說？朱子注元亨利貞之利曰：利者，生物之遂，物各得宜，不相妨害，於時為秋，於人為義而得其分之和，非說乎？顧未嘗以肅殺為嫌也。然則朱子所以致疑者，由先天之說先入於中，故曰主張太過也。

What is there that cannot be understood about these points? Xun corresponds to the time between spring and summer when all things have fully emerged from the earth, hence it is called "Qi" (harmonious). Observing the northern region, which receives little rain, once the wind blows, life qi becomes vigorous, which suffices to verify this. The time between summer and autumn is precisely when "Earth" is in its proper position, so using Kun to represent this position is appropriate, not merely referring to the earth itself. If we were to question it in this way, then in the Earlier Heaven arrangement, Xun is located in the southwest, so why should we not question whether there is no wind in the northeast? Similarly, all the other seven trigrams are subject to such scrutiny. Qian represents the period after the beginning of winter and before the winter solstice, hence it is said that yin and yang are in conflict at this time. Looking at the "Shu Guan Zhuan" which states that Qian represents cold and ice, if it is not placed in the northwest, where else should it be placed? All things are completed in autumn, so why cannot it be said to be joyful? Zhu Xi's commentary on the "Yuan Heng Li Zhen" explains the character "Li" (advantage) as meaning that all things are allowed to fulfill their nature, each thing finds its proper place without mutual obstruction. In the sequence of seasons, this corresponds to autumn; in human affairs, it corresponds to righteousness and harmony in the proper measure. Is this not precisely joy? Thus, Zhu Xi did not dislike the solemn and severe nature of autumn. Therefore, Zhu Xi's doubt arises only because the Earlier Heaven theory was previously accepted as authoritative, hence he overemphasized his position.

康節曰：乾坤交而為泰（言文王改先天圗之意。先天乾南坤北，交而為泰，故乾北坤南），坎離交而為既濟（先天離東坎西，交而為既濟，故離南坎北），乾生於子（先天乾居午而其生在子，故下而至北），坤生於午（坤居子而其生在午，故上而至南），坎終於寅（坎當申，交於離，終於寅），離終於申（離當寅，交於坎，終於申）。所謂交者，不取對待言之也。即以對待而論，則乾南坤北者，亦必乾北坤南而後泰之形可成也，今坤在西南、乾在西北；離東坎西者，亦必離西坎東而後既濟之形可成也，今離在上、坎在下，於義何居？藉曰再變而後為今位，是乾南坤北之後、離南坎北之前，中間又有一方位矣。乾位戌，坤位未，坎位子，離位午，於子午寅申皆無當也。

Shao Yong said: Qian and Kun intersect to form the hexagram Tai (this refers to King Wen's intention in modifying the Earlier Heaven diagram: in the Earlier Heaven, Qian is in the south and Kun in the north, and their intersection forms Tai, so in the Later Heaven, Qian moves to the north and Kun to the south). Kan and Li intersect to form the hexagram Ji Ji (in the Earlier Heaven, Li is in the east and Kan in the west, and their intersection forms Ji Ji, so in the Later Heaven, Li moves to the south and Kan to the north). Qian originates from Zi (in the Earlier Heaven, Qian is in the position of Wu but its vital energy is in Zi, so it moves down to the north), and Kun originates from Wu (Kun is in the position of Zi but its vital energy is in Wu, so it moves up to the south). Kan ends at Yin (Kan is in the position of Shen, and after intersecting with Li, it ends at Yin), and Li ends at Shen (Li is in the position of Yin, and after intersecting with Kan, it ends at Shen). However, what he called 'intersecting' is not based on opposing positions. Even if we consider opposing positions, if Qian is in the south and Kun in the north, they must become Qian in the north and Kun in the south for the hexagram Tai to be formed. But now Kun is in the southwest and Qian in the northwest. Similarly, if Li is in the east and Kan in the west, they must become Li in the west and Kan in the east for the hexagram Ji Ji to be formed. But now Li is above and Kan is below. Is this logically consistent? If we say it has changed again to reach its current position, then between the time when Qian was in the south and Kun in the north, and when Li was in the south and Kan in the north, there would be another set of positions in between. Moreover, the positions of Qian in Xu, Kun in Wei, Kan in Zi, and Li in Wu do not match the statements about Zi, Wu, Yin, and Shen.

康節又曰：震兌始交者也（陽本在上，陰本在下，陽下而交於陰，陰上而交於陽。震一陽在下，兌一陰在上，故為始交），故當朝夕之位；坎離交之極者也（坎陽在中，離陰在中，故為交之極），故當子午之位（四正皆為用位）；巽艮不交而陰陽猶雜也（巽一陰在下，艮一陽在上，適得上下本然，故為不交），故當用中之偏；乾坤純陽純陰，故當不用之位（東方陽主用，西方陰為不用）。夫氣化流行不息，無時不用，若以時過為不用，則春秋不用者子午，冬夏不用者卯酉，安在四正之皆為用位也？必以西南西北為不用之位，則夏秋之交、秋冬之交，氣化豈其或息乎？

Shao Yong also said: Zhen and Dui represent the beginning of interaction (Yang is originally above, Yin is originally below; Yang descends to meet Yin, and Yin ascends to meet Yang; Zhen has one Yang at the bottom, Dui has one Yin at the top, so they are considered the start of interaction), so they correspond to the early and late positions; Kan and Li represent the extreme of interaction (Kan's Yang line is in the middle, Li's Yin line is in the middle, so they are considered the peak of interaction), so they correspond to the Zi and Wu positions (the four cardinal directions are all useful positions); Xun and Gen do not interact, but Yin and Yang remain in their original positions (Xun has one Yin at the bottom, Gen has one Yang at the top, which exactly corresponds to their natural positions, so they are considered non-interacting), so they correspond to the biased positions among the useful ones; Qian and Kun are pure Yang and pure Yin, so they correspond to the unused positions (the East belongs to Yang and is associated with use; the West belongs to Yin and is considered unused). However, the process of qi transformation never stops, and there is no moment when it is not in action. If we consider a time as 'unused' once it has passed, then during spring and autumn, the Zi and Wu positions are considered unused, and during winter and summer, the Mao and You positions are considered unused; how can the four cardinal directions all be considered useful positions? If we must fix the Southwest and Northwest as unused positions, then during the transition from summer to autumn and from autumn to winter, would the process of qi transformation not continue?

康節又曰：乾坤縱而六子橫，易之本也（先天之位）；震兌橫而六卦縱，易之用也。由前之說，則後自坎離以外皆橫也；由後之說，則前自坎離以外皆縱也。圖同而說異，不自知其遷就與？是故離南坎北之位本無可疑，自康節以為從先天改出，牽前曳後，始不勝其支離。朱子求其所以改之之故而不可得，遂至不信經文，籲，可怪也。

Shao Yong also said: The trigrams Qian and Kun are arranged vertically while the six sons are arranged horizontally, which refers to the original arrangement of the Book of Changes (Earlier Heaven); the trigrams Zhen and Dui are arranged horizontally while the other six trigrams are arranged vertically, which refers to the function of the Book of Changes. According to the first explanation, in the Later Heaven diagram, except for Kan and Li, all others are arranged horizontally; according to the second explanation, in the Earlier Heaven diagram, except for Kan and Li, all others are arranged vertically. It is the same diagram yet the explanations differ before and after. He himself did not realize that he was adjusting the explanation to fit his own view. Therefore, the direction of Li in the south and Kan in the north has always been without doubt; since Shao Yong claimed that this arrangement was derived from the Earlier Heaven diagram, he pulled and pushed the positions, leading to a fragmented and disorganized system. Zhu Xi tried to find the reason why King Wen changed the diagram but could not find it, and he even doubted the authenticity of the text. How strange!

《魏志·管輅傳》注引《輅別傳》，謂劉邠曰：輅不解古之聖人何以處乾位於西北、坤位於西南。夫乾坤者，天地之象，然天地至大，為神明君父，覆載萬物，生長撫育，何以安處二位，與六卦同列？今按《說卦》之方位，秦漢諸儒未有疑之者，疑之自管輅始。蓋其時魏伯陽之學已行，乾南坤北之位略有端倪，輅心善之，因發難以導邠，而邠不能問，故未竟其說也。

In the "Records of the Three Kingdoms: Wei Annals: Guan Lu's Biography," the annotation cites "Guan Lu's Separate Biography," which records that Guan Lu said to Liu Bin: I do not understand why the ancient sages placed Qian (Heaven) in the Northwest and Kun (Earth) in the Southwest. Qian and Kun represent the images of Heaven and Earth, which are extremely vast and extensive, serving as divine sovereigns and fathers, covering and supporting all things, nurturing and cultivating them. Why then are they placed in these two directions, ranked equally with the other six trigrams? Now, examining the directional arrangement in the "Sayings on the Trigrams," the scholars of the Qin and Han dynasties never doubted it, and doubt began with Guan Lu. Perhaps at that time, the teachings of Wei Boyang had already spread, and the idea of placing Qian to the south and Kun to the north had already begun to appear. Guan Lu agreed with this idea in his heart, so he deliberately raised the question to guide Liu Bin. However, Liu Bin did not ask further questions, so Guan Lu did not finish his explanation.

朱子酷愛《參同契》，八卦之方位斷從先天，遂覺出震齊巽等無一不可疑，入者主之，出者奴之，勢所必至也。至謂此章與卦變俱是成卦後用意推說，則又儗非其倫矣。林徳久深斥劉牧之鉤隠，可謂卓識，而獨於先天方位則附會其意而為之辭，亦以康節非牧流輩耳。然二人品格雖相去懸絶，而圖學之無當於經則一也，徳久豈未之思乎？

Zhu Xi loved The Zhou Changes Treatise on the Combination of the Three, and when it came to the eight trigrams and their directions, he decisively adopted the Earlier Heaven theory. Therefore, he regarded statements such as 'Emerging from Zhen' and 'Harmonizing with Xun' as all doubtful, since the dominant ones were treated as masters and the excluded ones as servants, which was inevitable. As for his claim that the chapter 'On the Explanation of the Trigrams' is similar to the theory of trigram transformation, being an explanation developed after the trigrams were formed, this comparison is even more inappropriate. Lin Zhi (Dejiu) severely criticized Liu Mu's Hooking the Hidden Diagram, which can be considered as having excellent insight. However, he still forcedly interpreted the Earlier Heaven directions and rephrased them, merely because Shao Yong was not of the same caliber as Liu Mu. Yet, although the moral character of these two people differs greatly, their studies of the trigrams and their relation to the classics are equally irrelevant. Did Dejiu not consider this point at all?

右論邵子文王八卦方位。

In the above section, the authenticity and the name and reality of the "King Wen's Eight Trigrams Diagram" transmitted by Shao Yong are examined.

《繫辭傳》曰：易之為書也不可逺，為道也屢遷。變動不居，周流六虛，上下無常，剛柔相易，不可為典要，唯變所適。

The Great Treatise says: The Book of Changes is not to be neglected, for the Dao it embodies is ever changing. The lines move without remaining in one place, circulating among the six line positions, rising and falling without fixed pattern. The strong lines and the weak lines alternate with each other, and cannot be regarded as fixed standards; they only adapt themselves to the changing circumstances.

白雲郭氏曰：易之為道，數遷而變動未嘗止，周流六爻，或以下而升上，或由上而降下，以剛易柔，以柔易剛，不可以常道拘也，唯變所適而已，此之謂易之道也。

White Cloud Guo Yong said: The Dao discussed in the Book of Changes is constantly shifting and changing without ever stopping. It flows through the six lines, some rising from the bottom to the top, some descending from the top to the bottom, using a strong line to replace a flexible one, and a flexible line to replace a strong one. It cannot be confined by fixed rules, but rather adapts itself according to the changes—this is called the Dao of the Book of Changes.

漢上朱氏曰：訟彖曰「剛來而得中」，隨彖曰「剛來而下柔」，蠱彖曰「剛上而柔下」，噬嗑彖曰「剛柔分，動而明」，賁彖曰「柔來而文剛」「分剛上而文柔」，無妄彖曰「剛自外來而為主於內」，大畜彖曰「剛上而尚賢」，咸彖曰「柔上而剛下」，損彖曰「損上益下」，又曰「損剛益柔」，益彖曰「損上益下」，又曰「自上下下」，渙彖曰「剛來而不窮，柔得位乎外而上同」，節彖曰「剛柔分而剛得中」。

Zhu Zhen's "Hanshang Yixuan" lists numerous examples from the Commentary on the Judgment that use the movement and interaction of lines to explain how hexagrams are formed. For instance, the Commentary on the Judgment of the "Strife" hexagram says "the strong line comes and occupies the center," the "Following" hexagram says "the strong line comes and is below the flexible line," the "Guilt" hexagram says "the strong line is above and the flexible line is below," the "Breaking Up" hexagram says "the strong and flexible lines are divided, and movement brings clarity," the "Brightness" hexagram says "the flexible line comes and adorns the strong line," and also says "the strong line is above and adorns the flexible line," the "Without Regret" hexagram says "the strong line comes from outside and becomes the dominant line inside," the "Great Accumulation" hexagram says "the strong line is above and honors the virtuous," the "Intimacy" hexagram says "the flexible line is above and the strong line is below," the "Loss" hexagram says "loss from above benefits below," and also says "loss of the strong benefits the flexible," the "Increase" hexagram says "loss from above benefits below," and also says "the strong line comes from above to benefit below," the "Dispersal" hexagram says "the strong line comes without end, and the flexible line occupies the outer position and unites above," and the "Restraint" hexagram says "the strong and flexible lines are divided, and the strong line occupies the center." These several examples are the textual basis upon which later scholars established the theory of hexagram transformation.

剛者，陽爻也；柔者，陰爻也。剛柔之爻，或謂之來，或謂之分，或謂之上下，所謂唯變所適也。此虞氏、蔡景君、伏曼容、蜀才、李之才所謂自某卦來之說也。

Here the term "yang" refers to a yang line, and "yin" refers to a yin line. The lines of yang and yin are sometimes said to "come," sometimes to "split," and sometimes to "ascend" or "descend." This is exactly what the Great Treatise says: "It adapts itself to change." This is the theory of changing hexagrams, which was advocated by Yu Fan, Cai Jingjun, Fu Manrong, Shu Cai, Li Zhicai, and others, who claimed that "this hexagram comes from a certain hexagram."

東坡蘇氏曰：凡易之所謂剛柔者，皆本諸乾坤也。乾施一陽於坤，以化其一陰而生三子，皆一陽而二陰，凡三子之卦有言剛來者，明此本坤也而乾來化之；坤施一陰於乾，以化其一陽而生三女，皆一陰而二陽，凡三女之卦有言柔來者，明此本乾也而坤來化之。

Su Shi's Dongpo Commentary on the Changes says: All the concepts of yang and yin in the Book of Changes originate from the two trigrams Qian (Heaven) and Kun (Earth). When Qian gives a yang line to Kun, it transforms one of Kun's yin lines, producing the three trigrams Zhen (Thunder), Kan (Water), and Gen (Mountain), which are all trigrams with one yang line and two yin lines. Whenever the Commentary on the Judgment mentions 'yang comes' in a hexagram containing any of these three trigrams, it indicates that the original hexagram was based on Kun, and Qian transformed it. When Kun gives a yin line to Qian, it transforms one of Qian's yang lines, producing the three trigrams Xun (Wind), Li (Fire), and Dui (Lake), which are all trigrams with one yin line and two yang lines. Whenever the Commentary on the Judgment mentions 'yin comes' in a hexagram containing any of these three trigrams, it indicates that the original hexagram was based on Qian, and Kun transformed it.

東谷鄭氏汝諧曰：易始於畫，畫始於乾坤。自乾坤而為八卦，乾坤之變極矣；自八卦而為六十四，八卦之變極矣。八卦皆乾坤所生，六十四卦皆八卦所生，此作易之本旨也。傳易者懼其說之簡易而無以自托於艱深之地，於是有互體卦變之說。又云：乾坤大父母也，復姤小父母也。夫父母一也，安得大小之別？

Eastern Valley's Zheng Ruoxie said: The Book of Changes began with drawing trigrams, and drawing trigrams began with Qian and Kun. From Qian and Kun, the eight trigrams were derived, and the transformation of Qian and Kun reached its limit; from the eight trigrams, the sixty-four trigrams were derived, and the transformation of the eight trigrams also reached its limit. All eight trigrams originated from Qian and Kun, and all sixty-four trigrams originated from the eight trigrams. This is the true intention behind composing the Book of Changes. Those who transmit the Book of Changes feared that their explanations were too simple, and thus could not be grounded in profound matters. Therefore, they invented terms such as "interchangeable structures" and "trigram transformations." They also said that Qian and Kun are the great parents, while Fu and Gou are the small parents. Parents are only one level, so where does the distinction between great and small come from? In his view, terms such as "interchangeable structures" and "trigram transformations" are merely products of those transmitting the Book of Changes who deliberately made things complicated.

按：《參同契》云「乾坤者，易之門尸，眾卦之父母」，是眾卦皆生於乾坤也。李、邵為先天之學，而其卦圖乃以復、姤、臨、遯、泰、否、壯、觀皆為生卦之母，則是顯背伯陽矣，希夷之傳豈若是乎？既失《參同》之旨，又非《彖傳》之意，東谷譏之有以也。

Hu Wei commented: The "Zhou Yi San Tong Qi" says, "Qian and Kun are the gateways of the Book of Changes, and the parents of all other hexagrams." This shows that all other hexagrams come from Qian and Kun. Li Zhi Cai and Shao Yong studied the earlier heaven doctrine, but their hexagram diagrams treated Fu, Gu, Lin, Duan, Tai, Poi, Da Zhuang, Guan, and others as the mothers of the hexagrams, which openly contradicts Wei Boyang's view. Could Chen Tuan's (Xiyi's) transmission be like this? It has abandoned the main idea of the "San Tong Qi" and also deviates from the original meaning of the Commentary on the Judgment. Eastern Valley Zheng RuXie criticized them, and there is a reason for that.

《彖傳》曰：泰，小往大來，吉亨，則是天地交而萬物通也，上下交而其志同也；內陽而外陰，內健而外順，內君子而外小人，君子道長，小人道消也。否之匪人，不利君子貞，大往小來，則是天地不交而萬物不通也，上下不交而天下無邦也；內陰而外陽，內柔而外剛，內小人而外君子，小人道長，君子道消也。

The Commentary on the Judgment says: The卦 of Tai, "small things recede and great things come, auspicious and smooth," refers to the mutual interaction between Heaven and Earth leading to the smooth flow of all things, and the mutual interaction between above and below leading to harmony of hearts and minds. The inner trigram is yang and the outer trigram is yin, with inner strength and firmness and outer softness and compliance, using the gentleman internally and expelling the petty person externally, thus the way of the gentleman grows and the way of the petty person declines. The卦 of Pi, "non-human rejection, not favorable for the gentleman's constancy, great things recede and small things come," refers to the non-interaction between Heaven and Earth leading to the obstruction of all things, and the non-interaction between above and below leading to the failure of the state. The inner trigram is yin and the outer trigram is yang, with inner weakness and outer strength, using the petty person internally and expelling the gentleman externally, thus the way of the petty person grows and the way of the gentleman declines.

黃氏《象數論》曰：卦變之說，由泰否二卦小往大來、大往小來而見之，而夫子《彖傳》所以發明卦義者於是為多，固易中一大節目也。上經三十卦，反對之為十二卦；下經三十四卦，反對之為十六卦；乾、坤、頤、大過、坎、離、中孚、小過不可反對，則反其竒偶以相配。卦之體兩相反，爻亦隨卦而變，顧有於此則吉、於彼則凶，於此則當位、於彼則不當位。從反對中明此往來倚伏之理，所謂兩端之執也。行有無妄之守，反有天衢之用；時有豐亨之遇，反有羇旅之悲。非以此卦生彼卦也，又非以此爻換彼爻也。

Huang Zongxi's "Discussion on the Images and Numbers of the Book of Changes" says that the concept of changing hexagrams arises from the two hexagrams "Tai" and "Po" which show "small going away and great coming in" and "great going away and small coming in." Confucius' Commentary on the Judgment mainly elaborates on the meanings of hexagrams through this method, which is originally one of the major aspects of the Book of Changes. In the upper section of the Book of Changes, there are thirty hexagrams, paired in opposition (by reversing the hexagrams) to form twelve groups; in the lower section, there are thirty-four hexagrams, paired in opposition to form sixteen groups. The eight hexagrams "Qian," "Kun," "Yi," "Da Guo," "Kan," "Li," "Zhong Fu," and "Xiao Guo" when reversed remain the same hexagram, so they cannot be paired in opposition. Instead, their odd and even lines are completely reversed to be matched with each other. Within a hexagram, the structure is opposite in pairs, and the lines also change accordingly with the hexagram. Thus, there is a distinction between being auspicious here and inauspicious there, being appropriate here and inappropriate there. Understanding the principles of movement and concealment through opposition is called "holding both ends." In practice, "Wu Wang" emphasizes holding on without recklessness, while its reversal is "Da Xu" which represents the open path of heaven. In terms of fortune, the hexagram "Feng" signifies prosperity and success, while its reversal is "Lv" which represents the loneliness of a traveler. This does not mean that one hexagram gives rise to another, nor does it mean that one line is exchanged for another.

按：易有聖人之道四，變居一焉。易窮則變，變則通，通則久，變者易中之大義也。觀孔子之言曰「上下無常，剛柔相易」，「內陽而外陰」「內柔而外剛」，則凡《彖傳》之剛柔往來上下內外，皆主卦變而言可知矣。然諸儒概以一爻言之，故唯三陰三陽之卦可通，而二陰二陽之卦則不可通，無妄「剛自外來」、升「柔以時升」之類是也，唯以反對言之則無不可通。蓋卦可以該爻，而爻不可以該卦，卦變則爻隨而動矣。坤索乾得震坎艮，以一剛為主；乾索坤得巽離兌，以一柔為主。《彖傳》所稱剛柔，或指卦，或指爻，隨文立義可也。大抵三陰三陽，泰否以卦言，餘皆以爻言；二陰二陽則必以卦言，然其所主者，陽卦之一剛、陰卦之一柔耳。

Hu Wei commented: The Book of Changes contains four principles of the sage's way, and "change" is one of them. The Book of Changes reaches its limit and thus must change; only through change can it become unobstructed, and only through unobstruction can it endure long. "Change" is a major principle in the Book of Changes. Looking at Confucius' words, "the upper and lower are without constant position, and the yang and yin alternate," and also "the inner is yang and the outer is yin," "the inner is soft and the outer is strong," then all the discussions in the Commentary on the Judgment about the coming and going of yang and yin, and the upper and lower, inner and outer, are all referring to the change of the hexagram. This can be definitely concluded. However, the scholars of later generations generally discussed only one line, so only the hexagrams with three yin and three yang can be explained, while those with two yin and two yang cannot be explained. For example, in the hexagram Wuwang, "yang comes from outside," and in the hexagram Sheng, "yin rises with the right time." Only by using the concept of "opposite" can all these be explained. Because a hexagram can encompass its lines, but a line cannot encompass a hexagram; when a hexagram changes, its lines naturally change accordingly. The hexagram Kūn seeks the hexagram Qián and obtains Zhèn, Kǎn, and Gèn, taking the single yang line as the main one; the hexagram Qián seeks the hexagram Kūn and obtains Xùn, Lí, and Duì, taking the single yin line as the main one. The yang and yin mentioned in the Commentary on the Judgment sometimes refer to the hexagram, and sometimes to the line, and the meaning is established according to the text. Generally, the hexagrams with three yin and three yang, such as Tai and Pǐ, are discussed in terms of the hexagram, while the others are discussed in terms of the line. However, for the hexagrams with two yin and two yang, they must be discussed in terms of the hexagram, yet what they emphasize is still only the single yang line in the yang hexagram and the single yin line in the yin hexagram.

右論古卦變。

In the above section, the discussion examines the ancient concept of changing hexagrams as the basis for the Commentary on the Judgment.

一陰一陽之卦各六，皆自復、姤而變。復、姤：師（初之二）、同人（初之二）；謙（初之三）、履（初之三）；豫（初之四）、小畜（初之四）；比（初之五）、大有（初之五）；剝（初之上）、夬（初之上）。

Yu Fan's first category of hexagram transformation diagrams: there are six hexagrams with one yang line and six hexagrams with one yin line, all derived from the hexagrams of Fu (复) and Guo (姤). Fu (复), with one yang line in the first position, and Guo (姤), with one yin line in the first position, are the main hexagrams from which transformations occur. When the first line and the second line are exchanged, Fu becomes Shi (师) and Guo becomes Tongren (同人); when the first line and the third line are exchanged, they become Qian (谦) and Lü (履); when the first line and the fourth line are exchanged, they become Yu (豫) and Xiaoxu (小畜); when the first line and the fifth line are exchanged, they become Bi (比) and Dàyǒu (大有); when the first line and the top line are exchanged, they become Bo (剥) and Guai (夬). The term "initial line to second line" refers to moving the first line to the second position and exchanging the two lines, and so on with the rest.

二陰二陽之卦各九，皆自臨、遯而變。臨、遯：升（初之三）、無妄（初之三）；解（初之四）、家人（初之四）；坎（初之五）、離（初之五）；蒙（初之上）、革（初之上）；明夷（二之三）、訟（二之三）；震（二之四）、巽（二之四）；屯（二之五）、鼎（二之五）；頤（二之上）、大過（二之上）。

The second category: the hexagrams with two yang lines and those with two yin lines each have nine hexagrams, all derived from the hexagrams 临 (Qin, Approaching) and 遯 (Run, Retreating). Taking 临 and 遯 as the base hexagrams, the lines are exchanged as follows: exchanging the first and third lines, 临 becomes 升 (Sheng, Ascending) and 遯 becomes 无妄 (Wuwang, No Pretense); exchanging the first and fourth lines, they become 解 (Jie, Resolution) and 家人 (Jia Ren, Family); exchanging the first and fifth lines, they become 坎 (Kan, Water) and 离 (Li, Fire); exchanging the first and sixth lines, they become 蒙 (Meng, Innocence) and 革 (Ge, Revolution); exchanging the second and third lines, they become 明夷 (Mingyi, Bright Abode) and 讼 (Song, Litigation); exchanging the second and fourth lines, they become 震 (Zhen, Thunder) and 巽 (Xun, Wind); exchanging the second and fifth lines, they become 屯 (Zun, Obstruction) and 鼎 (Ding, Cauldron); exchanging the second and sixth lines, they become 颐 (Yi, Nourishment) and 大过 (Da Guo, Great Excess). Including the original hexagrams 临 and 遯 themselves, each forms a total of nine hexagrams.

三陰三陽之卦各十，皆自泰、否而變。泰、否：恆（初之四）、益（初之四）；井（初之五）、噬嗑（初之五）；蠱（初之上）、隨（初之上）；豐（二之四）、渙（二之四）；既濟（二之五）、未濟（二之五）；賁（二之上）、困（二之上）；歸妹（三之四）、漸（三之四）；節（三之五）、旅（三之五）；損（三之上）、咸（三之上）。

The third category: the three yang hexagrams and the three yin hexagrams each have ten hexagrams, all derived from the hexagrams of Tai (three yang below) and Po (three yin below). Taking Tai and Po as the main hexagrams, the first and fourth lines are exchanged to produce the hexagrams of Heng and Heng; the first and fifth lines are exchanged to produce the hexagrams of Jing and Shihe; the first and sixth lines are exchanged to produce the hexagrams of Gu and Sui; the second and fourth lines are exchanged to produce the hexagrams of Feng and Huan; the second and fifth lines are exchanged to produce the hexagrams of Ji Ji and Wei Ji; the second and sixth lines are exchanged to produce the hexagrams of Ben and Kun; the third and fourth lines are exchanged to produce the hexagrams of Gui Mei and Zhen; the third and fifth lines are exchanged to produce the hexagrams of Jie and Lu; the third and sixth lines are exchanged to produce the hexagrams of Shen and Xian. Combined with the original hexagrams of Tai and Po, each forms a total of ten hexagrams.

四陰四陽之卦各九，皆自大壯、觀而變。大壯、觀：重大過（初之五）、重頤（初之五）；重鼎（初之上）、重屯（初之上）；重革（二之五）、重蒙（二之五）；重離（初之上）、重坎（二之上）；兌（三之五）、艮（三之五）；睽（三之上）、蹇（三之上）；需（四之五）、晉（四之五）；大畜（四之上）、萃（四之上）。

The fourth category: the four yang trigrams and the four yin trigrams each have nine variations, all derived from the trigrams 《大壮》 (Great Strength) and 《观》 (Observation). Using 《大壮》 and 《观》 as the main trigrams for transformation: exchanging the first and fifth lines produces 《大过》 (Great Excess) and 《颐》 (Nourishment); exchanging the first and top lines produces 《鼎》 (Vessel) and 《屯》 (Initiation); exchanging the second and fifth lines produces 《革》 (Change) and 《蒙》 (Obstinacy); further transformation produces 《离》 (Fire) and 《坎》 (Water); exchanging the third and fifth lines produces 《兑》 (Lake) and 《艮》 (Mountain); exchanging the third and top lines produces 《睽》 (Strife) and 《蹇》 (Obstruction); exchanging the fourth and fifth lines produces 《需》 (Necessity) and 《晋》 (Progress); exchanging the fourth and top lines produces 《大畜》 (Great Accumulation) and 《萃》 (Gathering). Any trigram marked with the character 「重」 indicates that these trigrams have already appeared in the category of two yin and two yang, and are therefore listed again here.

變例之卦二：中孚、小過。凡變卦皆從乾坤來：乾、坤。

There are two other hexagrams that belong to special cases: Zhongfou and Xiaoguo. They cannot be derived by the usual method of moving a single line, and thus require separate rules. In the end, all transformed hexagrams originate from Qian and Kun, so the diagram ultimately traces back to Qian and Kun as its fundamental sources.

黃氏《象數論》曰：古之言卦變者莫備於虞仲翔，其法以兩爻相易，主變動者止一爻。四陰四陽即二陰二陽之卦也，其變不收於臨遯之下者，以用臨遯生卦，則主變須二爻皆動而後餘卦可盡，不得不別起觀、壯。有四陰四陽而不用五陰五陽之夬、剝者，以五陰五陽之卦已盡於姤、復，無所俟乎此也。

Huang Zongxi in his "Discussion on the Imagery and Numerical Calculations of the Book of Changes" said that ancient people discussed the transformation of hexagrams, and none explained it more thoroughly than Yu Fan. His method was to exchange the positions of two lines, but the actual dominant line causing the change was only one. A hexagram with four yin lines and four yang lines is essentially the same as a hexagram with two yin lines and two yang lines, since they are just viewed from the perspective of yin and yang. They are not included under the names of "Guan" and "Dun" because if one uses "Guan" and "Dun" to generate new hexagrams, the main changing line would have to move together with another line, which would be insufficient to generate all the other hexagrams. Therefore, it was necessary to establish the hexagrams "Guan" and "Da Zhuang" as starting points. Since there are hexagrams categorized as four yin and four yang, but there are no hexagrams for five yin and five yang such as "Guai" and "Bo," it is because the hexagrams with five yin and five yang have already been fully covered under the names "Gou" and "Fu," so there is no need to establish them separately.

中孚、小過為變例之卦，何也？中孚從二陰之卦，則遯之二陰皆易位；從四陰之卦，則大壯三四一時俱上。小過從二陽之卦，則臨之二陽皆易位；從四陰之卦，則觀三四一時俱上。所謂主變之卦以一爻升降者，至此而窮，故變例也，猶反對之卦至乾坤坎離頤大過中孚小過而亦窮也。虞氏之卦變脈絡分明如此。當時所著《周易注》《周易集林》今既不傳，其見於李鼎祚《易解》中者語焉不詳，朱漢上據之以定虞氏卦變，遂有此然彼否之異，無怪趙汝楳謂其錯雜無統也。某追尋其緒，而後知漢上之誤。

Why are the hexagrams Zhongfu and Xiaoguo set up as special cases? If Zhongfu is classified as a hexagram with two yin lines, then both yin lines of Dun would have to move simultaneously; if it is classified as a hexagram with four yin lines, then the third and fourth lines of Dazhuang would have to move upward together. If Xiaoguo is classified as a hexagram with two yang lines, then both yang lines of Lin would have to move simultaneously; if it is classified as a hexagram with four yin lines, then the third and fourth lines of Guan would have to move upward together. The general rule of changing one line up or down is exhausted here, so it is necessary to establish special cases. This is similar to the method of opposing hexagrams, which is exhausted in the eight trigrams: Qian, Kun, Kan, Li, Yi, Da Guo, Zhongfu, and Xiaoguo. Yu Fan's theory of hexagram transformation was originally clear and distinct. Unfortunately, his works, the Zhouyi Zhushu and Zhouyi Jilin, are no longer available, and the version preserved in Li Dingzuo's Zhouyi Jiejie is vague and unclear. Zhu Zhen used this to establish the system of Yu's hexagram transformation, leading to contradictions and inconsistencies. It is no wonder that Zhao Ru Mei criticized it as being disorderly and lacking unity. By tracing its origins, I have come to realize that the error lies with Zhu Zhen.

然四陰四陽與二陰二陽畢竟相錯，不能不有重出之卦。此八卦者（重於大壯者為大過、鼎、革、離，重於觀者為頤、屯、蒙、坎），其主變屬之臨遯乎？屬之大壯觀乎？抑兼屬之乎？其說有時而窮也。以《彖傳》證之，如無妄之「剛自外來」（遯之初三相易，皆在內卦，非外來），晉之「柔進上行」（觀之四五相易，皆在上卦），暌之「柔進上行」（大壯三上相易，柔為下行），蹇之「徃得中」（觀三上相易，不得為中），皆不能合，此虞氏之短也。

However, the categories of four yin and four yang, and two yin and two yang, inevitably intertwine, leading to repeated hexagrams. These eight repeated hexagrams (those repeated under the hexagram of Great Strength are Great Excess, Cauldron, Revolution, and Fire; those repeated under the hexagram of Observing are Nourishment, Initial, Childhood, and Water), to which their primary and transformed hexagrams should belong—should they belong to the hexagrams of Approaching and Retreat, or to Great Strength and Observing, or both? This is not coherent. Let us now verify with the Commentary on the Judgment: The hexagram of No False Movement says "Yang comes from outside" (according to Yu's interpretation, it is the first and third lines of Retreat hexagram exchanged, both lines being in the inner trigram, not coming from the outer trigram). The hexagram of Progress says "Yin advances upward" (it is the fourth and fifth lines of Observing hexagram exchanged, both lines being in the upper trigram, so "advancing" does not apply). The hexagram of Estrangement says "Yin advances upward" (it is the third and top lines of Great Strength hexagram exchanged, but Yin actually moves downward). The hexagram of Obstruction says "Going to obtain the center" (it is the third and top lines of Observing hexagram exchanged, but the center position is not obtained)—all of these do not match, which reveals the weakness of Yu's theory of hexagram transformation.

蘇子瞻言剛柔相易皆本諸乾坤，程子亦專以乾坤言卦變，本之蜀才曰「此本乾卦」「此本坤卦」，荀爽曰「謙是乾來之坤」，非創論也。但三陰三陽之卦此往彼來顯然可見，其它則來者不知何來，徃者不知何往。如無妄「剛自外來」，外卦之乾未嘗損一剛也，而云自外來，不已背乎？故朱子曰：程子専以乾坤言卦變，然只是上下兩體皆變者可通，若只一體變者則不通。蓋已深中其病矣，然較之虞氏而下鑿空為說者，某以為獨優也。

Su Shi said that the mutual transformation of yin and yang is based on Qian and Kun, and Cheng Yi also specialized in explaining hexagram changes through Qian and Kun; this originates from Su Cai's statement 'this hexagram originally comes from Qian' and 'this hexagram originally comes from Kun,' as well as Xun Shuang's statement 'the hexagram of Qian is the yang line coming to Kun.' This is not their original idea. However, for hexagrams with three yin and three yang lines, it is clearly visible which line moves and which line comes; for other hexagrams, it is unclear where the coming line comes from or where the going line goes. For example, the hexagram Wuwang says 'yang comes from outside,' but the outer trigram Qian remains unchanged with no reduction of a yang line, yet it says yang comes from outside, which is not self-contradictory? Therefore Zhu Xi said: Chengzi specialized in explaining hexagram changes through Qian and Kun, but only when both upper and lower trigrams change does his explanation make sense; if only one trigram changes, it does not make sense. This has already pointed out the flaw. However, compared to those who made up theories like Yu Fan and others, I (Huang Zongxi) think Chengzi's theory is still the best.

右論虞氏卦變。

The previous section examines the theory of changing hexagrams in Yu Fan's school and its merits and drawbacks.

