The two energies push and transform each other, naturally giving rise to an orderly sequence.

八卦自乾坤而成，六十四卦自八卦而變，其義人盡知之；而其所以成、所以變者，人或未之知也。本來天下之物物事事，莫外二氣之推蕩所成所變。二氣之推蕩自在流行，自然生化，與天地間一切物事自相分合，實氣之自至，非有為主宰之、驅策之也。其氣自太極，而兩儀、而四象、而八卦，自生自成，莫之為而為，莫之致而至者也。而有其序焉，有其位焉，有其時焉，有其類焉，非漫然無章、雜然並陳者。故其生化不相害，推移往復不相亂，是則謂之道。

The Eight Trigrams are formed from the Trigrams of Heaven and Earth, and the sixty-four Trigrams are generated from the Eight Trigrams; this is something everyone knows. However, few understand why they are formed and why they change. In fact, all things in the world cannot escape the generation and transformation caused by the mutual interaction of yin and yang energies. The movement and transformation of these two energies occur naturally and spontaneously, giving rise to the generation and differentiation of all things in the world, which naturally come together and separate. This process is purely the result of the energy reaching that stage on its own, without anyone directing or driving it. This energy originates from the Taiji (Supreme Ultimate), giving rise to the two principles (yin and yang), then to the four images, and finally to the Eight Trigrams. It develops and forms itself naturally, without anyone making it happen or prompting it. Yet, it has order, direction, seasons, and categories, and is not chaotic or disorderly. Because of this, its generation and transformation do not interfere with each other, and its movement and return do not become confused. This is called the "Dao."

道猶路也。路有自至，有近有遠，有水陸舟車之宜，有關山驛旅之便，各不亂也，故行者利之，居者安之。天地之生化亦如是也：有其跡之可驗也，有其名之可紀也，有其外之可度、內之可測，大之可計，小之可數，雖繁而不雜，多而不亂者，有一定不易之統緒也。

"The concept of 'Dao' originally refers to a path. Each path leads to its proper destination, some being near, some far; some are suitable for water travel, some for land travel; some require boats, some require carts. Along the way, there are passes, mountains and rivers, as well as inns and relay stations, all arranged in an orderly manner without confusion. Thus, travelers find convenience and residents find stability. The generation and transformation of heaven and earth are also like this: there are traces that can be verified, names that can be recorded, external aspects that can be measured, internal aspects that can be inferred, large things that can be calculated, small things that can be counted. Although dense, they do not contradict each other; although numerous, they do not become disorderly. This is because there is a fixed and unchanging order within them."

雖大而無外，細而無內，莫不可擬以象，可繫以辭者，以其永久不息，終古如一也。故得其本，知其末；明其往，知其來；推其初，知其終；質其顯，知其隱，如合符契也。彼八卦固自乾坤出，而六十四卦則自八卦生，其序至明，其位至清，其推移變化，至一不二。故觀一足以知十，察此足以見彼，祇在就其象而核之耳。

It is vast without an outer boundary, and minute without an inner boundary; nothing cannot be compared with the "image" or explained with the "words" of the text. This is because it never ceases, remaining constant throughout the ages. Therefore, grasping the fundamental principle allows one to understand the details; knowing the past enables one to foresee the future; deducing the beginning allows one to know the end; examining the obvious reveals the hidden, just as a symbol perfectly matches its counterpart without the slightest discrepancy. The Eight Trigrams originally arise from the trigrams Qian (Heaven) and Kun (Earth), and the sixty-four trigrams come from the Eight Trigrams. Their sequence is extremely clear, their positions very distinct, and the principles of their transformation remain consistent without wavering. Thus, seeing one is enough to know ten; examining one side is enough to see the other. The key lies only in verifying through the trigrams' images.

如乾坤之變，而離坎六卦成，祇由其卦象，索其為乾為坤者幾何，則知其出自乾抑坤，或乾坤之和，或乾之幾而坤之幾，皆能瞭然矣。六十四卦之成於八卦也亦然：除八卦外，為五十六卦，屬於乾者幾，坤者幾，其它者幾，或由乾之消、坤之息，或由坤之進、乾之退，或其它之消息進退，皆可於卦象中見之。

For example, when the trigrams Qian and Kun change once, the other six trigrams, Kan and Li among them, are formed. By examining the hexagram's structure and counting how many lines belong to Qian and how many belong to Kun, one can clearly see whether the hexagram originates from Qian or Kun, or whether it is a combination of both, and in what proportion. The same principle applies to the sixty-four hexagrams generated from the eight trigrams: besides the eight original trigrams, there are fifty-six others. By checking how many lines belong to Qian, how many to Kun, and how many to the other trigrams, one can determine whether these hexagrams arise from the decline of Qian and the growth of Kun, or from the advance of Kun and the retreat of Qian, or from the waxing and waning of the other trigrams. All of this can be clearly seen from the hexagram's structure.

故卦之變成於八卦，始出於兩儀，有一定之序者也，而合於一太極焉。卦雖有八，有六十四；爻雖有六，有四十八，有三百八十四，合之亦一太極耳。以太極銜兩儀而行，卦爻隨二氣以變，初無他物也。雖卦有象，爻有名，或所象所名無盡，總不外二氣之消長生化耳。故物物事事雖不可窮，卦爻有可盡者也。明乎此義，則知卦爻之所自成也。

Therefore, the changes of the hexagrams arise from the Eight Trigrams, but originally they began from the Two Principles. There is a definite order, and ultimately they all converge into the Supreme Ultimate. Although the hexagrams may be eight or sixty-four, and the lines may be six, forty-eight, or three hundred and eighty-four, altogether they do not exceed the Supreme Ultimate. The Supreme Ultimate carries the Two Principles in its operation, and the hexagrams and lines change along with the movement of yin and yang. There is nothing else. Although the hexagrams have images and the lines have names, the images and names are numerous beyond count, yet they all remain within the ebb and flow of the two principles. Therefore, although things are endless, the hexagrams and lines are limited and can be counted. Understanding this principle, one can know how the hexagrams and lines are formed.

