Chapter Seventeen: All Sixty-Four Hexagrams Have Symbolic Representations

64卦，皆有取象。其為名義，無不反對。十七章

Each of the sixty-four hexagrams represents a specific object or phenomenon, not only a few of them. Also, the names and meanings of the hexagrams are not without pairs of opposites that correspond to each other. This chapter instructs readers to study the entire text through two clues: "the image" and "the opposition in names." (Chapter Seventeen)

《易》之取象，世所知者數卦而已，如頤、如鼎、如噬嗑之類是。殊不知《易》者，象也，依物象以為訓，古64卦皆有取象。如屯象草木，蒙象童稚，需象燕賓，訟象飲食，師象軍陣，比象翼戴，家人象家正，睽象覆家，餘卦盡然。一人諸卦，名義無不反對。如噬嗑以貪饕，賁以節飾，履以蹈艱危，小畜以享尊富，臨以出而治人，觀以入而處己，豐以富盛，旅以困窮。自余推之，其名義反對，無不然者，此學《易》之大病也。

The images used in the Book of Changes are known to people only in a few hexagrams. For example, the hexagram Yi uses the image of the mouth and cheek, the hexagram Ding uses the image of a cooking pot, and the hexagram Shihe uses the image of something being held in the mouth. People do not realize that the Book of Changes itself is based on images, and that its teachings are established according to the forms of things. Therefore, all sixty-four hexagrams have their respective images. For example, Tun uses the image of grass and trees beginning to grow, Meng uses the image of a young child in ignorance, Xu uses the image of setting a banquet for guests, Song uses the image of quarrels arising from food, Shi uses the image of a military formation, Bi uses the image of many yin lines supporting one yang line, Jiaoren uses the image of the proper order within a family, Kui uses the image of family affairs collapsing and becoming discordant. The rest of the hexagrams are all similar. When one enters into the hexagrams, the names and meanings of the hexagrams are always opposite to each other. For example, Shihe talks about disaster caused by greed for food, while Ben talks about moderation and ornamentation; Lu talks about walking on a dangerous place, while Xiaxu talks about enjoying honor and wealth; Lin talks about going out to govern others, while Guan talks about entering to cultivate oneself; Feng talks about abundance and prosperity, while Lu talks about hardship and poverty. The rest follow the same pattern. Failing to see this is a major problem in studying the Book of Changes.

諸卦名義，須究端的。名義不正，《易》道懸絕。十八章

Each trigram's name and its contained meaning must be thoroughly examined and accurately determined. Once the name and meaning are not properly established, the entire doctrine of the Book of Changes becomes disconnected from people, and cannot be resumed. This chapter argues that the names of the trigrams are not arbitrary labels, but are determined by the opposing relationships within the trigram diagrams. (Chapter Eighteen)

《易》卦名義，古今失其正者，二十餘卦，師、比、小畜、履、同人、大有、謙、豫、臨、觀、噬嗑、賁、無妄、大畜、頤、大過、漸、歸妹、豐、旅、中孚、小過是也。蓋師以正眾，比以興王，二卦以武功創業，湯武之卦也。同人窮而在下，大有達而在上，二卦以文德嗣位，舜禹之卦也。

The names and meanings of the hexagrams in the Book of Changes have been misunderstood throughout history, with over twenty hexagrams losing their correct interpretations. These include: Army, Following, Small Accumulation, Treading, Fellowship, Great Possession, Humility, Joy, Approaching, Observing, Breaking the Ribs, Brightness, No Regret, Great Accumulation, Nourishment, Great Excess, Gradual Progress, Return of the Wife, Abundance, Travel, Middle Trust, and Small Excess. To explain them individually: Army refers to using military strength to correct the world, and Following refers to the unity of people leading to the rise of a dynasty. These two hexagrams discuss establishing a foundation through military power, belonging to the type of kings like Tang of Shang and Wu of Zhou. Fellowship refers to being in a lower position yet harmonizing with others, and Great Possession refers to being in a higher position and possessing the world. These two hexagrams discuss inheriting a great position through virtue, belonging to the type of kings like Yu of Yu and Yu of Xia.

履以陰德而蹈艱危，以致小畜之安富，人臣之事也，無妄以陰德而踐災眚，以致大畜之喜慶，人君之事也，臨以陽來，宜出而有為；觀以陰生，宜入而無為。廉則止在象後而存義，豫則動在象前而知幾。中孕則始生，小過則夭折。頤則成人而養生，大過則壽終而喪死。漸以正而進，歸妹以說而合。噬嗑以貪而致罪，賁以義而致飾。豐則得所歸而富盛，旅則失所基而困窮。凡此二十餘卦，其名義顯然，見於卦畫反對，有不可掩著如此，當諦觀之也。《大傳》曰：“天而當名。”苟名義不當，則一卦無所歸宿也，故曰：《易》道懸絕也。

