The Circular Diagram of the Sequence of Hexagrams

孔子《繫辭傳》，敘上下篇九卦曰：“履，德之基也；謙，德之柄也；復，德之本也；恆，德之固也；損，德之修也；益，德之裕也；困，德之辨也；井，德之地也；巽，德之制也。”

Confucius in the Great Treatise discusses nine hexagrams from the upper and lower parts, saying: "The hexagram of Footsteps is the foundation of virtue, the hexagram of Humility is the handle of virtue, the hexagram of Returning is the root of virtue, the hexagram of Constancy is the firmness of virtue, the hexagram of Loss is the cultivation of virtue, the hexagram of Gain is the abundance of virtue, the hexagram of Difficulty is the test of virtue, the hexagram of Well is the place of virtue, and the hexagram of Following is the restraint of virtue." This is what is later called the "Three Statements and Nine Hexagrams."

先儒以其卦推配上下經皆相對，蓋《乾》與《咸》、《恆》對，《履》與《損》，《益》對，《謙》與《困》、《井》對，《復》與《巽》、《兌》對，每以下篇兩卦，對上篇一卦，凡十二卦而二篇之數適齊矣，然十二卦之中，又止取九卦者，《乾》、《咸》其始也，《兌》其終也，略其終始，而取其中間之卦，以著陰陽消息盛衰之漸，故止於九。前所推上下篇各四節，陰陽消息盛衰之次，與此圖密合。

Previous Confucian scholars used these nine trigrams to match them, discovering that the upper and lower sections correspond exactly one by one: The trigram Qian corresponds with Xian and Heng, the trigram Lie corresponds with Sun and Yi, the trigram Qian corresponds with Kun and Jing, and the trigram Fu corresponds with Xun and Dui. Each time, the two trigrams from the lower section are paired with one from the upper section, making a total of twelve trigrams, and the number of trigrams in the upper and lower sections matches perfectly. However, among these twelve trigrams, Confucius only selected nine. The reason is that Qian and Xian mark the beginning of one end, while Dui marks the end of the other end. By omitting the beginning and the end, only the middle trigrams are chosen to illustrate the gradual process of the waxing and waning of yin and yang. Therefore, only nine trigrams are selected. The selection and omission clearly show Confucius' intention of using trigrams to illustrate virtue. The previous division of the upper and lower sections into four parts each, showing the order of the waxing and waning of yin and yang, exactly matches this circular diagram.

先儒有以雜卦為互卦者，今用其說而詳推之。

Among the scholars of previous dynasties, some argued that the basis of the "Zagua" (Miscellaneous Hexagrams) is actually the method of the nuclear hexagram. Here we adopt their view and elaborate on the reasoning in detail.

此互卦之根也，唯其方成四畫時，所互有此十六卦，故六十四卦成後，以中爻互之，只此十六卦，既以六爻循環互之，亦只此十六卦。四畫互成十六卦、又以其中二畫觀之，則互《乾》、《坤》、《剝》、《復》、《大過》、《頤》、《姤》、《夬》者，皆中二爻為太陽太陰者也；互《漸》、《歸妹》、《解》、《蹇》、《睽》、《家

This diagram represents the origin of the nuclear hexagram. The four trigrams, Sun Yang, Sun Yin, Minor Yang, and Minor Yin, intersect in pairs, resulting in a total of sixteen combinations, hence called "sixteen matters." This is because when the diagram reaches the stage of four lines, only these sixteen hexagrams can be derived through mutual interaction. Therefore, after all sixty-four hexagrams are completed, using the fourth line as the center for mutual derivation still results in only these sixteen hexagrams. Further mutual interaction through all six lines remains within these sixteen hexagrams. After forming sixteen hexagrams through the four lines, one should examine the middle two lines: those hexagrams derived from the hexagrams Qian, Kun, Bo, Fu, Da Guo, Yi, Guo, and Gua all have the middle two lines as Sun Yang or Sun Yin. Those derived from the hexagrams Jie, Gui Mei, Jie, Jian, Kui, and Jia (the original text here is interrupted, and the following titles are connected to the titles of two other diagrams).

