Yi Jing Zheng Shi (易經證釋)

一、易自伏羲畫卦，亦文亦畫，本合圖畫文字為一。雖太極等圖，繫後人傳出，源流自遠，講易時應並及各圖，以資參證。一、易為聖人明天道以立極，立人道以制教，本為明道而作，有關內修性命功甚多，故講易應注意道功。

The first point: The Book of Changes began with Fuxi drawing the trigrams. It is both text and image, originally combining figures and characters into one. For example, diagrams like the "Taiji Diagram" although passed down by later generations, have their origins in ancient times. Therefore, when explaining the Book of Changes, one should also discuss various diagrams, using them to refer to and verify each other. The second point: The Book of Changes is a book used by sages to explain the heavenly way, establish standards, confirm human conduct, and set up education. Its original intention is to clarify the great way, and it involves a lot of inner cultivation concerning life and nature. Therefore, when explaining the Book of Changes, one should pay attention to the aspect of "the way and its practice."

一、易既本天地之道為教，內中多闡神鬼之德、陰陽之情，習易者必有敬信之誠，而講易時應注重人神因果之理。一、易明神道，為明性命之源，吉凶禍福均屬易中固有之義。凡人生窮達壽夭，皆有定數，不可妄乾，則習易者必明行藏之所宜、得失之有定；故講易時應注重吉凶悔吝之說，而求其毋悖於數也。

Rule three: Since the Book of Changes is based on the principles of heaven and earth to carry out education and moral guidance, it often discusses the virtues of ghosts and spirits and the circumstances of yin and yang. Therefore, those who study the Book of Changes must approach it with sincere reverence and faith, and when explaining the Book of Changes, they should emphasize the principles of cause and effect between humans and spirits. Rule four: The Book of Changes reveals the ways of spirits in order to show the origin of life and death. Good fortune and misfortune, prosperity and adversity, longevity and short life are all inherent principles in the Book of Changes. There is a fixed destiny for a person's life, which should not be violated. Those who study the Book of Changes must understand when to emerge and when to retreat, and gain and loss are determined by fate. Therefore, when explaining the Book of Changes, emphasis should be placed on the concepts of 'good fortune, misfortune, regret, and hardship,' striving to conform to the laws of destiny.

一、易者，包乎道德、性情、數象各類而言者也。言文必顧義，言數必徵象，因名思義，因類辨物，因詞審情，不可偏執；故講易時務求其貫通一切，而洞明聖人立教之旨。一、易之言吉凶重在數，言數重在象。數見其氣，象別其類，以徵人事之所合，即以測天道之所宜。而見象必因著龜，明數必候氣運；天乾地支、五運六氣，皆易所重；故講易時應並及占筮之術、測驗之方。

Article 5: The Book of Changes discusses matters in terms of morality, nature, numbers, and images. When discussing words, one must consider their meaning; when discussing numbers, one must verify them through images. One should infer meaning from names, distinguish things by their categories, and examine reality through words. One must not be confined to a single aspect. Therefore, when studying the Book of Changes, one must seek a comprehensive understanding in order to fully grasp the purpose of the sage's teachings. Article 6: The Book of Changes discusses fortune and misfortune, focusing on numbers; and when discussing numbers, it focuses on images. Numbers reveal the movement of qi, while images distinguish the categories of things. These are used to verify whether human affairs are in harmony, and also to predict what is suitable in the heavenly way. To see images, one must rely on yarrow stalks and turtle shells; to clarify numbers, one must wait for the movement of qi. Heavenly stems, earthly branches, the five movements and six qi are all valued in the Book of Changes. Therefore, when discussing the Book of Changes, one should also include the methods of divination and the ways of verification.

一、易之為教，原以授民全生之道，推之成人成物，以至治國平天下，莫不貫通，而原始要終為第一義。人之習易，亦當求其先後，不可好為素隱行怪之談；故講易雖不能如王弼之掃象，亦不可如費氏之徒以災異言也。一、易道博大精深，無不包被：內則修己以一天人，外則成人以一道德，而本未一以貫之，實時中也。習易者既諳斯義，必期實行，務求行動咸宜，言思不悖，而能有德以為世則，有道以為人師，庶可使易教重明，聖道彌廣。

Seventh: The Book of Changes, as a means of moral instruction, originally aims to teach the principles of preserving life to the people. When extended, it can achieve others and all things, leading to the governance of the state and the peace of the world, all seamlessly connected. The first principle is to investigate the beginning and conclude the end. When people study the Book of Changes, they should also observe the proper sequence and not be overly fond of obscure and eccentric interpretations. Therefore, in explaining the Book of Changes, one should not follow Wang Bi of the Wei dynasty who entirely dismissed the symbolic numbers and figures, nor should one follow the scholars of the Han dynasty like Fei Zhi who specialized in interpreting omens and anomalies. Eighth: The Way of the Book of Changes is vast and profound, encompassing all things. Internally, it is about cultivating oneself so that heaven and humanity become one; externally, it is about achieving others so that the Way and virtue become one. From the root to the end, it is unified by a single principle, which is exactly what the Doctrine of the Mean refers to as "the mean in time." Those who study the Book of Changes, having understood this, must put it into practice, ensuring that their actions are appropriate, their words and thoughts are not against reason. They should be able to become a model of virtue for the people and a teacher of others through the Way, thus hoping to restore the clarity of the Book of Changes' teachings and expand the great Way of the sages.

一、易之為教，始於古聖，闡於道宗，成於儒者。言既精微，旨尤玄妙，固賅各教之義，集諸派之大成。習易者當以聖人天下為公之心，一本有教無類之旨，不可自存門戶，有入主出奴之見，以自狹而聖人之教也。一、易傳至今，注說不一，漢宋各異派，儒道不同宗，遂致議論紛歧，爭持齟齬，徒亂人意，何裨聖經？今茲講易，務求闡明微言，表章至道，不執於宗派之習，不徒為同異之求。即令漢宋諸儒有所卓見，能探經旨，不睽經義，仍可互相引證，期其貫通；無問其人，祇徵於是，則於聖人講示之後，又可多得研究之助云爾。

Rule nine: The Book of Changes is a teaching of moral cultivation that originated with the sages of the ancient times, was elaborated upon by the Daoist school, and finally took shape in the hands of the Confucian scholars. Its language is already extremely subtle, and its principle is even more profound. It originally integrates the teachings of various schools, being the culmination of all doctrines. Those who study the Book of Changes should hold the mind of the sages, "the world as a common possession," and universally follow the principle of "teaching without discrimination." They should not establish their own schools, nor hold the prejudice of exalting their own school and excluding others, which would instead narrow the moral cultivation of the sages. Rule ten: The Book of Changes has been passed down to the present day, with various interpretations and commentaries. Han learning and Song learning belong to different schools, and Confucianism and Daoism have different emphases, leading to endless disputes and contradictions, which only confuse people's minds and do no good to the sacred classics. This time, in explaining the Book of Changes, we must clarify the subtle words and promote the highest principles, not being bound by the habits of any particular school, nor focusing only on differences and similarities. Even if scholars of Han and Song schools have their own unique insights, as long as they can grasp the original meaning of the text and not contradict the meaning of the classics, they can still be cited and referenced to achieve a comprehensive understanding. We should not concern ourselves with who says it, but only whether it conforms to the correct principles. In this way, in addition to the teachings of the sages, we can also gain further assistance in our studies.

以上各條，係為講易之前必知之事。以易經至不易明，必先知其研習之道，方不為歧途所誤。略指大概，以告讀者，或亦極深研幾之一助焉。

All these entries are essential knowledge to be understood before beginning the study of the Book of Changes. Since the Book of Changes is extremely difficult to comprehend, one must first clarify the proper approach to studying it, in order not to be led astray by wrong paths. Here, only a general outline is given to inform the reader, which may offer some assistance in understanding the phrase "extreme depth and subtle inquiry" from the Upper Great Treatise.

易道玄微，至於無名無形；易象廣博，包乎萬物萬事。蓋有天地以後，無物不在易中；未有天地以前，一氣即為易體。故先後天之名，首著於易；天地鬼神之情，盡備於易；性命道德之言，皆詳於易；生死變化之數，均述於易。

The Dao discussed in the Book of Changes is profound and subtle, reaching a level where it cannot be named or seen. The images taken from the Book of Changes are extensive and comprehensive, encompassing all things and events. After the formation of heaven and earth, there is nothing outside the scope of the Book of Changes; before the formation of heaven and earth, that primordial qi was the essence of the Book of Changes. Therefore, the terms "Earlier Heaven" and "Later Heaven" first appear in the Book of Changes; the forms of heaven, earth, ghosts, and spirits are fully recorded in it; discussions on nature, destiny, and morality are most detailed in it; and the numerical principles of birth and death transformations are also explained in it.

以言天地，則盡其神；以言人物，則概共逍。以言往，則溯諸無始而立其極；以言來，則推至無盡而明其化。以修，則道立而德成；以行，則事理而物順。以其功言，則成王道之治而無所為；以其體言，則符仙佛之真而大有得。以用於尋常，而不悖於情性；以致其遠大，而能底於中和。是為道德之宗、命數之本，天人之所由一，事物之所由平，政治以成，制作以著，君子小人各盡其德，聖愚賢否各適所成。雖取舍萬殊，而底於一道；雖變化盡態，而歸於至中。

Using the Yi Jing to explain heaven and earth, one can fully explain their mysterious nature; using it to explain people and things, one can roughly summarize the principles of all things. Looking back, it can trace back to the beginningless origin, establishing the fundamental basis for all existence; looking forward, it can extend endlessly, explaining the principles of change. Using it for cultivation, one can establish the Way and achieve virtue; using it for action, one can make things reasonable and external matters smooth. In terms of its effects, it can achieve the governance of the Way of the King while appearing to do nothing; in terms of its essence, it can conform to the true reality realized by immortals and Buddhas, thus gaining great benefit. Applying it in daily life, it does not contradict human nature; pushing it to great heights, it can return to the state of "zhonghe" (harmony in the middle). Therefore, it is the master of morality and the root of destiny, the place where heaven and humanity can be united, and the source from which all affairs and things are settled. Politics relies on it to be established, systems and objects rely on it to be set up; gentlemen and petty people each fulfill their virtue, sages, fools, virtuous persons, and the unvirtuous each achieve their proper state. Although choices and rejections may differ greatly, in the end they all return to the same Way; although changes may exhaust all forms, in the end they all return to the ultimate middle path.

蓋本諸天道之常，仿於大道之則，宜於人物之情性，辨於幽明之感通。故在天地間，生成者莫能外；從事物間，行止者莫能違。允宜為萬古之師、萬類所倚。以為教化，則包諸宗；以為文章，則造至極。苟非至聖，孰能為之。

The Book of Changes is based on the constant principles of heaven's way, following the great Dao's principles, conforming to the nature of people and things, and distinguishing the communication between the hidden (ghosts and spirits) and the manifest (human affairs). Therefore, in the world of heaven and earth, whatever is born and formed cannot go beyond its scope; in the realm of things, whatever moves and stops cannot violate its standards. It truly deserves to be called the teacher of all generations and the fundamental reliance of all beings. Using it for education, it can encompass all schools of thought; using it for writing, it can reach the highest perfection. If one is not the highest sage, who could compose such a book?

故夫子備言其精，諸儒各贊其要，合五經以證其終始，勵眾善以徵其初成。不可視為古書，同諸舊史；不可作為文藝，比之詩詞。精益求精，必實行而後得；博而反約，必貫通而有成。是以講演不厭其詳，研求尤須盡力。珍聞而寶藏於心，等諸拳拳之顏子；集思而實行於事，毋負循循之尼山。庶易道獲見重明，後生不迷古訓，則世運亦將成大治，萬國盡化於斯文矣！是為序。

Therefore, Confucius explained the subtle aspects of the Book of Changes thoroughly, and later Confucian scholars each emphasized its essential points. They combined it with the Five Classics of Poetry, Book of Documents, Rites, Music, and Spring and Autumn Annals to verify its beginning and end, encouraging people to be virtuous and testing its initial effectiveness. It should not be regarded merely as an ancient text, treated equally with old historical records; nor should it be considered as a literary work, compared with poetry. To pursue excellence, one must practice it personally to gain understanding; to return from breadth to simplicity, one must integrate and comprehend it fully. Therefore, when explaining, there is no objection to being detailed, and when studying, one must strive with all one's effort. When encountering precious principles, one should treasure them in the heart, like Yan Hui, who is praised in the Doctrine of the Mean as 'clinging to them with sincerity and devotion'; gathering the thoughts of many and applying them to practical affairs, without failing to live up to Confucius' painstaking guidance at Nishan. In this way, the Way of the Book of Changes may once again become clear, and later scholars will not lose themselves in ancient teachings, so the world's affairs will move toward great order, and all nations will be nurtured by this continuous culture. This is the conclusion of this preface.

易者，古聖人作也。傳於庖犧，紹述於神農、軒轅，繼承於堯舜及夏后氏，周文因而變化之，以成今傳之經。蓋庖犧時，因河圖、洛書之見也，而明察天地之象，概論人物之情：上以窮生化之初，下以辨變易之軌；幽以探於神鬼，明以合於日月；遠以徵於四極，近以求於一心，而後知天地生成、物類化育。

The Book of Changes was composed by ancient sages. It was passed down by Fuxi, then continued by Shen Nong and the Yellow Emperor, and further transmitted through Yao, Shun, and the Xia dynasty. It was only during the time of King Wen of Zhou that it was adapted and transformed from previous teachings, becoming the classic we have today. When Fuxi lived, it was because the Yellow River Chart and the Luo Writing appeared that he was able to discern the patterns of heaven and earth, and to summarize the conditions of people and things. He explored the origin of all generation and transformation, clarified the rules of change, investigated the hidden aspects of ghosts and spirits, and verified the brightness of the sun and moon. He looked far to the extreme corners of the world and looked near to his own mind. Only then did he understand how heaven and earth were generated and how all things were nurtured.

情性本於道，氣質成於神。有其用必有其本，有其後必有其先。陰陽必循環以為行，水火必生制以為用。物必有極，事必有中。見諸外者，形質之消長，而變化以成；存於中者，氣神之營運，而中極有立。道者，依體以用而不窮；天者，依道以行而不息。是以有本則不失其序，有道則不盡於用。以不二為德，則生生不已；以至中為體，則循環無端。皆順乎自然，適於至道。無為而無不為，無思而無不中，無慮而無不得。

Human emotions and nature are rooted in the Dao. Human qi and form are condensed by the Shen. If there is function, there must be its essence; if there is later, there must be prior. Yin and Yang must cycle and return to achieve their operation. Water and fire must both generate and restrain each other to fulfill their function. All things have a limit, and all affairs have a center. What is apparent is the growth and decline of form and material, through which transformation is completed; what is contained is the movement of qi and Shen, through which the central and correct pivot is established. The Dao is the essence upon which function depends, and its use is inexhaustible. The Heaven is the operation following the great Dao, never ceasing. Therefore, having a root ensures order, and having the Dao ensures function is not exhausted. Taking "not dual" as virtue allows continuous generation; taking "extreme center" as essence allows cycling without end. All this follows nature and conforms to the highest Dao. Thus, there is no action yet all is done, no thought yet all is accurate, no planning yet all is attained.

故明道之為道，則天地人物莫外道以生成；明天之為天，則生長盈虛莫非氣所運用；明生之為生，則吉凶壽夭不出數之進退；明數之為數，則行藏出處宜因時之推移。時者屬乎天，位者隸於地。天地者，人物生存傷殺之宰；時位者，事物消長代謝之機。由天地以後言，則人物自天地出；由天地以前言，則天地自道成。所謂形上為道，形下為器；道器之間，一以貫之，是謂之易。故作易以明一切，凡先天後天人物，莫不歸於易。

Understanding why "Dao" is called Dao, one realizes that nothing in heaven, earth, or human beings can be generated without Dao. Understanding why "Heaven" is called Heaven, one realizes that all growth, fullness, and waning are due to the movement of Qi. Understanding why "Sheng" is called Sheng, one realizes that fortune and misfortune, longevity and short life, all follow the rise and fall of "Shu." Understanding why "Shu" is called Shu, one realizes that whether one should take office or retire depends on the movement of the times. "Time" is governed by Heaven, and "position" is controlled by Earth. Heaven and Earth are the masters that allow beings to live and also cause them to suffer harm and destruction; time and position are the key factors in the growth and change of things. From the perspective after Heaven and Earth were formed, human beings and all things originated from Heaven and Earth. From the perspective before Heaven and Earth were formed, Heaven and Earth themselves originated from Dao. The "Great Treatise" of the upper part says, "What is above form is called Dao, and what is below form is called objects." The relationship between Dao and objects is connected by a single principle, which is called "Yi." Therefore, the sages created the Book of Changes to explain everything. Whether it is the Earlier Heaven, the Later Heaven, human beings, or things, all are included in the Book of Changes.

易者，一也、中也、極也。無始而有始，無形而有形，無名而有名。易者，自有以溯無也，自無以推有也；有無均齊於易，故易作而有無以名。天地既奠，日月山河各有其紀，飛潛木石各有其類，世代遞嬗、歲時遷移各有其序，生長收藏、盈絀美惡各有其名，而一於不一，同於不同。各因所適所宜，以始以終，其所維繫之道、往來之途，各因所合所制，以成以敗，皆統於易，以歸中極，而順於天道。故易立而萬類以定。

The concept of "Yi" (Change) is "One," is "Center," is "Extreme." It originally had no beginning yet had a beginning, originally had no form yet had a form, originally had no name yet had a name. The "Yi" can trace "Being" back to "Non-being," and derive "Being" from "Non-being"; thus, "Being" and "Non-being" are treated equally within the "Yi." Therefore, once the "Yi" was established, "Being" and "Non-being" acquired names. Once heaven and earth were set in place, the sun and moon, mountains and rivers each had their own order. Birds, fish, grass, trees, and stones each had their own categories. Generations succeeded each other, and the four seasons shifted in their own order. Growth and harvest, fullness and emptiness, beauty and ugliness each had their own names. Yet within the "Not One," there is the "One," and within the "Not the Same," there is the "Same." All things begin and end according to their proper place. The paths they rely upon and the ways they travel also succeed or fail according to their meeting and constraints. All these are governed by the "Yi," culminating in the central and upright pivot, thus aligning with the Way of Heaven. Therefore, once the "Yi" was established, all things found their proper place.

天地之間，人為貴。人之生也，受天地之中氣而有性命，順造化之推移而辨等名，因生養老死之道而有人事，因喜怒美惡之感而有人情。而有以適之、全之、利之、導之，以底於成德；而有以教之、誨之、鑑之、臨之，以盡其原始要終之道。是皆備於易，故易立而人道以全。

Between heaven and earth, humans are the most esteemed. When humans are born, they receive the harmonious qi from heaven and earth, thus possessing nature and destiny. Following the changes of the universe, distinctions of rank and status are established. Because of the process of birth, nurturing, aging, and death, human affairs come into being. Because of the feelings of joy, anger, preference, and aversion, human emotions arise. Therefore, there are various methods to adapt to them, preserve them, guide them, and lead them, so that people may cultivate virtue. There are also various methods to educate them, instruct them, provide them with lessons, and personally supervise them, so that the principle of examining the beginning and concluding the end may be fully explained. All these contents are fully included in the Book of Changes. Therefore, once the Book of Changes is established, the way of human beings is complete.

夫聖人之於天道也，通於神明，見於隱微；於人道也，明於性情，備於教政；於物之宜、事之利也，詳於本末，昭於變化。而後立易以告於天下，垂於有眾，使天下不迷所生化之道，不失其修為之德，不惑神鬼之靈，不悖性命之則，而皆生成安樂，與物同壽，與天地同德，日月同明，鬼神同其吉凶，氣運同其變化。而後聖人成物之道盡，成己之德宏，而天下無不被其德、悅其道。此則聖人立易教民之功，可並天地覆載；其明誠修道之行，即同於治平政刑之施。

The sage, in regard to the heavenly way, can communicate with the divine and perceive hidden things; in regard to human affairs, can understand human nature and qualities, and fully carry out education and governance; in regard to whether things are suitable or beneficial, can thoroughly examine the beginning and end, and clearly observe changes. Only after this did he create the Book of Changes to enlighten the people and set an example for all, so that people would not lose the principles of generation and transformation, would not lose the virtue they have cultivated, would not be confused by the supernatural, and would not violate the principles of life and nature. Thus, all people can live in comfort and prosperity, live as long as the myriad things, share the virtue of heaven and earth, shine with the brightness of the sun and moon, share the fortune and misfortune of the spirits, and follow the changes of the vital energies. At this point, the sage's way of completing things is complete, and his virtue of perfecting himself is great, and no one is left without his grace or not convinced by his way. This is the sage's achievement in creating the Book of Changes to educate the people, which can be compared with the covering of heaven and the bearing of earth; his practice of self-cultivation and sincerity, and the cultivation of the great way, is equivalent to governing the country and bringing peace to the world, and implementing laws and punishments.

故易之立也為教民，而人之明易，為率聖人之教，以致於自明誠者也。天下人類，果皆率是教以立其誠，則易之道成矣。易者，有易之義，言將易天下也；有不易之義，言示其體不易，而後其用不盡也；有簡易之義，言推始於太一，而立本不二，以成其無息之德，達其用中之道也。知斯三義，而後明易，易豈易言乎哉！

Therefore, the creation of the Book of Changes was to educate the people, and for people to understand the Book of Changes is to follow the teachings of the sages, seeking to attain the state of "self-realization leading to sincerity." If all people could establish their sincerity according to this teaching, then the way of the Book of Changes would be realized. The character "易" has three meanings: first, "change" (bian yi), meaning that it is used to transform the world; second, "unchanging" (bu yi), meaning that it reveals the constant nature of the fundamental essence, and only because it is unchanging can its function be inexhaustible; third, "simplicity" (jian yi), meaning that it traces the origin of all things back to "Taiyi" (the Ultimate Oneness), establishes a single and pure foundation, thus achieving an endless virtue and attaining the use of maintaining the middle way. Only after understanding these three meanings can one speak of truly comprehending the Book of Changes—the Book of Changes is not something that can be easily discussed!

今先將講易之法說明。講時採用一善本為準，五經各本向多用朱本；唯易經，朱本有未善，不及後世來氏本。不過來氏所演圖表過繁，祇宜參考，難為讀本。

First, explain the method of studying the Yi. When beginning, select a good edition as the basis. For the five classics, the commonly used edition has traditionally been Zhu Xi's annotated version. However, Zhu Xi's "The Original Meaning of the Zhou Changes" has some shortcomings and is not as comprehensive as Lai Zhide's "Collected Commentaries on the Zhou Changes" from later generations. Nevertheless, Lai's charts and diagrams are too complicated and are only suitable for reference, not for use as a textbook.

今奉夫子命，就來本節取必要圖表，附列經文之前，去其繁而存其精，以便初學。因言易用圖表，前人均有傳圖，為講習之用；漢時儒者失之，乃傳於道家及術數者流。儒人祇重文字訓詰，雖有所得，不以附經本，使圖表無傳，非易之不用圖表也。

Now, following the mandate of Confucius, I will select the necessary charts from Lai Zhide's edition and append them before the text of the Classic, omitting the complicated and retaining the essential parts, to facilitate the study of beginners. As for the use of charts in explaining the Book of Changes, previous scholars had already passed down diagrams for instructional purposes. However, during the Han dynasty, the Confucian scholars lost these diagrams, and they instead came into the hands of Daoist and numerological schools. The Confucian scholars only focused on textual interpretation and etymology, and even if they had insights, they were unwilling to include the diagrams in the main text, leading to the loss of these charts—this does not mean that the Book of Changes originally did not use charts.

宋時以周邵之所習，得於道家，參於術數之書，經程朱審擇，加於經本之前，易於是有圖說；而不得其全，不明其用，仍無補於易。來氏復增演之，以廣其旨，固較詳備矣，而不明其統系，不知其用之主賓、義之先後，猶難使習者一目瞭然。今就所演加以審正，為之講明，以見古人易教之全，而竟易道之用，庶於後世讀者有所裨益。至其錯誤或疑謬之處，隨時指正可也。

By the Song dynasty, the diagrams studied by Zhou Dunyi and Shao Yong were derived from Daoist sources and also referenced numerological texts. These diagrams were later reviewed and selected by Cheng Yi and Zhu Xi, and were added before the main text of the Book of Changes, thus giving rise to the diagrammatic explanations of the Book of Changes. However, these diagrams were incomplete and their purposes were not clearly understood, so they did not greatly assist in understanding the Book of Changes. Lai Zhide further expanded and elaborated on them, making his explanations more detailed than those of his predecessors. Yet he did not fully grasp the systematic relationships among the diagrams, nor did he understand the order of priority in their application and in their philosophical meanings. Therefore, his work still failed to make the diagrams easily comprehensible to learners. Now, by examining and correcting his elaborations, we can explain each diagram in detail, so that people can see the complete teaching of the Book of Changes as presented by ancient scholars, and fully reveal the practical applications of the principles of the Book of Changes, hoping to benefit future readers. As for any errors or doubtful points, they can be corrected as they are pointed out.

又曰：言易本天道，而習易則人事也。言天道則重氣數，言人事則重象。以氣數言象，是天道；以象言氣數，是人事。因氣數難知，象易見也。先有氣數而後生象，此天道之自然；先明象而後明氣數，此人事之次序。要皆本末之道也。

It is also said that the study of the Book of Changes is based on the heavenly way, while the practice of the Book of Changes relates to human affairs. When discussing the heavenly way, the emphasis is on "qi and numbers," while when discussing human affairs, the emphasis is on "images." Starting from qi and numbers to explain images follows the path of the heavenly way; starting from images to infer qi and numbers follows the path of human affairs. This is because qi and numbers are difficult to know directly, while images are easy to observe. First there is qi and numbers, then images arise, which is the natural order of the heavenly way; first understanding images, then inferring qi and numbers, is the sequence in human affairs. In summary, all of this is about the principle of "origin" and "result."

如見天災時變而知天意，即由象以知氣數，是由末達本者也；而象因氣數所生成，非有象而後氣數至，是由本及末之道也。故明本不必求末，而不及本者，必自末始。

For example, observing natural disasters and anomalies in the seasons to infer the will of Heaven is to deduce the destiny from the manifestations, which is 'from the end to the origin'. However, the manifestations are generated by the destiny, not that the manifestations come first and then the destiny follows. This is 'from the origin to the end'. Therefore, those who have already understood the origin do not need to look at the manifestations, while those who have not yet reached the origin must start from the manifestations.

今之災變多矣。天之風雨旱潦不必論，即物之為變亦夥矣：蛆出道上，雞生雙首，種種怪異，非象之見耶？至於蝗蝻之災，又其至明者，皆氣數所感化而然。欲明氣數，但求之象，即知天變之不已矣！故災有天災，異有物異，而莫非氣數為之，而亦非人心召之，人之變異尤多矣！

The current calamities and strange occurrences are numerous. Not only are the heavenly phenomena such as rain, wind, drought, and floods not to be overlooked, but also there are many abnormal occurrences among creatures: maggots crawling on the roads, chickens giving birth to two heads, and various strange happenings. Are these not manifestations of "images" (xiang)? As for locusts' larvae causing disasters, it is even more evident. These are all caused by the changes in the vital energy and destiny. To understand the vital energy and destiny, one should look at these images, and thus realize that the changes in heavenly phenomena have never ceased. Therefore, calamities may come from above, and strange occurrences may arise from abnormal phenomena among creatures; none of them are not caused by the vital energy and destiny, nor are they not brought about by human hearts. The changes within people themselves are even more numerous.

怪產奇病且不必數，即風尚之壞、情性之乖，或致逆倫悖理，鮮恥敗德，皆自人心之非成之。人心如斯，欲氣數之不變，得乎？此古人重天變而必責於人事也。氣數雖自天定，而變為災福，則人所感召。人祇知天災之難堪，不知人心之難善，是重末忘本，如浮舟海中，欲其不動，何可得也。易者易也，以人易天，以天易數，皆有必至之勢、固然之理。精於易者，唯求易其不善為善，而可易其災害為福。是則聖人以易為教之本旨，端在此乎。

Strange births and rare diseases need not be listed one by one. Just consider the moral corruption and perverse dispositions that lead to violations of human relationships and disorder in affairs, along with the lack of shame and the destruction of virtue. All these are caused by evil in the human heart. When the human heart reaches such a state, can it still expect the natural order to remain unchanged? This is why ancient people paid great attention to celestial anomalies and always traced them back to human actions. Although the natural order is determined by heaven, whether it turns into calamity or blessing depends on human actions. People only realize the difficulty of enduring natural disasters, but they do not realize the difficulty of turning the human heart toward goodness. This is focusing on the branches while neglecting the root, like trying to keep a boat from moving while it floats on the sea. How could that be possible? The Book of Changes is about transformation: changing heaven through human effort, and changing destiny through heaven, all have their inevitable trends and natural reasons. Those who truly understand the Book of Changes only seek to transform their own evils into goodness, thus turning calamity into blessing. The intention of the sages in using the Book of Changes as a teaching is probably precisely this.