伏羲之卦象，為象氣之初行，道之始用。天地既奠，人物以生，其數初見，其象漸成，其卦之序有異於文王之易，故名之為先天卦象。然既有象，是已有生成可言；既有物，是已有名類可辨，非如太極之先天尚無所有者。不過伏羲之創作時，為物也簡，為名也寡，所象者氣之所至，非有是物而後象以卦，乃有是氣而後象之。其後因其象而得其物，物乃備，是伏羲之卦在物先也。非先天，乃先物，以物言之為先天耳。

The hexagrams of Fuxi represent the initial stage when qi begins to move and the Dao starts to function. After heaven and earth have become stable, human beings and things come into being, and numbers first appear, leading to the gradual formation of images. Its sequence of hexagrams differs from that of King Wen's Book of Changes, hence it is called "Earlier Heaven Hexagrams." However, since there are already images, there is already something to talk about in terms of generation; since there are already things, there are already categories and names to distinguish them. It is not like the true "Earlier Heaven" stage of the Taiji, which is completely empty. At the time Fuxi created the hexagrams, things were still simple and names were few. What he represented was the movement of qi, not that there was already such a thing before using hexagrams to represent it. Rather, it was the presence of that qi that led to the creation of the hexagrams. Later people followed the hexagrams to seek out corresponding things, and thus things became complete. This shows that Fuxi's hexagrams came before things. Therefore, they are not "before heaven," but "before things." It is only from the perspective of things that they are called "Earlier Heaven."

至其制卦，純本於氣，而其所重，純在於象，初未致其用以極其變也。六十四卦、三百八十四爻，雖隨時皆成，亦就其本體變化象之，未及其變體之用。蓋將以示天地之生成，人物之生化，而模其形，指其途，以教於眾，使知天之為天，地之為地，人物之為人物而已，初未演其用也。故其卦象，猶懸則以示民，如天之文，地之理，其象顯而變化有度，其義明而往來有紀，乃發天道之端，而立人道之極，故為易之始基。

As for the method of constructing hexagrams, it is entirely based on qi; what he emphasized was entirely the image. At that time, it was not pursued to the practical level to exhaust all its variations. Although the sixty-four hexagrams and the three hundred and eighty-four lines were already present at that time, they were only taken as images based on the fundamental changes, without involving the application after transformation. His intention was to show how heaven and earth were generated, and how people were born and transformed, to depict its form, to indicate its path, and to teach people to understand why heaven is heaven, earth is earth, and people are people. He did not elaborate on its specific applications. Therefore, his hexagrams are like hanging a set of rules for the people to see, like the patterns in the sky and the patterns on the earth: the images are clear and the changes have definite measures, the meanings are clear and the movements have definite order, thus opening up the beginning of the heavenly way and establishing the standard for human conduct, and thus becoming the initial foundation of the Book of Changes.

而後世諸易之所本也。此卦象之名先天，與文王之名後天者，一屬體，一屬用，一屬成則，一屬變例，其同異自其序可見者也。夫伏羲既立卦矣，寧不盡推其變而極其用哉？則由為時太古，文字未傳，初無遺者。後之可考者，有連山歸藏之易，即文王所資以作後天卦序者也。卦本無異，以序而異；伏羲之卦，留其本則，而文王之卦，通其變例，其用不同耳。

Later interpretations of the Yi all take it as their basis. This set of hexagrams is called "Earlier Heaven," while King Wen's set is called "Later Heaven." One belongs to the "essence," and the other to the "application"; one represents a fixed principle, and the other a flexible regulation. Their differences and similarities can be seen from the order of the hexagrams. Since Fuxi established the hexagrams, could he not have explored their transformations thoroughly and fully utilized their functions? It is only because the era was too ancient and writing had not yet been passed down that nothing was left behind. What later generations could still observe were the two other Yi texts, the Lianshan and Guicang, which were precisely the basis upon which King Wen created the Later Heaven hexagram order. The hexagrams themselves are not different; what differs is their sequence. Fuxi's hexagrams preserve the fundamental principles, while King Wen's hexagrams convey the flexible regulations, differing only in their application.

然卦始自伏羲，則習易必先成則，以探其本，本達而後可言用也。故卦之用，必從文王；而卦之習，必溯伏義。伏羲之卦為後聖所採，以制作文物者多矣，其氣所象不易故也。物有生化，氣永存也；物有成壞，氣常在也。故言物不可盡，言氣則有度有紀。伏羲之卦名先天者，以依於氣而先於物也，非太極之先天也。

However, since the trigrams were first created by Fuxi, studying the Book of Changes must begin with mastering this established system in order to explore its fundamental principles. Only when the fundamentals are understood can one talk about applying them. Therefore, when discussing the use of trigrams, one must follow King Wen; when discussing the study of trigrams, one must trace back to Fuxi. There are many examples in later generations of sages who adopted Fuxi's trigrams to create various rites and artifacts, because the qi represented by Fuxi's trigrams remains unchanged. Things are born and transformed, but qi remains constant; things are formed and decay, but qi remains ever present. Therefore, talking about "things" is endless, but talking about "qi" has degrees and order. Fuxi's trigrams are called "Earlier Heaven" because they are based on qi and precede things, not because they refer to the empty state of the Taiji.

伏羲之卦，既屬先天之象，則其卦所象，為氣而非物，其繫物名者，多後人為之辭也。且卦少物眾，不可以物象者，則別名之，要皆非伏羲所名也。不獨六十四卦如是，八卦亦如是。故□為天而名乾，□為地而名坤。□者，卦象氣者也；天地者，象物者也；乾坤者，別名者也。別名亦有其義，為指事或會意；物名則象物者也。如巽之為風又象木，離之為火又象日，皆一物不可盡其象，而後名之以巽以離；然巽與離之義，不訓為風木及火日也。是則別名非象物者也。且古人尚有他名者，至文王始釐定今名，以其知者眾，而含義廣也。故習易時先知其名，與卦有同異，不可執名以求之也。