互《乾》、《坤》、《既濟》、《未濟》之十六卦，即諸卦之所互而成者也，故十六卦又只成《乾》、《坤》、《既濟》、《未濟》四卦，猶十六事之歸於四象也，蓋四象即《乾》、《坤》、《既濟》、《未濟》之具體，故以太陽三疊之即《乾》，以太陰三疊之即《坤》，以少陰三疊之即《既濟》，以少陽三疊之即《未濟》。《乾》、《坤》、《既濟》、《未濟》統乎《易》之道矣，故《序卦》、之雜卦》皆以是終始焉。

The previous diagram is titled "Sixteen Hexagrams Interacting to Form Four Hexagrams Diagram." The character "咸" should be read as "成." The sixteen hexagrams that can be generated through mutual interaction are precisely those formed by the mutual transformation of each hexagram; and when these sixteen hexagrams interact again, they only result in the four hexagrams: Qian, Kun, Ji Ji, and Wei Ji. Just as sixteen things ultimately reduce to the four trigrams, the four trigrams Qian, Kun, Ji Ji, and Wei Ji are the specific forms of the four trigrams. Stacking three layers of the sun produces Qian, stacking three layers of the moon produces Kun, stacking three layers of the lesser yin produces Ji Ji, and stacking three layers of the lesser yang produces Wei Ji. The four hexagrams Qian, Kun, Ji Ji, and Wei Ji encompass all the principles of the Book of Changes, so both the "Xugua" and "Zagua" treat these four hexagrams as the beginning and end. (The original text mistakenly writes "之杂卦" instead of "《杂卦》.")

《乾》、《坤》，體也；《既濟》、《未濟》，用也。故以《乾》、《坤》始之，《既濟》、《未濟》終之。中間則左方六卦，《剝》、《復》、《漸》、《歸妹》、《解》、《蹇》為陽卦，皆以《震》、《艮》為主，而統於《乾》、《坤》，右方六卦，《姤》、《夬》、《大過》、《頤》、《睽》、《家人》為陰卦，皆以《巽》、《兌》為主，而統於《既濟》、《末濟》，故圖之外一層者，六十四卦也；次內一層者，所互之十六卦也；又次內一層者，十六卦，所互之四卦也。

The trigrams 乾 and 坤 are the "body," while 既济 and 未济 are the "function": 乾 and 坤 determine the essence of yin and yang, while 既济 and 未济 show the effects of water and fire interacting or not. Therefore, the diagram starts with 乾 and 坤 and ends with 既济 and 未济. In the middle section, the six trigrams on the left side—剥, 复, 渐, 归妹, 解, 蹇—are all yang trigrams, each primarily associated with 震 and 艮, and all subordinate to 乾 and 坤; the six trigrams on the right side—姤, 夬, 大过, 颐, 睽, 家人—are all yin trigrams, each primarily associated with 巽 and 兑, and all subordinate to 既济 and 未济. Therefore, the outermost layer of this diagram arranges the sixty-four trigrams, the next layer arranges the sixteen trigrams they interact with, and the innermost layer arranges the four trigrams these sixteen trigrams interact with. Layer by layer, moving inward, it clearly shows that the sixty-four trigrams interact with each other, yet they never go beyond the scope of these four trigrams.

以其象限觀之，則皆互《乾》、《坤》者居前，互《既濟》、《未濟》者居後，以其左右觀之，則左方者皆統於《乾》、《坤》，右方者皆統於《既濟》、《未濟》也。

Looking at the quadrants on the diagram, all hexagrams that contain both Qian and Kun are placed first, while those containing Ji Ji and Wei Ji are placed later. When considering the left and right halves, the hexagrams on the left are all associated with Qian and Kun, and those on the right are associated with Ji Ji and Wei Ji. These two perspectives complement each other, making the overall structure of the diagram clear and easy to understand.

為互卦之主，不在互卦之內者，十四卦《乾》互之得《乾》，《坤》互之得《坤》，《既濟》互之得《耒濟》、《未濟》互之得《既濟》，此四卦者不可變，故不在互卦之內也。

There are fourteen hexagrams that are the main ones of the nuclear hexagram, but they are not included in the group from which the nuclear hexagram is derived. The hexagram Qian remains Qian when transformed by the nuclear hexagram method, and the hexagram Kun remains Kun. The hexagram Ji Ji transforms into Wei Ji, and the hexagram Wei Ji transforms into Ji Ji (the original text says 'Lei Ji' but it should be 'Wei Ji'). These four hexagrams either remain unchanged or only alternate between each other, so they are not included in the list of nuclear hexagrams.

陽卦六，《剝》、《復》者，《震》、《艮》交於《坤》者也；《漸》、《歸妹》者，《震》、《艮》交於《巽》、《兌》者也；《解》、《蹇》者，《震》、《艮》交於《坎》者也，故《震》、《艮》為互陽卦之主。陰卦六，《垢》、《夬》者，《巽》、《兌》交於《乾》者也；《大過》、《頤》者，《巽》、《兌》關於《震》、《艮》者也；《睽》、《家人》者，《巽》、《兌》交於《離》者也，故《巽》、《兌》為互陰卦之主。