The卦 of Lu is characterized by the virtue of gentle compliance and concealment, stepping on difficult and dangerous ground, thereby obtaining the卦 of Xiao Xu, which brings stability and abundance. This is the conduct of a minister. The卦 of Wu Wang is characterized by the virtue of gentle compliance and concealment, bearing calamities, thereby obtaining the卦 of Da Xu, which brings joy. This is the conduct of a ruler. The卦 of Lin represents the arrival of yang energy, which is appropriate for emerging and taking action. The卦 of Guan represents the initial emergence of yin energy, which is appropriate for retreating and maintaining quietude. The卦 of Qian stops after the image is complete, thus being able to uphold righteousness. The卦 of Yu acts before the image is complete, thus being able to foresee subtle changes. The卦 of Zhong Fu is the beginning of life, while the卦 of Xiao Guo represents an early death in the middle of life. The卦 of Yi is the care and maintenance after growth, while the卦 of Da Guo represents mourning and burial at the end of life. The卦 of Jie progresses gradually by maintaining correctness, while the卦 of Gui Mei unites with joy. The卦 of Shi He incurs guilt due to greed for food, while the卦 of Ben is adorned with appropriate embellishment. The卦 of Feng signifies achieving a resting place and prosperity, while the卦 of Lu signifies losing one's foundation and hardship. These more than twenty卦 have clear names and meanings, which can be seen clearly through their opposition in the trigrams. They are evident and cannot be concealed, and should be carefully examined. The "Great Treatise" of the "Commentary on the Hexagrams" says, "Opening and giving a proper name" — when explaining the meaning, it should be given an appropriate name. If the name is not properly established, the meaning of the卦 will have no basis, hence the Way of the Book of Changes is left hanging in the air.

一卦之中，凡具八卦。有正有伏，有互有參。十九章

In any compound hexagram, there are actually eight trigrams contained within. There are the original trigrams formed by the upper and lower parts, the hidden trigrams formed by each part changing, the two interacting trigrams formed by the middle four lines, and the combined trigrams formed by the interaction of the two interacting trigrams. This chapter teaches that a single hexagram is not a fixed structure of six lines, but a living structure capable of generating the eight trigrams. (Chapter Nineteen)

正謂上下二體也，伏謂二體從變也，互謂一卦有二互體也，參謂二互體參合也。與本卦凡八，是謂一卦具八卦也，然一卦何以具八卦？蓋一卦自有八變，如乾一變姤，二便遁，三變否，四變觀，五變剝，六變晉，七變大有，八變復乾是也。因其所然，以見天地萬物理無不通也。《莊子》論久竹生青寧，青寧生程，程生馬，馬生人，人死反入於機，萬物皆出於機人於機，其一節論變化之理，無所不通如此。

"The 'zheng' refers to the upper and lower trigrams of the primary hexagram; 'fu' refers to the hexagrams obtained by changing the yin and yang of each of these two trigrams completely; 'hu' refers to the two inter-trigrams formed by the second, third, and fourth lines, and the third, fourth, and fifth lines within a hexagram; 'can' refers to the hexagram formed by combining these two inter-trigrams. These, together with the primary hexagram, make a total of eight, so it is said that one hexagram contains all eight trigrams. So why can one hexagram contain all eight trigrams? Because one hexagram inherently has eight layers of change: taking Qian as an example, one change results in Gou (the first line changes), two changes result in Dun (the second line changes), three changes result in Pǐ, four changes result in Guān, five changes result in Bō, six changes result in Jin (the wandering soul), seven changes result in Dà Yǒu (the returning soul), and eight changes bring it back to Qian (the original text 'er bian dun' should be 'er bian dun'). Based on this existing principle, we can see that the principles of heaven and earth and all things are interconnected everywhere. The 'Zhi Le' chapter of the 'Zhuangzi' talks about how a long bamboo produces Qingning, Qingning produces Cheng, Cheng produces Ma, Ma produces Ren, and when people die, they return to the mechanism of the Dao, and all things come from this mechanism and return to it; this passage discussing the principle of change is exactly the same, being universally interconnected."

64卦，唯乾與坤。本之自然，是名真體。二十章

Of the sixty-four hexagrams, only the hexagrams Qian (Heaven) and Kun (Earth) are rooted in nature and not formed by combining other elements; this is called the "true essence." The other hexagrams are all formed by combining these two. (Chapter Twenty)

太始者，氣之始，是為乾。太始者，形之始，是為坤，皆本之自然，無所假合也。故其卦畫純一不駁，倒正不變，是名真體。

"The Tai Shi" is the beginning of qi, corresponding to the Qian hexagram; "Tai Su" is the beginning of form, corresponding to the Kun hexagram (the original text uses "Tai Shi" in both instances, but the latter should be taken from the "Lie Zi · Tian Rui" as "Tai Su"). Both of these originate from nature and are not formed by combining other elements. Therefore, their hexagram patterns are pure and undivided, and the six lines remain the same whether reversed or not, hence they are called "Zhen Ti."