Fuxi's trigrams belong to the Earlier Heaven imagery, so the trigrams represent qi rather than physical objects; the practice of attaching concrete names to them is mostly a later addition. Moreover, since there are few trigrams but many physical objects, any trigram that cannot be represented by a single physical object will take another name. These names were not determined by Fuxi. This applies not only to the sixty-four trigrams but also to the eight trigrams. Therefore, the symbol 「□」 represents heaven and is named "Qian," while the symbol 「□」 represents earth and is named "Kun." These two symbols represent qi; "heaven" and "earth" refer to physical objects; "Qian" and "Kun" are separate names. These separate names also have their own meanings, either being indicative or symbolic. The actual names of physical objects are those that directly represent the objects themselves. For example, "Xun" represents wind and also symbolizes wood, while "Li" represents fire and also symbolizes the sun. This is because a single physical object cannot fully capture all the meanings, so separate names like "Xun" and "Li" are used. However, the meanings of "Xun" and "Li" cannot be interpreted as wind and wood or fire and sun. This shows that these separate names are not used to represent physical objects. Furthermore, ancient people had other names for these trigrams, and it was only King Wen who standardized the current names, as these names are widely recognized and have broad meanings. Therefore, when studying the Book of Changes, one should first understand that the names of the trigrams may be similar or different from the trigrams themselves, and one should not rigidly focus on the names to interpret the meanings of the trigrams.

欲明卦之象，必求象之變化在爻位也。或陰或陽，必自其卦爻求之，始得伏羲之卦義也。伏羲之時，初無文字，所具者卦爻之畫而已，以畫之進退升降，知氣之消長往復；以畫之變化遷移，知氣之生成同異。故習之者，必列其卦爻以按之也。伏羲卦序以八卦為綱，每卦屬者共八，明自其本卦所生化也。然每卦之間，有連貫之氣，非截然獨立者也。如乾坤之卦，固相連而成變化者，非祇在本卦綱下也，其它亦然，故必會通而求，則其序可見。

In order to understand the images of the hexagrams, one must seek their changing images through the lines. Whether a line is yin or yang must be determined by the line drawings of the hexagram, in order to grasp the original meaning of Fuxi's establishment of the hexagrams. In Fuxi's time, there were no written characters, only the line drawings of the hexagrams. From the movement and changes of the lines, one can understand the waxing and waning of qi; from the transformation and migration of the lines, one can understand the generation and differences of qi. Therefore, those who study must arrange the hexagram lines one by one for comparison. Fuxi's sequence of hexagrams takes the Eight Trigrams as the main framework, with each group containing the Eight Trigrams, indicating that these eight trigrams are all generated from the main trigram of the group. However, there is a continuous flow of qi between the groups, and they are not isolated or independent of each other. For example, the hexagrams Qian and Kun are inherently connected and generate changes together, not merely existing within their own group. The same applies to the other groups. Therefore, one must integrate and understand them as a whole, so that the order of the hexagram sequence becomes clear.

此八宮之外有圓方圖二者，以其連貫生化自成方圓，象天地之氣自相統屬也。圓者象天，方者象地，方在圓中，象天之包地。其卦則象天上地下之物，及天地間之物也，象其氣之周流終始，非限於何物也。故觀伏羲之卦，先八卦之變化，次六十四卦之推移，次六十四卦本宮之序次，及方圓各圖，以求其所以生化之跡，以驗其所由周行之氣，因以見天地生成之序，人物生化之次，皆可明瞭。則於伏羲作卦之意已知，而全易卦象之義可得。既得其本，再求其用；既得其則，再極其變，而後及於文王之卦，其終始可一覽而盡矣。是則習易者所當知也。

This is why, in addition to the eight trigrams, there are two other forms of diagrams, namely the circular diagram and the square diagram. Because the continuous transformation and generation of the trigrams naturally form both the square and the circle, which are used to represent the relationship of mutual inclusion between the energies of heaven and earth. The circle represents heaven, and the square represents earth. The square diagram is placed within the circular diagram, symbolizing that heaven encompasses earth. The trigrams in the diagram represent both things on heaven and earth and things between heaven and earth. They symbolize the continuous flow and cycle of energy, not limited to any specific object. Therefore, when studying the trigrams of Fuxi, one should first examine the changes of the eight trigrams, then the progression of the sixty-four trigrams, followed by their order within each palace, and finally the circular and square diagrams. From these, one can trace the traces of their generation and verify the circulation of energy. In this way, one can see the order of generation of heaven and earth, the levels of transformation of human beings, and everything becomes clear. In this manner, the intention of Fuxi in creating the trigrams becomes known, and the meaning of the trigrams in the Book of Changes is fully understood. Having grasped the fundamental principle, one can then seek its application; having understood the principle, one can further explore its variations. Then, one can proceed to study the trigrams of King Wen, and from beginning to end, everything can be clearly understood. This is the proper order that students of the Book of Changes should know.

卦之變化，自其本宮所生者，則其本氣所變也；自他宮生者，則間他氣所變也。如乾宮卦，自乾所變，若坤宮有乾卦所生者，則二宮之氣共化也。八宮皆相通，唯乾與坤，離與坎，震與巽，艮與兌，皆相對，半屬本宮，半屬對宮，以氣之相當，而變之必至也。如乾三變則受坤氣，四變以下，皆坤卦之來化，此定例也。

The transformation of hexagrams, if they arise from their own palace, is a result of the energy of that palace itself. If they arise from another palace, then they are a mixture of the energy from that other palace. For example, the hexagrams of the Qian palace come from Qian. If a hexagram appears in the Kun palace that originates from Qian, then it is the result of the combined energies of both the Qian and Kun palaces. The eight palaces are all interconnected, but there are four pairs of opposing palaces: Qian and Kun, Li and Kan, Zhen and Xun, and Gen and Dui. Therefore, each palace's transformed hexagrams consist of half from its own palace and half from its opposing palace, because the energies are equal. For example, the Qian palace begins to receive the energy of Kun from the third transformation onward, and from the fourth transformation onward, it is entirely influenced by the energy of Kun. This is a fixed pattern.

