The sage's explanation, as passed down by Zisi.

太極圖者，自易象溯而上之，乃示其初之象也。天地之生也，依是象以生成；更依是氣之推行變化，以生成萬物。其始則簡，其繼則繁；其本則合，其用則分；而實有定序與方位，有數量與名類，非無紀無序者也。

The Taiji diagram traces back from the hexagrams of the Book of Changes to illustrate the initial form. The generation of heaven and earth follows this form; subsequently, through the movement and transformation of this vital energy, all things come into being. It began simple and later became complex; its essence is unified, yet it differentiates in application. However, there is indeed a definite order and direction, along with numbers and categories, and it is not chaotic or disorderly.

蓋天地出於太極，其象固大，大則難考；人物生於天地，其形已小，小則易徵。徵其小，自得其大；以其生也同，而氣之行也一，不以大小有殊也。故言天者，必先求之人；言大者，必先求之小。物物有一太極，苟求之則自見，不疑為無征也。凡有生之物，皆同此氣行而化，皆同此太極之象者也。

Heaven and Earth arise from the Taiji, and its image is naturally vast. Being too vast makes it difficult to examine. Humans and objects exist between Heaven and Earth, and their forms are already small. Being small makes them easy to verify. By examining small things, one can naturally understand the principles of great things. This is because their mode of generation is the same, and the movement of qi is also the same, without distinction based on size. Therefore, to discuss Heaven, one must first seek it within the human body; to discuss the great, one must first seek it in the small. Every object contains a Taiji. As long as one is willing to seek, it will naturally become visible, without needing to doubt whether it can be verified. All living things rely on the movement of qi to change and transform, and all possess the image of Taiji.

太極者，至極也。古文「太」字同大，大者無與比擬，言獨有而絕無，不可復加也；故有大一、大初、大素、諸名，皆示其獨有無復加者。太極亦然：以至境不可復進，曰極；而極之不可復加，曰太極。蓋自是以上，無可擬也，故凡物自大極始。然大極者，不可作上下看，或左右看，以端為極也，祇宜作中心講；蓋極必有所立，必有其位，其處必至中也。

The meaning of "Taiji" is ultimate. In ancient texts, the character "Tai" is often used interchangeably with "Da," which refers to something incomparable, unique, and without anything that can be added to it. Therefore, ancient books have terms like "Da Yi," "Da Chu," and "Da Su," all indicating something unique and unattainable. Taiji is also like this: reaching a point where it cannot go any further is called "ji," and since this "ji" itself is also incomparable, it is called "Taiji." Because there is nothing above or beyond it, all things begin from Taiji. However, the "ji" in Taiji should not be understood as an endpoint in terms of up or down, left or right; instead, it should be understood as the "center." Because "ji" necessarily has a position, and that position must be in the middle.

若無所立，不得謂之極，以無定也；無其位，不得謂之極，無所守也；非至中，不得謂之極，不可久也。唯有所立，則定於一而不二；唯有其位，則守於常而不失；唯其至中，則久於運用無所窮；故名之極，猶北辰之為北極也。天之極定於北辰，地之極定於南北極；而世界之極，則定於太極也，以至其極，無復與比故也。何以為至極無比？則以其所立雖定而無定，雖有位而無常位，雖至中而無常中；不似北辰之天極，南北端之地極也。

If there is no established position, it cannot be called the Ultimate, because it lacks a fixed standard; if it has no fixed place, it cannot be called the Ultimate, because it has nothing to hold onto; if it is not in the center, it cannot be called the Ultimate, because it cannot last long. Only by having an established position can it remain fixed without wavering; only by having a fixed place can it maintain the norm without losing its position; only by being in the center can it be used continuously without exhausting itself—thus it is called the Ultimate, just as the North Star is called the Northern Pole Star. The Ultimate of Heaven is fixed at the North Star, the Ultimate of Earth is fixed at the two poles, and the Ultimate of the entire world is fixed at the Taiji, because at this Ultimate, there is nothing that can be compared to it. Why is it said to be the ultimate? Because its established position is definite yet not fixed, it has a place yet no fixed place, it is in the center yet has no fixed center—this is different from the Heavenly Ultimate of the North Star and the Earthly Ultimates of the two poles.

夫既曰極，而曰無常，豈非異於極之為極乎？曰：非無常也，言無常而有常耳。以隨所在而立，所至而位，所行而至中也；故曰無極之極，曰太極焉。夫有之與無，同用異途；上之與下，同名異方；神之與形，同生異類；道之與器，同用異勢。故天地既判，人物斯生；形神所分，陰陽乃別；此太極之為至極，恰介乎兩者之中也。

Since it is called "the Ultimate," yet it is said to be without constant form, is it not contradictory to the very nature of being the Ultimate? The answer is: it is not truly without constant form, but rather that within its constant form there is an ever-changing aspect. Because it establishes itself according to its location, determines its position according to where it goes, and resides in the center according to where it moves, it is called "the Ultimate of the non-Ultimate," that is, the Taiji. The existence and non-existence have the same function but different ways; the upper and lower have the same name but different directions; the spirit and form are both generated but belong to different categories; the Dao and the vessel have the same function but different forms. Therefore, once heaven and earth are divided, human beings and things come into being; once form and spirit are separated, yin and yang become distinct. And the reason Taiji is the ultimate is precisely because it is exactly in the middle between the two extremes.

由此以上，皆屬於無者、上、神者、道者，由此以下，則屬於有者、下者、形者、器者；兩者之中，乃為極，而太極乃居之，故曰至中，而有位，有所立也。然有既名，無未嘗無；下既分，上未嘗隱；形既生，神未嘗少；器既成，道未嘗亡；則兩者宛轉生化，遷變相隨，未嘗一日異。

From here upwards, everything belongs to 'non-being,' to the superior, to the spiritual, and to the Dao; from here downwards, everything belongs to 'being,' to the inferior, to form, and to objects. In the middle between these two extremes lies the ultimate center, and the Taiji resides here, hence it is said to be 'most central' and to have a position and establishment. However, although the term 'being' has been established, 'non-being' has not truly vanished; although 'inferior' has been distinguished, 'superior' has not disappeared; although form has emerged, the spiritual has not diminished; although objects have been created, the Dao has not been lost. This shows that the two sides are interdependent, constantly transforming and changing, always accompanying each other without ever separating for a single day.

而極之為極，亦未嘗一時失其中與其位也；而亦未嘗執其中與位，執則失之；故有常而無常，故日物物有太極。取喻於小，足知其大；取譬於近，足證其遠；故太極者，極而非極，異乎物之兩端，天地之極也。果明乎此，可與言太極矣！

And this ultimate principle is called the Ultimate because it has never for a moment lost its center or its position; yet it has not rigidly clung to this center and position, for doing so would have caused it to lose them. Therefore, it is both constant and changeable. Hence, it is said, "Each thing has its own Taiji." Using small examples as analogies, one can infer the great; using nearby things as illustrations, one can verify distant ones. Therefore, Taiji is an ultimate principle that is ultimate yet different from ordinary extremes; it differs from the two ends of things and is the ultimate of heaven and earth. If one truly understands this, then one can discuss Taiji with him.