The remaining ten trigrams are divided into two groups, yin and yang. The six yang trigrams are: 《Bao》 and 《Fu》 are formed by the intersection of Zhen, Gen, and Kun; 《Jian》 and 《Jian》 are formed by the intersection of Zhen, Gen, and Kan; 《Jie》 and 《Jian》 are formed by the intersection of Zhen, Gen, and Kan. Therefore, Zhen and Gen are the main trigrams generating the yang trigrams. The six yin trigrams are: 《Gou》 and 《Guai》 are formed by the intersection of Xun, Dui, and Qian; 《Da Guo》 and 《Yi》 are formed by the intersection of Xun, Dui, and Zhen, Gen; 《Kui》 and 《Jia Ren》 are formed by the intersection of Xun, Dui, and Li. Therefore, Xun and Dui are the main trigrams generating the yin trigrams. These ten trigrams, together with the previous ones 《Qian》, 《Kun》, 《Ji Ji》, and 《Wei Ji》, total fourteen trigrams, all of which are derived from the mutual interaction of the trigrams. These trigrams themselves are not listed among the trigrams being interacted with. Zhen and Gen are single yang trigrams, while Xun and Dui are single yin trigrams, thus serving as the main trigrams for the mutual generation of the yang and yin groups respectively.

以三畫言之，《艮》陽極而《震》陽生也；以六畫言之，《剝》陽極而《復》陽生也，故《剝》《復》象《艮》《震》而為陽卦之首。以三畫言之，《兌》陰極而《巽》陰生也；以六畫言之，《夬》陰極而《姤》陰生也，故《夬》、《姤》象《兌》、《巽》而為陰卦之首，《乾》、《坤》之用在《否》、《泰》，猶《坎》、《離》之用在《既濟》、《未既》也，故《否》、《泰》、《乾》、《坤》之交，而為《既濟》、《未濟》之宗，此十卦亦不在互卦之內，《雜卦》中遇此數卦，皆從本卦取義，不用互體，其餘自《比》、《師》以後，《需》、《訟》

In terms of the three-line primary trigrams, 《Gen》(Mountain) represents yang reaching its peak, while 《Zhen》(Thunder) represents yang just beginning to emerge. In terms of the six-line composite trigrams, 《Bo》(Splitting) represents yang reaching its peak, and 《Fu》(Return) represents yang just beginning to emerge. Therefore, 《Bo》 and 《Fu》 take the form of 《Gen》 and 《Zhen》, serving as the leading trigrams of yang trigrams in the inter-trigram structure. Similarly, in terms of the three-line primary trigrams, 《Dui》(Lake) represents yin reaching its peak, while 《Xun》(Wind) represents yin just beginning to emerge. In terms of the six-line composite trigrams, 《Guai》(Breaking) represents yin reaching its peak, and 《Gou》(Meeting) represents yin just beginning to emerge. Therefore, 《Guai》 and 《Gou》 take the form of 《Dui》 and 《Xun》, serving as the leading trigrams of yin trigrams in the inter-trigram structure. The functions of 《Qian》(Heaven) and 《Kun》(Earth) are embodied in 《Pu》(Obstruction) and 《Tai》(Great Crossing), just as the functions of 《Kan》(Water) and 《Li》(Fire) are embodied in 《Ji Ji》(Great Completion) and 《Wei Ji》(Not Yet Completed). Therefore, 《Pu》 and 《Tai》 are both the trigrams formed by the interaction of 《Qian》 and 《Kun》, and also the main trigrams of 《Ji Ji》 and 《Wei Ji》. Together with the previous examples, these ten trigrams are not included in the inter-trigram structure. When encountering these trigrams in 《Zagua》, they are always interpreted based on the primary trigram, not the inter-trigram structure. As for the remaining trigrams, starting from 《Bi》(Following) and 《Shi》(Army) down to 《Xu》(Waiting) and 《Song》(Contention), the original text here is interrupted, followed by the title of the next section of the diagrammatic explanation.

自《乾》、《坤》至《晉》、《明夷》二十八卦，為陽卦。皆互《剝》、《復》、《漸》、《歸妹》、《解》、《蹇》，凡上經之卦十八，而雜下經十卦於其中。自《井》、、》夬、、、《困》至《需》《訟》二十八卦，為陰卦。皆互《姤、《》《大過》《頤》《睽》、《家人》，凡下經之卦十八，而雜上經十卦於其中。

The *Zagua* (Miscellaneous Trigrams) begins with the trigrams *Qian* (Heaven) and *Kun* (Earth) and ends with *Jin* (Progress) and *Mingyi* (Darkness), covering a total of twenty-eight trigrams, belonging to the group of yang trigrams. The trigrams interrelated with this group are *Bo* (Decrease), *Fu* (Return), *Jian* (Gradual Progress), *Gui Mei* (Return of the Wife), *Jie* (Release), and *Jian* (Obstruction). In this group, eighteen trigrams are from the Upper Canon, and ten are from the Lower Canon. From *Jing* (Well) and *Kun* (Obstruction) to *Xu* (Necessity) and *Song* (Contention), there are also twenty-eight trigrams, belonging to the group of yin trigrams. The trigrams interrelated with this group are *Gou* (Meeting), *Guai* (Decision), *Daguo* (Great Excess), *Yi* (Nourishment), *Kui* (Strife), and *Jiaoren* (Family). In this group, eighteen trigrams are from the Lower Canon, and ten are from the Upper Canon (the original text has a misprint here, with the trigram names incorrectly placed within book marks, such as 「》Guai、、、」「《Gou、《》」, which are printing errors).