六子重卦，乾坤雜氣。悉是假合，無有定實。二十一章

The six minor trigrams and the sixty-four hexagrams are all composed of the two energies of Heaven and Earth, and they are all temporary combinations without any fixed and real essence. This chapter directly derives a view that everything is provisional and transient from the structure of the trigrams. (Chapter Twenty-One)

六子假乾坤以為體，重卦合八卦以為體。若分而散之，則六子重卦皆無有定體也。若今天地清明，陰陽不雜，則六子何在？六子不交，則品物何在？以是知人間萬事，悉是假合。陰陽一氣，但有虛幻，無有定實也。

The six trigrams borrow the forms of the trigrams Qian and Kun to form their own bodies, and the compound hexagrams combine two single trigrams to form their own bodies. If these borrowed and combined parts are disassembled and returned, the six trigrams and the compound hexagrams would no longer have a fixed essence. Imagine a situation where heaven and earth are perfectly clear, and yin and yang are completely separate and not mixed. Then where would the six trigrams be? If the six trigrams do not combine, where would all things and categories be? From this we can see that all things in the world are temporarily assembled. Originally, yin and yang are just one qi, and all appearances they manifest are illusory, with no fixed reality.

卦義未審，須求變復。不唯辭合，義實通明。二十二章

If the meaning of a hexagram is not clear, one should use the methods of "change" and "reversal" to seek clarification. "Change" involves moving one line, while "reversal" involves flipping the entire yin and yang of the hexagram. The hexagram obtained through these methods will not only align with the line statements of the original hexagram but also make the meaning clear and coherent. (Chapter 22)

變為一爻之變，復為一體之復。即復變之辭而觀之，自然之義，無不與本卦吻合，以見陰陽之氣。如蒙上九曰：“擊蒙。”變為師，上六則云“小人勿用。”屯初九曰：“以貴下賤，大得民也。”變為比，初六則云“有孚比之，無咎。”此一爻之辭合也。如大有上體復需，有飲食之燕；下體復晉，有昭明之德。升上體復姤，姤一陰升；下體複復，復一陽升。此一體之義合也。苟卦義未審，能以此求之，自然明矣。

"Change" refers to altering one line, while "reversal" means flipping the yin and yang of the upper or lower trigrams entirely. When examining the line statements of the changed hexagram and the reversed hexagram, the natural meaning is found to align perfectly with the primary hexagram. This demonstrates the actual movement of yin and yang energy. For example, the line statement of the upper ninth line in the Meng hexagram is "Strike the confusion," and when this yang line is changed to yin, it becomes the Shi hexagram, whose upper sixth line states "Do not use the petty person." This means removing confusion and not using petty people, which fits perfectly. Another example is the line statement of the initial ninth line in the Tun hexagram, which says "Use the noble to humble the lowly, thus gaining the people's support." When this yang line is changed to yin, it becomes the Bi hexagram, whose initial sixth line says "Have sincerity and compare with others," which has no error—humble oneself to gain the people's support and sincerity in mutual affection, which also fits perfectly. This is an example where the line statements align. Another example is the Da You hexagram (lower Qian, upper Li). When the upper trigram Li is reversed to become Kan, it becomes the Xu hexagram, whose Great Image mentions "The gentleman uses feasting and music," implying the meaning of feasting. When the lower trigram Qian is reversed to become Kun, it becomes the Jin hexagram, which has the virtue of "Light emerging from the earth." The Sheng hexagram (lower Xun, upper Kun), when the lower trigram Xun is reversed to become Zhen, becomes the Fu hexagram, which represents the rising of the first yang line. When the upper trigram Kun is reversed to become Qian, it becomes the Guo hexagram, which represents the rising of the first yin line. This is an example where the meaning of the entire hexagram aligns. If one cannot understand the meaning of a hexagram, using this method will naturally clarify it.

古今傳易，舛訛為多。履畜八體，最為害義。二十三章

From ancient times to the present, the Book of Changes has accumulated many errors. Among these, the reversal of the order of the Lu hexagram and the Xiao Xu hexagram, as well as the incorrect pairing of the Eight Trigrams with the eight body parts of a person in the Shuo Gua chapter, have caused the deepest harm to the meaning. This chapter is the only place in the entire text where the original version is directly corrected. (Chapter Twenty-Three)

按卦序，當先履而後小畜。今小畜在先，則二卦畫象反對，文義繆亂，而不可考。又以八卦本對八體，獨闋其鼻。乃以巽言股，股即係是也。若股可言，則又遺其肱，且與羲皇八卦不相應也。茲蓋傳者舛誤耳，能不害義乎？試辨之，一柔自姤變同人，同人變履，履變小畜，小畜變大有，猶之一剛自復變師，又變謙，又變豫，又變比，皆自然之序不易也。今謙既在豫上，則知履不當在小畜下。當密探宣尼述九卦，以履為用九，謙用十五，復用二十四，皆《龍圖大衍》定數。則履在小畜上，為第九卦也明矣。又履與無妄對義，既以大畜反無妄而居下，則知小畜反履而居下無疑矣。今序卦非宣尼旨，失其本真也。