夫太極之象，示天地之生成，生化之循環，陰陽二氣之遞嬗，萬物之生成變化，自無入有，自始至終，蓋無不包在象中也。故易之卦象，肇始於太極；而推溯萬有之源，亦唯太極。言物必始於有，言生成變化，必本於氣之動靜；太極為初有，而具動靜者也。故推而上之極於是，推而下之始於是；推而內之立於是，推而外之本於是。以是為宗，而後可以推及其它；以是為始，而後可以推至無盡。以天地之氣，通行而無所滯，故其為象也圓，為物也周流不窮，為用也無息不二；而太極為之極，以定其位，守其中，以御無盡，而行無窮。

The image of the Supreme Ultimate represents the cycle of creation and transformation of heaven and earth, the alternation of yin and yang energies, and the generation and change of all things. It encompasses the transition from non-existence to existence, from the beginning to the end—nothing is excluded from this image. Therefore, the hexagrams of the Book of Changes originate from the Supreme Ultimate; to trace the origin of all things, one must return to the Supreme Ultimate. Whenever discussing 'things,' one must begin with 'existence'; whenever discussing generation and transformation, one must take the movement and stillness of qi as the foundation. The Supreme Ultimate is the original 'existence' and also possesses both movement and stillness. Therefore, moving upward, its limit lies in it; moving downward, its beginning lies in it; moving inward, its basis lies in it; moving outward, its source remains in it. Taking it as the central principle, one can then extend to other things; taking it as the starting point, one can then derive endlessly. Because the qi of heaven and earth flows continuously without obstruction, its image is circular, as a thing it is ever-circulating, as a function it is unceasing and undivided. The Supreme Ultimate establishes this extreme, to determine its position, to maintain its center, thus governing the boundless and driving the endless.

故天地不離其度，萬物不乖其序；而易之卦象，遂本是以立以成以用；始終於易，以盡其變化；而後天地之道以見，人物之數以明，鬼神之德以知；而後有形者適其生成，有氣者通其變化；合陰陽而歸於太和，匯萬類而統於太一，同萬行而期於至中；以言乎道，則道至矣！以言乎物，則理備矣！以言乎事，則情見矣！以言乎天下，無不咸宜；而行之無不得，守之無所失；是以為教之本，易之源；固非聖人莫之能知，亦非聖人莫之能言者矣！

Therefore, heaven and earth do not deviate from their measures, and all things do not violate their order; the hexagrams of the Book of Changes are established, realized, and applied according to these principles, running through the entire Book of Changes from beginning to end, to exhaust all transformations. In this way, the way of heaven and earth becomes evident, the numbers of people and things become clear, and the virtues of ghosts and spirits can be understood; tangible things thus receive their generation, and things with qi thus experience their transformations. Yin and yang combine to achieve "Great Harmony," all kinds of beings converge under "Great Oneness," and numerous actions all return to "Ultimate Center." In terms of the Way, the Way reaches its ultimate; in terms of things, the principles are complete; in terms of affairs, the actualities are revealed; in terms of the world, there is nowhere that is inappropriate. Following it leads to success, and adhering to it ensures no loss. Therefore, it is the foundation of education and the source of the Book of Changes—this has always been known and spoken about by sages, not something that sages could simply know or speak about without it.

夫子於中庸述其義，曰：「時中」，於大學述其境，曰「至善」，曰「無所不用其極」，此「極」字與太極同一義；蓋有物必有則，有則必有極；太極為一切之極，凡在有者，皆有極；而凡有用者，皆必有此極；此即中庸「時中」之義也。簡名之曰：「道」。故傳曰：「一陰一陽之謂道」，而太極即自陰陽成；人生受命於天，而有性；性亦合於太極也。故曰：「成之者性」，性成於善，太極之行，至善也；故曰：「繼之者善」，此太極者統一切事物而言之者也。

Confucius explains its meaning in the "Zhongyong" as "shi zhong" (timeliness and centering), and its realm in the "Daxue" as "zhi shan" (supreme goodness), also saying "wu suo bu yong qi ji" (nothing is used without reaching its extreme). The character "ji" (extreme) here is the same as "Taiji" (Supreme Ultimate). Since there is something, there must be a principle, and since there is a principle, there must be an extreme; Taiji is the extreme of all things. All that exists has its extreme, and all that is useful must also have this extreme—this is the meaning of "shi zhong" in the "Zhongyong," which is simply called "Dao." Therefore, the "Xici Zhuan" says, "One yin and one yang is called Dao." Taiji is composed of yin and yang. When a person is born, they receive their destiny from heaven, thus having a nature, which conforms to Taiji. Therefore, the "Xici Zhuan" says, "Cheng zhi zhe xing ye" (what is formed is nature). Nature becomes good, and the movement of Taiji itself is supreme goodness, so the "Xici Zhuan" also says, "Ji zhi zhe shan ye" (what is continued is goodness). The Taiji discussed here encompasses all things.

非僅以一物名之，凡有名者，皆合於太極；不問其為物、為事、為道、為器、為形、為神也；苟可言者，必自太極始；有行有守者，必依太極以行以守之也。蓋太極之為道也，道之為一陰一陽也；無能外陰陽以生成，故無能離道，亦無不合於太極也；雖然，太極固自生成者；人之生成中，而不克明太極之道，則為忘生之本；聖人乃以教教之，使明其生；而易之義於是見也。

It is not merely used to name something. Whatever has a name conforms to the Taiji, whether it is an object, an event, a principle, a tool, a form, or a spirit; whatever can be spoken of must necessarily begin with the Taiji. Whatever is acted upon or maintained must necessarily act and maintain according to the Taiji. Because the Taiji is the Dao, and the Dao is "one yin and one yang." Nothing can be generated without yin and yang, so nothing can be separated from the Dao, and nothing is inconsistent with the Taiji. Nevertheless, the Taiji itself generates itself spontaneously. Although people are born within this process of generation, they cannot comprehend the way of the Taiji, which means they have forgotten the fundamental nature of their own life. Therefore, the sages use education and guidance to teach people to understand why they live — this is the meaning of the Book of Changes revealed here.

故易之溯太極，為制卦也，為以卦寓其教也；卦之所象，事事物物，皆道之所在；亦太極之所運行，無他物也；二氣之消長盈虛，以成天地間之生成變化；而易象之以示人耳，是易之教，盡在太極中，天地萬物原在太極中；故易不得外之以為教，人之求易之明，而不從太極始，將何以見易哉？故傳曰：「易有太極」，其一語也，鄭重之矣！

Therefore, the Book of Changes traces back to the Supreme Ultimate in order to create the hexagrams and to寄托 the teachings within them. The various things symbolized by the hexagrams are all manifestations of the Way, and they are all within the scope of the Supreme Ultimate's movement. There is nothing else beyond this. The waxing and waning, fullness and emptiness of the two energies, yin and yang, cause the generation and transformation of all things in the universe. The Book of Changes merely symbolizes these phenomena for people to see. Thus, the teachings of the Book of Changes are entirely contained within the Supreme Ultimate, and the heavens and the myriad things are also contained within the Supreme Ultimate. Therefore, the Book of Changes cannot establish its teachings apart from the Supreme Ultimate. If people wish to understand the Book of Changes, but do not start from the Supreme Ultimate, how can they see the Book of Changes? Hence, the Great Treatise says, "The Book of Changes contains the Supreme Ultimate"—this single sentence carries immense weight.