乾坤二卦為易之門、萬物之祖圖第一（舊本曰功成無為圖）：乾，老陽；坤，老陰。乾坤相索三變六卦不反對圖第二：（坤體而乾來交）頤、小過、坎；（乾體而坤來交）大過、中孚、離。

Li Zhi Cai's "Diagram of Opposing Changes" first diagram is titled "Diagram of the Two Trigrams Qian and Kun as the Gate of the Book of Changes and the Ancestral Root of All Things" (old editions title it "Diagram of Achieving Success Without Action"): Qian is the old yang, and Kun is the old yin. The second diagram is titled "Diagram of Qian and Kun Seeking Each Other, Resulting in Six Hexagrams Without Opposition": those hexagrams formed by the interaction of Qian lines with the body of Kun are Yi, Xiao Guo, and Kan; those formed by the interaction of Kun lines with the body of Qian are Da Guo, Zhong Fu, and Li. These six hexagrams together with Qian and Kun, when reversed, still form the original hexagram, hence called "without opposition."

乾卦一陰下生反對變六卦圖第三：姤、同人、履；夬、大有、小畜。坤卦一陽下生反對變六卦圖第四：復、師、謙；剝、比、豫。

The third diagram is titled "Diagram of the Qian Trigram with One Yin Line Below Producing the Opposite and Transforming Six Trigrams": Below the Qian trigram, a yin line arises to form the Gou trigram. The yin line then ascends successively to become Tongren and Lü. The trigrams opposing these three trigrams (by inversion) are Guai, Dayou, and Xiaoxu. The fourth diagram is titled "Diagram of the Kun Trigram with One Yang Line Below Producing the Opposite and Transforming Six Trigrams": Below the Kun trigram, a yang line arises to form the Fu trigram. The yang line then ascends successively to become Shi and Qian. The trigrams opposing these three trigrams are Po, Bi, and Yu.

乾卦下生二陰各六變反對變十二卦圖第五：遯、訟、旡妄；大畜、需、大壯；暌、兌、革；家人、巽、鼎。坤卦下生二陽各六變反對變十二卦圖第六：臨、明夷、升；觀、晉、萃；蹇、艮、蒙；解、震、屯。

The fifth diagram is titled "Diagram of the Lower Generation of Two Yins from the Qian Trigram, Changing Six Times to Oppose and Transform into Twelve Trigrams": From the Qian Trigram, two yin lines are generated below, forming the Duan Trigram. It then successively transforms into the Song Trigram, the Wuwang Trigram (the original text reads "旡妄," where "旡" is an alternative character for "无," meaning "no"), and its opposing trigrams are the Da Xu Trigram, the Xu Trigram, and the Da Zhuang Trigram. Further transformation leads to the Kui Trigram (original text reads "暌"), the Dui Trigram, and the Ge Trigram, with opposing trigrams being the Jia Shen Trigram, the Xun Trigram, and the Ding Trigram. The sixth diagram is titled "Diagram of the Lower Generation of Two Yangs from the Kun Trigram, Changing Six Times to Oppose and Transform into Twelve Trigrams": From the Kun Trigram, two yang lines are generated below, forming the Lin Trigram. It then successively transforms into the Mingyi Trigram and the Sheng Trigram. Its opposing trigrams are the Guan Trigram, the Jin Trigram, and the Cui Trigram. Further transformation leads to the Jian Trigram, the Gen Trigram, and the Meng Trigram, with opposing trigrams being the Jie Trigram, the Zhen Trigram, and the Tun Trigram.

乾卦下生三陰各六變反對變十二卦圖第七：否、恆、豐；泰、咸、旅；歸妹、節、既濟；漸、渙、未濟。坤卦下生三陽各六變反對變十二卦圖第八：泰、損、賁；否、益、嗑噬；蠱、井、未濟；隨、困、既濟。

The seventh diagram is titled "Diagram of the Lower Trigram Qian Generating Three Yin Lines, Each Changing Six Times and Opposing to Form Twelve Diagrams": Below the trigram Qian, three yin lines are generated to form the trigram Pu, which successively changes to Heng and Feng. Opposed to these are Tai, Xian, and Lu. Further changes result in Gui Mei, Jie, and Ji Ji, with their opposites being Zhen, Hun, and Wei Ji. The eighth diagram is titled "Diagram of the Lower Trigram Kun Generating Three Yang Lines, Each Changing Six Times and Opposing to Form Twelve Diagrams": Below the trigram Kun, three yang lines are generated to form the trigram Tai, which successively changes to Shen and Ben. Opposed to these are Pu, Yi, and Shi He (the characters "Keh Shi" are reversed in the original text). Further changes result in Gu, Jing, and Wei Ji, with their opposites being Sui, Kun, and Ji Ji.

林氏《易裨傳》外篇曰：李挺之變卦反對圖八篇、六十四卦相生圖一篇，漢上朱氏以為康節之子伯溫傳之於河陽陳四丈，陳傳之於挺之。長楊郭氏序李氏象學先天卦變曰：陳圖南以授穆伯長，伯長以授李挺之，挺之以授邵堯夫、陳安民，安民以授兼山。卦變一義，橫渠、伊川罕言，而兼山獨得之。康節本為先天易學，而《觀物外篇》亦曰：體者八變，用者六變，是以八卦之象不易者四、反易者二，以六變而成八也（不易者四，謂乾坤坎離也；變易者二，謂震艮巽兌也）。重卦之後，不易者八，反覆者二十八（不易者乾坤坎離頤小過中孚大過，變易者二十八，餘五十六卦也），以三十六變而成六十四也。

Lin Zhi's "Easy Transmission · Outer Chapter" says: Li Zhi Cai's eight chapters on "The Diagram of Changing Hexagrams" and one chapter on "The Diagram of Mutual Generation of the Sixty-Four Hexagrams" were considered by Zhu Zhen's "Han Shang Yi Zhuan" to have been passed down by Shao Boyun, the son of Shao Yong, to He Yang Chen Sizhang, who then passed them to Li Tingzhi. A family named Guo from Changyang wrote a preface for Li's "Xiang Xue," discussing the transmission of the earlier heaven hexagram changes: Chen Tuan (Tuan Nan) passed them to Mu Xiu (Bochang), who passed them to Li Tingzhi, who then passed them to Shao Yong (Yaofu) and Chen Anmin, and Chen Anmin passed them to Jianshan Guo Zhongxiao. The principle of hexagram changes was rarely discussed by Zhang Zai (Hengqu) and Cheng Yi (Yichuan), but Jianshan Guo Zhongxiao alone received the true transmission. Shao Yong originally studied earlier heaven Yi, but in his "Guanwu Waiwen," he also said: the body has eight changes, and the use has six changes. Therefore, among the eight trigrams, four cannot change, and two groups can be reversed. By using six changes, the eight trigrams are formed. After the eight trigrams are overlapped, eight cannot change, and twenty-eight pairs can be reversed. The eight that cannot change are Qian, Kun, Kan, Li, Yi, Xiao Guo, Zhong Fu, and Da Guo. The twenty-eight pairs that can be reversed are the remaining fifty-six hexagrams paired two by two. In total, thirty-six changes form the sixty-four hexagrams.

又曰：乾坤之位可易也，坎離名可易而位不可易也，震巽位可易而名不可易也，兌與艮名位皆可易也。離肖乾，坎肖坤，中孚肖乾，頤肖離，小過肖坤，大過肖坎，是以乾坤坎離中孚頤大小過皆不可易也。

Shao Yong also said: The positions of the Qian and Kun trigrams can be exchanged. The names of the Kan and Li trigrams can be exchanged, but their positions cannot. The positions of the Zhen and Xun trigrams can be exchanged, but their names cannot. The names and positions of the Dui and Gen trigrams can both be exchanged. The form of Li resembles Qian, and the form of Kan resembles Kun. The hexagram Zhongfou resembles Qian, the hexagram Yi resembles Li, the hexagram Xiaoguo resembles Kun, and the hexagram Daguo resembles Kan. Therefore, the eight hexagrams Qian, Kun, Kan, Li, Zhongfou, Yi, Daguo, and Xiaoguo cannot be reversed or exchanged.

又曰：卦之反對皆六陽六陰也。在易則六陽六陰者十有二對也，去四正則八陽四陰、八陰四陽者各六對也，十陽二陰、十陰二陽者各三對也（此以三陰三陽為主而變也。六陰六陽十二對者，否變泰、咸、恆、豐、旅、漸、歸妹、渙、節、既濟、未濟六對；四正，初經則乾坤坎離，重卦則頤、中孚、大過、小過。八陽四陰、八陰四陽各六對者，遯變大壯、需、訟、無妄、大畜、暌、家人、兌、革六對，臨變觀、明夷、晉、升、萃、蹇、解、艮、震、蒙、屯六對。十陽二陰、十陰二陽各三對者，姤變夬、同人、大有、履、小畜三對，復變剝、師、比、謙、豫三對，凡五十六也。而此有三十對者，否泰司啟閉之節，既濟未濟當四隅之位，所以重用一卦）。

Shao Yong also said: the opposition of hexagrams, when viewed together, are all six yang and six yin. In the Book of Changes, within a pair, there are twelve pairs of six yang and six yin; excluding the four cardinal hexagrams, there are six pairs each of eight yang and four yin, and eight yin and four yang. There are three pairs each of ten yang and two yin, and ten yin and two yang. (This is based on the transformation of hexagrams with three yin and three yang.) The twelve pairs of six yin and six yang refer to the series of the hexagram of 'Obstruction' (否) producing 'Great Crossing' (泰), 'Salutation' (咸), 'Permanence' (恒), 'Brightness' (丰), 'Travel' (旅), 'Gradual Progress' (渐), 'Return of the Wife' (归妹), 'Dispersal' (涣), 'Restraint' (节), 'Final Completion' (既济), and 'Final Non-Completion' (未济), totaling six pairs. The four cardinal hexagrams, in the case of three lines, are Qian, Kun, Kan, and Li; in the case of six lines, they are 'Nourishment' (颐), 'Middle Trust' (中孚), 'Great Excess' (大过), and 'Small Excess' (小过). The six pairs each of eight yang and four yin, and eight yin and four yang refer to the series of 'Retreating' (遯) producing 'Great Strength' (大壮), 'Need' (需), 'Contention' (讼), 'No Expectation' (无妄), 'Great Accumulation' (大畜), 'Strife' (睽), 'Family' (家人), 'Lake' (兑), 'Change' (革), totaling six pairs; and the series of 'Approaching' (临) producing 'Observation' (观), 'Darkness' (明夷), 'Advance' (晋), 'Rise' (升), 'Convergence' (萃), 'Obstruction' (蹇), 'Resolution' (解), 'Mountain' (艮), 'Thunder' (震), 'Ignorance' (蒙), 'Initiation' (屯), totaling six pairs. The three pairs each of ten yang and two yin, and ten yin and two yang refer to the series of 'Meeting' (姤) producing 'Decisive Action' (夬), 'Harmony' (同人), 'Great Possession' (大有), 'Footsteps' (履), 'Small Accumulation' (小畜), totaling three pairs; and the series of 'Reversion' (复) producing 'Decay' (剥), 'Military' (师), 'Comparison' (比), 'Humility' (谦), 'Joy' (豫), totaling three pairs. In total, there are fifty-six hexagrams. Here only thirty pairs are listed, because 'Obstruction' (否) and 'Great Crossing' (泰) govern the closing and opening of seasons, and 'Final Completion' (既济) and 'Final Non-Completion' (未济) are at the four corners, so some hexagrams are used twice.

乾坤本也，坎離用也，乾坤坎離上篇之用也；咸兌艮也，恆震巽也，兌艮震巽下篇之用也；頤大過小過中孚，二篇之正也。故曰：至哉，文王之作易，其得天地之用乎！大抵卦變八圖，陽在下者以升為變，在上者以降為變，故升降之對，此為升則彼為降，此為降則彼為升。

Heaven and Earth are the fundamental principles, while Water and Fire represent their functions. Heaven, Earth, Water, and Fire are the key elements of the Upper Classic. The Hexagram Xian is composed of Dui and Gen, and the Hexagram Heng is composed of Zhen and Xun. Dui, Gen, Zhen, and Xun are the functional elements of the Lower Classic. The Hexagrams Yi, Da Guo, Xiao Guo, and Zhong Fu represent the main forms of both the Upper and Lower Classics. Therefore, it is said: How great is King Wen's creation of the Book of Changes! He must have grasped the functions of Heaven and Earth. In general, the rule for the eight trigrams is: if a yang line is in the lower position, it changes by rising; if a yang line is in the upper position, it changes by descending. Therefore, a pair of opposing hexagrams, one is rising, the other is descending; one is descending, the other is rising.

然康節先天之學不泥書言，而猶有卦變之說，何邪？曰：大易之道，本之氣數之自然，觀先天圖則可知出生之統體矣。今六十四卦兩兩相比，若近於反對者，觀序卦之先後皆有深意，要非三陰三陽反對不反對雲者。近世復有上經三十卦、下經三十四卦反對不反對，皆本八卦以求合於十有八變者，其巧愈甚矣。要之卦變之義，易之一端耳，若以為易道盡於是，要非康節所以望後世者，姑錄之以為外篇之首。

Someone asked: Shao Yong's study of the Earlier Heaven does not rely on words, so why does it still retain the concept of changing trigrams? The answer is: The great way of the Book of Changes is based on the natural flow of qi and numbers. By looking at the Earlier Heaven diagram, one can understand the overall generation of all things. Now, the sixty-four trigrams are arranged in pairs next to each other, appearing somewhat like 'opposites'. But if we examine the order of the sequence of trigrams, there is deep meaning within, not merely about three yin and three yang, or opposition and non-opposition. In recent times, some people have tried to reduce the opposition and non-opposition of the upper and lower parts of the Book of Changes to the eight trigrams, in order to conform to the number of 'eighteen changes'. This is even more of a forced interpretation. In summary, the meaning of changing trigrams is only one aspect of the Book of Changes. If one thinks that the way of the Book of Changes lies entirely in this, then perhaps this is not what Shao Yong intended for later generations. Let us merely record this here as the beginning of the 'Outer Treatise'.

顧氏《日知録》曰：卦變之說不始於孔子，周公繫損之六三已言之矣，曰「三人行則損一人，一人行則得其友」，是六子之變皆出於乾坤，無所謂自復、姤、臨、遯而來者，當從《程傳》（蘇軾、王炎皆同此說）。

Gu Yanwu's "Rizhilu" says that the theory of changing hexagrams was not started from Confucius. When the Duke of Zhou explained the "Xin" hexagram's sixth line in the third position, he already mentioned it, saying, "When three people walk together, one should be reduced; when one walks alone, he will find a companion." This shows that the changes of the six subsidiary hexagrams all originate from Qian and Kun, and there is no idea that they come from Fu, Gu, Lin, or Duan. Therefore, we should follow Cheng Yi's explanation in his "Yi Zhuan" (Su Shi and Wang Yan hold the same view).

黃氏《象數論》曰：虞仲翔之釋比曰「師二上之五得位」，蜀才曰「此本師卦，六五降二，九二升五」，亦已發其端矣，特未以此通之於別卦也。至李挺之所傳變卦反對圖，可謂獨得其真，而又與六十四卦相生圖並出，則擇焉而不精也。其後來知徳頗以此說變，而以反對者為綜，竒偶相反者為錯，於頤、過八卦相反之外，取反對者而亦復錯之，不知竒偶相反之中暗寓反對，非別出一義也。若又有相反一義，何以卦爻略不之及乎？為卦爻之所不及者，可以無待於補矣。

Huang Zongxi's "Discussion on the Imagery and Numerical Calculations of the Book of Changes" says that Yu Fan explained the "Comparison" hexagram by saying, "The second line of the 'Army' hexagram moves up to the fifth position and thus attains the correct position." Shu Cai said, "This hexagram originally comes from the 'Army' hexagram, with the sixth line moving down to the second position and the ninth line moving up to the fifth position." This already initiated the idea of opposing interpretations, but it was not extended to other hexagrams. Until Li Zhishi's "Diagram of Opposing and Transforming Hexagrams," one could say he truly grasped the essence of this concept. Unfortunately, he also simultaneously presented a "Diagram of Mutual Generation of the Sixty-Four Hexagrams," which shows that his selection was not sufficiently refined. Later, Lai Zhide extensively adopted this view in discussing transformation, calling those that are oppositely inverted "zong," and those with entirely opposite even and odd lines "cuo." In addition to the eight hexagrams that are oppositely related, he further reversed those that were already oppositely related, yet he did not realize that the opposite relationship is already implicitly contained within the opposite of even and odd lines, and is not a separate principle. If there were indeed another meaning of "opposite," why do the hexagram statements and line statements never mention it? Since it is not addressed in the hexagram and line statements, there is no need to supplement it.

（渭按：大傳「參伍以變，錯綜其數」，主蓍策而言，來氏斷章取義為錯綜圖，殊非經旨。其說以為一左一右曰錯，一上一下曰綜。錯本圓圖，自乾坤至復姤凡六十四；綜本序卦，自屯蒙至既濟未濟凡二十八。此圖於經無所用，故後不復著。）

(Hu Wei's commentary: The "Great Treatise" says "by combining three and five, the changes are made, and the numbers are interwoven," which originally refers to the process of divining with yarrow stalks. Lai Zhide took this passage out of context and used it to create the "Interwoven Diagram." This approach is not in line with the original meaning of the classic text. His explanation is that one on the left and one on the right is called "错" (interweaving), and one above and one below is called "综" (summing up). "错" is based on Fuxi's circular diagram, arranging from Qian and Kun to Fu and Guo, making up the sixty-four hexagrams; "综" is based on the "Order of Hexagrams" passage, arranging from Tun and Meng to Ji Ji and Wei Ji, making up twenty-eight pairs. This diagram is of no use in interpreting the classics, so it is not included in the following text.)

按：六十四卦兩兩相比，無不反對，其陰陽相背者八卦，雖無變體，亦反對也。反對實文王演卦之一義，《彖傳》本此以釋經，剛柔之往來上下一覽而得，不可謂孔子之說非文王之說也。李氏反對圖首列乾坤二卦為易之門，則諸卦宜皆出於乾坤，而乃乾坤下生之卦，一陰生自姤，一陽生自復，二陰生自遯，二陽生自臨，三陰生自否，三陽生自泰，何其紛糾之甚也！

Hu Wei remarked: The sixty-four hexagrams are arranged in pairs adjacent to each other, and there is no pair that is not opposite (inverted); among them, the eight hexagrams whose yin and yang are completely opposite, although their hexagram forms remain unchanged when inverted, they are still considered opposite in terms of their odd and even opposites. Opposites are indeed one of the meanings of King Wen's hexagram arrangement. The Commentary on the Judgment bases its interpretation on this principle, and the movement and interaction of firm and yielding elements can be clearly seen. It cannot be said that Confucius's explanation is not in line with King Wen's. Li Zhicai's diagram of opposites begins with the hexagrams Qian and Kun as the gateways of the Book of Changes, so all hexagrams should be derived from Qian and Kun. However, the hexagrams he refers to as being generated from Qian and Kun are: the hexagram of one yin is derived from Gou, the hexagram of one yang is derived from Fu, the hexagram of two yins is derived from Duan, the hexagram of two yangs is derived from Lin, the hexagram of three yins is derived from Pí, and the hexagram of three yangs is derived from Tai. How chaotic this becomes!

康節親受此圖，故有乾坤大父母、姤復小父母之說。夫乾坤生六子是為八卦，因而重之遂為六十四，六十四卦皆乾坤之所生也。姤、復、遯、臨、否、泰同在六十四卦之中，安能生諸卦乎？然姤復以一爻升降，其蹤跡猶可尋求；遯臨否泰則兩三爻遞為升降，而否泰、二濟未免重出，益雜亂而無章矣。乾坤雖諸卦所自出，第以《象傳》證之，則唯三陰三陽者可通，而二陰二陽者不可通，不如専主反對之為得也。

Shao Yong personally received the transmission of this diagram, so there is the saying "Qian and Kun are the great parents, while Gou and Fu are the small parents." Qian and Kun give rise to six sons, which are the Eight Trigrams. The Eight Trigrams, when paired two by two, form the sixty-four hexagrams, and all sixty-four hexagrams are generated from Qian and Kun. Gou, Fu, Duan, Lin, Pǐ, and Tai are also among the sixty-four hexagrams; how can they then give rise to the other hexagrams? However, Gou and Fu only involve a single line moving up or down, so their origins can still be traced. Duan, Lin, Pǐ, and Tai, on the other hand, require several lines to move up and down in turn, and Pǐ, Tai, Ji Ji, and Wei Ji inevitably involve repeated lines, making their origins even more chaotic. Although Qian and Kun are indeed the sources of all hexagrams, when verified by the Yi Jing, only the hexagrams with three yin and three yang lines make sense, while those with two yin and two yang lines do not. In the end, it is still more appropriate to focus on the concept of "opposition."

康節以文王所演為後天，則卦變似非先天之學。然其論卦之反對曰：乾坤本也，坎離用也，乾坤坎離上篇之用也；咸兌艮也，恆震巽也，兌艮震巽下篇之用也。此即《參同契》以乾坤坎離牝牡震巽艮兌之意；而乾坤大父母、姤復小父母，則又圓圖陽生子中、陰生午中之精義也。乃知卦變亦希夷所傳，均屬先天之學，故朱子附列於邵子六圖之後雲。

Shao Yong regarded the hexagrams derived by King Wen as Later Heaven, so the transformation of hexagrams seems not to belong to the Earlier Heaven school. However, when he discussed the opposition of hexagrams, he said: Qian and Kun are the origin, Kan and Li are the function; Qian, Kun, Kan, and Li represent the functions of the Upper Canon. The hexagram Xian is composed of Dui and Gen, and the hexagram Heng is composed of Zhen and Xun; Dui, Gen, Zhen, and Xun represent the functions of the Lower Canon. This is exactly the intention of the "Zhou Yi Cang Tong Qi" which uses Qian, Kun, Kan, and Li as furnace and cauldron, and uses Zhen, Xun, Gen, and Dui to distinguish yin and yang. Moreover, "Qian and Kun are the great parents, Guo and Fu are the small parents," which is precisely the essence of the Earlier Heaven circle diagram "Yang is born in the middle of Zi, Yin is born in the middle of Wu." From this we can know that the transformation of hexagrams also belongs to the tradition of Chen Tuan (Xiyi), and thus is part of the Earlier Heaven school. Therefore, Zhu Xi included it after Shao Yong's six diagrams.

（乾坤者，諸卦之祖）姤，乾一交而為姤；復，坤一交而為復。凡卦一陰五陽者皆自復卦而來，復一爻五變而成五卦：師、謙、豫；比、剝。凡卦五陽一陰者皆自姤卦而來，姤一爻五變而成五卦：同人、履、小畜；大有、夬。

Li Zhicai's "Diagram of Mutual Generation of the Sixty-Four Hexagrams": (The hexagrams Qian and Kun are the ancestors of all other hexagrams.) The hexagram Gou is formed by the initial interaction between Qian and Kun; the hexagram Fu is formed by the initial interaction between Kun and Qian. All hexagrams with one yin line and five yang lines originate from Fu. The line of Fu rises step by step, changing five times to form five hexagrams: Shi, Qian, Yu, Bi, and Bo (the heading here does not match the listed hexagrams; the listed hexagrams are actually those with one yang line and five yin lines, so it should be a mistake and should read "one yang line and five yin lines"). All hexagrams with five yang lines and one yin line originate from Gou. The yin line of Gou rises step by step, changing five times to form five hexagrams: Tongren, Lü, Xiaoxu, Dàyǒu, and Guai.

遯，乾再交而為遯；臨，坤再交而為臨。凡卦四陰二陽者皆自臨卦而來，臨五復五變而成十四卦：（第一四變）明夷、震、屯、頤；（第二復四變）升、解、坎、蒙；（第三復三變）小過、萃、觀；（第四復二變）蹇、晉；（第五復一變）艮。凡卦四陽二陰者皆自遯卦而來，遯五復五變而成十四卦：（第一四變）訟、巽、鼎、大過；（第二復四變）無妄、家人、離、革；（第三復三變）中孚、大畜、大壯；（第四復二變）睽、需；（第五復一變）兌。

The hexagram "Dun" is formed by the second intersection of Qian and Kun; the hexagram "Lin" is formed by the second intersection of Kun and Qian. All hexagrams with four yin lines and two yang lines originate from "Lin." "Lin" undergoes five cycles of transformation, with each cycle generating further changes, resulting in fourteen hexagrams: in the first cycle, four transformations produce "Mingyi," "Zhen," "Zun," and "Yi"; in the second cycle, four more transformations produce "Sheng," "Jie," "Kan," and "Meng"; in the third cycle, three transformations produce "Xiao Guo," "Cui," and "Guan"; in the fourth cycle, two transformations produce "Jian" and "Jin"; and in the fifth cycle, one transformation produces "Gen." All hexagrams with four yang lines and two yin lines originate from "Dun." "Dun" also undergoes five cycles of transformation to generate fourteen hexagrams: in the first cycle, four transformations produce "Song," "Xun," "Ding," and "Da Guo"; in the second cycle, four more transformations produce "Wu Wang," "Jia Ren," "Li," and "Ge"; in the third cycle, three transformations produce "Zhong Fu," "Da Xu," and "Da Zhuang"; in the fourth cycle, two transformations produce "Kui" and "Xu"; and in the fifth cycle, one transformation produces "Dui."

否，乾三交而為否；泰，坤三交而為泰。凡卦三陰三陽者皆自泰卦而來，泰三復三變而成九卦：（第一三變）歸妹、節、損；（第二復三變）豐、既濟、賁；（第三復三變）恆、井、蠱。凡卦三陽三陰者皆自否卦而來，否三復三變而成九卦：（第一三變）漸、旅、咸；（第二復三變）渙、未濟、困；（第三復三變）益、噬嗑、隨。

The hexagram "否" is formed by the third intersection of Qian and Kun; the hexagram "泰" is formed by the third intersection of Kun and Qian. All hexagrams with three yin and three yang lines originate from the hexagram "泰." The hexagram "泰" undergoes three cycles of transformation, each cycle involving three changes, resulting in nine hexagrams: in the first cycle, three changes produce "归妹," "节," and "损"; in the second cycle, three further changes produce "丰," "既济," and "贲"; in the third cycle, three more changes produce "恒," "井," and "蛊." Similarly, all hexagrams with three yang and three yin lines originate from the hexagram "否," which also undergoes three cycles of three changes each, producing nine hexagrams: in the first cycle, three changes produce "渐," "旅," and "咸"; in the second cycle, three further changes produce "涣," "未济," and "困"; in the third cycle, three more changes produce "益," "噬嗑," and "随." This shows that the mutual generation diagram specifically takes the change of one line in the lower trigram, while the opposite diagram involves changes in both the upper and lower trigrams.

林氏《易裨傳》外篇曰：李挺之六十四卦相生圖，其傳授見於反對圖中。漢上朱氏曰：始虞氏卦變，乾坤生坎離，乾息而生復、臨、泰、大壯、夬，坤消而生姤、遯、否、觀、剝。自復來者一卦（豫），自明夷來者四卦（明夷、解、升、震），自泰來者九卦（蠱、賁、恆、升、井、歸妹、豐、節、既濟），自大壯來者六卦（需、大畜、大過、睽、鼎、兌），自夬來者一卦（同人），自遯來者五卦（訟、無妄、家人、革、巽），自否來者八卦（隨、噬嗑、咸、益、困、漸、渙、未濟），自觀來者五卦（晉、蹇、頤、萃、艮），自剝來者一卦（謙）。

Lin Zhi's "Easy Bi Zhuan · Outer Chapter" says: The transmission lineage of Li Zhi Cai's "Diagram of the Mutual Generation of the Sixty-Four Hexagrams" has already been mentioned in the entry on "Diagram of the Changing Hexagrams." Zhu Zhen's "Han Shang Yi Zhuan" states: At first, Yu Fan explained the changing hexagrams, where Qian and Kun generated Kan and Li. The qi of Qian, when it grows, produces the hexagrams Fu, Lin, Tai, Da Zhuang, and Gua. The qi of Kun, when it declines, produces the hexagrams Gu, Duan, Pǐ, Guan, and Po. The hexagram Yu comes from Fu, four hexagrams come from Ming Yi (Bright Abundance), nine hexagrams come from Tai, six hexagrams come from Da Zhuang, one hexagram comes from Gua, five hexagrams come from Duan, eight hexagrams come from Pǐ, five hexagrams come from Guan, and one hexagram comes from Po. This is the complete spectrum of Yu Fan's hexagram changes as compiled by Zhu Zhen.

而屯生於坎，蒙生於艮，比生於師，頤、小過生於晉，睽生於大壯或生於無妄，旅生於賁或生於噬嗑，中孚生於訟，小畜變需上，履變訟初，姤無生卦，師、比、同人、大有四卦闕。李鼎祚取蜀才、虞氏之書補其三卦（大有闕），而頤卦虞以為生於晉，侯果以為生於觀。今以此圖考之，其合於圖者三十有六卦，又時有所疑，不合者二十有八卦。

In addition, the hexagram Zhun arises from Kan, Meng from Gen, Bi from Shi, Yi and Xiao Guo from Jin, Kui is said by some to arise from Da Zhuang and by others from Wu Wang, Lu by some from Ben and by others from Shi He, Zhong Fu from Song, Xiao Xu arises from the top line of Xun, and Lu arises from the first line of Song. Guo does not arise from any other hexagram, while Shi, Bi, Tong Ren, and Da You are missing from the account. Li Dingzuo supplemented three hexagrams from Shu Cai and Yu Fan (Da You remains unexplained). Yu Fan believed Yi arises from Jin, while Hou Guo believed it arises from Guan. Now, comparing this diagram of mutual generation with the diagram, thirty-six hexagrams agree with it, while twenty-eight are sometimes doubtful and do not match.

夫自下而上謂之升，自上而下謂之降，升者生也、息也，降者消也。陰生陽，陽生陰，陰復生陽，陽復生陰，升降消息，循環無窮，然不離於乾坤：一生二，二生三，至於三極矣，故曰乾坤大父母也，姤復小父母也。嘗考之，諸儒之論相生者始於虞翻、蜀才，近世漢上朱氏用以解易。然卦之六十有四，由八卦相錯而成也，未有先有復、姤、臨、遯、泰、否而後有諸卦者。傳曰「八卦成列，象在其中矣；因而重之，爻在其中矣」，考夫震巽坎離艮兌相合而後成卦，今謂震坎艮生於臨、巽離兌生於遯，母乃顛倒而不通邪？

In general, movement from the lower to the upper is called "ascending," and movement from the upper to the lower is called "descending." Ascending means generation and increase, while descending means decline and reduction. Yin generates Yang, and Yang generates Yin; Yin again generates Yang, and Yang again generates Yin. Ascending and descending, increase and reduction, cycle endlessly, yet they never depart from Qian and Kun. One gives rise to two, two give rise to three, and when it reaches three, it reaches its limit. Therefore, Qian and Kun are called the great parents, while Guo and Fu are called the small parents. I have examined this: scholars have discussed the mutual generation of hexagrams, beginning with Yu Fan and Shu Cai, and in recent times Zhu Zhen used this to explain the Book of Changes. However, the sixty-four hexagrams are formed by the intermingling of the eight trigrams. There is no reason to believe that Fu, Guo, Lin, Duan, Tai, and Po came first, and then the other hexagrams followed. The Great Treatise says, "When the eight trigrams are arranged in order, the images are already present; when they are overlaid, the lines are already present." This shows that Zhen, Xun, Kan, Li, Gen, and Dui combine with each other to form the hexagrams. Now, however, it is said that Zhen, Kan, and Gen arise from Lin, and Xun, Li, and Dui arise from Duan. Is this not reversing cause and effect and making the explanation incoherent? In Lin Zhi's view, this is the fundamental flaw in the mutual generation diagram.

邵康節曰：無極之前，陰含陽也；有象之後，陽分陰也。陰為陽之母，陽為陰之父，故母孕長男而為復，父生長女而為姤，是以陽起於復而陰起於姤也。又曰：易始於乾坤而交於復姤，蓋剛交柔而為復，柔交剛而為姤，自此而變無窮矣。由前之說，則陽生於子、陰生於午之義也；由後之說，則十二闢卦剛柔相摩之義也。

Shao Yong said: Before the ultimate void, yin contained yang; after there was form, yang differentiated into yin. Yin is the mother of yang, and yang is the father of yin. Therefore, the mother gave birth to the eldest son to form the hexagram Fu, and the father gave birth to the eldest daughter to form the hexagram Guo. Thus, yang energy begins with Fu and yin energy begins with Guo. He also said: The Book of Changes begins with Qian and Kun, and comes together in Fu and Guo; when hardness meets softness it becomes Fu, and when softness meets hardness it becomes Guo, thus changes are endless. According to the first statement, this means that yang is born at Zi and yin is born at Wu; according to the second statement, this refers to the mutual friction of the twelve trigrams. These two passages, one based on the mutual root of yin and yang, and the other based on the interaction of hardness and softness, are both cited by those who advocate the theory of mutual generation.

今論卦變相生之說曰：易於賁曰「柔來而文剛，剛上而文柔」，節曰「剛柔分而剛得中」，無妄曰「剛自外來而為主於內」，大傳曰「剛柔相推，變在其中矣」，是故有斯義也。要之六十四卦之變皆本於八卦，而八卦之重又本於乾坤之竒偶。今卦之反對則兼上下體，六十四卦相生則専用下卦為變，是亦一家之學耳，謂易道盡在於是則未也，姑取其大概著於篇。

Now we discuss the idea of mutual generation in changing hexagrams: The Book of Changes says in the hexagram Bi, "A flexible line comes and adorns the strong line; the strong line above is divided and adorned by the flexible line." In the hexagram Jie, "The strong and flexible lines are divided, and the strong line is in the center." In the hexagram Wuwang, "The strong line comes from outside and becomes the dominant line inside." The Great Treatise says, "The strong and flexible lines push each other, and change is within this." Therefore, there is indeed this meaning in the change of hexagrams. In summary, the changes of the sixty-four hexagrams are based on the eight trigrams, and the stacking of the eight trigrams is based on the odd and even lines of Qian and Kun. Now, "opposition of hexagrams" takes both upper and lower trigrams into account, while "generation of the sixty-four hexagrams" uses only one line of the lower trigram as the changing line. This is merely one school of thought; if one says that the way of the Book of Changes is entirely contained in this, it cannot be considered accurate. We may briefly record this in this section. Lin Zhi's intention was to explain that although the idea of changing hexagrams is indeed present in the classic texts, it should not be extended into a complete system of generating hexagrams.

黃氏《象數論》曰：六十四卦相生圖不以觀、壯四陰四陽之卦為主變，可以無虞氏重出之失矣。然臨遯自第二變以後，主變之卦兩爻皆動，在《彖傳》亦莫知適從，又不如虞氏動以一爻之有定法也。方實孫有《易卦變合圖》，與相生圖同，至兩爻交動則稍更其次序。

Huang Zongxi's "Discussion on the Images and Numbers of the Book of Changes" says that the "Diagram of the Mutual Generation of the Sixty-Four Hexagrams" does not take hexagrams such as "Observing" and "Great Strength" which have four yin and four yang lines as the main changing hexagrams, thus avoiding the problem of Yu Fan's repeated generation of hexagrams. However, in the case of "Approaching" and "Retreating," after the second change, both lines of the main changing hexagram move together, and when compared with the "Commentary on the Judgment," it is unclear which line should be followed, making it less clear-cut than Yu's method of changing only one line at a time. Fang Xisun created the "Diagram of the Combined Changes of the Hexagrams," which is largely similar to the mutual generation diagram, but slightly altered the order in cases where two lines interact and change.

朱風林升分為內外體，有自十闢卦所變者（乾坤無變，故十二闢卦去之為十卦）：一陽在內體自復變凡二卦（師、謙），一陽在外體自剝變凡二卦（豫、比），二陽在內體自臨變凡二卦（升、明夷），二陽在外體自觀變凡二卦（晉、革），二陽在內體一陽在外體自泰變凡九卦（與相生圖同）；一陰在內體自姤變凡二卦（同人、履），一陰在外體自夬變凡二卦（小畜、大有），二陰在內體自遯變凡二卦（無妄、訟），二陰在外體自大壯變凡二卦（需、大畜），二陰在內體一陰在外體自否變凡九卦（與相生圖同）。

Zhu Sheng (Feng Lin) analyzed a hexagram by dividing it into inner and outer parts to explain change. There are ten hexagrams derived from the twelve dividing hexagrams (the hexagrams of Heaven and Earth remain unchanged, so the twelve dividing hexagrams minus these two leave ten hexagrams): one yang line in the inner part comes from the hexagram "复" (Returning), resulting in two hexagrams ("师" (Military) and "谦" (Humility)); one yang line in the outer part comes from the hexagram "剥" (Splitting), resulting in two hexagrams ("豫" (Enjoyment) and "比" (Comparison)); two yang lines in the inner part come from the hexagram "临" (Approaching), resulting in two hexagrams ("升" (Rising) and "明夷" (Bright夷)); two yang lines in the outer part come from the hexagram "观" (Observing), resulting in two hexagrams ("晋" (Progress) and "革" (Change)); two yang lines in the inner part and one yang line in the outer part come from the hexagram "泰" (Peace), resulting in nine hexagrams (the same as in the mutual generation diagram). One yin line in the inner part comes from the hexagram "姤" (Meeting), resulting in two hexagrams ("同人" (Same People) and "履" (Following)); one yin line in the outer part comes from the hexagram "夬" (Deciding), resulting in two hexagrams ("小畜" (Small Accumulation) and "大有" (Great Possession)); two yin lines in the inner part come from the hexagram "遯" (Retreating), resulting in two hexagrams ("无妄" (No Pretense) and "讼" (Litigation)); two yin lines in the outer part come from the hexagram "大壮" (Great Strength), resulting in two hexagrams ("需" (Waiting) and "大畜" (Great Accumulation)); two yin lines in the inner part and one yin line in the outer part come from the hexagram "否" (Obstruction), resulting in nine hexagrams (the same as in the mutual generation diagram).