易經上下篇，文王所制。其卦象本伏羲以來所有卦辭爻象，參古易而加入新義，此今之經文也。繫辭上下傳、說卦傳、文言各類文章，則夫子蒐集古聖所傳、各易所用，而與文王易有相發明者。序卦傳則夫子就文王之卦序而說明其義趣也。雜卦象則夫子參合各易，變通文王之序而推衍其變化也。故傳皆成於夫子。文王之經，夫子之傳，乃為今易之本。經文雖不盡作於文王，而文王總其成，以卦序實文王所制也；傳文雖不盡成於夫子，而夫子約其要，以刪訂十翼，實夫子之功也。

The Book of Changes consists of two parts, compiled by King Wen of Zhou. The hexagrams in it follow all the hexagram statements and lines from Fuxi's time, and also incorporate new meanings from various ancient versions of the Book of Changes, resulting in the present text of the classic. The articles such as the Upper and Lower Great Treatises, the Discourses on the Hexagrams, and the Discourses on the Meaning of the Hexagrams were collected by Confucius from the teachings of ancient sages and the various versions of the Book of Changes, and they complement and clarify King Wen's Book of Changes. The Discourse on the Order of the Hexagrams explains the meaning of the hexagram sequence arranged by King Wen. The Discourse on the Miscellaneous Hexagrams combines various versions of the Book of Changes, altering the order of King Wen's hexagrams and elaborating on their transformations. Therefore, all the "transmissions" were completed in Confucius' hands. King Wen's "Classic" combined with Confucius' "transmissions" forms the foundation of the present version of the Book of Changes. Although the classic text is not entirely composed by King Wen, he compiled it as a whole, since the hexagram sequence was indeed arranged by him. Although the "transmissions" were not entirely written by Confucius, he summarized and edited them into the "Ten Wings," which is truly his contribution.

此易經一書，雖曰自伏羲始，不過有其卦耳；雖曰歷神農、黃帝、唐、虞、夏、商各易之變，不過間存其詞，見其義耳。故名之周易，實文王與夫子二聖之作。微文王，無周易；微夫子，周易之義不全。以經文簡，而當時憂讒畏譏，有不能盡諸文章者，故曰書不盡言，言不盡意。以此夫子必為補之，補之不可雜於經，故列為傳。

The book of Changes, although said to have begun with Fuxi, in reality Fuxi had only the hexagrams. Though it went through changes during the reigns of Shen Nong, the Yellow Emperor, the Xia Yao, Yu Shun, the Xia and Shang dynasties, in reality it only occasionally preserved some phrases and revealed a little meaning. Therefore, it is called the Zhou Changes, but in fact it was written by King Wen and the Master. Without King Wen, there would be no Zhou Changes; without the Master, the meaning of the Zhou Changes would be incomplete. Because the classic text is too concise, and King Wen was in a state of distress, fearing slander and criticism, some things could not be fully expressed in writing. Therefore, the Great Treatise says, "Writing cannot fully express speech, speech cannot fully express meaning." Because of this, the Master had to supplement it; but the supplement could not be mixed with the classic text, so it was set apart as a "Transmission."

傳者，明有所傳也；繫辭者，明其繫於經也。凡繫、傳、文言之類，皆為周易不可少之文章。以周易之義，待文而後盡；若無之，則周易猶殘闕也。而夫子十翼之功，不在文王下，且文王未言者，亦得夫子為詳其略而顯其微，此足見夫子憲章之功矣。

Called "Zhuan," it indicates that it has a transmission; called "Xì Cí," it indicates that it is attached to the classic text. All texts such as "Xì Cí," "Zhuan," and "Wényán" are essential parts of the Zhou Changes. Because the meaning of the Zhou Changes is not fully explained until these texts are present; without them, the Zhou Changes would be incomplete. The contributions of the Master in composing the "Ten Wings" are no less than those of King Wen; moreover, where King Wen did not speak, the Master elaborated on the brief and revealed the subtle, thereby clearly demonstrating the Master's achievement of "Xian Zhang Wen Wu" (adhering to and explaining the ways of the former kings).

經文與傳之有同異者，則由傳採自他易，傳於先賢，有所授也；或與傳文參差互出者，則由經文義有未盡，得於言外而為補述也。故傳文中上下繫傳，全為輔證經文不足者。凡古人制作，取義必專，立旨必純，故成一家言，有獨重之義與旨，而不雜他說；即有摭拾者，亦其言與其義旨同，雖言不同而實同。此不得視為合各家言，文王之易亦如是也。

There are differences and similarities between the text of the Classic and the Commentary, because the Commentary draws from other versions of the Book of Changes, passed down by wise men of previous generations, each with its own origin; sometimes the texts of the Commentaries differ from each other and contradict one another, because the meanings in the Classic are not fully explained, and need to be supplemented with explanations beyond the text. Therefore, the Upper and Lower Commentaries on the Great Treatise are all used to complement and verify the deficiencies in the Classic. All ancient writings take meaning with a single focus and establish a clear purpose, so they can form their own distinctive schools of thought, emphasizing particular meanings and purposes, without mixing in ideas from other schools; even when they borrow from earlier sources, the borrowed words are consistent with their own meaning and purpose, differing only in wording but not in essence. Therefore, they should not be regarded as a compilation of views from different schools—King Wen's Book of Changes is also like this.

故所不錄者，唯宜補之於傳，而以繫傳名之，明其義本經文應有，以未得列入，別立為傅而繫之於經云耳。故繫傳上下，含義最宏，取例最多，凡以前各易及涉於數象者，無不採錄。雖言近雜紀，義若旁搜，而皆本易中固有之理，與氣數必明之道。如河圖、洛書、二氣五行、九宮甲子、五音六律、五運六氣，以及天文地理、日星軌度、歲時節候之類，凡屬於氣之所化、形之所生，數有推移、象有升沉者，皆易也，皆易象固有者也，故皆宜採之以證易，而見易之廣大神用。此係傳所摭拾，非一家言：大之性道之功，小之術數之學，明則日用起居之事，玄則神天幽渺之說，皆詳載焉。苟讀經而不先讀之，則將不知易之用矣！

All explanations not included in the main text should be supplemented in the "Transmission" and named "Xixi" to indicate that these principles were originally part of the main text but were omitted and thus established as a separate transmission attached to the main text. Therefore, the Upper and Lower Xixi transmissions contain the most extensive meanings and the most numerous examples. All previous interpretations of the Book of Changes and all matters related to numbers and symbols are included. Although they appear to be miscellaneous notes, seemingly collecting various ideas, they are all based on the inherent principles of the Book of Changes and the essential paths needed to understand the principles of qi and numbers. For example, the Yellow River Chart and the Luo Writing, the two energies of yin and yang, the Five Phases, the Nine Palaces and the Jiazi cycle, the Five Tones and the Six Laws, the Five Movements and the Six Energies, as well as astronomical and geographical knowledge, the movements of the sun and moon and the stars, and the seasonal changes and climatic conditions throughout the four seasons—all these belong to the transformations of qi and the manifestations of form, and involve changes in numbers and the rising, falling, sinking, and floating of symbols. All of these belong to the Book of Changes and are inherently present in the Book of Changes' symbolic system. Therefore, they should all be collected to verify the Book of Changes, thereby demonstrating its vast and profound nature. It is clear that the Xixi transmissions do not represent the views of a single school: they cover great matters such as the cultivation of the mind and the Way, and small matters such as divination and numerology; they include practical daily affairs and profound theories about heavenly spirits and the mysteries of the unseen. All these are thoroughly recorded. If one only reads the main text without first reading the transmissions, they would not know how to apply the Book of Changes.

繫傳者，由習易言，較經尤要。經限於體制，故辭約義簡；傅則無所限也，而其辭贍，其義宏，上下古今、鉅細顯隱，無不及也。故其言易，有先天、有後天、有連歸、有本宮、有歲象、闢卦之類；其言數象也，有河圖、洛書，有太極兩儀，有天地生成數，有五運六氣、甲子歲會之圖。其為古聖所發明者，自伏羲卦象變為文字，神農醫藥，黃帝曆數，及諸制作、文物器具、設立教政、開天下先者，無不可由傳中知之。雖為一經之傳，實儗於上世之史。其義則由於中國文化自易卦始；易卦以前雖有難稽，其可考者皆在易卦後也，皆仿諸卦象者也。

In terms of studying the Book of Changes, the Commentary is more important than the classic text itself. The classic text is constrained by its format, so its language is concise and its meaning is brief; the Commentary, however, is not constrained, so its language is rich and its meaning is vast, covering all aspects from above to below, from ancient to modern, from great to small, from obvious to hidden. Therefore, it discusses the Book of Changes, including the Earlier Heaven, the Later Heaven, the Classic of Continuous Mountains and the Classic of Returning Concealment, as well as concepts like the original palace, the annual phenomena, and the method of dividing the hexagrams. It discusses numbers and symbols, including the Yellow River Chart, the Luo Writing, the Taiji and the two principles, the numbers of heaven and earth generation, and the diagrams of the five movements and six qi, as well as the cycle of the Jiazi years. As for the inventions of ancient sages, from the transformation of the hexagrams into characters by Fuxi, to the medicine of Shen Nong, the calendar and mathematics of the Yellow Emperor, and various creations, cultural artifacts, the establishment of education and governance, and the pioneering achievements in the world, all of these can be known from the Commentary. Although it is merely a commentary on a single classic, it can be compared to ancient historical records. This is because Chinese culture originally began with the hexagrams of the Book of Changes: events before the hexagrams are difficult to verify, but all verifiable events are after the hexagrams, and all of them were derived from the hexagrams.

故易卦實包天地，納古今而弗遺。言人道者必從之，以明為人之生；言天道者必因之，以明天地之建。故名曰易，既太易，亦太一也，為萬有之始，以上無所有也。故曰易，言自此而後變易；變易則無者為有，一者為眾矣。此易道至廣至高，而繫傳之辭以繁、義以博，職是故也。

Therefore, the hexagrams of the Book of Changes indeed encompass heaven and earth, include past and present, and leave nothing out. Those who discuss human affairs must follow it in order to understand the fundamental principles of being a person and establishing oneself; those who discuss heavenly affairs must rely on it in order to understand how heaven and earth are established. Hence it is called "Change," which is both "Great Change" and "Great Oneness," the beginning of all things, and there is nothing above it. It is called "Change" because from here onwards change begins; once change occurs, what was originally non-existent becomes existent, and what was originally one becomes many. The way of the Book of Changes is so vast and lofty, and hence the words of the "Commentary on the Hexagrams" are therefore rich and its meanings are therefore broad, precisely for this reason.

易之為書，傳自上古。伏羲氏始畫八卦，初具規模；後之聖人紹述推衍，制卦既備，列爻亦明。唐虞三代，各有演習，分為連山、歸藏、乾坤之易。文王重加纂序，宏以文章，變其占例，著為典則；周公紹之，詳陳論議，博採遺言，撰為至教。是今傳之易也。

The book of Changes, called the Yijing, has been passed down from ancient times. Fuxi first drew the Eight Trigrams, but they were only in their initial form. Later sages continued to explain and develop them, establishing the trigrams completely and arranging the lines clearly. Tang Yao, Yu舜, and the Xia, Shang, and Zhou dynasties each practiced their own versions, dividing them into three types: Lianshan, Guicang, and Guanqian. King Wen of Zhou reorganized them, expanded them with words, changed the system of divination, and created a set of rules. The Duke of Zhou continued his work, elaborately explaining and arguing, widely collecting the sayings left by previous generations, and compiled the highest teaching. This is the Yijing that is passed down today.

上古無文字，制作文物均極簡陋。伏羲覽河圖、洛書而後制卦象，是則文字之所始也。雖當時類無文章，有如圖畫，實則象意之字，猶之鳥官氏之象形字也。字雖傳於鳥官，畫實創於伏羲。其象形之字、會意之文，多取義結繩，制於歷代，非創自鳥官也。以記載無史，傳說難詳，故莫能盡考所自作耳。

In ancient times, there were no written characters, and all tools and objects were extremely simple. After observing the Yellow River Chart and the Luo Writing, Fuxi established the trigrams, which marked the beginning of writing. Although it was not yet considered as written text, it appeared as pictures, but in fact it was meaningful characters, similar to the pictographs of the Shao Hao era of the Bird Officials. Although these characters were passed down by the Bird Officials, the pictures were indeed created by Fuxi. These pictographic characters and ideographic symbols mostly derived their meanings from the ancient practice of knot-tying for record-keeping, and were gradually established over generations, not solely invented by the Bird Officials. Since there were no historians to record events at that time, and legends are difficult to verify in detail, it is impossible to determine exactly who created each particular character.

而易之卦象，則傳之最久，固昭昭於人耳目，知為伏義之創制焉。其後聖人推其義、宏其用，以為制作之本、典型之由，故尤重之，蓋歷代文物莫不祖述於易也。易之所作，既因圖書，傳之天然，有非人為；其推衍變化，皆天地自然之序；其運用本末，皆造化自在之則。固非人制之，乃人為明之耳。創之者然，述之者然，紹演變化者亦然。以其本末天道、終始運數，有定序，有極則，不得有所易也。故易者，天道所自見、運數所由明，而備於人天相合之教者也。

But the hexagrams of the Book of Changes have been passed down for the longest time, clearly visible to all people, and everyone knows they were created by Fuxi. Later sages elaborated on its meaning and expanded its applications, using it as the foundation for various creations and the origin of rituals and systems, so they especially valued it—no cultural institutions or systems throughout history have not drawn from the Book of Changes. Since the Book of Changes was created based on the Yellow River Chart and the Luo Writing, it is a natural revelation, not man-made. Its patterns of derivation and transformation follow the natural order of heaven and earth; its principles of application, beginning and end, are inherent in the workings of nature. Therefore, it was not made by people, but rather people revealed it. The creator was like this, the narrator was like this, and those who further developed its transformations were also like this. Because it follows the principles of heaven from beginning to end, and the course of fate in an orderly way, with a definite sequence and a final standard, it does not allow for arbitrary changes. Thus, the Book of Changes is the place where the heavenly way reveals itself, where the course of fate becomes clear, and also a complete system of teaching that enables people to align with heaven.

卦象之制，亦本氣數之盈虛而定，其多少變易，莫非天地自然之物所合者也。卦序之制，雖各易不同，亦本於氣運之往復進止，循環以成，莫非天地常變之道所孚者也。卦之有本末內外及生成消息之象，爻之有時位變化、天地人鬼之象，易之有天地父母、萬物萬事之類，占之有吉凶禍福、因果感應之類，皆本於天地固有者也。卦序之有先後天之別，卦用之有主客體用之別，易之有門戶、槖鑰、奇偶、正反之名，占之有來去、變異、從違、動靜之名，亦皆天道人道固然者也。

The establishment of hexagrams is based on the waxing and waning of qi. The variations in the number of lines in hexagrams are all in harmony with natural phenomena in the universe. The sequence of hexagrams, although different among various books of the Book of Changes, is all derived from the movement and return of qi, the forward and backward motion, and the cyclical repetition, thus conforming to the constant and changing principles of heaven and earth. Hexagrams have images of origin and end, inside and outside, generation and decline. Lines have changes in time and position, and images of heaven, earth, humanity, and spirits. The Book of Changes has categories such as heaven and earth, parents, and all things and all matters. Divination has terms such as good fortune and misfortune, calamity and blessing, cause and effect, andsympathetic response. All of these are based on things that heaven and earth originally possess. The sequence of hexagrams is divided into Earlier Heaven and Later Heaven. The use of hexagrams is divided into main and guest, body and function. The Book of Changes has terms such as 'doorway', 'key', 'odd and even', 'positive and negative'. Divination has terms such as 'coming and going', 'change and variation', 'following and opposing', 'movement and stillness'. All of these are as they are in the way of heaven and humanity.

蓋易者，聖人睹天地之序，測日月之度，明人物之情，達神鬼之德，而推其始終本末、生成變化之道，及夫人物事理所宜之類，明夫氣數消長、時地遷移，以合於人生，立為人道，而教民勿迷者也。易之為道至矣。

The Book of Changes is the sage's observation of the order of heaven and earth, calculation of the movement of sun and moon, clarification of the conditions of people and things, and understanding of the virtues of ghosts and spirits. Thus, it investigates the principles of the origin and development of all things, from beginning to end, from root to detail, and the proper categories of people, things, affairs, and principles. It clarifies how the vital energies wax and wane, and how time and place change, to suit human life and establish the way of being a person, guiding the people so they do not lose their way. The way embodied in the Book of Changes can be said to have reached its peak.

天之所授，神之所明，聖人從而演之以告人耳。雖天地末有之前，尚在易中，況天地乎？雖天地難知之道，尚可推知，況人物乎？故易者，其德顯，其道微，其用明，其體不可見；其大無外，其細無內。觀其象可盡其義，通其意可孚於神。雖立人道以始終，而歸於天道；雖驗氣數於既往，而極於末來。是以歷代聖人莫不諄諄焉：論之以闡其精，廣之以達其神，分合之以窮其變化，微驗之以明其氣數，唯恐人之未能盡其義理。故象外詳其辭，經外者著其傳，輔以圖序，參以蓍龜，其先覺覺民之心，已可見矣。

The Yi Classic discusses what is bestowed by Heaven and revealed by the divine, and the sages merely follow it, unfolding its principles to inform the people. Even the condition before Heaven and Earth came into being is included within the scope of the Yi, let alone Heaven and Earth themselves. Even the profound mysteries of Heaven and Earth can be understood, let alone human beings and things. Therefore, the Yi Classic has manifest virtue, subtle principles, clear function, yet its essence is invisible. It is great beyond the outer, and minute beyond the inner. Observing its images, one can fully grasp its meaning; comprehending its use, one can harmonize with the divine. Though it establishes the beginning and end of human affairs, it ultimately returns to the principles of Heaven; though it verifies the destiny of past events, it ultimately extends to the future. Therefore, sages of all ages have repeatedly emphasized: explaining it to clarify its subtleties, expanding it to grasp its mysteries, dividing and combining it to exhaust its transformations, and carefully verifying it to explain its destiny, fearing that people may not fully understand its meaning. Thus, in addition to its images, it is accompanied by words; beyond its main text, there are commentaries; it is supported by diagrams and sequences; and it is verified by yarrow stalks and oracle bones. The earnest concern of the enlightened ones to awaken the people is evident.

餘於文周之遺，習之既久，卒通其義，不敢負先聖垂教之意，更集其說以筆之書，授於二三子。既承文周之作，道備言審，象當義充，足盡他易之旨，故於連山等略其說，而唯周易是傳焉。然讀斯易，亦可包舉他易，以其為言精，為義廣，讀其一足盡其餘也。若有志者將更求之，亦易達連山歸藏之文矣。今當講周易之先，略述其大旨所闡，以資參究焉。

I have studied the legacy left by King Wen and the Duke of Zhou for a long time, and finally understood its meaning and principles. I dare not fail to live up to the intention of the sages who left these teachings for us. Therefore, I gathered the views of various schools and wrote a book to pass on to my disciples. Since I have inherited the works of King Wen and the Duke of Zhou, the reasoning is complete, the words are careful, the hexagrams are appropriate, and the principles are full. It is sufficient to include the meaning of all other books of Change. Therefore, I have omitted the discussion of the "Lianshan" and others, and only passed on the "Zhou Yi." However, reading this "Zhou Yi" is equivalent to understanding all other books of Change, because its statements are precise and its meanings are broad. If one understands this one, he will have mastered the rest. If someone with a strong will wishes to go further, he will find it easy to understand the texts of the "Lianshan" and the "Guicang." Now, before I begin to explain the "Zhou Yi," I will first briefly outline its main principles for everyone to study and refer to.

講易較難於他經，非望文釋義者也。易之始作，既在上古，經歷代聖人敷文陳義，其間增滅已多。欲明作者之心，必略文而求象；然初習者舍文字外，恆不解象之真義。歷代聖人亦以此故，始推衍其旨，詳述其文，而後卦有卦辭，爻有爻辭，彖象分詮，文言附釋。猶以為末盡，則更敷演其義，博採所聞，或繫詞，或說序，以成傳文，麗於經語。

Interpreting the Book of Changes is more difficult than interpreting other classics, and one cannot rely on the meaning of words alone. The Book of Changes was first composed in ancient times, and through the ages, sages have elaborated its words and explained its principles, with many additions and revisions in between. To understand the original intention of the author, one must temporarily set aside the words and seek meaning through the images. However, beginners who abandon the words often fail to grasp the true meaning of the images. For this reason, sages began to elaborate on its meaning and explain its words in detail, thus giving each hexagram its hexagram statement and each line its line statement. The Commentary on the Judgment and the Image Commentary explain these separately, while the Wenyan provides additional explanation. Still finding it insufficient, they further expanded on its meaning, widely collecting materials they had heard, composing the Great Treatise, the Explanation of the Hexagrams, and the Order of the Hexagrams, and writing commentaries attached to the main text.

其所陳釋，亦非一人之言，蓋得之師傳，參諸他本，集合其說，序列成章，無非以易道精宏，神用莫極，變化無盡，推測維艱。且以三易有殊，取材致用，不一類，不同科，較彼量此相得必多，去短留長，歸奇於正。而辭有不備，文有難宣，或略於經則詳於傳，或重於卦則輕於爻，意有互參，用有聯及，則不獨象之宜重，文亦必詳；經之宜求，傳亦必讀。是習易者固當知也。

These statements are not the words of a single person, but have been passed down by teachers and compared with other versions, gathering together the views of different schools and arranging them in order. The reason for doing this is simply because the principles of the Book of Changes are profound and vast, with its mysterious effects without end, its transformations boundless, and its interpretation extremely difficult. Moreover, the three versions of the Book of Changes differ from each other, their sources and methods of use not being the same. By comparing and weighing them against each other, one can gain much more, eliminating the shortcomings and retaining the strengths, correcting the deviant to the correct path. As for the wording, there are always incomplete parts, and meanings that are hard to express fully. Therefore, where the text is brief, the commentary explains in detail; where emphasis is placed on the hexagrams, the lines are relatively omitted. In meaning, they should be referred to mutually, and in application, they should be connected with each other. In this way, not only should the images be valued, but the wording must also be explained thoroughly. The classics should be studied, and the commentaries must also be read. This is something that those who study the Book of Changes should already know.

古人初制象時本以會意，雖文不傳，而畫已具，當視所畫之象為最簡之文。厥後文字既建，言詞漸繁，於原象之下引申其意，綴為文辭，則文字者既原象之廣義，當視其辭為漸明漸繁之象，不可分為二也。蓋象亦會意之文，文亦釋意之象，千古聖人後先同揆，作雖異時，義無二致。故讀易者象辭並重：先熟其辭，知象之會意有定義也；後習其象，知文之釋意有微旨也。二者通之，無所疑惑，則易道可見，聖人之心可明，而後用之不違，推之能化。神明之德、天人之道，蓋莫不盡於象與辭焉。

In the beginning, when ancient people created the trigrams, they originally followed the path of meaning through association. At that time, although there were no written characters passed down, pictures had already been formed, and the images drawn should be regarded as the most concise form of writing. Later, when writing systems were established, language became gradually more elaborate, and then the meanings of the original images were extended and combined into words. Therefore, writing is actually an extension of the original image, and these words should be regarded as gradually clearer and more complex images. We should not treat them as two separate things. The image is meaning through association, and writing is the explanation of meaning; for thousands of years, sages have followed the same principle, even though their creations were in different eras, the meaning remains the same. Therefore, those who study the Book of Changes should give equal importance to both the images and the words. First, read the words thoroughly, understanding the definite meaning of the images; then study the images, understanding the subtle implications hidden in the words. When both aspects are fully understood, there will be no doubts in the mind, and the way of the Book of Changes will become clear, the mind of the sages will be understood, and using it will not lead to mistakes, and its application will be able to reach all changes. The divine virtue and the great way of heaven and humanity are probably fully contained within the images and words.

且易之為用，重在變化。以人之智慧，通天下之故，達神鬼之情，必於變化中得之。象之會意，以象一事一物一時一地者也，而通其變，則必合他象而通參之；辭者釋意以辨類，亦當合他卦爻之辭而通參之。故習易者，象外求象，辭中索辭，如審物然，上下四旁、內外形狀，必通知之，非據一面而能盡其變化也。易之變化亦有定序，則須合全易之象辭通參之。天道不變，雖雙仍不亂其序，故序者，天下之定則也。而易之序則序卦傳為主，此讀易必及之。易卦之序有數種，其用不同，故所序異。而周易之序，則凡今天下所通行之則，莫不依以變化。後所得者，雖變不止此，尚有待於後聖，然今日之數則無違於此。

Moreover, the function of the Book of Changes lies in its emphasis on transformation. Human wisdom must understand the origins of all things under heaven and the conditions of ghosts and spirits, and this can only be achieved through the study of transformation. The images (xiang) are used to symbolize particular things, objects, times, or places; to understand their transformations, one must refer to other images in conjunction. The words (ci) explain meanings and distinguish categories, and they should also be considered together with the words of other hexagrams and lines. Therefore, those who study the Book of Changes must seek images beyond images and meanings within meanings, like examining an object carefully, considering all aspects—above and below, all directions, internal and external forms—without relying solely on one aspect to fully grasp its transformations. The transformations of the Book of Changes also follow a certain order, which requires the consideration of all the images and words of the entire Book of Changes. The heavenly way remains constant, and even when there are changes, it does not disrupt its order. Thus, "sequence" (xu) is the established rule for the world. The sequence of the Book of Changes is mainly based on the "Sequence of Hexagrams" (Xugua Zhuan), which is essential for studying the Book of Changes. The sequence of the hexagrams has several different forms, each with different purposes, so their arrangements vary. As for the sequence of the Zhou Changes, it is the universally accepted principle of the present age, and all changes follow it. Although later generations may achieve further transformations, they still await the wisdom of future sages; however, within the current era, these transformations will not exceed this scope.

易之有體用者，亦由序卦之殊。如伏羲之序異於文王，連山歸藏之易異於周易，後人始有先後天之名。田先天不變，後天重在變；先天不用，後天重在用。由道言之，先天為主，後天為從；由人事言之，皆在後天，一至先天，無所為矣。故周易之用，為人道也，因時之宜，立道之極，而原始要終之事也。先天之易常靜，後天之易常動；而靜中有動，故先天必生後天；動中有靜，故後天不離先天。二者異途同歸，知其一則通其二。斯文王之聖智，乃能盡其變化，而建立周易之極，以全易之用也。

The reason the "Book of Changes" has both "essence" and "application" is due to the difference in the order of the hexagrams. For example, the sequence of Fuxi is different from that of King Wen, and the "Book of Changes" in "Lianshan" and "Guicang" differs from the "Zhou Changes." Later scholars thus introduced the terms "Earlier Heaven" and "Later Heaven." The Earlier Heaven remains unchanged, while the Later Heaven emphasizes change; the Earlier Heaven does not focus on practical use, while the Later Heaven emphasizes practical application. From the perspective of the Dao, the Earlier Heaven is the main aspect, and the Later Heaven is the subordinate; from the perspective of human affairs, all human activities are based on the Later Heaven. Once one enters the realm of the Earlier Heaven, there is no action to be taken. Therefore, the use of the "Zhou Changes" is for human affairs, following the suitability of the times and establishing the standards of the Dao, doing the work of investigating the beginning and concluding the end. The Earlier Heaven's "Book of Changes" is often in a state of stillness, while the Later Heaven's "Book of Changes" is often in motion; stillness contains motion, so the Earlier Heaven necessarily gives rise to the Later Heaven; motion contains stillness, so the Later Heaven cannot be separated from the Earlier Heaven. Although their paths differ, they ultimately converge, and understanding one allows one to comprehend the other. It was precisely due to King Wen's wisdom that he was able to exhaust these changes, establish the standard for the "Zhou Changes," and thus enable the full realization of the function of the "Book of Changes."

夫伏羲之時，豈無所用哉？豈不盡其變化以適人事哉？何以必待文王而後明也？是蓋有故焉。上古之時，人事簡略，民習於道，上有所制，下則循之，既無所多需於變化，亦無所窮於用。且以文字未備，傳佈難廣，作者心通其用，知者神會其變化，有其體已足矣。

Did the Book of Changes have any use in the time of Fuxi? Did he not already exhaust all changes to adapt to human affairs? Why then did it have to wait until King Wen to be made clear? There must be a reason. In ancient times, human affairs were simple, and the people were accustomed to following the Dao. What was set above was followed below, so there was little need for change, and the usefulness of the Book of Changes was not fully exhausted. Moreover, at that time writing was not yet complete, and transmission was difficult, so the author understood its use in his mind, and those who knew it grasped its changes through spiritual intuition. Having this 'body' was enough.