伏羲八卦所自始，固溯源太極，而合乎河洛二圖者也。河圖以天地合化，生成五行；已分四方，即四象也。洛書以五行生變，而為九宮；四方之外，加為四隅；遂分列八方，即八卦之象也。中五者，太極本位；九宮名太乙本宮，太乙雖在中央，而以時行臨於八宮；故九宮皆有太乙至臨之時，而八方皆受太乙之氣；八卦之象亦然，由四象而分為八卦，虛其中以位太極；太極雖無象，其位固在；而其氣運行於八卦，則八卦皆太極之象；分則為八卦，合則一太極；此天地自然之象數也。

The origin of the Eight Trigrams of Fuxi goes back to the Taiji, and at the same time corresponds with the two diagrams, the Yellow River Chart and the Luo Writing. The Yellow River Chart generates the Five Phases through the combination of the heavenly and earthly energies, and already distinguishes the four directions, which are the Four Symbols. The Luo Writing forms the Nine Palaces through the transformation of the Five Phases, adding the four corners outside the four directions, thus dividing into the eight directions, which are the images of the Eight Trigrams. The central 'five' is the position of the Taiji; in the Nine Palaces it is called 'Taiyi's original palace'. Although Taiyi resides in the center, it follows the sequence of time to visit the eight palaces in turn, so each of the nine palaces has the presence of Taiyi, and each of the eight directions receives the energy of Taiyi. The image of the Eight Trigrams is also like this: the Four Symbols are divided into the Eight Trigrams, leaving the center for the Taiji to occupy. Although the Taiji has no image, its position exists definitely; and its energy circulates among the Eight Trigrams, so each of the Eight Trigrams is an image of the Taiji. When viewed separately, they are the Eight Trigrams; when viewed together, they form one Taiji—this is the natural image and number of heaven and earth.

太極何以無象？則以易之重在變，而推其用，故隱其體；以體為先天，非如後天之有形也；太極之為太極，言其氣之如是行，生化之如是成；不可以物擬之，故不象之也。然太極之氣，無時不在；所行之道，無地不至；其所生化者，自物見之；故列八卦，即有太極；太極自存八卦之中，見八卦即見太極。猶道不可見，而以德見之；神不可名，而以形名之。

Why does the Taiji have no image? Because the Book of Changes focuses on "change," emphasizing the application and transformation of its principles, so it conceals its essence. The essence belongs to the Earlier Heaven, unlike Later Heaven things which are tangible and visible. Taiji is called Taiji merely to indicate that qi flows in this way and that generation and transformation occur in this manner; it cannot be compared to any specific object, so it is not given an image. However, the qi of Taiji is always present, its path reaches everywhere, and the things it generates can be seen in physical forms. Therefore, as soon as the Eight Trigrams are arranged, Taiji is already included within them; Taiji inherently exists within the Eight Trigrams, and seeing the Eight Trigrams is equivalent to seeing Taiji. This is similar to how the Dao itself is invisible, but can be seen through virtue; and how the divine itself cannot be named, but can be given a name through form.

先天者，麗於後天；道者，存於器；得其一，則知其二；不待別求之也。故八卦之位虛太極，而八卦之用，皆太極之用也；以太極有名無位，有位無象；故易有用無體，非無體也，見用即知體，體在用中也；傳所謂：「神無方，易無體」者，即此義也。神者，指太乙之神；無方，無定方也；言太乙雖居中宮，而周行八方無定也；易無體，則極之不顯其象，而其用存於八卦；不獨八卦、六十四卦、三百八十四爻、皆有所用，皆太極之用也。用見而體藏，故曰：「無體」，後人不明此義，遂不解「無體」之謂何也。

The Earlier Heaven depends on the Later Heaven, and the Dao exists within the vessels; mastering one side allows one to know the other, without needing to seek it separately. Therefore, the positions of the Eight Trigrams leave the center empty for the Taiji. All the functions of the Eight Trigrams are the functions of Taiji. Since Taiji has a name but no position, has a position but no image, the Book of Changes is useful but has no form. This does not mean it truly has no form, but rather, when one sees the function, one knows there is a form, and the form is hidden within the function. The Great Treatise says, "The spirit has no fixed direction and the Book of Changes has no form," which refers precisely to this. "Spirit" refers to the God of Taiyi; "no fixed direction" means it has no fixed location, indicating that although Taiyi resides in the Central Palace, it circulates through all eight directions without a fixed place. "The Book of Changes has no form" means that Taiji does not display its own image, but its function is寄托 in the Eight Trigrams. Not only the Eight Trigrams, but also the sixty-four Trigrams and the 384 lines, all functions are the functions of Taiji. The function is revealed while the form is hidden, hence it is called "no form." Later people did not understand this principle, so they did not know what "no form" really means.

夫天地之大，為神者一，為形者萬；為體者一，為用者萬；故有上下道器之殊。太極體道而用神，為名可名，而物不可擬；合之則一，分之則萬；皆此太極也。如：合天地，一太極也，而天地間萬物皆有太極在；道，一太極也，而天下萬物皆有太極在；太極不可得而象者，恐象之而人疑為物也；故雖有太極之圖，祇可視為虛擬之象，不得認為一物也；不得為物，而物皆有之。

The heavens and earth are vast, and though there is only one "spirit" (shen), there are countless forms (xing). There is only one "body" (ti), yet there are countless functions (yong). This is why there is a distinction between the Way of the Ultimate (xingxiang) and the material things (qi). The Taiji has the Way as its body and the spirit as its function. Its name can be spoken, but its substance cannot be compared. When combined, it is one; when separated, it is countless, yet all are the same Taiji. For example, if we look at the heavens and earth together, they form one Taiji, yet all things in the world also contain their own Taiji. The reason Taiji cannot be given a symbolic image is to prevent people from thinking of it as a physical object. Although there is a Taiji diagram, it should be regarded as a conceptual image, not as a real thing. It cannot be considered an object, yet all things contain it.

故易卦不列太極，而全易卦爻皆存之；伏羲一畫開天，豈非以一擬太極哉？則凡卦爻，莫非自此一來；固莫非太極之象，何事再象之乎？通者迖之，執者昧之，觀八卦之象，固無在而非太極，視人之能見得否耳。

Therefore, the hexagrams in the Book of Changes do not list the Taiji separately, yet the entire Book of Changes, with its hexagrams and lines, everywhere contains the Taiji. Fuxi created the world with a single stroke, and that stroke is not precisely the symbol of the Taiji? If this is so, then every hexagram and every line originates from that single stroke, and thus every hexagram and line is an image of the Taiji. Why then should we need to establish another symbol for it? Those who are enlightened can reach this level, while those who are rigidly attached are blinded by it. Looking at the images of the Eight Trigrams, there is nowhere that is not the Taiji; it is only a matter of whether people can see it or not.

伏羲畫卦，始於太極，已見前講。所畫八卦者，純本太極陰陽並行之象，及河洛五行九宮之圖者也。太極之陰陽兩儀，非同等同類各據一方者也，非守位不移者也，非分行不侔者也。其生也有序，化也有次，交也有多寡，行也有往復；一消一長，一降一升，非劃然兩截也；一盈一虛，一錯一綜，乃合而有得者也。

Fuxi began drawing the trigrams from the Taiji, as mentioned earlier. The eight trigrams he drew were entirely based on the image of yin and yang in Taiji, as well as the Five Phases and the nine-square grid of the Yellow River Chart and the Luo Writing. The two principles of yin and yang divided from Taiji are not simply equal and opposite, each occupying one side. They are not fixed in position, nor do they move independently without relation. They have a sequence of origin and a sequence of transformation, with varying degrees of interaction and movement. They alternate in growth and decline, in rising and falling, not divided into two separate halves. They are full and empty, disordered and interwoven, and only through mutual coordination do they achieve harmony.