自《乾》、《坤》至《噬嗑》、《賁》，為陽卦之正。首《剝》、《復》，次《漸》，《歸妹》，次《解》、《蹇》。自《兌》、《巽》至《晉》、《明夷》，為陽封之變。首《漸》、《歸妹》。次《剝》、《復》，次《解》、《蹇》。自《井》、《困》至《否》、《泰》為陰卦之變。首《睽》、《家人》，次《垢》、《央》，次《大過》、《頤》。自《大壯》、、，為陰卦之正。首《垢》《》、，《遯》至《需》《訟》、夬，次《大過》《頤》次《睽》、《家人》。

From the hexagrams of Qian and Kun to those of Shihe and Ben, these are the "correct" (zheng) hexagrams among the yang hexagrams, arranged with Bao and Fu leading first, followed by Jie and Guimi, then Xie and Jian. From Dui and Xun to Jin and Mingyi, these are the "change" (bian) hexagrams among the yang hexagrams (the original text's "yang fen" should be "yang hexagrams"), arranged with Jie and Guimi leading first, followed by Bao and Fu, then Xie and Jian. From Jing and Kun to Po and Tai, these are the "change" hexagrams among the yin hexagrams, arranged with Kui and Jiaoren leading first, followed by Gou and Guai, then Daguover and Yi. From Da Zhuang and Dun to Xu and Song, these are the "correct" hexagrams among the yin hexagrams, arranged with Gou and Guai leading first, followed by Daguover and Yi, then Kui and Jiaoren (the last pair of hexagrams in the original text have incorrect and misplaced names; "gou" is a mistake for "gou" and "yang" is a mistake for "guai"). Each of the four sections is organized around three pairs of interacting hexagrams, alternating between correct and change, in a well-ordered sequence.

乾剛坤柔。《周易》首《乾》、《坤》，故《序》、《雜卦》皆不《易》焉。以互卦論之，唯《乾》、《坤》、《既濟》、《未濟》四卦互之，仍得《乾》、《坤》、《既濟》、《未濟》，不與它卦相變。然《既擠》猶變為《未濟》，《未濟》猶變為《既濟》，唯《乾》仍得《乾》，《坤》仍得《坤》，其體一定而不可變者也。

The "Zage" opens with "Qian is strong and Kun is yielding." The "Zhou Yi" begins with the hexagrams "Qian" and "Kun," so both the "Xugua" and "Zage" sections maintain this order without alteration. Regarding the nuclear hexagrams, only the four hexagrams "Qian," "Kun," "Jiji," and "Weiji" change into each other, still resulting in "Qian," "Kun," "Jiji," and "Weiji," without transforming into any other hexagrams. However, when "Jiji" changes into its nuclear hexagram, it becomes "Weiji" (the original text "ji qi" should be "ji ji"), and when "Weiji" changes into its nuclear hexagram, it becomes "Jiji." Only "Qian" remains "Qian" when it changes, and "Kun" remains "Kun" when it changes, indicating that their nature is fixed and unchangeable.

《易》之道主於變易變易，《序卦》者，時之相生，變易者也。《雜卦》者，事之相對，變易者也。然非有不易者以為之體，則所謂“乾坤毀無以見易”者，而變化何自生哉！是故先之以《乾》、《坤》，然後別互卦之陰陽以次之。

The principles of the Book of Changes are primarily about change. The "Sequence of Hexagrams" discusses the mutual generation of circumstances, which belongs to the category of change; the "Miscellaneous Hexagrams" discusses things in pairs, which also belongs to change. However, if there is no unchanging principle serving as their foundation, then it would be as the "Great Treatise" says, "If Heaven and Earth were destroyed, there would be no way to see change." From where would change arise? Therefore, first the hexagrams of Heaven and Earth are presented, then the yin and yang of the mutual hexagrams are distinguished, and they are arranged in order.