有自六子卦所變者：二陽分在內外，不處震之主爻者自震變（蹇、蒙），不處坎之主爻者自坎變（小過、頤），不處艮之主爻者自艮變（解、屯）；二陰分在內外，不處巽之主爻者自巽變（睽、革），不處離之主爻者自離變（中孚、大過），不處兌之主爻者自兌變（家人、鼎），各得二卦。其自十闢卦所變者以一爻升降，其自六子卦所變者以兩爻升降。自三陰三陽而外，主變之卦多、所生之卦少，何其頭緒之紛紜也！（渭按：朱風林卦變支離破碎，全屬杜撰，而且於經無所用，故後不復著。）

There are also those derived from the six sons' trigrams: two yang lines are placed in the inner and outer trigrams, and those not occupying the main line position of the Zhen trigram are derived from Zhen (the trigrams of Jian and Meng); those not occupying the main line position of the Kan trigram are derived from Kan (the trigrams of Xiao Guo and Yi); those not occupying the main line position of the Gen trigram are derived from Gen (the trigrams of Jie and Tun). Two yin lines are placed in the inner and outer trigrams, and those not occupying the main line position of the Xun trigram are derived from Xun (the trigrams of Kui and Ge); those not occupying the main line position of the Li trigram are derived from Li (the trigrams of Zhong Fu and Da Guo); those not occupying the main line position of the Dui trigram are derived from Dui (the trigrams of Jia Ren and Ding). Each category gives rise to two trigrams. Those derived from the ten trigrams use one line's movement, while those derived from the six sons' trigrams use two lines' movement. Except for the trigrams with three yin or three yang lines, the number of main and changing trigrams is greater while the number of generated trigrams is smaller, resulting in a very confused situation. In other words, Zhu Sheng expanded the main and changing trigrams from the ten trigrams to the six sons' trigrams, and relaxed the rule from one line's movement to two lines' movement, yet the regulations became even more chaotic. (Hu Wei's comment: Zhu Sheng's trigram transformations are fragmented and entirely fabricated, and have no use in interpreting the classics, so they are not included in the following text.)

按：李挺之言卦變，莫善於反對，莫不善於相生，反對者經之所有，相生者經之所無也。六十四卦相生圖，蓋從乾坤三索之義而推之於六畫以為卦變：純乾純坤一交而為姤、復，再交而為遯、臨，三交而為否、泰，是亦可以已矣。而又以姤初之一陰、復初之一陽遞升以訖於上，遯臨之二陰二陽、否泰之三陰三陽亦如之。夫姤復以一爻主變，猶有定法；若遯臨否泰，則兩爻俱動，或獨升，或同升，主變者非一，紛然而無統紀矣。且六子純卦亦不過因而重之，今乃謂震坎艮生於臨、巽離兌生於遯，有是理乎？甚矣此圖之為贅肬也。

Hu Wei commented: Li Zhicai discussed the transformation of hexagrams, and the best example is "opposition," while the worst is "mutual generation." This is because opposition is something already present in the classic text, whereas mutual generation is not. The "Diagram of Mutual Generation of the Sixty-Four Hexagrams" probably extended the idea that the trigrams Qian and Kun generate the six sons through triple repetition to the hexagrams, using it as a method of transformation. Pure Qian and pure Kun first intersect to form Gu and Fu, then intersect again to form Duan and Lin, and finally intersect three times to form Pi and Tai. At this point, the explanation could have ended. However, Li went further, taking the yin line of the first line of Gu and the yang line of the first line of Fu, and moving them one by one upward until the top line. Similarly, the two yins and two yangs of Duan and Lin, and the three yins and three yangs of Pi and Tai, were also moved upward in sequence. Gu and Fu, which change based on one line, still have a clear rule. But for Duan, Lin, Pi, and Tai, two lines must move together; sometimes they rise individually, sometimes together, and more than one line becomes the main changing line, leading to confusion and lack of order. Moreover, the pure hexagrams of the six sons are merely formed by stacking the eight trigrams. Now, to say that Zhen, Kan, and Gen are generated from Lin, and Xun, Li, and Dui are generated from Duan, is there such a principle in the world? This diagram is really like an unnecessary tumor.

邵子《皇極經世書》曰：天地之本，其起於中乎？是以乾坤屢變而不離乎中也。又曰：自下而上謂之升，自上而下謂之降，升者生也，降者消也，故陽生於下，陰生於上，是以萬物皆反生也。又曰：陰生陽，陽生陰，陰復生陽，陽復生陰，是以循環而無窮也。《乾坤吟》曰：道不逺於人，乾坤只在身，誰能天地外，別去覓乾坤。

Shao Yong's "The Supreme Principles Governing the World" says: The fundamental principle of heaven and earth is probably initiated from the center. Therefore, the trigrams Qian and Kun change repeatedly but never deviate from the center. He also says: Movement from below to above is called rising, and movement from above to below is called descending; rising is generation, descending is decline. Therefore, yang energy is generated from below, and yin energy is generated from above, so all things grow in reverse. He also says: yin generates yang, yang generates yin, yin again generates yang, yang again generates yin, so they cycle endlessly without end. In his "Ode to Qian and Kun," he says: The great way is not far from the human body; Qian and Kun are only within oneself. Who can run outside of heaven and earth to seek for Qian and Kun elsewhere?

俞氏曰：乾坤，陰陽之純；坎離，陰陽之交。乾純陽為天，故居中之上；坤純陰為地，故居中之下；坎陰中含陽為月，離陽中含陰為日，故居乾坤之中。其餘六十卦，自坤中一陽之生而至五陽，則升之極矣，遂為六陽之純乾；自乾中一陰之生而至五陰，則降之極矣，遂為六陰之純坤。一升一降，上下往來，蓋循環而無窮也。

Yu Yan (Shi Jian) said: Qian and Kun are the pure forms of yin and yang. Kan and Li are the combined forms of yin and yang. Qian, being purely yang, represents heaven, so it is placed above the central axis; Kun, being purely yin, represents earth, so it is placed below the central axis. Kan is yin containing yang and thus represents the moon, while Li is yang containing yin and thus represents the sun, so they are placed between Qian and Kun. The remaining sixty hexagrams arise from Kun by producing one yang, accumulating to five yangs, and then reaching the extreme, becoming the fully yang Qian; similarly, from Qian by producing one yin, accumulating to five yins, and then reaching the extreme, becoming the fully yin Kun. One rising and one descending, moving up and down continuously, is the cycle without end.

天地如此，人身亦如此。子時氣到尾閭，丑寅在腰間，卯辰已在脊膂，午在泥丸，未申酉在胸膈，戌亥則又歸於腹中，此一日之升降然也。一息亦然：呼則自下而升於上，吸則自上而降於下。在天則應星而如斗指子午，在地則應潮而如月在子午，子午蓋天地之中也。《參同契》云「合符行中」，又云「運移不失中」，又云「浮游守規中」。人能知吾身之中以合乎天地之中，則乾坤不在天地而在吾身矣。

Heaven and earth function in this way, and the human body also functions in this way: during the Zi hour, the qi moves to the tailbone; during the Chou and Yin hours, it moves along the waist; during the Mao, Chen, and Si hours, it moves along the spine; during the Wu hour, it reaches the mud-wan (the top of the head); during the Wei, Shen, and You hours, it moves along the chest; and during the Xu and Hai hours, it returns to the abdomen. This is the rising and falling within a day and night. In breathing, it is also the same: when exhaling, the qi rises from below to above; when inhaling, the qi descends from above to below. In the heavens, it corresponds with the star patterns, such as the handle of the Big Dipper pointing to Zi and Wu; on the earth, it corresponds with the tides, such as the moon reaching the Zi and Wu positions. Zi and Wu are the central positions of heaven and earth. The "Zhou Yi Cang Tong Qi" says "coinciding with the symbol and moving in the center," and also says "the movement shifts but does not lose the center," and also says "floating and drifting while keeping to the central path." If a person can recognize this "center" within his own body and align it with the "center" of heaven and earth, then the heavens and earth are not outside but within himself.

按：希夷先天之學，《參同契》之的傳也。伯陽所言無非丹道，其曰「二用無爻位，周流行六虛，往來既不定，上下亦無常」，蓋借易剛柔往來上下以明人身二氣之升降，與夫子《彖傳》所言不同指。而李氏六十四卦相生圖于丹道絶無交涉，安在其為先天邪？竊疑穆修受學於希夷，唯有反對圖，而相生則李氏以意為之，頗縁飾以儒者之義理，故其圖彷佛虞仲翔，多與《彖傳》相合。

Hu Wei remarked: Chen Tuan's (Xiyi) study of the Earlier Heaven is indeed the direct transmission of the Zhou Changes (I Ching) Compendium of the Supreme Ultimate. Wei Boyang's teachings all pertain to alchemy, and when he said, "Two uses have no yao positions, the Zhou flows through the six voids, coming and going are not fixed, up and down have no constant," he was using the concept of the interplay of yin and yang in the I Ching to explain the rising and falling of the two energies in the human body. This is not the same as what Confucius explained in the Commentary on the Judgment. As for Li Zhici's diagram of the mutual generation of the sixty-four hexagrams, it has nothing to do with alchemy. Why is it considered part of the Earlier Heaven tradition? I privately suspect that Mu Xiu learned only the Opposition Diagram from Chen Tuan. As for the Mutual Generation Diagram, it was probably created by Li Zhici himself, and he even embellished it with Confucian principles. Therefore, this diagram seems to follow Yu Fan's approach, and it is likely that it was made to conform to the Commentary on the Judgment.

唯石澗直圖，上乾下坤而坎離居中，正得乾坤為鼎器、坎離為藥物之意；又據邵子天根月窟之說，自坤中一陽生而升至五陽，遂為六陽之純乾，自乾中一陰生而降至五陰，遂為六陰之純坤，一升一降，上下往來，與伯陽之義脗合。且諸卦皆生於乾坤，無姤復小父母之疵；而四陰二陽與坎並列，四陽二陰與離並列，亦皆井然有條理，無重出之病，勝李氏二圖逺甚。

Only Yu Yanyan (Shi Jian)’s "Earlier Heaven Diagram" correctly places Qian above and Kun below, with Kan and Li in the middle, fully matching the alchemists' original meaning of "Qian and Kun as the furnace and cauldron, Kan and Li as the medicinal ingredients." It also follows Shao Yong's theory of "the heavenly root and the lunar cave," starting with a single yang rising from Kun to reach five yang, thus forming pure Qian with six yang; and a single yin descending from Qian to reach five yin, thus forming pure Kun with six yin. This rising and falling, moving up and down, completely aligns with Wei Boyang's meaning. Moreover, it allows each trigram to originate from Qian and Kun, avoiding the problem of "Gou Fu Xiao Parents." The trigrams with four yin and two yang are grouped with Kan, and those with four yang and two yin are grouped with Li, all arranged in an orderly manner without the fault of repeating trigrams. This is much better than the two diagrams by Li Zhichai.

然石澗未嘗自名為卦變也，第因邵子有橫圖、圓圖、方圖而更作先天直圖以申其意。自余觀之，此圖既非六十四卦之次序，又非六十四卦之方位，正可作卦變圖耳。異哉！石澗能於三百餘歲後紹聞知之統，使呼吸上下往來之象一望瞭然，真希夷先天之學，而邵子之所不及圖者也，故附列李氏二圖之末，以質於後之君子。

However, Yu Yan himself did not call it the Diagram of Changing Hexagrams. He only made another diagram called The Straight Diagram of Earlier Heaven because Shao Yong had the Horizontal Diagram, the Circular Diagram, and the Square Diagram. According to my view, this diagram is neither the sequence of the sixty-four hexagrams nor their directional arrangement. It can be used exactly as a Diagram of Changing Hexagrams. How remarkable! Yu Yan was able to continue the tradition known through oral transmission three hundred years later, making the imagery of rising and falling, ascending and descending clearly visible at a glance. This is truly the Earlier Heaven learning of Chen Tuan, and it is something Shao Yong did not draw. Therefore, it is appended after the two diagrams of Li Zhici, to seek the opinion of later scholars.

右論李氏卦變。

In the previous section, the discussion examines the merits and authenticity of the two diagrams transmitted by Li Zhicai, namely the "Diagram of Changing Hexagrams" and the "Diagram of Mutual Generation of the Sixty-Four Hexagrams."

《本義》圖說曰：《彖傳》或以卦變為說，今作此圖以明之，蓋易中之一義，非畫卦作易之本指也。

Zhu Xi's "Diagram Explanation" in The Original Meaning of the Zhou Changes says: The Commentary on the Judgment sometimes establishes its teachings through changes of hexagrams. Now I make this diagram to explain it clearly; this is only one layer of meaning in the Book of Changes, not the original intention of drawing hexagrams and composing the Book of Changes.

凡一陰一陽之卦各六，皆自復、姤而來（五陰五陽卦同圖異）：剝、比、豫、謙、師、復；夬、大有、小畜、履、同人、姤。

The first category: all the hexagrams with one yang line and those with one yin line each have six, and they all come from the hexagrams of 《Fu》 and 《Gou》 (five yin and five yang hexagrams are the same as this diagram, but with different names). The six hexagrams with one yang line are 《Bo》, 《Bi》, 《Yu》, 《Qian》, 《Shi》, and 《Fu》, which represent a single yang line moving down from the top position to the initial position step by step. The six hexagrams with one yin line are 《Gua》, 《Da You》, 《Xiao Xu》, 《Lv》, 《Tong Ren》, and 《Gou》, which represent a single yin line moving down from the top position to the initial position step by step.

凡二陰二陽之卦各十有五，皆自臨、遯而來（四陰四陽卦同圖異）：頤、屯、震、明夷、臨；蒙、坎、解、升；艮、蹇、小過；晉、萃；觀。大過、鼎、巽、訟、遯；革、離、家人、無妄；兌、睽、中孚；需、大畜；大壯。

The second category: All the hexagrams with two yang lines and those with two yin lines each have fifteen hexagrams, all derived from the hexagrams of 临 (Approaching) and 遁 (Retreating) (the hexagrams with four yin and four yang lines are the same as this diagram, but with different names). The hexagrams of the 临 series are in order: 颐 (Nourishing), 屯 (Obstruction), 震 (Thunder), 明夷 (Bright Abundance), 临 (Approaching); 蒙 (Youth), 坎 (Water), 解 (Release), 升 (Ascending); 艮 (Mountain), 蹇 (Obstruction), 小过 (Minor Excess); 晋 (Progress), 萃 (Gathering); 观 (Observing). The hexagrams of the 遁 series are in order: 大过 (Great Excess), 鼎 (Tripod), 巽 (Wind), 讼 (Contention), 遁 (Retreating); 革 (Change), 离 (Fire), 家人 (Family), 无妄 (No Falsehood); 兑 (Lake), 睽 (Disconnection), 中孚 (Middle Trust); 需 (Necessity), 大畜 (Great Accumulation); 大壮 (Great Strength). Zhu Xi's diagram does not limit movement to only one line as Yu Fan did, but instead arranges all possible changes of two lines rising and falling together, so the number of hexagrams in each category is much greater than in Yu Fan's system.

凡三陰三陽之卦各二十，皆自否、泰而來：損、節、歸妹、泰；賁、既濟、豐；噬嗑、隨；益；蠱、井、恆；未濟、困；渙；旅、咸；漸；否。

The third category: All trigrams with three yang lines and all trigrams with three yin lines each have twenty, and they all come from the trigrams 《否》 and 《泰》. The lineage of 《泰》 is as follows: 《损》, 《节》, 《归妹》, 《泰》; 《贲》, 《既济》, 《丰》; 《噬嗑》, 《随》; 《益》; 《蛊》, 《井》, 《恒》; 《未济》, 《困》; 《涣》; 《旅》, 《咸》; 《渐》; 《否》.

咸、旅、漸、否；困、未濟、渙；井、蠱；恆；隨、噬嗑、益；既濟、賁；豐；歸妹；泰。

The series of 《Pu》 includes sequentially: 《Xian》, 《Lu》, 《Jian》, 《Pu》; 《Kun》, 《Wei Ji》, 《Huan》; 《Jing》, 《Gu》; 《Heng》; 《Sui》, 《Shi Ke》, 《Yi》; 《Ji Ji》, 《Ben》; 《Feng》; 《Gui Mei》; 《Tai》. It is evident that the series of 《Tai》 and 《Pu》 interweave with each other, and the same hexagram appears in both series.

凡四陰四陽之卦各十有五，皆自大壯、觀而來（二陰二陽圖已見前）：大畜、需、大壯；睽、兌；中孚；離、革；益；無妄；鼎、大過；巽；訟；遯。萃、晉、觀；蹇、艮；小過；坎、蒙；解；升；屯、頤；震；明夷；臨。

The fourth category: All the hexagrams with four yang lines and those with four yin lines each have fifteen hexagrams, all derived from the hexagrams of 《Dazhuang》 and 《Guan》 (these hexagrams have already appeared in the previous diagram of two yin and two yang). The lineage of 《Dazhuang》 proceeds in order as: 《Daxu》, 《Xu》, 《Dazhuang》; 《Kui》, 《Dui》; 《Zhongfou》; 《Li》, 《Ge》; 《Yi》; 《Wuwang》; 《Ding》, 《Daguo》; 《Xun》; 《Song》; 《Dun》. The lineage of 《Guan》 proceeds in order as: 《Cui》, 《Jin》, 《Guan》; 《Jian》, 《Gen》; 《Xiaoguo》; 《Kan》, 《Meng》; 《Jie》; 《Sheng》; 《Zun》, 《Yi》; 《Zhen》; 《Mingyi》; 《Lin》.

凡五陰五陽之卦各六，皆自夬、剝而來（一陰一陽圖已見前）：大有、夬；小畜；履；同人；姤。比、剝；豫；謙；師；復。

The fifth category: All five yang hexagrams and all five yin hexagrams each have six variations, all derived from the hexagrams 《Guai》 and 《Bao》 (these hexagrams have already appeared in the previous section of one yin and one yang diagram). The lineage of 《Guai》 proceeds in order as: 《Dàyǒu》, 《Guai》; 《Xiǎoxù》; 《Lǚ》; 《Tóngrén》; 《Gòu》. The lineage of 《Bao》 proceeds in order as: 《Bǐ》, 《Bao》; 《Yù》; 《Qiān》; 《Shī》; 《Fù》.

黃氏《象數論》曰：朱子言以《彖傳》考之，說卦變者凡十九卦，蓋言成卦之由，《彖傳》不言成卦之由則不言所變之爻，此是朱子自言其卦變也。《繫辭傳》曰「爻者，言乎變者也」，易中何卦不言變？辭有隠顯，而理無不寓，即證之《彖辭》，亦非止十九卦也。

Huang Zongxi's "Discussion on the Imagery and Numerical Calculations of the Book of Changes" says: Zhu Xi said that according to the Commentary on the Judgment, the nineteen hexagrams that discuss change are explained in terms of the origin of the hexagrams. The Commentary on the Judgment does not explain the origin of the hexagrams, so it does not specify the changing lines. This is Zhu Xi's own explanation of his method of discussing change in hexagrams. However, the Great Treatise says, "A line refers to change." Which hexagram in the Book of Changes does not discuss change? The words may be hidden or explicit, but the principles are present everywhere. Taking the Commentary on the Judgment as a standard, there are not only nineteen hexagrams that discuss change.

訟「剛來而得中」，以需之反對觀之，彼得正又得中，此但得中不能得正。泰否之往來，所謂反其類。隨「剛來而下柔」，蠱「剛上而柔下」，二卦反對：蠱上之剛自外卦來，初居二三之下；隨初剛自下而上，上柔自上而下。噬嗑「柔得中而上行」，賁「柔來而文剛，分剛上而文柔」：前卦謂六二上行為五，後卦言六五自外卦而入內，初九從下卦而至上。無妄「剛自外而為主於內」，大畜「剛上而尚賢」：無妄之初九自大畜上爻外卦來，為內卦之主；大畜之上九自無妄初爻而上。咸「柔上剛下」，恆「剛上柔下」：咸指上六九三，恆指九四初六。

The hexagram "Zheng" says "the strong comes and occupies the center." By looking at its opposing hexagram "Xu," we see that in "Xu," the nine at the fifth position (nine in the center) is both correct and central, while in "Zheng," it only occupies the center but not the correct position. "Tai" and "Pou" discuss mutual movement, which is referred to as "returning to their kind." "Sui" says "the strong comes and is below the flexible," while "Gu" says "the strong is above and the flexible is below," and these two hexagrams are opposing each other: in "Gu," the strong at the top line comes from the outer trigram and is located below the second and third lines; in "Sui," the strong at the first line comes from below and rises, while the flexible at the top line comes from above and descends. "Shi He" says "the flexible occupies the center and rises upward," while "Ben" says "the flexible comes and adorns the strong; the strong ascends and adorns the flexible." The former refers to the six at the second position rising to the fifth position, while the latter refers to the six at the fifth position coming from the outer trigram into the inner trigram, and the nine at the first position rising from the lower trigram to the upper position. "Wu Wang" says "the strong comes from outside and becomes the master within," while "Da Xu" says "the strong is above and values the virtuous." In "Wu Wang," the nine at the first line comes from the top line of "Da Xu," which is the outer trigram, and becomes the master of the inner trigram; in "Da Xu," the nine at the top line comes from the first line of "Wu Wang" and rises upward. "Xian" says "the flexible is above and the strong is below," while "Heng" says "the strong is above and the flexible is below." In "Xian," it refers to the sixth line above and the ninth line below; in "Heng," it refers to the ninth line above and the sixth line below.

晉「柔進而上行」，明夷之六二上行為六五；睽「柔進而上行」，家人之六二上行為六五。蹇「往得中也」，解「其來復吉，乃得中也」：蹇之九五自解內卦，故曰往；解之九二自蹇外卦，故曰來。升「柔以時升」，升上卦之柔皆萃卦所升。鼎「柔進而上行」，鼎五由萃二而上。漸「進得位」，漸九五當歸妹居二為不得位。渙「剛來而不窮」者，節五來二；「柔得位乎外而上同」者，柔在三失位，在四得位。此朱子所謂十九卦之《彖辭》，皆以反對為義者也。

The hexagram "Jin" says "the flexible advances upward," which refers to the line six two of "Mingyi" moving upward to become line six five. The hexagram "Kui" also says "the flexible advances upward," which refers to the line six two of "Jiaoren" moving upward to become line six five. The hexagram "Jian" says "going forward attains the center," and the hexagram "Jie" says "its coming back is auspicious, attaining the center." The line nine five of "Jian" comes from the inner trigram of "Jie," so it is called "going forward"; the line nine two of "Jie" comes from the outer trigram of "Jian," so it is called "coming back." The hexagram "Sheng" says "the flexible rises with the right timing," and the flexible lines in the upper trigram of "Sheng" all come from the hexagram "Cui." The hexagram "Ding" says "the flexible advances upward," and its line five comes from line two of "Cui." The hexagram "Jian" says "advancing attains the right position," and the line nine five of "Jian" is in the second position in "Guimei," which is not the right position. The hexagram "Huan" says "the strong comes without being exhausted," referring to the line five of "Jie" moving to the second position; it also says "the flexible attains the right position in the outer trigram and unites above," referring to the flexible line in the third position losing the right position, but in the fourth position attaining the right position. This is what Master Zhu said about the nineteen hexagram "Tuan Ci," in fact all of them can be explained by using the opposing trigrams.

需「位乎天位以正中也」，自訟九二而來，得中又得正。損「損下益上，其道上行」，益「損上益下，自上下下」：由損觀之，似以三爻益上爻；由益觀之，似以四爻益初爻。小畜「密雲不雨」，反對為履，履下之兌澤氣成云，故曰宻雲；兌變而巽，風以散之，故曰不雨。大有「應乎天而時行」，方其同人在二之時應乎天也，今時行而居其位。謙「地道卑而上行」，地道指坤，豫在下卦為卑，謙在上卦為上行。臨「至于八月」，觀二陽在上，臨二陽在下，自臨至觀歴八爻，故言八月。復「七日來復」，剝一陽在上，復一陽在下，自剝至復歴七爻，故言七日。

The hexagram "Xu" says, "It is in the position of the heavenly position, and it is correct in the center," which comes from the line Nine in the Second of "Song." It has both the center and the correctness. "Sun" says, "Loss from below benefits above, and its way goes upward." "Yi" says, "Loss from above benefits below, and it benefits all below." From "Sun," it seems as if the Third Line is used to increase the Top Line; from "Yi," it seems as if the Fourth Line is used to increase the First Line. "Xiu" says, "Dense clouds without rain." Its opposite is "Li." "Li" has the lower trigram Dui (Lake), which represents the lake's vapor rising to form clouds, hence "dense clouds." Dui changes to Xun (Wind), and the wind disperses the clouds, hence "without rain." "Da You" says, "It responds to heaven and acts in accordance with the time." When it was still "Tong Ren," with the soft line in the Second position, it was "responding to heaven." Now, moving in accordance with the time, it has moved to the Fifth position. "Qian" says, "The earth's path is low but ascends upward." "Earth's path" refers to Kun. In "Yu," Kun is the lower trigram, hence "low"; in "Qian," Kun is the upper trigram, hence "ascends upward." "Lin" says, "Until the eighth month there is misfortune." "Guan" has two yang lines above, while "Lin" has two yang lines below. Counting from "Lin" to "Guan" involves eight lines, hence the eighth month. "Fu" says, "After seven days it returns." "Bo" has one yang line above, while "Fu" has one yang line below. Counting from "Bo" to "Fu" involves seven lines, hence seven days.

明夷「初登于天」言晉，「後入于地」言明夷。夬「所尚乃窮」，對姤為言。井「改邑不改井」，兌為剛滷之地，變而為巽則「近利市三倍」，是改邑也；坎不變，是不改井也，皆對困言之。歸妹「征凶，位不當也」，漸之二五皆當位，至歸妹皆不當。旅「柔得中乎外」，在豐為得中乎內。巽「柔皆順乎剛」，兌「剛中而柔外」，兌柔不順乎剛，巽柔中而剛外，二卦相反。既濟「剛正而位當」，未濟不當位，二卦亦相反。此朱子十九卦以外亦皆以反對為義者也。反對之窮而反其竒偶以配之，又未嘗不暗相反對於其間：如中孚上爻之翰音，反對即為小過初爻之飛鳥；頤之口實，由大過之兌；大過士夫、老夫，由頤之艮震。此序卦之不可易也，奈何諸儒之為卦變紛然雜出而不能歸一乎？

The hexagram Mingyi says "initially ascending to heaven" refers to the hexagram Jin, while "later entering the earth" refers to Mingyi itself. The hexagram Guai says "the object of pursuit has reached its limit," which refers to Guo. The hexagram Jing says "changing the city but not the well":兑 represents salt land, and when it becomes Xun, it becomes "close to profit threefold," which is "changing the city"; Kan remains unchanged, which is "not changing the well" — all referring to Kun. The hexagram Guimei says "journeying brings misfortune, for the position is inappropriate": in the hexagram Zhen, the second and fifth lines are in proper position, but in Guimei, they are not. The hexagram Li says "the soft is in the middle of the outer," while in Feng, the soft is in the middle of the inner. The hexagram Xun says "all the soft are in harmony with the strong," while the hexagram Dui says "strong in the middle and soft on the outside": the soft in Dui does not harmonize with the strong, while in Xun, the soft is in the middle and the strong is outside, making the two hexagrams opposites. The hexagram Ji Ji says "the strong and the soft are in proper position," while Wei Ji has improper positions, making them opposites. These are examples of Master Zhu's nineteen hexagrams, where opposites are used to establish meaning. As for the eight hexagrams where the method of opposition is exhausted and the odd and even lines are completely reversed, there is still an implicit opposition: for example, the top line of Zhongfu, "the sound of a crane ascending to heaven," when reversed, corresponds to the first line of Xiaoguo, "a flying bird brings misfortune"; the hexagram Yi talks about "mouthfuls," derived from Da Guo's Dui mouth; Da Guo talks about "scholars" and "old men," derived from Yi's Gen and Zhen. This is precisely the reason why the order of the hexagrams in Xugua cannot be changed. Unfortunately, various scholars have discussed hexagram changes, producing many different interpretations, yet they have never reached a single conclusion.

朱子變卦圖，一陰一陽與五陰五陽相重出，二陰二陽與四陰四陽相重出，泰與否相重出，除乾坤之外，其為卦百二十有四，蓋已不勝其煩矣。易之上下往來皆以一爻升降為言，既有重出，則每卦必有二來，從其一則必舍其一，以《彖傳》附會之，有一合必有一不合。就其所謂一來者，尚有兩爻俱動，並其二來，則動者四爻矣。

Master Zhu's diagram of changing hexagrams shows pairs of yin and yang, five yin and five yang, each reappearing with each other; two yin and two yang, four yin and four yang, also reappearing with each other; and the hexagrams Tai and Po also reappear. Except for the hexagrams Qian and Kun, the list includes a total of 124 hexagrams, which is really cumbersome. In the Book of Changes, the concept of movement up and down refers to the movement of one line. If there is a recombination, then each hexagram must have two origins. Following one origin necessarily excludes the other, and using the Commentary on the Judgment to fit it will result in some agreement and some disagreement. Even if we consider only one origin, two lines must move together. If we combine both origins, then four lines would be moving.

原諸儒卦變之意，所以明其自復、姤、臨、遯、否、泰、大壯、觀、夬、剝而來者，以其卦惟此一爻之故變為別卦，是以脈絡可尋而定為主變。使一卦之中頭緒紛然，爻爻各操其柄，則彼卦之體已不復存，猶可認其自某所而來乎？

Investigating the original intention of various scholars discussing changes in hexagrams, they point out that certain hexagrams are derived from the hexagrams of Fu, Gu, Lin, Duan, Pǐ, Tai, Da Zhuang, Guan, Guai, and Bo, because these hexagrams only require changing one line to become another hexagram, and their lineage is clear and traceable, so they are designated as the main hexagrams of change. If a hexagram has many complicated elements, with each line independently capable of change, then the original essence of that hexagram would no longer exist, and how could we recognize from where it originated?

朱子雖為此圖，亦自知其決不可用，所釋十九卦《彖辭》盡舍主變之卦，以兩爻相比者互換為變：訟則自遯（二三相換），泰則自歸妹（三四相換），否則自漸（三四相換），隨則自困（初二相換）、自噬嗑（五上相換）、自未濟（初與二、五與上相換），蠱則自賁（初二相換）、自井（五上相換）、自既濟（初與二、五與上相換），噬嗑則自益（四五相換），賁則自損（二三相換）、自既濟（五上相換），無妄則自訟（初二相換），大畜則自需（五上相換），咸則自旅（五上相換），恆則自豐（初二相換），晉則自觀（四五相換），睽則自離（二三相換）、自中孚（四五相換）、自家人（二與三、四與五相換），蹇則自小過（四五相換），解則自升、升則自解（皆三四相換），鼎則自巽（四五相換），漸則自渙（二三相換）、自旅（四五相換），渙則自漸（二三相換）。凡十九卦，而主變者二十有七，或來自一卦，或來自兩卦三卦，多寡不倫，絶無義例。

Master Zhu made this diagram but himself knew it could not be used, so when explaining the nineteen hexagrams' "Tongci" (Commentary on the Images), he completely abandoned the main and changing hexagrams in the diagram, instead using the exchange of adjacent two lines to explain the change. The hexagram "Song" comes from "Dun" (lines two and three exchanged), "Tai" comes from "Gui Mei" (lines three and four exchanged), "Po" comes from "Jian" (lines three and four exchanged), "Sui" comes from "Kun" (lines one and two exchanged), from "Shi He" (lines five and upper exchanged), and from "Wei Ji" (lines one and two, five and upper exchanged), "Gu" comes from "Ben" (lines one and two exchanged), from "Jing" (lines five and upper exchanged), and from "Ji Ji" (lines one and two, five and upper exchanged), "Shi He" comes from "Yi" (lines four and five exchanged), "Ben" comes from "Sun" (lines two and three exchanged) and from "Ji Ji" (lines five and upper exchanged), "Wu Wang" comes from "Song" (lines one and two exchanged), "Da Xu" comes from "Xu" (lines five and upper exchanged), "Xian" comes from "Lv" (lines five and upper exchanged), "Heng" comes from "Feng" (lines one and two exchanged), "Jin" comes from "Guan" (lines four and five exchanged), "Kui" comes from "Li" (lines two and three exchanged), from "Zhong Fu" (lines four and five exchanged), and from "Jia Ren" (lines two and three, four and five exchanged), "Jian" comes from "Xiao Guo" (lines four and five exchanged), "Jie" comes from "Sheng" and "Sheng" comes from "Jie" (both lines three and four exchanged), "Ding" comes from "Xun" (lines four and five exchanged), "Jian" comes from "Huan" (lines two and three exchanged) and from "Lv" (lines four and five exchanged), "Huan" comes from "Jian" (lines two and three exchanged). The total number of hexagrams explained is nineteen, but the ones serving as main and changing hexagrams amount to twenty-seven, some coming from one hexagram, some from two or three, with varying numbers, no consistent pattern. In other words, the main and changing hexagrams he set in the diagram were not used at all when interpreting the classics.

就以其法推之，此十九卦中朱子之所舉者亦有未盡：訟之自無妄（初二相換）、自巽（三四相換），隨之自既濟（三四相換），蠱之自未濟（三四相換），噬嗑之自未濟（初二相換）、自賁（三四相換）、自隨（五上相換），賁之自蠱（初二相換）、自噬嗑（三四相換），無妄之自家人（三四相換），大畜之自睽（三四相換），咸之自困（二三相換），恆之自井（四五相換），晉之自艮（三四相換）、自萃（五上相換），睽之自大畜（三四相換）、自兌（五上相換），蹇之自坎（二三相換）、自萃（三四相換）、自艮（五上相換），解之自震（初二相換）、自小過（二三相換）、自坎（四五相換），升之自明夷（初二相換），鼎之自離（初二相換）、自大過（五上相換），漸之自否（三四相換），渙之自益（初二相換）、自未濟（四五相換）。復得二十九卦，而兼之者不與焉。

Following his method, we can continue to deduce further. Among the nineteen hexagrams, those cited by Master Zhu are still incomplete. The hexagram "Shou" (Judgment) can also come from "Wu Wang" (No Pretense) by swapping the first and second lines, or from "Xun" (Wind) by swapping the third and fourth lines. The hexagram "Sui" (Following) can also come from "Ji Ji" (Completion) by swapping the third and fourth lines. The hexagram "Gu" (Restraint) can also come from "Wei Ji" (Not Yet Completed) by swapping the third and fourth lines. The hexagram "Shi He" (Breaking the Bones) can also come from "Wei Ji" (Not Yet Completed) by swapping the first and second lines, from "Ben" (Beauty) by swapping the third and fourth lines, or from "Sui" (Following) by swapping the fifth and top lines. The hexagram "Ben" (Beauty) can also come from "Gu" (Restraint) by swapping the first and second lines, or from "Shi He" (Breaking the Bones) by swapping the third and fourth lines. The hexagram "Wu Wang" (No Pretense) can also come from "Jia Ren" (Family) by swapping the third and fourth lines. The hexagram "Da Xu" (Great Accumulation) can also come from "Kui" (Opposition) by swapping the third and fourth lines. The hexagram "Xian" (Attraction) can also come from "Kun" (Obstruction) by swapping the second and third lines. The hexagram "Heng" (Permanence) can also come from "Jing" (Well) by swapping the fourth and fifth lines. The hexagram "Jin" (Progress) can also come from "Gen" (Mountain) by swapping the third and fourth lines, or from "Cui" (Gathering) by swapping the fifth and top lines. The hexagram "Kui" (Opposition) can also come from "Da Xu" (Great Accumulation) by swapping the third and fourth lines, or from "Dui" (Lake) by swapping the fifth and top lines. The hexagram "Jian" (Obstruction) can also come from "Kan" (Water) by swapping the second and third lines, from "Cui" (Gathering) by swapping the third and fourth lines, or from "Gen" (Mountain) by swapping the fifth and top lines. The hexagram "Jie" (Release) can also come from "Zhen" (Thunder) by swapping the first and second lines, from "Xiao Guo" (Small Excess) by swapping the second and third lines, or from "Kan" (Water) by swapping the fourth and fifth lines. The hexagram "Sheng" (Ascending) can also come from "Ming Yi" (Darkness Illuminated) by swapping the first and second lines. The hexagram "Ding" (Vessel) can also come from "Li" (Fire) by swapping the first and second lines, or from "Da Guo" (Great Excess) by swapping the fifth and top lines. The hexagram "Jian" (Gradual Progress) can also come from "Po" (Obstruction) by swapping the third and fourth lines. The hexagram "Huan" (Dispersal) can also come from "Yi" (Increase) by swapping the first and second lines, or from "Wei Ji" (Not Yet Completed) by swapping the fourth and fifth lines. This adds another twenty-nine hexagrams, not counting those with multiple sources.