故自陰之始，至陰之終，陽之消，至陽之息，皆遞為加減乘除，而象其氣之上下往復，皆序為東南西北，而分其數為奇偶盈虛。故其名有等，位有級，類有大小，象有經緯，以成其變化，而賅天地萬物之始終者也。故兩儀遞分為四，四象遞變為八，八卦於是成象矣，合之河洛亦恰同。

Therefore, from the beginning to the end of yin, and from the decline of yang to its growth, they proceed in succession with additions, subtractions, multiplications, and divisions, symbolizing the reciprocal movement of qi upwards and downwards. They also arrange the directions east, south, west, and north in order, dividing their numbers into odd and even, full and empty. Thus their names have ranks, their positions have levels, their categories have sizes, their images have both longitudinal and lateral aspects, thereby producing various transformations and encompassing the beginning and end of all things in the universe. Thus the two principles are successively divided into four parts, the four images are successively transformed into eight parts, and the eight trigrams have thus become complete. When compared with the Yellow River Chart and the Luo Writing, they are perfectly consistent.

河洛之圖，由天地之數成五行，由五行之位變九宮；五行除中央則仍四象，九宮除中央則仍八卦也。中央者太極也。八卦以中央為虛，故列八方而虛其中，實則中央太極仍自在也。八卦之象，本於太極，合於河洛，而象天地萬物之生成變化者；生成無盡，變化無窮，八卦之用亦無垠也。

The Yellow River Chart and the Luo Writing are composed of the numbers of Heaven and Earth to form the Five Phases, and then the Five Phases are arranged according to their directions to form the Nine Palaces. If the Central element is removed from the Five Phases, the remaining are the Four Symbols; if the Central position is removed from the Nine Palaces, the remaining are the Eight Trigrams. The Central position is the Taiji. The Eight Trigrams leave the Central position empty, arranging only the eight directions and leaving the center vacant, but the Taiji in the center still exists. The images of the Eight Trigrams originate from the Taiji and correspond with the Yellow River Chart and the Luo Writing, symbolizing the generation and transformation of all things in the universe. Since generation has no end and transformation has no limit, the use of the Eight Trigrams is also boundless.

易傳曰：「神無方，易無體。」此即指八卦之虛中位也。中為太極，元氣周流，主之者神，行無定方；太極為體，八卦成用，太極既虛，故曰無體。此八卦既立之後，用其變化，而至無盡；雖曰無體，體見於用，猶神之無方而無不在也。

The *Great Treatise* of the *Commentaries on the Changes* says: "The spirit has no fixed place and the *Book of Changes* has no fixed form." This refers precisely to the empty position among the Eight Trigrams. The center is the Taiji, where the primordial qi circulates. It is governed by the spirit, which operates without a fixed direction. The Taiji is the essence, and the Eight Trigrams are its manifestations; since the Taiji is left empty, it is said to "have no form." This means that after the Eight Trigrams are established, their transformations are applied endlessly. Although it is said to "have no form," the essence is revealed through its use, just as the spirit, though without a fixed position, is present everywhere.

夫伏羲作卦之始，初無文字，卦象則象形之字也；其命名也，即象物之名。故□為乾象天，即天字；天之古文，即如□卦之象，象陽氣之聚於上也。□為象地，即地字，象地之形；地成於山水，其左為山，右為水，後人其狀為地也。□離為火，即火字也；火為旁實中虛，如□，後人變為火字，或作□，仍□象也。

Fuxi began drawing trigrams without using written characters; the trigrams themselves were pictographic symbols. When naming the trigrams, he used the names of the things they represented. Therefore, the trigram Qian (☰) symbolizes Heaven, and it is the character "tian" (heaven); the ancient form of "tian" resembles the image of the trigram Qian, representing the gathering of yang energy at the top. The trigram Kun (☷) symbolizes Earth, and it is the character "di" (earth); it depicts the shape of the earth. The earth is composed of mountains and water, with mountains on the left and water on the right, so later people wrote the character "di" based on this shape. The trigram Li (☲) represents fire, and it is the character "huo" (fire); the shape of fire is solid on both sides and hollow in the middle, just like the trigram Li. Later people changed it into the character "huo" or wrote it in other forms, but it still retains the image of the trigram Li.

□為坎為水，即水字，象水之形，後人變為□，仍□象也。□為震為雷，象天下之電光流照，即雷字也，後人變□，仍□象所化。□為艮為山，象山在地面，高出於土，即山字，後人變為□，有作□者，仍□象也。□為巽為風，又為木，象風行天空，木枝葉分披，後人變為□，或□仍□象也。

The trigram Kan (☵) represents water. It is the character "water" (水), which originally depicted the shape of flowing water. Although later forms of the character changed, it still retains the image of the Kan trigram. The trigram Zhen (☳) represents thunder. It symbolizes the flashing lightning across the sky, and it is the character "thunder" (雷). Although the character's form has changed over time, it still originates from the image of the Zhen trigram. The trigram Gen (☶) represents mountain. It symbolizes a mountain standing on the earth, rising above the soil, and it is the character "mountain" (山). Although later forms of the character have changed, it still reflects the image of the Gen trigram. The trigram Xun (☴) represents wind and also wood. It symbolizes the wind blowing through the sky and the branches and leaves of trees hanging down. Although the character has changed in form over time, it still originates from the image of the Xun trigram.

□為兌為澤，象水之在澤，如湖沼之類；後人以其從水出，變為□，象水之瀦，而後流之意；又為說言，象舌動而口啟也。此皆最初之字，象形者也；雖以去古久遠，遷變已多，不盡相同，而其意仍在。且坎離二象，仍如初也。坎之水，離之火，其象既似，其數亦同，則一覽可知者矣。因水火二者，陰陽之樞紐，天地之運用其自然之象，永古如斯，則字象亦不變也。況八卦明氣與數者也。

The trigram Dui (☱) represents a marsh or lake, symbolizing water accumulating in a low area, like a pond or marsh. Later people changed its form because it originated from water, taking the meaning of water gathering and then flowing out. Dui also means "to speak," referring to the act of speaking, which symbolizes the tongue moving and the mouth opening. These are the earliest characters, belonging to the category of ideographic symbols. Although they are very old and have undergone many changes in form, their original meanings have been preserved. Moreover, the images of Kan (☵) and Li (☲) remain the same as before. Kan represents water and Li represents fire; their images are similar, and their numbers are the same, so they can be easily recognized. Since water and fire are the key elements of yin and yang, and are natural phenomena in the operation of heaven and earth, they have remained unchanged throughout history. Moreover, the Eight Trigrams were originally used to explain the principles of qi and numbers.

氣有陰陽，數有奇偶，故天為陽奇，地為陰偶。其所生者陽則奇，陰則偶，亦如之。而陽卦多陰，陰卦多陽，明陰陽必交互而後見其用也。所謂自然之理，自致至焉，不假人為者也。試觀八卦之名及其字，即可以知其數與氣，其符合者純自然自在，非聖人所為也。

The concept of "qi" has a distinction between yin and yang, and the concept of "number" has a distinction between odd and even. Therefore, heaven belongs to yang and its number is odd, while earth belongs to yin and its number is even; everything generated by heaven and earth follows this principle, with yang numbers being odd and yin numbers being even. However, among the eight trigrams, yang trigrams often have more yin lines, and yin trigrams often have more yang lines. This clearly shows that yin and yang must intermingle and penetrate each other in order to manifest their functions. Pure yin or pure yang in isolation is inactive and accomplishes nothing. This is what is meant by the natural principle: things naturally reach their stage and position without the need for artificial arrangement. By examining the names and forms of the eight trigrams, one can discern their numbers and qi. The four aspects of name, form, number, and qi are all naturally inherent and exist in their own way, not deliberately created by sages.