“《比》樂《師》憂；《臨》、《觀》之義，或與或求；《屯》見而不失其居，《蒙》雜而著。《震》起也；《艮》，止也，《損》、《益》，盛衰之始也。”此八卦皆互體為《剝》、《復》，而雜《震》、《艮》二卦於其中，蓋《震》、《艮》陽卦之主，而《剝》、《復》之具體也。

The "Zage" says: "The hexagram 'Bi' is joyful, while 'Shi' is cause for concern; 'Lin' and 'Guan' signify one of giving and the other of seeking; 'Zun' is the emergence of things without losing their proper place, while 'Meng' is the state of childish confusion that gradually becomes clear. 'Zhen' is the beginning of action, while 'Gen' is the cessation of movement; 'Sun' and 'Yi' mark the beginning of decline and growth respectively." The mutual relations of these eight hexagrams are all based on 'Bo' and 'Fu', with 'Zhen' and 'Gen' incorporated in between, because 'Zhen' and 'Gen' are the main representatives of yang hexagrams, which are the specific forms of 'Bo' and 'Fu'—'Fu' has one yang line at the bottom, matching the image of 'Zhen'; 'Bo' has one yang line at the top, matching the image of 'Gen'.

自《比》、《師》、《臨》、《觀》、《屯》、《蒙》，皆上經之卦，而《損》、《益》獨為下經之卦，《震》、《艮》亦下經之卦也，故決於《損》、《益》之前，上經之卦六，比師一陽，《臨》、《觀》、《屯》、《蒙》二陽，次《漸》、《歸妹》“《大畜》，時也：《無妄》，災也。《萃》聚而《升》不來也。”此四卦，皆互體為《漸》、《歸妹》，陽卦以上經居前，下經居後，故先《大畜》、《無妄》，後《萃》、《升》。

The hexagrams "Bǐ," "Shī," "Lín," "Guān," "Zūn," and "Méng" are all from the Upper Canon, while "Sǔn" and "Yì" belong to the Lower Canon, as do "Zhèn" and "Gèn." Therefore, "Zhèn" and "Gèn" are placed before "Sǔn" and "Yì"—after all the hexagrams of the Upper Canon have been listed, the Lower Canon hexagrams "Zhèn" and "Gèn" are introduced first, followed by "Sǔn" and "Yì" to conclude this section. Among the six hexagrams of the Upper Canon, "Bǐ" and "Shī" each contain only one yang line, while "Lín," "Guān," "Zūn," and "Méng" each contain two yang lines, increasing from fewer to more. Next, the group of hexagrams with mutual structures of "Jiān" and "Guīmèi" are discussed: "Záguà" states, "Dàxù" is waiting for the right time to act, "Wúwàng" is suffering misfortune without cause. "Cuì" is gathering, and "Shēng" is ascending without returning." The mutual structures of these four hexagrams are all "Jiān" and "Guīmèi." The arrangement of the group of yang hexagrams follows the order of Upper Canon first and Lower Canon later, so "Dàxù" and "Wúwàng" are listed first, followed by "Cuì" and "Shēng."

《謙》輕而《豫》怠也。《噬嗑》，食也；《賁》，無色也。”此四卦，皆互體為《解》、《蹇》，《謙》、《豫》一陽，《噬嗑》、《賁》二陽。以上為陽卦之正。

The Zage says: "The hexagram Qian is about self-abasement and humility, and Yu is about ease and indolence. Shihe is taken as the image of eating, and Ben is taken as the image of plainness and colorlessness." The mutual trigrams of these four hexagrams are all Jie and Jian. Among them, Qian and Yu each have only one yang line, while Shihe and Ben each have two yang lines, still increasing from fewer to more. All of these belong to the "correct" category within the yang hexagrams.

“《兌》見而《巽》伏也”。《震》、《艮》交於《兌》、《巽》，而成《漸》、《歸妹》，下文將敘《漸》、《歸妹》，故以《兌》、《巽》先之。“《隨》，無故也；《蠱》，則飭也”。此兩卦，互體為《漸》、《歸妹》，上首《剝》、《復》者，天行也，此首《漸》、《歸妹》者，人事也。

The *Zage* says: "The *Dui* trigram is manifest on the outside, and the *Xun* trigram is hidden within." The *Zhen* and *Gen* trigrams intersect with *Dui* and *Xun* to form the hexagrams *Jian* and *Gui Mei*. The following text will discuss a group of hexagrams whose interacting trigrams are *Jian* and *Gui Mei*, so the *Dui* and *Xun* trigrams are placed first. It also says: "The *Sui* hexagram is not following old ways, and the *Gu* hexagram is to rectify and reform." The interacting trigrams of these two hexagrams are precisely *Jian* and *Gui Mei*. Previously, the correct form of the yang hexagrams was led by *Bo* and *Fu*, representing the movement of heaven; here, the changing form of the yang hexagrams is led by *Jian* and *Gui Mei*, representing the interaction between human affairs.