唯最末仍返本宮，以歸於本原，明氣化之終歸始也，此本宮變化之序也。方圓各圖，則以卦為主，凡其卦之氣屬某者，不問其宮，與各卦同序。如乾卦凡屬乾者，不問在乾宮與別宮，皆列於一序，交錯各宮以成卦序。因天地之氣，流行八方，本無界限，氣之所至，則卦象見焉。以此可氣之周流，不限本宮，而天地間之物，不出兩氣之生化分合也。故豎之則成行，橫之則成列，圓之則成環，方之則成塊；氣之所至則成形，象之所見則成物，初無可泥也，不過行有度，至有紀，不相亂耳。

Only the last transformation returns to its original palace, going back to its own origin, to indicate that the process of transformation ultimately returns to the beginning. This is the order of transformation within the original palace. As for the square diagram and the circular diagram, they instead take the "hexagram" as the main focus: regardless of which palace a hexagram originally belongs to, it is grouped together with other hexagrams of the same type. For example, the hexagram Qian (Heaven): all hexagrams belonging to the category of Qian, whether they appear in the Qian palace or another palace, are arranged in the same sequence. Thus, the hexagrams from different palaces interweave to form a new sequence of hexagrams. This is because the vital energies of heaven and earth flow through the eight directions, without any boundaries; wherever the energy goes, the hexagram appears there. From this we can see that the energy circulates throughout, not restricted by its original palace. Likewise, the physical things in the world cannot escape the generation and combination of the two energies, yin and yang. Therefore, looking vertically, it forms rows; looking horizontally, it forms columns; circling around, it forms rings; and looking in square form, it forms blocks. Wherever the energy goes, form is created; wherever the image appears, things are formed. Originally, it cannot be confined to a single perspective. However, its movement follows a certain measure, and its arrival is governed by order, so there is no confusion among them.

故卦相象錯綜，氣數往來，天地之大，萬物之眾，無一非所生化者，則無在不有其氣也。觀乎伏羲卦象，知氣之所化，而萬物生成；知氣之所行，而萬物消長。氣至有象，氣行有序；象徵其物，序徵其數。高下大小，遠近來去，莫不可征，則天地人物，生化變易，莫不可知者矣。故曰卦象，言卦以象之也。天地尚在象內，況其下者乎？故物物事事，有名無名，總在卦中，就象驗之，無遁情矣。故易者，通天地之造化，明天下之亹亹者也。

Therefore, the various hexagrams take their images from each other, either inverting or combining them, with the flow of qi constantly changing; the vastness of heaven and earth and the multitude of things are all generated and transformed by this qi, and there is no place that does not contain this qi. Observing the hexagrams of Fuxi, one can understand how qi transforms, thus knowing how all things are generated; knowing how qi moves, one can understand how all things increase and decrease. When qi arrives, there is an image; when qi moves, there is an order; the image can confirm what kind of thing it is, and the order can confirm what number it corresponds to. High and low, big and small, far and near, coming and going, none of these cannot be verified, so the generation, transformation, and change of heaven, earth, and human beings can all be understood. Therefore, it is called "hexagram images," meaning using hexagrams to represent things. Even heaven and earth are within the scope of representation, let alone things below heaven and earth. Therefore, all things, whether named or unnamed, are included in the hexagrams. By examining the hexagram images, nothing can escape verification. Therefore, the study of the Book of Changes is a discipline that comprehends the creation and transformation of heaven and earth, and elucidates the principle of ceaseless diligence in the world.

易象莫先於伏羲之卦，由八而六十四，綱舉目張，條分縷晰；有體有用，有正有變。其體不見而用昭，其變無盡而正一；必從其生自化，而求其推移之跡；必由其所位所行，而求其氣數之類，非一覽可盡者也。奇正錯綜，參伍變化；其義詳於象，昭於辭，而引申於傅，不待贅述。茲所欲為之言者，卦象之所自成，伏羲文王之易之所自異而已。

The study of the images in the Book of Changes has no earlier origin than the trigrams of Fuxi. From the eight trigrams, the sixty-four trigrams were derived. When the main framework is established, the details unfold clearly, like threads neatly arranged. Within this structure, there is both form and function, correctness and transformation. Its form is not apparent, but its function is evident; its transformation is endless, yet its correctness remains consistent. To study it, one must follow its own development and evolution to trace its changes. One must also rely on its position and direction of movement to determine the categories of its qi and numbers. It is not something that can be fully understood with a single glance. The odd and the correct interweave in a complex manner, changing in groups of three and five. These principles are already thoroughly explained in the trigrams and in the line statements, and further elaborated in the Commentaries on the Book of Changes. Therefore, there is no need for me to repeat them. What I wish to discuss here is only how the trigrams were formed, and the differences between Fuxi's Book of Changes and King Wen's Book of Changes.

夫卦而言象，有所象也；非為物象，物不可盡舉也；非為事象，事不可盡稱也；蓋象夫氣化，而仿於天地造化之機者也。天地造化，無大小多寡，莫不出入於機；機動則生，機轉則化；機散則消，機靜則息；皆依於大氣，符於真宰，而包乎萬物萬事，立於至中至一者也。故卦有所始焉，始於太極；有所仿焉，仿於河洛之圖；皆自上而下，自一而眾；自神而形，以少御多，以虛類實者也。卦名虛也，卦象少也。

When discussing hexagrams and speaking of "images" (xiang), it means they indeed represent something. What they represent is not specific physical objects, since physical objects are endless; nor are they specific events, since events are countless. What they represent is "qi transformation" (qi hua), which is modeled after the principle of creation and transformation in heaven and earth. All creation and transformation in heaven and earth, regardless of their size or number, originate from and return to this principle. When the principle moves, there is birth; when it changes, there is transformation; when it disperses, there is destruction; when it is still, there is cessation. All these depend on that great atmospheric force, conform to the true sovereign, encompass all things, and establish themselves in the most central and unified position. Therefore, hexagrams have their beginning, starting from the Taiji; they have an object they imitate, which is the Yellow River Chart and the Luo Writing. All these proceed from above to below, from one to many, from the formless divine to the tangible form, using the few to control the many, and the empty to encompass the real. The names of hexagrams are originally empty, and their images are originally few.