八卦之氣數，生化之所繫，皆自四象來。如乾與兌，太陽也；坤與艮太陰也；坎與巽，少陽也；離與震，少陰也。陰生陽，陽生陰，二氣周流，循環無窮，其數則有先後，其位則有上下。屬於陽者，近天而數奇；屬於陰者，近地而數偶。天地者陰陽之總樞，故乾坤為父母；水火者陰陽之大用，故坎離為樞機。此四者居四方之正。震巽艮兌者，陰陽之變化，消息盈虛終始之事也，故四者在四偶，以輔翼其生化，而變通其氣數。此卦之有八，為天地萬物之總象也。

The qi and numbers of the Eight Trigrams are the key factors in the generation and transformation of all things. They all derive from the Four Images: "Qian" and "Dui" come from the Sun, "Kun" and "Gen" come from the Great Yin, "Kan" and "Xun" come from the Lesser Yang, and "Li" and "Zhen" come from the Lesser Yin. Yin can generate Yang, and Yang can generate Yin; the two energies circulate endlessly, without beginning or end. However, in the process of circulation, there is a distinction in the order of numbers and a differentiation in their positions. All yang trigrams are close to Heaven and are assigned odd numbers, while all yin trigrams are close to Earth and are assigned even numbers. Heaven and Earth are the central hub of yin and yang, so the trigrams "Qian" and "Kun" are called the parents trigrams. Water and fire are the greatest functions of yin and yang, so the trigrams "Kan" and "Li" are called the pivot and mechanism. These four trigrams occupy the four cardinal directions of east, south, west, and north. The four trigrams "Zhen," "Xun," "Gen," and "Dui" deal with the changes of yin and yang, which involve the waxing and waning, fullness and emptiness, beginning and end of things. Therefore, they are placed in the four corners to assist the four central trigrams in generating and transforming all things, allowing the qi and numbers to change and flow. The reason the trigrams are exactly eight is because these eight are sufficient to fully represent the total image of Heaven and Earth and all things.

夫伏羲作卦，以象明氣數生化者也。而生必有始，化必有終；有其氣，則有其物；有其數，則有其類。天地至大，萬物至眾，而約之於八卦。其所象者簡，而所推者繁；所舉者易，而所變者多，則由其用之不窮也。天地一陰陽也，萬物亦一陰陽耳，故萬物雖生化無盡，不得外於天地，即不得外於八卦也。八卦之始終可得言也，而變化不可測；八卦之名物可得類也，而遷移有無窮，此所以名之曰卦。言以一卦萬，以簡御繁，以易御眾，其為德不二，故能成其大也。此就八卦之名類氣數略言之耳。

Fuxi drew the eight trigrams in order to explain how qi and numbers generate and transform. Whenever something is generated, there must be a starting point; whenever something is transformed, there must be an end. There is a particular kind of qi, which gives rise to a particular kind of thing; there is a particular kind of number, which gives rise to a particular kind of tribe. The heavens and earth are extremely vast, and all things are extremely numerous, yet they are all contained within the eight trigrams. The images taken by the trigrams are very simple, yet the principles inferred from them are extremely complex; the examples given are very easy, yet the situations that arise from them are extremely varied. This is because the function of the trigrams is boundless. The heavens and earth are merely yin and yang, and all things are also merely yin and yang. Therefore, even though all things continuously generate and transform, they cannot go beyond the heavens and earth, nor can they go beyond the eight trigrams. The beginning and end of the eight trigrams can be explained clearly, but their transformations are beyond measurement. The things referred to by the trigrams can be classified, but their transformations have no end. This is precisely why they are called 'trigrams'. The phrase 'one trigram encompasses myriad things' means using simplicity to manage complexity and using ease to manage multiplicity. Its virtue is singular and unchanging, thus achieving its vastness. The above is only a brief explanation of the names, categories, and qi and numbers of the eight trigrams.

伏羲八卦，自象言之則包舉天地萬物之象，自數言之則納天下之數，自氣言之，則通二五之氣。其設象有物，制卦有則：物者天地生成之物，則者河洛太極之象。故卦有大小，地有方位，行有次序，有往來之度，有變化之形，有奇偶對待之數，有陰陽分合之情。故卦有名有義有位有時，有交合之類，變易之事，雖簡而不遺於物，雖繁而不乖於道，此其本於自然，成於固有者，非作者有意為之也。

The eight trigrams drawn by Fuxi encompass, in terms of imagery, the forms of all things in heaven and earth; in terms of numbers, they include all numbers under heaven; in terms of qi, they connect the two qi of yin and yang and the five phases' qi, known as the "two and five qi." The trigrams are based on real objects generated by heaven and earth, and they follow principles derived from the Yellow River Chart, the Luo Writing, and the image of the Taiji. Therefore, there are distinctions between large and small trigrams, fixed directions of east, west, south, and north, a sequence of their movements, a measure of their coming and going, forms of change, odd and even numbers in contrast, and the interplay of yin and yang. Thus, each trigram has a name, meaning, position, time, categories of interaction, and phenomena of change. Though concise, they do not omit any object; though intricate, they do not contradict the constant way. All of this originates from nature and is formed according to inherent principles, not devised by the person drawing the trigrams based on personal intent.

如八卦之氣數，與河洛太極之圖合，自分陰陽，自成上下。乾為天而居上，坤為地而居下，此天地自然之位也。陽從天下，陰從地上，陰陽上下，天地以交，生成乃見，此河圖之象也。生成之數，首水次火：水以陰藏陽，火以陽包陰；水則潤下而隨陽升，火則炎上而隨陰降，陽左陰右。故離東坎西，以象日月：日為陽則東昇，月為陰則西出，其象亦天地自然者也。

The eight trigrams' energies and numbers fully correspond with the Yellow River Chart, the Luo Writing, and the diagram of the Taiji. Thus, yin and yang naturally differentiate, and the positions of above and below naturally form. "Qian" represents Heaven and occupies the upper position, while "Kun" represents Earth and occupies the lower position. This is the inherent order of Heaven and Earth. Yang energy descends from Heaven, while Yin energy ascends from Earth. The interaction between Yin and Yang above and below gives rise to the generative power, which is the image presented by the Yellow River Chart. Regarding the numbers of generation, water is mentioned first, then fire: water, with its Yin form, contains Yang, while fire, with its Yang form, contains Yin. Water has a nature of moistening and descending, yet it rises with Yang energy; fire has a nature of rising and blazing, yet it descends with Yin energy. Yang is on the left, Yin on the right, so "Li" is located in the east and "Kan" in the west, symbolizing the sun and moon. The sun belongs to Yang, thus rising from the east; the moon belongs to Yin, thus appearing from the west. This image also arises naturally from Heaven and Earth.

天三生木，則陽氣切生於陰。陽在天為風，在地為木，風行於空，木生就上，故震在東北，巽在西南。陽息則陰消，陰虛則陽動，亦天地之氣自然分合也。地四天九，金以生成。金藏於山而耀其質，含英則靜而居地，飛光則動而近天。山乃厚藏，陽因陰用；澤乃流潤，陰以陽耀。故艮為山而居西北，以附於地；兌為澤而處東南，以麗於天。陰陽自分，方位以異，亦天地萬物自然之象也。

According to the numbers generated by the Yellow River Chart, "Heavenly Three gives birth to Wood," meaning that the yang energy follows the yin to emerge. This yang energy manifests in the sky as wind and on the earth as wood; wind moves through the void, and wood grows upward, so "Zhen" is located in the Northeast and "Xun" is located in the Southwest. When yang energy grows, yin energy recedes; when yin energy weakens, yang energy arises. This is the natural division and union of the energies of heaven and earth. Now looking at "Earthly Four gives birth to Metal, Heavenly Nine completes it," metal is thus generated. Metal is hidden in mountains and reveals its brilliance; when it is contained and holds its essence, it is still, so it resides on the earth; when it shines brightly, it is active, so it is near the sky. Mountains are substantial and store things, and yang energy arises through yin; marshes are flowing and moist, and yin brilliance arises through yang. Therefore, "Gen" represents mountains and resides in the Northwest, attached to the earth; "Dui" represents marshes and is located in the Southeast, attached to the sky. Yin and yang stand separately, hence their different positions. This is also the natural image of heaven, earth, and all things.