次《剝》、《復》“《剝》，爛也；《復》，反也。”此兩卦，不用互體，但取《剝》、《復》之義，此言《剝》以歸於《復》，篇終言《姤》以終於《夬》，皆扶陽之意。次《解》、《蹇》“《晉》，晝也；《明夷》，誅也”。此兩卦，互體為《解》、《蹇》。以上：為陽卦之變。除篇終八卦自立義例外，餘皆入陰陽正卦，其變者，唯各舉兩卦以見義而已。自《乾》、《坤》至此，為陽卦者二十八。

Next are the hexagrams of the type 《Bō》 and 《Fù》: 《Zá Guà》 says, "《Bō》 means decay and rot, 《Fù》 means return and revival." These two hexagrams do not use the mutual trigrams, but derive their meaning directly from 《Bō》 and 《Fù》 themselves. Here, from 《Bō》 it leads to returning to 《Fù》, and at the end of the chapter, from 《Gòu》 it leads to finally reaching 《Guài》, all with the intention of supporting the yang energy. Next are the hexagrams of the type 《Jiě》 and 《Jiǎn》: 《Zá Guà》 says, "《Jìn》 is like daylight shining bright, 《Míng Yí》 is suffering from being punished." The mutual trigrams of these two hexagrams are exactly 《Jiě》 and 《Jiǎn》. All of these belong to the yang hexagrams under the category of "change." Except for the last eight hexagrams, which are given separate interpretations, all the others are classified under the two groups of yin and yang as "normal hexagrams"; those under "change" only mention two hexagrams to illustrate their meaning. From 《Qián》 and 《Kūn》 up to here, there are a total of twenty-eight yang hexagrams.

“《井》通而《困》相遇也”。此兩卦，互體為《睽》、《家人》，陽卦之變，首於《漸》、《歸妹》者，《震》、《艮》交於《巽》、《兌》，陽中之陰也，陰卦之變，始於《睽》、《家人》者，《巽》、《兌》交於《離》，陰中之陰也，陽主正，自天道而，人事，陰主變，自人事而天道。

The *Zagua* says: "The *Well* hexagram signifies unending communication, and the *Obstruction* hexagram signifies meeting and encountering obstacles." The interacting trigrams of these two hexagrams are *Kui* and *Family*. The transformation of yang hexagrams begins with *Zhan* and *Guimei*, because these are where Zhen and Gen intersect with Xun and Dui, belonging to yang within yang. The transformation of yin hexagrams begins with *Kui* and *Family*, because these are where Xun and Dui intersect with Li, belonging to yin within yin. Yang is primarily about correctness, derived from the heavenly way extended to human affairs; yin is primarily about transformation, derived from human affairs traced back to the heavenly way. These two paths proceed in opposite directions, complementing each other perfectly.

次《姤》、《夬》“《咸》，速也；《恆》，久也。”此兩卦，互體為《姤》、《夬》。次《大過》、《頤》“《渙》，離也；《節》，止也。”六十四卦中，有兩卦只互得一卦者，如《剝》、《復》只互得《坤》，《姤》、《夬》只互得《乾》，《渙》、《節》只互得《頤》，《豐》、《旅》只互得《大過》。

Next are the hexagrams of the type 《Gou》 and 《Guai》: 《Zage》 says, "《Xian》 is quick response, 《Heng》 is enduring steadfastness." The mutual hexagrams of these two are exactly 《Gou》 and 《Guai》. Then there are the hexagrams of the type 《Da Guo》 and 《Yi》: 《Zage》 says, "《Huan》 is dispersion, 《Jie》 is restraint." Among the sixty-four hexagrams, some consist of two hexagrams that share the same mutual hexagram. For example, 《Bo》 and 《Fu》 both share 《Kun》 as their mutual hexagram; 《Gou》 and 《Guai》 both share 《Qian》; 《Huan》 and 《Jie》 both share 《Yi》; 《Feng》 and 《Lv》 both share 《Da Guo》. These pairs of hexagrams are essentially reverses of each other, with the same yin and yang in the fourth line, so their mutual hexagrams result in only one hexagram.

“《解》，緩也；《蹇》，難也。《睽》，外也；《家人》，內也。《否》、《泰》，反其類也， ”《解》、《蹇》、《睽》、《家人》，皆互體為《既濟》、《未濟》，故次於陰變卦之後。《否》、《泰》不在互卦之內，而為《既濟》、《未濟》之根者也，故次於《既濟》、《未濟》之後。

The "Zagua" says: "The hexagram 'Jie' signifies relief, while 'Jian' signifies difficulty; 'Kui' signifies separation from the outside, while 'Jiaoren' signifies harmony from within; 'Pu' and 'Tai' signify mutual opposition." The four hexagrams 'Jie,' 'Jian,' 'Kui,' and 'Jiaoren' all have the same nuclear hexagram 'Ji Ji' and 'Wei Ji,' so they are placed after the changing of yin hexagrams. 'Pu' and 'Tai' were not originally included in the nuclear hexagrams, yet they are the roots of 'Ji Ji' and 'Wei Ji,' so they are placed after 'Ji Ji' and 'Wei Ji.' This arrangement clearly shows that all yin hexagrams ultimately lead to 'Ji Ji' and 'Wei Ji.'