According to the order of the hexagrams, it should first be "Gou" and then "Xiao Xu". Now, the "Xu Gua" places "Xiao Xu" before "Gou", which disrupts the opposing relationship between the two hexagrams and makes the meaning entangled and difficult to examine. Moreover, the eight trigrams were originally paired with the eight parts of the human body, yet the nose is missing, and instead the trigram "Xun" is paired with the thigh, which is "gu". If it can be paired with the thigh, why is the arm missing? Furthermore, this method of pairing does not align with the original positions of the trigrams as arranged by Fuxi. These are errors introduced by those who transmitted the text, and can they not affect the meaning? Let me clarify this: take the example of a single yin line ascending among five yang lines. When it is in the first position, it is "Gou"; when it rises to the second position, it is "Tong Ren"; when it reaches the third position, it is "Lv"; when it reaches the fourth position, it is "Xiao Xu"; and when it reaches the fifth position, it is "Da You". Similarly, a single yang line ascending among five yin lines, when in the first position, it is "Fu"; in the second position, "Shi"; in the third position, "Qian"; in the fourth position, "Yu"; and in the fifth position, "Bi". These are natural sequences that cannot be altered. Now, since the "Xu Gua" places "Qian" before "Yu" (third before fourth), it is clear that "Lv" should not be placed before "Xiao Xu". Further examination of Confucius' three times mentioning the nine hexagrams in the "Xi Ci Xia", where "Lv" is called "Yong Jiu", "Qian" is called "Yong Shiwu", and "Fu" is called "Yong Ershisi", all indicate the fixed numbers of the "Long Tu" and the great derivation. Therefore, "Lv" being placed before "Xiao Xu" and occupying the ninth position is clear. Moreover, the hexagrams "Lv" and "Wu Wang" are yin and yang opposites. Since "Da Xu" follows "Wu Wang" and is placed below it, it is evident that "Xiao Xu" should follow "Lv" and be placed below it, without doubt. The current "Xu Gua" is not the original intention of Confucius and has lost its original form.

八體，乃艮為鼻，巽為手耳。《傳》曰：“鼻者，面之山也。”又曰：“風能鼓舞萬物，而手之所以舞也，”蓋乾為首，坤為腹，天地定位也。坎為耳，離為目，水火相逮也。艮為鼻，兌為口，山澤通氣也。巽為手，震為足，雷風相薄也。此羲皇八卦之應矣，其理昭昭。但學者承誤效尤，見不高遠，其失至此。真人閔之，故開其眼目。

As for the correct pairing of the eight trigrams, it should be Gen paired with the nose and Xun paired with the hands. The ancient text says, "The nose is the mountain on the face," so Gen, the mountain trigram, is paired with the nose. It also says, "Wind can move all things, just as the hands can dance," so Xun, the wind trigram, is paired with the hands. Thus, Qian is paired with the head, Kun with the abdomen, corresponding to "Heaven and Earth are positioned"; Kan is paired with the ears, Li with the eyes, corresponding to "Water and Fire complement each other"; Gen is paired with the nose, Dui with the mouth, corresponding to "Mountain and Marsh communicate through air"; Xun is paired with the hands, Zhen with the feet, corresponding to "Thunder and Wind clash." This aligns with the four pairs of directions in the eight trigrams as described in the "Shuo Gu" text, and the reasoning is clear. It is only because scholars have followed old mistakes and imitated each other, with limited vision, that they have reached this error. Master Ma Yi, with compassion, has pointed this out, opening their eyes for them.

畫卦取象，本為特物。見於曰用，無所不合。二十四章

The images used in drawing the trigrams were originally designed for specific things. They appear in people's daily lives and activities, fitting perfectly in every aspect. This chapter opposes treating the Book of Changes as a book written on bamboo slips or silk for people to recite, and instead advocates that it is actually a set of living principles that can be verified at any time and in any situation. (Chapter 24. The original text "曰用" refers to "日用".)

羲皇畫卦，非謂出私意。撰寫一《易》道於方冊上，以誨人也。特以順時應物，則以見於曰用之間耳。以粗跡言之，如以錢博，六純字，乾也。六純背，坤也。差互，六子也。若反則未勝，至純則乾坤成矣。又如優人呈伎，壯者任其難，六子也。老者斂其利，乾坤也。此皆理之自然。即此理以察其餘，則是行止坐臥纖悉舉天下皆《易》，無可揀擇者。但百姓昏昏，曰用之而罔覺矣。

Fuxi drew the trigrams, not by his own will, to write a set of the principles of the Book of Changes and put them on bamboo slips to teach people. He merely followed the seasons and responded to things, presenting the principles in daily life. Taking a simple example: for instance, when tossing coins for gambling, if all six are heads, that is pure yang, Qian; if all six are tails, that is pure yin, Kun; if heads and tails are mixed, that is the six sons. When heads and tails are mixed and the outcome is not yet decided, but when the toss results in a pure number, then Qian and Kun form a complete situation. Another example is when an actor performs on stage, the young and strong take on the difficult roles, which is the six sons; the old ones sit back and reap the benefits, which is Qian and Kun. These are all natural principles. By observing this principle, one can see that walking, standing, sitting, and lying down, all subtle actions, are part of the Book of Changes, and there is nothing in the world that can be excluded. However, the common people are dull and unaware, using it every day without realizing it.