虛則所類不滯於物，少則所徵不失其中。故易之道，神而明；易之用，大而化，非聖人不能知其故，而立其義也。夫天地萬物，莫不自無入有，自一而眾；故象造化者亦如之，河洛之圖，太極之象，皆如是也。河圖之數，自一至十；洛書之數，起一終九；太極之數，由一生二；八卦之數，自一化八，其義同也。

Because it is empty, it can unify all things without being stuck to any particular object; because it is few, it can verify things without losing the middle and upright. Therefore, the principles of the Book of Changes are profound and clear, and its functions are vast and nurturing; only a sage could understand its reasons, and no one could establish its meanings. All things in heaven and earth have no instance that does not proceed from "nothingness" to "being," and from "one" to "many." Therefore, the things used to represent creation follow the same pattern: the diagrams of the Yellow River Chart and the Luo Writing, the image of the Supreme Ultimate, all conform to this. The numbers of the Yellow River Chart run from one to ten, the numbers of the Luo Writing start at one and end at nine, the numbers of the Supreme Ultimate go from one to two, and the numbers of the Eight Trigrams arise from one to eight—what they discuss is actually the same principle.

故大氣之動，而為兩儀；二氣之合，而成五行；二五之化，而分九宮；其變愈多，其物愈眾，而莫不自一始也。河洛之圖，雖不見生化之序，而其方位與所得之數，已可明其所始矣！積之則成物，分之則化生，由數證之，可知其氣。故河圖之數，一六在北，二七在南；三八居東，四九居西；五十在中。此五行由二氣之合化者也。

Therefore, that great mass of qi moved and became the two principles, yin and yang; when the two principles of yin and yang combined, they formed the Five Phases; and when yin and yang together with the Five Phases transformed, they differentiated into the Nine Palaces. The more they changed, the more things came into being, yet none of them was not originated from the "one." The diagrams of the Yellow River Chart and the Luo Writing, although they do not directly indicate the order of generation and transformation, can already reveal the starting point of generation and transformation through their directions and the numbers assigned to them. When numbers accumulate, they condense into physical forms; when they disperse, they generate life. By using numbers as evidence, one can understand the nature of qi. Therefore, the numbers in the Yellow River Chart are: one and six in the north, two and seven in the south, three and eight in the east, four and nine in the west, and five and ten in the center. This is the pattern showing how the Five Phases were formed from the combination of the two principles of yin and yang.

洛書之數，一九三七居四正，二四六八居四隅，五在中宮。此九宮由二五之分化者也。數止此數，物已變易，則可知物雖殊而氣猶同，名雖萬而機猶一也。河圖象其初生，數定於位，各有所合；洛書象其既化，數之往復順逆，錯行不已，以適其方。故河圖之位，至洛書而變也。

The numbers of the Luo Shu are arranged as follows: one, nine, three, and seven are placed at the four cardinal points, while two, four, six, and eight are located at the four corners. The number five is in the Central Palace. This is the pattern of the Nine Palaces formed by the differentiation of yin and yang and the Five Phases. The numbers remain the same, but the things have changed; thus, although things are diverse, their qi remains the same, and although there are countless names, the "machine" remains one. The He Tu represents the initial stage of all things, with numbers fixed in their respective positions, each having its own complement. The Luo Shu represents the stage after transformation, with numbers moving forward and backward, in order and reverse, interweaving continuously to adapt to their respective positions. Therefore, the directional arrangement of the He Tu changes in the Luo Shu.

洛書之數，為天下之大化；其縱橫往來，皆極變易之觀；其所象者多，故所用者廣；其所生化者眾，故所變易者神。其數以一居北，九居南，三居東，七居西，已異河圖；而一之左，非二而為八；九之次，非八而為二，互易其位，以成其用，更殊於河圖者矣。蓋以此遷移，生出變化，而見天地間造化之妙，御用之神爾。

The numbers of the Luo Book represent the greatest transformation in the world: they move both horizontally and vertically, pushing the image of change to its extreme. Since they symbolize many things, their applications are extensive. Because they generate numerous transformations, the changes appear marvelous. Its numbers are one in the north, nine in the south, three in the east, and seven in the west, which is already different from the He Tu. Moreover, the number one's left is not two but eight, and the number nine's next is not eight but two. They have exchanged positions to fulfill their function, thus differing even more from the He Tu. It is precisely through such movement and transformation that various changes arise, revealing the subtle workings of heaven and earth and the marvelous application of their principles.

故其數無論如何數之，合三數皆十五；去中數則自成各數，得中數則同一數；以中五執生化之樞機，為萬有之立宰也。故數之變不離十五，而其中不離於五，十亦五所生也。天下萬物自五行生，而五行自二氣合化，此數之始終也。河洛之言數者如此，而氣在數中；太極則以氣寓數者也。

Therefore, the numbers in the Luo Shu, no matter how they are counted, whenever three numbers along a line are added together, the total is always fifteen. If the central number is removed, each direction has its own original number; if the central number is added back, all directions become the same number. This is because the central number "five" controls the mechanism of generation and transformation, acting as the master of all things. Therefore, changes in numbers cannot be separated from fifteen, and the core of fifteen cannot be separated from "five," for even the number ten comes from "five." All things in the universe arise from the Five Phases, which themselves come from the combination of yin and yang energies. This is the beginning and the end of "number." The Yellow River Chart and the Luo Shu discuss numbers in this way, and qi is contained within numbers; as for the Taiji, it is the embodiment of numbers within qi.

太極以兩儀互抱而周行，一消一長，一盈一虛；氣之始終，即可見數之進退，奇陽而偶陰也。陽者左行，陰者右行；二者不可截然兩途也，必參伍而後見其變化之用，故仍當合河洛之數以觀之。此卦象之數，必仿於河洛，而同於太極。太極明氣之升降，河洛明數之乘除，卦則合二者而象之也。

The Taiji is the mutual embracing and flowing of the two principles (Wu Wei): one decreasing and one increasing, one full and one empty. From the beginning and end of the qi, we can see the advance and retreat of numbers—odd numbers belong to Yang, even numbers belong to Yin. Yang moves to the left, Yin moves to the right; but these two cannot be entirely separated into independent paths. They must intermingle and interact with each other to demonstrate the function of change. Therefore, they should still be viewed together with the numbers of the He Tu and Luo Shu. This means that the numbers of the hexagrams must follow the patterns of the He Tu and Luo Shu, and also connect with the Taiji. The Taiji explains the rising and falling of qi, the He Tu and Luo Shu explain the multiplication and division of numbers, and the hexagrams combine these two aspects to form their symbolic representations.