迨文字既成，文物漸備，迄乎三代，其用易已繁，其變化亦多。彼連山歸藏者，即述前人之口傳，會伏羲之本象，而以盡其變化，致其用，而後制之。文王之卦，正猶是也：上依伏羲之本卦，下采連歸之變例，沿其舊制益其新規，而後周易以成。周易既成，連歸可不復用。於是伏羲與文王二易，一體一用，一本卦，一變例，兩者著明，易道大備。

When writing was developed and systems and objects gradually became more complete, by the time of the Xia, Shang, and Zhou dynasties, the use of the Book of Changes had become frequent, and its transformations also increased. The two other books of change, the Lianshan and Guicang, were created to record the oral traditions of earlier times, combining the original hexagrams of Fuxi, in order to exhaust all its transformations and fully utilize its functions, and then they were compiled into books. King Wen's hexagrams were also like this: the upper part relied on the original hexagrams of Fuxi, while the lower part adopted the transformations from the Lianshan and Guicang, continuing the old system while adding new rules, and thus the Zhou Changes were completed. Once the Zhou Changes were completed, the Lianshan and Guicang could no longer be used. Thus, the two Books of Changes of Fuxi and King Wen, one representing the essence and the other the application, one the original hexagram and the other the transformation, both became clear, and the way of the Book of Changes became greatly complete.

吾故曰易之為易，成於歷代聖人，非一人所作也。伏羲啟之，諸聖紹之，以其本天地自然之序，故作者異而易不異，易序異而易道不異。文王之易固源於歸藏，歸藏源於連山，而莫不出自伏羲。伏羲雖僅傳其體，而用仍紹於周易，則二者合而易以全，更無分於伏羲文王。不過周易傳自文王，今遂名之為周易耳。讀者要當視為一易，不可以其傳述之人不同，而謂有二易也。

Therefore I say: The reason why the Book of Changes is called the Book of Changes is because it was jointly completed by the sages of successive generations, not the work of a single person. Fuxi initiated it, and the other sages continued it. Since it is based on the natural order of heaven and earth, the authors may differ but the Book of Changes remains the same; the order of the hexagrams may differ, but the principles of the Book of Changes remain unchanged. King Wen's Book of Changes certainly originated from the Book of Changes of the Duke of Zhou, which in turn originated from the Book of Continuous Mountains, and all of them ultimately come from Fuxi. Although Fuxi only passed down the "body" (the structure), the "application" (the practical use) was continued by the Book of Changes. Thus, the combination of both makes the Book of Changes complete, and there is no need to distinguish between the Book of Changes of Fuxi and that of King Wen. The only difference is that the Book of Changes was passed down by King Wen, and hence it is now called the Book of Changes of the Zhou dynasty. Readers should regard them as a single Book of Changes, and should not say there are two Books of Changes merely because they were transmitted by different people.

夫易之有三者，非三易也，易之三變例也。既有三變，已備天地人之數，為用已足，雖有他變，終不出乎三者。文王之易，合三者而一之，故言卦之變與易之用，以周易為主，此吾贊易取文王序卦之由也。卦變雖從文王，本卦必溯伏羲，故說卦兼及二者次序。後人不明易之用有正變，不知伏羲文王之卦同異之義，不解連山歸藏不用之由，妝加揣測，不獨易道不明，既易之自出，亦不復曉；或摭拾殘編以爭執異辭，或採取他易以辨別圖序，皆失吾贊易原意者也。要知末有周易，則不得不採用連歸；既有周易，則從周已足。此吾有從周之嘆也。

The Book of Changes has three forms, not three separate books, but three variations of the Book of Changes. Since there are these three variations, the numbers of heaven, earth, and humanity are complete, and they are already sufficient for use; even if there are other variations, they cannot go beyond these three. King Wen's Book of Changes combines the three into one, so when discussing the changes of hexagrams and the use of the Book of Changes, we should take the Zhou Yi as the main reference. This is why I use King Wen's hexagram order when explaining the Book of Changes. Although the changes of hexagrams follow King Wen, the original hexagram must be traced back to Fuxi. Therefore, the "Sayings of the Hexagrams" includes the order of both Fuxi and King Wen. Later people did not understand the distinction between the standard and variant forms of the Book of Changes, did not comprehend the differences between the hexagram orders of Fuxi and King Wen, and did not understand why the Lianshan and Guicang were abandoned. They made wild speculations, resulting not only in the confusion of the principles of the Book of Changes but also in not knowing where the Book of Changes originated. Some people argue over fragmented old texts to dispute different interpretations, while others use other forms of the Book of Changes to distinguish between diagrams and orders, all of which deviate from my original intention in explaining the Book of Changes. One must know that before the Zhou Yi was established, the Lianshan and Guicang had to be used. Once the Zhou Yi was established, following the Zhou system was sufficient. This is the reason for my exclamation, "I follow the Zhou."

夏商遺典，固不可考。連山歸藏之易，吾於杞宋猶及見之，初亦以為可取；及參之周易，始知二者已在其中矣，故從周易。易中諸辭，非盡文王之作，多沿二易之舊，今猶在也。而周易之精，不在辭之美備，而在序之精當，以能參天地二道，立人道之極，全變化之用，明始終之義，非如連歸所取義狹而立極有偏也。故合伏羲之旨，盡易之變化者，唯周易為宜，此文王之所以聖者歟。夫易之有異同，既可知矣；而習易之應從周易，又無疑矣。顯後人猶不達者，則以及門之士末嘗將經傳詳為講釋，以明旨趣；二三子好事者，又竊取連歸之本，授於門人。迨漢之興，言易者遂有同異，雖非乖離不稽之說，究為門戶爭執之階，此則易道之不幸也。

In the Xia and Shang dynasties, the remaining classics are indeed difficult to verify. I once saw the two books of the Yi, namely the Lianshan and Guicang, in the states of Qi and Song, and at first I thought they were worth considering. But when I compared them with the Zhou Yi, I realized that their contents were already included in the Zhou Yi. Therefore, I followed the Zhou Yi. Many of the phrases in the Yi are not entirely the work of King Wen, but mostly inherited from the old texts of the two other Yi. They are still preserved today. The excellence of the Zhou Yi lies not in the perfection of its language, but in the proper arrangement of its hexagrams. It combines the principles of heaven and earth, establishes the standard for human conduct, preserves the function of change, and explains the meaning of beginning and end. It is unlike the Lianshan and Guicang, which have narrow interpretations and an unbalanced standard. Therefore, to conform to the principles of Fuxi and to exhaust the changes of the Yi, the Zhou Yi is the most suitable. This is probably why King Wen was considered a sage. The differences and similarities among the various schools of the Yi are now clear; studying the Yi should follow the Zhou Yi, and there is no doubt about it. However, later people have not fully understood this, because my disciples have not thoroughly explained the classics and their commentaries to clarify their meaning. Some students, out of personal interest, have secretly obtained copies of the Lianshan and Guicang and passed them on to their own disciples. When the Han dynasty arose, scholars who studied the Yi began to have disputes over different interpretations. Although these views are not entirely wrong, they have become the starting point of factional disputes, which is truly unfortunate for the way of the Yi.

然以今傳之本，既無詳解之文，則他山之石，可以攻玉，取其所異以證其同，亦足以明周易之精美，而直探文王之心矣。易之言讖緯，誇占驗，及其以本宮生變為序，以納甲合歲為用者，其書雖殊，亦屬古人之遺，參而求之，尤足推廣周易之用，蓋雖近雜，亦非無益。是在讀者知以周易為宗，勿認客作主，則占驗之說，正可為修省之助，而生變之異，又可例易道之宏，其所益於易固自有在焉。

However, in today's transmitted versions, since there are no detailed explanatory texts, one may take the saying "He who takes a stone from another mountain can polish jade" (from the Book of Songs, Xiao Ya, He Ming), and use the differences among various schools to verify their commonalities, thereby clearly seeing the elegance of the Zhou Yi and directly understanding King Wen's intent. As for books in Yi studies that discuss omens, exaggerate divination results, and use "ben gong" to generate variations in order, or employ "najia" to coordinate with years and years to apply them, although they differ from the Zhou Yi, they are also remnants from ancient times. Referring to them for study can further expand the applications of the Zhou Yi. Although these contents may seem miscellaneous, they are not without benefit. The key lies in the reader knowing to take the Zhou Yi as the main focus, not treating secondary matters as the main. In this way, statements about divination can help people cultivate themselves and examine their conduct, while the differences in variations can serve as evidence of the vastness of the Yi Dao. Their contributions to the Yi are inherently valuable.

易道至微，包義至廣，仁者見仁，智者見智，易固具仁智矣，而見者則依人而殊。非貫通之，誠不明易之為易，而聖人之教不得全行於世，雖曰讀易無益也，故必先明易之本義。夫「易」者：賅象數以明氣，辨時位以明用，詳變化以明生，測順逆以明吉凶，徵名類以明動靜，驗二五以明終始本末，會天人以明性情道德。其含義無盡，致用不窮，其稱名不一，取類至廣，然有其始終焉：推事物之情，溯天地之道，以人立極，有其道也。故習易者有其例，不明其例，則莫知其旨，而例者，指象數也。

The Way of the Book of Changes is extremely subtle and its included principles are extremely broad, so the Great Treatise says, "The benevolent person sees it and calls it benevolence; the wise person sees it and calls it wisdom." The Book of Changes originally contains both benevolence and wisdom, but people's interpretations differ according to their own nature. If it is not integrated, one will truly not understand why the Book of Changes is called the Book of Changes, and the sages' teachings will not be fully practiced in the world. In that case, reading the Book of Changes would be of no benefit. Therefore, one must first understand the fundamental meaning of the Book of Changes. The term "Easy" refers to the comprehensive use of "images" and "numbers" to explain qi, distinguishing "time" and "position" to explain application, elaborating on change to explain the continuous generation of life, predicting favorable and unfavorable conditions to explain good and bad fortune, verifying names and categories to explain movement and stillness, examining the dual and the five (yin and yang and the Five Phases) to explain beginning and end, origin and outcome, and integrating heaven and humanity to explain nature, emotion, morality and virtue. Its meaning is endless, its use is infinite, its names are not limited to one, and its analogy is extremely broad, yet it has its own order. By investigating the nature of things, tracing back to the great Way of heaven and earth, and using human beings as a standard, this is its method. Therefore, studying the Book of Changes requires "examples" (general principles and rules). Without understanding these general principles, one cannot grasp its essence. The so-called general principles refer to images and numbers.

象數者，圖畫文言之所示也。不先求於圖畫文言，則不明象數；不明象數，則不知易之本體及其變化。若拘拘於經文，兢兢於名類，此為文藝之事，而非以極深研幾也。如乾者，必先求其圖之所示，何以為□；必先考其爻之所名，何以為九；必先溯其氣之所始，何以為陽；必先察其道之所存，何以為天。皆必徵於象數而後知之。知之而後可言其德，可名其用，可數其變化，可質其所分合，可因例而明其爻之所占、文之所釋，而後經文可得而釋也。此凡習易者均當如此。夫子韋編三絕，所用心亦如此，決非徒誦其經，熟其訓詁，即足了事者。而講易之先，必自例始；例明而後通貫一切，庶無惑於經文之義；此為講易第一事。

The concepts of "image" and "number" refer to the meanings revealed through diagrams and text. Without first seeking understanding from the diagrams and text, one cannot comprehend the principles of image and number; without understanding image and number, one cannot grasp the essence and transformations of the Book of Changes. If one merely focuses on the text and gets bogged down in terminology and categories, that is the approach of literary study, not "reaching the profound and examining the subtle." For example, the "Qian" hexagram must first clarify what its diagram represents and why its hexagram is drawn in that form (the original diagram is missing here); it must first examine why its line is called "nine"; it must first trace the origin of its energy and why it is considered "yang"; it must first investigate the underlying principles and why it is symbolized as "heaven." All these must be understood through the study of image and number. Only after understanding these can one discuss its virtues, its functions, its transformations, and its distinctions and combinations. Only then can one understand what each line represents and what the text explains, and only then can the text be properly interpreted. All those who study the Book of Changes should follow this approach. Confucius read the Book of Changes so thoroughly that he wore through the ropes binding the bamboo slips three times; his diligence was precisely in this, not merely memorizing the text or mastering the meanings of words. Therefore, before discussing the Book of Changes, one must first grasp the general principles; only after understanding the general principles can one comprehend everything and avoid confusion over the meaning of the text. This is the first essential matter in studying the Book of Changes.

夫易自伏羲氏以後，象數卦儀，傳之既久，因其用不同，而取義有異；故有連山、歸藏、乾坤三易之分；實以一為三，非有他易也。連山首艮以明人道，夏代承用之；歸藏首坤，以重地道，商承用之；乾坤首乾，以尊天道，周承用之。以所首不同，故取義各異，正與夏正建寅，商正建丑，周正建子，其義一也。非歲序異，歲首異耳。故明人道者，以人為先；重地道者，以地為先；尊天道者，以天為先。實則易道備天地人，先後雖殊，場道不異，殊其用耳。

The Book of Changes has been passed down since Fuxi, with its images, numbers, hexagrams, and rituals. Because of different uses, the meanings derived from it have varied, leading to the distinction of three versions of the Book of Changes: the Lianshan, the Guicang, and the Qiankun. In reality, these are three different forms of the same Book of Changes, not three separate books. The Lianshan begins with the Gen hexagram, used to explain human affairs, and was used during the Xia dynasty; the Guicang begins with the Kun hexagram, used to emphasize the earth's principles, and was used during the Shang dynasty; the Qiankun begins with the Qian hexagram, used to honor the heavenly principles, and was used during the Zhou dynasty. Because the first hexagram differs, the meanings derived also differ. This is similar to the way the Xia calendar took the寅month as the first month of the year, the Shang calendar took the丑month as the first month, and the Zhou calendar took the子month as the first month. It is not that the order of the year has changed, but only that the name of the first month has changed. Therefore, the one that explains human affairs places humans first, the one that emphasizes the earth's principles places the earth first, and the one that honors the heavenly principles places heaven first. In reality, the Book of Changes encompasses heaven, earth, and humanity. Although the order of precedence differs, the principles of the Book of Changes remain the same; the difference lies only in their application.

周雖重天道，而兼二代之制，故文王重演坎離之卦，以合三為一，而同於乾坤之易；乾坤之易，伏羲固已立制，而坎離之易，則文王為之紹述者也。後人名之曰「先天易」「後天易」，其實一體一用耳。

The Zhou dynasty, although emphasizing the heavenly way, also adopted the systems of the Xia and Shang dynasties. Therefore, King Wen reworked the trigrams Kan and Li, integrating the systems of the three dynasties into one, making them consistent with the Book of Changes based on Qian and Kun. The system of the Book of Changes based on Qian and Kun was already established by Fuxi. As for the Book of Changes based on Kan and Li, it was King Wen who continued and developed it. Later generations referred to them as the "Earlier Heaven Book of Changes" and the "Later Heaven Book of Changes," but in reality, one discusses the fundamental principles and the other discusses practical applications.

蓋乾坤易、明位者也；坎離易、用時者也；雖次序不同，而其為易也無異。以乾坤之易，不能外坎離，坎離之用，亦不能不本乾坤；二者相參，而後變化以大，不獨二易以合用，即三易亦由是以同功。此坎離之易，包括乎一切，而為天地既奠以後所不可少者，以其用之廣，而變化之神也；此習易者必先知之。知其一而求其二與三，則三二皆歸於一，以一概易，名符義當。誠哉聖人之心，足以通天地，並日月矣！

The "Qian and Kun" aspect of the Book of Changes deals with directions, while the "Kan and Li" aspect deals with timing and application. Although the order is different, both aspects belong to the Book of Changes without distinction. The "Qian and Kun" aspect cannot be separated from Kan and Li, and the application of Kan and Li cannot be done without relying on Qian and Kun. They complement each other, allowing for great transformations. Not only should these two aspects be used together, but all three aspects of the Book of Changes also achieve the same effect. The reason why the "Kan and Li" aspect can encompass everything and become an essential part after the establishment of heaven and earth is because of its wide application and mysterious transformations. This is something those who study the Book of Changes must first understand. Once one understands one aspect, seeking the others will eventually lead to the unity of three into one. Using this "one" to encompass the Book of Changes, the name and meaning are perfectly aligned. The wisdom of the sages is truly remarkable, capable of connecting heaven and earth and standing equal with the sun and moon!

故文周之後，夫子必兢兢焉以祖述之，而為文以著其義；使伏農暨文周之業，永垂無盡，此則夫子贊易之微志也。夫易有數義焉：以其至易，本於太一也，故自無始至有始，推之無盡，無不可知，此一義也。以其不易也，立本於中，致用於極，中極不變，永執其中，其道乃久，故能行變化而無息，主生成而不測，此一義也。以其變易也，順天地之消息，應氣數之盈虛，與時遷移，其道莫窮；故能握化之鈞，得循環之道；唯通以變，因適而宜，此一義也。

Therefore, after King Wen and the Duke of Zhou, the Master surely carefully continued their work, recording it in writing to reveal its principles, so that the achievements of Fuxi, Shennong, King Wen, and the Duke of Zhou would be perpetually transmitted. This is the profound intention of the Master in commenting on the Book of Changes. The character "易" contains several meanings. The first is "至易" (simplicity): it takes "Taiyi" as its foundation, so from no beginning to the emergence of a beginning, it extends endlessly, and nothing is unknowable. The second is "不易" (constancy): it establishes its root in "zhong" (the center) and extends its function to "ji" (the extreme). Zhong and Ji remain constant, and by always holding fast to this center, its way can endure, thus enabling it to carry out transformation endlessly and govern creation beyond measure. The third is "变易" (change): it follows the waxing and waning of heaven and earth, responds to the full and empty of qi, and adapts with the shifting circumstances, with the path never ending. Therefore, it can grasp the key of the workings of nature and comprehend the laws of cycles; only by being fully enlightened can one respond to change, and by adapting appropriately to each situation, one can achieve the right fit.

易之為道，有本末始終，有體用內外，包乎萬有，極乎無盡，推之無窮，而無為無不為。此至誠之德，中和之功，天人之所合，事物之所順；而明乎玄微，探乎繁嘖；至簡且易，至久且廣者也，此易之名與義也。

The Dao expressed in the Book of Changes has a beginning and an end, a root and a branch, a body and a function, an inner aspect and an outer aspect. It encompasses everything, reaches the utmost limitlessness, and is inexhaustible in its unfolding. It appears to do nothing yet accomplishes everything. This is precisely the virtue of "utmost sincerity" mentioned in the Doctrine of the Mean, and the effect of "harmony in the middle," the meeting point of heaven and humanity, the basis for the smooth operation of all things. It can illuminate the subtle and profound, and explore the complex and chaotic. It is both simple and easy, yet profound and vast. This is the meaning of the term "Yi" and its significance.

至易之為象，上日下月，日月者，陰陽之所昭，而天地之道所見者也。以天之道，由日而明，地之道，由月以見；日月代行，天地不息，此坎離代乾坤為主，而水火成陰陽之用。此在體用既合，情性同見之時，而後知乎天地之道，曲成之妙者也。故明易者，必先明坎離之易，由下溯上，由外及內，由人及天，皆必然之序，不可臘者也。

As for the formation of the character 「易」, it consists of a 「日」 on top and a 「月」 below. The sun and moon serve as the means by which yin and yang are revealed and the principles of heaven and earth become evident: the heavenly way is made clear through the sun, and the earthly way is made visible through the moon. The sun and moon take turns in their movement, and thus heaven and earth continuously generate and sustain life. This is why 「坎」 and 「离」 take the place of 「乾」 and 「坤」 in the central position, with water and fire embodying the function of yin and yang. Only when the essence and function are combined and emotion and nature are fully revealed can one understand the subtle aspect of the way of heaven and earth, which is to 「曲成万物」 (as stated in the Great Treatise, meaning to accomplish all things in a subtle and comprehensive way). Therefore, to understand the Book of Changes, one must first understand the part of the Book of Changes related to 「坎」 and 「离」. One should trace back from the lower to the upper, from the outside to the inside, and from human affairs to the heavens. This is the natural sequence and cannot be skipped or rushed.

且日者元陽之象，其體亦太極之象，故為□、即□，亦中字之形也；太極之體一，為萬有之母，而易自太極始。日者生物之根，凡物不得日之光熱則不生，是日即生物之母。勿者，古文物字；上日下勿，示生生之象，亦明天下萬物自生之源。其取意固精，而為文卻顯。故知日月為易，則知天地以陰陽而神其變化，亦即知乾坤之易，以坎離而明其功用也。

Now speaking of the "day" (日), it represents the original yang, and its essence is also the image of the Taiji. Therefore, the symbol it takes (the original text here has a missing diagram) is exactly the shape of the character "中" (center). The essence of Taiji is "one," which is the mother of all things, and the Book of Changes (Yi Jing) begins precisely from Taiji. The sun is the fundamental source for the growth of all things; without the light and heat of the sun, nothing can grow, so the sun is the mother of all living beings. "Wu" (勿) is the ancient form of the character "物" (thing); the character "Yi" has "day" on top and "wu" below, showing the image of continuous generation and also indicating the origin from which all things in the world arise on their own. Its meaning is indeed profound, and its character formation is very clear. Therefore, understanding that the sun and moon together form the character "Yi" means understanding that heaven and earth bring about changes through yin and yang, and also understanding that the Yi of the Qian and Kun is manifested through Kan and Li.

知□為易，則知天下萬物，莫不生於太一，育於元陽，而易之為教，莫外於溯萬有之始終，推萬物之生成長育，更由是以明天道人道之體用，及夫事物變化消息之數運也。故易辭雖簡，為義極宏，其道至深，為言必備。苟欲洞明其故，則固不外求之象數與文辭也；而易之象數，則盡乎形氣之精；易之文辭，則概乎義理之至。不深研而通其趣，則必有所滯；不廣征而匯其歸，則必有所失。此見仁見智之說，所由來也，習易者可不勉哉！

Understanding that symbol (the original text's diagram is missing) is the "Yi," one also understands that all things in the world arise from "Taiyi" and are nourished by "Yuanyang." As a means of education, the "Yi" is essentially about tracing back the beginning and end of all things, investigating the generation and growth of all things, and from there explaining the principles and applications of the Way of Heaven and Humanity, as well as the numbers and movements of change and transformation in things. Therefore, although the words of the "Yi" are concise, their meaning is extremely vast; its principles are very profound, yet its expressions must necessarily be complete. If one wishes to thoroughly understand the reasons behind it, in the end, it can only be sought from both the symbolic representations and numerical calculations and the textual expressions. The symbolic representations and numerical calculations of the "Yi" exhaust the subtle aspects of form and qi; the textual expressions of the "Yi" summarize the ultimate meaning of principles. Without deep study and understanding of its subtleties, one will inevitably encounter obstacles; without extensive evidence and summarizing its overall essence, one will inevitably miss something. This is the origin of the saying "seeing it as benevolence or wisdom," how can those who study the "Yi" not strive diligently!

夫易：明數者也，而數本乎氣，氣本於陰陽，陰陽本於太極，故太極為易之始。太極者，一也，其初無名無形，由元氣之凝而為光；光生氣，氣成形，形成質，故物之始生，必先有氣。斯氣也，流行天地之間，分合萬有之體，而不可見。

The Yi is the study of numbers. Numbers are based on qi, qi is based on yin and yang, and yin and yang are based on the Taiji. Therefore, the Taiji is the beginning of the Yi. The Taiji is referred to as "one." It was originally nameless and formless, and from the gathering of primordial qi, it transformed into light. Light produced qi, qi condensed into form, and form coalesced into substance. Therefore, when all things first began to arise, there must have been qi first. This qi flows throughout the universe, separating and combining the forms of all things, yet itself remains invisible.

見其形質焉，因氣之分合多少偏全，而形質不齊，故數不等而象不一，求其象而後知其數，明其數而後辨其氣。氣有陰陽，數有奇偶，因分合而有四五，因偏全而有善惡；此氣之變化也。因生物之時地有多寡，因境遇之變遷而有大小；此數之消長也。因所受之殊，而形質有殊；因所合之異，而性情有別；此象之進退也。

What people can see are form and substance: because the division and combination of qi varies in quantity and in completeness, forms and substances differ, so the numbers vary and the images differ. One must first obtain the image in order to know the number, and then clarify the number in order to discern the qi. Qi divides into yin and yang, number divides into odd and even; due to differences in division and combination there are four (the Four Symbols) and five (the Five Phases), and due to differences in completeness and partiality there are good and evil, which are changes in qi. Due to differences in time and place of birth, there are variations in quantity, and due to changes in circumstances, there are differences in size, which are the waxing and waning of numbers. Due to differences in what is received, forms and substances differ, and due to differences in what is combined, temperament and disposition differ, which are the advancement and retreat of images.

蓋氣自太極以下日分，分而仍合；故兩儀、四象、五行、皆以次名，數自太一以下，亦漸散，而仍復聚，故天一地二、至天九地十、推而五十、六十四、百四十四、二百一十六、而萬一千五百二十之數以別，象自太極以下，由氣數之推移變化，而諸物生成，名類日多，反覆日眾，以仍循環終始，故八卦六爻之互相乘除，太陰少陽之互相推化，以成萬物之形，類萬有之情，名萬事之制，而不可窮盡，此皆順乎生化之序，有不期然而然者。

The qi originates from the Taiji and is divided layer by layer downward, yet remains united, thus giving rise to terms such as "two principles" (liang yi), "four images" (si xiang), and "five phases" (wu xing) in sequence. Numbers also descend from "Taiyi" and gradually disperse, yet remain gathered, thus leading from "Heaven One, Earth Two" up to "Heaven Nine, Earth Ten" as recorded in the "Great Treatise" (Xici Shang Wen) regarding the numbers of heaven and earth. From there, it is further extended to the great derivation number of fifty, the sixty-four hexagrams, one hundred and forty-four (Kun's number), two hundred and sixteen (Qian's number), until ten thousand one hundred and fifty-two (the number representing all things), each with its distinct classification. The images originate from the Taiji and are generated through the movement and transformation of qi and numbers, leading to the emergence of various things, with their names and categories increasing day by day, their interweaving becoming more intricate, yet still following a cycle with beginning and end. Therefore, the six lines of the eight trigrams interact with each other through multiplication and division, while the Taiyin and Shaoyang interact and transform, thus forming the forms of all things, distinguishing the conditions of all things, and establishing the standards for all affairs, without end. All these follow the order of generation and transformation, occurring naturally without intention.

故總而言之：則一生二，二生三，三生萬物，分而言之，則太極以下，氣數與象，各以類別，不可勝紀。以自上而下，則言之如此；如自下溯上，則必就其已見者征之，此求象為第一步。因象者於外，存於現在，耳之所聞，目之所見，手足之所執持者，固易為徵。徵其象則得其數與氣，而後因其例，以辨其吉凶福禍；循其時地，以辨其道德性情，而後行止有方，動定有則，而用乃著，而道乃彰，而後聖人立教之心可見矣！故習場莫先於象數，明象數莫先於例。易之明例，實習渴之下手處，故講易必自例始，以其已知，求未知也。

In summary, this is what the Book of Dao (Laozi) says: "From one comes two, from two comes three, and from three come all things." When considered separately, below the Taiji, the qi, numbers, and images are categorized into different classes, and there are too many to count. Going from above to below, the situation is as described; but if we want to trace back from below to above, we must use the already manifested things as evidence. At this point, seeking the image (xiang) is the first step. Because the image is outside, existing in the present, it is something that can be heard by the ears, seen by the eyes, and held by the hands and feet, and thus is easy to verify. By examining the image, we can determine its number and qi; then, by following the general principles, we can distinguish between good and bad fortune, and by considering time and place, we can discern moral character and temperament. After this, action and stillness have direction, movement and stability have rules, and function becomes evident, the great Dao becomes clear, and the intention of the sage in teaching can be seen. Therefore, studying the Yi (Book of Changes) has no priority over the images and numbers. Understanding the images and numbers has no priority over the general principles. Truly understanding the general principles is the starting point of studying the Yi, so explaining the Yi must begin with the general principles—using what is already known to seek what is unknown.

夫易自伏羲畫卦，分列陰陽以定其位，重為六爻以明其時；乾坤為體，易行其中，乾坤成列，易立於中，二者體用之分，時位之辨，相錯以行，相交以變，生生不已，變化無盡。故由八卦而成六十四，六爻而推至三百八十四，皆本一氣循環，二五互用，以成其象，以寓其數，以行其氣。

The Book of Changes has been in existence since Fuxi created the eight trigrams. It divides yin and yang to determine the positions of each line, and combines three lines into six lines to show the time of each line. Qian and Kun are the fundamental principles; the Book of Changes operates within them. The Great Treatise says, "When Qian and Kun are arranged, the Book of Changes is established within them." Qian and Kun have distinctions between principle and function, and between time and position. They intermingle in operation and intermingle in transformation, continuously generating and transforming endlessly. Therefore, from the eight trigrams comes the sixty-four trigrams, and from the six lines comes the 384 lines. All of this is based on the cycle of one breath, the mutual interaction of yin and yang and the five phases, used to form its images, to embody its numbers, and to move its qi.