中爻之義，足為造化。納音為切腳，其理則一。二十五章

The mutual structure formed by the second, third, fourth, and fifth lines of a hexagram represents the mechanism of generation and transformation. This is the same principle as that of the nayin sound elements in the sixty jiazi and the method of taking characters for phonetic annotation: they all arise from the interaction of two things to produce a third. (Chapter 25)

納音，甲為木，子為水，甲子交合則生金。切腳，如德為父，紅為母，德紅反切即東字。卦體亦然。上體為乾，下體為坤，交錯乃生六子，即中爻二三四五也。二三四五，造化之氣，參互成卦。如屯中有剝，蒙中有復，主此一卦每具於四卦中，皆得禍福倚伏之象。如屯、比、觀、益中皆有剝、蒙、師、損中皆有復是也。

First, the concept of nayin: the heavenly stem Jia belongs to wood, and the earthly branch Zi belongs to water. When Jia and Zi combine, the nayin produces metal (Jiazi and Yichou are called "sea metal"). Then there is the method of reverse cutting: using "de" as the upper character (father) and "hong" as the lower character (mother), the combination of "de" and "hong" produces the sound of "dong". The hexagram structure is similar. The upper part is Qian (Heaven), and the lower part is Kun (Earth). When these two parts intersect, they generate the six sons, which manifest as the second, third, fourth, and fifth lines on the hexagram. These four lines contain the vital energy of transformation and creation. They intersect and interconnect to form another hexagram. For example, the hexagram Zun (Sprouting) contains the hexagram Bo (Breaking Up) — the second, third, and fourth lines of Zun form Kun, and the third, fourth, and fifth lines form Gen, forming the hexagram Bo (Mountain over Earth). The hexagram Meng (Youth) contains the hexagram Fu (Returning) — the second, third, and fourth lines of Meng form Zhen, and the third, fourth, and fifth lines form Kun, forming the hexagram Fu (Earth over Thunder). The same mutual hexagram often appears in four different hexagrams, revealing the image of mutual dependence and concealment of fortune and misfortune. For instance, the hexagrams Zun, Bi, Guan, and Yi all contain Bo. The hexagrams Meng, Shi, Shen (and also Lin) all contain Fu (the original text only mentions three hexagrams, and "Lin" is likely missing).

反對正如，甲子乙丑。有本有餘，氣序自然。二十六章

The opposition between hexagrams is like the pairing of Jia with Yi and Zi with Chou: the first is the main energy, and the second is the remaining energy of the main energy. The hexagrams are arranged in this alternating order because it follows the natural sequence of energy, not because the sage intentionally arranged them. (Chapter 26)

大凡一物，其氣象必有本有餘。餘氣者，所以為陰也。本，其陽也。如十干甲乙，乙者甲之餘氣也。丙丁，丁者丙之餘氣也。如十二支子丑，丑者子之餘氣也。寅卯，卯者寅之餘氣也。卦亦由是。坤者，乾之餘氣也。蒙者，屯之餘氣也。訟者，需之餘氣也。痺賄，師之餘氣也，且乾而後坤，屯而後蒙，需而後訟，師而後比，雖故有其義，然其所以相次者，皆其餘氣也，自然之理耳。學者不悟，謂聖人固以次之，是未知反對關鍵之鍵也，失之遠矣。

In general, any thing must be divided into its original qi and residual qi. Residual qi refers to the yin aspect, while original qi refers to the yang aspect. For example, among the ten heavenly stems, Yi is the residual qi of Jia; Ding is the residual qi of Bing. Among the twelve earthly branches, Chou is the residual qi of Zi; Mao is the residual qi of Yin. The trigrams are the same: Kun is the residual qi of Qian, Meng is the residual qi of Tun, Song is the residual qi of Xu, and Bi is the residual qi of Shi (the original text mistakenly writes 「bì huì」 instead of 「bǐ zhě」). Therefore, after Qian comes Kun, after Tun comes Meng, after Xu comes Song, and after Shi comes Bi. Although the order of these trigrams has its own meaning as explained in the 「Xu Gua」, the reason they follow one after another is due to the continuity of residual qi, which is a natural principle. Scholars who do not understand this mistake the key point of the concept of opposition, and they are far off the subject.

每卦之體，六畫便具。天地四方，是為六虛。二十七章

Each trigram's structure, when its six lines are arranged, completes the six directions: heaven, earth, and the four cardinal directions, which is called "six voids." This chapter opposes interpreting the "six voids" as the six lines themselves, and instead advocates that the six lines merely represent these six directions. (Chapter 27)

初爻為地，上爻為天，二爻為北，五爻為南，四爻為西，三爻為東。天地四方，每卦之體，皆具此義，是為六虛。《大傳》：“變動不拘，周流六虛”正謂此耳。學者不悟，謂六虛天地四方，乃六畫也，殊不知六畫乃天地四方之象。此之謂紙上工夫，不知落處也。

The first line represents the earth, the top line represents heaven, the second line represents the north, the fifth line represents the south, the fourth line represents the west, and the third line represents the east. Heaven and earth together with the four cardinal directions make up the meaning of each hexagram, which is called "six voids." The *Great Treatise* says, "The movement is not fixed, it flows through the six voids" (the original text "bu ju" should be "bu ju"), referring exactly to this. Scholars fail to understand, thinking that the six lines of the hexagram are equivalent to the six directions of heaven, earth, and the four cardinal points. But they do not realize that the six lines are merely symbolic representations of heaven, earth, and the four cardinal directions. This is called making efforts only on paper without understanding where it actually applies.