是故卦象，其象自虛，而用可實；其數自一，而變可百；其氣自同，而生化可無盡，皆本乎自然者也。言卦象必徵以物，言數必徵以名，言氣必徵以類；是滯也，不知易之為易者也，易豈得而執者哉？故一象之徵，此殊而彼異；一數之合，今是而昨非；一氣之推遷，來如此而往如彼，不相侔也。如懸則以測事物，則可；若謂此即事物也，則不可。

Therefore, the images of the hexagrams: their images are originally empty, yet they can be applied concretely; their numbers are originally just one, yet they can change into a hundred; their qi is originally the same, yet it can generate endlessly — all of these are based on nature. If one insists on taking a specific physical object to ground the images, or a specific term to ground the numbers, or a specific category to ground the qi, then that is 'stagnation', and it shows one does not understand why the Book of Changes is called the Book of Changes — the Book of Changes is nowhere fixed. Therefore, the same image used for verification may be like this here, but different there; the same number used for matching may be valid today but not yesterday; the same movement of qi may be like this when coming, but different when going, and they are not equal. It is acceptable to use the hexagrams as a standard to measure things, but to say that the hexagrams themselves are those things is wrong.

故曰：卦者，卦也；卦之取象，非以物實之也。虛則用大而化，神而明；實則不化不明，故觀象必通其義焉。卦雖此於六十四，其象可盡天下萬事萬物；其數無盡，其氣無窮；由其常，則至中至一；極其用，則至奇至神，此言易所當知也。

Therefore, the "gua" is the "gua"; the imagery of the gua is not filled with concrete objects. It is precisely because it is empty that its function is vast and capable of generating and nurturing, and it is profound and clear. Once it becomes concrete, it can neither generate nor clarify. Therefore, observing the imagery must be understood in terms of its meaning and principles. Although the gua only reaches a total of sixty-four, its imagery encompasses all things under heaven. Its numbers are endless, and its energy has no boundaries. In its normal state, it is extremely upright and focused; when its function is pushed to its extreme, it becomes extremely strange and marvelous. This is something those who discuss the Book of Changes should understand.

伏羲之畫卦也，自八卦始；其初止於三爻，以符於洛書之象；而分為八方，以本於河圖之數；而定為對偶，以推於太極之氣；而立為爻與序，可自其卦位卦體見之也。乾坤之為陽與陰也，其位正對；坎離亦然，以坎為陰中陽，離為陽中陰，由體而進於用也。

Fuxi began with the Eight Trigrams. Initially, they only had three lines, used to correspond with the image of the Luo Writing; they were arranged into eight directions, based on the numbers of the Yellow River Chart; they were established as pairs of opposites, used to infer the Qi of the Taiji; and then the lines and their order were set down—these can all be seen from the directions of the trigrams and their forms. "Qian" and "Kun" represent Yang and Yin respectively, and their positions are directly opposite; "Kan" and "Li" are also like this, because "Kan" contains Yang within Yin, and "Li" contains Yin within Yang, thus already moving from the level of "body" to the level of "function."

故同於乾坤，此四正之卦也。震兌巽艮，分列於旁；由震而兌，為陰消陽長；由巽至艮，為陽退陰升；介乎坎離之間，屬於乾坤之類；各歸其體，各成其用；以符氣之升降，數之乘除，故分列四旁，而為四隅之卦者也。位如河洛，行如太極；賅氣數而分陰陽，以進退而見生化者也。

Therefore, the trigrams Kan and Li are of the same type as Qian and Kun, and these four trigrams occupy the four cardinal positions. The trigrams Zhen, Dui, Xun, and Gen are arranged around them: from Zhen to Dui, it represents a phase where yin energy declines and yang energy increases; from Xun to Gen, it represents a phase where yang energy retreats and yin energy rises. They are situated between Kan and Li, yet in terms of classification they belong to Qian and Kun. Each returns to its own nature and realizes its own function, in accordance with the movement of qi and the operations of numbers, hence they are arranged on the four sides, becoming the four corner trigrams. Their positions are derived from the Yellow River Chart and the Luo Writing, and their movement follows the Taiji; they integrate qi and numbers, distinguishing yin and yang, and manifest generation and transformation through advancement and retreat.

故八卦以陰陽分之，屬陽者四，隨乎乾；屬陰者四，統乎坤；其序則左右也，其行則順逆也；其數則奇偶也，其位則相對與相反也；皆以二氣辨焉，以符太極，而本河洛者也。故卦有序，有行，有數，有位；以明氣之始終，生化之推移，有一定也；以見天地之道，萬物萬事之變遷，有無盡也。

Therefore, the Eight Trigrams are divided according to yin and yang: the four trigrams belonging to yang follow "Qian (Heaven)," while the four trigrams belonging to yin are unified under "Kun (Earth)." Their order is divided into left and right, their movement is divided into順 and 逆, their numbers are divided into odd and even, and their positions are either relative or opposite; all of these are distinguished by the two principles of yin and yang, to conform with the Taiji, and originate from the He and Luo diagrams. Therefore, the trigrams have order, movement, numbers, and positions: this explains that the beginning and end of qi and the transformation of generation follow definite rules; it also reveals that the way of heaven and earth and the changes of all things are boundless.

試就其三畫之卦證之：乾為陽綱，其爻□；其用九，三九二十七，其數奇也。坤為陰統，其爻□；其用六，三六一十八，其數偶也。坎艮震之爻，為乾者一，為坤者二；其數皆二十一，皆奇也，是皆為陽。離兌巽之爻，為乾者二，為坤者一；其數皆二十四，皆偶也，是皆為陰。

Let us use the trigrams to verify this. "Qian" (Heaven) is the trigram of all yang lines; its lines are all yang lines. A yang line is called "nine," so three nines total twenty-seven, which is an odd number. "Kun" (Earth) is the trigram of all yin lines; its lines are all yin lines. A yin line is called "six," so three sixes total eighteen, which is an even number. For the trigrams "Kan" (Water), "Gen" (Mountain), and "Zhen" (Thunder), each has one yang line from "Qian" and two yin lines from "Kun." Calculating their totals, they all sum to twenty-one (nine plus six plus six), which is odd, so these three trigrams are all yang. For the trigrams "Li" (Fire), "Dui" (Lake), and "Xun" (Wind), each has two yang lines from "Qian" and one yin line from "Kun." Calculating their totals, they all sum to twenty-four (nine plus nine plus six), which is even, so these three trigrams are all yin.