陽者從陽而樂交陰，陰者隨陰而喜順陽。天地既立其樞，六物因之而定；水火既分其用，四象由之而行。風雷震於東西，以成寒暑之令；山澤列於南北，以見生化之機。此八卦之方位有所定也。易傳曰，天地定位，山澤通氣，雷風相博，水火不相射。此指伏羲八卦之方位也。

The yang elements follow yang but are pleased to combine with yin; the yin elements follow yin but are pleased to submit to yang. Once heaven and earth have established their positions, the remaining six trigrams are determined accordingly. Once water and fire have taken charge of their great functions, the four yin-yang pairs follow their movements. Wind and thunder clash in the east and west, thus forming the seasons of cold and heat; mountain and marsh are arranged in the south and north, thus revealing the mechanisms of generation and transformation. This is how the positions of the eight trigrams are established. The "Sayings on the Trigrams" from the Book of Changes states: "Heaven and earth are positioned, mountains and marshes communicate their energies, thunder and wind interact, water and fire coexist without opposing each other." This refers to the positioning of the trigrams of Fuxi.

至八卦之次序，則本於太極兩儀之象，而分陰分陽，順逆以相交，成往復循環之數，亦與河洛同。蓋太極之變易，河洛之生成，陰陽二氣，自生至老，自始迄終，有其序也；而以數紀之，則次序乃明。八卦亦然：乾為陽統，坤為陰統；乾數為九，紀陽之老，坤數為六，紀陰之終。此二氣之樞，為各數之宰。循環者由陰始，行陰者由陽起，故陽自上統下，陰自下統上；左之卦上統於乾，右之卦下環於坤，一順一逆，而成環行。

As for the order of the Eight Trigrams, it is based on the image of the Supreme Ultimate and the Two Principles: from this, yin and yang are divided, and they intersect in a way that is alternatingly in order, forming a cycle of numbers, which is also consistent with the Yellow River Chart and the Luo Writing. The transformation of the Supreme Ultimate, the generation of the Yellow River Chart and the Luo Writing, in the end, all represent the process of yin and yang qi from birth to old age, from beginning to end, with an inherent order; by using numbers to record this, the order becomes clear. The Eight Trigrams are also like this: "Qian" encompasses all yang, and "Kun" encompasses all yin; the number of Qian is nine, marking the maturity of yang qi, and the number of Kun is six, marking the end of yin qi. These two are the hubs of the two qi, and also the masters of the other numbers. The cycle begins with yin, but the movement of yin depends on yang to initiate it, so yang governs from above downward, and yin governs from below upward: the trigrams on the left column are governed upward by Qian, and the trigrams on the right column are governed downward by Kun, alternating in direction, forming a circular movement.

陰乃繼陽，陽乃交陰。故自乾數之，則次為兌，次為離，次為震，又次為巽，次為坎，次為艮，次為坤，以成一序，相貫而相得，莫見其盡也。蓋乾者純陽，靜則陰生矣；坤者純陰，動則陽生矣。以陽交陰，則生者必有死；以陰繼陽，則盈者必有虛。一往一來，一進一退，乃見其次序焉。故太陽有二，太陰有二，少陽少陰亦然，以有始則有終，有來則有往，其行之自至也。

Heavenly Yang connects with Earthly Yin, and Earthly Yin again connects with Heavenly Yang. Therefore, starting from "Qian" (Heaven), the sequence follows "Dui" (Lake), then "Li" (Fire), then "Zhen" (Thunder), next "Xun" (Wind), then "Kan" (Water), then "Gen" (Mountain), and finally "Kun" (Earth). This forms a continuous sequence where each follows the previous, and they complement each other, with no end in sight. This is because "Qian" is pure Yang, and when it becomes still, Yin arises; "Kun" is pure Yin, and when it moves, Yang arises. When Yang connects with Yin, there must be birth and death; when Yin connects with Yang, there must be fullness and emptiness. One going forward and one returning, one advancing and one retreating, the order is thus revealed. Therefore, the Great Yang is paired with two trigrams, the Great Yin is paired with two trigrams, and the Lesser Yang and Lesser Yin each are also paired with two trigrams: there is beginning and there is end, there is coming and there is going. This is the natural progression of the vital energy, reaching its stage naturally.

觀其卦象，則自知之。如一日然：日午夜子定其樞，晨夕定其行，而自午至夕，自夕至子，自子至晨，自晨至午，氣有異同，數有進退，象有盈虛消長，此自然之理，非有所為也。故卦之次序亦象之。陰陽二氣，無一息之停，其序不亂；日月往來，無一時之失，其度不乖者，則由於有自然之次序也。

By observing the trigrams, one naturally understands. This is like the movement of a day and night: noon and midnight fix the north and south ends as the pivot points, while dawn and dusk fix the east and west ends as the course. From noon to dusk, from dusk to midnight, from midnight to dawn, and from dawn to noon, the energy is sometimes the same and sometimes different, the numbers advance and retreat, the images are sometimes full and sometimes empty, sometimes decreasing and sometimes increasing — all of this follows the natural order, and there is no one behind manipulating it. Therefore, the sequence of the Eight Trigrams is also arranged in this way. The yin and yang energies never cease, yet their sequence is never confused; the sun and moon move without ever missing their appointed time, and their measures are never violated, because there is originally a natural order within them.

故八卦成列，則次序見，而推之無盡，變之無窮，猶依此序，未嘗有差；以合天道，以類萬物，無不咸得，則序之效也。故有卦象，則有卦位以定其方，有卦序以定其行。方定則可守，行定則可遵；有守有遵，則可久可大。此易之道，大而無盡，久而不息者也。

Therefore, once the eight trigrams are arranged in a sequence, the order becomes evident. Afterwards, no matter how far the deductions go or how complex the transformations become, they still follow this order without any error. Using it to correspond with heavenly principles and to classify all things, there is nothing that does not fit perfectly. This is the effectiveness of "order." With the trigram images, there are trigram positions to determine direction; with the trigram sequence, there is a determination of movement. When direction is fixed, there is a standard to rely on; when movement is fixed, there is a path to follow. By having both a standard to hold fast to and a path to follow, one can achieve longevity and vastness. The reason why the Way of the Zhou Changes is vast and boundless, enduring and unceasing, lies precisely here.

八卦之象物，雖有天地水火風雷山澤之名，然舉其類，不止此也。蓋物之生也日繁，氣之所賦，數之所同，有難盡舉，此則以其類而統之耳。如乾象天，以其純陽也，其數九，其氣陽，則凡類是者皆其屬也；他卦亦然，有是象者皆附是類。以象言之，不以物名之，故於所象之物名外，另為之名，非其不限於此物也。

The things represented by the Eight Trigrams, although named after things like heaven, earth, water, fire, wind, thunder, mountain, and marsh, are in reality far more than just these eight categories. Because the kinds of things in the world are increasing day by day, and since all things that share the same kind of qi and the same number are too numerous to be listed individually, they can only be grouped together by category. For example, the trigram "Qian" represents heaven because it is purely yang. Its number is nine, and its qi is yang. Therefore, all things that share these characteristics are included under this trigram. The same applies to the other trigrams; any thing that shares the same symbolic meaning is included in that category. The trigrams are based on symbolic meaning rather than on a specific object, so they have names separate from the things they represent. This does not mean that a trigram is limited to representing only one specific thing.