此二十九卦者，以為有用乎，則為《彖辭》之所不及；以為無用乎，不應同一卦變，在一卦中，其可以附會《彖辭》者從而取之，其不可以附會《彖辭》者從而置之。朱子云「某之說卻覺得有自然氣象」者安在也？且易所謂往來上下者，自內之外謂往，自外之內謂來，上者上卦也，下者下卦也。今兩爻互換，同在內卦而謂之往，同在外卦而謂之來，同在上卦而曰下，同在下卦而曰上，即欲附會之而有所不能矣。是朱子之卦變兩者俱為無當，宜乎其說之不能歸一也。

Are these twenty-nine hexagrams useful? The "Tu Cis" does not mention them at all. If we say they are useless, they are also hexagram transformations, so why, within a single hexagram, should those that can be connected to the "Tu Cis" be used, while those that cannot be connected be ignored? Master Zhu said his interpretation "feels natural," but where exactly is this naturalness? Moreover, in the "Book of Changes," "coming and going" and "up and down" refer to movement from the inner trigram to the outer trigram as "coming," and from the outer trigram to the inner trigram as "going." "Up" refers to the upper trigram, and "down" refers to the lower trigram. Now, if two lines are exchanged and both are within the inner trigram, it is called "going," but if both are within the outer trigram, it is called "coming." If both are in the upper trigram, it is called "down," and if both are in the lower trigram, it is called "up." This is impossible to connect. It is evident that Master Zhu's hexagram transformation, whether the main transformed hexagram on the diagram or the method of exchanging two lines when interpreting the text, is not logically consistent. That is why his explanation has never been unified.

按：邵子言重卦不易者八，反覆者二十八，以三十六變而為六十四，卦變之義數言盡之矣，據此以釋《彖傳》亦足矣。李挺之相生圖已傷煩碎，況朱子之所定乎？棃洲一一指擿，無微不彰。但朱子専取十九卦者，第就《彖傳》所謂剛柔往來上下內外者而求之，其它則未暇及。棃洲續舉諸卦中，唯損、益二卦似不當遺，何也？《彖傳》曰「損剛益柔」，又曰「損下益土，其道上行」，又曰「損上益下，自上下下」，則剛柔上下之義備矣，正可與十九卦並舉，何獨遺之？其它只言剛柔而不言往來上下，則其義即本卦可見，不必求之卦變，固不在此例。

Hu Wei commented: Shao Yong said that in the process of composing the sixty-four hexagrams, there are eight that remain unchanged, and twenty-eight pairs that can be reversed, resulting in thirty-six transformations. The meaning of these transformations can be explained in a few words, and according to this, one can interpret the Commentary on the Judgment adequately. Li Zhichai's diagram of mutual generation is already too complicated, and how much more so is Zhu Xi's system? Huang Zongxi (Liyou) pointed out each detail clearly and thoroughly. However, Zhu Xi only selected nineteen hexagrams, focusing specifically on the aspects of yin and yang moving up and down, inside and outside, as discussed in the Commentary on the Judgment. The rest were not considered. Among the additional hexagrams Huang Zongxi mentioned, only the hexagrams of "Loss" and "Gain" seem to be omitted. Why is that? The Commentary on the Judgment says, "Loss involves the strong and benefits the weak," and also says, "Loss from below benefits above, and the way proceeds upward," and further says, "Loss from above benefits below, and the superior governs the inferior." The meaning of yin and yang moving up and down is already complete, and these two hexagrams can be mentioned together with the nineteen. So why were they omitted? The other hexagrams only discuss yin and yang without mentioning movement up and down, so their meaning is already evident in the primary hexagram itself, and there is no need to look for it in the transformations. Therefore, they are not included in this category.

然朱子欲以卦變附先天之後，當仍用李氏反對圖，猶不失希夷本指；今乃據相生圖以更定其法，煩碎甚於李氏，而及其釋經也，則又舍反對之卦，而泛泛焉以兩爻相比者互換為變，往來上下訖無定法，亦安用此圖為也？

However, since Master Zhu wished to attach the changing hexagrams after the Earlier Heaven diagrams, he should still have adopted Li Zhicai's "Diagram of Opposite Changing Hexagrams," which would have remained true to the original intent of Chen Tuan's school. Now, instead, he has established a new method based on the "Diagram of Mutual Generation of the Sixty-Four Hexagrams," which is more complicated than Li Zhicai's. Yet, when actually interpreting the classics, he discards the opposite hexagrams and vaguely uses the exchange of adjacent lines to explain change, with no fixed rule for movement up and down. Then, what is the use of this diagram?

經於六十四卦之首各列二體六畫，即卦變圖也，剛柔往來之義開卷瞭然，何以別圖為？或曰：誠用反對，則每卦必顛倒視之而後可以知《彖傳》之所謂，不亦勞乎？余曰：人之眼光雖至短，兩卦相去尺幅間，豈不能兼矚，而必須顛倒以視之？此言真兒童之見，疑乎其所不足疑。

The text of the Classic begins each of the sixty-four hexagrams with the upper and lower trigrams, forming a hexagram with six lines. This itself is a diagram of change, and the meaning of the interaction between the firm and the yielding is clearly visible once the book is opened. Why would another diagram be needed? Someone asked: If we really use the method of opposition, then each hexagram would have to be viewed upside down in order to understand the Commentary on the Judgment. Would that not be too troublesome? I replied: Even if a person's vision is short-sighted, two hexagrams are only a few inches apart; how could they not be seen together? Why must one turn the book upside down? Such remarks are truly the views of a child, questioning something that is not worth doubting.

右論朱子卦變。

In the previous section, the complexity and errors in Zhu Xi's diagram of changing hexagrams in The Original Meaning of the Zhou Changes are examined.

《本義》圖說曰：「右《易》之圖九。有天地自然之易，有伏羲之易，有文王、周公之易，有孔子之易。自伏羲以上皆無文字，只有圖畫，最宜深玩，可見作《易》本原精微之意。文王以下方有文字，即今之《周易》。然讀者亦宜各就本文消息，不可便以孔子之說為文王之說也。」

In the preface to the nine diagrams following the "Original Meaning of the Zhou Changes" by Zhu Xi of the Southern Song dynasty, he says: The above nine diagrams of the "Book of Changes" are presented. The study of the "Book of Changes" can be divided into several levels: there is the "Changes" that arise naturally from heaven and earth, the "Changes" drawn by Fuxi, the "Changes" explained by King Wen and the Duke of Zhou in their commentaries, and the "Changes" interpreted by Confucius in his annotations. From Fuxi upwards, there were no written characters, only pictures, and this level should be deeply contemplated, as it reveals the original intention and subtle mind of the sages in creating the "Book of Changes." From King Wen onwards, there were written characters, which is the "Book of Changes" we have today. However, those who study the "Book of Changes" should also understand the meaning and development of each level's text, and should not directly take Confucius' interpretations as those of King Wen.

震川歸氏《易圖論》曰：「夏為《連山》，商為《歸藏》，周為《周易》，經別之卦，其數皆同。雖三代異名，而伏羲之易，即《連山》而在《連山》，即《歸藏》而在《歸藏》，即《周易》而在《周易》，未嘗別有所謂伏羲之易也。後之求之者，即其散見於《周易》之六十四卦者是已。」又曰：「以圖說《易》自邵子始。吾怪夫儒者不敢以文王之易為伏羲之易，而乃以伏羲之易為邵子之易也。」

In his work "Yitu Lun" ("Treatise on the Diagrams of the Book of Changes"), the Ming dynasty scholar Gu Yi Guang, known as Master Zhenchuan, said that during the Xia dynasty, the Book of Changes was called the "Lianshan" ("Continuous Mountains"), during the Shang dynasty it was called the "Guicang" ("Collection of the Hidden"), and during the Zhou dynasty it was called the "Zhouyi" ("Book of Changes"). The number of the main hexagrams and the additional hexagrams are the same in all three dynasties. Although the names differ across the three dynasties, the Book of Changes of Fuxi is contained within each of them. In the "Lianshan," it is contained within the "Lianshan"; in the "Guicang," it is contained within the "Guicang"; in the "Zhouyi," it is contained within the "Zhouyi." There has never been a separate existence of a Book of Changes solely belonging to Fuxi. Later scholars who wish to seek the Book of Changes of Fuxi should look for it among the sixty-four hexagrams of the "Zhouyi." Gu Yi Guang also said that using diagrams to explain the Book of Changes began with Shao Yong of the Northern Song dynasty. I find it strange that the scholars of later times dared not regard the Book of Changes of King Wen as the Book of Changes of Fuxi, but instead regarded the Book of Changes of Fuxi as the Book of Changes of Shao Yong.

按：《本義》卷首列九圖於前，而總為之說。所謂天地自然之易，《河圖》《洛書》也；伏羲之易，先天八卦及六十四卦次序、方位也；文王之易，後天八卦次序、方位及六十四卦之卦變也（《本義》卦變圖，朱子為釋《彖傳》而作，非康節反對之旨，故屬之後天）。是皆著為圖者。

Hu Wei's commentary: In the first volume of The Original Meaning of the Zhou Changes, nine diagrams are first listed and then summarized. Zhu Xi's reference to "the easy of heaven and earth in their natural state" refers to the Yellow River Chart and the Luo Writing. His reference to "the easy of Fuxi" refers to the Earlier Heaven Trigrams, as well as the sequence diagram and the directional diagram of the sixty-four hexagrams. His reference to "the easy of King Wen" refers to the sequence diagram, directional diagram, and the hexagram transformation diagram of the Later Heaven Trigrams. The hexagram transformation diagram in The Original Meaning was created by Zhu Xi to explain the Commentary on the Judgment, and it is not the "opposition" meaning of two hexagrams being reversed as in Shao Yong's theory. Therefore, it is categorized under the Later Heaven. All these are parts that are drawn as diagrams.

伏羲有畫而無辭，文王擊彖，周公繫爻，孔子作十翼，皆遞相發揮以盡其義，故曰「聖人之情見乎辭」。辭者，所以明象數之難明者也。而朱子顧以為三聖人之易専言義理，而象數闕焉，是何說與？且易之所謂象數，蓍卦焉而已。卦主象，蓍主數；二體六畫，剛柔雜居者，象也；大衍五十，四營成易者，數也。經文粲然，不待圖而明。若朱子所列九圖，乃希夷、康節、劉牧之象數，非易之所謂象數也，三聖人之言胡為而及此乎？

Fu Xi had only the hexagram figures without any written statements. King Wen composed the hexagram statements, the Duke of Zhou added the statements for the top line, and Confucius wrote the Ten Wings, elaborating layer by layer to fully explain the principles of the Book of Changes. Therefore, the Great Treatise says, "The feelings of the sage are revealed in the words." The written statements are used to clarify the aspects of the images and numbers that are difficult to understand. However, Zhu Xi instead claimed that the Book of Changes interpreted by King Wen, the Duke of Zhou, and Confucius only focused on the principles, and the images and numbers were entirely absent. What kind of view is this? Moreover, the images and numbers mentioned in the Book of Changes are nothing more than the divining stalks and the hexagrams. The hexagrams deal with the images, while the divining stalks deal with the numbers; the upper and lower parts, and the six lines drawn, with the yao (lines) alternating between yang and yin, constitute the "image." The great derivation number fifty, after going through four procedures to form one change, constitutes the "number." The text is clear and explicit, and can be understood without the diagrams. As for the nine diagrams listed by Zhu Xi, they belong to the tradition of Chen Tuan, Shao Yong, and Liu Mu, which is a system of images and numbers different from the images and numbers discussed in the Book of Changes. Have the words of these three sages ever mentioned such things?

伏羲之世，書契未興，故有畫而無辭。延及中古，情偽漸啟，憂患滋多，故文王繫彖以發明伏羲未盡之意，周公又係爻以發明文王未盡之辭，一脈相承，若合符節。至於孔子，紹聞知之統，集群聖之大成，論者以為生民所未有。使伏羲、文王、周公之意而孔子有所不知，何以為孔子？既已知之而別自為說以求異於伏羲、文王、周公，非述而不作之指也。然則伏羲之象得辭而益彰，縱令深玩圖畫而得其精微，亦不外乎文王、周公、孔子所言之理，豈百家眾技之說所得而竄入其中哉？九圖雖妙，聴其為易外別傳，勿以冠經首可也。

In the time of Fuxi, written characters had not yet emerged, so there were only hexagram images but no textual explanations. By the middle ancient period, human emotions and sincerity and falsehood gradually arose, and worries and troubles increased day by day. Therefore, King Wen composed the hexagram statements to elaborate on the meanings that Fuxi had not fully expressed, and the Duke of Zhou added the statements of the top line to explain what King Wen had not fully conveyed. This transmission was continuous, like a seal and its counterpart fitting perfectly together. As for Confucius, he inherited the lineage of the sages' knowledge and wisdom, gathering the achievements of all the sages. Commentators believe he was a person without precedent in the history of mankind. If Confucius did not understand the intentions of Fuxi, King Wen, and the Duke of Zhou, then on what basis could he be called Confucius? If he did understand them, yet established a different theory to differ from Fuxi, King Wen, and the Duke of Zhou, that would contradict his principle of 'reciting without creating'. Thus, it can be seen that the hexagram images became more clear because of the textual explanations. Even if one deeply studied the images and grasped their subtle meanings, they would not go beyond the teachings of King Wen, the Duke of Zhou, and Confucius. How could the doctrines of the hundred schools and their various techniques be mixed in? Although the nine diagrams may be exquisite, let them remain as a separate tradition outside the Book of Changes, and do not place them before the main text.

右論四聖之易。

The previous section discusses the transmission of the Book of Changes among the four sages: Fuxi, King Wen, the Duke of Zhou, and Confucius.

《宋史·隠逸傳》：陳摶字圖南，亳州真源人。始四五歲，戲渦水岸側，有青衣媼乳之，自是聰悟日益。及長，讀經史百家之言，一見成誦，悉無遺忘，頗以詩名。後唐長興中，舉進士不第，遂不求祿仕，以山水為樂。自言嘗遇孫君仿、麞皮處士二人者，髙尚之人也，語摶曰：「武當山九室巖可以隠居。」摶往棲焉，因服氣辟穀，歴二十餘年，但日飲酒數杯。移居華山雲臺觀，又止少華石室，每寢處多百餘日不起。

The "Song Shi · Yinyi Zhuan" records that Chen Tuan, whose name is Tu Nan, was from the Zhenyuan County of Bozhou. When he was about four or five years old, he was playing by the side of the Wu River when an old woman wearing green clothes fed him milk, and from then on he became increasingly intelligent and quick-witted. When he grew up, he read the classics, historical texts, and works of the various schools of thought, memorizing them after reading them once without forgetting. He was also well known for his poetry. In the Changxing period of the Later Tang dynasty, he took the imperial examination but failed, and thus ceased to seek official positions, enjoying the pleasure of touring mountains and rivers. He himself said that he had met two virtuous men, Sun Junfang and Zhangpi Chushì, who told him, "The Jiushi Rock in Wudang Mountain is a suitable place for seclusion." Chen Tuan then went there to live, and from then on practiced the art of breathing in qi, abstaining from grain, and drank only a few cups of wine each day for more than twenty years. Later he moved to YunTai Guan in Huashan, and then to a stone chamber in the Shao Hua Mountains. Each time he lay down to sleep, he often remained in bed for over a hundred days without getting up.

周世宗好黃白術，有以摶名聞者。顯徳三年，命華州送至闕下，留止禁中月餘，從容問其術。摶對曰：「陛下為四海之主，當以致治為念，奈何留意黃白之事乎？」世宗不之責，命為諫議大夫，固辭不受。既知其無他術，放還所止，詔本州島長吏歲時存問。

After the Later Zhou Shizong, Chai Rong, liked the alchemy practice of turning base metals into gold and silver called "Huang Bai Shu", someone reported Chen Tuan's reputation to him. In the third year of Xiande, Shizong ordered the Huazhou authorities to send Chen Tuan to the capital, and kept him in the palace for over a month, calmly asking about his alchemy techniques. Chen Tuan replied, "Your Majesty, as the ruler of the whole country, should focus on governing the state, how could you be concerned with alchemy for turning metals into gold and silver?" Shizong did not blame him, and appointed him as a Jianyi Da Fu, but he firmly refused the appointment. After Shizong realized that he had no other alchemy techniques, he let him return to his original residence, and issued an imperial decree ordering the local officials to visit him according to the seasons.

太平興國中來朝，太宗待之甚厚。九年復來朝，上益加禮重，謂宰相宋琪等曰：「摶獨善其身，不乾勢利，所謂方外之士也。摶居華山已四十餘年，度其年經百歲。自言經承五代離亂，幸天下太平，故來朝覲。與之語甚可聴。」因遣中使送至中書。

During the Taiping Xingguo period, Chen Tuan entered the imperial court, and Emperor Taizong of Song treated him very generously. In the ninth year of Taiping Xingguo, he entered the court again, and Emperor Taizong showed him even greater respect and esteem. He told the chancellor Song Qi and others, "Chen Tuan only seeks to cultivate himself in solitude, not pursuing power and wealth. He is considered a person from outside the worldly affairs. He has lived on Huashan Mountain for more than forty years, and he estimates his age to be over a hundred. He himself says that he has personally experienced the chaos of the Five Dynasties, and he is glad that the country is now peaceful, so he has come to pay homage. It is worth listening to him." Thus, he sent an imperial messenger to take Chen Tuan to the Zhongshu Province.

琪等從容問曰：「先生得玄黙修養之道，可以教人乎？」對曰：「摶山野之人，於時無用，亦不知神仙黃白之事、吐納養生之理，非有方術可傳。假令白日沖天，亦何益於世？今聖上龍顏秀異，有天人之表，博達古今，深究治亂，真有道仁聖之主也。正君臣協心同徳、興化致治之秋，勤行修煉，無出於此。」琪等稱善，以其語白上，上益重之。下詔賜號希夷先生，仍賜紫衣一襲，留摶闕下數月，放還山。

Song Qi and others calmly asked, "Sir, you have attained the way of silent cultivation. Can you teach it to others?" Chen Tuan replied, "I am a hermit in the mountains, of no use to the present age. I do not understand the practices of alchemy or breathing exercises for longevity. I have no techniques to pass on. Even if I could fly to heaven during the day, what benefit would that bring to the world? Now the emperor has an extraordinary appearance, resembling a heavenly being, is well-versed in ancient and modern times, and deeply studies the principles of governing and chaos. He is truly a virtuous and wise ruler. At this time when the king and ministers should unite in harmony, promote moral education, and achieve a well-governed world, speaking of diligent cultivation is not as important as this." Song Qi and others praised him, and reported his words to the Taizong emperor, who valued him even more. Thus, an imperial edict was issued granting him the title "Xihi Scholar," and a set of purple robes was bestowed upon him. He was kept in the capital for several months before being sent back to the mountains.

端拱初，忽謂弟子蔣徳升曰：「汝可於張超谷鑿石為室，吾將憩焉。」二年秋七月，石室成。摶手書數百言為表，其略曰：「臣摶大數有終，聖朝難戀，已於今月二十二日化形於蓮華峰下張超谷中。」如期而卒，經七日支體猶溫，有五色雲蔽塞洞口，彌月不散。

In the first year of the Duan Gong era, Chen Tuan suddenly told his disciple Jiang De Sheng: "You can go to Zhang Chao Valley to carve a stone chamber, and I will rest there." In the seventh month of the second year of Duan Gong, the stone chamber was completed. Chen Tuan himself wrote a few hundred characters as a memorial, stating in general terms: "I, Chen Tuan, have reached the end of my life span. Although I am fond of the holy dynasty, I cannot stay long. I have transformed and left my body on the 22nd of this month in Zhang Chao Valley beneath the lotus peak." He indeed died as scheduled. His body remained warm for seven days, with a cloud of five colors covering the entrance of the cave, which lasted for a whole month.

摶好讀《易》，手不釋卷，常自號扶搖子，著《指玄篇》八十一章，言導養及還丹之事，宰相王溥亦著八十一章以箋其指。摶能逆知人意。齋中有大瓢掛壁上，道士賈休復心欲之，摶已知其意，謂休復曰：「子來非有他，蓋欲吾瓢耳。」呼侍者取以與之，休復大驚，以為神。

Chen Tuan liked to read the Yi Jing, never putting it down, and often called himself "Fuyaozi." He wrote a book called "Zhi Xuan Pan" with eighty-one chapters, discussing practices of guiding breath and cultivating longevity, as well as alchemy for immortality. The chancellor Wang Pu also wrote eighty-one chapters to explain the meaning of Chen Tuan's work. Chen Tuan could foresee what others were thinking. In his study, there was a large gourd hanging on the wall. A Taoist named Jia Xiufu wanted it, and Chen Tuan had already known his thoughts. He said to him, "You have come without any other intention, but only to want this gourd of mine." Then he told his attendant to bring it down and give it to Jia Xiufu. Jia Xiufu was greatly surprised, thinking him a divine person.

有郭沆者，少居華陰，夜宿雲臺觀，摶中夜呼令趣歸，沆未決，有頃復曰：「可勿歸矣。」明日沆還家，果中夜母暴得心痛幾死，食頃而愈。華陰隠十李琪，自言唐開元中郎官，已數百歲，人罕見者。闗西逸人呂洞賓有劍術，百餘歲而童顏，步履輕疾，頃刻數百里，世以為神仙，皆數來摶齋中，人咸異之。

There was a man named Guo Hang who lived in Huayin when he was young. One night he stayed at YunTai Guan. Chen Tuan called him in the middle of the night to go home immediately. Guo Hang hesitated, but after a while Chen Tuan said, "You need not go back." The next day, when Guo Hang returned home, his mother suddenly had a severe pain in her chest and was almost dying, but after a meal's time she recovered. A hermit named Li Qi from Huayin claimed to have been a court official in the Kaiyuan era of the Tang dynasty, and he had lived for hundreds of years, but few had ever seen him. Lü Dongbin, a reclusive person from Guanxi, was skilled in sword techniques, looked like a child despite being over a hundred years old, and could walk swiftly and travel hundreds of miles in a moment. Everyone in the world regarded him as a god. These people often visited Chen Tuan's study, and at that time, everyone found it very strange.

錢希白《洞微志》曰：上即位初，鄧州觀察使錢太博若水，雍容文雅，亦近世竒士，堅乞罷樞務，遂拜禮部貳卿，充集賢院學士。其日晚，餘往謁賀，諸客退，獨相留後廳同坐，因云：某初應舉欲求解，遂往華陰謁陳先生，通刺後蒙倒屣相迎。臨出執手，約後十日卻相訪。至期徑往，迎入山齋，地爐中已先有一僧擁衲對坐，某揖之，寒暄之禮亦甚簡傲。少年壯氣，頗不平之。良久，僧熟視某而謂陳曰：「無此骨法。」二公皆微笑，雖驚異其言而不敢詢問。更有他客至，乃逡巡先退。

In the Song Dynasty, Qian Yi (style name Xibai) recorded in his book "Dongwei Zhi" that when the current emperor first ascended the throne, Qian Ruoshui, the commander of Dengzhou and the middle attendant of the crown prince, was calm and composed, with refined manners, and was considered a remarkable person of his time. He firmly requested to be relieved of his post in the Military Secretariat, and was instead appointed as the deputy minister of the Ministry of Rites and served as an academician in the Jixian Academy. That evening, I went to congratulate him. After all the other guests had left, he alone kept me in the back hall, sitting with me. Then he said: When I first took the imperial examination, I wanted to obtain the qualification for recommendation, so I went to Huayin to visit Master Chen Tuan. I presented my name card, and he welcomed me with great courtesy, even taking off his shoes to greet me. Before I left, he held my hand and promised to visit me again in ten days. When the time came, I went directly to his residence, and was welcomed into his study. There, I saw a monk already sitting by the earth stove, clad in a robe. I bowed to him, but his greetings were very brief and somewhat arrogant. At that time, I was young and full of ambition, and I felt somewhat resentful. After a while, the monk looked at me carefully and said to Chen Tuan, "He does not have this bone structure." Both of them smiled slightly. Although I was surprised by his words, I did not dare to ask further questions. At that moment, another guest arrived, so I hesitated and left first.

次日，某獨往見陳，且問僧名及言者何事。陳曰：「此即白閣道者也，道行髙潔，學通天人，至於知人尤為有神仙之鑑。欲勸留學道，中心不決，遂請道者質疑。他云：見足下非神仙骨法，學道亦不能成，但卻得好官，能於急流中勇退耳。又云：他本在太白山，累歲方一到此。」某再求見，終不可得。人生萬事，知不可以力取。（張端義《貴耳集》云：僧即麻衣道者。）

The next day, I went alone to see Chen Tuan and asked about the monk's name and the meaning of what he had said. Chen Tuan replied, "That was the White Pavilion Daoist, whose virtue is pure and lofty, and whose knowledge connects heaven and humanity. As for discerning people's character, he has the eyesight of a immortal. I had originally intended to persuade you to stay and study the Dao, but I was uncertain, so I invited the Daoist to resolve my doubts. He said: 'You do not have the bone structure of a immortal, so you cannot achieve mastery in the Dao. However, you can become an excellent official and be able to step back courageously from turbulent situations.' He also said that he originally lived in Taibai Mountain and came here only once every few years." Qian Ruoshui tried again to meet the monk, but could not find him. From this, one can see that all things in life cannot be forced by strength. (According to Zhang Duanyi of the Southern Song Dynasty's "Gu Er Ji," that monk was the Hemp-Robed Daoist.)

按：希夷，老氏之徒也。著《指玄篇》，言導養還丹之事，則其能養生也可知矣。觀賈、郭二事及預決亡日，則其能知來也可知矣。養生，魏伯陽之學也；知來，管輅、郭璞之術也。至所與遊者多異人，化形之後有異徵，則其為神仙者流又可知矣。先天圖於造化陰陽之妙，不無所窺見，要之為道家之易，而非聖人之易，其可以亂吾經邪？

Hu Wei's commentary: Chen Tuan was a person from the Daoist school of Laozi. He wrote the "Zhi Xuan Chapter," discussing practices of guiding breath and cultivating longevity, as well as alchemy for immortality, showing his skill in cultivating the body. Looking at his ability to see through the cases of Jia Xiufu and Guo Hang, as well as his accurate prediction of the day of his own death, it is evident that he could foresee the future. Cultivating the body is the kind of study followed by Wei Boyang of the Eastern Han dynasty in the "Zhou Yi Cang Tong Qi"; foreseeing the future is the kind of divination practiced by Guan Lu of the Three Kingdoms and Guo Pu of the Jin dynasty. As for the fact that he associated with many extraordinary people and had unusual signs after his death, it is clear that he belonged to the category of immortals. The Earlier Heaven diagram has some insight into the profound mysteries of the transformation of yin and yang, but ultimately it is Daoist interpretation of the Yi, not the Yi of the sages. How can it be used to disturb our scriptures?

朱子《答蔡季通書》曰：陰君丹訣，見濓溪有詩及之，當是此書（《雲笈七籖》載《陰真君傳》，言陰長生者，新野人也，師事馬明生，受太清金液神丹，白日昇天，臨去著書九篇。又陰真君自序曰：惟漢延光元年，新野山之子受仙君神丹要訣，道成去世，副之名山。蓋即此所謂陰君丹訣也。濂溪學本希夷，留心丹道，此亦其一證）。

In a letter to Cai Yuan ding (whose courtesy name was Jitong), Zhu Xi said: The so-called "Yin Jun Dan Jue" refers to a book. I have seen Zhou Dunyi mention it in a poem, and it should be this very book. (Hu Wei notes: The "Yun Ji Qi Jian" records "The Transmission of Yin Zhenjun," which says that Yin Changsheng was from Xinye, studied under Ma Mingsheng, and received the method of the Taiqing Jinye Shen Dan (Golden Elixir Divine丹). He then flew to heaven on a clear day, and before leaving, he wrote nine chapters. Yin Zhenjun's own preface says that in the first year of Yanyang during the Han dynasty, a son of Xinye Mountain received the essential secret of the divine elixir from the immortal, achieved immortality, and died, and copied another version to hide in a famous mountain. This is probably what is referred to as the "Yin Jun Dan Jue" here. Zhou Dunyi's learning originated from Chen Tuan, who was attentive to the alchemical practices, which is also evidence for this.)

彼之行此而壽考，乃吃豬肉而飽者。吾人所知，蓋不止此，乃不免於衰病，豈坐談龍肉而實未得嘗之比邪？《魏書》一哥已刻就，前日寄來此，必寄去矣。校得頗精，字義音韻皆頗有據依，逺勝世俗傳本，只欠教外別傳一句耳。

Those people attained long life by following such cultivation practices, truly having eaten pork and been well-fed. The principles we understand go beyond this, yet we still inevitably grow old and fall ill. Is this not like sitting and talking about dragon meat without ever tasting a single bite? The book by Wei Boyang (the "Zhou Yi Cang Tong Qi") has already been engraved by my elder brother, and it was sent to me recently, and I suppose it has also been sent to you. The textual corrections are quite meticulous, with clear references to meanings and pronunciations, far surpassing the commonly circulated versions. It only lacks that one sentence passed down outside the teachings.

《書周易參同契考異後》曰：魏君，後漢人。篇題蓋仿緯書之目，詞韻皆古，與雅難通，讀者淺聞，妄輒更改，故比他書尤多舛誤。今合諸本更相讎正，其間尚多疑晦，未能盡祛，姑據所知寫成定本，其諸同異因悉存之，以備參訂雲。空同道士鄒欣。

Zhu Xi's "Commentary on the Book of Changes and the Comparative Study of the Huainan Texts" says: Wei Boyang was a person of the Later Han dynasty. This book's title is probably modeled after the names of the writings of the Confucian classics, and its language and rhyme are very ancient and obscure, making it difficult to understand in the style of the refined and orthodox literary style. Readers with limited knowledge often alter the text at will, so the errors in this book are especially numerous. Now, by comparing various editions, many difficult and obscure points remain, and they have not been completely resolved. Therefore, I have compiled a definitive version based on my own understanding, and have also preserved the differences among the various editions for reference and correction. The text ends with the signature "Zou Xin, the Taoist of Kungtong."

（雙湖胡氏曰：鄒欣即公姓名。向解者以為「鄒」者「朱」之轉，「欣」者「熹」之轉耳。後據《考異》本原有注云：按鄒本春秋邾子之國，《樂記》云「天地欣合」，鄭氏注「欣」當作「熹」，則「鄒欣」二字即「朱熹」二字，他人不解也。）

(Hu Wei notes: Hu Yigui, a scholar of the Yuan dynasty known as Master Shuanghu, said: "Zou Xin" refers to Zhu Xi's name. Previously, interpreters thought "Zou" was a phonetic variant of "Zhu" and "Xin" was a phonetic variant of "Xi". Later, based on the annotations in the "Kao Yi" edition of the "Cantongqi", it was stated that "Zou" originally refers to the state of Zou from the Spring and Autumn period, and the "Liji · Le Ji" contains the phrase "Tian di Xin he", with Zheng Xuan's commentary stating that "Xin" should be read as "Xi". Therefore, the two characters "Zou Xin" are actually "Zhu Xi", but others could not understand this.)

《題袁機仲所校參同契後》曰：予頃年經行順昌，憩篔簹鋪，見有題「煌煌靈芝，一年三秀，予獨何為，有志不就」之語於壁間者，三復其詞而悲之，不知題者何人，適興予意會也。慶元丁巳八月七日（時朱子年六十八），再過其處，舊題固不復見，而屈指歲月，忽忽餘四十年，此志真不就矣。道間偶讀此書，並感前事，戲題絶句：「鼎鼎百年能幾時，靈芝三秀欲何為。金丹歲晚無消息，重嘆篔簹壁上詩。」晦翁。

Zhu Xi wrote in "Commentary on the Afterword of Yan Jizhong's Edition of the Complete Discourse on the Supreme Harmony": When I passed through Shunchang in the past, I stopped at Yundang Pavilion and saw some words written on the wall: "Luminescent lingzhi, blooming three times a year, why am I alone, with aspirations unfulfilled." I recited these lines three times and felt deeply moved, not knowing who had written them, yet they coincided with my own feelings. In the fourth year of Dingsi (1207), on the seventh day of the eighth lunar month (at the time Zhu Xi was sixty-eight years old), I passed through there again, but the old inscription was no longer visible. Counting the years, it had been over forty years, and this aspiration had still not been realized. On the way, I偶然 read the book "Complete Discourse on the Supreme Harmony," and felt nostalgic for the past, and composed a humorous quatrain: How long can a hundred years be, when lingzhi blooms three times a year? The elixir of gold has yet to be achieved in old age, and I can only sigh again at the poem on the wall of Yundang Pavilion. Signed: Huiweng.

《調息箴》曰：鼻端有白，我其觀之。隨時隨處，容與猗移。靜極而噓，如春沼魚；動極而翕，如百蟲蟄。氤氳開闢，其妙無窮，孰其尸之，不宰之功。雲臥天行，非予敢議，守一處和，千二百歲。

Zhu Xi's "Regulation of Breathing" says: On the tip of the nose there is a white point, and I focus my mind on observing it. At all times and places, I calmly and freely regulate my breathing. When stillness reaches its extreme, I exhale as a fish in a spring pond breathes; when movement reaches its extreme, I inhale as creatures in hibernation withdraw. One mist, one vapor; one closure, one opening. Within this there is infinite subtlety. Who is in control of it? It is the natural function of nothing being controlled. A state like clouds resting high, or the heavens moving in their course, is not something I dare to comment upon. By holding fast to this 'one' and dwelling in the middle harmony, one can live to be one thousand two hundred years old.

《答王子耕書》曰：病中不宜思慮，凡百可且一切放下，専以存心養氣為務，但跏趺靜坐，目視鼻端，注心臍腹之下，久自溫暖，即漸見功效矣。

Zhu Xi in his letter "Answer to Wang Zigeng" says: During illness, it is not advisable to think and worry too much; all matters can be temporarily set aside, and the main focus should be on nurturing the mind and cultivating the original energy. One needs only to sit in meditation with the legs crossed, gaze steadily at the tip of the nose, and concentrate the mind below the navel. With time, that area will naturally become warm, and the effects will gradually become apparent.

按：養生、知來，皆希夷之能事，而朱子獨有取於養生者，蓋衰年病侵，欲藉是以卻之，使徳業更有所進耳。觀鼻端之白，嘆壁上之詩，疑龍鮓之難嘗，羨豬肉之易飽，所謂寓意於物而不留意於物也。故金丹之訣，不惟知之，而身欲試之。撰《參同契考異》，託名空同道士鄒欣；而序《啟蒙》則曰云臺真逸，跋《道徳經》則曰云臺子；及其奉祠雲臺也，又寄陸子靜書云：「熹衰病，幸叨祠祿，遂為希夷直下諸孫，良以自慶。」其嚮慕之誠如此，此《太極真圖》所以期於必得也。坎離龍虎，未必非易中之一義，但不可謂易専為是而作耳。

Hu Wei commented: The cultivation of life and the prediction of the future were the main skills of Chen Tuan, but Zhu Xi only used the aspect of life cultivation. Perhaps this was because Zhu Xi was old and sick, and he wanted to use this method to drive away his illness and still make progress in his moral and scholarly achievements. Looking at his actions, such as gazing at the white at the tip of his nose and sighing at the poetry on the wall, doubting that "dragon meat" is hard to taste and envying "pork" which is easy to eat, this is what is called "expressing meaning through things without being attached to them." Therefore, regarding the secret formulas of the golden elixir, he not only knew about them but also wanted to try them personally. He wrote "Commentary on the Differences of the Three Syntheses of the Zhou Yi," falsely attributing it to "Zou Xin, the Taoist of Kungtong." He signed himself as "Yuntai Zhenyi" when writing the preface to "The启蒙 of the Yi," and as "Yuntai Zi" when writing the跋 to the "Dao De Jing." When he was in charge of the Yuntai Temple's official salary, he sent a letter to Lu Jiuyuan saying, "I am old and sick, but I have been honored with the official salary, thus becoming the direct descendant of Master Xiyi. This is truly worth celebrating." His sincerity towards Chen Tuan reached such a level, which is why he insisted on obtaining the "True Diagram of the Taiji." The concepts of Kan and Li, dragon and tiger, may not be without meaning in the Yi, but it cannot be said that the Yi was specifically written for these concepts.