陽則從陽而歸乾，故乾為父，震坎艮為三男也；陰則從陰而歸坤，故坤為母，巽離兌為三女也。以數紀之，知其氣所至；以象測之，知其氣所行；故陽卦者，得陽氣而成陽數；陰卦者，得陰氣而成陰數，皆以象見之者也。

Those that belong to the Yang are aligned with Yang and enter into "Qian," so "Qian" is the father, and "Zhen," "Kan," and "Gen" are the three sons. Those that belong to the Yin are aligned with Yin and enter into "Kun," so "Kun" is the mother, and "Xun," "Li," and "Dui" are the three daughters. Using numbers to record them allows one to know the extent of the energy; using images to measure them allows one to know the direction in which the energy flows. Therefore, Yang hexagrams are formed by receiving Yang energy and embodying Yang numbers, while Yin hexagrams are formed by receiving Yin energy and embodying Yin numbers. All of these are revealed through the hexagram images.

卦有相對者，有相反者，有相對兼反者，皆以數見之，既氣之所至也。而必因以位以明之，因序以次之，以象氣之消長進退也。故卦象因位而別，因序而殊。八卦之位，乾坤居上下，相對也，亦兼反；坎離居左右，相反也，亦兼對。

The relationships between trigrams can be either 'opposite' or 'inverted,' or both opposite and inverted. These relationships can be seen through numbers, which reflect the movement of qi. However, it is also necessary to explain them through directions and to arrange them in order, to symbolize the waxing and waning, and the advancement and retreat of qi. Therefore, the images of the trigrams differ according to their directions and vary according to their order. In terms of the directions of the eight trigrams: Qian and Kun are positioned above and below respectively, which is 'opposite' and also 'inverted.' Kan and Li are positioned left and right respectively, which is 'inverted' and also 'opposite.'

此易見者也。若震與巽，則相對而非反也；艮與兌亦然。而震與艮，則相反而非對也；巽與兌亦然。蓋乾之與坤，離之與坎，皆位相當，而爻相反，以陰陽之不同也。震之與巽，艮之與兌，其位固當，其類則別，是陰陽相對而已，不相反也。

This layer is easy to see. As for "Zhen" and "Xun," they are relative but not opposite; "Gen" and "Dui" are the same. "Zhen" and "Gen" are opposite but not relative; "Xun" and "Dui" are also the same. Because "Qian" and "Kun," "Li" and "Kan," have corresponding directions, but their lines are completely reversed, this is due to their fundamental differences in yin and yang attributes. "Zhen" and "Xun," "Gen" and "Dui," although their directions correspond, their categories are different, which is only yin and yang being relative, not opposite.

若震之與艮，巽之於兌，一則陽在下，一則陰在上；一則陽多，一則陰多；其數相反，而其位不相當也，故為氣之升降消息之象者也。由對言之，則為配偶，或怨仇；由反言之，則為侵襲，或退讓。對者多異類，反者多同類；如震與巽，異類也，與艮，則同類；兌與艮，異類也，與巽則同類。

As for "Zhen" and "Gen," and "Xun" and "Dui," one has a yang line below and the other a yin line above; one has more yang lines, the other more yin lines; their numbers are exactly opposite, and their positions are not corresponding, so they are precisely used to symbolize the rising and falling, and the waxing and waning of qi. From the perspective of "opposition," their relationship is either that of spouses or enemies; from the perspective of "contrariety," their relationship is either of attack or retreat. Opposites are mostly of different kinds, while contraries are mostly of the same kind: for example, "Zhen" and "Xun" are of different kinds, while "Zhen" and "Gen" are of the same kind; "Dui" and "Gen" are of different kinds, while "Dui" and "Xun" are of the same kind.

異則本為敵也，同則原相近也；敵則對而無嫌於爭，近則違而適成其逆；故對者位之當，反者序之逆。以震遇艮為陽自反，以兌遇巽為陰自逆，其陽與陰消息不同也。故乾坤坎離對且反，震巽艮兌為對，震艮巽兌為反；以位與序證之，自可見也，即在三爻之陰陽數求之耳。

Since they are different kinds, they are naturally opposing each other; since they are the same kind, they are naturally close to each other. If they are opposing, it is not strange that they face each other and compete; if they are close, but then move in opposite directions, they actually become contradictory. Therefore, "opposition" refers to the alignment in direction, while "reversal" refers to the inversion in order. When "Zhen" meets "Gen," it is Yang turning against itself; when "Dui" meets "Xun," it is Yin reversing itself—this is because the waxing and waning of Yang and Yin differ. Therefore, Qian and Kun, Kan and Li are both opposing and reversing; Zhen and Xun, as well as Gen and Dui, belong to "opposition," while Zhen and Gen, as well as Xun and Dui, belong to "reversal." By using direction and order as references, this becomes clear. In the end, it is sufficient to look at the yin and yang numbers in the third line.

八卦之位，相對者，皆異類；相連者，則多同類。其序之次分二繫，以陽從陽，以陰從陰；而陽中有陰也，則陰從陽；陰中有陽也，則陽從陰，視其氣所至耳。乾坤為陽陰主，故陽卦從乾，陰卦從坤；而兌為少女，又從乾；艮為少男，又從坤，則陰陽互近之序也。

The directions of the Eight Trigrams are such that those that are opposite belong to different categories, while those that are connected are mostly of the same type. Their sequence is divided into two systems: yang follows yang, and yin follows yin. However, if yang contains yin, then yin follows yang; if yin contains yang, then yang follows yin, depending on the state of qi. Qian and Kun are the masters of yang and yin, so yang trigrams follow Qian, and yin trigrams follow Kun. However, Dui is the young girl, yet it also follows Qian, and Gen is the young boy, yet it also follows Kun—this is the order of yin and yang approaching and following each other.