蓋凡陽卦皆統於《乾》、《坤》，而尤以正卦為主，故《比》、《師》之前，首以《乾》、《坤》也，凡陰卦皆統於《既濟》、《未濟》，而尤以變卦為主，故《渙》、《節》之後，繫以《解》、《蹇》、《睽》、《家人》、《否》、《泰》也。以上為陰卦之變。

In general, all yang hexagrams belong to the hexagrams of Qian and Kun, with particular emphasis on the "original hexagram." Therefore, before the hexagrams of Bi and Shi, the hexagrams of Qian and Kun are placed first. All yin hexagrams belong to Ji Ji and Wei Ji, with particular emphasis on the "resulting hexagram." Therefore, after the hexagrams of Huan and Jie, the hexagrams of Jie, Jian, Kui, Jia Ren, and Po Tai are added in sequence. One is placed at the beginning, and the other at the end, forming a corresponding structure at the beginning and end. The entire structure of Zage is thus established: Qian and Kun are the fundamental principles, while Ji Ji and Wei Ji are the applications, which is consistent with the meaning of the earlier diagrams. The above all belong to the "resulting hexagrams" among the yin hexagrams.

“《大壯》則止，《遯》則遲也，：《大有》，眾也；《同人》，親也。《革》，去故也；《鼎》，取新也。”此六卦，皆百體為《姤》、《夬》，陰之《大壯》、《遯》，如陽之《臨》、《觀》，陰之《大有》、《同人》，如剛之《比》、《師》，前陽卦中先《比》、《師》，次《臨》、《觀》，此則先《大壯》，《遯》，次《大有》、《同人》者，陰卦先下經，後上經也，陰之《革》、《鼎》，如陽之《屯》、《蒙》。

The *Zagua* says: "The hexagram *Dazhuang* is strong and flourishing but should stop; *Dun* is retreating and hesitating. *Dayou* is having many possessions; *Tongren* is being close to others. *Ge* is changing away the old; *Ding* is taking up the new." The mutual relations of these six hexagrams are all *Gou* and *Guai* (the original text says "Baiti" but should be "Hutiti"). The yin hexagrams *Dazhuang* and *Dun* are like the yang hexagrams *Lin* and *Guan*; the yin hexagrams *Dayou* and *Tongren* are like the yang hexagrams *Bi* and *Shi* (the original text says "ru gang zhi" but should be "ru yang zhi"). Previously, the yang hexagrams were listed first as *Bi* and *Shi*, then *Lin* and *Guan*. Here, however, *Dazhuang* and *Dun* are listed first, then *Dayou* and *Tongren*, because the yin hexagrams are arranged with the lower section first and the upper section later. The yin hexagrams *Ge* and *Ding* are like the yang hexagrams *Zun* and *Meng*.

次《大過》、《頤》“《小過》，過也；《中孚》，信也。《豐》，多故；親寡，《旅》也。《離》上而《坎》下也。”此六卦，皆互體為《大過》、《頤》，《小過》、《中孚》、《豐》、《旅》在下經居先，《離》、《坎》在上經居後。

Next are the hexagrams such as 《Da Guo》 and 《Yi》: 《Za Gua》 says, "《Xiao Guo》 is about going beyond limits, 《Zhong Fu》 is about sincerity within; 《Feng》 is about many old matters, and being close to few is 《Lv》; 《Li》 is fiery upward and 《Kan》 is moist downward." The mutual hexagrams of these six are all 《Da Guo》 and 《Yi》. Among them, 《Xiao Guo》, 《Zhong Fu》, 《Feng》, and 《Lv》 belong to the lower canon, so they come first; 《Li》 and 《Kan》 belong to the upper canon, so they come later. This is exactly the common pattern where the group of yin hexagrams in the lower canon comes first, and those in the upper canon come later.

次《睽》、《家人》《小蓄》，寡也；《履》，不處也。《需》，不進也；《訟》，不親也。”此四卦皆互體為《睽》、《家人》，《小畜》、《履》一陰，《需》、《訟》二陰。以上為陰卦之正。自《井》、《困》至此為陰卦者亦二十八。

The next group includes the hexagrams 《Kui》 and 《Jiaoren》: 《Zage》 says, "《Xiaoxu》 is about having little to nurture, 《Lv》 is about walking but not being at ease; 《Xu》 is about waiting without advancing, 《Song》 is about litigation without attachment." (The original text has "Xiaoxu" instead of "Xiaoxu," and the quotation mark is missing.) The mutual trigrams of these four hexagrams are all 《Kui》 and 《Jiaoren》. Among them, 《Xiaoxu》 and 《Lv》 each have one yin line, while 《Xu》 and 《Song》 each have two yin lines, which also indicates an increase from few to many. All of these belong to the "correct" category within the yin hexagrams. From 《Jing》 and 《Kun》 to here, there are a total of twenty-eight yin hexagrams.