乾坤六子，其象與數。乾坤之位，皆包六子。二十八章

The trigrams Qian (Heaven) and Kun (Earth) and the six sons are related in such a way that whether viewed from their symbolic representations or numerical relationships, Qian and Kun always stand at the two extremes, encompassing the six sons entirely within them. This chapter aims to make people understand that the six sons cannot exist independently of Qian and Kun; they are always within the scope of Qian and Kun. (Chapter 28)

象謂坤卦上中下加三乾畫，便生三男。以乾卦上中下加三坤畫，便生三女。乾坤之體，皆在外，六子皆包於其中也。數謂若畫乾數三，巽離兌四，震坎艮五，坤六。坤數六，震坎艮七，巽離兌八，乾九。乾坤之策皆在外，六子皆包於其中也。此象之自然，有不可得而容心者。

First, the images: by replacing the lower, middle, and upper lines of the Kun hexagram with one line from the Qian hexagram (a yang line), we successively produce the three male hexagrams Zhen, Kan, and Gen. By replacing the lower, middle, and upper lines of the Qian hexagram with one line from the Kun hexagram (a yin line), we successively produce the three female hexagrams Xun, Li, and Dui. The Qian and Kun hexagrams remain at the outermost positions, while the six other hexagrams are all contained within. Now, regarding the numbers: according to the line numbers, a yang line counts as one and a yin line counts as two. Thus, Qian counts as three, Xun, Li, and Dui each count as four, Zhen, Kan, and Gen each count as five, and Kun counts as six—three and six are at the ends, while four and five are in the middle. According to the counting method used in divination (the "cè shù" or "counting numbers"), a yang line counts as three and a yin line counts as two. Thus, Kun counts as six, Zhen, Kan, and Gen each count as seven, Xun, Li, and Dui each count as eight, and Qian counts as nine—six and nine are at the ends, while seven and eight are in the middle. This shows that the counting numbers of Qian and Kun are always on the outermost positions, while the six other hexagrams are all contained within. This is how the hexagrams naturally are, and no one can arbitrarily add or change them.

爻數三百八十又四，以閏求之，其數吻合。二十九章

There are 384 lines in the 64 hexagrams, and this number must be verified using the leap year method to match exactly. This chapter opposes the Han scholars' method of using "six days and seven parts" to adjust the number of lines, and instead advocates that the number of lines originally corresponds to a year that includes a leap month. (Chapter 29)

爻數三百八十又四，真天文也。諸儒求合其數而不可得。或謂一卦六曰七分，或謂除震離坎兌之數，皆附會也。倘以閏求之，則三百八十四數，自然吻合，無餘欠矣。蓋天度或嬴或縮，至三年，乾坤之氣數始足於此也。由漢以來不悟，惟真人得其說。

The number 384 hexagrams is indeed derived from astronomy. Throughout history, scholars have tried to correlate it with the calendar system but have failed. Some used Mengxi's theory of hexagram qi, stating that one hexagram corresponds to six days and seven parts; others suggested first subtracting the four cardinal hexagrams—Zhen, Li, Kan, and Dui—before calculation. These approaches are all forced and arbitrary. If we use the method of intercalation, the number 384 naturally fits perfectly, neither more nor less. This is because the movement of the heavens sometimes has excess and sometimes lacks, requiring the accumulation of three years to add one intercalary month, thus completing the cycle of the qi of Heaven and Earth. Since the Han dynasty, no one has understood this principle, except Master Hemp-Robe who explained it.

二十四爻，求之八卦。畫純為疊，是為閏數。三十章

The 24 extra lines in the 384 lines compared to the 360 lines come from the Eight Trigrams. The lines in the eight pure hexagrams have already been counted again among all the hexagrams, and this repeated part is called "stacked numbers," which is also known as the leap year number. (Chapter Thirty)

一歲三百六十，而爻數三百八十四，則是二十四爻為餘也。以卦畫求之，是為疊數。何以言之？夫既有八卦矣。及八卦互相合體，以立諸卦。則諸卦者，八卦在其中矣。而別又有八純卦，則其合體八卦為重複，而二十四數為疊也。是以三百六十為正爻，與每歲之數合。而三百八十四，與閏歲之數合矣，則是閏數也。豈惟見於數，亦見於象。人知之該鮮矣。

There are 360 days in a year, but the number of lines in the trigrams is 384, which is 24 more. This extra 24 lines are called the 'remainder.' When looking at the hexagrams, this is referred to as 'stacking.' How is this explained? Since there are originally eight simple trigrams, when these eight trigrams are paired with each other, they form the 64 compound hexagrams. Thus, the 64 hexagrams already contain the eight simple trigrams. However, the eight pure trigrams (Qian, Kun, Zhen, Xun, Kan, Li, Gen, Dui) are each formed by stacking the same trigram upon itself. Therefore, the eight pure trigrams use the simple trigrams again, which are counted twice. Each simple trigram has 3 lines, so the eight pure trigrams account for 24 lines. Thus, the number 24 comes from 'stacking.' Therefore, 360 corresponds to the regular year's days, while 384 corresponds to the leap year's days, which is the leap number. This meaning is not only reflected in the numbers but also in the hexagram images. Few people truly understand this.