兌出於離變，艮由於坎進，故雖不類，而相從也。乾之左為巽，坤之旁為震；陽交於陰，陰交於陽，其氣之遞嬗也，故位從之。震者，坤之初得乾氣也；巽者，乾之始換坤象也；故長男近母，長女近父，以是交錯而孚於河洛之圖也。

"Duì" is derived from "Li," and "Gen" comes from "Kan" through a further step, so although they differ from the trigrams they originate from, they still follow them. "Qian" has "Xun" on its left, and "Kun" has "Zhen" beside it: yang enters into yin, and yin enters into yang, which is the mutual succession of energy, hence the determination of directions. "Zhen" is the trigram that "Kun" first receives the energy of "Qian"; "Xun" is the trigram that "Qian" first adopts the image of "Kun"; thus the eldest son is close to his mother, and the eldest daughter is close to her father. In this way, they alternate with each other, and correspond with the "Heavenly River Chart" and "Luo Writing."

河圖四方，天地之數，相合成物；洛書八方，陰陽之氣，往復成文，皆二者相錯也。故卦位序象之，然亦本於變化自然而然者也。氣至則象見焉，二者之行，必一陰一陽相互；以乾坤既立，餘物皆自天地之和生化，則不得獨行也。故陽卦以陰成，陰卦以陽成；而行也以交錯，至也以分合；各有其變化，則各具其數；各有其消長，則各殊其象，非截然不乾者也。

The Yellow River Chart is spread out in the four directions, with the numbers of heaven and earth paired together to generate all things; the Luo Writing is spread out in the eight directions, with the energies of yin and yang circulating and interacting to form patterns and structures. Both are results of the intermingling of yin and yang. Therefore, the positions and order of the trigrams are modeled after them, yet this too is based on the natural process of change. When the energy arrives, the image becomes apparent; and the movement of yin and yang must necessarily alternate between each other. Since the trigrams of Heaven and Earth have already been established, all other things arise from the harmonious union of heaven and earth, and thus cannot act independently. Therefore, yang trigrams rely on yin to be completed, and yin trigrams rely on yang to be completed; when they move, they alternate, but when they arrive, they separate and unite. Each has its own change, thus each has its own number; each has its own increase and decrease, thus each has its own image— they are not entirely separate from each other.

對者非仇則偶，反者非主則從，皆自其象數可測者也。夫氣之動也，有消長往來之形，故卦象有對反分合之別。以八卦之分陰陽，不過兩類，而乾坤主之。震坎艮屬陽，巽離兌屬陰；此易見者也。而離象日。且可代乾；坎象月，且以代坤；

Opposite trigrams are either enemies or partners; contrary trigrams are either dominant or subordinate: these distinctions can be known from their images and numbers. When energy arises, there are traces of increase and decrease, movement and stillness, so trigrams have distinctions of opposition, contradiction, separation, and union. When divided according to yin and yang, the eight trigrams fall into only two categories, ruled by Qian and Kun: Zhen, Kan, and Gen belong to yang, while Xun, Li, and Dui belong to yin, which is easy to see. However, Li represents the sun and can replace Qian; Kan represents the moon and can replace Kun.

則前之陰者為陽，陽者為陰矣！豈非氣有消長，象有往來；數有乘除，卦有升降乎？故陰者樂陽，其體陰者其用陽；陽者樂陰，其體陽者用陰；此一定不易者也。蓋先天之氣，至後天而變；變則用殊，其因於動也；動則變見，不動不變；

In this way, what was previously considered yin has now become yang, and what was previously considered yang has now become yin. This clearly shows that qi has both decline and growth, that phenomena have both coming and going, that numbers have both multiplication and division, and that hexagrams have both rising and falling. Therefore, the yin side delights in approaching yang; whatever has the nature of yin must necessarily have the function of yang. The yang side delights in approaching yin; whatever has the nature of yang must necessarily have the function of yin—this is an unchanging principle. Originally, the qi of the Earlier Heaven changes when it reaches the Later Heaven; once it changes, its function differs, and this change is caused by 'movement.' Only through movement can change be observed; without movement, there is no change.

則用不彰，而無所分於陰陽；既動既變，則用以明；而陰陽之象，不復渾淪；陰陽之途，亦隨遷易；此皆生成之例，造化之源；有必至者也。故陽卦多化於陰，陰卦多化於陽；進則變矣，退則復矣；其跡可求於象，其行可見於序，其至可審於位也。

If something remains unchanged, its function will not be evident, and thus yin and yang cannot be distinguished. Once it has moved and changed, its function becomes clear, and the image of yin and yang is no longer a single undifferentiated whole. The path of yin and yang also shifts and changes accordingly. These are the common principles of generation and the fundamental source of creation, a necessary stage that must be reached. Therefore, a yang hexagram tends to transform toward yin, and a yin hexagram tends to transform toward yang. If it progresses further, it changes; if it retreats, it returns to its original state. The traces of its transformation can be found in the hexagrams, its direction of movement can be seen in the order of the hexagrams, and the extent of its arrival can be examined in the positions of the hexagrams.

雖為卦八，其變化可無窮焉；此固聖人體察入微，徵考有目；蓋能明河洛之象，闡太極之形；推之而不差，用之而不忒也。夫河洛之數，陰陽相對，奇偶相生；皆示物之所生化，氣之所流行；而明天下之大本也。故卦象之，以畫示其數，以卦成其名；雖氣之不可見，而數之多少可計也；雖物不可形，而卦之大小可名也；

The trigrams, though only eight in number, can manifest infinite variations. This is the result of the sage's meticulous observation and solid verification: he clearly understood the images of the Yellow River Chart and the Luo Writing, and explained the form of the Supreme Ultimate, so his deductions have no errors and his applications are without mistakes. The numbers of the Yellow River Chart and the Luo Writing show the mutual relationship of yin and yang, and the mutual transformation of odd and even. They reveal how things are generated and transformed, and how qi flows, thus explaining the fundamental principles of the world. Therefore, the trigrams take their images from the Yellow River Chart and the Luo Writing, use lines to indicate their numbers, and use names to establish their designations. Although qi is invisible, the number of it can be counted; although things cannot be described in shape, the size of the trigrams can be named.