右論陳希夷。

The previous section discusses Chen Tuan's person and his scholarly contributions in relation to the diagrams of the Book of Changes.

《宋史·道學傳》：邵雍字堯夫，其先范陽人，父古徙衡漳，又徙共城。雍年二十遊河南，葬其親伊水上，遂為河南人。雍少時自雄其才，慷慨欲樹功名，於書無所不讀。始為學，即堅苦刻厲，寒不爐，暑不扇，夜不就席者數年。已而嘆曰：「昔人尚友于古，而吾獨未及四方。」於是踰河、汾，涉淮、漢，周流齊、魯、宋、鄭之墟。久之，幡然來歸曰：「道在是矣。」遂不復出。

The "Song Shi · Dao Xue Zhuan" records that Shao Yong, whose courtesy name was Yao Fu, had ancestors from Fan Yang. His father, Shao Gu, moved to Hengzhang, and later to Gongcheng. At the age of twenty, Shao Yong traveled through Henan, buried his parents by the Yi River, and thus became a resident of Henan. In his youth, Shao Yong was confident in his talents, ambitious, and eager to achieve fame. He studied extensively without any restrictions. When he began his studies, he was rigorous and disciplined, not lighting a furnace in cold weather, not using a fan in hot weather, and not sleeping in bed at night, continuing this for several years. Later he lamented, "Ancient people still sought to be friends with ancient people, yet I have not even traveled the four directions." Therefore, he crossed the Yellow River and Fen River, traveled through the Huai River and Han River, and visited the former territories of Qi, Lu, Song, and Zheng. After a long time, he suddenly realized and returned, saying, "The Way is here." From then on, he no longer went out.

北海李之才攝共城令，聞雍好學，嘗造其廬，謂曰：「子亦聞物理性命之學乎？」雍對曰：「幸受教。」乃事之才，受《河圖》《洛書》、宓羲八卦六十四卦圖象。之才之傳，逺有端緒，而雍探賾索隠，妙悟神契，洞徹蘊奧，汪洋浩博，德其所自得者。及其學益老，徳益劭，玩心髙明，以觀天地之運化、陰陽之消長，逺而古今世變，微而走飛草木之性情，深造曲暢，庶幾所謂不惑，而非依仿象類、億則屢中者。遂衍宓羲先天之旨，著書十餘萬言行於世，然世之知其道者鮮矣。

Li Zhicai, a man from the northern sea, served as the acting magistrate of Gongcheng County. He heard that Shao Yong was devoted to learning, and he visited him, saying, "Have you heard of the study of the principles of things and the nature of life?" Shao Yong replied, "I would be happy to learn." Thus, he became Shao Yong's student and received the diagrams of the Yellow River Chart, the Luo Writing, and the Eight Trigrams and the sixty-four hexagrams of Fuxi. The transmission of this school, led by Li Zhicai, had a long and clear lineage. Shao Yong, however, explored deeply and sought out the subtle, achieving a profound intuitive understanding and thoroughly grasping the hidden meanings. His learning was vast and profound, mostly derived from his own insights. As his knowledge became more refined and his virtue more cultivated, he focused on the lofty and sublime, observing the transformations of heaven and earth, the waxing and waning of yin and yang, the changes of ancient and modern events, and the nature of birds, beasts, and plants, all of which he studied thoroughly and comprehensively. He had reached a state close to what is called "not confused," rather than the kind of approach that relies on analogy and guesswork to make frequent correct predictions. Thus, he developed the principles of the Earlier Heaven learning of Fuxi, writing over a hundred thousand characters that circulated in the world, yet few people understood his learning.

熙寧十年卒，年六十七，贈秘書省著作郎，元佑中賜諡康節。雍髙明英邁，迥出千古，而坦夷渾厚，不見圭印，是以清而不激，和而不流，人與交久，益尊信之。河南程顥初侍其父識雍，議論終日，退而嘆曰：「堯夫，內聖外王之學也。」

Shao Yong died in the tenth year of the Xining era at the age of sixty-seven. The court posthumously awarded him the title of Secretary of the Imperial Academy. During the Yuanyou period, he was granted the posthumous name "Kangjie." Shao Yong was highly intelligent and outstanding, far surpassing those of all previous generations. However, he was humble and unassuming, not showing off his talents. Therefore, he was lofty yet not extreme, easygoing yet not tainted by the world. The more people interacted with him, the more they respected and trusted him. Cheng Hao, a native of Henan, once accompanied his father Cheng Xiang to meet Shao Yong. They discussed for the whole day, and after Cheng Hao left, he sighed, saying, "Master Yaofu's learning is the study of inner sagehood and outer kingship."

雍知慮絶人，遇事能前知。程頤嘗曰：「其心虛明，自能知之。」當時學者因雍超詣之識，務髙雍所為，至謂雍有玩世之意；又因雍之前知，謂雍於凡物聲氣之所感觸，輒以其動而推其變焉，於是摭世事之已然者，皆以雍言先之，雍蓋未必然也。

Shao Yong's insight and contemplation surpassed ordinary people, and he could foresee events. Cheng Yi once said, "His mind was pure and clear, so he naturally knew." At that time, scholars, because Shao Yong's insight was extraordinary, exaggerated his actions, even saying he had a carefree attitude towards the world. Also, because he could foresee things, they said that whenever he came into contact with the sounds and breath of things, he could judge their movements and predict their changes. Therefore, they took all the events that had already happened and claimed that Shao Yong had predicted them beforehand. In reality, Shao Yong may not have actually done so.

所著書曰《皇極經世》《觀物內外篇》《漁樵問對》，詩曰《伊川擊壤集》。邵子《無名公傳》曰：朝廷授之官，雖不強免，亦不強起。晚有二子，教之以仁義，授之以六經。舉世尚虛談，未嘗掛一言；舉世尚竒事，未嘗立異行。故其詩曰：「不佞禪伯，不諛方士，不出戶庭，直遊天地。」家素業儒，口未嘗不道儒言，身未嘗不行儒行。故其詩曰：「心無妄思，足無妄走，人無妄交，物無妄受。炎炎論之，甘處其陋；綽綽言之，無出其右。」羲、軒之書未嘗去手，堯、舜之談未嘗離口。當中和天，同樂易友，吟自在詩，飲歡喜酒。百年昇平，不為不偶；七十康強，不為不壽。此其無名公之行乎。

Shao Yong wrote the books "Huangji Jingshi", "Guanwu Neiwaizhuan", and "Yujiao Wen Dui". His poetry collection is called "Yichuan Jiyang Ji". In his self-written "Wuminggong Zhuan", he said: when the court conferred an official position upon him, he neither firmly refused nor insisted on taking office. In his later years, he had two sons, whom he taught with benevolence and righteousness, and instructed them with the Six Classics. When the world was full of empty and abstract discussions, he never said a single word about them; when the world was full of strange things, he never did a single strange act. Therefore, his poetry says: he did not flatter Buddhist masters, nor did he fawn over alchemists or mystics. He never left his home, yet he directly roamed through the universe. His family had been scholars for generations; he never ceased speaking the words of a Confucian, nor did he ever cease acting according to the deeds of a Confucian. Therefore, his poetry says: he never had false thoughts in his mind, never took false paths, never made false connections with others, nor accepted false gifts. When others boasted loudly with great ambition, he was content to live in a humble dwelling, and spoke calmly and freely about principles, yet no one could surpass him. The writings of Fuxi and Huangdi were never out of his hands, and the topics of Yao and Shun were never out of his mouth. He lived in a harmonious and peaceful age, and associated with friends who were pleasant and easygoing. He recited free and easy poetry, and drank joyful wine. In a hundred years, the world was peaceful and prosperous, which cannot be said not to be a good opportunity; at seventy years old, he was still healthy and strong, which cannot be said not to be longevity. This is probably the conduct of that "Wuminggong".

明道先生志康節之墓曰：昔七十子學於仲尼，其傳可見者，惟曽子告子思，所以授孟子者耳。其餘門人，各以其材之所宜為學，雖同尊聖人，所因而入者，門戸則眾矣。況後此千餘歲，師道不立，學者莫知其從來，獨先生之學為有傳也。先生得之於李挺之，挺之得於穆伯長，推其源流，逺有端緒，今穆、李之言及其行事，概可見矣。而先生醇一不雜，汪洋浩大，乃其所自得者多矣。然而名其學者，豈所謂門戶之眾各有所因而入者歟？語成徳者，昔難其居，若先生之道，就其至而論之，可謂安且成矣。

Cheng Hao's epitaph for Shao Yong says: Among the seventy disciples of Confucius, only the lineage from Zengzi to Zisi and then to Mencius can be traced. The other disciples studied according to their own aptitudes and talents, although they all revered the sage. However, the ways they approached learning were various. Moreover, for over a thousand years after that, the way of teaching was not established, and scholars could not even say where their learning came from. Only Shao's learning had a clear transmission. He received it from Li Zhicai (whose name was Tingzhi), who in turn received it from Mu Xiu (whose name was Boyang). Tracing its source, it is far back but has a clear lineage, and now the words and deeds of Mu Xiu and Li Zhicai can still be roughly seen. Shao's learning was pure and unadulterated, vast and boundless, mostly derived from his own insight. Thus, to name his learning, is it not just one of the many ways to approach learning, each with its own origin? As for those who have achieved moral excellence, it was rare to be called so before. But in terms of the depth of his attainment, Shao's way of learning can be said to be both secure and accomplished.

《程氏遺書》曰：堯夫之學，先從理上推意，言象數言天下之理，須出於四者，推到理處，曰：「我得此大者，則萬事由我，無有不定。」然未必有術，要之亦難以治天下國家。其為人則直是無禮不恭，惟是侮玩，雖天地亦為之侮玩。如《無名公傳》言「問諸天地，天地不對」「弄丸餘暇，時往時來」之類。

The "Chengshi Yishu" says: Shao Yong's studies first seek the meaning from the principle of "li." He discusses the principles of numbers and forms, and the principles of the world, all of which must be derived from the four concepts of yuan, hui, yun, and shi. When he investigated the principle, he said, "If I have mastered this fundamental principle, then all things will be under my control, and nothing will be unable to be stabilized." However, he may not have actually possessed practical methods, and in general, it would be difficult to use his ideas to govern the state and the country. As for his character, he was truly disrespectful and not reverent, always playing and mocking, even treating heaven and earth as objects of mockery. This is similar to what the "Wuming Gong Zhuan" says: "He asked the heavens and earth, but the heavens and earth did not respond," and "He played with a ball in his spare time, and time came and went."

君實篤厚，晦叔謹嚴，堯夫放曠。又曰：堯夫道雖偏駁，然卷舒作用極熟，又能謹細行。又曰：堯夫襟懷放曠，如空中樓閣，四通八達也。伯淳言邵堯夫病革，且言試與觀化一遭。子厚言觀化他人便觀得，自家又如何觀得化？嘗觀堯夫詩意，才做得識道理，卻於儒術未見所得。

Cheng also said: Sima Guang (style name Junshi) was sincere and solid, Lü Xizhe (style name Hui shu) was cautious and upright, and Shao Yong (style name Yaofu) was free-spirited and open-minded. He also said: Although Shao Yong's way was mixed and not pure, his ability to use it was extremely skillful, and he could also be careful in his conduct. He also said: Shao Yong's mind was free-spirited and open-minded, like a building in the air, with all roads leading to it. Cheng Hao (style name Bochun) said that when Shao Yong was seriously ill, he still said it was not wrong to try to observe the changes of the universe. Zhang Zai (style name Zihou) said: Observing the universe, one can observe others, but how can one observe one's own death? I once looked into the meaning of Shao Yong's poetry, and he could only understand some principles, but there was no sign of his having any deep insight into the learning of the Confucian scholars.

世人之學，博聞強識者豈少？其終無有不入禪學者，就其間特立不惑，無如子厚、堯夫，然其說之流，恐未免此弊。邵堯夫數法出於李挺之，至堯夫推數方及理。邵堯夫臨終時只是諧謔，須臾而去。以聖人觀之則亦未是，蓋猶有意也；比之常人，甚懸絶矣。他疾甚革，某往視之，因警之曰：「堯夫平生所學，今日無事否？」他氣微不能答。次日見之，卻有聲如絲髮來大，答云：「你道生薑樹上生，我亦只得依你說。」

People nowadays study diligently, and those who are widely learned and have strong memories are not rare. Yet none of them escape falling into the teachings of Chan Buddhism. Among them, those who stand out independently and are not misled by this, none surpass Zhang Zai and Shao Yong. However, their teachings, when passed down, might also fall into this same problem. Shao Yong's method of mathematics came from Li Zhichai, and it was Shao Yong who advanced from calculation to the study of principles. When Shao Yong was dying, he was just laughing all the time and passed away in an instant. Judged by the standard of the sages, this still falls short of perfection, because there is still an element of deliberate effort. However, compared to ordinary people, he was far beyond them. When his illness was severe, I (Cheng Yi) visited him and reminded him, "Master Yaofu, do you today have certainty in your learning without any doubts?" He was too weak to answer. The next day, I visited him again, and he managed to answer with a voice as thin as a hair, "You say ginger grows on trees, I can only follow your statement."

尹子曰：邵堯夫家以墓誌屬明道，太中、伊川不欲。因步月於庭，明道曰：「顥已得堯夫墓誌矣，堯夫之學可謂安且成。」太中乃許。

Cheng Yi's student Yin Tun said: Shao Yong's family entrusted the task of writing his epitaph to Cheng Hao. Cheng Hao's father Cheng Xiang, who had reached the rank of Taizhong Dafu, and his younger brother Cheng Yi all disapproved. Once, while walking in the courtyard under the moon, Cheng Hao said: "I have already decided how to write the epitaph for Yao Fu — Yao Fu's learning can be said to be both secure and accomplished." Only then did Cheng Xiang agree.

《上蔡語録》曰：堯夫易數甚精，自來推長厯者，至久必差，惟堯夫不然，指一二近事，當面可驗。明道云：「待要傳與某兄弟。」某兄弟那得功夫？要學須是二十年功夫。明道聞說甚熟，一日因監試無事，以其說推算之，皆合。出謂堯夫曰：「堯夫之數，只是加一倍法，以此知《太玄》都不濟事。」堯夫驚，撫其背曰：「大哥，你恁聰明。」伊川謂：「堯夫知易數為知天，知易理為知人。」堯夫云：「還須知易理為知天。」因說今年雷起甚處，伊川云：「堯夫怎知？某便知。」又問某處起，伊川云：「起處起。」堯夫愕然。他日伊川問明道曰：「加倍之數何如？」曰：「都忘之矣。」因嘆其心無偏繫如此。

Cheng Yi's disciple Xie Liangzuo's "Shangcai Yulu" says: Shao Yong's divination numbers are extremely refined. Those who have calculated long calendars in the past inevitably make errors over time, but Shao Yong never does. He can simply point out one or two recent events and verify them on the spot. Cheng Hao said: "He wants to pass this skill on to us brothers." But we brothers don't have the time for that. To learn it, one must spend twenty years. Cheng Hao had heard his words many times. One day, while supervising an exam with nothing to do, he used the method to calculate, and the results matched. Afterward, he told Shao Yong: "Yao Fu's numbers are just a method of doubling. From this we can see that Yang Xiong's "Tai Xuan" is completely useless." Shao Yong was surprised and patted Cheng Hao's back, saying: "Big brother, you are so smart." Cheng Yi said: "Yao Fu believes that understanding the numbers of the Book of Changes is knowing heaven, and understanding the principles of the Book of Changes is knowing people." Shao Yong said: "It is only by understanding the principles of the Book of Changes that one can know heaven." Once, when discussing where the thunder started this year, Cheng Yi said: "How did Yao Fu know? I know." Shao Yong asked again where the thunder started, and Cheng Yi said: "It starts from where it starts." Shao Yong was stunned and speechless. Later, one day Cheng Yi asked Cheng Hao: "What exactly is the method of doubling?" Cheng Hao said: "I have completely forgotten." Cheng Yi therefore praised him for not being fixated on this matter.

《朱子語類》：問：「康節學到不惑處否？」曰：「康節又別是一般。聖人知天命以理，它只是以術，然到得術之精處，亦非術之所能盡，然其初只術耳。」又曰：「想它看見天下之事，才上手來便成四截了，其先後緩急莫不有定，動中機會，事到面前便處置得下矣。只是用時須差異，須有些機權術數也。」老子窺見天下之事，卻討便宜，置身於安閒之地，雲清靜自治，邵康節亦有些小似他。問：「《淵源録》中何故有康節傳？」曰：「書坊自増耳。」（見《孟子》「楊子取為我」章下。）

In the "Zhu Zi Yu Le" it is recorded that someone asked: "Has Shao Yong's learning reached the point of not being confused?" Zhu Xi said: "Shao Yong is another kind of approach. The sages know heaven's mandate by principle, while he relied on techniques. However, when his techniques became refined, they could not be fully exhausted by techniques, yet he originally relied on techniques alone." Zhu Xi also said: "It seems that when he looked at the affairs of the world, he divided them into four parts as soon as they came into his hands, with clear order in terms of sequence and urgency, and his actions were always timely and effective. However, his application had to appear different from others, always involving some elements of strategy, tactics, and techniques." Laozi understood the affairs of the world thoroughly, yet he chose the easiest path, placing himself in a peaceful position, talking about quiet governance and self-cultivation. Shao Yong was somewhat similar to him. Someone asked: "Why does the 'Yi Luo Yuan Yuan Lu' include a biography of Shao Yong?" Zhu Xi said: "That was added by the bookshop itself." (This entry is found under the chapter "Yangzi Qu Wei Wo" in the "Mengzi.")

《答汪尚書書》曰：程、邵之學固不同，然二先生所以推尊康節者至矣。蓋以其信道不惑，不雜異端，班於溫公、橫渠之間，則亦未可以其道不同而遽貶之也。和靖之言，恐如孟子言伯夷、伊尹之於孔子為不同道之比，妄意其然，不識臺意以為然否？抑康節之學，抉摘窈微，與佛老之言豈無一二相似，而卓然自信，無所汙染，此其所見必有端的處，比之溫公欲護名教而不言者，又有間矣。

Zhu Xi's letter to Wang Shushang says: The learning of the two brothers of the Cheng family and Shao Yong is indeed different, yet the two Chengs have praised Shao Yong to the utmost. Perhaps it is because he had firm faith without confusion, without mixing in heresies, and thus could be placed between Sima Guang and Zhang Zai. Therefore, one should not lower his status just because their approaches differ. Yi Tun's (whose courtesy name is Hejing) view, perhaps resembles Mencius' statement that Boyi, I Yin, and Confucius were "different in their ways." I make this guess, but I do not know whether you think so. Moreover, Shao Yong's learning, by exploring the subtle and profound aspects, has some resemblance to the teachings of Buddhism and Taoism. Yet he had firm self-confidence and was not influenced by them, which shows that his insights must have practical grounding. This is one level higher than Sima Guang's attitude of not discussing matters simply to uphold the rites and norms.

厚齋王氏曰：張文饒云：「處心不可著（直略切，下同），著則偏；作事不可盡，盡則窮。」先天之學止是此二語，天之道也。愚謂邵子詩「夏去休言暑，冬來始講寒」，則心不著矣；「美酒飲教微醉後，好花看到半開時」，則事不盡矣。

In the Southern Song dynasty, the learned scholar Wang Yinglin of Houshazhai said: Zhang Xingcheng (style name Wenrao) said, "One's mind should not be attached; attachment leads to bias. Actions should not be carried to the extreme; when done to the extreme, there is no way out." The study of the Earlier Heaven is nothing more than these two sentences, which is the way of Heaven. Wang Yinglin himself believed that in Shao Yong's poem, "After summer, do not speak of heat; only when winter comes do we talk about cold," refers to not being attached to one's mind. And "Drink wine until slightly drunk, and appreciate flowers when they are half in bloom" refers to not doing things to the extreme.

按：邵子之學源出希夷，實老莊之宗派。但希夷一言一動，無非神仙面目；而邵子則不尚虛談，不立異行，不落禪機，不溺丹道，粹然儒者氣象，故二程樂與之遊。然觀其平日所論，微有不滿於邵子者：曰放曠，曰偏駁，曰無禮不恭，曰空中樓閣，曰儒術未見所得，曰其說之流有弊。瑕瑜不相揜，亦未可謂推尊之至也。

Hu Wei commented: Shao Yong's learning originated from Chen Tuan, and in fact belonged to the school of Laozi and Zhuangzi. However, Chen Tuan's every word and action presented the appearance of a immortal; while Shao Yong did not value empty and mysterious discussions, did not engage in novel and distinctive behavior, did not fall into the subtleties of Chan Buddhism, nor did he become addicted to alchemy. He displayed a pure Confucian demeanor, so the two Cheng brothers were willing to associate with him. However, looking at the Cheng brothers' usual discussions, they actually subtly expressed dissatisfaction with Shao Yong: they called him "reckless," "biased," "impolite and disrespectful," compared him to "a building in the air," said his Confucian learning had not yielded results, and warned that his teachings, if passed on, would bring about evils. The flaws and merits could not be concealed from each other, and it could not be said that the Cheng brothers revered him to the utmost.

及其為墓誌，則謂得之穆、李者，特因其材之所宜以為入道之門戸，則固以象數為一家之學矣。雖云自得者多，不止穆、李之所傳，然終不離乎象數。易道之大，無所不包，執一家之學而以為伏羲之精意全在於此，豈理也哉！

When Cheng Hao wrote the epitaph for him, he said that what he had received from Mu Xiu and Li Zhihai was merely suitable for his own talent and character, serving as a way to enter the Dao. This clearly regarded the images and numbers as the teachings of a single school. Although he himself had gained much through personal insight, not limited to what was passed down by Mu and Li, he could not escape the framework of images and numbers. The Way of the Changes is vast and inclusive, encompassing everything. To grasp the teachings of one school and claim that Fuxi's subtle intentions are entirely contained within it, how could such a notion be reasonable!

朱子於先天方位得養生之要，於加一倍法見數學之精，篤信季通，意固有在，吾何敢輕議，但不當列諸經首以為伏羲之易耳。明道適僧舍，見其方食而曰「三代威儀盡在是矣」，此偶然語也；設有人焉，掇浮屠之戒律冠於《禮經》之首，則荒矣。胡文定於內典獨稱《楞嚴》《圓覺》，亦謂彼教中有可取者耳；設有人焉，舉二書於《中庸》《論語》合為一編，則悖矣。故吾以為邵子之易與聖人之易，離之則雙美，合之則兩傷，學者不可以不審也。

Zhu Xi derived the principles of health preservation from the Earlier Heaven diagram, perceived the subtlety of mathematics through the method of doubling, and firmly believed in Cai Yuan Ding's statements, with his intentions clearly aimed somewhere, and I dare not lightly comment on them; however, it is inappropriate to place these diagrams at the beginning of the classics, treating them as the Yi of Fuxi. Cheng Hao went to a Buddhist monastery and saw the monks having their meal, then said, "The decorum of the Three Dynasties is all here," which was merely an incidental remark; if someone were to take Buddhist precepts and place them before the Li Jing, that would be absurd. Hu An Guo (posthumous name Wen Ding) praised the Lengyan Jing and Yuanjue Jing from the Buddhist scriptures, merely indicating that there are some commendable aspects in that teaching; if someone were to compile these two texts together with the Zhongyong and Lunyu into one book, that would be a misstep. Therefore, I believe that Shao Yong's Yi and the Yi of the sage are each excellent when separated, but both would be harmed if combined, and scholars must be cautious in distinguishing between them.

右論邵康節。

The previous section discusses the relationship between Shao Yong's teachings and the Earlier Heaven diagrams.

《宋史·隠逸傳》：譙定字天授，涪陵人。少喜學佛，折其禮歸於儒，後學《易》於郭曩氏，自見乃謂之象，一語以入。郭曩氏者，世家南平，始祖在漢為嚴君平之師，世傳易學，蓋象數之學也。定一日至汴，聞伊川程頤講道於洛，潔衣往見，棄其學而學焉，遂得聞精義，造詣愈至，浩然而歸。

The "Biography of the Recluse" in the "Song History" records that Qiao Ding, who was called Tianshuo, was from Fuling. He was young and fond of studying Buddhism, but later was convinced by Confucianism and turned to Confucian learning. Afterwards, he studied the "Book of Changes" with the Guo family, and when he had his own insights, he called them "Xiang" (images). He could directly enter the key point with a single sentence. The Guo family had lived in Nanping for generations, and their ancestor in the Han dynasty had been the teacher of Yan Junping. They had passed down the study of the "Book of Changes" through the generations, following the school of Xiangshu (images and numbers). One day, Qiao Ding went to Bianjing and heard that Cheng Yi, known as Master Yichuan, was lecturing on the Way in Luoyang. He then dressed himself neatly and went to pay his respects. He abandoned his previous studies and changed to follow Cheng Yi, thus hearing the subtle principles and deepening his understanding. He returned home with a sense of grandeur and fulfillment.

其後頤貶涪，實定之鄉也。北山有巖，師友游泳其中，涪人名之曰讀易洞。靖康初，呂好問薦之，欽宗召為崇政殿說書，以論弗合，辭不就。髙宗即位，定猶在汴，右丞許翰又薦之，詔宗澤津遣詣行在。至維揚，寓邸舍，窶甚，一中貴人偶與鄰，饋之食不受，與之衣亦不受，委金而去，定袖而歸之。其自立之操類此。

Later, Cheng Yi was exiled to Fuzhou, which was the hometown of Qiao Ding. There was a mountain cave in Beishan where master and disciple used to leisurely study and discuss, and the people of Fuzhou called it "Reading the Yi Classic Cave." In the early years of Jingkang, Lü Haowen recommended Qiao Ding, and Emperor Qinzong summoned him to serve as a lecturer in the Chongzhi Hall. However, due to disagreements in opinions, he declined the position. When Emperor Gaozong ascended the throne, Qiao Ding was still in Bianjing. The Right Chancellor of the Ministry of Personnel, Xu Han, again recommended him, and the court issued an edict ordering Zong Ze to prepare boats and carts to send him to the imperial court. When he arrived in Weiyang, he stayed in a guest house, living in poverty. A eunuch who happened to be his neighbor gave him food, but he refused to accept it; he also refused clothes. The eunuch left money and went away, and Qiao Ding used his sleeve to wrap the money and returned it. His conduct of self-reliance and integrity was roughly like this.

上將用之，會金兵至，失定所在，復歸蜀，愛青城大酉之勝，棲遁其中。蜀人指其地曰譙巖，敬定而不敢名，稱之曰譙夫子，有繪像祀之者，久而不衰。定易學得之程頤，授之胡憲、劉勉之，而馮時行、張行成則得定之餘意者也。定後不知所終，樵夫牧童往往有見之者，世傳其為仙雲。

Emperor Gaozong was about to appoint him, but just as the Jin army came, Qiao Ding lost his way and returned to the Sichuan region. He loved the beautiful scenery of Qingcheng Mountain and Dayou Mountain, and so he withdrew to live in seclusion there. The people of Sichuan pointed to his place of retreat and called it "Qiao Rock," showing respect for him and not daring to use his name directly. They called him "Master Qiao." Some even painted his portrait and worshipped it, and this tradition continued for a long time. Qiao Ding's study of the Book of Changes came from Cheng Yi, and he passed it on to Hu Xian and Liu Mianzhi. However, Feng Shixing and Zhang Xingcheng received his teachings later. Later, Qiao Ding's final destination was unknown. Often, shepherds and woodcutters would see him, and the world spread the legend that he had become an immortal.

初，程頤之父珦嘗守廣漢，頤與兄顥皆隨侍，遊成都，見治篾篐桶者挾冊，就視之則《易》也。欲擬議致詰，而蔑者先曰：「若嘗學此乎？」因指「未濟男之窮」以發問，二程遜而問之，則曰：「三陽皆失位。」兄弟渙然有所省，翌日再過之，則去矣。

At first, Cheng Yi's father, Cheng Xiang, served as the governor of Guanghan, and both Cheng Yi and his brother Cheng Hao were with him. Once they visited Chengdu and saw a bamboo worker carrying a book. When they approached to take a look, they found it was the Book of Changes. The Cheng brothers were about to find the right words to ask questions, but the bamboo worker spoke first, asking, "Have you studied this before?" Then he pointed to the sentence in the "Sequence of Hexagrams" "Wei Ji, the male's decline" and asked about it. The two Cheng brothers modestly asked him for an explanation, and he replied, "Because in the Wei Ji hexagram, the three yang lines are not in the right place." The brothers suddenly had a clear understanding. The next day, they went to find him again, but he had already left.

其後袁滋入洛，問《易》於頤，頤曰：「易學在蜀耳，盍往求之？」滋入蜀訪問，久無所遇，已而見賣醬薛翁於眉、卭間，與語大有所得，不知所得何語也。憲、勉之、滋皆閩人，時行、行成蜀人，郭曩氏及篾叟、醬翁皆蜀之隠君子也。

Later, Yuan Zi went to Luoyang and asked Cheng Yi about the Book of Changes. Cheng Yi said, "The study of the Book of Changes is in Sichuan, why not go there to seek it out?" Yuan Zi went to Sichuan to search for it, but did not meet anyone for a long time. Later, he met an old man selling sauce named Xue in between Muzhou and Qiongzhou, and had a conversation that brought him great insight, though he did not know exactly what he had gained. Hu Xian, Liu Mianzhi, and Yuan Zi were all from Fujian, while Feng Shixing and Zhang Xingcheng were from Sichuan. The Guo Nang family and the bamboo-woven craftsman and the old man selling sauce were all reclusive sages from Sichuan.

朱子《籍溪先生胡公行狀》曰：先生學《易》於涪陵處士譙公天授，久未有得。天授曰：「是固當然，蓋心為物漬，故不能有見，唯學乃可明耳。」先生於是喟然嘆曰：「所謂學者，非克己工夫也邪？」自是一意下學，不求人知，一旦揖諸生，歸隠於故山。

Zhu Xi's "Jixi Xiansheng Hu Gong Xingzhuang" says: Master Hu Xian studied the Book of Changes with Quaoding, a hermit in Fuling, but for a long time had no insights. Quaoding said, "This is naturally so, because the human mind is tainted by external things, so it cannot perceive clearly; only through learning can one understand." Master Hu then sighed and said, "So learning is not simply the effort to overcome one's own desires?" From then on, he devoted himself wholeheartedly to practical study, not seeking recognition from others. One day, he bowed to his students and left to retreat to the mountains of his hometown.

《與汪尚書書》曰：郭子和雲譙天授亦伊川黨事後門人。熹見胡、劉二丈說親見譙公自言，識伊川於涪陵，約以同居洛中，及其至洛，則伊川已下世矣。問以伊川易學，意似不以為然，至考其它言行，又頗雜於佛老子之學者，恐未得以門人稱也。以此一事及其所著象學文字推之，則恐其於程門亦有未純師者，不知其所謂卒業者果何事邪？

Zhu Xi in his letter to Wang Shushu said: Guo Yong, who goes by the name Zihe, claimed that Qiao Ding was a disciple of Cheng Yi after the Cheng Yi faction ban. I once heard two elders, Hu Xian and Liu Mianzhi, say that they personally heard Qiao Ding himself tell that he met Cheng Yi in Fuling and had agreed to live together in Luoyang later. When he arrived in Luoyang, Cheng Yi had already passed away. When asked about his view on Cheng Yi's study of the Book of Changes, his opinion seemed to be in disagreement. Further examining his other words and deeds, they were quite mixed with Buddhist and Laozi's teachings. Therefore, he cannot be considered a true disciple of Cheng's school. From this incident and his writings on the象学 (xiangxue, which refers to a system of divination), it seems that he did not fully inherit Cheng's teachings. I do not know what exactly is meant by the term '卒业' (zuoye, which refers to completing one's studies or finishing one's apprenticeship).

按：朱子此言，則譙定僅識伊川於涪陵，而入洛則不及見，史稱先受《易》於洛，後復從遊於其鄉者，妄也。徽宗朝蔡京用事，禁毋得挾元佑書，自是伊洛之學不行。時胡、劉二公皆在太學，而定適至，聞其嘗與伊川遊，故慨然師事之。所欲聞者義理也，而定本象數之學，不能有所益。定於伊川不純師，二公於定亦未純師也。

Hu Wei's commentary: According to Zhu Xi's words, Qiao Ding only met Cheng Yi in Fuping, and by the time he arrived in Luoyang, he was too late to meet him. The "Song History" says he first studied the Book of Changes in Luoyang and later studied with Cheng Yi in his hometown, which is untrue. During the reign of Emperor Huizong, Cai Jing was in power and banned the private possession of books from the Yuanyou period. From then on, the teachings of the Yi school from the Yi Luo tradition could not spread widely. At that time, Hu Xian and Liu Mianzhi were both in the Taixue, and just as Qiao Ding arrived, they heard that he had once studied with Cheng Yi, so they respectfully regarded him as their teacher. However, what they wanted to learn was the principles of meaning, while Qiao Ding's learning was mainly in the numerical and symbolic approach. Therefore, Qiao Ding could not be considered a pure disciple of Cheng Yi, and Hu Xian and Liu Mianzhi could not be considered pure disciples of Qiao Ding either.

故朱子雖遊二公之門，而不得見希夷之真圖，晚使蔡季通入峽乃購得之。「易學在蜀」亦必非伊川語，蓋其徒知象數非儒者所尚，故自附伊川之易以張其學，修史者不能裁擇，因而書之以為傳，實不然也。昔嚴君平著《老子指歸》，而郭曩氏始祖為其師，然則定所受者乃老子之易，其於聖人之道猶爝火之於日月也，何足選哉？何足選哉？

Therefore, although Zhu Xi studied under both Hu and Liu, he did not see Chen Tuan's true diagram, and only in his later years did he send Cai Yuan ding to the Three Gorges area to buy it. The statement "The study of the Book of Changes is in Sichuan" was certainly not said by Cheng Yi. It is likely that the disciples of that school knew that the method of images and numbers was not favored by Confucian scholars, so they attached themselves to Cheng Yi's study of the Book of Changes to promote their own school. Since historians could not decide which to take or reject, they simply copied it and wrote it into the biography, but in reality it was not the case. In the past, Yan Junping wrote the "Commentary on the Dao De Jing," and the ancestor of the Guo family was his teacher. Therefore, the tradition that Qiao Ding inherited was the Book of Changes based on Laozi, which is like a small torch compared to the sun and moon. How could it be worth mentioning? How could it be worth mentioning?

右論蜀隠者。

The above section discusses the origin of the Yi Jing studies of Qiao Ding and the school of hidden scholars from Shu.

李潛《麻衣道者正易心法序》曰：此書頃得之廬山一異人（或云許堅）。或有疑而問者，餘應之云：何疑之有？顧其議論可也。昔《黃帝素問》《孔子易大傳》，世尚有疑之，嘗曰：世固有能作《素問》者乎？固有能作《易大傳》者乎？雖非本真，是亦黃帝、孔子之徒也。餘於《正易心法》亦曰：世固有能作之者乎？雖非麻衣，是乃麻衣之徒也。胡不觀其文辭議論乎？一滴真金，源流天造，前無古人，後無來者，翩然於羲皇心地上馳騁，實物外真仙之書也。讀來十年方悟，浸漬觸類，以知易道之大如是也。得其人當與共之。

In the Northern Song dynasty, the recluse Li Qian of Lu Mountain wrote a preface for The Mind Method of the Orthodox Changes by the Hemp-Robed Daoist. He said: This book was recently given to me by a strange person from Lu Mountain (some say his name was Xu Jian). Some people doubted and asked questions, but I answered them: What is there to doubt? Just look at its arguments. In the past, there were people who doubted the Yellow Emperor's Inner Canon and the Great Commentary on the Changes by Confucius. I once said: How could there really be someone who wrote the Inner Canon? How could there really be someone who wrote the Great Commentary on the Changes? Even if it was not written by the original authors, it must have been written by someone from the same school as the Yellow Emperor or Confucius. I say the same about The Mind Method of the Orthodox Changes: How could there really be someone who wrote this book? Even if it was not written by the Hemp-Robed Daoist, it must have been written by someone from his school. Why not look at its words and arguments? It is truly like a single drop of pure gold, its source flowing naturally from heaven, preceding all ancient people and coming after none, freely galloping on the mind of Fuxi. It is truly a book of true immortals beyond worldly things. I read it for ten years before I understood it, layer by layer, gradually comprehending, and then I realized how vast the Way of the Changes is. When encountering the right person, it should be shared with him.