一歲之數，三百六十。八卦八變，氣數已盡。三十一章

A year consists of 360 days. Using the eight pure trigrams as the starting points of the eight palaces, each palace undergoes eight transformations, thereby completing the sixty-four trigrams. The eight kinds of qi—Heaven, Earth, Thunder, Wind, Water, Fire, Mountain, and Marsh—are thus fully exhausted. (Chapter 31)

乾、姤、遁、觀、剝、晉、大有，八變而復乾，則天之氣盡。坤、復、臨、泰、大壯、夬、需、比，八變而復坤，則地之氣盡。震、豫、解、恆、升、井、大過、隨，八變而復震。則雷之氣盡。艮、賁、大畜、損、睽、履、中孚、漸，八變而復艮，則山之氣盡。

The乾 palace follows the order of Qian, Guo, Dun, Po, Guan, Bo, Jin, Da You. After the eighth change it returns to Qian, indicating the exhaustion of the heavenly energy. The坤 palace follows the order of Kun, Fu, Lin, Tai, Da Zhuang, Guai, Xu, Bi. After the eighth change it returns to Kun, indicating the exhaustion of the earthly energy. The震 palace follows the order of Zhen, Yu, Jie, Heng, Sheng, Jing, Da Guo, Sui. After the eighth change it returns to Zhen, indicating the exhaustion of the thunder energy. The艮 palace follows the order of Gen, Ben, Da Xu, Shen, Kui, Li, Zhong Fu, Zhen. After the eighth change it returns to Gen, indicating the exhaustion of the mountain energy. Here, the term "change" refers to changing the first line, then the second, third, and fourth lines in sequence, up to the fifth line. After that, the fourth line is changed again as a wandering soul, and finally the lower trigrams are restored as a returning soul, ending with the return to the original palace.

離、旅、鼎、未擠、蒙、渙、訟、同人、八變而復離，則火之氣盡。巽、小畜、家人、益、無妄、噬嗑、頤、蠱。八變而復巽，則風之氣盡。兌、困、萃、咸、蹇、謙、小過、歸妹，八變而復兌，則澤之氣盡。凡此八卦，各八變，八八64數，則天、地、雷、風、水、火、山、澤之氣無餘蘊矣。是為一義。

The Li palace follows in order: Li, Lu, Ding, Wei Ji, Meng, Huan, Song, Tong Ren. After eight changes, it returns to Li, and the fire energy is exhausted. The Xun palace follows in order: Xun, Xiao Xu, Jia Ren, Yi, Wu Wang, Shi He, Yi, Gu. After eight changes, it returns to Xun, and the wind energy is exhausted. The Dui palace follows in order: Dui, Kun, Cui, Xian, Jian, Qian, Xiao Guo, Gui Mei. After eight changes, it returns to Dui, and the marsh energy is exhausted. The source text is missing the Kan palace. Its sequence should be Kan, Jie, Tun, Ji Ji, Ge, Feng, Ming Yi, Shi. After eight changes, it returns to Kan, and the water energy is exhausted; otherwise, the number of "eight eights making sixty-four" would be incomplete. Each of the eight palaces changes eight times, making eight eights sixty-four. Thus, the eight kinds of energies—Heaven, Earth, Thunder, Wind, Water, Fire, Mountain, and Marsh—have no remaining hidden essence. This is one interpretation.

數成於三，重之則六。其退亦六，是為乾坤。三十二章

The number of Qi comes from three. When three is overlaid once, it becomes six. The path of retreating is also six. These two sixes, one advancing and one retreating, form Qian and Kun. The trigrams with three lines and the hexagrams with six lines both originate from here. (Chapter 32)

夫氣之數，起於一，偶於二，成於三，無以加矣。重之則為六也。然三，少陽也。六，太陽也。三，春也。六，夏也。此乾之數也，是為進數。其退亦六。三，少陰也。六，太陰也。三，秋也。六，冬也。此乾坤之數也，是為退數，三畫為經卦，六畫為重卦者，凡以此而已。

The number of qi starts with one, pairs to form two, and completes at three, beyond which it cannot be added. When three is overlapped again, it becomes six. Following the ascending sequence: three is considered less yang, and six is considered yang; three corresponds to spring, and six corresponds to summer — this is the number of Qian, called ascending numbers. Following the descending sequence, it is also six: three is considered less yin, and six is considered yin; three corresponds to autumn, and six corresponds to winter — this is the number of Kun, called descending numbers. Three lines form the simple trigrams, and six lines form the compound trigrams, based on this principle.

