Book Nine of the Clear Explanation of the Book of Changes, compiled by Hu Wei of Deqing

《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 (JiaRen, 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 (DaGuo, 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."