故太極既立，自生兩儀；卦象既成，自生爻象；自然推衍者也。由乾坤定位之易，而見卦位之序；由坎離中立之易，而見卦氣之時行，變化雖多，次序不亂，皆二五所生化，順乎天地萬物之次，而相交合五生成者也。故欲知生化之跡，必列象而觀之，此圖畫為所必重也。故習易必先將易之圖象，觀察明晰，如乾坤定位之圖等，一一列前；審其生化之序，及其推移之數，而後得其卦之由來，此固為第一事也。

Therefore, once the Taiji is established, the two principles naturally arise; once the hexagrams are formed, the lines naturally emerge—these are all naturally derived. From the "Qian and Kun establishing their positions" aspect of the Book of Changes, one can see the order of the hexagram positions; from the "Kan and Li occupying the center" aspect, one can observe the movement of the hexagram energies with the seasons. Although changes are numerous, the order remains unconfused, all arising from the generation and transformation of yin and yang and the Five Phases, following the sequence of the universe and interacting to produce all things. Therefore, to understand the traces of generation and transformation, one must arrange the images and observe them, which is why diagrams are given such importance. Thus, studying the Book of Changes must first involve clearly understanding its various diagrams, such as the "Qian and Kun positioning diagram," and displaying them in order, examining the sequence of generation and transformation and the numerical progression, only then can one clarify the origins of each hexagram. This is the fundamental task.

讀易須先明易例：以其敷辭有定，陳象不二，必通其義，而後明其旨，必抉其情，而後達其用。如乾□，天也、父也、之例，必先熟記之，則卦中有乾象，或通乾象；及其比偶反類之象者，皆有孚於乾之義，即有類於乾之情，則其為象，必同於乾之物；如天也、父也、之類，此易示象之例，有不易者也。又如乾之卦辭「元享利貞」，其六爻之辭各異，而皆有其物與事以象之，則各卦中如有乾之辭，及其爻之辭，或比偶反類之辭，皆與乾通其義；必合對參之，以明其所指，而後知其辭之用，此易辭之例，必通解者也。

To study the Book of Changes, one must first understand its general principles. Because the Book of Changes uses fixed expressions and clear symbolic representations, one must understand its meaning to grasp its purpose, and must uncover its actual significance to comprehend its practical applications. For example, the hexagram Qian (Heaven) represents Heaven and Father; this general principle must be memorized first. Then, any other hexagram that contains the image of Qian, or is related to it, or is compared with it, paired with it, opposite to it, or similar to it, will conform to the meaning of Qian and be close to its characteristics. Therefore, the images it takes will necessarily be the same as those symbolized by Qian, such as Heaven and Father. This is the general principle of the Book of Changes in displaying images, which is fixed and unchanging. Another example is the hexagram statement of Qian, "Original, Auspicious, Advantageous, and Correct." Although its six line statements are different, each has a corresponding object or event as its symbol. Therefore, if any hexagram contains the statement of Qian or a line statement corresponding to Qian's lines, or if the statements are compared, paired, opposite, or similar, they will all be connected to the principles of Qian. One must compare and examine them together to understand what they refer to, and then one can know how to use these statements. This is the general principle of the Book of Changes' statements, which must be fully understood.

習易貴乎通，而用易在乎熟，苟執而不通，習而多忘，則何以窮天下之變，盡易道之蘊哉？蓋易者：以簡御繁，以顯探微者也，因其為用至廣，言文難備；為道至大，事物同賅，則不得不操其本，用其極，以不二之道，成不測之功；以至易之文，成至神之用，此所以僅六十四卦，三百八十四爻，而盡天下之事物與變化也。不先明此，則不能窺聖人制易之心，亦不能全易道之用，則雖治易終無益也。故貴在能熟其辭而通其象。

Learning the Book of Changes is valuable only when one can grasp its overall meaning, and using it depends on thorough mastery. If one rigidly adheres to a single aspect without understanding the whole, then after learning it, one is likely to forget most of it, and how can one then explore the changes of the world and fully comprehend the profound meaning of the Book of Changes? The Book of Changes is a book that uses simplicity to manage complexity and moves from the obvious to the subtle. Because its application is very broad, words and characters cannot fully express it; its principles are vast, encompassing all things, so one must grasp the fundamental principles and apply them to the extreme, using a single, pure method to achieve unpredictable results, and using extremely simple characters to produce extremely profound effects. This is why only sixty-four hexagrams and three hundred and eighty-four lines are sufficient to cover all things and changes in the world. Without first understanding this, one cannot glimpse the intention of the sage in creating the Book of Changes, nor can one fully utilize the principles of the Book of Changes. In that case, even if one studies the Book of Changes, it will ultimately be of no benefit. Therefore, the key lies in being able to read its words fluently and understand its images thoroughly.

易之為用，有獨用者，有合用者，有對偶者，有推移者；有反逆相成者，有正順相制者，其類不一，其例至多；則可就其象驗之。如各卦各爻，均有獨用之例，而相合亦成其用。其對偶推移，順逆正反，則成其生克變化之用，此當就其成例測之。

The use of the Book of Changes involves methods that take individual elements, combine them, pair them, follow sequences, oppose and complement each other, and regulate and constrain each other. There are many different types and rules, all of which can be verified through the images. For example, each hexagram and line can be used individually according to established norms, and they can also achieve their purposes when combined. As for opposing and complementary movements, following and reversing sequences, these form the functions of mutual generation and mutual control, leading to continuous change. All of these should be inferred according to existing established examples.

蓋乾坤二卦，各獨立而為天地父母；合則如泰否，其用不同，對偶推移，則如復姤遯臨之類；相生克以成變化，則如剝復損益既未濟之類，皆有定例可尋者也。至其比例交錯，由此通彼，由上化下，則如咸恆之乾坤，益損之離坎，各極其變而成其用，亦自成例；故必列象，觀其分合變化，驗其生克消息，而後得其用焉。

The trigrams Qian and Kun represent Heaven and Earth when they are separate; when combined, they form the hexagrams Tai and Po, each with different applications. Those that represent opposing transformations, such as Fu, Gu, Duan, and Lin, are of this kind. Those that form changes through mutual generation and control, such as Bo, Fu, Shen, Yi, Ji Ji, and Wei Ji, also follow certain rules. As for cases where things are compared and interwoven, leading from one to another and from above to below, such as the hexagrams Xian and Heng derived from Qian and Kun, and Yi and Shen derived from Li and Kan, each pushes transformation to its extreme and achieves its function, forming their own regular patterns. Therefore, one must arrange the images, observe their combinations and transformations, verify their generation and control, and then be able to grasp their applications.

故易有乾坤中立之序圖，有坎離上下之序圖，有其本宮變化之序，有依對偶推移之序，無非為極其用也。必先於其同以求其異，於其異以證其同，而後知其變化由來，生克消息之例也。是以習易，非僅釋文義，諳象一變為坎坎離上下之序圖，其原因如何？成用如何？而後知聖人易教之本旨，與吾人習易之何為。

Therefore, the Book of Changes has sequential diagrams such as "Heaven and Earth in the center" and "Kan and Li living apart above and below," as well as sequences arranged according to their original positions and those based on opposing transformations. All of these are meant to fully utilize its applications. One must first find differences from similarities and then verify similarities through differences, in order to understand the origin of changes and the principles of generation, overcoming, and decline. Therefore, studying the Book of Changes is not merely about explaining the meanings of the text; one must also clarify why the hexagrams change from "Heaven and Earth establishing positions" to the sequence of "Kan and Li above and below," what the reasons are for such a change, and what purposes are achieved thereby. Only then can one understand the fundamental intent of the sages in using the Book of Changes for teaching, as well as the true purpose of studying the Book of Changes.

易之八卦為綱，其所生化五十六卦為目，而乾坤二卦，又綱之綱，以各卦皆自是出，即萬物生於五行，五行成於二氣也。由其數言，八卦者生成之數，五十六卦則相生相制之數也，萬物雖眾，皆包於六十四卦，則一卦之分合變化，所賅者多矣！故必詳徵於爻。爻者本於乾坤之□、□，即數之九六也，無論何爻，不外□、□，即言萬物萬事，不出九六之數與陰陽之氣也。

The Book of Changes takes the Eight Trigrams as its main framework, and the remaining fifty-six trigrams derived from them as its details. The trigrams Qian and Kun are the main trigrams within the framework, as all other trigrams are generated from them. This is analogous to how all things arise from the Five Phases, and the Five Phases themselves are formed by the interaction of yin and yang. Numerically, the Eight Trigrams represent the generating numbers, while the fifty-six trigrams represent numbers that are both generated and restrained. Although all things are numerous, they are all included within the sixty-four trigrams. Therefore, the division and transformation of each trigram must be carefully examined. The lines (yao) originate from the two line symbols of Qian and Kun, that is, the yang line and the yin line. Numerically, these are represented as 'nine' and 'six'. No line can be outside these two, meaning that all things are contained within the numbers nine and six and the energies of yin and yang.

由其合觀之，則變化無盡；由其分言之，不過天地所賦之一耳。故乾坤為天下之樞機，而□、□為天下之本氣；九六為天下之總數，實為生化之所始終者也。雖究其生化，有不可盡，而溯其本始，則不離於是。是即中庸所謂天地之道不二，而生物不測也。故易者：示天地萬物終始者也。無論何物何事，莫不包於易中，即溯無始，以迄天地之滅，皆由易象盡之矣！

When combined, their changes are endless; when separated, they are merely the single principle given by heaven and earth. Therefore, Qian and Kun are the key elements of the world, the yin and yang lines are the fundamental qi of the world, and the numbers nine and six are the total numbers of the world. They are truly the beginning and end of generation and transformation. Although the process of generation and transformation is inexhaustible, tracing back to its origin cannot be separated from these. This is what the Doctrine of the Mean refers to as the way of heaven and earth being singular and unchanging, thus enabling the transformation and nurturing of all things beyond measure. Therefore, the Book of Changes is a book that reveals the beginning and end of heaven, earth, and all things. No matter what object or matter there is, it is all included in the Book of Changes. Even if we go back to the beginning without origin, or forward to the time when heaven and earth are destroyed, we can fully explain it through the images of the Book of Changes.

如以六十四卦次第列之為圖，即足以示天地世界之終始，即自乾坤以迄既未濟，其推移轉換，實一世界自然之序，而縮言之，即一人終始生化之例。其為變化者，則有方圓圖與歲序圖，及八宮之序，皆與經中次序相證，以互為用：因大數雖有定例，而變化甚多；必合各圖而後知其變例。如後人京氏之八宮，焦氏之歲序，與邵氏所傳於道家之方圓圖，皆易中自具之例，為推其變化，以與經本次序相證者也。

If the sixty-four hexagrams are arranged in order to form a diagram, it is sufficient to display the beginning and end of the universe: from the hexagram Qian (Heaven) and Kun (Earth) up to Ji Ji (Completion) and Wei Ji (Non-Completion), the transition and transformation in between truly represent the natural evolution of the world; in a smaller sense, it is also an example of a person's life from birth to death and the cycle of generation and decay. The forms that illustrate change include the "Square Diagram," "Circular Diagram," "Annual Sequence Diagram," and the order of the Eight Palaces, all of which correspond with and support the sequence of hexagrams in the classic text. Because although the great numbers have fixed rules, there are many changes within them, and one must refer to various diagrams to understand these variations. For example, the Eight Palaces hexagram sequence by Jing Fang, the annual sequence by Jiao Yanshou, and the Square and Circular Diagrams passed down from Daoism by Shao Yong, are all inherent principles in the Book of Changes, intended for the derivation of change and to verify the sequence in the classic text.

故大之足以盡宇宙之象，小之足以合歲時之紀，即一人一地一時之事，亦由是足以占之，此則因天地生化自然之例，固如是也，即其變例，亦不出於各圖之序，由正證變，皆如指掌；故可以明知未來，通達既往，而盡其變化，致其用也。是易之象雖簡，而含義無窮，習易者必詳求之，始全其用；而其道總不外往復於六十四卦之內也，其變例為圖尚多，此舉其至要而已傅者耳。習易之先，務熟記之。

If looked at from a grand perspective, it can fully encompass the phenomena of the universe; if looked at from a small perspective, it can fully correspond to the principles of the four seasons in a year. Even the affairs of a person, a place, or a moment can be predicted based on it. This is because the natural principles of generation and transformation of heaven and earth are inherently structured this way. Even its variations do not go beyond the order established by the diagrams. By using the standard examples to verify the variations, everything becomes clear as looking at one's own palm. Therefore, one can clearly foresee the future and thoroughly understand the past, fully grasp its changes and fully utilize its applications. It is evident that although the images in the Book of Changes are simple, their meanings are infinite. Those who study the Book of Changes must carefully explore them in order to fully realize their functions. The principles of the Book of Changes are always within the sixty-four hexagrams, constantly changing and recurring. There are many diagrams that illustrate variations, but here we only mention those that are most important and have already been passed down. Before studying the Book of Changes, one must memorize them thoroughly.

夫子命將易經要義，先為講釋，俾讀易者深解古聖演易之旨；文周說易之心，庶明儒教傳易原由，而知堯舜以來歷聖授受之薪傳要義。夫易自文王重演，周公繼之，夫子集其大成；而經文大明，義理大著；讀易者宜將繫辭、說卦、序卦、雜卦諸章，與全經，俱明解無遺，然後得聖人演易之旨，及吾人習易之用也。

The Master ordered first to explain the essential meaning of the Book of Changes, so that those who read the Book of Changes may deeply understand the purpose of the ancient sages in deriving the Book of Changes, and the intention of King Wen and the Duke of Zhou in explaining it. Thus, they may clarify the origin of Confucian transmission of the study of the Book of Changes, and know the essential teachings passed down by sages from Yao and Shun through the ages. The Book of Changes was first re-derived by King Wen, then continued by the Duke of Zhou, and finally synthesized by the Master, thus making the text of the Book of Changes clearly established and its principles greatly evident. Those who read the Book of Changes should explain all the chapters including the Great Treatise, the Explanations of the Trigrams, the Order of the Trigrams, and the Miscellaneous Trigrams, without any omission, so that they may understand the purpose of the sages in deriving the Book of Changes and the practical use of studying it.

四傳詳於易例，為輔翼易經之文，不讀四傳，不明易之為教也；故夫子於訂易時，特揭之，為易經參解以授弟子，俾明易之為易，故讀易必及四傳；易象至簡，卦辭亦略；欲通其用，舍先求之四傳，不能測其端倪。

The four commentaries, the Great Treatise, the Discourse on the Hexagrams, the Order of the Hexagrams, and the Miscellaneous Hexagrams, explain in detail the general principles of the Book of Changes. They are the supporting texts for the Book of Changes. Without reading these four commentaries, one cannot understand what the Book of Changes is as a means of moral instruction. Therefore, the Master deliberately included them when he compiled the Book of Changes, to serve as supplementary explanations for his disciples, enabling them to comprehend why the Book of Changes is called the Book of Changes. Thus, reading the Book of Changes necessarily involves studying these four commentaries. The images in the Book of Changes are extremely simple, and the statements of the hexagrams are also concise. To understand their application, one must first study the four commentaries, otherwise one will be confused.

蓋易起於上古，為時久遠，文字未興，雖具其象，亦如河圖、洛書，僅演其點畫而已，經神農軒轅以迄唐虞，代有增易，文字既制，政教益明，於易象之下，均加之演詞以著其義。因初傳於語言，難留久逸，相習固有師授，而易代輒忘；相用固有成規，而易地輒異，以至於夏商二代，各沿所習，各本其制，而有連山之易，歸藏之易，其取用既殊，而為義亦不一矣！

The Book of Changes originated in ancient times, its origins long ago. At that time, writing had not yet emerged, although there were already hexagrams, they were like the Yellow River Chart and the Luo Writing, merely arranging dots and lines. From the time of Shen Nong, the Yellow Emperor, through the Xia and Shang dynasties up to the Tang Yao and Yu Shun, each generation added and modified them. After writing was created, political orders and moral teachings became clearer, so they added explanatory texts beneath each hexagram to clarify their meanings. However, since the original transmission was oral, it was difficult to preserve for long. Although teacher-student transmission ensured continuity, changes in dynasties often led to loss of knowledge. Although using the tradition had its established ways, differences arose when applied in different places. By the time of the Xia and Shang dynasties, each followed its own tradition and based itself on its own system, thus giving rise to the Yi of Lianshan and the Yi of Guicang. Since their methods of use differed, the principles they established also varied.

至文王取而重演之，以成今傳之易，因恐後人疑其同異，忘其本來，始詳著其詞，以明其教，此四傅之作固為傳易為教者也。時代既殊，傳述又異；前之易者，徒存其象，今之詞者，乃備其文，故易道至周始昭，至夫子始定為經。

King Wen took them and re-examined them, thus making the Yi Jing as it is passed down today. Because he feared that later generations would be confused by the differences among various schools and would forget the original form, he began to write detailed explanations to clarify this teaching system—the four commentaries were originally written to transmit the Yi and to establish a teaching method. Since the times are different, the transmission has varied: the ancient Yi preserved only the images, while the present-day words complete the text. Therefore, the principles of the Yi became clear during the Zhou dynasty and were established as a classic in the hands of the Master.

夫子本文周之作，加以所習，而擴其義，敷詞具象，以次其序，明變著用，以列其圖，而後易之為易，有跡可尋，有文可讀，有圖可驗，有變化可征；不似前日之奧窈難稽，同異莫辨矣。故易教實成於夫子，而易義則備於四傳之文；欲知易者，必先知此，而後可進而求之也。

The Master based himself on the writings of King Wen and the Duke of Zhou, adding his own learning to elaborate on their meanings, arranging the words, listing the hexagrams in order, explaining changes and showing their applications through diagrams. Since then, the Book of Changes has become traceable, readable, verifiable through diagrams, and capable of being studied for its changes, unlike before when it was obscure and indistinct. Therefore, the actual teaching of the Book of Changes was completed in the hands of the Master, while its meanings were fully elaborated in the writings of the Four Transmissions. Those who wish to understand the Book of Changes must first realize this, and only then can they proceed further in their study.

易之起源，非乾坤也：蓋溯乾坤而上，則太極是也，然易有太極，是生兩儀之語，不見於經而見於傅；故必讀傅始知之也。易之為教，非言休咎已也，而在因休咎以悟性命，以道在人為性，易明人道，始於性善，「而繼之者善，成之者性」之語，亦詳傅中。

The origin of the Book of Changes is not merely the trigrams Qian and Kun: tracing back further than Qian and Kun leads to the Taiji. However, the statement "The Book of Changes has the Taiji, from which the two principles arise" is not found in the classic text but in the Great Treatise of the Upper Transmission. Therefore, one must read the transmission to understand it. As a means of education, the Book of Changes is not only about fortune and misfortune, good and bad; it is about using these to comprehend human nature and destiny. Because the Way manifested in human beings is called "nature" (Xing), the Book of Changes explains human conduct starting from the concept of "benevolent nature." The sentence from the Great Treatise of the Upper Transmission, "What is continued is goodness, and what is completed is nature," is also fully recorded in the transmission.

易之言數，始於圖書；自天一至地十，皆天地生成本數，而天一地二，大衍之數五十之語，亦在傳中；易之為用，以其變也；變始於錯綜參伍，以生化各卦：而參伍以變，錯綜其數之義，亦詳傳中。易之同異，在於序圖；以其本末始終，上下內外，各有其用，故有體有用，有同有異；而天地定位，帝出乎震，各方位序圖之說，亦詳傳中。

The Book of Changes deals with numbers, beginning with the Yellow River Chart and the Luo Writing. From "Heavenly One" to "Earthly Ten," these are the fundamental numbers generated by heaven and earth. The passage in the Great Treatise of the Upper Transmission, "Heavenly One and Earthly Two," as well as "The number of the Great Transformation is fifty," are all included in the transmission. The usefulness of the Book of Changes lies in its ability to change; change arises from "interweaving and combining," thus generating all the hexagrams. The meaning of "by combining and interweaving, numbers are transformed" in the Great Treatise of the Upper Transmission is also fully explained in the transmission. The differences and similarities among various schools of interpretation of the Book of Changes depend on the order of the hexagrams. Since beginning and end, upper and lower, inside and outside each have their own uses, there is both form and function, as well as both similarity and difference. The sections in the Discourse on Hexagrams, "Heaven and Earth are positioned" and "The Emperor arises from the震 (Thunder)," which discuss various diagrams of directional order, are also fully explained in the transmission.

易之遞嬗，大別有三：時代以殊，名類遂異；如連山、歸藏之易，次序不同，即體用生化之序，與男女之別，消長之象；其類皆異，其名皆殊；而本宮變化，與序卦次第，及連山、歸藏之首末位次，亦皆詳傳中。

The transformation and evolution of the Yi (Book of Changes) can generally be divided into three types: as times differ, the names and categories also change accordingly. For example, the two other books of Yi, the Lianshan (Continental Mountain) and the Guicang (Return to the Treasury), differ in their sequence of hexagrams. Therefore, the order of generation and transformation, the distinction between male and female, the waxing and waning images, and the categories all differ, as do their names. Moreover, the changes within each hexagram's own palace, the sequence of the Xugua (Order of Hexagrams), and the initial and concluding positions of the hexagrams in the Lianshan and Guicang are all detailed in the transmitted texts.

至如易之門戶，八卦之本義，六十四卦之時氣，與天地人所象之名類；少長老幼之期，上下內外之位，皆自有所合。一歲之遷移，八方之分合；古今世界之終始，與人事吉凶禍福之占驗；莫不詳於傅中。若不熟於傳，則中智以下，決不能探天地之妙，測陰陽之神；而以達於性命之源，明於行止動靜之道矣！故傳之作，為教後人之習易也。

As for the "doors" of the Book of Changes, the original meanings of the Eight Trigrams, the corresponding seasons and climatic conditions for each of the sixty-four hexagrams, and the names and categories of the phenomena represented by Heaven, Earth, and Humanity, as well as the corresponding periods for youth, middle age, old age, and childhood, and the positions corresponding to upper and lower, internal and external, all have their respective correspondences. The changes of the seasons throughout the year, the division and combination of the eight directions, the beginning and end of the world through time, and the divination of fortune and misfortune in human affairs are all thoroughly recorded in the commentaries. If one is not familiar with the commentaries, then those with average intelligence or below will absolutely be unable to grasp the profound mysteries of Heaven and Earth, comprehend the wonders of yin and yang, and thus understand the origin of life and death and the principles of movement and stillness. Therefore, the writing of the commentaries was precisely to teach later generations how to study the Book of Changes.

人求明易，不先明於傳文，是雖日讀經，恐無益於事；故夫子以其所得，指出其要，而集其義，為傳於經之前後，其循循誘人之心，足千古矣！雖其言得之先聖，非夫子一人所為，而其編訂之功，實為繼往開來之聖，讀者其毋負夫子之心焉爾。

A person wishes to understand the Book of Changes, but if he does not first clarify the transmitted interpretations, then even if he reads the classic text every day, it may not be of much use. Therefore, the Master summarized his insights and compiled the meanings into the transmitted text, arranging it before and after the classic text. His patient and gradual guidance for future generations is sufficient to serve as a model for all time. Although these words come from previous sages, not solely from the Master, his contribution in compiling them is indeed the work of a sage who connects the past with the future. Readers should not辜负 the Master's sincere intention.

且卦之象氣與數，必視其變化，而後得其未來，若僅執現象，則往復者不可知，將何以窮神知化哉？故通易必參全易之變化，非就一卦六爻之象，既足得其用也。又易者，因器明道者也，器可見，道不可見，必因有形以溯無形；有形者現具之象，無形則在無象之中，然棄有以求無，亦不得也：必求諸有而不執其有，方得其無焉，而非經文所盡也，必廣徵於先後天之圖，與本宮之序，及序卦之詞，而後知之，故必徵於傳文也。

Furthermore, the qi and numbers symbolized by the hexagrams must be observed through their changes before one can predict the future. If one only focuses on the present phenomena, the principle of cyclical repetition cannot be understood, and how can one speak of the saying in the "Great Treatise" part of the "Commentary" that "to exhaust the divine and know the transformation"? Therefore, to understand the "Book of Changes," one must refer to all its changes, not merely the images of a single hexagram with its six lines. Moreover, the "Book of Changes" uses tangible objects to explain the great principles. The objects are visible, but the principles are invisible; one must use the visible to trace the invisible. The visible is the present image, while the invisible is hidden within the absence of image. However, abandoning the "visible" to seek the "invisible" is also unattainable. One must seek the "visible" but not be attached to it, in order to reach the "invisible." These points cannot be fully explained by the text itself. One must widely consult the diagrams of the Earlier Heaven and Later Heaven, as well as the order of the palace and the words of the "Sequence of Hexagrams," before one can comprehend them. Therefore, one must seek evidence from the transmitted texts.

如先後天之圖，不見於經；即就乾坤之序，亦不知其位。唯「天地定位」一節，言先天八卦之位；「帝出乎震」一節，言後天八卦之序，皆足以證經文之不及者。如乾坤之序，為今易所定，始於乾，終於未濟，此固讀經可知者。而其本宮之序，則不在經中，又非徵於傳文不可。傳有云：「歸妹，女之終也」，乃明本宮之始終。

For example, the "Earlier Heaven Diagram" and "Later Heaven Diagram" are not depicted in the text; looking only at the sequence of trigrams following Qian and Kun, one cannot determine the positions of the eight trigrams. Only the passage in the "Commentary on the Changes" stating "Heaven and Earth are positioned, mountains and marshes communicate through the air" refers to the positions of the Earlier Heaven Trigrams; and the passage "The Emperor arises from Zhen, harmonizes with Xun" refers to the sequence of the Later Heaven Trigrams. These two passages are sufficient to explain what is not mentioned in the main text. As for the order of the trigrams, it is determined by the current version of the "Zhou Changes," beginning with Qian and ending with Wei Ji. This is something that can be known by reading the main text. However, the order of the eight trigrams within their respective palaces is not mentioned in the main text and must be verified from the commentary. The "Miscellaneous Changes Commentary" states "Guimei, the end of the female," which clearly indicates the beginning and end of the order of the eight trigrams within their respective palaces.

蓋序卦之次序，本於後天八卦之生化，而為用也；本宮之次序，則本先天八卦之生化，而為體也。體靜象坤，故歸妹為坤道之盡；後天用陽，而動象乾，故未濟為乾道之終。二者終始各異，致用亦殊，而必由傳考之，始得明其故。不特此也，連山首艮，歸藏首坤，六十四卦之序各異，即方圓與歲序圖皆不一。凡由乾坤變化而生者，皆有定序，而經但就文王所定者列之；若不徵於傳，則他易圖皆不得知。不獨不備於用，而經中各爻辭，恆有取前各易之舊者，其義亦難索解。譬之「歸妹，女之終也」一語，苟不知八宮次序，終於雷澤歸妹，則其義將不解矣！

The sequence arranged in the "Xugua Zhuan" originates from the generative and transformative relationships of the Later Heaven Trigrams, belonging to the "use" aspect. The order of the eight palaces' own palace sequences originates from the generative and transformative relationships of the Earlier Heaven Trigrams, belonging to the "essence" aspect. "Essence" is associated with stillness, symbolized by the Trigram of Earth (Kun), so when the eight palaces reach the hexagram "Guimei," it signifies the end of the Earth path. The Later Heaven Trigrams take Yang as their active principle, symbolizing Heaven (Qian), so when the "Zhouyi" reaches "Weiji," it signifies the end of the Heaven path. These two approaches differ in their beginning and end, thus their uses are different. One must consult the "Yi Zhuan" to understand the reasons behind these differences. Moreover, the "Lianshan Yi" of the Xia Dynasty began with the Trigram of Mountain (Gen), while the "Guicang Yi" of the Yin Dynasty began with the Trigram of Earth (Kun). The sequence of the sixty-four hexagrams differs in each case, and even the square diagram, circular diagram, and the sequence of hexagrams aligned with the seasons are not consistent. All hexagrams generated from the Trigrams of Heaven and Earth have fixed sequences, but the text of the Classic only lists the one determined by King Wen. Without consulting the explanatory texts, other Yi diagrams cannot be understood. This is not merely an incompleteness in usage. The statements in the text of the Classic often follow the old expressions from the "Lianshan" and "Guicang." Their meanings are thus difficult to grasp. For example, the statement "Guimei signifies the end of a woman's life" would make no sense without knowing that the sequence of the eight palaces ends with the hexagram "Guimei" (Thunder and Marsh).