凡物之數，有進有退。進以此數，退以此數。三十三章

All numbers of things have a forward half and a backward half. When advancing, this number is used; when retreating, the same number is still used. The measure for prosperity and decline is entirely the same. (Chapter 33)

大抵物理，其盛衰之數相半。方其盛也，既以此數。及其衰也，亦以此數。若一歲十二月，春夏為進數，秋冬為退數。晝夜十二時，自子為進數，自午為退數。人壽百歲，前五十為進數，後五十為退數。以至甲為進數，乙為退數。子為進數，丑為退數。細推物理，無為然。世儒論教，但衍為一律，殊不明陰陽進退之理，惟真人獨得其說。

In general, the principles of things are such that the numbers representing prosperity and decline each account for half. When something is flourishing, one uses the number of prosperity; when it declines, one still uses the same number. For example, a year has twelve months, with spring and summer being the numbers of advancement, and autumn and winter the numbers of retreat; a day and night have twelve hours, with the hours starting from Zi (midnight) being numbers of advancement, and those starting from Wu (noon) being numbers of retreat; human lifespan is a hundred years, with the first fifty years being numbers of advancement and the last fifty years numbers of retreat. This applies even to the heavenly stems, where Jia is the number of advancement and Yi the number of retreat, and to the earthly branches, where Zi is the number of advancement and Chou the number of retreat. Careful examination of the principles of things shows that nothing is not like this (the original text '无为然' should be '无不然'). The scholars of the Confucian tradition discuss numbers, reducing them to a general rule, completely failing to understand the principle that yin and yang have numbers of advancement and retreat. Only the Master Hemp-Robe explained this point.

凡具於形，便具五數。五數既具，十數乃成。三十四章

All things that have form possess the number five. When five is present, the number ten naturally follows. This is because all formed things must be square, and a square has four sides. Adding the center to the four sides makes five. When five expands, it becomes ten. (Chapter 34)

凡麗於氣者，必圓，圓者，徑一而圍三。天所以有三時者，以其氣也。凡麗於形者，必方。方者，徑一而圍四。地所以有四方者，以其形也。天數三，重之則六。地數五，重之則十。何謂十？蓋有四方，則有中央，為五。有中央四方，則為四維，復之中央，是為十也。菲特地為然，凡麗於形，便具十數，解若此也。

Anything attached to qi is necessarily round. A circle, according to ancient measurements, has a diameter of one and a circumference of three. Heaven has the number three, which refers to the three celestial bodies (sun, moon, stars), because it belongs to qi (the original text says "three times"). Anything attached to form is necessarily square. A square has a side length of one and a perimeter of four. Earth has four directions because it belongs to form. The number of heaven is three; when doubled, it becomes six. The number of earth is five; when doubled, it becomes ten. Why ten? With the four directions, there is a central point, making five in total. With the central point and the four directions, adding the four cardinal directions—northeast, southwest, northwest, and southeast—along with the central point counted again, it totals ten. Not only does earth have this, but anything attached to form also has the number ten, and the reasoning is the same (the original text says "菲特" which should be "非特").

大衍七七，其一不用。凡得一數，理自不動。三十五章

The great derivation number uses seventy-seven, totaling forty-nine, but one is left unused. Any that occupy the position of 'one' are the main source and the sovereign, by nature they should remain unmoved. (Chapter 35)

大衍之數五十。其用四十九，卦一而不用。不用之學，學者徒知一為太極不動之數，而不知義實落處也。何則？一者，數之宗本也。凡物之理，無所宗本則亂，有宗本焉，則不當用，用則復亂矣。且如輪之運，而中則止。如鉻之行，而大者後。如網之有綱，而綱則提之。如器之有柄，而柄則執之。如元首在上。手足為之舉。如大將居中，而士卒為之役。如君無為，而臣有為。如賢者尊，而能者使。是知凡得一者，宗也，本也，主也，皆有不動之理。一苟動焉，則其餘錯亂，而不能有所施設者矣。

The number of the Great Transformation is fifty, but only forty-nine are actually used, with one remaining unused (the source says "a single hexagram is hung" which means "one is set aside"). Regarding the study of this "unused one," scholars only know that it is the Taiji, the number that remains still. But they do not understand where exactly this idea is applied. Why? Because "one" is the root of numbers. The principle of all things depends on a root; without it, things become chaotic. Once a root is established, it should not be involved in operations, for if it is, chaos will result again. For example, the axle of a chariot remains still while the wheels turn; the main chariot moves forward while the most honored chariot is at the back; a fishing net has a main rope, which is used to lift the net; an object has a handle, which is used to hold it; the head remains still while the hands and feet move; the general remains in the central camp while the soldiers move about; the ruler remains inactive while the ministers act; the virtuous person is honored while the capable one is assigned tasks. From this we can see that anything occupying the position of "one" is the root, the origin, the master, and has the nature of remaining still. Once this "one" begins to move, everything else becomes chaotic and nothing can be carried out properly.