《正易心法》曰：卦象示人，本無文字，使人消息，吉凶嘿會。易道不傳，乃有周孔；周孔孤行，易道復晦。又曰：易道彌滿，九流可入，當知活法，要須自悟。又曰：世俗學解，浸漬舊聞，失其本始，易道淺狹。（卷首題云：希夷先生受並消息。）

The Mind Method of the Orthodox Changes says: The trigrams are revealed to people, originally without written words, allowing individuals to personally observe their changes, and to understand fortune and misfortune through silent comprehension. When the Way of the Changes was lost, there emerged the words of the Duke of Zhou and Confucius; yet when the teachings of the Duke of Zhou and Confucius were circulated alone, the Way of the Changes became obscure again. It also says: The Way of the Changes pervades everywhere, and all the schools of thought can enter through it. One should understand the living method, but the key still lies in personal enlightenment. It also says: The common interpretations are tainted by old hearsay, losing their original essence, and thus the Way of the Changes becomes shallow and narrow. (The book's preface is inscribed as 'Hixi Master received and transmitted the teachings.')

跋曰：五代李守正叛河中，周太祖親征，麻衣語趙韓王曰：「李侍中安得久？其城中有三天子氣。」未幾城陷，時周世宗與本朝太祖侍行。錢文僖公若水，陳希夷每見以其神觀清粹，謂可學仙，有升舉之分，見之未精，使麻衣決之，麻衣雲無仙骨，但可作貴公卿耳。夫以神仙與帝王之相，豈易識哉！麻衣一見決之，則其識為何如也。即其識神仙、識帝王眼目以論易，則其出於尋常萬萬也，固不容於其言矣。乾道元年冬十有一月初七日，玉溪戴師愈孔文撰。

The跋of this book says: During the Five Dynasties period, Li Shouzhen rebelled in Hezhong. Emperor Guo Wei, the founder of the Later Zhou dynasty, personally led the campaign. The Hemp-Robed Daoist told Zhao Pu (later enfeoffed as the Prince of Han) that "Li Shizhong cannot last long; there are three imperial energies within that city." Soon after, the city fell. At that time, Emperor Shizong of Later Zhou and the present Emperor Zhao Kuangyin were both with the army. Wenxi Gong Qian Ruoshui, whenever Chen Tuan saw him, always found him to have a divine and refined appearance, believing he could become a immortal. However, Chen Tuan himself could not judge accurately, so he invited the Hemp-Robed Daoist to decide. The Hemp-Robed Daoist said that he had no immortal bones, and could only become a high-ranking official. How could the appearance of a immortal and that of an emperor be easily recognized! The Hemp-Robed Daoist could judge it at a glance, so his insight must have been extraordinary. Based on his ability to recognize immortals and emperors, his interpretation of the Book of Changes must be far beyond ordinary people. His words are naturally not to be doubted. Written on the seventh day of the eleventh lunar month in the first year of Qiandao, by Dai Shiyu (given name Kongwen).

南軒張氏曰：嗚呼，此真麻衣道者之書也。其說獨本於羲皇之畫，推乾坤之自然，考卦脈之流動，論反對變復之際深矣，其自得者歟！希夷隠君實傳其學，二公髙視塵外，皆有長往不來之願，抑列御冦、莊周之徒歟？

Southern Song dynasty's Nanxuan Master Zhang Shi said: Ah, this is indeed the book of the Hemp-Robed Daoist. Its approach is based solely on Fuxi's hexagram diagrams, investigating the natural principles of Heaven and Earth, examining the flow of hexagram pulses, and discussing the depth of opposition and transformation, which is profound. It must be the result of his own personal insight! Chen Tuan, this reclusive gentleman, actually inherited his learning. Both of them looked down upon the world, holding a wish to leave behind the world forever, perhaps they were of the same kind as Lie Yukou and Zhuang Zhou?

雖然，概以吾聖門之法則未也。形而下者謂之器，或者有未察歟？其說曰：「六十四卦，惟乾與坤本之自然，是名真體。」又曰：「六子重卦，乾坤雜氣，悉是假合，無有定實。」餘則以為六子重卦，皆乾坤雜氣之妙用，真實自然，非假合也。希夷述其說曰：「學者當於羲皇心地上馳騁，無於周孔腳跡下盤旋。」予則以為學《易》者須於周孔腳跡下尋求，然後羲皇心地上可得而識。推此可概見矣。然其書之傳，固非牽於文義、鑿於私意者所可同年而語也。

Though this is true, if we apply our Confucian standards universally, it may not be sufficient. The principle that "what is below form is called an instrument" may not have been thoroughly examined by the author. The book says, "Among the sixty-four hexagrams, only Qian and Kun are based on nature, and this is called true essence." It also states, "The six subsidiary trigrams and the compound hexagrams are all mixed gases of Qian and Kun, mere combinations without fixed form or substance." I, however, believe that the six subsidiary trigrams and the compound hexagrams are the subtle workings of the mixed gases of Qian and Kun, real and natural, not mere combinations. Chen Tuan once said, "Scholars should roam in the mind of Fuxi, not circle around the footsteps of the Duke of Zhou and Confucius." I, however, think that those studying the Book of Changes must first seek within the footsteps of the Duke of Zhou and Confucius, only then can they understand the mind of Fuxi. From this, one can roughly see the point. Nevertheless, the fact that this book has been passed down is not something that can be compared with works that are overly constrained by meaning or forced by personal interpretation.

朱子《書麻衣心易後》曰：此書詞意凡近，不類一二百年前文字。如所謂「雷自天下而發，山自天上而墜」，皆無理之妄談；所謂「一陽生於子月而應在夘月」，乃術家之小數；所謂「由破體煉之乃成全體」，則爐火之末技；所謂「人間萬事悉是假合」，又佛者之幻語耳。其它此比非一，不容悉舉。

Zhu Xi said in "Commentary on the Heart of the Ma Yi Yi" that the words and meanings of this book are commonplace and shallow, not resembling writings from a hundred or two hundred years ago. For example, the book says "Thunder arises from heaven and mountains fall from heaven," which are all unreasonable nonsense; it says "the first yang is born in the month of Zi and is verified in the month of Mao," which is merely the petty tricks of fortune-tellers calculating time; it says "from broken form to complete form," which is merely the inferior techniques of alchemists' furnace refining; and it says "all worldly affairs are mere combinations," which is nothing but the Buddhist talk of illusions. There are many such examples in the book, not just one or two, too numerous to list one by one.

要必近年術數末流，道聴塗說，掇拾老佛醫卜諸說之陋者以成其書；而其所以託名於此人，則以近世言象數者必宗邵氏，而邵氏之學出於希夷，於是又求希夷之所敬，得所謂麻衣而托之。以為若是，則凡出於邵氏之流者莫敢議已，而不自知其說之陋，不足以自附於陳、邵之間也。

In the end, this must certainly be the work of recent practitioners of divination who have merely gathered together superficial remarks from various schools such as the old ways, Buddhism, medicine, and divination, to compile this book. As for why they attributed it to the Hemp-Robed Daoist, it is because modern scholars of symbolic and numerical divination necessarily revere Shao Yong, and Shao Yong's teachings came from Chen Tuan. Therefore, they sought out those respected by Chen Tuan, and found the so-called Hemp-Robed Daoist, and thus attributed the work to him. They thought that by doing so, anyone from Shao Yong's school would not dare to criticize them. But they do not realize that their own views are shallow and unworthy of association with Chen Tuan or Shao Yong.

《再跋麻衣易說後》曰：予既為此說，後二年假守南康，始至，有前湘陰主簿戴師愈者來謁，老且蹩，使其壻自掖而前。坐語未久，即及麻衣易說，問其師傳所自，則曰得之隠者；問隠者誰氏，則曰：「彼不欲世人知其姓名，不敢言也。」既復問之邦人，則皆曰書獨出戴氏，莫有知其所自來者。

Zhu Xi wrote in "Zai Ba Mai Yi Shuo Hou" that after I wrote the previous跋, two years later I was temporarily appointed as the military governor of Nan Kang. Upon arriving at my post, a man named Dai Shi Yu, who had previously served as the chief clerk of Xiang Yin, came to pay his respects. He was already old and lame, and his son-in-law had to help him walk forward. After sitting down and talking for a short while, he mentioned the "Mai Yi Shuo." I asked him where he had learned this book from, and he said he had obtained it from a hermit. When I asked the hermit's surname, he replied, "That person did not wish for the world to know his name, so I dare not say." Later, I asked the local people, and they all said that this book came only from the Dai family, and no one knew where it originated.

予後至其家，見幾間有所著雜書一編，取而讀之，則其詞語氣象宛然麻衣易也。予以是始疑前時所料三五十年以來人者，即是此老。既歸即取觀之，則最後跋語固其所為，而一書四人之文，體制規模乃出一手，然後深信所疑之不妄。

Later I went to his house and saw a collection of miscellaneous writings on the writing desk. I took it up and read it, and the words and style were exactly like the style of the Ma Yi Yi. I therefore began to suspect that the person I had previously inferred as "a person from the past thirty to fifty years" was actually this old gentleman. After returning home, I looked again at the book, and indeed the final colophon was written by him. Moreover, the writings of four people in the entire book shared the same style and structure, and I then firmly believed my suspicion was not a mistaken judgment.

是時戴病已昏，不久即死，遂不復可窮詰。獨得其易圖數卷，閱之又皆鄙陋瑣碎，穿穴無稽，如小兒嬉戲之為者。欲以其事馳報敬夫，則敬夫亦已下世。因以書語呂伯恭曰：「吾病廢有年，乃復為吏，然不為他郡而獨來此，豈天固疾此書之妄，而欲使我親究其實邪？」

At that time, Dai Shi Yu was already so ill that his mind was confused, and he died soon after, so there was no way to ask him further questions. All we could obtain were a few scrolls of his Yi diagrams. After looking through them, I found them to be trivial and superficial, full of forced interpretations without solid basis, like children playing games. I wanted to quickly inform Zhang Xi (whose courtesy name was Jingfu) about this, but he had already passed away. So I wrote a letter to Lu Zuqian (whose courtesy name was Bogong), saying, "I have been ill and inactive for many years. Now I have once again returned to official duties, yet I have not gone to any other prefecture but this one. Is it not possible that heaven itself detests the absurdity of this book, and has thus arranged for me to personally investigate the truth?"

時當塗守李壽翁侍郎雅好此書，伯恭因以餘言告之。李亟以書來曰：「即如君言，斯人而能為此言，亦吾所願見也，幸為津致使其一來。」予適以所見聞報之，而李已得謝西歸，遂不復出，不知竟以餘言為何如也。

At that time, Li Chun, the governor of Taiping Prefecture (located in Dangtu) and a deputy minister, had always been fond of this book. Lü Zuxian therefore told me what I had said, and Li Chun immediately wrote back saying, "Even if it is as you said, the fact that this person could say such things is something I would like to meet him for, so please introduce him to me so that he can come." I was about to reply to him with what I had seen and heard, but Li Chun had already resigned and returned westward, never to take up office again. I do not know what evaluation he ultimately had of my words.

《陳氏書録解題》曰：舊傳麻衣道者授希夷先生，崇寧間廬山隠者李潛得之，凡四十二章，蓋依託也。朱侍講云：南康主簿戴師愈撰，乃不唧溜底禪，不唧溜底修養法，不唧溜底時日法。

In the Southern Song dynasty, Chen Zhenwen of the Zhizhai Book Catalogue and Commentary said: It was traditionally believed that this book was passed down from the Hemp-Robed Daoist to Master Chen Tuan, the Recluse of Xiyi. In the Chongning period, a recluse named Li Qian on Mount Lu obtained it, and it had forty-two chapters. However, in reality, it was a forgery. Zhu Xi, who once served as a court lecturer, said: This book was written by Dai Shiyu, the chief clerk of Nan Kang. It is a mediocre work on Chan Buddhism, mediocre cultivation methods, and mediocre methods for choosing auspicious times.

王炎曰：洛水李壽翁侍郎喜論《易》，炎嘗問曰：「侍郎在當塗板行麻衣新說如何？」李曰：「程沙隨見屬。」炎曰：「恐託名麻衣耳。以撲錢背面喻八卦陰陽純駁，此鄙說也；以泉雲雨為陽水，以澤為陰水，與夫子不合。」李曰：「然。然亦有兩語佳。」炎曰：「豈非『學者當於羲皇心地上馳騁，不當於周孔腳跡下盤旋』邪？然此二語亦非也。無周孔之辭，則羲皇心地學者何從探之？」李無語。

Wang Yan said: A man from Luo River, the Vice Minister Li Chun (styled Shouweng), liked to talk about the Book of Changes. I once asked him: "What do you think of the new interpretation of the Ma Yi school published by the printing house in Dangtu?" Li Chun replied: "It was commissioned by Cheng Xiong (styled Shasui)." I said: "I fear it is just a pretended name of Ma Yi. Using the head and tail of a copper coin to illustrate the purity and mixture of the yin and yang of the Eight Trigrams is a shallow and vulgar way of explanation. To regard spring water, clouds and rain as yang water, and marshes as yin water, is inconsistent with Confucius' view." Li Chun said: "You are right. However, there are two sentences that are good." I said: "Are they not the ones that say, 'Scholars should run freely on the mind of Fuxi, not circle around the footprints of Confucius and Zhou Gong'?" But even these two sentences are wrong. Without the words of Zhou Gong and Confucius, how could scholars explore the mind of Fuxi?" Li Chun had no reply.

按：是書託名麻衣，序跋與書及注同出一手，其它踳駁之說無論，獨李壽翁所賞二語，貽誤學者不淺。然其言實出希夷，《觀物外篇》曰：「先天學，心法也。圖雖無文，吾終日言而未嘗離乎是。」亦即所謂「羲皇心地上馳騁，不於周孔腳跡下盤旋」也。麻衣，小說家以為即白閣僧相錢若水者，其人蓋孫君仿、麞皮處士之流，縱令是書真出麻衣，吾亦深惡而痛絶之，況戴師愈乎？

Hu Wei's commentary: This book is attributed to the Hemp-Robed Daoist. The preface, colophon, main text, and annotations all come from the same person. Other confused and disorderly statements are not worth discussing. Even just the two sentences praised by Li Chun, which have misled scholars greatly, actually originated from Chen Tuan. In the "Outer Chapter of Observing Things" from "The Imperial Ultimate Treatise," it says: "The study of the Earlier Heaven is a matter of the mind. Although the diagram lacks words, I have been discussing it all day long without ever departing from it." This is what is meant by "roaming on Fuxi's mind ground, not circling around the footprints of the Zhou and Confucius." As for the Hemp-Robed Daoist, the novelists consider him to be the monk who gave a physiognomy reading to Qian Ruoshui in the White Pavilion. This person is probably of the same kind as Sun Junfang and the Hermit of the Deer Skin. Even if this book were truly written by the Hemp-Robed Daoist, I would strongly dislike it, let alone if it were written by Dai Shiyu.

右論麻衣道者。

The previous section discusses the origins and forgery of the book "The Mind Method of the Orthodox Changes" attributed to the Hemp-Robed Daoist.

潛溪宋氏《溟涬生贊序》曰：溟涬生者，旴江廖應淮海學也。抱負竒氣，好研摩運世推移及方技諸家學。年三十遊杭，上疏言丁大全誤國狀，大全怒，中以法，配漢陽軍。生荷校行歌出都門，道旁觀者嘖嘖壯之。

In the early Ming dynasty, the scholar Song Lian, known as Master Qianxi, wrote a preface to his work "Zeng Xing Sheng Zan," stating that Zeng Xing Sheng was a person from Xujiang named Liao Yinghui, whose courtesy name was Hai Xue. He had great ambitions and a bold spirit, and he loved to study the changes of the world and various techniques from different schools. At the age of thirty, he traveled to Hangzhou and submitted a memorial exposing the misgovernment of Ding Duanquan. Ding Duanquan became very angry and used legal means to slander him, sentencing him to be sent to Hanyang Jun with chains. Liao Yinghui wore chains and sang songs as he left the city gate, and people around him praised his bravery and courage.

抵漢江濱，遇蜀道士杜可大，揖曰：「子非廖應淮邪？」生愕然曰：「道士何自知之？」可大曰：「宇宙太虛一塵耳，人生其間為塵幾何？是茫茫者尚瞭然心目間，矧吾子邪？然自邵堯夫以先天學授王豫天悅，天悅死無所授，同葬玉枕中。未百年而吳曦叛，盜發其冢，得《皇極經世體要》一篇、《內外觀象》數十篇，餘賄盜得之，今餘五十年，數當授子，吾俟子亦久矣。」

He walked by the Han River and met a Daoist from Shu, Du Keda. Du Keda bowed and said, "Are you not Liao Yinghuai?" Liao Yinghuai was surprised and asked, "How did the Daoist know that?" Du Keda replied, "The universe in the Great Void is no more than a single grain of dust. How many grains of dust can a person be in it? If I can clearly see such an endless expanse, how much more so can I see you? However, since Shao Yong passed on the study of Earlier Heaven to Wang Yu (whose courtesy name was Tianyue), and when Wang Yu died there was no one to pass it on, he buried the books together in his jade pillow. Less than a hundred years later, Wu Xi rebelled, and tomb robbers dug up his grave. They found one piece called "The Essentials of the Imperial Extent and the World's Order" and dozens of other pieces called "Inner and Outer Observations of the World." I bought them from the robbers with money. Now fifty years have passed, and according to the number, it should be passed on to you. I have been waiting for you as well."

乃言於上官，脫其籍，盡教以冢中書。其算由聲音起，生神鑑穎利，可大指畫未到者，生已先意逆悟，可大自以為不及。學既成，去隠宣、歙間。遇餘安裕弋陽，將教之，安裕勸生業《中庸》，生瞠目厲聲曰：「俗儒幾辱吾康節於地下矣。」

Du Ke Da appealed to the superior official on behalf of Liao Yinghuai, removing his status as a criminal and giving him all the books obtained from the tomb. The system of calculation started from sound. Liao Yinghuai was intelligent and quick to understand, so even where Du Ke Da had not yet explained, Liao Yinghuai had already grasped it. Du Ke Da thought he could not match Liao Yinghuai. After completing his studies, he left and lived in seclusion between Xuanzhou and Xishui. In Yiyang, he met Yu Anyu, who was about to teach him, but Yu Anyu advised him to study the Zhongyong. Liao Yinghuai looked at him angrily and shouted, "You, this vulgar scholar, are almost about to insult me in the afterlife, Shao Kangjie."

復去之杭，客賀外史家，晝市大衍數，夜沽酒痛飲，飲即吐，吐即飲，不醉如泥不休。醉中嘗大叫曰：「天非宋天，地非宋地，奈何奈何。」語聞賈似道，遣客叩之，生曰：「毋多言，浙水西地髮白時是其祥也。」似道未解，復召至，屏人與語，生曰：「明公宜自愛，不久宋鼎移矣。」似道惡其言，掩耳走。

He went again to Hangzhou and stayed with He Wai Shi. By day he practiced the divination method of Da Yan, and by night he bought wine and drank heavily, vomiting after each drink, then drinking again, not stopping until he was completely drunk. While drunk, he shouted loudly, "The sky is not the sky of the Song Dynasty, the earth is not the earth of the Song Dynasty, what shall we do, what shall we do?" This was reported to Jia Shidao, who sent his attendant to inquire. Liao Yinghuai said, "There is no need to say more; when the grass and trees in the western part of Zhejiang turn white, that will be the sign." Jia Shidao did not understand, so he summoned Liao again, dismissed the others, and talked with him. Liao said, "You should take care of yourself, for the imperial throne of the Song Dynasty is soon to change hands." Jia Shidao disliked these words and covered his ears and walked away.

生亦徑出，過曽淵子家索酒轟飲，酒酣作嬰兒啼曰：「大廈將焚，燕猶呢喃未已邪。」復賦歌以見意，都人士聞之，競指以為怪民，不與接，獨太學生熊睎聖猶時造其廬。生私執熊手謂曰：「吾端居層樓，聞空中戎馬百萬來，人鬼作哭泣聲。壬申襄樊陷，甲戌宮車晏駕，乙亥長江飛渡，似道亦殛死臨漳，丙子三宮播遷，諸王大臣皆南北亂走，噓吸事耳，子不去欲何為？」居亡何，宋事日非，沿江州郡望風奔潰。生大慟曰：「殺氣又入閩廣中，吾不知死所矣。」遂遁去，其言無一不驗。

Liao Yinghuai went straight out, passing by Zeng Yuanzi's house to drink wine and get drunk. When he was drunk, he imitated a baby's crying and said, "The great building is about to burn down, but the swallows are still chirping incessantly." He also composed a song to express his feelings. When the scholars in the capital heard this, they all rushed to call him a strange person, and refused to associate with him. Only the student of the Imperial Academy, Xiong Xiying, would occasionally visit his residence. Liao Yinghuai privately held Xiong Xiying's hand and said, "I am quietly living on the top of a high building, hearing a million soldiers and horses coming from the sky, and both men and ghosts are weeping. In the Renshen year, Xiangyang and Fancheng will fall, in the Jiaxu year the emperor will die, in the Yihai year the Yuan army will cross the Yangtze River, and Jia Shidao will be executed in Linding. In the Bingzi year, the three palaces will be forced to move, and all the princes and ministers will be running around north and south. These are all things that will happen in an instant. If you don't leave, what are you going to do?" Soon after, the situation of the Song dynasty became worse and worse, and the prefectures along the Yangtze River surrendered one after another. Liao Yinghuai was greatly grieved and said, "The killing atmosphere has reached Fujian and Guangdong. I don't know where I will die." Then he fled away. All his words came true.

後四年病死處州學中，年五十二，無子，一義女從之。生宗堯夫先天之學，頗自謂知《易》，每見諸易師傳疏，不問淺深，輒訕駁以為樂。及論後天，則尊羲畫為經，彖爻繋辭為傳，黜《文言》《彖》《象》二傳為九師之言，且謂《說卦》非聖筆不能作，上下《繫》乃門人所述，《序卦》直漢儒記耳。蓋生聰明絶人，未聞道而驟語數，故其論經多失中。

Four years later he died of illness while staying at the state school in Chuzhou, at the age of fifty-two, without any sons, only a daughter-in-law by adoption remained by his side. Liao Yinghui followed Shao Yong's theory of the Earlier Heaven, and took pride in his understanding of the Book of Changes. Whenever he encountered commentaries and interpretations from different schools of the Book of Changes, regardless of their depth, he would often criticize and refute them for fun. When discussing the Later Heaven system of the Book of Changes, he held the hexagram images of Fuxi as the fundamental principles, and considered the Hexagram Statements, Line Statements, and the Great Treatise as commentaries. He regarded the Wenyan and the two commentaries of Tai and Xiang as mere words of the nine schools of Han dynasty scholars, and even claimed that the Shuogua was not written by the sage, and that the upper and lower Great Treatises were merely records by his disciples, while the Xugua was simply the notes of Han scholars. Perhaps Liao Yinghui was exceptionally intelligent, but he began to discuss numbers before he had truly understood the Way, so his interpretations of the classics often went beyond the middle path.

然性使酒難近，又好訐人陰私，人面頸發赤不顧，罕有從其學者，唯國子簿吳浚、進士彭復樂師之。浚不卒業，復屢受唾斥不怨。生將遁時，召復至，口發例，手布籌，雖平昔所靳若終身不示人者，一舉授復。復後又授鄱陽傅立雲。

However, his nature was to take out his anger through drinking, making it hard for people to get close to him. He also liked to expose others' private matters, regardless of how red others' faces and necks became. Therefore, few people wanted to learn from him. Only Wu Jun, the chief clerk of the National Academy, and Peng Fu, an imperial examiner, were willing to take him as their teacher. Wu Jun did not finish his studies, while Peng Fu was repeatedly scolded and cursed by him but never held a grudge. When Liao Yinghuai was about to flee, he called Peng Fu over, speaking about the rules of calculation and arranging counting sticks with his hands. All those things he had been careful to keep secret, as if never to reveal them in his lifetime, were suddenly passed on to Peng Fu. Later, Peng Fu passed them on to Fu Liyun of Poyang.

或曰：生瀕死語女曰：「吾死後一月，朝中命山姓鳥名使者來徵吾及傅立，立當過吾門，汝可出藏書示之，立當以此致大官。」後皆如其言。所謂山姓鳥名，崔鵬飛也。生所著書有《玄玄集》《厯髓》《星野指南》《象滋綂會》《聲譜》《畫前妙旨》，數十萬言，今猶間傳於世。（贊不録。）

Someone said: Liao Yinghui, before he died, told his adopted daughter: "After I die, within a month, the court will send an envoy whose surname contains the character for mountain and whose name contains the character for bird to summon me and Fu Li. Fu Li will pass by my house, and you can give him the books I have hidden. He will use these books to attain high official rank." Later, everything turned out exactly as he had said. The person referred to as having a surname containing the character for mountain and a name containing the character for bird was Cui Pengfei. The books written by Liao Yinghui include "Xuanyuan Ji," "Lisui," "Xingye Zhi Nan," "Xiangzhi Tonghui," "Shengpu," and "Huazheng Miaozhi," totaling hundreds of thousands of characters, and they are still occasionally passed down today. (The praise by Song Lian is not included here.)

余自幼即見長老談溟涬生事，近見李淦性學及戚光子實所造文，又知生為詳。以生之精藝如此，而修《宋史》者不列之《方技傳》中，殊可恨也，故予愍之，特序之，又傷易道之微，激而贊之。惜乎予文蕪陋，不能永生也，然餘情亦至矣。濂志。

Song Lian also said: I have heard from elders since childhood about the story of Ming Xing. Recently, having seen the writings of Li Gan (whose courtesy name is Xingxue) and Qi Guang (whose courtesy name is Zishi), I have come to know his life more thoroughly. With his skills reaching such a high level, yet the compilers of the "Song History" did not include him in the "Biographies of the Masters of the Arts and Techniques," which is truly regrettable. Therefore, I feel pity for him and have specially written an introduction for him; I also feel sorrow for the decline of the Yi doctrine, and thus have written a eulogy for him. Alas, my writings are disorderly and crude, unable to make his name last long, but my intention has been fulfilled. Song Lian records.

按：程可久云「易以道義配禍福，得正而斃則吉，詭遇獲禽則凶」，此千古格言也。嚴君平精於卜筮，與人子言依於孝，與人臣言依於忠，猶不失開物成務之意。管輅善言《易》，亦嘗以謙、壯諷何晏，請上追文王六爻之旨，下思尼父彖象之義，未嘗近舍周孔，逺宗羲畫也。

Hu Wei commented: Cheng Xiong (styled Kejiu) said, "The Book of Changes uses moral principles to match fortune and misfortune. To die upholding righteousness is auspicious, while using improper means to hunt animals is inauspicious." This is a saying of lasting value. Yan Junping was skilled in divination. When speaking with someone's son, he would return to the principle of filial piety, and when speaking with a subject, he would return to the principle of loyalty. He did not deviate from the original meaning of the Book of Changes, which is "to open up things and accomplish affairs." Guan Lu was good at discussing the Book of Changes. He once used the hexagrams of "Modesty" and "Great Strength" to advise He Yan, urging him to look up to the six-line interpretations of King Wen and to reflect on the meanings of the "Tao" and "Xiang" sections of Confucius. He never abandoned the teachings of the Duke of Zhou and Confucius in order to far away from the hexagrams of Fuxi.

自先天之學興，而易道之蓁蕪甚矣。廖應淮自謂得康節真傳，而其所談者唯禍福，無一字及於道義，罔知忌諱，屢觸危機，其不為京房、郭璞，特幸而免耳。驗之最大者莫如宋亡，而究竟分毫無補，亦安用前知為也？

Since the study of the Earlier Heaven system arose, the Way of the Book of Changes has become overgrown with weeds and in disarray. Liao Yinghuai claimed to have inherited the true transmission of Shao Yong, but what he discussed was only fortune and misfortune, without a single word concerning moral principles. He completely lacked awareness of taboos and repeatedly violated dangerous situations. He did not suffer the fate of Jing Fang and Guo Pu, but this was merely a fortunate escape from disaster. The greatest verification of his predictions was the fall of the Song dynasty, yet it provided no help at all for the situation. So what is the use of knowing beforehand?

餘安裕勸讀《中庸》，蓋以索隠行怪，聖人之所不為，而無道不黙，亦非明哲保身之事，故微辭以規之，而應淮不自覺寤，詆為俗儒。其於《易》也，訕侮程、張，卑視周、孔，二篇獨尊羲畫，十翼専取《說卦》，鄙倍之論，全無忌憚，豈僅失中而已邪？

Yu Anyu advised him to read the Zhongyong, because seeking obscure things and behaving strangely are not what the sages would do, and refusing to remain silent in an age of disorder is not the way of a wise person who seeks self-preservation. Therefore, he advised him in a gentle manner. However, Liao Yinghuai remained completely unaware, and instead insulted those who were considered vulgar scholars. Regarding the Yi, he ridiculed Cheng Yi and Zhang Zai, despised the Duke of Zhou and Confucius, and only revered Fuxi's hexagrams in the upper and lower parts of the text. From the Ten Wings, he only took the Shuogua, and his crude and unreasonable remarks showed no restraint at all. This was not merely "not following the middle way."

世俗溺於所聞，爭言象數，黃口小兒人人慾為邵子，而二篇十翼束之髙閣，邪說橫行，聖真滅息矣。雖曰末流之極弊，抑先天心法之傳有以導之使然也。其後劉秉忠、李俊民等専治《皇極經世》數，而顧以《易》鳴，唯資中黃澤楚望謂當因孔子之言上求文王、周公之意，可謂粹然一出於正。然非屏棄九圖，則黃霧不披，青天白日終不可得而見也。

Common people are immersed in what they hear, competing to talk about the figures and numbers, even young children all want to be like Shao Yong. Meanwhile, the upper and lower parts of the Book of Changes and the Ten Wings are left gathering dust, false doctrines spread widely, and the true meaning of the sages is thus lost. Though this can be said to be the extreme corruption of the later generations, it is also the result of the transmission of the Earlier Heaven method. Later, Liu Bingchong and Li Junmin and others specialized in the numerical theories of the Huangji Jingshi, yet they ended up making their fame through the Book of Changes. Only Huang Ze of Zizhong (whose name was Chuwang) advocated that one should seek the original intention of King Wen and the Duke of Zhou according to the words of Confucius, which can be said to be purely following the right path. However, if one does not abandon those nine diagrams, the yellow mist will not disperse, and the clear sky and bright sun will never be seen.

右論溟涬生。

In the previous section, the discussion criticizes the tendency of the Liao Yinghuai school to focus exclusively on fortune and misfortune, pointing out the drawbacks of this approach.

王氏弼《周易略例·明象篇》曰：夫象者，出意者也；言者，明象者也。盡意莫若象，盡象莫若言。言主於象，故可尋言以觀象；象主於意，故可尋象以觀意。意以象盡，象以言著，故言者所以明象，得象而忘言；象者所以存意，得意而忘象。猶蹄者所以在兔，得兔而忘蹄；筌者所以在魚，得魚而忘筌也。然則言者，兔之蹄也；象者，魚之筌也。

Wang Bi of the state of Wei wrote in his "Outline of the Zhou Changes: The Clarification of the Images" that the "image" is used to express meaning, and "words" are used to explain the image. To exhaust meaning, there is nothing better than the image; to exhaust the image, there is nothing better than words. Words depend on the image, so one can follow words to observe the image; the image depends on meaning, so one can follow the image to observe meaning. Meaning is exhausted through the image, and the image is made clear through words, so words are used to explain the image, and once the image is obtained, words can be forgotten. The image is used to preserve meaning, and once meaning is obtained, the image can be forgotten. This is like a rabbit trap, which is used to catch rabbits, and once the rabbit is caught, the trap is forgotten; a fish basket is used to catch fish, and once the fish is caught, the basket is forgotten. Thus, words are like the rabbit trap, and the image is like the fish basket.

是故存言者，非得象者也；存象者，非得意者也。象生於意而存象焉，則所存者乃非其象（所存者在意）也；言生於象而存言焉，則所存者乃非其言也（所存者在象）。然則忘象者，乃得意者也；忘言者，乃得象者也。得意在忘象，得象在忘言。故立象以盡意，而象可忘；重畫以盡情，而畫可忘也（盡和同之意，忘其天火之象；得同志之心，拔茅之畫可棄）。

Therefore, those who cling to words have not truly grasped the image; those who cling to the image have not truly grasped the meaning. The image arises from the meaning, yet clinging to the image means one is not grasping the true image (Tang Dynasty Xing Zhu's commentary: the true image lies in the meaning). Words arise from the image, yet clinging to words means one is not grasping the true words (commentary: the true words lie in the image). Thus, those who can forget the image are the ones who truly grasp the meaning; those who can forget the words are the ones who truly grasp the image. Grasping the meaning lies in forgetting the image; grasping the image lies in forgetting the words. Therefore, the sages established images to exhaust the meaning, yet the images can be forgotten; they used overlapping hexagrams to express the feelings, yet the hexagrams can also be forgotten (commentary: once one understands the meaning of "Tongren" and "tong," one can forget the "Heavenly Fire" image of the lower Kan and upper Qian in the "Tongren" hexagram; once one attains the heart of unity and harmony, the "Bamboo Pulling" line drawing in the "Tai" hexagram can be discarded).

是故觸類可為其象，合義可為其徵。義苟在健，何必馬乎？類苟在順，何必牛乎？（《大壯》九三有乾亦云羝羊，《坤》卦無乾彖亦云牝馬。）爻苟合順，何必坤乃為牛？義苟應健，何必乾乃為馬？（《遯》無坤，六三亦稱牛；《明夷》無乾，六二亦稱馬。）而或者定馬於乾，案文責卦，有馬無乾，則偽說滋漫，難可紀矣。互體不足，遂及卦變；變又不足，推致五行。一失其原，巧愈彌甚，縱復或值，而義無所取，蓋存象忘意之由也（失魚兔則空守筌蹄，遺健順則空說龍馬）。忘象以求其意，義斯見矣。

Therefore, all things that are connected can be established as its image, and all meanings that are consistent can be taken as its verification. If the meaning lies in being strong and vigorous, why must it necessarily be a horse? If the nature of things lies in being gentle and yielding, why must it necessarily be an ox? (Note: The hexagram Da Zhuang (Great Strength) has the Qian trigram but still refers to 'ram,' while the Kun hexagram, which does not have the Qian trigram, still refers to 'female horse' in its hexagram statement.) If the line is in harmony with being gentle and yielding, why must it necessarily be the Kun trigram to be an ox? If the meaning corresponds to being strong and vigorous, why must it necessarily be the Qian trigram to be a horse? (Note: The hexagram Duan (Retreat), which does not have the Kun trigram, still refers to an ox in line six three; the hexagram Ming Yi (Dark Light), which does not have the Qian trigram, still refers to a horse in line six two.) Some people insist on fixing the horse exclusively to the Qian trigram, and they demand that the hexagram structure must match the wording. When there is a horse but no Qian trigram, they fabricate explanations, claiming there are too many to remember. When the mutual trigrams do not make sense, they resort to hexagram transformations; when hexagram transformations do not make sense, they refer to the Five Phases. Once the original meaning is lost, the situation becomes worse, even if occasionally correct, there is no value in the meaning. This is all due to clinging to the image while forgetting the meaning. (Note: If you lose the fish and the rabbit, you can only empty-handedly hold onto the fishing net and the hoof.) If you abandon the strong and vigorous and the gentle and yielding, you can only talk about dragons and horses in vain. Forgetting the image and seeking the meaning, the meaning will naturally appear.

陵陽李氏心傳《丙子學易編》曰：自周之衰，言《易》者寖失羲、文之意，而牽合破碎，或反資以為亂，故夫子作《十翼》，専以義理明之。其後讖緯之學興，而飛伏、互體之文，壬遁、九宮之說，紛紛然並出，皆托《易》以行世。至王輔嗣乃獨辭而闢之，其視兩漢諸儒可謂賢矣，惜其溺於時好，乃取莊、老之妄以亂周、孔之實，故《易》之道終不明於世。

In the Southern Song dynasty, Li Xinchuan from Linyang wrote in his work "Bingzi Xue Yi Bian" that since the Zhou dynasty declined, those who studied the Book of Changes gradually lost the original meaning intended by Fuxi and King Wen. They made forced interpretations, leading to fragmented and confused explanations. Some even used these interpretations as a basis for causing chaos. Therefore, Confucius composed the Ten Wings, using principles and meanings to clarify the Book of Changes. Later, the study of prophecies and omens became popular, along with various methods such as flying and hidden numbers, mutual forms, the Six壬 system, and the Nine Palaces. All these emerged together, all pretending to be based on the Book of Changes and spreading throughout the world. It was only Wang Bi (whose courtesy name was Fusi) who wrote independently to oppose these trends, and compared to the scholars of the Two Han dynasties, he could be considered wise. Unfortunately, he was immersed in the prevailing trends of his time and used the false doctrines of the Zhuangzi and Laozi to confuse the practical principles of Duke Zhou and Confucius. Thus, the Way of the Book of Changes was never fully clarified in the world.