以經文次序，明明終於末濟，與歸妹何涉？是則女終之義，實非取於今易者也。況一曰男，一曰女，對舉而言，即分屬乾坤二者。乾道成男，坤道成女，固有明解；而未濟之男窮，即指乾氣之盡；歸妹之女終，即指坤氣之盡。然序卦終以未濟，可見本乾道之始終也；本宮則本坤道，斯為不同。而不同者正其同也，由於先後天也，合之則同，分之則異，未有離體用為之者，故異仍同。

According to the order of the text, it clearly ends with the hexagram "Wei Ji," so how is it related to "Gui Mei"? This shows that the meaning of "female's end" is not derived from the present version of the Zhou Yi. Moreover, the Zang Guà Zhuan mentions "male" in one sentence and "female" in another, contrasting them, which clearly assigns them to the hexagrams Qian and Kun respectively. The Xi Ci Zhuan says, "The way of Qian produces the male, and the way of Kun produces the female," which is clear: the "male's end" in Wei Ji refers to the end of the Qian energy, while the "female's end" in Gui Mei refers to the end of the Kun energy. The Xu Guà ends with Wei Ji, indicating that it follows the beginning and end of the Qian way; the eight palaces, however, follow the Kun way, which is the difference between them. Yet this difference is precisely their similarity, because they originate from the Earlier Heaven and Later Heaven respectively: when viewed together, they are one matter, but when viewed separately, they become two. There has never been a system that separates "body" and "function" to establish another set, so although they appear different, they are still based on the same principle.

人之既生，神形同具，性情兩全，若分則死矣。然性情自別，神形亦殊，又不可混為一談。是以言易必廣徵其異，以歸於同。易之序卦為主，餘皆為參互之用；以餘合一，則異皆同，故易經但取其一，夫子亦仍之。而恐人之忘其餘也，則備述於傳，以為習易之助，俾讀者得會通之，而勿失其宗也。故傳者，習易所必先讀者也。

When a person is born, both spirit and body are present, and nature and emotion are both complete. If they are separated, the person dies. However, "nature" and "emotion" are fundamentally different, and "spirit" and "body" are also distinct and cannot be confused. Therefore, in explaining the Book of Changes, one must widely examine the differences among various schools of thought and finally return to a single fundamental principle. The sequence of hexagrams in the Book of Changes is mainly based on the order established in the "Sequence of Hexagrams," while other arrangements are used as references and cross-verifications. By incorporating all other arrangements into this one, all differences are unified. Therefore, the Book of Changes selects only one arrangement, and Confucius, when compiling the classic, continued to use it. However, he was also concerned that later generations might forget the other arrangements, so he recorded them all in the "Commentaries on the Changes" as supplementary material to help learners integrate and understand the principles of the Book of Changes, so they do not lose the main purpose of the study of the Changes. Therefore, the "Commentaries on the Changes" are essential for those who wish to study the Book of Changes.

易之始終，為象天地之氣運數紀，而有先後天之不同。以先天包無始迄無終，未有物也；後天則自天地既生，萬物皆具生化，有終有始者也。故形神各類，有無異名；道器並行，人天別用，非諳其故，不知易之為易也。自太極以下，迄於萬物之終，為一天地，而其象則自乾坤始，以天地之外，難具名也。然雖無物而可象，物以名別，必有形與神；象以氣數別，故雖無形有神，仍可類以名，辨以義也。人之生也，後於天地，則人事所關，必在後天之中。雖神流太虛，氣通無始，而形限其動，跡循於有，不可外天地以言人事也。

The entire discussion in the Book of Changes is about depicting the movement of the heavens and earth and the principles of numbers and patterns, hence the distinction between Earlier Heaven and Later Heaven. Earlier Heaven encompasses the period from the beginningless to the endless, when there were no specific things; Later Heaven begins after the heavens and earth had already come into being, and all things have the capacity to grow and change, thus having a beginning and an end. Therefore, "form" and "spirit" belong to different categories, and "being" and "non-being" have different names; "Dao" and "objects" coexist without contradiction, and "human" and "heaven" each have their own functions. Without understanding this reason, one cannot comprehend why the Book of Changes is called the Book of Changes. From the Taiji down to the ultimate end of all things, it is considered as one heaven and earth, yet its hexagrams begin with Qian and Kun, because the realm beyond heaven and earth is difficult to name. However, even without specific things, one can still establish images: things are distinguished by names, so they must have form and spirit; images are distinguished by qi and numbers, so even though they are formless, they still have spirit, and can still be named according to categories and distinguished according to meaning. Since human beings come into being after heaven and earth, anything related to human affairs must fall within the scope of Later Heaven. Although human spirit can wander through the boundless void and breath can connect with the beginningless, the body limits its activities, and its movements can only take place within the realm of "being," so when discussing human affairs, one cannot ignore heaven and earth.

故文王定卦，溯始乾坤，而明易致用，必以後天為主。然恐人之囿於器而忘道，執於有而遺無，遂失所生，不知所歸，故卦詞皆參以先天，更於傳中補著其用。如天火同人、水地比，皆先天之名，以後天離坎，即先天乾坤同處一位，故曰同、曰比，不獨以天火、地水為同氣也。所有各卦義皆如是，意在使人不忘本來，而有以見道於象也。

Therefore, King Wen arranged the order of the hexagrams, tracing back to Qian and Kun as the starting point, and in explaining the practical application of the Book of Changes, he necessarily relied on the Later Heaven arrangement. Yet he feared that people would be confined by the tangible "objects" and forget the "Dao," clinging to the "having" and missing the "non-having," thus losing their origin and not knowing where to return. Therefore, the hexagram statements are filled with the principles of the Earlier Heaven, and the "Commentaries on the Changes" further explain their usage. For example, "Tongren" (Union) is Heavenly Fire, and "Bi" (Following) is Water over Earth. The names of these two hexagrams are derived from the principles of the Earlier Heaven: in the Later Heaven, the hexagram Li (Fire) is located in the south, which is the position of Qian (Heaven) in the Earlier Heaven; in the Later Heaven, the hexagram Kan (Water) is located in the north, which is the position of Kun (Earth) in the Earlier Heaven. Since Qian and Li share the same position, it is called "Tong" (Union); since Kun and Kan share the same position, it is called "Bi" (Following). This is not merely because Heaven and Fire, or Earth and Water, are similar in nature. The meaning of each hexagram is determined in this way, with the intention of reminding people not to forget their original source, so that they may see the "Dao" within the hexagram images.

夫易之為教，端重人道，而先必明原始要終之義。不明先天，將何以見其始終，而致其原要之功哉！故先後天之易，不可偏廢也。易之有先後天，非二易也，其為用仍一致，猶人之性情神形，不過靜動之間耳。果通其一，則必達其二。如一卦也，但明其後天之象，不足用也，必兼先天之象而一之，方得致其全功。而於人之占驗也亦然，明其所占之卦，此現在事也，必通先天，而後吉凶可征，變化可見。

The Book of Changes, as a means of moral instruction, places the greatest emphasis on human affairs. However, one must first understand the principle of "returning to the beginning and concluding at the end" as explained in the Great Treatise. Without grasping the Earlier Heaven, how can one clearly discern the beginning and end of things, thus achieving the ability to trace back to the origin and conclude at the end? Therefore, the Earlier Heaven and Later Heaven aspects of the Book of Changes cannot be neglected. The Book of Changes has both Earlier Heaven and Later Heaven, but they are not two separate Books of Changes; their functions remain consistent, just as a person's nature and emotion, spirit and form, are merely distinctions between stillness and movement. If one truly understands one aspect, they must also understand the other. For example, with regard to a single hexagram, merely understanding its Later Heaven image is insufficient; one must also consider its Earlier Heaven image together in order to achieve complete effectiveness. This is also true in divination: understanding the hexagram one has drawn only reveals the current situation; only by comprehending the Earlier Heaven can one determine fortune and misfortune and perceive change.

蓋後天為一時，先天則概來往。易以知來、數往為用，不求之先天，將何以成其逆數之用哉？故易者，不能分先後天而為言。文王之易，雖取後天之序，而用則仍本先天，此義後人全不知之，或爭為先，或爭為後，偏而不得其體用之全，辨而不明其變化之道。雖兢兢於文字之學、著龜之數，及其得辭，一無所驗，反不如街頭賣卜者之偶中。豈易之不可信耶？人之不明易也。

The Later Heaven system governs only the present moment, while the Earlier Heaven encompasses both the past and the future. The "Commentary on the Hexagrams" says, "To understand the past is to follow the sequence; to know the future is to reverse the sequence." The function of the "Book of Changes" lies in predicting the future and tracing back the past; without seeking it in the Earlier Heaven, how could it achieve its function of reversing the sequence? Therefore, when discussing the "Book of Changes," we cannot separate the Earlier Heaven and Later Heaven and discuss them individually. Although King Wen's "Book of Changes" adopted the Later Heaven sequence for its arrangement, its application still relied fundamentally on the Earlier Heaven. This principle was completely misunderstood by later generations, leading some to insist on the superiority of the Earlier Heaven, while others insisted on the Later Heaven, each clinging to one side and failing to grasp the full scope of principle and application. They argued endlessly without understanding the changes involved. These people, despite their painstaking efforts in textual interpretation and the number of yarrow stalks and turtle shells, when they actually cast a divination, found nothing accurate, and ended up being worse than street fortune-tellers who occasionally guessed correctly. Is the "Book of Changes" unreliable? No, it is people who have not properly understood the "Book of Changes."

矧易道以簡易御繁難，必先明其所以簡、所以易，而後可以致其繁與難於目前也。舍合先後天參之，則將不知其所以簡易，以象既窮而辭復盡，何以見其變化哉？簡易雲者，言象外也；而能御繁難者，則因有象中象、辭中辭耳。天地之數，由於氣運，有定序也，因是皆成往復對待之象，易之所占，悉依此律。如乾坤、屯蒙、需訟、咸恆、既末濟之類，無非相偶以進；乾坤也，坎離也，震巽艮兌也，皆成對偶之象，而以往復參錯為序。如屯蒙需訟，其類相反，而相繼以生化也。

Moreover, the Way of the Book of Changes is to use simplicity to manage complexity. One must first understand why it is "simple" and why it is "easy," before one can confront and deal with complex matters. If one does not refer to both the Earlier Heaven and Later Heaven together, one will not comprehend why it is called simple. Since the hexagrams have already been exhausted and their statements have already been fully expressed, from where else can one observe their transformations? The term "simple" refers to what lies beyond the images. Yet it is precisely because within the images there are further images, and within the statements there are further statements, that the Book of Changes is able to manage complexity. The numbers of heaven and earth arise from the movement of qi, following a fixed order, thus forming the alternating and opposing hexagrams. Divination in the Book of Changes entirely depends on this principle. For example, the hexagrams such as Qian, Kun, Zun, Meng, Xu, Song, Xian, Heng, Ji Ji, and Wei Ji all advance in pairs. Qian and Kun, Kan and Li, Zhen and Xun, Gen and Dui also form opposing pairs, and are arranged in order through alternating and intersecting patterns. Hexagrams such as Zun and Meng, Xu and Song, though opposite in their categories, generate transformations that follow one another in sequence.

因天地之氣，有生必有死，有合必有分，以生克而後成變化，此必至之勢也。若不循環，則氣絕矣。唯其往者必復，生者必化，而成循環無盡之象，始成天地萬物之序。如一年也，春秋冬夏，皆相對以成歲，而冬盡必春，夏盡必秋，往復循環，萬年不改。易之氣運，正如斯例。其間變化，或稍遲速，或有餘不足，則運氣有主客勝復，猶春之溫、夏之熱、秋之涼、冬之寒，或有應否之差，或有反令之災也，其在人事則善惡所感耳。然大致不忒，以其運序定自先天，故不忒也。

The vital energy of Heaven and Earth, when there is generation, there must be death; when there is union, there must be separation. It is through mutual generation and mutual control that change is formed, which is an inevitable trend. If there is no cycle, the vital energy would be cut off. Because what goes away must return, and what is generated must transform, it forms a continuous cycle, thus creating the order of the universe and all things. Just as in a year, spring and autumn, winter and summer, are paired to form a year. After winter comes spring, and after summer comes autumn, repeating endlessly without change for ten thousand years. The Book of Changes also describes the movement of vital energy in this way. The changes sometimes occur more quickly or slowly, sometimes in greater or lesser amounts, leading to the dominance and retaliation of the main and guest energies. Just as spring should be warm, summer hot, autumn cool, and winter cold, but sometimes these conditions are fulfilled and sometimes not, even leading to disasters where the seasons are reversed. In human affairs, this is simply the result of good and evil deeds. However, the overall pattern does not go wrong, because this order was established in the Earlier Heaven, so it cannot be wrong.

一易之變化，以後天為用，則有不能盡知之事；合之先天，則無疑矣。蓋後天之事，輒因人之感召而異，而先天者，則在人事以上；故先天多靜，後天多動。合而參之，動靜不失其序；若偏一象，則不失於此，必迷於彼。坤之先迷後得，即指此也。習易既通，無復迷矣。故欲窮易之用，必先通乎先後天之象，精求其變化而不失其中，則何患乎迷。

The same changes in the Book of Changes, if only the Later Heaven is used, some matters cannot be fully understood; but when the Earlier Heaven is combined with the Later Heaven, difficulties become clear. Because the Later Heaven often changes according to human influence, while the principles of the Earlier Heaven lie above human affairs; thus, the Earlier Heaven is inclined to stillness, and the Later Heaven is inclined to movement. When both are considered together, movement and stillness each maintain their proper order; if one only relies on one aspect of the hexagram, errors will occur either at the beginning or at the end. The hexagram statement of the Earth (Kun) says, "Firstly lost, then gained the master," which refers exactly to this. Once one thoroughly understands the Book of Changes, one will no longer be confused. Therefore, to fully grasp the use of the Book of Changes, one must first understand both the Earlier Heaven and Later Heaven hexagrams, carefully examine their changes without deviating from the middle path, and then what fear is there of confusion?

易之為易，固重在變易，以天地間之物無不變者。有形則變速，不變者必無形之物。故恆存之體必無息，唯至誠能之，息則變矣！天地之悠久，亦不息耳。人物之生，一息一變，故隨息而生死，不可復續，此聖智所悲，而必教人以至誠，蘄無息以免於變。易之為教，其旨如是，故示人以變，而使之有惕於心；象物隨變以盡，警人之慎其終給。其以卦參伍變化，皆明人物之變化不可免者也。

The Book of Changes is called "Yi" because it emphasizes "change" or "transformation," since nothing in the universe remains constant. Physical things change quickly, while what remains unchanged must be an intangible essence. Therefore, the fundamental nature that can endure forever must be in constant motion; only the most sincere and steadfast can achieve this. Once it stops, change must occur. The reason heaven and earth are so enduring is precisely because they never cease moving. The life of humans and all things changes with each breath, thus life and death follow each inhalation and exhalation. If this process is interrupted, it cannot be resumed, which is why sages and wise people deeply regret this. Therefore, they teach people to maintain the highest sincerity, hoping to avoid cessation and thus prevent destruction. As a means of moral instruction, the Book of Changes aims at this, so it presents change to people, arousing their vigilance. It uses hexagrams to depict how all things are consumed by change, reminding people to be cautious about their own endings. It repeatedly and intricately demonstrates change through its lines and hexagrams, all to show that change is inevitable for both people and things.

因氣使然，不復久駐，隨息以盡，不知歸處。故示人以生死自來，及身所歸宿，以人道立極而求其誠，以窮理盡性而求其合於天地。雖曰以變言，實盼人之無變也。人異於物，物莫能逃於變，故生死隨形；人則有其性靈，本含不變之體。苟怵於物之變，而重其性靈，順天地之氣，而存其神，知氣數之化，而致其誠，則性命固而神氣永葆，雖在變化中，而不隨其變化，超乎物而與天地共存。則真人以上，不為氣所賊，是則得道之士，足與言易之教矣！

This is all due to the influence of qi; it cannot last long, and is exhausted with breathing. The self does not know where it will return to. Therefore, the Book of Changes points out to people: from where do life and death come, and where does the body ultimately return? It urges people to establish the principles of human conduct and pursue the concept of "cheng" (sincerity). By thoroughly investigating physical phenomena and fully expressing one's innate nature, one can strive to harmonize with heaven and earth. Although the Book of Changes speaks of "change," it actually hopes that people remain unchanging. Humans differ from things: things cannot escape change, so life and death are determined by their forms. Humans, however, possess a point of spiritual essence, which inherently contains an unchanging principle. If one can be alert upon seeing the change and destruction of things, thus valuing one's spiritual essence, follow the qi of heaven and earth to preserve one's spirit, understand how the flow of qi transforms, and cultivate to the highest sincerity, then one's life and destiny will be secure, one's spirit and energy will be preserved, and even amidst change, one will not be swept along by it. One will transcend all things and coexist with heaven and earth forever. When one reaches this level, it is the realm beyond that of a true person, no longer harmed by qi. Only such a person who has attained enlightenment is qualified to discuss the moral teachings of the Book of Changes.

蓋聖人作易，為憫人之變而不可久，化而不復歸，生而瞢瞢，死而渺渺，不知所來，不知所往，戾乎氣而不測於順逆，昧乎數而無擇于吉凶；雖稟天地之中，而不能葆；雖具性靈之真，而不克全，遂與物同變化，而神形俱盡，實為悖夫生生之則，反乎天地之道。故乃為易以告斯民，指其去來，明其禍福，象其氣數，示其所宜否，而使有所循；更諄諄以言，墾懇其辭，勸其善而戒其惡，導之存省，以致於誠明，詔之仁義，使盡其性。故其文日：「乾道變化，各正性命。」又曰：「君子終日乾乾夕惕若厲，無咎。」無非教民知天而立命，修己而合道耳。

The sage composed the Book of Changes out of compassion for the fact that people are unable to maintain their existence for long, and once transformed, they cannot return to their original state. While alive, they are confused and uncertain; when dead, they are vague and unknowable, not knowing where they came from or where they are going. They fail to discern the movement of the vital energy and cannot determine whether it is in harmony or not. They are ignorant of the principles of numbers and do not know how to seek good fortune and avoid misfortune. Although they receive the harmonious vital energy from heaven and earth, they cannot retain it. Although they possess the true nature of the spirit, they cannot realize it. Thus, they are subject to change and destruction, with both spirit and form completely disappearing. This is truly contrary to the principle of continuous generation and also violates the way of heaven and earth. Therefore, the sage composed the Book of Changes to inform people about their origin and destination, clarify their fortune and misfortune, use hexagrams to depict their destiny, indicate what should be done and what should not be done, so that they may follow a path. Moreover, he repeatedly exhorts them earnestly, urging them to be virtuous and warning them against wrongdoing, guiding them to preserve their original mind and constantly examine themselves, so as to attain the state of sincerity and clarity. He also teaches them with benevolence and righteousness, enabling them to fully realize their innate nature. Therefore, the Commentary on the Judgment of the Qian Hexagram says, "The way of heaven brings about change, and each thing establishes its own destiny." The line statement of the third line of the Qian Hexagram says, "The superior man is diligent all day and cautious all night, as if in danger." If he remains diligent all day and cautious all night, he will not commit any mistakes. This is simply teaching the people to understand the way of heaven and establish their own destiny, to cultivate themselves and align with the great way.

其示象，必明指天道如何，人道如何，何者吉，何者凶，何者可違，何者宜從，非徒述其休咎已也。故易者，聖人教民之作也，其以成人之德，為至誠之行，中庸所謂位天地、育萬物者也。夫誠則明，前知之道，必在至誠；易之知來，固重在「誠」字之一字。習易致用者其細味斯語。

The Book of Changes presents hexagrams, clearly explaining how the heavenly way is and how the human way is, what is auspicious, what is ominous, what can be reversed, and what should be followed. It does not merely state the fortune and misfortune. Therefore, the Book of Changes is a work by the sages to educate the people, cultivating human virtue and putting into practice the highest sincerity, as stated in the Doctrine of the Mean: "Achieving the mean and harmony, the heavenly and earthly positions are established, and all things flourish." When sincerity is attained, clarity follows. The ability to foresee must be based on the highest sincerity. The Book of Changes' ability to predict the future lies precisely in the character of "sincerity." Those who study the Book of Changes and wish to apply it in practice should carefully reflect on this statement.

易之為書，自來僅具圖象，無文章也。至唐虞以後，始由象而增以字，由言而演而為文。文字既傳，圖象反晦，此則後人舍本逐末之過也。要知伏羲畫卦之時，未有文字，語言可口傳，不可記錄，僅以圖象載之版冊，而將意義傳於語言。果不得其師，則不明其義，徒執圖象，不能通其用故也。

The book of Changes originally contained only diagrams and images, without any written words. Only after the time of Emperor Yao and Emperor Shun did characters appear, and words were used to explain the images, evolving into written texts. As the written words spread, the original images became obscure, which is the fault of later generations who neglected the source for the sake of the superficial. We should know that when Fuxi drew the trigrams, there were no written characters. People could pass down the meaning by oral tradition, but could not record it. Therefore, they carved the images on wooden boards and transmitted the meaning through spoken words. If one did not receive direct instruction from a teacher, it would be impossible to understand its meaning. Holding only the diagrams would not be sufficient to comprehend their use.

然既有圖象，復得師傳，則雖無文字可誦，而仍有語言代釋，其傳不失，所資於圖象者大矣。及用文字之後，則意義均宣於文章，圖象之玄微，反不若文字之明顯。故文章日多，而習者不知重圖象，徒習為文章，演講文字訓詁，不復從圖象中究其精深、宏其體用。

However, since there are both images and direct transmission from the teacher, even without written texts to recite, there are still oral explanations to convey the meaning, so the transmission will not be interrupted, and the role of the images is significant. Once written characters are used, the meanings are expressed through texts, and the subtle and profound implications of the images become less clear compared to the clarity of written words. Thus, writings become more and more numerous, yet those studying the Book of Changes no longer value the images, focusing instead on writing and explaining words, and no longer exploring the profound aspects of the images or expanding their principles and applications.

蓋自周秦而後，易之圖象已漸亡矣。然今之所存者文字，由文字而能探易之用，亦猶古之僅有圖象，由圖象而能盡易之義，其得失頗同，要皆偏於一端，不克見易道之全。是以欲明易教，必兼圖象文字而並重焉。以文字釋圖象，則無待思索之煩；以圖象證文字，則不蹈虛疏之弊。是易之為書，二者不可缺一也。

Since the Zhou and Qin dynasties, the images of the Book of Changes have gradually been lost. However, today what remains is the text, and through the text we can still explore the application of the Book of Changes. This is similar to the ancient times when only the images existed, and through the images one could fully understand the principles of the Book of Changes. The strengths and weaknesses of the two methods are almost the same, and both are biased in one direction, failing to see the complete picture of the Way of the Book of Changes. Therefore, to understand the teachings of the Book of Changes, both images and text must be given equal importance. Using text to explain the images removes the trouble of painstaking contemplation; using images to verify the text prevents falling into the trap of emptiness and superficiality. Thus, the Book of Changes requires both images and text; neither can be missing.

今日之易，多有詳於文字，而忘圖象。雖卦畫猶存，而圖象不備；間有補者，而不得編列之序，不解體用之道，雖有其圖，不充其義，是皆易本之失。茲既講易，當先正之，俾圖象之用，與文字同；文字之精，與圖象合。則習是書，能直探古人之心，而有以昌明易教，其所益於世，抑大矣哉。

The version of the Book of Changes that is passed down today tends to elaborate extensively on the text, yet it has forgotten the images. Although the hexagrams are still present, the images are incomplete; occasionally someone attempts to supplement them, but they cannot be arranged in the correct order. They do not understand the principle of form and function. Thus, although images are present, their meaning remains empty, which represents a fundamental deficiency in the study of the Book of Changes. Now, if we are to discuss the Book of Changes, we should first correct this issue, making the function of the images equal in importance to the text, and ensuring that the meaning of the text corresponds with the images. By studying the book in this way, we can directly grasp the intentions of the ancients, thus reviving the moral education of the Book of Changes, and its benefits to society would be great.

易之有圖，自伏羲以來亦漸加多，至周大備，秦漢乃遺之。連山、歸藏易，皆由圖以別其用者，無圖則不知有何以異也。古來圖象，皆為紀氣數之變，明天道之用者，故日圖讖。以其明未來之事，合神鬼之吉凶，為占卜之憑依，示人禍福休咎者也。故圖與卦同一用，雖簡略不文，而足以記數明變，如河圖洛書是也。

The Book of Changes has diagrams, which have gradually increased since Fuxi. By the Zhou dynasty, they were most complete, but they were lost during the Qin and Han periods. Both the Linked Mountains Changes and the Return of Concealment Changes rely on diagrams to distinguish their respective usages; without diagrams, one cannot see what differences they have. Diagrams from ancient times were used to record changes in qi and explain the operation of the heavenly way, so they are also called "diagrams and prophecies." Because they can reveal future events, conforming to the auspicious and inauspicious matters governed by spirits and ghosts, they serve as evidence for divination, indicating calamity, blessing, good, and evil to people. Therefore, the function of diagrams and hexagrams is the same. Although diagrams are brief and not written in words, they are sufficient to record numbers and clarify changes. The Yellow River Chart and the Luo Writing belong to this category.

一切圖象，皆始於河圖洛書，故二者為圖象之袓，亦易卦之所本也。易之圖象，自不外河圖洛書，而河圖洛書，非獨易所有也。易之所有者，如太極圖、兩儀四象八卦圖、六十四卦圖，及伏羲先天卦位、文王後天卦位、六十四分合變化諸圖表。

All diagrams originate from the Yellow River Chart and the Luo Writing, so these two are the ancestors of diagrams and the fundamental basis for the hexagrams of the Book of Changes. The diagrams of the Book of Changes naturally do not go beyond the scope of the Yellow River Chart and the Luo Writing, but the Yellow River Chart and the Luo Writing are not exclusive to the Book of Changes. The diagrams belonging to the Book of Changes itself, such as the Taiji diagram, the Two Principles, the Four Symbols, the Eight Trigrams diagram, the diagram of the sixty-four hexagrams, the diagram of the positions of the Earlier Heaven hexagrams by Fuxi, the diagram of the positions of the Later Heaven hexagrams by King Wen, and various charts showing the division and transformation of the sixty-four hexagrams.

與卦象生化、卦氣奇偶、卦用分合，其餘合日月之度、參音律數、納乾支之氣、明蓍龜之情，以及各卦變例、序卦次序、天地人之位、來往之時，各有圖表以紀其用，皆同河圖洛書，為易之圖象也。其間既經遺失，不傳已久，後人雖補之，有未能合原本者，應逐一審定，明其次序，以為習易者之途徑，亦以紹述古易本之精神。讀者其留意焉。

In addition, there are explanations concerning the generation and transformation of hexagrams, the odd and even principles of hexagram energies, and the division and combination of hexagram applications. There are also other methods such as those coordinating with the movement of the sun and moon, referencing musical scales and numerical systems, incorporating the energies of heavenly stems and earthly branches, explaining the nature of yarrow stalks and tortoise shells used in divination, and detailing variations among hexagrams, the sequence in the "Sequence of Hexagrams," the positions of heaven, earth, and humanity, and the temporal order of coming and going. Each of these has charts to record their usage. These, like the Yellow River Chart and the Luo Writing, all belong to the imagery of the Book of Changes. However, these have been lost over time and have not been passed down. Later scholars, although they have attempted to supplement them, have not fully aligned with the original. Therefore, they should be examined one by one, their order clarified, and used as an entryway for those studying the Book of Changes. This also serves to carry forward the original spirit of the ancient Book of Changes. Readers should pay close attention to this.

易之為道，本氣與數，而習易者，必求之象與圖，前已言之矣。易言氣數，純本天地自然之象。猶一年也，自春而夏而秋而冬，為二氣所周流，成四時之往復；以分言之，為月十二，為日三百六十。而其氣則有木火士金水，與太少陰陽之類；其數則有四時，十二月，上中下三旬，各日之名，皆以紀其氣數所至，而使人知天道之流行也。

The study of the Book of Changes fundamentally rests on "qi" and "numbers," and those who learn the Book of Changes must seek understanding through "images" and "diagrams," as mentioned earlier. The Book of Changes discusses qi and numbers based entirely on the natural phenomena of heaven and earth. Take a year, for example: from spring to summer, from summer to autumn, and from autumn to winter, the two qi forces of yin and yang circulate and transform, forming the recurring cycle of the four seasons. If we break it down further, a year consists of twelve months and three hundred and sixty days. Among these, "qi" includes the five phases—wood, fire, earth, metal, and water—as well as categories such as the sun, lesser sun, great yin, and lesser yin. As for "numbers," they include the four seasons, twelve months, the upper, middle, and lower three weeks, and the names of each day. These are all used to mark the progress of the circulation of qi and numbers, so that people may understand how the heavenly way flows.