此□象天，於天之名外，別名日乾；□象地，於地之名外，別名日坤；示□不止象天地也，故別稱之為乾坤。他卦皆然，不可以名泥其象也。故曰象不曰物，猶之二氣，不曰氣，曰儀也。凡物之生成，皆有其氣數，則有所象；象何卦者屬何類，其多不可盡述，述其易見聞而名之。而恐人泥於名物，乃別名之；又恐人之不能推演其象，乃別述卦象於傳。雖所舉較多，實未盡也。

Therefore, the symbol 「□」is used to represent heaven, and in addition to the name "heaven," it is called "Qian"; the symbol 「□」is used to represent earth, and in addition to the name "earth," it is called "Kun." This indicates that the symbols represent more than just heaven and earth, hence they are called Qian and Kun. The other hexagrams are also like this; one should not be confined by names and thus hinder understanding of the hexagram images. Therefore, it is said to be "image" rather than "thing," just as yin and yang energies are not called "energy" but "yi." All things have their energies and numbers, and thus have corresponding images; a thing that corresponds to a particular hexagram belongs to that category. These categories are numerous and cannot all be mentioned, so only those that are easily known are named. To prevent people from being attached to names and things, separate hexagram names are established; to prevent people from not being able to deduce the hexagram images, the "Discourse on the Hexagrams" further explains the images of each hexagram. Although it mentions many, it still does not exhaust all.

且天地間事事物物，生化無盡期，則分類無盡數，名不盡名，紀不盡紀。由其化合而得者，則自其所合之象合之；由其化分而來者，則自其所分之象分之，此在人之推之也。如八卦之象，固以天地水火風雷山澤之物名之，而八卦有分合而成者，則將自天地水火風雷山澤之分合而象之也。推之至六十四卦、三百八十四爻，各有所象，有所合，有所分，有所變化，其所得之事物，亦自其象推之，無不知也。

In the space between heaven and earth, all things are constantly being generated and transformed without end, and classification is never fixed. There are endless names and endless records. If something is formed through combination, it should be examined based on the several images it combines with; if something is formed through division, it should be examined based on the several images it divides from. This requires people to seek and infer on their own. For example, the eight trigrams were originally named after actual things such as heaven, earth, water, fire, wind, thunder, mountain, and marsh. However, the eight trigrams can also be combined or divided to form new trigrams. Therefore, one must examine the combination and division of these eight elements to derive new images. This process continues through the sixty-four trigrams and the 384 lines, with each trigram and line having its own image, combination, division, and transformation. From these, one can infer all things, and nothing is beyond understanding.

故易象以簡象繁，以少象眾，由其本推之，可無盡也。夫乾坤之名，與六十四卦之名，名其象耳，不可泥於物；物不止此名，而象則同。如陰陽之為物，可千萬以至無盡，而象同於兩儀；五行亦然，九宮亦然。凡同此氣數，同此生成者，皆同此象，或事或物，或隱或顯，或神或形，或過去，或未來，皆同在象中，皆得推而類之也。故象者象氣數也，非象物，物從而象之耳。故在□之卦曰乾曰天，不過名其卦而舉天以象之，非謂以□象天已也。其它皆作如是觀。

Therefore, the imagery used in the Book of Changes is concise yet comprehensive, using few symbols to represent many things, and from the fundamental principles, it can be extended endlessly. The names "Qian" and "Kun," as well as the names of the sixty-four hexagrams, are merely names given to the "image" (xiang). One should not be rigidly attached to a particular physical object; physical objects are far more numerous than these names, yet their images are the same. For example, yin and yang as physical entities can be countless and infinite, yet their image is unified under the two principles (two yin and yang). The Five Phases (Wu Xing) and the Nine Palaces (Jiu Gong) are also like this. Whatever has the same qi and number, and is generated in the same way, belongs to the same image—whether it is an event or an object, whether it is hidden or manifest, whether it is an invisible spirit or a tangible form, whether it has already occurred or is yet to come, all are included within the image and can be inferred by category. Therefore, the "image" (xiang) represents qi and number, not a specific physical object; physical objects are merely included within the image. Therefore, referring to the hexagram "□" as "Qian" or as "Heaven" is merely giving it a name and using "Heaven" as an image for it; it does not mean that "□" can only be used to image Heaven. All other hexagrams should be viewed in the same way.

伏羲作卦，以象天地萬物，而自無之有，自始至終，無不包舉。所制卦象，初不必皆有其物也，而物之生成者自合焉；初不必皆有其事也，而事之遷變者自孚焉。蓋本於氣化而推之也。合而言之，則卦有物；分而言之，物自物，卦自卦。且卦簡而物事繁，一卦不止一物一事也。故言物以象卦，言事以名卦，為自未達本，不可盡也。必由卦以象物以名事，而後推之無盡，所謂由本以及末也。

Fuxi drew the trigrams to symbolize the universe and all things: from 'nothingness' to 'existence', from beginning to end, nothing is beyond its scope. At first, the trigrams were not necessarily each corresponding to a specific object, yet naturally all things generated by heaven and earth correspond with them; nor were they necessarily each corresponding to a specific event, yet naturally all changing affairs of mankind correspond with them. This is because the trigrams originally derived from the transformation of qi. In summary, the trigrams contain things; when separated, things are things and trigrams are trigrams, and they are not equivalent. Moreover, since there are few trigrams but many things and events, one trigram encompasses far more than one thing or event. Therefore, using specific objects to compare with trigrams, or using specific events to name trigrams, is like seeking the root from the branches, and can never be complete. One must instead start from the trigrams to symbolize things and to name events, then one can derive endlessly, which is called 'from the root to the branches'.

伏羲首制八卦，以象天地水火風雷山澤，而天下之物與事未可盡也，乃重之以極其變，變之以通其化。變化既生，其用乃宏，而八者重之為六十四，六者重之為三百八十四，此皆本於八卦之變、三爻之化而成者也。卦雖盡於六十四，而卦之用未盡；爻雖盡於三百八十四，而爻之用無窮。以其變化之率言之，則適止於六十四卦、三百八十四爻也。

Fuxi first created the Eight Trigrams to represent Heaven, Earth, water, fire, wind, thunder, mountain, and marsh. However, the things and events in the world are far more than these eight can fully encompass. Therefore, he overlapped the three-line trigrams in pairs to exhaust all possible changes. Furthermore, within these changes, he sought unity and connection to understand the generation and transformation of all things. Once change began, the function of the trigrams became vast: the Eight Trigrams overlapped to form the sixty-four Trigrams, and the three lines combined to form the 384 lines. All of these originated from the transformation of the Eight Trigrams and the change of the three lines. Although the trigrams stop at sixty-four, their use is never exhausted; although the lines stop at 384, their use is endless. However, in terms of the fixed pattern of change, it just so happens that the number stops at sixty-four trigrams and 384 lines.