按：王氏筌蹄之喻，雖出於莊子而其義不同。其所謂忘言忘象者，亦謂學《易》者觀象玩辭，期於自得，久之當有所融釋脫落耳，非若為先天之學者欲盡棄周孔之言，専於羲皇心地上馳騁也。即其卦爻之解，間有涉於虛無者，亦皆莊老之微旨，與坎離龍虎之說精觕相去逺矣。故伊川教人且看王輔嗣、胡翼之、王介甫三家《易》，以其所主在義理，不為百家眾技所惑也。宋人奉陳、邵為伏羲，而顧斥輔嗣為莊老，吾不知其何說矣。

Hu Wei's commentary: Wang Bi's metaphor of "筌蹄" although originates from the "Zhuangzi," has a different meaning. What he said about forgetting words and images is merely referring to those who study the "Yi" to observe the images and play with the words, hoping to achieve understanding on their own, and after a long time, naturally achieving a fusion and shedding of superficial aspects. It is not like those who study the Earlier Heaven school, who would completely discard the words of the Duke of Zhou and Confucius, and instead focus solely on Fuxi's mind. Even if he occasionally touched upon the concept of nothingness in explaining the hexagrams and lines, it was still the subtle meaning of the doctrines of ZHUANG and LAO, and was far removed from the crude practices of alchemy involving the坎离 and dragon and tiger. Therefore, Cheng Yi advised people to first study the "Yi" by Wang Bi, Hu Yuan (whose courtesy name was Yizhi), and Wang Anshi (whose courtesy name was Jiefu), because their focus was on the meaning and principles, and they would not be misled by the techniques of the hundred schools. The Song dynasty people regarded Chen Tuan and Shao Yong as Fuxi, yet they criticized Wang Bi as being associated with ZHUANG and LAO. I really don't know what this statement means.

程子《易傳序》曰：《易》，變易也，隨時變易以從道也。其為書也，廣大悉備，將以順性命之理，通幽明之故，盡事物之情，而示開物成務之道也。聖人之憂患後世，可謂至矣。去古雖逺，遺經尚存，然而前儒失意以傳言，後學誦言而忘味，自秦而下，蓋無傳矣。予生千載之後，悼斯文之湮晦，將俾後人沿流而求源，此傳所以作也。

Cheng Yi's preface to the Cheng Family Commentary on the Zhou Yi says: What is called the Yi is change, changing with the times to conform to the Dao. This book is vast and comprehensive, used to follow the principles of human nature and destiny, to understand the causes of both the hidden and the manifest, and to exhaust the nature of things, thus revealing the principle of "opening things and accomplishing affairs." The sages worried for future generations, reaching the extreme. Though the ancient times are far away, the transmitted texts remain, yet earlier Confucian scholars lost the original meaning and only passed on the words, while later scholars recited the words and forgot the meaning. Since the Qin dynasty, it can be said there has been no true transmission. I was born a thousand years later, lamenting the obscuring and darkness of this tradition, wishing for later generations to follow the tributaries back to the source. This commentary is written for that purpose.

《易》有聖人之道四焉：以言者尚其辭，以動者尚其變，以制器者尚其象，以卜筮者尚其占。吉凶消長之理，進退存亡之道，備於辭，推辭考卦，可以知變，象占在其中矣。君子居則觀其象而玩其辭，動則觀其變而玩其占。得於辭不達其意者有矣，未有不得於辭而能通其意者也。至微者理也，至著者象也，體用一源，顯微無間。觀會通以行其典禮，則辭無所不備。故善學者求言必自近，易於近者非知言者也。予所傳者辭也，由辭以得其意，則在乎人焉。

The Book of Changes contains the four aspects of the Way of the sage: those who use it to discuss value its words, those who use it to act value its changes, those who use it to make objects value its images, and those who use it for divination value its omens. The principles of good and evil, increase and decrease, and the methods of advancement, retreat, survival, and demise are all fully expressed in the words. By examining the words and studying the hexagrams, one can understand the changes, and the images and omens are included within them. The gentleman in peace observes the images and savors the words; when acting, he observes the changes and savors the omens. Some people obtain the words but cannot grasp their meaning, yet no one can grasp the meaning without the words. The most subtle is principle, the most evident is the image; principle and application arise from the same source, and there is no gap between the evident and the subtle. Observing the interconnectedness of things and applying them to the rites and institutions, the words will be fully encompassed. Therefore, those who are good at learning must begin with the words, and those who neglect the words are not truly understanding words. What I transmit is the words; as for understanding the meaning from the words, that lies with each individual.

《遺書》：張閎中以書問「《易》之義本起於數」，程子答曰：謂義起數則非也。有理而後有象，有象而後有數。《易》因象以知數，得其義則象數在其中矣。必欲窮象之隠微，盡數之毫忽，乃尋流逐末，術家所尚，非儒者之務也，管輅、郭璞之學是已。又曰：理無形也，故因象以明理；理見乎辭者也，則可由辭以觀象，故曰「得其義則象數在其中矣」。

The "Cheng Family Legacy" records that Zhang Hongzhong wrote a letter asking, "The principles of the Book of Changes originally arise from numbers." Cheng Yi replied that it is incorrect to say the principles arise from numbers. There is first principle, then image, then number. The Book of Changes uses images to understand numbers and to grasp its meaning; thus, both image and number are included. If one insists on exploring the subtle aspects of images and calculating the minutest details of numbers, that is chasing the stream and neglecting the source, a pursuit favored by magicians, not the proper concern of a Confucian scholar. This is the kind of learning followed by Guan Lu and Guo Pu. Cheng Yi also said: principle has no form, so images are used to explain principle; principle manifests in words, so one can observe images through words. Therefore, it is said, "When one grasps its meaning, both image and number are included."

朱子曰：自秦漢以來，考象辭者泥於術數，而不得其弘通簡易之法；談義理者淪於空寂，而不適乎仁義中正之歸。求其因時立教，以承三聖，不同於法而同於道者，則惟伊川先生程氏之書而已。後之君子誠能日取其一卦若一爻者熟復而深玩之，如已有疑將決於筮而得之者，虛心端意，推之於事而反之於身，以求其所以處此之實，則于吉凶消長之理、進退存亡之道，將無所求而不得，邇之事父，逺之事君，亦無處而不當矣。

Zhu Xi said: Since the Qin and Han dynasties, those who have studied the images and words of the divination texts have been confined to divination techniques and have not attained the broad and straightforward way; those who have discussed principles have fallen into emptiness and nothingness, and have not reached the proper path of benevolence and righteousness. To find someone who can teach according to the times, continuing the teachings of the three sages Fuxi, King Wen, and Confucius, with different methods but the same way of the Dao, there is only Cheng Yi's writings. If later gentlemen truly take one hexagram or one line from them and read them repeatedly, deeply pondering them, as if they had a doubt in their mind and were about to use divination to decide, and just happened to receive this hexagram or line, then with humility and sincerity, applying them to affairs and reflecting on themselves, seeking the real principles to deal with the present situation, they will have no difficulty in understanding the principles of fortune and misfortune, increase and decrease, and the methods of advancement and retreat, survival and death. In the near term, they will be filial to their father, and in the distant term, they will be loyal to their sovereign, and there will be no inappropriate place.

鄱陽馬氏端臨曰：按伊川之《易》，精於義理而略於卜筮象數，此固先儒之說。然愚嘗以為《易》之象數卜筮，豈出於義理之外？蓋有此理則有此象、有此數，而卜筮之說，其所謂趨吉避凶、恵迪從逆雲者，又未嘗不一出於義理。平時本諸踐履，則觀象玩辭，此義理也；一旦謀及卜筮，則觀變玩占，亦此義理也，初不必岐而二之。

In the Yuan dynasty, Ma Duolin from Poyang said: According to Cheng Yi's "Cheng氏 Transmission of the Zhou Changes," it is precise in the principles and theories but brief in the divination symbols and numbers. This is the standard evaluation of earlier Confucian scholars. However, I have always thought that the symbols and numbers of the Zhou Changes and divination, how could they exist outside the principles? If there is this principle, then there must be this symbol and this number. As for the statements in divination, such as seeking good fortune and avoiding misfortune, following the virtuous path brings good fortune, and opposing the virtuous path brings misfortune, these are also all derived from the principles. Usually, taking practical action as the foundation, observing the symbols and studying the words, this is the principles. When there is a matter to consult divination, observing the changes and studying the divination, this is still the principles. There is no need to divide them into two separate aspects.

項氏《周易玩辭》自序曰：「君子居則觀其象而玩其辭，動則觀其變而玩其占」，讀《易》之法盡於此矣。《易》之道四，其實則二，象與辭是也。變則象之進退也，占則辭之吉凶也。不識其象，何以知其變？不通其辭，何以決其占？然而聖人因象以措辭，後學因辭而測象，則今之讀《易》，所當反覆紬繹、精思而深味者，莫辭若也。於是作《周易玩辭》。

In his preface to the "Zhou Yi Wan Ci" (Commentary on the Zhou Yi), Xiang Anshi of the Southern Song dynasty said: "A gentleman in peace observes its images and savors its words; when taking action, he observes its changes and savors its divination." The method of reading the Zhou Yi is fully explained here. The principles of the Zhou Yi have four aspects, but in reality there are only two, namely the image and the words. Change refers to the movement of the image; divination refers to the fortune or misfortune of the words. Without understanding the image, how can one know the change? Without understanding the words, how can one judge the divination? Yet the sages based their words on the images, while later scholars base their interpretations of the images on the words. Therefore, today in reading the Zhou Yi, the most important thing is to repeatedly draw out the meaning, think deeply, and savor the words. Thus, he wrote this work, the "Zhou Yi Wan Ci."

又曰：程子平生所著，獨《易傳》為全書，安世受而讀之三十年矣。今以其所得於《易傳》者述為此書，而其文無與《易傳》合者，合則無用述此書矣。世之友朋，以《易傳》之理觀吾書，本末條貫，無一不本於《易傳》者；以《易傳》之文觀吾書，則未免有「使西河之民疑汝於夫子」之怒。知我者此書也，罪我者此書也。

Xiang Anshi also said: Cheng Yi's entire life's writings consist only of the "Commentary on the Changes" which is a complete work. I have studied and recited it for thirty years. Now I have compiled my insights gained from the "Commentary on the Changes" into this book. The words in this book are nowhere the same as those in the "Commentary on the Changes"; if they were the same, there would be no need to write this book. If friends in the world use the principles from the "Commentary on the Changes" to examine my book, they will find that from beginning to end, the reasoning is coherent and nothing is not based on the "Commentary on the Changes". But if they use the words of the "Commentary on the Changes" to examine my book, they would inevitably incur the criticism of "making the people of Xihexiang doubt you as if you were Confucius". Thus, this book is both the one that understands me and the one that accuses me.

鄱陽馬氏《周易玩辭序》曰：《易》有聖人之道四，變與象居其二焉。自義理之學大明，而變象之說幾晦，先儒欲救其弊，則曰：「聖人當時自可別作一書明言義理以詔後世，何用假託卦爻，為此艱深隠晦之辭乎？」愚嘗以為變之說不一：有隨時之變，如彖、象、小象、文言、繫辭各自一義是也；有逐爻之變，如九六七八、陰陽老少是也；有逐卦之變，如剛柔往來、互體飛伏是也。

Ma Duanlin, in his preface to Xiang Anshi's "Commentary on the Zhou Changes," said that the "Book of Changes" contains four aspects of the sage's way, among which "change" and "image" account for two. Since the study of rational principles has become prominent, the discussion of "change" and "image" has almost become obscure. Previous scholars wanted to correct this bias, so they asked: "Why did the sage not write another book to clearly explain the principles and inform future generations, but instead use the hexagrams and lines, writing in obscure and difficult language?" I have thought that the concept of "change" is not only one. There is change according to time, such as the meaning formed by the "Commentary on the Judgment," the "Great Image," the "Small Image," the "Words of the King," and the "Great Treatise." There is also change according to each line, such as the distinctions of nine, six, seven, eight, and the yin and yang, old and young. There is also change according to each hexagram, such as the mutual transformation of yin and yang, the interaction of soft and hard, and the mutual generation and concealment of the hexagrams.

象之說亦不一：有卦畫之象，陰陽竒耦、三連六斷是也；有大象之象，天地風雷、山澤水火是也；有《說卦》之象，乾為馬、坤為牛、乾為首、坤為腹之類是也。至簡要者隨時之變也，至支離者逐卦之變也，至精微者卦畫之象也，至瑣碎者《說卦》之象也。必研究其簡要精微者，而不拘泥其支離瑣碎者，則曰象曰變，固無非精義至理之所寄也，豈有二哉？

The concept of "xiang" (image) also has various interpretations: there is the image of trigrams, such as the odd and even lines representing yin and yang, and the connected three lines of Qian (Heaven) versus the broken six lines of Kun (Earth); there is the image of great things, such as the eight elements of heaven, earth, wind, thunder, mountain, marsh, water, and fire; and there is the image from the "Shuo Gu" (Commentary on the Trigrams), such as taking the horse as Qian and the ox as Kun, or taking the head as Qian and the abdomen as Kun. Among these, the most concise and clear is the changing with the times, while the most fragmented is the changing of each trigram; the most subtle is the image of the trigram lines, while the most trivial is the image from the "Shuo Gu." If one focuses on studying the concise and subtle aspects without being bound by the fragmented and trivial ones, then the so-called "xiang" and "bian" (change) are originally not separate things but both寄托 (寄托 means寄托, which can be translated as "寄托" or "convey") profound meanings and principles. How could they be entirely different things?

按：象、辭、變、占四者，說《易》之綱領也。伊川歸重於辭，平庵因之。愚則謂辭本乎象，象尤不可忽，故夫子曰「聖人立象以盡意，繫辭焉以盡其言」，又曰「八卦以象告，爻彖以情言」。象者，二體六爻之畫是也，而王輔嗣以乾牛坤馬之類當之。朱子謂如「初九潛龍勿用」一辭中四者俱備：初九，變也；潛龍，象也；勿用，占也。愚則謂潛龍、牝馬等語，若詩之比興，總謂之辭，非夫子之所謂象。平庵云：凡卦辭皆曰彖，凡卦畫皆曰象，未畫則其象隠，已畫則其象著，故指畫為象，非謂物象也；大象總論六畫之義，小象各論一畫之義，故皆謂之象；其曰天、曰龍者，自因有象之後推引物類以明之耳，本稱《易》象，非此之謂也。斯言可以正諸儒之失。未筮謂之辭，筮得其辭謂之占，亦非但「勿用」二字為占也。

Hu Wei's commentary: The four aspects of image, statement, change, and divination are the main points for explaining the Book of Changes. Cheng Yi focused on the statement, and Xiang Anshi (who styled himself Ping'an) followed his view. I think the statement originates from the image, and the image is especially important. Therefore, Confucius said, "The sage established images to express meaning, and attached statements to fully express the meaning," and also said, "The eight trigrams use images to convey, and the lines and the form express the situation." The term image refers to the two trigrams above and below and the six lines of the hexagram. However, Wang Bi used such interpretations as the乾 trigram representing an ox and the坤 trigram representing a horse to substitute for the image. Zhu Xi thought that the phrase "Initial Nine, the dragon is hidden and not used" contains all four elements: "Initial Nine" is the change, "the hidden dragon" is the image, and "not used" is the divination. I think that phrases like "the hidden dragon" and "the female horse" are similar to the metaphor and allusion in the Book of Poetry, and they should be considered as statements, not the image as Confucius mentioned. Xiang Anshi said: all hexagram statements are called the form (tuan), and all hexagram diagrams are called images (xiang). When the diagram is not drawn, the image is hidden; when it is drawn, the image becomes visible. Therefore, the diagram is called the image, not the physical image. The Great Image summarizes the meaning of the six lines, while the Small Image discusses the meaning of each line separately, so they are all called images. As for talking about heaven and dragon, that is deriving from the image of the hexagram and using things from the world to explain it. Originally, the term "image" in the Book of Changes refers to this. These words can correct the mistakes of the scholars. When there is no divination, it is called the statement; when divination is made and the statement is obtained, it is called divination. It is not only the two words "not used" that count as divination.

京山郝氏敬《談經》曰：羲畫始呈玄旨，苞絡如夜半子，陽初動，晨光未熹。夏、商之易不可覩矣，然使其無憾，文王必不更演《易》。至文王、周公抽厥玄緒，但其辭旨深約，如平旦昧爽，曲房晏起，尚未知曙。迨夫子《十翼》，讚揚幽隠，畢達揭日月而行康莊，大明中天矣。旋罹秦火，六籍散越而《易》獨存，後生捧完璧，誠斯文大幸。奈何更生異端，稂莠其真苗，磔裂其同體，妄謂羲聖有不傳之秘，使緯稗蠭起，詆夫子《十翼》為一家言，離經叛道莫此為甚。

In the Ming dynasty, He Jing from Jingshan wrote in his work "Tan Jing" that Fuxi first presented the hexagrams with profound meaning, encompassing all things like the moment of the first hour of the night, when the yang energy was just beginning to stir and the morning light had not yet brightened. The Yi of the Xia and Shang dynasties is no longer visible, but if the Yi of that time had been perfect, King Wen would certainly not have proceeded to develop the Yi. When King Wen and the Duke of Zhou drew out the profound threads within, their words were deep and concise, like the early morning when the sky is just beginning to lighten, and those who slept late in a deep room still did not know it was already daylight. Later, when Confucius composed the Ten Wings, he explained all the subtle and hidden aspects, making everything clear, as if lifting the sun and moon to walk along the broad and open path, with the sun shining brightly in the sky. Then came the Qin dynasty's burning of books, and the Six Classics were scattered, but the Yi alone was preserved. The later generations holding this intact jade tablet were truly a great fortune for the scholarly tradition. Unfortunately, there arose heretical interpretations, using weeds to confuse the true seed, splitting what was originally one into many, falsely claiming that Fuxi had another secret meaning not passed down, leading to a flood of spurious writings and false interpretations. They even slandered Confucius' Ten Wings as merely one person's opinion, and there is no greater deviation from the classics than this.

近時博士家承邵、朱之說，謂三聖不同易，病分經合傳之非古，歸咎王弼，此不能三年之喪而緦小功之察也。夫謂經傳不可合者，以書同而道異、言同而人異，如《春秋》諸傳於經，則誠未可合也；羲、文、周、孔，奚不合之有？由孔子視三聖為古，自視為傳；由今視四聖，則皆古也，皆經也。孔子何遂不如左、公、谷傳《春秋》？世儒不病左、公、谷合《春秋》，而病《十翼》合《易》，以伸「四聖不同易」之說，謬也。

Modern scholars who interpret the classics have followed the views of Shao Yong and Zhu Xi, believing that the Book of Changes created by Fuxi, King Wen, and Confucius are different, and they criticize the combination of the classic text with its commentaries as not following ancient practices, blaming Wang Bi for this. This is like saying one cannot observe the three-year mourning period, yet insisting on the details of lighter mourning clothes and minor mourning rites. The argument against combining the classic with its commentaries is based on the idea that although the texts are the same, the doctrines differ, and although the words are the same, the people differ. Indeed, the commentaries of the various schools on the Spring and Autumn Annals cannot be combined with the classic text. But why should the works of Fuxi, King Wen, the Duke of Zhou, and Confucius not be combined? From Confucius's perspective, the three sages were ancient figures, and his own work was the commentary; from today's perspective, all four sages were ancient figures, and all were classics. How could Confucius be considered inferior to the commentators Left Zhuan, Gongyang, and Gu Liang of the Spring and Autumn Annals? The current scholars do not criticize the practice of combining the three commentaries with the Spring and Autumn Annals, yet they criticize the combination of the Ten Wings with the Book of Changes, using this to support the idea that the four sages had different versions of the Book of Changes. This is absurd.

邵堯夫造為先天方圓等圖，好事詫為新竒，修煉羽流緣飾龍虎、鉛汞、奼女、嬰兒為《參同》《悟真》等書，乍見竒僻，叩之不過存神馭氣以求長生，而珍秘自喜，援易為口實。聖人作易，易簡開物，患人不知；而小說誣世，唯恐人知，心術已冰炭矣。《禮》云：「假鬼神、時日、卜筮疑眾者殺。」學者反尊崇其說，甚矣人之好怪也。

In the Northern Song dynasty, Shao Yong (styled Yao Fu) created diagrams such as the Earlier Heaven circle and square. Those who liked novelty regarded these as extraordinary theories. Taoist alchemists further embellished them with cryptic terms like "dragon and tiger," "lead and mercury," "young girl," and "infant," compiling works such as the "Threefold Concordance of the Zhou Changes" and the "True Words of Enlightenment." At first glance, these seem strange and obscure, but upon further inquiry, they are nothing more than attempts to control spirits and energies in pursuit of longevity. Yet they treat these as secret treasures, boast about them, and even cite the Zhou Changes as justification. The sages composed the Zhou Changes to be simple and clear, to enlighten the people and accomplish affairs, fearing that people would not understand. These petty doctrines, however, deceive the public and fear being exposed, their intentions being as opposite as ice and charcoal. The "Rites of Zhou: The System of Government" states: "Those who deceive the people by pretending to communicate with ghosts and spirits, using time, days, divination, and卜筮 should be put to death." Scholars instead revere such doctrines, and the people's fondness for the strange has become extremely serious.

《學易枝言》曰：羲聖世無文字，三才義理無憑發揮，爰始畫卦設象，不得已也。設有文字，便敷演成辭，豈好為隠乎？揚雄識字既多，而索隠鉤藏，別構方、州、部、家為《玄》儗易，則心勞而日拙矣。

Hao Jing's "Xue Yi Zhi Yan" says: In the time of Fuxi, there were no written characters, so the principles of heaven, earth, and humanity could not be expressed or elaborated, thus he began to draw trigrams and establish symbolic images, which was indeed a necessity. If there had already been written characters at that time, Fuxi would have composed written texts instead, would he have liked to be obscure and ambiguous? Yang Xiong of the Western Han dynasty knew enough characters, yet he deliberately sought out obscure and obscure words, created the terms "fang," "zhou," "bu," and "jia," and wrote the "Tai Xuan" to imitate the "Zhou Yi," which is called using one's mind more and more clumsily.

易爻辭象義誠有不可盡解者，前人不傳，後人何述？要之，精微中之易簡，愚不肖可知；易簡中之精微，聰明才辯者未悉。如管公明、郭景純卜筮，焉可謂之非易？然亦四道之一端耳。子云：「知之為知之，不知為不知。」三才之要，人所當知者，王輔嗣、程正叔諸君子所言，不可勝用矣。

The line statements and symbolic meanings in the Zhou Changes indeed have aspects that are difficult to fully comprehend, and since the ancients did not pass them down, how can later generations presume to elaborate on them? In the subtle and profound, the simple and plain can be understood even by the dull and unskilled; but in the simple and plain, the subtle and profound may not be fully grasped even by the wise and eloquent. The divination practices of Guan Lu of the Wei dynasty and Guo Pu of the Jin dynasty, though remarkable, can hardly be considered as the entire Zhou Changes. They are merely one aspect among the four elements of "words, images, transformations, and divination." Confucius said, "To know is to know; not to know is not to know." The essential meanings concerning the three elements of heaven, earth, and humanity have already been thoroughly explained by scholars such as Wang Bi and Cheng Yi.

聖人作易，立人之道而已；學易者，亦學為立人之道而已。又曰：朱元晦謂孔子之易非文王、周公之易，愚謂孔子贊易，秖為立人之道，學者日用切要而言，誠有之。但聖人說理發揮人道，即函蓋三才萬象無不脗合，與羲、文、周公無二。

The sages composed the Book of Changes in order to establish the principles of human conduct; those who study the Book of Changes merely learn to practice these principles. It is also said that Zhu Xi (whose courtesy name was Yuanhui) believed that Confucius' version of the Book of Changes was not the same as that of King Wen and the Duke of Zhou. I think that Confucius' commentary on the Book of Changes focused on establishing human conduct and the most essential aspects for daily life, and this view indeed has some truth to it. However, the sages explained the principles and developed human conduct, and in doing so, they encompassed the three elements and all phenomena, with everything harmonizing perfectly. This is no different from that of Fuxi, King Wen, and the Duke of Zhou.

按：莊生曰「易以道陰陽」，此非周之言，而古之言也。蓋古者三易之法掌於太卜，一曰《連山》，二曰《歸藏》，三曰《周易》，其經卦皆八，其別皆六十有四。非但彖爻之辭自為一書，即如《春秋》內外傳所載諸繇辭亦不得與焉。其所見者唯二體六畫剛柔雜居之象，以為道陰陽宜也。至扵文王繫彖、周公繫爻，則固以陰陽推之於人事，而所言無非仁義中正之歸矣。孔子作十翼，則又發彖爻之蘊，竭盡而無餘焉。聖人之所以窮理而盡性，君子之所以反身而寡過，皆在此書，奚止道陰陽哉！

Hu Wei said: Zhuang Zhou said, "The Book of Changes is about yin and yang," but this statement was not Zhuang Zhou's own idea, but rather an old saying passed down from ancient times. In the ancient times, there were three schools of the Book of Changes, all under the charge of the Grand Astrologer: the Lianshan, the Guicang, and the Zhouyi. All of them had eight single trigrams and sixty-four compound trigrams. At that time, not only were the interpretations of the trigrams and line statements by King Wen and the Duke of Zhou not yet compiled into a single book, but even the divination statements recorded in the Zuo Zhuan and Guoyu were not included. All that people could see were the upper and lower parts of the trigrams, with the six lines alternating between firm and yielding. Therefore, it was natural to say that the Book of Changes is about yin and yang. But when King Wen attached the trigram interpretations and the Duke of Zhou attached the line statements, they had already extended yin and yang to human affairs, and everything they discussed was ultimately about benevolence, righteousness, and correctness. Confucius composed the Ten Wings, which further elaborated the meanings of the trigram and line statements thoroughly. The sages used this book to investigate heavenly principles and exhaust human nature, and the gentlemen used it to examine themselves and reduce their mistakes. All of this is contained in this book, how could it be merely about yin and yang?

微三聖之辭，則伏羲作易之旨鬱而不明，萬古如長夜矣，而顧謂三聖不如伏羲，何歟？且夫三才之道，在天曰陰陽，在地曰剛柔，在人曰仁義，其為性命之理則一也。《洪範》由天道以推之人道，《中庸》由人道以合之天道，蓋天人之理未有不歸於一致者也。三聖所重在人道，而天地之道亦無不備焉。伏羲時未有文字，不得已而畫竒耦以垂教，陰陽可以畫見，而仁義不可以畫見，故說者但以為道陰陽，而不知伏羲之旨専在立人之道也。

If there were no writings by the three sages, Wen Wang, the Duke of Zhou, and Confucius, the original intention of Fuxi in composing the Book of Changes would remain obscured and unclear, leaving future generations in darkness for all time. Yet some people claim that the three sages were not as great as Fuxi. What is the reasoning behind this? Furthermore, the principle of the three elements: in heaven it is called yin and yang, in earth it is called hardness and softness, and in human beings it is called benevolence and righteousness. The principle of life and destiny is the same. The Book of Documents, Hong Fan, extends the principles of heaven to human affairs, while the Zhongyong from the Book of Rites brings human affairs back to harmony with heaven. This shows that the principles of heaven and human beings are ultimately consistent. The three sages focused on human affairs, yet the principles of heaven and earth are fully included. At the time of Fuxi, there were no written characters, so he had to use symbolic drawings, with odd numbers representing yang and even numbers representing yin, to convey moral teachings. Although yin and yang can be expressed through hexagrams, benevolence and righteousness cannot be represented by hexagrams. Therefore, those who explain the Book of Changes focus only on yin and yang, without realizing that Fuxi's original intention was to establish the principles of human conduct.

苟其有文字，則亦必言及仁義矣。伏羲而無言也；伏羲而有言，安知不與三聖同辭乎？老莊之徒掊擊仁義，故厭薄周孔之辭，以為不足道；儒者不能辭而闢之，反為之推波助瀾，尊伏羲不言之教，抑三聖闡幽之辭，豈不悖哉！仲輿解經多所創穫，而尤不喜宋儒，愚未敢深信；獨論易數則最為精確，其曰「聖人作易，立人之道而已」，此語大有裨於來學，故特表而出之，且為之暢其指趣焉。

Suppose there had already been writing at that time, Fuxi would certainly have spoken about benevolence and righteousness. Fuxi merely did not leave behind words; if Fuxi had expressed himself, how could one be sure he would not have said exactly what the Three Sages did? Laozi and Zhuangzi's school attacked benevolence and righteousness, thus looking down upon the words of the Duke of Zhou and Confucius, considering them unworthy of mention. The Confucian scholars are unable to refute this on rational grounds, and instead further promote it, elevating Fuxi's method of teaching without words and diminishing the subtle explanations of the Three Sages. Is this not reversing the fundamental and the secondary? He Jing (whose name is Zhongyu) has many original insights in interpreting classics, especially his dislike for the Neo-Confucians, which I dare not fully believe. However, his interpretations of the Book of Changes are particularly accurate. He said, "The sage composed the Book of Changes, merely to establish the principles of human conduct." This statement is of great benefit to later learners, so I specially highlight it and explain its meaning clearly.

東涯陳氏言《易疑》自序曰：易非聖人卜筮之書也，卜筮以聖人之書爾。伏羲畫卦，原神於太乙，起數於陰陽，類象於萬物，通幽於神明，和順於道徳性命，無乎弗括。文王於卦為之辭以明其象類，周公於爻為之辭以盡其變化，孔子於卦爻為之彖、象、文言、繫辭、說、序、雜卦，以闡羲、文、周公之義理，使學者修此而吉，悖此而凶，淵乎廣矣，而非作之以卜筮也。

In his preface to "Yi Yi" ("Doubts on the Book of Changes"), Chen Yuan of the Ming dynasty said: The Book of Changes was not written by the sages for divination. Rather, divination made use of the sages' writings. Fuxi drew the trigrams, originally derived from "Taiyi" and connected with the divine and mysterious. He began with the principles of yin and yang, took images from all things, communicated with the divine in the hidden, and harmonized with morality, life, and destiny. It encompasses everything. King Wen attached commentaries to the trigrams to explain the things symbolized by the trigrams. The Duke of Zhou attached commentaries to the lines to exhaust the changes of the lines. Confucius further composed the Commentary on the Judgment, the Image Commentary, the "Wenyan," the Great Treatise, the "Shuogua," the "Xugua," and the "Zagua" for the trigrams and lines, to elaborate on the meanings of Fuxi, King Wen, and the Duke of Zhou. This enables those who study the Book of Changes to cultivate themselves and achieve good fortune, or to violate it and bring misfortune. How profound and extensive this is! It was not written for divination.

子曰：「易有聖人之道四焉」，辭、象、變、占是也。孔子見卦爻之有辭象變占，言焉而廣大，動焉而吉凶，制器焉而網罟舟楫之用，卜筮焉而神物大衍之策，斯徧舉之矣，而未嘗専於卜筮也。夫易何止五經之原、天地神化之奧，而於卜筮之技精之則末矣。秦漢諸儒考象辭則泥術數，論義理則淪空寂，而不知孔子之易先義理而托象數者也。蓋體其卦爻之蘊，察乎辭象變占之理，通乎言動制器卜筮之用，用之所向即理也，理之所協即占也，占之所利即用也，是孔子之易也，而非専於卜筮明矣。是故學者索卜筮於卦爻之外，參《程傳》於《本義》之中，斯孔子之易備矣，作《易疑》。

Confucius said, "The Book of Changes contains four kinds of the way of the sage: words, images, transformation, and divination." Confucius saw that the hexagrams and lines together contain words, images, transformation, and divination. In terms of speech, they are vast and comprehensive; in terms of action, they reveal good and bad fortune; in terms of making tools, they have the function of making nets and building boats and rafts; in terms of divination, they involve the use of yarrow stalks and turtle shells, as well as the great derivation method. This presents all four aspects, without focusing solely on divination. The Book of Changes is not only the source of the Five Classics and the profound mystery of heaven and earth's divine transformation, but even if one masters the art of divination, it is still only a minor aspect. Scholars of the Qin and Han dynasties who studied the images and words became entangled in divination techniques, while those who discussed principles became lost in emptiness. They did not understand that Confucius' Book of Changes prioritizes principles and寄托s them in images and numbers. If one can comprehend the implications of the hexagrams and lines, understand the principles of words, images, transformation, and divination, and integrate the functions of speech, action, tool-making, and divination, then the function points to principle, principle aligns with divination, and divination serves practical use. This is the Book of Changes as Confucius intended it, clearly not focusing solely on divination. Therefore, scholars should seek divination beyond the hexagrams and lines, and refer to Zhu Xi's "The Original Meaning of the Zhou Changes" and Cheng Yi's "Yichuan's Commentary on the Changes" to fully understand Confucius' Book of Changes. Thus, the book "Easy Doubts" was written.

朱氏綬《易經精蘊》自序曰：周子曰「聖人之精，畫卦以示；聖人之蘊，因卦以發」。其蘊維何？凡彖、象、文言、繫辭、說卦皆是。宋儒以《周禮》言大卜掌三易，故専作卜筮之書，歴詆大聖理義之言，不少假借。愚於此大懼，深求其病，只在「太卜掌三易」之一言耳。不知易有理、有象、有數：理即蘊之發，象即精之寓，數因一以積。畫卦示象之吉凶，繫辭論理之吉凶，數之吉凶未之明，故立筮人掌三易以辨九筮之吉凶也。

In his preface to "The Essence of the Book of Changes" ("Yijing Jingyun"), Zhu Shou of the Ming dynasty (styled Wenpei) said: Zhou Dunyi once said, "The subtle essence of the sage is displayed through drawing the trigrams; the hidden meaning of the sage is expressed through the hexagrams." What is meant by "hidden meaning"? It refers to the Commentary on the Judgment, the Image Commentary, the "Wenyan" section, the Great Treatise, and the "Shuogua" section. The Song dynasty scholars, because the "Rites" said that the Grand卜官 (too-bu) was in charge of the three Books of Changes, concluded that the Book of Changes was solely a book for divination, and thus criticized the great sages' discussions on principles and reason, showing no tolerance. I am deeply worried about this, and upon thoroughly investigating the root of this problem, I found it lies in the single phrase "the Grand卜官 (too-bu) is in charge of the three Books of Changes." They did not understand that the Book of Changes contains principles, images, and numbers: principles are the expression of hidden meaning, images are the dwelling place of subtle essence, and numbers are formed by gradually accumulating from one. Drawing the trigrams is to display the images and their fortune or misfortune, while the Great Treatise discusses the principles and their fortune or misfortune. As for the fortune or misfortune of numbers, it has not yet been explained. Therefore, the "Rites" also established the official "Shirren" (sacrificial official) to manage the three Books of Changes, in order to distinguish the fortune or misfortune of the nine methods of divination.

觀象玩辭，聖人體易、君子學易以成盛徳大業，至矣；庸人不能，故立占人、筮人。七八九六揲蓍求卦，不過筮更、筮咸，尤細事耳。易無不該，天地有此數，不立筮法以成變化，則天地間缺此一藝，非謂易道易象舉在此筮，専作卜筮之書也。夫子欲加年學易，期無大過，豈在占筮乎？

Observing the hexagrams and contemplating their words, the sages thus comprehend the Way of the Book of Changes, and the gentleman thus studies the Book of Changes to cultivate great virtue, this is the highest level; ordinary people cannot reach it, so they set up the official positions of "zhan ren" and "shi ren." Using seven, eight, nine, and six to divide the yarrow stalks for divination is merely part of the nine types of divination in the "Rites of Zhou," such as "zhi geng" and "zhi xian," which are even minor details. The Book of Changes encompasses everything; since there is such a system in the world, it is necessary to establish a method of divination to complete the transformations; this does not mean that the principles of the Book of Changes and its hexagrams are entirely contained in divination, nor that the Book of Changes is a book solely for divination. Confucius wished to live longer to study the Book of Changes, hoping to avoid great mistakes, was his intention really about divination?

況占筮専於動而不主於靜，一於用而不求於體，求諸神而不求諸已，失無算矣。使一委之卜筮，而平日無玩易之功，遇吉行之而已，遇凶避之而已，君子將何以自強不息？將何以厚徳載物？學者無用辨悔吝之介，無用震無咎之悔，六十四卦訓戒之言皆作虛文矣。洪惟聖朝用易為首經取士，而只在占筮授受，豈不誤甚？無由挽之回車就道，徒抱憤耳。自知得罪於先儒，取譏當世，獨賴聖人為之依歸，用以自解雲。

Moreover, divination only concerns itself with movement and not with stillness, seeks only utility and not substance, and seeks solely from ghosts and spirits without turning inward to examine oneself. Thus, mistakes are numerous and countless. If everything is left to divination, and one has no daily practice in contemplating the principles of the Book of Changes, then when fortune is favorable one follows it, and when misfortune arises one flees from it. Then, how can a gentleman uphold the virtue of self-renewal without cease? How can he embody the virtue of cultivating great virtue to carry all things? Those who study the Book of Changes would not need to discern the relationship between subtle signs and regret, nor rely on repentance to achieve movement without error. The admonitions of the sixty-four hexagrams have all become empty words. Our dynasty has taken the Book of Changes as the primary classic for selecting officials, yet it has only been taught in the realm of divination. Is this not a great mistake? There is no way to restore it to the right path, and we can only lament in vain. I am fully aware that this will offend the predecessors of the school and invite ridicule from contemporaries. Yet I can only rely on the words of the sages to explain myself.