例如七月七日，其數皆陽，而時屬秋，其氣為金，而質屬陰，以陽遇陰，為配偶之象，故有天孫河鼓相會之事。應其氣數，以為節令，非無稽也。一年各月，均有此氣數合值之日，均為名節。徵其數則知其氣，覘其氣則知其象。故象者，在天有其景，在地有其形，統名之日：「文」。莫非天地之象，而莫非氣數自然之序，故星躔日軌、水道陸形，皆有定度。聖人則之，以著為教，而後人知天地之事非荒渺者也。

For example, on the seventh day of the seventh lunar month, both the moon and the day are yang numbers seven. However, the season is autumn, and autumn belongs to metal, which has a yin nature. When a yang number meets a yin quality, it represents a harmonious pairing. Hence, the legend of Zhinu (the Celestial Weave) and Niu Lang (the Cowherd) meeting on this day. Determining the seasonal changes based on the numerical patterns is not without foundation. Among the twelve months of the year, there are days when the qi and numbers align perfectly, and these days have become famous festivals. By examining the numbers, one can understand the qi; by observing the qi, one can grasp the image or phenomenon. The term 'image' (象) is manifested in the sky as scenery and on the earth as forms, collectively referred to as 'wen' (文). None of these are not the manifestations of heaven and earth, nor are they not the natural order formed by the interaction of qi and numbers. Therefore, the paths of stars, the orbit of the sun, the flow of rivers, and the shape of the land all have fixed measures. Sages modeled their teachings upon these, and later generations came to understand that the affairs of the world are not fantastical or indistinct.

唯易最詳，以其本氣數而示圖象也，故習易必自象與圖始。天地雖大，易則至簡，由已知已見，推於未知未見，無不合也。故覽圖象，足以盡天地之妙，通氣數之神。神也者，司氣數而宰造化，天地萬物，莫非自神主之；故易之為教，以神道終始，而易之圖象，既始於龍龜之圖書，以明其神用也。神用無極，神德不測，故易道無窮。易之妙用，必由圖象始可以覘之。往復生化，奇偶變遷，皆圖象所示。智者見智，仁者見仁，則圖象者，正如天地之文，昭昭在目；而欲窮其極，雖聖智有不逮，是在學者善體會之耳。

Only the Book of Changes (Yi) explains things most thoroughly, because it is based on the principles of qi and numbers, and it presents images and diagrams. Therefore, studying the Yi must begin with its images and diagrams. Though heaven and earth are vast, the Yi is extremely concise. From what is already known and seen, it extends to what is not yet known or seen, and there is no inconsistency in this reasoning. Therefore, by examining the images, one can fully understand the profound mysteries of heaven and earth and grasp the "spirit" behind the principles of qi and numbers. The term "spirit" refers to the level that governs the principles of qi and numbers and controls the transformation of all things. Nothing in heaven and earth exists without its guidance, so the teachings of the Yi are always connected to the spiritual path. The Yi begins with the image of the dragon horse carrying a diagram and the divine turtle carrying a book, precisely to illustrate this miraculous function of the spirit. The function of the spirit has no boundaries, and its virtue is beyond measurement, so the way of the Yi has no end. The subtle applications of the Yi can only be understood by examining its images. All movements, transformations, odd and even changes are revealed through the images. The wise see wisdom in them, the benevolent see benevolence in them; the images are like the writings of heaven and earth, clearly visible before us. However, to fully explore their depths, even sages and wise men may find their limits, and this requires scholars to be good at understanding and grasping them themselves.

圖象者，易之所以示其物類與氣數之消長變化也。如乾之為 ，坤之為 ；而乾坤合為泰或否，變為復或姤，則陳其象。如泰為 ，以乾在坤下；如否為 ，則坤在乾下。觀此象，則知二卦皆乾坤各半合成者也。又如復為 ，以震在坤下，震為長男，一陽初生，乾交坤而成震；姤為 ，則巽在乾下，巽為長女，坤交乾而成巽，亦乾坤初交之象，為陰陽初變之機。則觀二卦之象，即可見乾坤交合相生之類；必以陰陽為根，以陽者合陰，則為異類，而交陰則為異物，由其氣之變否觀之也。

The images in the Book of Changes are used to display the categories of things and the changes in their vital energies. For example, the Qian trigram is drawn with three lines of pure yang, and the Kun trigram is drawn with three lines of pure yin. When Qian and Kun are combined with Qian on the bottom and Kun on the top, it forms the Tai hexagram; when Qian is on top and Kun on the bottom, it forms the Po hexagram. Further transformation leads to Fu and Gou. These transformations are all shown through the images. The Tai hexagram has Qian below and Kun above; the Po hexagram has Kun below and Qian above. By observing these two hexagrams, one can see that they are both formed by the combination of half of Qian and half of Kun. Similarly, the Fu hexagram has Zhen below and Kun above. Zhen represents the Elder Son, and the initial emergence of one yang line signifies the union of Qian and Kun to form Zhen. The Gou hexagram has Xun below and Qian above. Xun represents the Elder Daughter, and it is formed by the union of Kun and Qian. These two hexagrams also represent the initial union of Qian and Kun, symbolizing the beginning of the transformation of yin and yang. Observing these hexagrams reveals the categories of mutual generation between Qian and Kun. All of this is based on yin and yang: when yang combines with yin, it produces something different; when yang enters yin, it forms a new substance, which must be judged by whether the energy has undergone a qualitative change.

泰否反類，天地未易；復姤異物，乾坤已變。故乾坤之合，不謂之異物，以氣雖反而未變；若既交，則變矣。如巽震為乾坤所變，其氣與乾坤殊，故象亦異。則觀象可知氣數，而得象可辨物類，雖千萬變，猶可尋索，祇在就其圖象，而征其終始耳。故欲知易之名物別類，必先省諸圖象。

The hexagrams Tai and Po are merely inverted versions of each other, with heaven and earth remaining unchanged. However, Fu and Gou have already produced different elements, indicating that the principles of heaven and earth have changed. Therefore, the union of heaven and earth is only a combination of upper and lower, not the emergence of new things, because the energies, though in opposite positions, have not changed. Once true interaction occurs, transformation takes place. For example, Xun and Zhen are produced after the interaction of heaven and earth, and their energies differ from those of heaven and earth, hence their hexagrams are different. From this, we can see that observing the hexagrams allows us to understand the energies and numbers, and obtaining the hexagrams enables us to distinguish different categories of things. Even though there are countless changes, they can still be traced and examined, as the key lies in examining the hexagrams to confirm their origins and destinations. Therefore, to understand the names and classifications of various things in the Book of Changes, one must first focus on the hexagrams.

夫列圖觀象，以探其本末始終，必先察其體用，及其變化，而由大及細，由卦及爻，由內及外，由初及終，必求其所生成消長之數、盈虛變易之氣；而更比類及物，觀其中爻，較其互卦，以與本卦參，而後可得其故焉。

Lay out the diagram to observe the hexagram, in order to investigate the beginning and end of things. First, clearly identify its "body" and "function" and the changes within it: proceed from the general to the specific, from the whole hexagram to each line, from the inner trigram to the outer trigram, from the first line to the top line. Determine the numbers of its generation and decline, the movement and stillness of its vital energy. Then further classify and apply it to specific things, examining the direction of the middle lines, compare the hexagram formed by the middle lines, called the "nuclear hexagram," and refer it to the primary hexagram, thus clarifying the underlying reasons.

蓋圖象者，以物示其氣數，非一物一名可以盡之，必求其始終，極其變化，而後知氣數之所至，與物類之辨、性情之分，各得其徵。如天也，非為蒼蒼其色已耳；知天者，必考日月星辰之行，風雲雨露之變，神鬼之德，生物成物之道，而後得天之為天也。

Images use specific things to display their qi and numbers, but no single thing or name can fully express them. One must trace their beginning and end, exhaust their changes, then understand where the qi and numbers have reached, as well as the distinctions among things, the divisions of their nature and temperament, each of which can be verified. Take "Heaven" for example; it is not merely the blue and vast appearance. A true understanding of Heaven must involve examining the movement of sun, moon, stars and constellations, the changes of wind, clouds, rain and dew, the virtue of spirits and ghosts, and the principles of nurturing and completing all things. Only then can one truly comprehend what makes Heaven what it is.

故觀卦必徵諸一切，必因其生成來往，而定其吉凶禍福，則由明其情性、知其好惡故也。所好者吉，惡者凶；所生者福，克者禍。故必詳求之，而後可言占驗也。夫圖象者，如地圖焉，習地圖者必明其它之所在，及名物之所出，並其山川田野之勢，連接境界，道途遠近，人物之所贍養，皆熟知之。苦僅聞其名，則何益於用？

Therefore, when interpreting a hexagram, one must verify all aspects and determine fortune or misfortune based on its generation and transformation. This is because one must first understand its nature and disposition, knowing what it favors and what it dislikes. What it favors is auspicious; what it dislikes is inauspicious. What it generates or assists brings blessings; what it controls or restrains brings calamity. Thus, one must thoroughly investigate before engaging in divination. The image is like a map; those who study maps must understand the locations of various places, the origins of different resources, the terrain features, the boundaries between regions, the distances of roads, and the means by which local people sustain themselves. These details must be thoroughly memorized. If one only knows the name of a place, how can that be of any practical use?

故察卦貴明其用，而列圖觀象貴詳其變，非僅識其名、紀其形，即足也。且觀象重在觀其變，生成變化，為天地自然之數，以天地既奠，凡物均以對待而生。對待者，陰陽也。有陰必有陽，有生必有死，故有名必有對待：生以死名，長以消名，善以惡名，美以丑名，以相形而成，故有此即有彼，既由一陰一陽之相偶也。

Therefore, studying the hexagrams should focus on understanding their purpose, and observing the images and figures should focus on clarifying their transformations, not merely recognizing names or memorizing shapes. Moreover, the key to observing phenomena lies in examining their changes. The generation and transformation are inherent natural principles of heaven and earth: once heaven and earth are established, all things are produced in pairs.the so-called "tongdai" (mutual opposition) refers to yin and yang. Where there is yin, there must be yang; where there is birth, there must be death. Therefore, whenever there is a particular term, there must necessarily be another term that is its opposite: there can be a term "death" only because there is "life," "consumption" only because there is "growth," "evil" only because there is "good," "ugliness" only because there is "beauty." All these are established through mutual contrast. Thus, the presence of one aspect implies the presence of its counterpart, which comes precisely from the pairing of "one yin and one yang."

故陰陽者，非止言氣，凡對待以名者，皆陰陽之類也。人執陰陽為氣，與不認有陰陽，皆不通道者也。果無對待，則無陰陽，如天地之先，則無陰陽。故太極既立，兩儀隨生；不曰氣而曰儀，既明其類，不限於氣也。無論事物時位之名類，皆有陰陽，故以儀名。

Therefore, "yin and yang" are not merely referring to qi. Any pair of opposites that are defined in relation to each other falls under the category of yin and yang. Some people cling to the idea that yin and yang are only about qi, while others completely deny the existence of yin and yang. Both views are not in line with reason. If there are no two opposing aspects, then there can be no yin and yang. For example, before heaven and earth were formed, there could be no yin and yang. Therefore, once the Taiji is established, the two principles (two yi) arise immediately. It is precisely for this reason that it is called "yi" rather than "qi"—to emphasize that it refers to a category, not limited to qi. Whether it is about things, objects, times, or positions, each has its own yin and yang. Hence, the term "yi" is used to refer to it.

儀者，言名而釋義，指物而辨情，亦猶象也。凡物皆有兩象，故太極之後，必生兩儀；而易卦之變，必相對待，如乾與坤，坎與離也。其序也，亦由對列而成，觀其對列之象，知陰陽之錯行而不紊也；觀其變易之序，知陰陽之交合而不乖也。大之例天地世界之生成之始終，小之例人物日用之起居作息，其數不可易，其氣有必至者。故必列圖以觀，詳其始終變化，而後得性情物類，以致其用，決非昧昧者，徒於一卦一爻之辭可求者也。

The term "yi" refers to explaining the meaning of a name and distinguishing the nature of an object by referring to the actual thing, and its function is similar to "xiang." All things have both positive and negative aspects, so after the Taiji (Supreme Ultimate), two principles must arise, known as the Two Principles (liang yi). The changes in the hexagrams of the I Ching also necessarily occur in pairs, such as Qian and Kun, Kan and Li. The order in which the hexagrams are arranged is also based on their opposing pairs: by observing their paired arrangement, one can understand how yin and yang intermingle and operate without disorder; by observing their changing sequence, one can understand how yin and yang combine without contradiction. On a larger scale, this can be used to infer the origin and development of the universe; on a smaller scale, it can be used to understand the daily activities and routines of people and things. Its numbers are unchangeable, and its energies will inevitably arrive at their time. Therefore, one must present the diagram for observation, thoroughly understand its beginning and transformation, and only then can one grasp the nature of things and achieve practical results; this is not something that can be attained by those who are confused and rely only on the words of a single hexagram or line.

易以乾坤終始，而溯源太極。乾坤為兩儀之最大者，亦為萬物之最先者，故能始終萬物，無不包容。八卦、六十四卦、三百八十四爻，無非乾坤卦爻推變而來；雖六十四卦變自八卦，而八卦之六仍分自乾坤。故乾坤為易門戶，亦易之總樞也。乾道象天，坤德象地，乾坤即天地也。天地之德，以人而彰；人之德，鼎立天地間，故人道立於乾坤之中，而合乾坤之德以成人道。乾道成男，坤道成女，而人道遂始終於咸怛與既未濟，以明人與天地稱三才也。

The Book of Changes takes the trigrams Qian and Kun as its beginning and end, tracing its origin back to the Taiji. Qian and Kun are the greatest among the two principles and the first to exist among all things, thus they can pervade the beginning and end of all things, encompassing everything. The eight trigrams, the sixty-four trigrams, and the three hundred and eighty-four lines all originate from the lines and trigrams of Qian and Kun; although the sixty-four trigrams are derived from the eight trigrams, the other six trigrams besides Qian and Kun in the eight trigrams still come from the differentiation of Qian and Kun. Therefore, the Great Treatise says that Qian and Kun are the "gate" of the Book of Changes, as they are the central hub of the entire Book of Changes. The trigram Qian takes its image from Heaven, and the trigram Kun takes its image from Earth, so Qian and Kun represent Heaven and Earth. The virtues of Heaven and Earth depend on humans to be manifested, and human virtue stands equal with the virtues of Heaven and Earth, so human morality is established between Qian and Kun, combining the virtues of Qian and Kun to achieve human morality. The Great Treatise says, "The way of Qian produces the male, and the way of Kun produces the female," thus human morality begins with the trigrams Xian and Heng and ends with the trigrams Ji Ji and Wei Ji, indicating that humans, along with Heaven and Earth, are called the "three elements."

由卦觀之，先天屬艮，人道所始；後天坎離，人道之用，皆在乾坤之中，以維繫萬物，而共覆載之德，以燛理陰陽，而建中和之功。故觀易象當以人道為主，如中極既建，則萬物咸宜，此六爻之德，以中爻為重也。大扺聖人以易示教，首重人道，雖尊天地，兼萬物，而以人終始之。故日：「天地大義人終始。」觀象習易，必求乎人道所存，而後聖人之心可見也。

From the trigrams, in the Earlier Heaven arrangement, the human path is associated with Gen (Mountain), which represents the beginning of the human path; in the Later Heaven arrangement, Kan (Water) and Li (Fire) are in command, representing the application of the human path. These are situated between Qian (Heaven) and Kun (Earth), used to sustain all things, jointly bearing the virtue of heaven covering and earth supporting, to regulate yin and yang and establish the principle of harmony. Therefore, observing the images of the Book of Changes should focus on the human path. Once the central principle is established, all things will find their proper place. This is why in the six lines of the hexagram, the second and fifth lines, which represent the central principle, are most important. Generally, the sages used the Book of Changes to teach, first emphasizing the human path, although they revered heaven and earth and considered all things, they always maintained the human path throughout. Therefore, it is said, "The great principles of heaven and earth begin and end with humanity." To study the Book of Changes through observing its images, one must first seek the human path, only then can one see the mind of the sages.

夫易者，示人以變易也，以天道之變易，定人道之變易；以人道之變易，合天道之變易。故以天人為言：天道至微，人道則顯；天道無為，人道則勤；天道無名，人道則眾。為類極殊，而必齊之一之，此所以謂之易也。

The Book of Changes is about showing change to people: it uses the change of heaven's way to determine the change of human affairs, and uses the change of human affairs to harmonize with the change of heaven's way. Therefore, it always contrasts heaven and humanity: the way of heaven is extremely subtle, while the way of humanity is clearly evident; the way of heaven is inactive, while the way of humanity is diligent and unceasing; the way of heaven has no names, while the way of humanity has numerous names. The two are of vastly different categories, yet they must be brought together and unified, which is why it is called "Change."

由象言之，同此八卦，而體用殊；同此六爻，而動靜殊。由數言之，同此九也，而老少殊；同此六也，而上下殊。故為物簡，而為義眾；為名一，而為類多。得其本末，則由一及萬如解索；不知其由，則處常應變猶觸藩。故習易者，於易外求易，以盡其變；於象中分象，以通其神，而後得聖人之心，垂象示教之意也。

From the perspective of imagery, the same eight trigrams have different principles and applications; the same six lines also differ in their active and passive states. From the perspective of numbers, the same 'nine' can be distinguished as old yang or young yang; the same 'six' can be differentiated between the top line and the bottom line. Therefore, as a thing it is simple, but as a principle it is extremely complex; although the name is one, the categories are numerous. Once one understands its beginning and end, then from one can infer a thousand things, as smoothly as untangling a rope. But if one does not understand its origin, then dealing with constant situations and responding to changes would be like the ram in the Great Strength hexagram colliding with a fence, unable to advance or retreat. Therefore, those who study the Book of Changes should seek the Change beyond the Book of Changes to exhaust its transformations; they should further divide the imagery within the imagery to grasp its subtle aspects, only then can they understand the mind of the sage and comprehend the original intention of the sage in setting forth the hexagrams for teaching.

觀象也，必觀其來往動定，必辨其分合交錯，必類物以別名，審情以辨性，而不失其中極焉。蓋卦象以一象眾，亦猶言道以一馭萬。中極者，一也，一以貫之，方謂之通。故變化者，本於不變；動由不動，生由無生。必先明其故，方可以執象用易也。

When observing phenomena, one must pay attention to their movement and stillness, distinguish their separation and combination, and classify them according to specific things to differentiate their names. One should examine their characteristics to understand their nature, and always remain consistent with the "central point." The hexagram uses a single image to symbolize many things, just as a single principle governs all things in teaching. The "central point" refers to the "one." Only by being able to unify everything through this "one" can one be called thorough. Therefore, all changes originate from the unchanging; movement arises from non-movement, and generation arises from non-generation. One must first understand this principle before using the hexagrams to apply the Book of Changes.

夫執象觀易，譬之觀棋，何者生，何者死，何者進，何者退，皆應瞭然胸中，洞明目下，始得其生克變化之用。如乾坤二象，原屬陰陽大用，而乾之大始，坤之成物，一生一成，一始一終，皆在象中見之。蓋陽生陰成，陽始陰終，此氣之自然者。陽數用九，陰數用六；九為天數之終，六為數之始，河圖之例也。以陰代陽，以始至終，循環往復，以成其用，此數之自然者。

Looking at the hexagrams to understand the Book of Changes is like looking at a game of chess: one must clearly know which positions are alive, which are dead, which should advance, and which should retreat. Only then can one truly grasp the principles of their interactions and transformations. For example, the hexagrams Qian (Heaven) and Kun (Earth) represent the greatest functions of yin and yang. The Great Treatise says, "Qian knows the beginning of all things, and Kun completes the formation of things." One represents the beginning and the other the completion; one initiates and the other concludes, and these distinctions can be seen in the hexagrams. Yang represents the beginning and life, while Yin represents completion and conclusion. Yang starts, and Yin concludes, following the natural order of qi. The number for Yang is nine, and for Yin it is six. Nine is the last of the odd numbers, and six is the beginning of the even numbers, as established by the Yellow River Chart. Yin follows Yang, continuing from the beginning to the end, cycling and transforming to fulfill their functions, following the natural order of numbers.

合氣數觀之，則知象之生死進退、分合消長，無不明暸。故日：「觀象知數，觀數知氣。」數成於氣，象見於數。由上言之，明氣出於道，得道之士，不言數象；由下言之，則氣無形，附數以行；數無質，附象以成。不求於象，安知氣數。易，逆數也，由下推上，由已知求未知，故必自象始。此聖人教人觀易之道，以中人之智，必如是也。若不明象，何以探易，又何以探天地之妙、萬物之賾哉。故觀象貴精，習易宜細也。

When we combine the concept of qi with numbers, the rise and fall, movement and stillness, and growth and decline of the hexagrams become clear. Therefore, it is said: "Observing the images reveals the numbers; observing the numbers reveals the qi." Numbers arise from qi, and images manifest through numbers. From a higher perspective, qi originates from the Dao, and those who have attained the Dao do not need to discuss numbers or images. From a lower perspective, qi has no form and must rely on numbers to be expressed; numbers have no substance and must rely on images to take shape. Without seeking from the images, how can we understand qi and numbers? The "Sayings of the Hexagram" states, "The Book of Changes is inverse in numbers," meaning it proceeds from the lower to the higher, from the known to the unknown, so it must begin with images. This is the method the sages teach for observing the Book of Changes, and for those of average ability, it is essential. If one does not understand the images, on what basis can one explore the Book of Changes? And on what basis can one investigate the profound mysteries of heaven and earth and the myriad things? Therefore, observing images must be done with precision, and studying the Book of Changes must be done with care.

夫子之言至精詳。蓋陰陽二數相抱相接，而合化以成諸數，其用則九六，以九為陽數之純數，六為陰數之純數，故也。試以九乘各數，其得數不變；以六乘之亦然，而他數不能矣！至陰數逆行，人多知之；而始四終六，則往往不解，不知此河圖明明次列之序。

The Master's words are extremely detailed and precise. The two categories of numbers, yin and yang, embrace and connect with each other, combining to generate various numbers. Their representatives are "nine" and "six," because nine is the pure number of yang, and six is the pure number of yin. If you multiply nine by any number, the sum of the digits of the result will always reduce back to nine; the same applies to six. Other numbers do not have this property. As for the reverse order of yin numbers, most people are aware of it. However, why yin numbers start from "four" and end at "six" is often unclear. But in fact, this sequence is clearly presented in the Yellow River Chart.

今試以純陰數六，乘陽數一三五七九，其所得數即六八十二四，恰為陰數之反；從左而右，則為四十二八六逆行之序，與河圖合。又如以九乘陽數一三五七九，其得數亦恰為陽數之反，即九七五三一；從左而右則為順行之序，亦合河圖。又如以九除陽數一三五七九，其得數合其餘數；若以九除陰數，其餘數仍同陰數。

Now try using the pure yin number six to multiply the yang numbers one, three, five, seven, and nine, resulting in six, eighteen, thirty, forty-two, and fifty-four. Taking only the last digits gives six, eight, ten, two, and four, which are exactly the reverse of the yin numbers. When read from left to right, this becomes four, two, ten, eight, and six, which matches the arrangement of yin numbers in the Yellow River Chart. Similarly, using nine to multiply the yang numbers one, three, five, seven, and nine gives nine, twenty-seven, forty-five, sixty-three, and eighty-one. Taking the last digits results in nine, seven, five, three, and one, which are the reverse of the yang numbers. Reading from left to right restores the original order of one, three, five, seven, and nine, which also conforms to the Yellow River Chart. Furthermore, when nine is used to divide the yang numbers, the remainders are still those yang numbers; similarly, when nine is used to divide the yin numbers, the remainders are still those yin numbers.

由此可見九六之用，與陰數逆行之序，皆屬自然，毫無牽強，此所以聖人取則而可證之河圖者。此解近人頗有悟之者，獨未之其本於河圖自然之序耳。但其用心已足許矣！夫天地之數，皆始於河圖，而闡明於易；惜讀者棄河圖不講。又因易傳文字錯簡，前後脫略不全；遂不復知傳中天一地二，一叚文字，繫解釋河圖者。更不知所言關乎數之根本，囫圇吞棗，終不得聖人立言之旨，誠可慨矣！

This shows that the use of the numbers nine and six, as well as the reverse order of the yin numbers, all come from nature, without any forced arrangement. This is why the sage took them as a model and found confirmation of them in the Yellow River Chart. Recently, some people have also come to understand this, but they have not yet realized that these principles are based on the natural order of the Yellow River Chart. Nevertheless, their efforts are commendable. The numbers of heaven and earth all originate from the Yellow River Chart, and are explained in the Book of Changes. Unfortunately, those who read the Book of Changes have neglected the Yellow River Chart. Moreover, because the text of the Book of Changes' commentaries is disordered, with missing parts and incomplete passages, no one now knows that the passage "Heaven is one, Earth is two; Heaven is three, Earth is four" originally explained the Yellow River Chart. They also do not realize that what is discussed relates to the fundamental principles of numbers. Instead, they merely swallow the whole thing without understanding, and thus fail to grasp the original intention of the sage's words, which is truly regrettable.

河圖所含理數，至精極宏，不易講盡；此不過撮其大要，為講易所必知者。若專研數學，貫通天人；則當於此進而求之，以窮其變化，而神其用；庶於天下數，莫不了然；即推至過去未來，亦如指掌。則此寥寥十數中，有無盡之神妙在；大可為專書以繹其義，而傳其道焉。

The principles and numerical techniques contained in the Yellow River Chart are extremely subtle and vast, difficult to fully explain. Here, only the main points are summarized, focusing on the parts essential for understanding the Book of Changes. If someone specializes in mathematics and aims to comprehend the workings of heaven and human affairs, they should proceed further from here, exhaustively exploring its transformations and fully applying its uses to a miraculous extent. In this way, they would be able to understand all numerical systems in the world; even when calculating past and future events, they would be as clear as looking at their own palms. Clearly, within these ten numbers lies infinite subtlety and mystery, sufficient to write an entire book to elaborate on its principles and spread its teachings.

又曰：講易先自圖解始，以示易之初僅圖象，並無文字可讀也。然圖象者，非機械之類，含有深微妙用，亦如文字之變化靡盡也。故觀圖象而能會通，則全部易經文義已在中矣！猶之太極圖，明二氣之始終動靜，以生成萬物；雖萬言不盡其蘊，而圖則皆在此圓圈中，一覽無遺。此其神妙之用，實非聖人莫能為之，莫能知之。人苟從而窮究其故，以深會其微妙，方知古人圖象不虛作；更見易經文字之不待言也。

It is also said that studying the Book of Changes should begin by understanding its diagrams, which were originally used to explain the meaning of the Book of Changes before there were written characters. However, these diagrams are not rigid mechanical things; they contain subtle and profound functions, just like written characters, which are also infinite in variation. Therefore, if one can understand the diagrams thoroughly and integrate their meanings, the entire meaning of the Book of Changes will be contained within them. For example, the Taiji diagram shows how the interaction between yin and yang generates all things through their movement and stillness. Even if one writes ten thousand words, it would be impossible to fully express its depth. But when drawn as a diagram, all its meaning is contained within that single circle, clearly visible at a glance. This kind of miraculous function is something that even the sages could not create or fully comprehend. If people can follow this path to investigate its reasons deeply and thoroughly understand its subtleties, they will realize that the ancient diagrams were not drawn in vain, and they will also understand that the written words of the Book of Changes do not need to be excessive.

今時人昧於道，忘其性；以精微之教，視為荒渺之談；而造成亂世末劫，行同禽獸；以陷於苦海，莫之拔度，斯豈聖人所及料哉？大劫且臨，至教將絕；大道不復，人類奚存？有心救世者，要從易中原推致亂之故，而得挽回之途；是則吾人講易，不僅為習古明經已耳。

Nowadays people have lost the great way, forgotten their true nature, and regard profound teachings as absurd and empty talk. Thus, chaos and the end of the age have come about, with people's behavior becoming like that of beasts, trapped in suffering with no one to rescue them. Could this have been what the sages foresaw? As a great calamity is about to arrive, the highest teachings will soon be cut off; the great way will no longer be restored, and how can humanity continue to exist? Those who sincerely wish to save the world should investigate from the Book of Changes the causes of calamity and disorder, in order to find a way to reverse the situation. In this light, our study of the Book of Changes today is not merely about learning ancient texts and understanding the classics.

又日：夫子所講五行相得有合之理，及土數用五之故；實為中國文化根本，亦即探索造化之源；指明氣數之用，為一切言數者之所本。蓋二氣雖分，未成形也；必再分為五行，而後化成萬物。五行之成，在天有寒暑風燥溼之令，在時有春夏秋冬四季之候；在味有酸苦咸甘之辨，在色有青赤白黑黃之分；皆以五為例，即五行也。

It is also said that the principle of the Five Phases "mutually supporting and harmonizing" explained by the Master, as well as the reason why the Earthly Number "five" is used for the element of earth, is indeed the fundamental aspect of Chinese culture. It is also the way to explore the origin of creation and to clarify the use of numerical patterns, serving as the foundation for all those who study numerology. Although yin and yang energies have separated but have not yet taken form, they must be further divided into the Five Phases, only then can all things be generated. Once the Five Phases are established, they manifest in the heavens as the five climatic energies: cold, heat, wind, dryness, and dampness; in the sequence of seasons as spring, summer, autumn, winter, and the additional season of late summer; in flavors as sour, bitter, salty, sweet, and pungent; and in colors as green, red, white, black, and yellow—all based on the number "five." This is the essence of the Five Phases.