蓋卦之為象三，以象天地人，各有陰陽，乃重之為六爻。六爻者，體用俱備，陰陽咸具之卦也，故卦成於六爻，天地人也。八卦之爻皆六，分陰分陽，而天地之氣以見。由六爻之變，而八卦成六十四卦，四十八爻成三百八十四爻，此皆自本推之末也。天地生成，自少而眾；人物生化，自簡而繁。雖有終始之殊，究無氣數之異，故八者變為六十四，四十八者變為三百八十四，皆自氣數之分合者也。

The basic structure of a hexagram consists of three lines, used to represent the three categories of heaven, earth, and humanity, known as the "Three Principles." Each of these three principles has both yin and yang aspects, so they are doubled to form six lines. A hexagram with six lines has both form and function, and includes both yin and yang, so it is said that a hexagram is completed through the six lines, and what is formed is heaven, earth, and humanity. After the eight trigrams are overlapped, each trigram becomes a hexagram with six lines. Within the six lines, yin and yang are differentiated, and the energies of heaven and earth are thus revealed. Through the movement of the six lines, the eight trigrams expand into sixty-four hexagrams, and forty-eight lines expand into three hundred and eighty-four lines. All of this is a process from the fundamental to the detailed. The generation of heaven and earth proceeds from few to many; the generation of people and things proceeds from simple to complex. Although there are differences in the order of beginning and end, the principle of qi and numbers remains the same. Therefore, eight trigrams become sixty-four hexagrams, and forty-eight lines become three hundred and eighty-four lines, all arising from the division and combination of qi and numbers.

氣數分合，有綱有紀，有起有止；卦之與爻，有統有屬，有錯有綜，以象之也。八卦之分變而成六十四，由其卦象之推移可見者也。一卦所變為八，八八為六十四，故八卦為綱也。四十八爻之變為三百八十四爻，其象亦同，由卦之象見之也。蓋爻者卦之支體，卦變則爻隨之。爻始於□、□，即兩儀也。

The division and combination of qi and numbers are not chaotic: there is a main principle, order, a beginning, and an end. The relationship between hexagrams and lines is similar: there are those that are overarching, those that are subordinate, those that are "wrong" (yin and yang exchanged), and those that are "complementary" (up and down reversed). These relationships are used to take symbolic meanings. The eight trigrams differentiate into sixty-four hexagrams, and this can be seen from the transformation of the hexagram images: each hexagram transforms into eight trigrams, and eight multiplied by eight equals sixty-four, so the eight trigrams are the main framework. Similarly, the forty-eight lines transform into three hundred and eighty-four lines, following the same principle, which can be seen from the hexagram images. Because lines are the limbs of the hexagram, when the hexagram changes, the lines also change. Originally, the lines had only two forms: the yang line "—" and the yin line "--", which are the two yin and yang lines.

積爻為卦，不離兩儀，故爻之變不出於□、□之推往移往復。卦以爻成，故爻變而卦亦隨之。以卦言，則爻隨卦變；以爻言，則卦以爻變，實則皆氣數之變也。如八卦自□變，而□自成，則由□變者，莫不由變也。六爻成卦，六位成章，故卦有六變，□六變，而成八卦，即□、□六八之數，合之為四十八爻。因其六位之易，而自有□之體。

The accumulation of lines forms a hexagram, and the materials used in this accumulation never go beyond the two principles, yin and yang. Therefore, the changes of the lines are merely the interaction between yang and yin. Since a hexagram is composed of lines, when a line changes, the hexagram also changes. From the perspective of the hexagram, it is the lines that change with the hexagram; from the perspective of the lines, it is the hexagram that changes due to the lines. In reality, both statements refer to the same thing—the change of qi and numbers. For example, the eight trigrams arise from the change of yang lines, and yin lines naturally follow as a result. Therefore, anything that arises from yang lines must also arise from change. Six lines make up a hexagram, and the six line positions are arranged in an orderly manner, so each hexagram has six layers of change. After six changes, the eight trigrams are formed, which is the product of multiplying six and eight, resulting in a total of forty-eight lines. Because the six line positions can be interchanged, the structure of the hexagram is thereby established.

故以八變。八者，後天之木數，物之初生也，以象生化之序，故八卦之變亦盡於八。以其變化之序言之，則凡□者必變為□，□者變為□。自其三位之爻言之，則其變者自下之爻始，六位之爻亦然。故初變自下之爻，由下遞上，六變而至上位，與其對位本二者合之，則八變也。

Therefore, each palace uses "eight" as the limit for change. "Eight" is the number of wood in the Later Heaven Five Phases, representing the beginning of things, and is used to symbolize the order of generation and transformation. Hence, the changes of the Eight Trigrams also stop at eight. In terms of the order of change, any yang line must change to a yin line, and any yin line must change to a yang line. For a three-line trigram, the change begins from the first line; the same applies to a six-line trigram. Therefore, the first change starts from the first line, proceeding upward step by step, and after six changes it reaches the top line. Adding two more changes, namely "opposite position" (youhun) and "original position" (guihun), the total becomes exactly eight changes.

故有一宮八卦之變象焉。其對位者，如天與地，水與火，雷與風，山與澤，皆正對也，亦陰與陽也。本位者，言返其本主也，如天之歸天，地之歸地，各復其本原，猶陰還陰，陽還陽也。故名對位曰游魂，反位曰歸魂。往者必復，終者仍始之道也，亦由氣至而自致也。故變終於不變，此變之常度也。

Therefore, each palace has eight trigrams' changing forms.the so-called「对位」 refers to the mutual opposition between heaven and earth, water and fire, thunder and wind, mountain and marsh, which are pairs of opposites, that is, the relationship between yin and yang.the so-called「本位」 means returning to its original position, like heaven returning to heaven, earth returning to earth, each returning to its own origin, just as yin returning to yin and yang returning to yang. Therefore, the change of the opposite position is called 「游魂」, and the change of returning to the original position is called 「归魂」. What has gone away must return, and the end is still the beginning. This is the constant way of heaven and earth, and it is the natural result of the qi reaching that point. Therefore, when change reaches its end, it returns to a state of unchange, which is the regular pattern of change.

八卦之變以此而極於八，八八六十四卦，而其變已盡，其氣已極。盡則反始，極則復生，雖有變者，仍還於初，不必更推之也，故卦終於八八，而全易之卦已成矣。爻隨卦動，卦以爻成，卦盡則爻亦盡，卦終則爻亦終，此爻亦盡於八之四十八，而止於三百八十四爻，雖有變者，不更推之矣。夫數本於氣，循環無端，寧有終極？而曰盡者，言其一段也，如以三百六十五日紀一歲也，天地之數皆至是而更轉也，故卦爻盡焉，盡而未嘗盡也。

The changes of the Eight Trigrams stop at eight, for eight multiplied by eight gives sixty-four Trigrams, and at this point the changes have reached their limit, and the energy has reached its peak. When something reaches its limit, it returns to the beginning; when it reaches its peak, it begins anew. Even if there are further changes, they still return to the original, and there is no need to go further. Therefore, the Trigrams end at the number eight multiplied by eight, and the entire Book of Changes is thus complete. The Lines move with the Trigrams, and the Trigrams are formed by the Lines. When the Trigrams reach their limit, so do the Lines; when the Trigrams end, so do the Lines. Therefore, the Lines are also limited by eight multiplied by forty-eight, ending at three hundred and eighty-four Lines. Even if there are further changes, they are not pursued further. In reality, numbers arise from energy, which is cyclic, having no beginning or end. How can there be a true limit? The term "limit" refers only to a particular segment, just as using three hundred and sixty-five days to mark a year—when the cycle of the heavens and earth reaches this point, it simply begins again. Therefore, the Trigrams and Lines have a limit, but this "limit" is not a true exhaustion.