“《大過》，顛也；《姤》，遇也；柔遇剛也。《漸》，女歸待男行也。《頤》，養正也；《既濟》，定也。《歸妹》，女之終也；《未濟》，男之窮也。《夬》，決也，剛決柔也，君子道長，小人道憂也。”

The final section of the "Zagua" says: "The hexagram 'Da Guo' signifies overturning, 'Gou' signifies meeting, with the flexible meeting the strong. 'Jian' signifies a woman's marriage, which requires the man to come and take her. 'Yi' signifies nourishing with correctness, 'Ji Ji' signifies each attaining its proper place. 'Gui Mei' signifies a woman's destiny, 'Wei Ji' signifies a man's hardship. 'Guai' signifies decision, with the strong decisively removing the flexible; the way of the gentleman increases, while the way of the petty person becomes anxious." These eight hexagrams are no longer paired in opposition as before, but are arranged in a sequence of mutual reversals, forming their own pattern.

以上五十六卦，皆以兩相對，如《序卦》之例，獨此八卦錯綜而不反對者，以見卦之有互，不獨中四爻可互，六爻循環皆可互也，卦卦皆然，獨舉大過一卦者，中四爻以陽居之，唯《大過》一卦，且自初爻起，而正卦左旋，互卦右轉，恰始於《姤》，終於《夬》而《乾》，得易道用陰而尊陽之意也。

The above fifty-six hexagrams are all paired oppositely, following the same structure as the "Xu Gua." However, the eight trigrams at the end are arranged in a mixed order rather than being paired oppositely. The intention is to show that hexagrams have mutual relationships, not only the middle four lines can form mutual relationships, but also the six lines can be interrelated in a cyclic manner. This principle applies to all hexagrams. The reason for specifically mentioning the hexagram "Da Guo" is that it is the only one where all four central lines are occupied by yang lines. Moreover, starting from the first line, the primary hexagram rotates to the left, while the nuclear hexagram rotates to the right, beginning with "Gou," proceeding to "Guai," and finally returning to "Qian." This sequence aligns with the principle of the "Yi" doctrine, which values yang and uses yin.

故案圖觀之，自初至四為《姤》，自上至三為《漸》，自五至二為《頤》，自四至初為《歸妹》，自三至上為《夬》，自二至五為《乾》，然夫子傳文無《乾》者，《乾》在篇首，《夬》盡則為純《乾》，首尾相生之義也，《既濟》、《未濟》不在互卦之內，故以義附於此，自陰陽相遇之後，如《漸》之得禮，如《頤》之養正，則為《既濟》而定矣。如《歸妹》之越禮失正，則為《未濟》而窮矣，故必決陰邪以伸陽道，然後“君子道長，小人道憂也”。《既濟》、《未濟》統六十四卦之義，故《雜卦》以是終篇，與《序卦》同。

Therefore, looking at the diagram: from the first line to the fourth line, the mutual hexagram is 《Gou》; from the top line to the third line, the mutual hexagram is 《Jian》; from the fifth line to the second line, the mutual hexagram is 《Yi》; from the fourth line back to the first line, the mutual hexagram is 《Gui Mei》; from the third line to the top line, the mutual hexagram is 《Guai》; from the second line to the fifth line, the mutual hexagram is 《Qian》. Confucius's commentary does not mention 《Qian》, because 《Qian》 is already listed at the beginning. 《Guai》 reaches a decisive conclusion, and when yin is exhausted, it becomes pure 《Qian》, which is exactly the meaning of mutual generation between beginning and end. 《Ji Ji》 and 《Wei Ji》 are not included in the mutual hexagrams, so they are only appended here according to their meanings. After yin and yang have met, if they follow the rites as in 《Jian》, or are nourished properly as in 《Yi》, they become 《Ji Ji》 and achieve stability; but if they transgress the rites as in 《Gui Mei》, they become 《Wei Ji》 and fall into hardship. Therefore, one must eliminate yin and evil to promote the way of yang, and then there will be the situation of "the gentleman's way prevails and the petty person's way is troubled." 《Ji Ji》 and 《Wei Ji》 encompass the meanings of all sixty-four hexagrams, so 《Za Gua》 concludes the entire text with these two hexagrams, following the same approach as 《Xu Gua》. The entire text ends here.