猶之二氣曰陰陽，曰柔剛，曰仁義，曰天地，曰乾坤，曰寒熱，曰日夜，曰正反，曰善惡，曰是非，皆以兩相對。是故曰：「兩儀」，而不限於氣；五行亦然。曰：「五行」者，示其周流無盡，合乎道之運行也；或屬於氣，或屬於數，或屬於時，或屬於物，或屬於事，不限於一類。

Just as yin and yang, it can be called yin and yang, or soft and strong, or benevolence and righteousness, or heaven and earth, or Qian and Kun, or cold and heat, or day and night, or right and wrong, good and evil, right and wrong. All of these are pairs of opposites. Therefore it is called "two principles" and not limited to the category of "qi." The Five Phases are also like this. Calling it "Five Phases" is to indicate that it flows endlessly and conforms to the operation of the Dao. It may belong to qi, or to numbers, or to seasons, or to things, or to events, and is not confined to any single category.

故曰：「五行」。兩儀總其綱，五行任其目；為天地萬物一切之母體，凡有生有成有形有名有類者，皆不得外。是以生存長育，變化推遷，以遂其造化之用。二氣五形行者，即造化之樞紐，萬物之胚胎；為天下之祖氣，萬有之特性也。二氣以簡，而不能極生化之用；而藉五形，以成其錯綜變化之妙。

Therefore it is called the "Five Phases." The two principles encompass the general framework, while the Five Phases handle the specific details. They are the fundamental essence of all things in heaven and earth; anything that has birth, growth, form, name, category, cannot escape this scope, thus there is growth, nourishment, change, and transformation, completing the function of creation. Yin and Yang energies and the Five Phases are precisely the key to creation, the embryonic form of all things, the primal energy of the world, and the essential nature of all existence. Since the two energies are too simple, they cannot fully express the process of generation and transformation, so they rely on the Five Phases to achieve the intricate and complex changes.

五行以化，漸移其初始之真；故仍托於二氣，以成其主宰之神。故二五為生生之源，天下萬物，莫不以之相維相繫；並育不害，並行不亂，以成其生化之序；而世界一切於是出焉。乃曰二五構精，萬物化生；此河圖所指，必以五行配二氣；以見天地之生成，氣數之相得，而各有合得也。

After the Five Phases have been generated and transformed, they gradually depart from their original essence, so they still rely on the two energies of yin and yang to form the divine principle that governs them. Therefore, the number two (yin and yang) and the number five (the Five Phases) are the continuous sources of generation. All things under heaven depend on them to sustain each other, to grow together without conflict, and to function harmoniously without disorder, thus forming the order of generation. Therefore, the "Taisi Tu Shuo" says, "The essence of two and five combines in a subtle way and coagulates," through which all things are generated. This is exactly what the Yellow River Chart indicates: one must pair the Five Phases with the two energies of yin and yang to see how heaven and earth are generated, and how the energies and numbers "cooperate" while each maintaining their own harmony.

至於五行之數，大都用成數，而土則用生數；試觀月令，即知為土主中央，五為中數；而成數之十，仍生數之倍；二五無異一十，用五即足；且天地妙用，常藏十不用；故數老於九，若十則反轉為一；以成其循環之道。故數未有用十者，以此土用五而不及十；學者須明乎此義，方明數之用，亦明天地之心在五；以五立極，合於中和之德，時中之道；其妙義不可盡矣！

As for the numbers used in the Five Phases, they mostly employ the "completed numbers" six, seven, eight, nine, and ten, but earth alone uses the "originating number" five. If we look at the "Liji · Yue Ling," we can see that earth governs the center, and five is exactly the middle number among one to nine; the completed number "ten" is merely double the originating number "five." There is no difference between two fives and one ten, so using five is sufficient. Moreover, the subtle workings of heaven and earth often conceal the number "ten" and do not use it. Therefore, the number nine is considered the oldest, and when it reaches ten, it reverses back to one, thus forming a cycle. Therefore, numbers never use ten; earth only takes five and does not reach ten, for the same reason. Scholars must understand this point clearly in order to grasp the use of numbers and also comprehend that the heart of heaven and earth lies in the number five. Using five to establish the central point is in harmony with the virtue of balance and the principle of appropriate timing. The profound meaning within is endless.

夫子前講河圖，為天地自然之數；其始終包萬物之生成，萬事之吉凶成敗；故易本此而示人以修養省存，趨避逆順之道，蓋莫非氣為之也。天地為萬物父母，言萬物必自天地始；而萬物之生成，得天地之氣，其數亦分天地之數。河圖溯物之生成，明五行所出；二氣所運，而以數示之，其旨深矣。

The Master previously spoke of the Yellow River Chart, saying that it is the natural numbers of heaven and earth, covering from beginning to end the generation of all things and the fortune, success and failure of all affairs. Therefore, the Book of Changes uses it to guide people in cultivating their bodies and minds, examining and nurturing themselves, and understanding how to seek good fortune and avoid misfortune, as well as how to choose and reject things according to the right path. All of this ultimately depends on the principle of "qi." Heaven and earth are the parents of all things; when speaking of all things, one must begin with heaven and earth. Since the generation of all things comes from the qi of heaven and earth, their numbers are derived from the numbers of heaven and earth. The Yellow River Chart traces the origin of all things, explains where the Five Phases come from, and how the two qi of yin and yang operate, expressing them through numbers. Its intention is profound.

蓋氣無形而難言，數有名而可紀；故以數代氣，數之所在，即氣之所至；數之幾分，即氣之幾分；以數之分合，而知氣之變化；以數之順逆，而知氣之吉凶；其言數，皆言氣也。氣有精粗，有動靜；數有奇偶，有多寡；由數明氣，則生化之跡，無不知之；故河圖實以數示造化之本者也。

The qi has no form and is difficult to describe with words; numbers have names and can be recorded, so numbers are used to represent qi. Where the numbers are, qi is there as well; how much the numbers are, so much is the qi. By the combination and division of numbers, we can understand the changes of qi; by the order and disorder of numbers, we can know the fortune and misfortune of qi. Therefore, whenever numbers are discussed, it is actually about qi. Qi has both refined and coarse aspects, as well as moving and still aspects; numbers have odd and even, as well as more and less. By using numbers to understand qi, the process of generation and transformation becomes fully known. Thus, the Yellow River Chart is actually using numbers to reveal the fundamental principles of creation and transformation.

數之為用，自一至十；為一切數之本，無論何數，皆自此生化；故一至十之數，實包無盡數也；知其變化，不可盡於用；不知，則不得其用；數者能示變化，而通鬼神；夫數既出於氣，氣有陰陽，故數亦有陰陽；陽奇陰偶，陽屬天，陰屬地；以二者之分合，而萬有以生成變化；不獨五行也。

The use of numbers begins from one to ten, which are the fundamental numbers from which all other numbers are generated and transformed. Therefore, the numbers from one to ten actually contain an infinite number of other numbers. Understanding their transformations allows for endless application; without understanding, one cannot utilize them. Numbers can reveal changes, hence they are connected to spirits and deities. Since numbers originate from qi, and qi has yin and yang, numbers also have yin and yang: odd numbers are yang and even numbers are yin; yang belongs to heaven, and yin belongs to earth. Through the separation and combination of these two, all things are generated and transformed, not only in the Five Phases.

而五行為生變之始，故舉之以例萬物；五者生變，由數知之；必將數之奇偶，位之順逆；相合而生成，變化乃見；圖中之一三五七九，奇數順行；四二十八六，偶數逆行；而其合也，遂成一與六，二與七，三與八，四與九，五與十，各當其位；以生成水火木金土，依次列北南東西中；以示五者之所自出，本乎數之相得有合也；亦氣之相生有成焉耳。

The Five Phases are the beginning of generation and transformation, so they are used as a model for all things. To understand how the Five Phases generate and transform, one must refer to numbers. The odd and even numbers must be combined with the direction of movement, clockwise or counterclockwise, so that the process of generation can be seen and transformation can be demonstrated. On the Yellow River Chart, the odd numbers one, three, five, seven, and nine move counterclockwise; the even numbers four, two, ten, eight, and six move clockwise. When these two sets meet, they form pairs: one with six, two with seven, three with eight, four with nine, and five with ten. Each pair occupies its proper direction, thus generating water, fire, wood, metal, and earth, arranged in order in the north, south, east, west, and center. This shows the origin of the Five Phases, which arise from the mutual combination of numbers, indicating the mutual generation of energies leading to their formation.

故知一之與六，兩數相得，而水之生成，得天地之氣若幾分也；火木金土皆然，皆由天地之氣，奇偶之數，恰相得而合也；故易曰：「一陰一陽謂之道」。數之順逆偕行，以循環始終；於是生化之道見焉。以奇偶之數，一陰一陽猶男女也；而夫婦之道，即人生之始；人以男女配偶，而生息無盡；數以奇偶配合，而生化無窮；此天地造化之妙也。

From this we can see that the numbers one and six complement each other. The generation and formation of water come from taking a portion of the qi from heaven and earth. Fire, wood, metal, and earth are also like this, all formed by the proper combination of the qi from heaven and earth and the even and odd numbers. Therefore, the Great Treatise says, "One yin and one yang is called the Way." Numbers can move in a forward or reverse direction, and they rotate together in a cycle, thus revealing the principles of generation and transformation. In terms of odd and even numbers, one yin and one yang are like one man and one woman; the way of husband and wife combining is the beginning of human life. Humans continue their lineage through male and female partners, while numbers generate infinite transformations through the combination of odd and even. This is the marvelous creation of heaven and earth.

故數之一三五七九，皆陽皆奇；二四六八十，皆陰而隅。二者相得有合，而五行生成；陽道虛，陰道實；陰統於陽。陽包其陰；皆自然配偶，各有其序；故奇數合偶數，仍為奇；奇數合奇數，反為偶；偶數合偶數，仍為偶；以見陽之統攝陰，而不可亢；陰之順承陽，而不可離；亢則害，離則乖；唯相得有合，而後成其生化也。

Therefore, the numbers one, three, five, seven, and nine are all yang and odd numbers; two, four, six, eight, and ten are all yin and even numbers. These two aspects combine to form the Five Phases. Yang is empty and yin is substantial; yin belongs to yang, and yang contains yin. They are naturally complementary and have their own order. Thus, when an odd number is added to an even number, the result is still an odd number; when two odd numbers are added together, the result is even; when two even numbers are added together, the result is still even. Therefore, yang controls yin but should not be excessive, and yin follows yang but should not deviate. Excessiveness brings calamity, deviation leads to disorder. Only when they complement and combine with each other can they achieve the function of generating and transforming life.

河圖之數，天地之本數也；其用自其變化而生。五行之物，萬物之根本也；其生化自其分合而成。蓋有天地而有萬物，有天地之大數，而後有萬物之數可紀；故有序有類有名，而後成其德；萬物並育而不相害，道並行而不相悖；此德之見也。此「道」字，即指一陰一之道，言二氣並行而不亂其序，則由有數也。

The numbers of the Yellow River Chart are the fundamental numbers of heaven and earth, and their function arises from their own changes. The Five Phases are the fundamental elements of all things, and their generation and transformation come from their division and combination. Only with heaven and earth can there be all things; only with the great numbers of heaven and earth can the numbers of all things be recorded. Thus there is order, classification, and names, and then the "de" of things is established. The Zhongyong says, "All things grow together without harming each other, and the ways run parallel without contradicting each other," which is the manifestation of "de." Here the term "Dao" refers to the Dao of "one yin and one yang," meaning that the two energies of yin and yang operate together without disorder, precisely because there is "number" within them.

猶物之陳於室，高下遠近，各如其分；此數之所見也。人之智愚賢否，貴賤壽夭，各有其數，以定其分；而能守其分，安其數，是為知命；以命自天，知命者，安於天命之數，而不失其序；以順承天生我之德，而養育其中和之氣；是為明道。道不離二氣，知乎數而和於氣，則成道之士也。故易者，言數以明道，達命以知天者也。

This is like objects arranged in a room, each placed at its proper height and distance, which is the manifestation of "number" in daily life. A person's intelligence or foolishness, virtue or vice, wealth or poverty, longevity or short life, each has its own number, thus determining its proper position. To hold fast to one's position and be content with one's number is called "knowing one's destiny." Destiny comes from Heaven; those who know their destiny accept the number set by Heaven's mandate without disturbing its order, thus following the virtue bestowed by Heaven and cultivating the harmonious energy within oneself, which is called "understanding the Way." The Way cannot be separated from the dual energies of yin and yang. Those who understand number and can harmonize with the energies are the ones who achieve the Way. Therefore, the Book of Changes is about using number to explain the Way and using destiny to understand Heaven.

夫易之言數，自河圖始；河圖之數，即易之數；如水火木金土五者，易之乾坤離坎震兌也；由用言之，則坎離坎震兌，分合水火木金四氣之象；而艮為土，此後天之卦也；若在先天，則乾坤震兌為四方，而坎離在中；其氣數各有所合也。以一六之水，為天地二氣初化；二七之火，三八之木，四九之金，五十之土，皆依次而生成者；陽生則陰成者，陰生則陽成。

The Book of Changes begins with numbers from the Yellow River Chart. The numbers of the Yellow River Chart are the numbers of the Book of Changes: for example, water, fire, wood, metal, and earth correspond to the trigrams Qian, Kun, Li, Kan, Zhen, and Dui in the Book of Changes. In practical application, the trigrams Kan, Li, Zhen, and Dui correspond to the images of water, fire, wood, and metal respectively, while Gen corresponds to earth, which is the arrangement of the Later Heaven trigrams. In the Earlier Heaven arrangement, Qian, Kun, Zhen, and Dui are located in the four directions, while Kan and Li are in the center, and their energies and numbers are matched accordingly. The number one combined with six forms water, which is the initial generation of the energies of heaven and earth. The number two combined with seven forms fire, three with eight forms wood, four with nine forms metal, and five with ten forms earth, all generated in sequence. All yang numbers are responsible for generation, and they are completed by yin numbers; all yin numbers are responsible for generation, and they are completed by yang numbers.

二氣更互以生以成，五行於是出，萬物於是生；其生化之道，不離乎此圖之序；其賦與之命，不外乎此圖之數；數之所在，即二五之所分合；凡二五之所分合；凡屬後天之生物，莫不由此二五之分化也。數有終始，運行有序；命有善惡，道有先後；皆氣之所偏全有所合也。不合不生，故必合而有得也；此天地生化之妙用，亦世界自無入有之次第也。

Yin and yang energies interact with each other; one is responsible for generation, and the other for completion. The Five Phases arise from this interaction, and all things are born from it. The pathways of their generation and transformation cannot depart from the order established by the Yellow River Chart. The destiny they receive is also beyond the numbers listed in the Yellow River Chart. Wherever numbers exist, there is the division and combination of yin and yang energies and the Five Phases. Everywhere where these energies and phases combine, all things born under the Later Heaven originate from the differentiation of 'two' and 'five'. Numbers have a beginning and an end, and their movement follows a certain order. Destiny has good and evil, and the Way has precedence and succession. These are all due to the partiality and completeness of the energies, each having its own coordination. Without combination, there is no generation, so combination is essential for results. This is the subtle function of heaven and earth in generating things, and also the sequence by which the world moves from 'nothing' to 'something'.

數之所合，易卦而外，則乾支為最易知；以其習見習聞也。天乾之數，甲乙為木，丙丁為火，戊已為土，庚辛為金，壬癸為水，其數同也；地支之數，寅卯為大，巳午為火，申酉為金，亥子為水，辰戌丑未為土，其數合也。皆以五行分配，而相生相制；以成其生化之用，與圖相同；故易卦有納甲之義。

The combination of numbers is easiest to understand besides the Yi hexagrams, because people are familiar with the heavenly stems and earthly branches. The numbers of the heavenly stems: Jia and Yi belong to wood, Bing and Ding to fire, Wu and Ji to earth, Geng and Xin to metal, and Ren and Gui to water; they all have the same numbers. The numbers of the earthly branches: Yin and Mao belong to wood, Si and Wu to fire, Shen and You to metal, Hai and Zi to water, and Chen, Xu, Chou, and Wei, the four branches, belong to earth; their numbers also correspond with each other. Both heavenly stems and earthly branches are assigned according to the Five Phases, and they generate and control each other, thus fulfilling their functions of creation and transformation. This is consistent with the Yellow River Chart, so the Yi hexagrams have the system of "Najia" (stem assignment).

蓋卦象人或不知，而乾支則易知；乾支固無異於卦，皆以示氣之運行，二五之化合；或以卦示其象，或以乾支繫其名；其實皆出河圖，亦猶數算之代名也。因氣數不易記，故以之代，而便於習究也；如甲乙屬木，即震巽也；丙丁屬火，即離；庚辛屬金，即兌；壬癸屬水，即坎；戊已屬土。即坤艮也。

The principles of divination are not easily understood by ordinary people, but the Heavenly Stems and Earthly Branches are familiar to everyone. In fact, the Heavenly Stems and Earthly Branches are essentially the same as the trigrams, both used to represent the movement of qi, the combination of yin and yang, and the Five Phases. Some use trigrams to show their symbolic meanings, while others use the Heavenly Stems and Earthly Branches to name them. In the end, both originate from the Yellow River Chart, just like symbols in mathematics. Since the movement of qi is difficult to remember, the Heavenly Stems and Earthly Branches are used as substitutes, making it easier to study and examine. For example, Jia and Yi belong to wood, corresponding to the trigrams Zhen and Xun; Bing and Ding belong to fire, corresponding to the trigram Li; Geng and Xin belong to metal, corresponding to the trigram Dui; Ren and Gui belong to water, corresponding to the trigram Kan; Wu and Ji belong to earth, corresponding to the trigrams Kun and Gen.

而其為用則與此稍異；以乾納甲壬，示陽氣之初動；坤納乙癸，示陰氣之偕行；震巽以木而納庚辛，示木受制而後成用也；坎離納戊己，以水火之用成於土也；兌艮納丙丁，以金受火制，土為火生，各得其用也。故其數與原位異，此先後天之殊，體用之不同也；然此所納亦有異同，則用者取義不一也。

But the application of the Najia system differs slightly from the above five-phase attributions: the Qian trigram is assigned Jia (Ren), indicating the initial emergence of yang energy; the Kun trigram is assigned Yi (Gui), indicating the concurrent movement of yin energy. The Zhen and Xun trigrams, which belong to wood, are assigned Geng and Xin (metal stems), indicating that wood must first be restrained by metal before it can function properly. The Kan and Li trigrams are assigned Wu and Ji (earth stems), because the functions of water and fire depend on earth to be fulfilled. The Dui and Gen trigrams are assigned Bing and Ding (fire stems), because metal requires fire for refinement and earth is nurtured by fire, allowing each to function properly. Therefore, the numbers assigned in the Najia system differ from the original five-phase directional attributions. This is the distinction between Earlier Heaven and Later Heaven, as well as the difference between form and function. However, different schools have slight variations in their assignments, due to differing interpretations by those who apply them.

如歸藏異乎連山，周易異乎歸藏；皆後天之用，非關先天之體用也；其義詳洛書中。河圖洛書一體一用，各有其指也；故在圖之數，方位相當；次序無亂，與伏羲之卦象同；而為一切數之根本，有不易者也。圖中之數，雖自一至九；而五十二數，卻在中心；故分數時，應分陽數一三七九，與陰數二四六八相對以合；另提五十二數為中心立極。

For example, the method of incorporating numbers in the "Guicang Yi" differs from that in the "Lianshan Yi," and the method in the "Zhou Yi" differs again from that in the "Guicang Yi." These all belong to the later heaven usage and have nothing to do with the earlier heaven's principles. The reason for this will be explained in detail when discussing the Luo Shu. The He Tu and the Luo Shu each have their own focus; one represents the fundamental structure, and the other represents the application. Therefore, the numbers on the He Tu are arranged in a way that their positions correspond with each other, and their order remains clear and orderly, consistent with the hexagrams drawn by Fuxi. The He Tu is the root of all numbers and cannot be altered. Although the numbers on the He Tu range from one to nine, the numbers five and ten are placed at the center. Therefore, when arranging the numbers, the yang numbers one, three, seven, and nine should be paired with the yin numbers two, four, six, and eight respectively. The numbers five and ten should be separated and placed at the center to establish the central point.

依陰數逆行之例，與陰數之始四終六；則一三七九，與四二八六適恰相當；而生成之功見，生化之序明；而五十二數亦正相當。若不如是，則位與數失，陰與陽乖；不克生成萬物矣！故一三七九陽數，必順次行；四二八六陰數，必顛倒而逆行；此必然之理。人知陽數順行，而不知陰數逆行；遂不明數之大用，此惑也。

According to the established practice of the yin numbers moving in reverse order, with the yin numbers starting from 'four' and ending at 'six', the numbers one, three, seven, and nine correspond one by one with four, two, eight, and six: one corresponds with four, three with two, seven with eight, and nine with six. Thus, the function of generation becomes evident, and the sequence of generation and transformation becomes clear. The numbers five and ten in the center also each take their proper positions. If they were not arranged in this way, the positions and numbers would be misaligned, yin and yang would be discordant, and thus, the generation of all things would not occur. Therefore, the yang numbers one, three, seven, and nine must necessarily proceed in order, while the yin numbers four, two, eight, and six must necessarily move in reverse. This is an inevitable principle. People only know that yang numbers proceed in order, but do not know that yin numbers move in reverse, thus failing to understand the great function of numbers, which is a great confusion.

夫使陰數亦如陽之順序而行，則一與二，三與四，五與六，七與八，九與十，相對而論，皆不能合；更何生成之功可言？蓋必一順一逆，一依次，一倒行；方能合其位，而成其用；而後一與四合，二與三合，七與八合，九與六合，五與十合，相得而皆有合；以成中極之數皆五也。故曰：「天數五，地數五。」五位相得而有合也。

Suppose the yin numbers were arranged in the same order as the yang numbers, then one would pair with two, three with four, five with six, seven with eight, and nine with ten. When compared in pairs, none of them would produce the central number. How could there be any generative power then? It is necessary for one to proceed in order and the other to go in reverse, one to follow the sequence and the other to go backwards, so that each can be matched with its proper position and fulfill its function. In this way, one and four combine to make five, two and three combine to make five, seven and eight combine to make fifteen, nine and six combine to make fifteen, and five and ten combine to make fifteen. Each combination produces the central number, and all of them are based on the number five. Therefore, the Great Treatise says, "Heavenly numbers are five, earthly numbers are five. The five positions interact and each has its corresponding match."

言合乎五，即合天地之心；在道言之，即合中和之德，示人執中用之道也；蓋數十而位五，唯五乃中；不得其五，即不得其中；不得其中，必有所偏；偏則害生，安能致生成之用？通天地之心哉。故五位之合，必依陰數逆行，而後得之也。

The concept of "harmony with the number five" refers to aligning with the heart of heaven and earth; from the perspective of the Dao, it means aligning with the virtue of moderation and harmony. It is indicating that people should adhere to the middle path and use the method of the middle. There are a total of ten numbers, yet only five directions exist. Only the number five is in the center; without this five, one cannot attain the middle; without the middle, there will certainly be some bias. Once there is a bias, calamity arises, how then can one achieve the accomplishment of creation and connect with the heart of heaven and earth? Therefore, the combination of the five directions must follow the rule of reversing the yin numbers, only then can it be attained.

且陽順陰逆，氣之自然；逆之雲者，對陽順言；其實不過一往一復，一左一右而已。陰氣原與陽對行，陽左則陰右，陽先則陰後，陽升則陰降，自然而然，非圖之有異也；如晝夜寒暑，互相推移，而日歲以成；若同一途，則一氣獨用，不復有生化之功矣！故言數不明可證於象，以象之明見於目也。

Heavenly stems move in a positive direction while earthly branches move in a negative direction, which is natural for the energies. The term "reverse" merely refers to the contrast with the positive movement of heavenly stems; in reality, it is simply a back and forth, left and right movement. Yin energy naturally moves in the opposite direction of yang: when yang moves left, yin moves right; when yang is ahead, yin is behind; when yang rises, yin descends. All of this happens naturally, without any special arrangement in the Yellow River Chart. Just as day and night, cold and heat alternate to form a day and a year; if they followed the same path, there would only be one kind of energy acting alone, and there would be no process of generation and transformation. Therefore, when numbers cannot be fully explained, we can find confirmation through images, because images are clearly visible before us.

今就圖象證之，亦自可見；陽自一左旋至九，序位皆順；陰自四右旋至六，序位倒逆；而恰合一六、三八、二七、四九、五十，之五行數，不待移易；即此可知天地大數，不離陰陽生化之功，不外陰陽順逆之用；而萬物以生，萬事以立，其微妙固非難測者矣！

Now referring to the Yellow River Chart for verification, it becomes clear: the yang numbers start from "one" and rotate left until "nine," with their positions all in order; the yin numbers start from "four" and rotate right until "six," with their positions all in reverse. In this way, exactly five sets of the Five Phases numbers are formed: one and six, three and eight, two and seven, four and nine, five and ten. There is no need for further movement or adjustment. From this alone, we can understand that the great numbers of heaven and earth cannot be separated from the generative power of yin and yang, nor can they go beyond the use of yin and yang in order and reverse; all things are generated from this, and all affairs are established upon this. The subtle nature within is not something difficult to comprehend.

天一生水，地六成之；地二生火，天七成之；天三生木，地八成之；地四生金，天九成之；天五生土，地十成之。

Heavenly numbers "one" produces water, and earthly numbers "six" complete it; earthly numbers "two" produce fire, and heavenly numbers "seven" complete it; heavenly numbers "three" produce wood, and earthly numbers "eight" complete it; earthly numbers "four" produce metal, and heavenly numbers "nine" complete it; heavenly numbers "five" produce earth, and earthly numbers "ten" complete it. These five groups of numbers live apart in the five directions: water from one and six is in the north, fire from two and seven is in the south, wood from three and eight is in the east, metal from four and nine is in the west, and earth from five and ten is in the center. Each group consists of one odd and one even number, one heavenly and one earthly, thus enabling the five phases to be generated.

易傳曰：河出圖，洛出書，聖人則之。此言河圖洛書所由來也。天地之間，運行者氣，紀量者數，顯示者象，而主其中御之以合度者道。道兼神形，氣數則神之見也，象則形之呈也。凡天文地理，可紀可指可名者，皆不外此三類，而皆不離乎道。

The Great Treatise says, "The Yellow River produced the chart, and the Luo River produced the writing; the sage followed them," which explains the origin of the Yellow River Chart and the Luo Writing. In the universe, what is constantly in motion is "qi," which is used to measure as "numbers," and what is manifested is "images." The principle that governs and controls these, bringing them into harmony with order, is "the Dao." The Dao encompasses both the spiritual and the physical: qi and numbers are manifestations of the spiritual, while images are expressions of the physical. All that can be recorded, identified, or named in astronomy and geography falls within these three categories, yet none can exist apart from the Dao.

河圖者，天地自然氣數所賦，而成其自然之象也。蓋天地既奠，神形全具，有其氣者有其數，有其數者有其象。河圖之出，以象之顯也；其象之所示則數也，其數之所在則氣也。氣有陰陽，名曰兩儀，言既生成之後，必有此兩者之質，以為其成物之本也。兩儀化合，遂分為水火木金土五者之氣，名曰五行。

The Yellow River Chart is a natural phenomenon formed by the inherent energies and numbers of heaven and earth. Once heaven and earth were established, both spirit and form were complete: there is energy, and thus there is number; there is number, and thus there is image. The Yellow River Chart appeared because the image became visible; the image indicates the number, and the number exists where the energy is. Energy is divided into yin and yang, called "the Two Principles" — this means that after heaven and earth were formed, there must necessarily be yin and yang as the fundamental qualities that transform all things. The Two Principles combine with each other, thus differentiating into the five energies of water, fire, wood, metal, and earth, called "the Five Phases."

言兩儀既化，必有是五者流行其間，以辨其性而別其類，亦物之始成所秉者也。兩儀既見，五行乃名；二五構精，萬有始生，此屬天地萬物生生之本，莫之能外者也。五行之氣，因二為五，雖五仍二，然言其本質，必自五者始。後人或云為四，或云為三，其意大同，究不若別之為五，適合天地自然之氣與數。試證之河圖，可見其旨矣。

This refers to the fact that once the two principles (yin and yang) combine, there must be the five elements circulating among them, used to distinguish the nature of things and differentiate their categories. This is also the nature that all things receive at their initial formation. After the two principles manifest, the five elements gain their names; when the yin and yang energies interact with the essence of the five elements, all things begin to arise. This is the fundamental principle of the continuous generation and transformation of all things in the universe, and nothing is exempt. The energies of the five elements are divided from the two (yin and yang). Although they are called five, they are still rooted in two. However, when discussing the essence of things, one must start with these five. Later scholars have proposed dividing them into four or three, with similar intentions, but ultimately, dividing them into five is more accurate, precisely conforming to the natural energies and numbers of heaven and earth. By referring to the Yellow River Chart, this meaning becomes clear.