二泉邵氏寳序《精蘊》曰：易為性命道徳之原，而開物成務，仲尼贊之詳矣。惟其道無不備，故百氏宗之。卜筮者，技之至微者也。自朱子《本義》一出，學者翕然從之。夫方術談於庸醫，聴者不能什一；惟夫和、扁一言，雖或盡變軒岐之書，人將謂其有據也。朱子名冠諸儒，道行今古，誠吾儒之和、扁矣，専主卜筮之說，疇不謂其有據乎哉？庠序以之而教人，科目因之而取士，習尚成風，安固而不搖矣。

In the Ming dynasty, Shao Bao, who was known as Erquan, wrote a preface for the book "The Essence of the Changes." He said that the Book of Changes is the source of life and morality, and it can enlighten the people's wisdom and accomplish affairs. Confucius has already described it in great detail. Because its principles are complete in all aspects, all the schools of thought have revered it. Divination and fortune-telling are merely the most subtle of skills. Since Zhu Xi's "The Original Meaning of the Zhou Changes" was published, scholars have followed it enthusiastically. The same kind of technique, if spoken by a mediocre doctor, would be believed by only a tenth of the people; but if it were said by famous doctors like Hui He and Bian Que, even if all the medical books passed down from the Yellow Emperor and Qibo were changed, people would still consider it to have a basis. Zhu Xi's reputation surpassed all other scholars of the Confucian tradition, and his teachings have been widely circulated throughout history. Indeed, he is the medical Hui He and Bian Que of our Confucian school. His focus on divination and fortune-telling, who would not consider it to have a solid foundation? Schools use it to teach students, and the imperial examinations rely on it to select talents. Once the trend is established, it becomes firmly rooted and unshakable.

嗚呼！此文佩朱公所以深懼，而《精蘊》之書不容於不作也。書凡二十四卷，一以孔子義理之言為主，按卦推辭，隨爻悉義，一覽之間而四聖之心昭然在目，其有功於斯道也大矣。雖然，《本義》無心於晦道，《精蘊》豈有心於矯弊哉？一念所主而得失因之，紫陽有知，必將感其救正之功也，君曰有罪，夫豈然哉！

Alas, this is precisely the reason why Mr. Zhu Wenpei felt deep concern and was compelled to write the "Essence of the Book of Changes." The entire work consists of twenty-four volumes, all based primarily on Confucius' explanations of principles. It deduces the meanings of the verses by examining the hexagrams and elaborates on each line in detail. Upon reading it, one can clearly see the intentions of the four sages: Fuxi, King Wen, the Duke of Zhou, and Confucius. Its contribution to the study of the Book of Changes is indeed great. However, the "Original Meaning" was not intended to obscure the Way of the Changes, nor was the "Essence" deliberately meant to criticize current affairs. It was simply based on the author's own thoughts, and thus success or failure resulted from this. If Zhu Xi, known as the Purple Yang Master, were aware of this from below, he would surely appreciate the merit of this work in rectifying the Way. Zhu himself said "there is guilt," but where could such a thing be true?

都氏穆序《精蘊》曰：客有問穆者曰：「易有卜筮之道乎？」穆曰：「然。」「主卜筮而作乎？」曰：「否。請以水喻：崑崙上源，發而為江、漢、河、淮，以迨溝、澗、溪、渠，皆水也。居溪者曰水以溪而生也，濱澗者曰水以澗而出也，舉一廢百，知水不亦淺乎？」孔子曰：「假我數年，卒以學易，可以無大過矣。」夫以大成之聖，欲學易以免過，易之道可知矣，豈卜筮所可盡哉？

In the Ming dynasty, Du Mu (style name Xuanjing) wrote a preface for the book "The Essence of the Book of Changes." He said that a guest asked him, "Does the Book of Changes contain the principles of divination?" I replied, "Yes." The guest then asked, "Was the Book of Changes primarily composed for the purpose of divination?" I replied, "No. Let me use water as an example. The source of the Kunlun Mountains flows into the Yangtze River, Han River, Yellow River, and Huai River, and continues to gullies, ravines, streams, and canals, all of which are water. Those living by the stream say water comes from the stream, while those living by the ravine say water comes from the ravine. Focusing on one and ignoring the rest is a very shallow understanding of water." Confucius said, "Give me a few more years, and I will eventually master the Book of Changes, thereby avoiding major mistakes." With a sage like Confucius, who has synthesized the wisdom of the past, still wanting to study the Book of Changes to avoid mistakes, it is evident how profound the principles of the Book of Changes are. How could divination possibly encompass all of its depth?

顧氏《日知録》：舜曰「官占惟先蔽志，昆命於元龜」，《詩》云「爰始爰謀，爰契我龜」，《洪範》曰「謀及乃心，謀及卿士，謀及庶人，謀及卜筮」，孔子之贊易也，亦曰「人謀鬼謀」。[祖伊告紂，言格人元龜，亦先人後龜。]夫庶人至賤也，而猶在蓍龜之前，故盡人之明而不能決，然後謀之鬼焉。故古人之於人事信而有功，於鬼也嚴而不瀆。

In the Qing dynasty, Gu Yanwu's "Rizhilu" states that Shun said, "Before consulting the oracle, one must first decide in one's own mind, and then entrust it to the big turtle." The "Shijing · Daying · Mian" says, "First they planned, then they burned the turtle to obtain a sign." The "Shangshu · Hongfan" says, "First consult one's own mind, then consult the ministers, then consult the common people, and only then consult divination." Confucius praised the "Yi," also saying, "human planning and divine planning." [Zu Yi advised King Zhou, mentioning "ge ren" and the big turtle, also prioritizing human judgment before the turtle.] The common people are the most humble, yet they are placed before the yarrow stalks and the big turtle. This shows that one should exhaust human wisdom before seeking guidance from ghosts and gods. Therefore, ancients trusted human affairs and achieved practical results; they revered ghosts and gods without being disrespectful or disrespectful.

子之必孝，臣之必忠，此不待卜而可知也，其所當為，雖凶而不可避也。故曰「欲從靈氛之吉占兮，心猶豫而狐疑」，又曰「用君之心，行君之意，龜策誠不能知此事」。善哉屈子之言，其聖人之徒歟！

A son must surely be filial, and a subject must surely be loyal; this can be understood without divination. Whatever is one's duty, even if an unfavorable omen is obtained, it should not be avoided. Therefore, Qu Yuan in his "Li Sao" says, "I wish to listen to the auspicious divination of Lingfen, yet my heart hesitates and wavers." In his "Bu Ju," he also says, "Follow your own heart, act according to your own will; the turtle shells and yarrow stalks cannot know such matters." Qu Yuan's words are indeed excellent; he must surely be considered a disciple of the sages.

《卜居》，屈原自作，設為問答，以見此心非鬼神吉凶之所得而移耳。王逸序乃曰「心迷意惑，不知所為，往之太卜之家，決之蓍龜，冀聞異策，以定嫌疑」，則與屈子之旨大相背戾矣。洪興祖《補註》曰「此篇上句皆原所從，下句皆原所去，時之人去其所當從，從其所當去，其所謂吉乃原所謂凶也」，可謂得屈子之心者矣。

"The卜居" is a work written by Qu Yuan himself, in which he presents a series of questions and answers to demonstrate that his heart is not swayed by the fortune or misfortune of ghosts and gods. However, Wang Yi of the Eastern Han dynasty, in his preface, said that Qu Yuan was "confused and puzzled, not knowing what to do, so he went to the house of the diviner and asked for divination using yarrow stalks and turtle shells, hoping to receive different advice to determine the difficult situation." This interpretation contradicts Qu Yuan's original intention. Hong Xingzu of the Song dynasty, in his "Supplement to the Chu Ci," said: "In this passage, the upper sentence is what Qu Yuan intended to follow, and the lower sentence is what he intended to abandon. However, people at that time abandoned what they should have followed and followed what they should have abandoned. What they called auspicious was actually what Qu Yuan called inauspicious." This can be considered as understanding Qu Yuan's true intention.

《禮記·少儀》：「問卜筮曰：義與？志與？義則可問，志則否。」子孝臣忠，義也；違害就利，志也。卜筮者，先王所以教人去利懷仁義也。

The Li Ji · Shao Yi says: "When asking someone about divination, one should ask: is the matter about righteousness or about personal interest? Matters of righteousness may be consulted, but those of personal interest should not." Filial piety towards one's father and loyalty towards one's sovereign are matters of righteousness; avoiding misfortune and pursuing benefit are matters of personal interest. Divination, is precisely the means used by the former kings to teach people to eliminate personal gain and to hold fast to benevolence and righteousness.

石駘仲卒，無適子，有庶子六人，卜所以為後者，曰「沐浴佩玉則兆」。五人者皆沐浴佩玉，石祁子曰「孰有執親之喪而沐浴佩玉者乎」，不沐浴佩玉，石祁子兆，衛人以龜為有知也。南蒯將叛，枚筮之，遇《坤》之《比》，曰「黃裳元吉」，子服恵伯曰「忠信之事則可，不然必敗。外強內溫，忠也；和以率貞，信也，故曰黃裳元吉。黃，中之色也；裳，下之飾也；元，善之長也。中不忠，不得其色；下不共，不得其飾；事不善，不得其極。且夫易不可以占險，猶有闕也，筮雖吉，未也」，南蒯果敗。是以嚴君平之卜筮也，與人子言依於孝，與人弟言依於順，與人臣言依於忠，而髙允亦有「筮者當依附爻象，勸以忠孝」之論，其知卜筮之旨矣。

The *Book of Rites* *Tan Gong* records that a nobleman of the State of Wei, Shi Dai Zhong, died without a legitimate son, only six illegitimate sons. They divined who should succeed him, and the oracle said, "Those who bathe and wear jade will have a good omen." Five of them went to bathe and wear jade, but Shi Qi Zi said, "It is unreasonable to bathe and wear jade while mourning one's father," and did not do so. The good omen fell upon Shi Qi Zi, and the people of Wei therefore believed that the turtle was endowed with wisdom. The *Zuo Zhuan* records that Nan Kuan, a minister of the Ji family of Lu, was about to rebel, but he did not explain his reasons before divining with the *Yi* (Book of Changes). He obtained the *Kun* hexagram transforming into the *Bi* hexagram, and the line statement was "Yellow undergarments bring great good fortune." Zi Fu Hui Bo said, "This applies only to matters of loyalty and trustworthiness; otherwise, it will certainly lead to failure. Being strong on the outside and gentle within is loyalty; following the right path with harmony is trust. Therefore, it says 'Yellow undergarments bring great good fortune.' Yellow is the central color; undergarments are the lower garment; 'yuan' is the greatest of all virtues. If one's heart is not loyal, he is unworthy of the color; if one is not respectful in his position, he is unworthy of the garment; if the matter is not virtuous, he cannot reach the highest level. Moreover, the *Yi* is not suitable for predicting dangerous matters, and there are still deficiencies. Although the divination was favorable, it is not truly favorable." Later, Nan Kuan indeed failed. Therefore, Yan Zun (styled Junping) of the Han dynasty, when divining for others, would follow filial piety when speaking to a son, obedience when speaking to a younger brother, and loyalty when speaking to a minister. Gao Yun of the Northern Wei also said, "A diviner should rely on the line images and use loyalty and filial piety to advise people." They both understood the essence of divination.

《申鑑》[後漢荀悅撰]：或問卜筮，曰：「徳斯益，否斯損。」曰：「何謂也？」「吉而濟，凶而救，之謂徳；吉而恃，凶而怠，之謂損。」

In the "Shen Jian" [a work written by Xun Yue of the Eastern Han dynasty], someone asked about divination and fortune-telling, and the answer was: "Those who have virtue gain benefit, while those without virtue suffer loss." The questioner then asked, "How does this mean?" The answer was: "If one receives a favorable omen and makes efforts to achieve it, or receives an unfavorable omen and takes measures to remedy it, this is called having virtue. But if one relies on a favorable omen and becomes complacent, or encounters an unfavorable omen and becomes slack, this is called suffering loss."

君子將有為也，將有行也，問焉而以言，其受命也如向，告其為也，告其行也。死生有命，富貴在天，若是則無可為也，無可行也，不當問，問亦不告也。易以前民用也，非以為人前知也；求前知非聖人之道也。是以《少儀》之訓曰「毋測未至」。

A gentleman will consult the yarrow stalks for guidance only when he is about to take action or make a decision. The yarrow stalks respond immediately, as if echoing the question, and tell him what to do. However, matters such as birth and death, which are determined by fate, and wealth and poverty, which are in the hands of heaven, are not things that can be acted upon. Therefore, one should not ask about them. The Book of Changes is meant to guide the people in their daily lives, not to predict the future. To seek foreknowledge is not the way of the sages. Therefore, the admonition in the Book of Rites, "Do not speculate about things that have not yet come to pass," is given.

郭璞嘗過顏含，欲為之筮，含曰：「年在天，位在人，修已而天不與者，命也；守道而人不知者，性也。自有性命，無勞蓍龜。」《文中子》：子謂北山黃公善醫，先寢食而後針藥；汾陰侯生善筮，先人事而後說卦。

Guo Pu once visited Yan Han, a Jin dynasty man, intending to use divination for him. Yan Han said, "Longevity is determined by heaven, official position is determined by people. If one cultivates oneself but heaven does not grant it, that is fate; if one adheres to the right path but the world does not understand it, that is nature. I have my own life and destiny, so there is no need to trouble with the yarrow stalks or the turtle shell." In the Sui dynasty, Wang Tong's "Zhongwenzi" said that Beishan Huanggong was skilled in medicine, first regulating a patient's sleep and diet, then using needles and medicine; Fen Yin Housheng was skilled in divination, first clarifying human affairs, then explaining the hexagrams.

《金史·方伎傳》序曰：古之為術，以吉凶導人而為善；後世術者，以休咎導人而為不善。

The preface of the "Jin Shi · Fang Ji Zhuan" says: In ancient times, those who practiced numerology and divination used auspicious and inauspicious signs to guide people toward doing good deeds; but in later generations, the diviners used misfortune and blessing to lead people into doing evil.

易為卜筮之書，與醫藥、種樹並稱，秦人之見也，然其說亦有所自來。古者太卜所掌，唯夏商以來相傳之繇辭，如《左氏》之所載者；而文王、周公易象之書，則藏於周、魯之太史氏。故陳厲公時，周史始有以《周易》見陳侯者，陳侯使筮之，而有《觀》六四之占；及昭公二年，韓宣子來聘，觀書於太史氏，始見《易象》與《魯春秋》，可見易象之書他國不皆有。孔子十翼則作於晚年，而傳之商瞿子木，尚未流行於世。[杜預曰：汲縣有發舊冢者，得《周易》上下篇，與今正同，而無彖、象、文言、繫辭，疑於時仲尼造之於魯，尚未播之於逺國也。]

Hu Wei said: To regard the Book of Changes as a book of divination, placing it alongside medicine and tree planting, is the view of the Qin people. However, this view has its origin. In ancient times, the office of the Grand卜 (diviner) was responsible only for the divinatory verses passed down from the Xia and Shang dynasties, similar to those recorded in the Zuo Zhuan. The books on the images of the Book of Changes composed by King Wen and the Duke of Zhou were kept in the royal archives of the Zhou dynasty and the archives of the Grand Historian in Lu. Therefore, during the reign of Chen Li Gong, a Zhou dynasty historian brought the Book of Changes to Chen Hou, who asked him to perform a divination, resulting in the divination of the sixth line of the fourth hexagram in the Guan hexagram. In the second year of Lu Zhao Gong, the Jin state's Han Xuanzi came to visit, and upon viewing the books in the Grand Historian's office, he saw the images of the Book of Changes and the Lu Spring and Autumn Annals—this shows that the books on the images of the Book of Changes were not available in all states. Confucius composed the Ten Wings in his later years, passing them on to his disciple Shang Qu (whose name was Zi Mu). At that time, these writings were not yet widely circulated. [Du Yu said: Someone in Jixian opened an ancient tomb and found the upper and lower parts of the Book of Changes, which were exactly the same as the current version, but without the Tu, Xiang, Wenyan, and Xici. He suspected that Confucius composed these essays while in Lu and had not yet spread them to distant states.]

秦僻在西垂，何由得見？李斯未必知，即知之亦必不信，其以易為卜筮之書無足怪者，而儒者遂謂易専為卜筮而作。夫伏羲既畫八卦而即制蓍為筮法，孔子贊易亦以蓍龜為神物而深明其用，謂易為卜筮之書無甚礙，但謂伏羲作易専為卜筮，而文王、周公、孔子卻說出許多義理，非伏羲之本義，是則大可疑耳。

The state of Qin was located in the western frontier, so from where could they obtain these books? Li Si might not have known, and even if he did, he would certainly not have believed them. It is not strange that he regarded the Book of Changes as a book for divination; however, it is strange that the Confucian scholars also claimed that the Book of Changes was specifically composed for divination. Fuxi first drew the Eight Trigrams and then immediately established the method of using the yarrow stalks for divination. Confucius praised the Book of Changes and regarded the tortoise shells and yarrow stalks as divine objects, deeply understanding their functions, saying that the Book of Changes was a book for divination. This itself was not a great problem. But if one were to say that Fuxi created the Book of Changes specifically for divination, while King Wen, the Duke of Zhou, and Confucius explained many meanings and principles in it, which were not Fuxi's original intention, this would be highly questionable.

夫義理必藉文字以傳，伏羲時書契未興，故立象以盡意。卦畫有形而義理無形，有形者可見而無形者不可見，然其意實在立人之道曰仁與義也。三聖遞相祖述，發揮仁義之旨，而伏羲之意乃大白於天下，安得謂孔子之易非文王、周公之易，文王、周公之易非伏羲之易乎？伏羲之易有畫無辭，農夫、紅女、百工、商賈皆得而用之者也。[如後世楚巫打瓦、越人雞卜，雖無辭亦自有占法。]

The principles of meaning must be transmitted through written words. However, during the time of Fuxi, writing had not yet emerged, so he established hexagrams to express his thoughts. The hexagrams have form, but the principles they represent are formless. What has form can be seen, but what is formless cannot be seen. Yet Fuxi's intention was to establish the principles of human conduct, namely benevolence and righteousness. The three sages, Confucius, King Wen, and the Duke of Zhou, passed down and developed these principles of benevolence and righteousness, thus making Fuxi's original intention clear to the world. How can one say that Confucius' Book of Changes is not King Wen's or the Duke of Zhou's Book of Changes, and that King Wen's and the Duke of Zhou's Book of Changes is not Fuxi's Book of Changes? Fuxi's Book of Changes had hexagrams but no written text, so farmers, weavers, artisans, and merchants could all use it. Just as in later times, the "dawa" divination of the people of Chu and the "chijub" divination of the people of Yue, although without written text, had their own methods of divination.

若夫夏商以來之繇辭及文王、周公之彖爻，唯卜史能用之；至於孔子之十翼，則卜史亦不能知，唯士大夫好學深思者能知之耳。蓋易至孔子而其道始為處憂患、無大過之具，與《詩》《書》《禮》《樂》同其切要，人倫日用所不可斯須去者，而非徒卜筮之書矣。幸而秦火不及，學者得見完書，上之可以窮理而盡性，下之可以反身而寡過。顧徒以農夫、紅女、百工、商賈不能用，而欲崇不言之教，視《繫辭》如糟粕，毋乃過為髙論，墮老莊之環中而不覺也乎？

As for the divination statements from the Xia and Shang dynasties, as well as the images of King Wen and the line statements of the Duke of Zhou, these were only accessible to the diviners and historians. But by the time of Confucius' Ten Wings, even the diviners and historians could not understand them, and only learned and thoughtful scholars could grasp their meaning. Generally speaking, the Book of Changes became a means for people to deal with worries and avoid great misfortunes when it came into Confucius' hands. It is as essential as the Book of Poetry, the Book of Documents, the Book of Rites, and the Book of Music, indispensable in daily life and human relations. It is no longer just a book for divination. Fortunately, it was not destroyed by the burning of books during the Qin dynasty, allowing scholars to see the complete text. Looking upward, it can be used to understand principles and the nature of things; looking downward, it can help people examine themselves, reduce mistakes, and improve their conduct. Now, however, merely because farmers, weavers, craftsmen, and merchants do not use it, some people would praise the method of teaching without written words, and regard the Great Treatise as mere dross. Is this not speaking too highly of it, and falling into the trap of the Taoist and Daoist schools without realizing it?

且夫卜筮之事，非君子所常有也。善當為，惡不可為，乃心自明，何必筮？死生富貴非人之所能為，亦焉用筮？惟天下大事，人但能料其可否，而氣數推移，有非鬼神不能知者，是之謂大疑，於是乎謀及乃心，謀及卿士庶人，而復謀及卜筮焉，故曰「人謀鬼謀，百姓與能」。然必其居也有觀象玩辭之學，而後其動也有觀變玩占之明。[動謂將有為、將有行。《洪範》曰「龜筮共違於人，用靜吉，用作凶」，靜即此所謂居，作即此所謂動也。]

Now, as for divination by tortoise shells and yarrow stalks, it is not something that a gentleman would often resort to. What is good should be done, and what is evil should not be done; one's mind is clear and certain, so why bother with divination? Death, life, wealth, and honor are not within human control, so why need divination? Only in matters of great importance under heaven, where people can only judge whether something is feasible or not, and where the movement of destiny and principles is something beyond the knowledge of ghosts and spirits, does this become a matter of great doubt. Then one first consults one's own mind, then consults the ministers and common people, and only then consults divination. Therefore, the Great Treatise says, "Consulting human minds and consulting spirits, the people and the capable are involved." But it is certainly necessary to have the study of observing celestial phenomena and playing with the words of the classics during ordinary times, so that when taking action, one can have clear judgment based on observing changes and divination. [The term "动" refers to when there is about to be action or movement. The Book of Documents, the Book of Hong Fan, says, "If divination by tortoise shells and yarrow stalks contradicts human opinion, then it is safe to remain quiet and follow the norm; but if there is action, it will be ominous." The term "静" here refers to "居," and "作" refers to "动." ]

計一歲之中，居之時多，動之時少，及其動也，不疑之事什九，可疑之事什一，其大疑者又加少焉，君子之於卜筮亦未嘗數數也。聖人豈専為卜筮而著一書，使天下後世之人日日端策拂龜，聴命於鬼神而不務民義也哉？亭林論卜筮十則，可以箴宋人之膏肓，餘故備錄之，而綴以管見如此。

In the course of a year, there are more times of stillness than of action; when action is taken, there are nine tenths of matters that do not require doubt, and only one tenth that is doubtful, and among these, those that qualify as 'great doubt' are even fewer. Thus, it is evident that the gentleman does not frequently resort to divination. Could the sage have written a book solely for divination, making people of later generations constantly handle the yarrow stalks and polish the turtle shells, blindly relying on ghosts and spirits rather than devoting themselves to the righteous affairs of the people? Gu Yanwu's (styled Tingle林) ten discussions on divination can effectively cure the deep-rooted illness of the Song dynasty scholars, so I have copied them all down and added my own simple comments as above.

《日知録》曰：孔子論易，見於《論語》者二章而已：曰「假我數年，五十以學易，可以無大過矣」；曰「南人有言曰：人而無恆，不可以作巫醫。善夫！不恆其徳，或承之羞」，子曰「不占而已矣」。是則聖人之所以學易者，不過庸言庸行之間，而不在乎圖書象數也。今之穿鑿圖象以自為能者，畔也。

The "Rizhilu" says: Confucius' discussion of the "Yi" is found in the "Lunyu" only in two chapters: one is "Give me a few more years, until I am fifty, then I will study the "Yi" and will not commit great mistakes"; the other is "There is a saying among the southern people: if a person lacks perseverance, he cannot even become a shaman or a physician. This is well said! The "Heng" hexagram's ninth trigram in the third line says 'If one cannot maintain virtue for a long time, he will bring disgrace.' Confucius then says 'Such a person does not need to consult the oracle.' This shows that the sage's study of the "Yi" lies in ordinary speech and conduct, not in the Yellow River Chart and Luo Writing, nor in the study of symbolic numbers and images. Now those who fabricate images to show off their abilities have strayed from the way of the sage.

記者於夫子學易之言而即繼之曰「子所雅言，詩、書、執禮，皆雅言也」，是知夫子平日不言易，而其言詩、書、執禮者皆言易也。人苟循乎詩、書、執禮之常而不越焉，則自天佑之，吉無不到矣。故其作《繫辭傳》，於悔吝無咎之旨特諄諄焉，而《大象》所言，凡其體之於身、施之於政者，無非用易之事。

The recorders of the "Analects" wrote immediately after Confucius' words about studying the Book of Changes that "Confucius often spoke about the Book of Poetry, the Book of Documents, and upholding ritual, which were all the topics he discussed daily." This shows that Confucius did not often talk about the Book of Changes, but when he spoke about the Book of Poetry, the Book of Documents, and upholding ritual, he was actually always speaking about the Book of Changes. If a person follows the constant principles of the Book of Poetry, the Book of Documents, and upholding ritual without exceeding them, then heaven will protect him, and good fortune will surely come. Therefore, Confucius composed the "Great Treatise" and especially emphasized repeatedly the themes of regret, worry, and how to avoid mistakes. What is discussed in the "Great Image Commentary" is all about what is manifested within oneself and applied in governance, and none of it is not the use of the Book of Changes.

然辭本乎象，故曰「君子居則觀其象而玩其辭」，觀之者淺，玩之者深矣。其所以與民同患者，必於辭焉著之，故曰「聖人之情見乎辭」。若「天一地二」「易有太極」二章，皆言數之所起，亦贊易之所不可遺，而未嘗専以象數教人為學也。是故「出入以度」「無有師保，如臨父母」，文王、周公、孔子之易也；希夷之圖、康節之書，道家之易也。自二子之學興，而空疎之人、迂怪之士舉竄跡於其中以為易，而其易為方術之書，於聖人寡過反身之學去之逺矣。

However, the words of the text originate from the hexagram images, so it is said, "A gentleman in peace observes the hexagrams and savors the line statements." Observation is only a superficial level, while savoring is a deeper level. The reason sages share the worries of the common people is certainly to express it through words, so it is said, "The mind of the sage is revealed in the words." As for the chapters "Heaven is one, Earth is two" and "The Book of Changes has the Taiji," these are both discussing the origin of numbers, and they are indispensable parts when praising the Book of Changes. But Confucius did not exclusively teach people to study the Book of Changes through images and numbers. Therefore, statements such as "Coming and going follow a system and order" and "Even without a teacher or guardian by one's side, it is as if facing one's parents" are the Book of Changes of King Wen, the Duke of Zhou, and Confucius. The diagrams of Chen Tuan (who was called Xiyi) and the writings of Shao Yong (who was posthumously honored as Kangjie) belong to the Daoist interpretation of the Book of Changes. Since the doctrines of these two people arose, the superficial and eccentric scholars all took refuge in them, treating them as the Book of Changes, thus turning their interpretation of the Book of Changes into a book of divination techniques, and it has long been far removed from the scholarly study of sages to correct mistakes and examine oneself.

黃氏《象數論序》曰：夫易者，範圍天地之書也，廣大無所不備，故九流百家之學俱可竄入焉；自九流百家借之以行其說，而於易之本意反晦矣。《漢·儒林傳》：孔子六傳至菑川田何，易道大興。吾不知田何之說何如也。降而焦、京，世應、飛伏、動爻、互體、五行、納甲之變無不具者。吾讀李鼎祚《易解》，一時諸儒之說蕪穢康荘，使觀象玩占之理盡入於淫瞽方技之流，可不悲夫！

In the preface to his book "Discussion on the Images and Numbers of the Book of Changes" (Yixue Xiangshu Lun), Huang Zongxi of the Qing dynasty said: The Book of Changes is a book that encompasses the heavens and the earth, vast and comprehensive, so that the doctrines of the nine streams and hundred schools can all be found within it. Since the nine streams and hundred schools have used it to promote their own views, the original meaning of the Book of Changes has become obscured. The "Book of Han · Biographies of the Literati" says: Confucius' study of the Book of Changes was passed down through six generations to Tian He of Zichuan, and the way of the Book of Changes became greatly flourishing — yet I do not know what exactly Tian He's teachings were. Later, during the Western Han dynasty, Jiao Yanshou and Jing Fang appeared, and all sorts of variations such as world and response lines, flying and hidden lines, moving lines, mutual forms, the five phases, and the stem assignment method (najia) were fully developed. When I read Li Dingzuo's "Collected Explanations of the Zhou Changes" from the Tang dynasty, I saw that the views of the various scholars of that time had turned the main path into a wasteland, causing the principles of observing phenomena and divination to fall entirely into the hands of witches, blind men, and technical practitioners. How could one not feel sorrowful about this!

有魏王輔嗣出而注易，得意忘象，得象忘言，日時歲月、五氣相推悉皆擯落，多所不闗，庶幾潦水盡而寒潭清矣。顧論者謂其以老莊解易，試讀其注，簡當而無浮義，何曽籠落玄旨，故能逺歴於唐，發為《正義》，其廓清之功不可泯也。然而魏伯陽之《參同契》、陳希夷之圖書逺有端緒，世之好竒者卑王注之淡薄，未嘗不以別傳私之。

During the Cao Wei period, Wang Bi came forward to annotate the Yi, advocating that one could forget the images once the meaning was grasped, and forget words once the images were understood. He completely discarded the system of pushing together days, hours, years, months, and the five elements, considering them largely irrelevant to the Yi. This approach brought about a clarity akin to stagnant water receding and a cold pond becoming clear. However, critics claimed he interpreted the Yi through the philosophy of Laozi and Zhuangzi. Upon reading his annotations, they are concise, appropriate, and free from vague discussions; how could they be said to use abstract principles to obscure the text? Therefore, his annotations were able to be passed down to the Tang dynasty and developed into The Correct Meaning of the Zhou Changes. His contribution to clarifying Yi studies cannot be overlooked. Nevertheless, the works of Wei Boyang from the Eastern Han dynasty, the Zhouyi Cantongqi, and the scholarly traditions of Chen Tuan originated much earlier. People who are curious often find Wang Bi's annotations too shallow and tend to regard these other works as secret teachings passed down through another lineage, secretly valuing them.

逮伊川作《易傳》，收其崑崙旁薄者散之於六十四卦中，理到語精，易道於是而大定矣。其時康節上接种放、穆修、李之才之傳，而創為河圖先天之說，是亦不過一家之學耳。晦庵作《本義》，加之於開卷，讀易者從之，後世頒之學官，初猶兼《易傳》並行，久而止行《本義》，於是經生學士信以為羲、文、周、孔其道不同，所謂象數者又語焉而不詳，將夫子之韋編三絶者須求之賣醬箍桶之徒，而易學之榛蕪蓋仍如京、焦之時矣。自科舉之學一定，世不敢複議，稍有出入其說者，即以穿鑿誣之。

Cheng Yi, known as Master Yichuan, composed the Yichuan Commentary on the Changes, dispersing those comprehensive and vast principles into the sixty-four hexagrams. His explanations were thorough and his wording precise, and thus the doctrine of the Changes was finally established. At that time, Shao Yong inherited the teachings of Zhongfang, Mu Xiu, and Li Zhici, and established the theory of the Yellow River Chart and Earlier Heaven. This was merely a single school of thought. Zhu Xi, who was known as Hui'an, wrote The Original Meaning of the Zhou Changes, and placed these diagrams at the beginning of the text. Those who read the Changes then began to follow them. Later, the government issued these texts to the schools, initially using them together with the Yichuan Commentary on the Changes. But over time, only The Original Meaning was used. Thus, scholars and students of the classics mistakenly believed that Fuxi, King Wen, the Duke of Zhou, and Confucius each had their own doctrines, and the discussion of images and numbers became vague and unclear. As a result, the very book that Confucius studied so diligently, which he turned the pages of three times, was now sought after from commoners such as those who sold sauce or repaired barrels. The decline of the study of the Changes is probably no different from the time of Jing Fang and Jiao Yanshou. Since the imperial examination system became the sole standard, people dared not raise any objections. Any slight deviation from the established views was regarded as forced and fabricated.

夫所謂穿鑿者，必其與聖經不合者也，摘發傳注之訛，復還經文之舊，不可謂之穿鑿也。河圖洛書，歐陽子言其怪妄之尤甚者，且與漢儒異趣，不特不見於經，亦是不見於傳。先天之方位，明與出震齊巽之文相背，而晦翁反致疑於經文之卦位。生十六、生三十二，卦不成卦，爻不成爻，一切非經文所有，顧可謂之不穿鑿乎？

What is called forced interpretation must refer to things that contradict the sages' classic texts; as for pointing out errors in the commentaries and restoring the original meaning of the classics, this cannot be called forced interpretation. The Yellow River Chart and the Luo Writing, Ouyang Xiu said, are the most absurd among superstitious doctrines, and they differ from the approach of the Han scholars. Not only are they not found in the classics, but they are also not mentioned in the commentaries. The arrangement of the Earlier Heaven diagram clearly contradicts the words in the "Sayings on the Trigrams" that "the Emperor comes forth from Zhen, and is in harmony with Xun." Zhu Xi, instead, doubted the positions of the trigrams in the classic. As for the claim that the Eight Trigrams generate sixteen and then thirty-two, the trigrams cease to be trigrams, and the lines cease to be lines; all of these are not found in the classics. How can they not be considered forced interpretation?

晦翁曰：「談易者譬之燭籠，添得一條骨子則障了一路光明，若能盡去其障，使之統體光明，豈不更好？」斯言是也，奈何添入康節之學，使之統體皆障乎！世儒過視象數以為絶學，故為所欺，餘一一疏通之，知其於易本了無干涉，而後反求之《程傳》，或亦廓清之一端也。

Zhu Xi said: "Studying the Book of Changes is like a lantern; adding one frame blocks a path of light. If we could remove all the obstructions and let it shine through completely, would that not be better?" What he said is correct, yet he himself added in Shao Yong's system, making the whole thing full of obstructions! Scholars of the Confucian tradition have placed too much emphasis on the images and numbers, treating them as a lost art, thus being blinded by them. I have clarified each point, making people realize that these have nothing to do with the Book of Changes, and then returning to Cheng Yi's Yichuan Commentary on the Changes, this might also be a way to clarify the study of the Book of Changes.

按：史，魏正始中，何晏、王弼等好《老》《莊》書，祖尚虛無，以六經為聖人之糟粕，天下士大夫慕效成風，迄江左而未艾，故范寧謂王、何之罪深於桀、紂。今觀弼所注易，各依彖爻以立解，間有涉於老莊者亦千百之一二，未嘗以文王、周公、孔子之辭為不足貴而糟粕視之也。獨為先天學者，欲盡廢周孔之言而専從羲皇心地上尋求，是其罪更浮於王、何矣。儒者不之闢，而反助其狂瀾，以為三聖人之易非即伏羲之易，何邪？亭林、棃洲之論大有造於易學，故殿之篇末，以告天下之習非而不悟者。

Hu Wei said: According to historical records, during the Zhengshi period of the Cao Wei dynasty, He Yan and Wang Bi and others favored the "Laozi" and "Zhuangzi", cherished emptiness and nothingness, and regarded the Six Classics as the dregs of the sages. The scholars of the whole country followed this trend, and this practice continued until the Southern and Northern Dynasties. Therefore, Fan Ning of the Eastern Jin dynasty said that the crimes of Wang Bi and He Yan were deeper than those of Jie and Zhou. Now, looking at Wang Bi's commentary on the "Zhou Yi", he based his interpretations on the彖辞 and爻辞, and occasionally referred to Laozi and Zhuangzi, but this was only a small fraction, less than one or two percent. He never regarded the words of Wen Wang, the Duke of Zhou, and Confucius as worthless dregs. Instead, those who study the Earlier Heaven school would discard the words of the Duke of Zhou and Confucius entirely, and seek only in the "mind" of Fuxi. This is a greater crime than that of Wang Bi and He Yan. Scholars of Confucianism do not refute them, but instead encourage this trend, claiming that the "Yi" of the three sages is not the "Yi" of Fuxi. What is the reason for this? Gu Yanwu and Huang Zongxi (who was called Lizi) made great contributions to the study of the "Yi", so I have placed their discussions at the end of this book, to warn those who have become accustomed to wrong practices without realizing it.

右論學易正宗。

The above section discusses the orthodox method of studying the Book of Changes.