河圖之中，點畫成象，自一至十，各相連而不混，相離而不乖，其數之自然，足見其氣之自在也。氣之動也，以二氣之分合而後化，故生成之數，必屬於天地，天地者，二氣之所生也。物之生化，以五者為類，而水火木金土，以辨以名，以成其五行。水火木金土者，五行之所主也。故河圖之數，生成自天地，而名類止於水火木金土，而天下萬物莫不盡於是。

In the Yellow River Chart, numbers are formed by dots, arranged from one to ten, connected yet not confused, separated yet not discordant. The arrangement of numbers is so natural, showing the free flow of qi. When qi moves, it relies on the division and combination of yin and yang to generate things. Therefore, the numbers of generation and completion must belong to heaven and earth, and heaven and earth themselves are produced by the yin and yang. The generation and transformation of all things are categorized into the five phases, namely water, fire, wood, metal, and earth, used for distinguishing and naming, thus forming the Five Phases. Water, fire, wood, metal, and earth are precisely the elements each of the Five Phases governs. Therefore, the numbers in the Yellow River Chart originate from heaven and earth, yet their categories are limited to these five elements, yet they encompass all things under heaven.

是故河圖之象，即天地生化終始之圖；其氣與數，即天下萬有分合變化之本，斯所以為天道之所見也。而聖人則之，因以明天道，以立天下萬物有生成變化之規，而述之為易，則河圖者易之所自仿也。易傳曰：「天一地二，天三地四，天五地六，天七地八，天九地十。天數五，地數五，五位相得而各有合。天數二十有五，地數三十，天地之數五十有五。」雲者，即河圖中之數也。

Therefore, the image of the River Chart represents the beginning and end of the generation and transformation of heaven and earth; its qi and numbers are the fundamental principles of the division, combination, and change of all things under heaven, which is the way of the heavenly Dao made manifest. The sage took it as a model, used it to explain the heavenly Dao, established rules for the generation and transformation of all things in the world, and recorded it as the Book of Changes. Thus, the River Chart is the model that the Book of Changes imitates. The Great Treatise says: Heaven has one, Earth has two; Heaven has three, Earth has four; Heaven has five, Earth has six; Heaven has seven, Earth has eight; Heaven has nine, Earth has ten. The numbers of Heaven are five in total, and the numbers of Earth are five in total. These five numbers correspond to each other in the five directions, each having its own pairing. The total of the Heaven numbers is twenty-five, and the total of the Earth numbers is thirty; altogether, the numbers of Heaven and Earth total fifty-five. What it says is precisely the numbers found in the River Chart.

河圖以天地統全數，以水火木金土分配各數，而建立天地萬物萬數之本，以明天下之物，莫不有數，莫非生成於天地，而得其氣與數以成其氣數。自河圖言之，則氣數者自然成形；自物言之，則氣與數皆出自天地。

The Yellow River Chart uses the categories of "Heaven" and "Earth" to encompass all numbers, distributing each number among the elements of water, fire, wood, metal, and earth, thereby establishing the fundamental numbers of all things in the universe. It explains that nothing in the world lacks a number, and nothing is not generated from Heaven and Earth, nor does it not receive the qi and numbers from Heaven and Earth to form its own qi and numbers. From the perspective of the Yellow River Chart, qi and numbers naturally take form; from the perspective of all things, qi and numbers originate from Heaven and Earth.

蓋天地亦在此氣數中也。未有天地，氣數已具；既有天地，氣數周流，以成萬物。故氣數者，自天地以下，莫之能外也。今言河圖氣數溯始於天地，蓋自有象言之，即自天地建立以後，而推溯萬物生化所本、萬有氣數所由而已。

Because heaven and earth themselves are included in this cycle of qi and numbers. Before heaven and earth came into being, the cycle of qi and numbers was already present; once heaven and earth appeared, the cycle of qi and numbers flowed continuously to transform all things. Therefore, this cycle of qi and numbers, starting from heaven and earth, includes everything without exception. Now, when we say that the cycle of qi and numbers in the Yellow River Chart should be traced back to heaven and earth, it refers to the aspect of "having form," meaning from the time heaven and earth were established, we go back to investigate the fundamental basis for the generation of all things and the origin of the cycle of qi and numbers.

圖中自天一至地十，為數之根本，亦生成之根源。天一生水，地六成之，則言水之生成之由來：以天之一，合地之六，而後水之生成始全；分之則水者得天之一以生，地之六以成。天生地成，是其氣之備天地也。

In the diagram from "Tian Yi" to "Di Shi," these numbers represent the fundamental principles and the source of generation. "Tian Yi Sheng Shui, Di Liu Cheng Zhi" explains the origin of water: water is formed by combining the heavenly number "one" with the earthly number "six." Separately, water is generated by the heavenly number "one" and completed by the earthly number "six." Heaven gives birth and earth completes; thus, the energy of water encompasses both heaven and earth.

天一地六，是其數之賅天地也，而水以成，此五行之一所自生也。火也、木也、金土也亦然，而土為其中心，故五十在中，水火木金四者，皆依乎土以立也。如一加五為六，故水為一六；二加五為七，故火為二七；三加五為八，故木為三八；四加五為九，故金為四九；土則五加五為十，故土為五十，此數所自合也。

Heavenly One and Earthly Six show that the number for water includes both Heaven and Earth, thus forming water. This is the origin of one of the Five Phases. Fire, Wood, Metal, and Earth are similar, with Earth occupying the center. Therefore, the numbers five and ten are placed in the center. Water, Fire, Wood, and Metal all depend on Earth to stand firm. For example, one plus five equals six, so water is paired with one and six; two plus five equals seven, so fire is paired with two and seven; three plus five equals eight, so wood is paired with three and eight; four plus five equals nine, so metal is paired with four and nine; Earth is five plus five equals ten, so Earth is paired with five and ten. This is the origin of how each primary number combines with another. Each primary number must be added to the central Earth number five to form the corresponding secondary number.

天之數五，一三五七九；地之數五，二四六八十；生之數五，一二三四五；成之數五，六七八九十。其分也皆五，五則中央之數，中而不偏，動而能和，中和天地之道，土之德也。故五行皆以五為其根，皆麗於土以為生，此自然之序也。天數之累為二十五，即一三五七九之和也；地數累為三十，即二四六八十之和也。

Heavenly numbers consist of five: one, three, five, seven, and nine; earthly numbers also consist of five: two, four, six, eight, and ten. The generating numbers are five: one, two, three, four, and five; the forming numbers are also five: six, seven, eight, nine, and ten. No matter how they are divided, each group contains five numbers, and the number five is the central number—residing in the middle without bias, capable of movement and harmony. Middle harmony is the way of heaven and earth, and it is also the virtue of earth. Therefore, the five phases all take five as their root, and they depend on earth to grow, which is the natural order. The total of heavenly numbers is twenty-five, which is the sum of one, three, five, seven, and nine; the total of earthly numbers is thirty, which is the sum of two, four, six, eight, and ten.

二者雖分各半而數異，則即生有形之後，得天者不足，地者有餘也。天地之總和五十有五，即二十五加三十，以成天地生成全數，為大衍之數而餘五。五即中央之數，二氣之全，五行之本，為天地數之妙用，即河圖之中，天地之心也。明此五數之妙用，則通天地之數，直見天地之心，而萬物生化之序，無不明矣。

Although the numbers of Heaven and Earth each take up half, their total is not equal, which indicates that after the emergence of tangible things, they receive one part from Heaven but find it insufficient, while receiving one part from Earth and find it excessive. The total of the numbers of Heaven and Earth is fifty-five, composed of twenty-five and thirty, forming the complete number of the generation of Heaven and Earth. Compared to the "Great Derivation" mentioned in the "Great Treatise," which states that the number of great derivation is fifty, there is an extra five. This "five" is the number of the center, the complete form of yin and yang energies, the foundation of the Five Phases, and the key to the function of the numbers of Heaven and Earth. It is also the center of the Yellow River Chart, the heart of Heaven and Earth. Understanding the subtle function of this "five" allows one to grasp the numbers of Heaven and Earth, directly see the heart of Heaven and Earth, and thus have no difficulty in understanding the order of the generation and transformation of all things.

故一至十者，天地生成之數根；而五者，天地生成數之中極。此河圖四列各數，而獨以五十建立中極，其旨趣之微妙，有不盡矣。五位相得各有合者，言數各五而必合，始能致生化之用。如一天數也，生數也；六地數也，成數也，二數合而後水以成。

Therefore, the numbers from one to ten are the fundamental numbers of the generation of heaven and earth, while the number five is the central point of the numbers of heaven and earth generation. The Yellow River Chart arranges each number in the four directions, but uses five and ten alone to establish the central point. The subtle meaning behind this is endless. The phrase "the five positions interact and each has its complement" means that the numbers of heaven and earth each have five, and they must combine in pairs to exert the function of generation and transformation. For example, "one" is a heavenly number and also a number of generation; "six" is an earthly number and also a number of completion: these two numbers combine to form water.

以合則前數化，新數成。一六既合，天地之氣已化，而水乃成。此由數之合也。水之成分，得天之一，地之六，故水中所含者屬天者一，屬地者六。天地既化，水數乃見。凡五行之生化皆然，皆由二氣之合也。五行亦有合矣。

When numbers combine, the original numbers transform and new numbers are formed. Once one and six combine, the qi of heaven and earth is transformed, and water takes shape, resulting from the combination of numbers. The components of water come from heaven as 'one' and from earth as 'six', so the part of water that belongs to heaven is 'one', and the part that belongs to earth is 'six'. Only when the qi of heaven and earth has combined and transformed does the number of water become apparent. All the generation and transformation of the Five Phases are like this, resulting from the combination of yin and yang qi. Each of the Five Phases also combines with others in its own way.

如水與木，木與火、火與土、土與金、金與水，各以其合而生化萬物，則各以其數之合，而生成新數，故變化至無窮焉。然二氣之合與分，恆相得；五行則或得或否，如水與火、火與金、金與木、木與土、土與水，皆相害相制而不相得，則數之因亦有相消相除相加相乘之異。其相得也，則生成之；其制害也，則克化之。

For example, water and wood, wood and fire, fire and earth, earth and metal, metal and water, each combine according to the principle of mutual generation to produce all things. Similarly, they combine according to numerical relationships to generate new numbers, hence the endless changes. However, yin and yang, whether combined or separated, always complement each other. The Five Phases, on the other hand, sometimes complement and sometimes do not. For instance, water and fire, fire and metal, metal and wood, wood and earth, and earth and water all mutually harm and control each other, and do not complement. Therefore, in numerical operations, there are distinctions of mutual cancellation, division, addition, and multiplication: those that complement each other generate new results, while those that mutually harm or control each other are transformed or eliminated.

由其數驗之可知者也。故天一與地六合，一陰一陽，合乎道也。若天一與地二，則不則生成矣。若天一與天三，更無所生成，以其不相得而不能合也。故生化之序，必因相得而後合，合則生成之功見。不得則相反，反則變化之數成。

This can be known by verifying through numbers. Therefore, the heavenly number "one" combines with the earthly number "six," representing one yin and one yang, in accordance with the Dao. If the heavenly number "one" is paired with the earthly number "two," nothing is generated; if the heavenly number "one" is paired with another heavenly number "three," nothing is produced either, because they are not compatible and thus cannot combine. This shows that the order of generation must first involve compatibility before combination; once combined, the function of generation becomes evident. If they are not compatible, they turn to the opposite, and once they turn to the opposite, the numerical changes are formed thereby.

故天一至地十之數，實包舉天下生成變化之數，以至無盡，不可紀極，而莫外於合否二字。由是可見天地造化之源，萬物生成變化之序，皆在河圖中，展轉推求，以窮其氣數所至，則無不知之。如天一地十之數，實數之根；二氣者氣之本；五行者萬物生成之本，皆造化之始基。

Therefore, the ten numbers from Heaven One to Earth Ten actually encompass all numbers of generation and transformation in the world, extending infinitely and beyond counting. In the end, they come down to the two characters "he" (union) and "bu he" (non-union). From this we can see that the origin of heaven and earth's creative power and the order of generation and transformation of all things are entirely contained in the Yellow River Chart. By thoroughly investigating the places where the vital energies reach, there is nothing that remains unknown. Numbers such as Heaven One to Earth Ten are indeed the root of all numbers; yin and yang energies are the fundamental nature of qi; the Five Phases are the fundamental basis for the generation of all things—these are all the initial foundations of creation.

天地人物之原質，由一而二而三，而後萬物以生以成，其道固昭昭矣。二者兩儀，三者兩儀合化五行是也。二五構精，妙合而凝，天地因縕，萬物化醇，此由三而生萬物也。故河圖天地之數，生成之本數也；五行分合之數，萬物所自生化之本也。

The original material of heaven, earth, human beings and things comes from one to two, then from two to three, and only then can all things be generated and formed. This principle is clear and evident. The so-called "two" refers to the two principles (wuxiang), and the so-called "three" refers to the five phases formed by the combination and transformation of the two principles. The "Taiji Tu Shuo" says, "the essence of two and five combines and solidifies," and the "Xici Zhuan" says, "heaven and earth blend and interact, and all things are transformed into purity," which refers to the generation of all things from "three." Therefore, the numbers of heaven and earth on the He Tu are the fundamental numbers of generation; the numbers of the division and combination of the five phases are the fundamental principles for the generation and transformation of all things.

由其位言之，則按乎天地之定序，南北東西方位，而相得者也。故一六以水居北，三八以木居東，二七以火居南，四九以金居西，五十以土建立中極，以應四方而通天地。此地為世界中心，憑之以測天地之生長萬物，所謂極也。天地之極，即數之中，即五也。

From the perspective of direction, the River Chart arranges numbers according to the fixed order of heaven and earth, pairing them with the four cardinal directions—north, south, east, and west—so that each number complements the others. Thus, one and six combine to form water, located in the north; three and eight combine to form wood, located in the east; two and seven combine to form fire, located in the south; four and nine combine to form metal, located in the west; and five and ten combine to form earth, establishing the center. This central position is the center of the world, used to measure the growth of all things in heaven and earth, which is referred to as the 'extreme' or 'pole.' The extreme of heaven and earth is the center of numbers, which is 'five.'

河圖言五十，洛書則僅言五，以五已足賅十。十即二五，天地根數，祇存純數，不必及其餘盈，故言五而土之數已足，不似水之必兼一六也。其所合也，往往因其生化見之，故一六之合，二七之合，皆孚自然之序。

The Yellow River Chart places both "five" and "ten" at its center, while the Luo Writing only marks a single "five," because five is sufficient to encompass ten. Ten is merely two fives, and the fundamental numbers of heaven and earth retain only the purest one, without needing to consider the extra part. Therefore, it is enough to mention "five," as the number for earth is already sufficient. Unlike water, which must be paired with one and six, the combination of numbers often becomes apparent through their process of generation and transformation. Thus, one and six combine, and two and seven combine, all in accordance with the natural order.

而五與二五之十，尤可見矣。若言五則十已見，雖三五四五，仍不失其五，故不必徵於成數，而已知土之數之為十五。蓋以天之五，地之十，合而言之為十五，去其十仍存五。此五數示土已足，其數雖一而內藏十矣。此為言數者所當知也。

The number "five" and the number "ten" formed by two fives are especially evident in this relationship. As soon as the number five is mentioned, the number ten is already included within it. Even with three fives or four fives, they still do not depart from the five. Therefore, there is no need to refer to the number of completion, and we already know that the number associated with earth is fifteen. This is because the heavenly number five combined with the earthly number ten makes fifteen. If we subtract the ten, five remains. Using the number five to represent earth is sufficient, as it appears as a single number on the surface but contains the ten within it. This is something those who study numbers should understand.

河圖之數，以二數合而成一象，故十數合為五，以成水火木金土，唯其合也。有變化見焉。以六為成數之始，又地數也；九為天數之終，又成數也，二數實天地之主數。故易乾用九，坤用六。乾天也，陽也；坤地也，陰也。陽數用九，陰數用六，此中亦有自然之序存焉。

The numbers of the River Chart combine two numbers into one image, so ten numbers are grouped into five sets to form water, fire, wood, metal, and earth. The key lies in the concept of 'combination'. 'Six' is the first of the completed numbers and belongs to the earth numbers; 'Nine' is the last of the heavenly numbers and also a completed number. These two numbers are truly the main numbers of heaven and earth. Therefore, the Qian hexagram in the Book of Changes is called 'Use of Nine', and the Kun hexagram is called 'Use of Six'. Qian represents heaven, which is yang; Kun represents earth, which is yin. Yang numbers take nine, and yin numbers take six, and there is a natural order within this.

試就河圖觀之，自北之陽數一始，轉東之三，南之七，西之九，與中央之五，其次自然順行，為一三五七九，是陽數始一終九。九則陽氣已極，曰老陽，亦曰純陽，故乾取之為用。再就圖之陰數觀之，陽終則陰始。陽數終於西之九，即交於同方之四；陰數自四始，轉而南之二，東之八，北之六，合中央之十，其次亦自然逆行，為四二十八六，是陰數始四終六。以六為至陰，陰氣亦極於六，故陰數用六。

If we examine the River Chart, the yang numbers begin at the north with 'one', move to the east with 'three', then to the south with 'seven', and finally to the west with 'nine'. Adding the central 'five', the sequence naturally proceeds in order as one, three, five, seven, nine. This shows that the yang numbers start with one and end with nine. When yang reaches nine, it has reached its extreme, called 'old yang' or 'pure yang', so the Qian hexagram uses it. Now looking at the yin numbers: when yang reaches its end, yin begins. The yang number ends at nine in the west, and the yin number starts at four in the same direction. The yin numbers move from four, to two in the south, then to eight in the east, then to six in the north, and adding the central 'ten', the sequence naturally proceeds in reverse order as four, two, ten, eight, six. This shows that the yin numbers start with four and end with six. Six is the most yin, and yin energy reaches its extreme at six, so the yin number uses six.

以與陽九相接而正相得。蓋以圖平列其數觀之，陽之數自一至九，陰之數自四至六，自成一環，不待移易。陽氣方終，陰氣即起；陰氣甫盡，陽氣即伸。陽老於西而陰即始於西，陰極於北而陽即始於北。二者相環相合，以成五行，周流無盡，以遂其生生不息之道。

Six is connected with the yang number nine, and they complement each other perfectly. If you lay out the numbers on the diagram flat, the yang numbers run from one to nine, and the yin numbers run from four to six, each forming a circular pattern without the need for adjustment. As soon as the yang energy completes its cycle, the yin energy begins; and as soon as the yin energy is exhausted, the yang energy renews itself. When the yang energy reaches its old age in the west, the yin energy begins exactly in the west; when the yin energy reaches its extreme in the north, the yang energy begins exactly in the north. They are interlocked and interdependent, thus forming the Five Phases, flowing endlessly to accomplish the way of continuous generation and renewal.

而天地以立，萬有以生，一切事物，於以循環變化，此則大氣自然之序，大道自存之規，莫之為而為，莫之致而至者也。唯聖人則之，而制為易以象其度。而因陰陽之盡，知乾坤之用在九與六，故取九六以代乾坤。全易無非由乾坤生，則全易之數無非自九六出。九在易即一，六在易即 ， 與 即九與六。

Heaven and Earth thus become established, and all things arise from this. All things then undergo cycles of change. This is the natural order of the atmosphere and the inherent principles of the Great Way. It is not done by anyone, yet it is naturally accomplished; it does not require anyone to promote it, yet it naturally comes to be. Only the sage takes inspiration from it, creating the Book of Changes to imitate its principles. Also, because yin and yang have each reached their extremes, it is known that the principles of Heaven and Earth are embodied in the numbers "nine" and "six." Therefore, "nine" and "six" are used to represent Heaven and Earth. The entire Book of Changes arises from Heaven and Earth, so the numbers in the entire Book of Changes arise from nine and six. In the Book of Changes, "nine" represents the continuous yang line, while "six" represents the broken yin line. These two lines, one yang and one yin, are precisely the numbers nine and six.

故卦中有 者，名曰九，如初九、九二、九三、九四、九五、上九，是也。卦中有一者，名日六，如初六、六二、六三、六四、六五、上六，是也。人不知九六之來自河圖之數，而不明用九用六，與一之為九， 之為六何義，實由不習河圖，遂不解九六之為陽陰之主數。陽主九，陰主六，唯河圖中已明示之。易雖言九六，未指所出，後人莫能解。故河圖者，全易所本，欲明易象而忘河圖，宜其惝怳於文字間，而不得聖人取象之旨趣矣。

Therefore, in the hexagrams, any yang line is called "nine," such as initial nine, nine in the second, nine in the third, nine in the fourth, nine in the fifth, and nine at the top. Any yin line is called "six," such as initial six, six in the second, six in the third, six in the fourth, six in the fifth, and six at the top. People do not know that the numbers nine and six come from the Yellow River Chart, so they fail to understand what "use nine" in the hexagram Qian and "use six" in the hexagram Kun mean. They also do not understand why a single yang line is called nine and a single yin line is called six. This is indeed because they do not study the Yellow River Chart, so they do not realize that nine and six are the main numbers representing yang and yin respectively. Yang is primarily associated with nine, and yin is primarily associated with six. This point was clearly indicated by the Yellow River Chart long ago. The Book of Changes mentions nine and six, but does not point out their origin. Thus, later people have no way to understand them. Therefore, the Yellow River Chart is the fundamental basis of the entire Book of Changes. If one wishes to understand the symbolic meanings of the Book of Changes but ignores the Yellow River Chart, one can only wander through words and fail to grasp the intent of the sage in taking symbols.

河圖之數，因陰陽之分合變化無盡，而萬物之氣數由此以見，全易卦爻皆由此推移轉變而來，以象天下萬物萬事。其始則仍是二氣五形而已。圖中之象雖寥寥，而生化之物不可紀極。不僅此也，就圖數之次序，而推及其未來與其過去，則天地未生之前，與世界變遷之例，皆可由此數以得之。蓋數者推之千萬無盡也，加減乘除而已，或分、或合、或奇、或偶，各致其用，用無窮則所生化亦無窮，要在知其用耳。

The numbers of the Yellow River Chart change endlessly due to the combination and separation of yin and yang. The vital energies of all things are revealed through these numbers, and the hexagrams and lines of the entire Book of Changes are derived from them, used to symbolize all things under heaven. Tracing back to its origin, it is still no more than the two energies of yin and yang and the Five Phases. Although the images on the chart are few, the things generated from them are countless. Moreover, following the sequence of numbers on the chart, one can predict the future and trace back to the past. Even the state before the creation of heaven and earth and the patterns of change in the world can be deduced from these numbers. Numbers, when used for deduction, are endless, yet they are merely addition, subtraction, multiplication, and division. Sometimes they are divided, sometimes combined, sometimes odd numbers are used, sometimes even numbers, each serving its purpose. Because their use is endless, the things they generate are also endless. The key lies in whether one understands how to use them.

乾坤用九六為天地大用，亦數之總綱，由九六而生化者不可紀極，而不外乎中極，此圖中以五為中心也。試就陰陽各數直列之，一三五七九與四二十八六，兩者相偶而加之，其和皆五。此即天地之心，為陰陽二數之中極，亦陰陽二氣之中和。天以此立極，世以此立樞，萬物以此為紐，故並育不害，並行不悖，並生存往復不失其序。此神之所存，道之所見，而為易之中極者也。

Heavenly Stem and Earthly Branch are derived from nine and six, which represent the greatest function of Heaven and Earth, and also the overall principle of numbers. The myriad things generated from nine and six do not go beyond the scope of "central extremity," which is why the Yellow River Chart takes five as its center. Try to list the numbers of yin and yang separately: one, three, five, seven, nine and four, two, ten, eight, six. When paired and added together, the results are either five or fifteen, with the last digit always being five. This is the heart of Heaven and Earth, the central extremity of the two categories of numbers, and the harmonious balance of the two energies of yin and yang. Heaven relies on it to establish the central extremity, the world relies on it to establish its pivot, and all things rely on it as a connecting link, thus enabling them to grow together without conflict, to move together without contradiction, and to exist and return in cycles without disorder. This is where the "spirit" resides and where the "Dao" manifests, and it is precisely the central extremity of the Book of Changes.

故陽者順行而奇，陰者逆行而偶，而皆集於中五，以為主宰之區，以行鬼神，而通變化，此所謂位之相得而有合者，以其建中立極，而不失其次也。河圖言數本乎氣，通乎道，實天地之精華，自然流露，而垂象於人，以示其例，非偶然所值者，亦非怪誕難稽者。

Therefore, the yang numbers proceed in order to form odd numbers, while the yin numbers reverse to form even numbers. Yet all of them converge at the central "five," using it as the central point of governance, by which the movement of ghosts and spirits and the transformation of things are carried out. This is what the Great Treatise says: "The five positions interconnect and each has its corresponding element." Because it establishes the center, defines the extreme, and does not disrupt the order of each. The River Chart discusses numbers, whose origin lies in qi, and which connect to the Dao. It is truly the essence of heaven and earth naturally revealed, presenting the trigrams to mankind, to indicate principles. It is not accidental, nor is it absurd and unfounded.

聖人則之，而易象以成，言道者之所宗，言數者之所本，即一切方術，亦莫不由是以為推衍之準，實人文所自始也。聖人在世感於天神，而圖乃見，圖為聖人出也。故欲深究圖之妙義，必自聖人所作之易求之。易者依圖為象，推衍其用，其例固繁，而其初則河圖之所見而已。

The sages took it as their model, thus enabling the formation of the images in the Book of Changes. It is revered by those who speak of the Way and relied upon by those who deal with numbers; even all kinds of esoteric arts take it as their standard for deduction. Indeed, it is the starting point of human civilization. When the sages were alive, they communicated with heavenly spirits, and the River Chart appeared. One could say that the chart emerged for the sages. Therefore, to deeply explore the profound meaning of the River Chart, one must seek it in the Book of Changes composed by the sages. The Book of Changes established its images based on the chart, and deduced its applications. Although the rules are numerous, when tracing back to the beginning, they are no more than what the River Chart reveals.

戴九履一，左三右七，二四為肩，六八為足，五在中央。

The "Luo Writing" arranges nine numbers in the following way: nine is placed at the top in the southern position, like the crown on one's head; one is placed at the bottom in the northern position, like the shoes on one's feet; three is in the left eastern position, and seven is in the right western position, standing side by side on both sides; two is in the southwest, and four is in the southeast, living apart in the upper two corners, like the two shoulders of a person; six is in the northwest, and eight is in the northeast, living apart in the lower two corners, like the two legs of a person; five is alone in the center, serving as the hub of the numbers of the eight directions. The entire image resembles a person standing upright: nine is the head, one is the feet, three and seven are the left and right arms, four and two are the two shoulders, eight and six are the two legs, and five stands in the position of the heart and abdomen. After this arrangement, looking horizontally, we have four, nine, two; three, five, seven; and eight, one, six. Looking vertically, we have four, three, eight; nine, five, one; and two, seven, six. Looking diagonally, we have four, five, six; and two, five, eight. In each case, the sum of the three numbers is fifteen. The pairs facing each other, nine and one, three and seven, two and eight, four and six, when added together, each total ten.

河圖洛書，同一數也，而象異，以體用之分也。天地生化萬物，自其先言之，則為不易者也；自其後言之，則日易者也。故有體用之殊焉。體者一成不易，示其極也；用者隨事而易，明其變也。天地之大，萬物自生，變化自出，體用之間為氣數之所至。明其體而後知其本源，明其用而知其變化。

The Yellow River Chart and the Luo Writing both use the same set of numbers from one to ten, but the images they present are different. This is because they have the distinction of "body" and "function." The transformation of heaven and earth to generate all things, when viewed from the source before all things come into being, is a constant and unchanging aspect. However, when viewed from the aspect of things already existing and in motion, it is a constantly changing aspect. Therefore, the same set of numbers can manifest in two different forms: body and function. The "body" once established does not change, and is used to indicate the ultimate principles of heaven and earth. The "function," on the other hand, varies with specific things, and is used to explain the changes in heaven and earth. Heaven and earth are so vast, and all things naturally grow and change, and the distinction between body and function lies exactly where the movement of qi and numbers reach. Understanding the body allows one to know the origin of all things; understanding the function allows one to know the changes of all things.

蓋氣數同而所以氣數不同也。河圖者氣數之大體，洛書者氣數之變化，以不息之德，成無盡之用。此變化之例，有不可盡言，而洛書則舉其大用耳。洛書之謂象，亦猶河圖，生於二氣，分於五行，本於天地之數，成於陰陽之類，而名一貫實異也。

The principles underlying the two diagrams are essentially the same, but the reasons for their formation differ. The "Yellow River Chart" presents the fundamental structure of the numbers and energies, while the "Luo Writing" shows their specific transformations. Through the ceaseless virtue of heaven and earth, these numbers and energies achieve infinite functions. The rules of transformation are numerous and cannot all be explained, so the "Luo Writing" merely highlights the most important aspects. The "images" referred to in the "Luo Writing" are, like those in the "Yellow River Chart," generated by the dual forces of yin and yang, divided according to the "Five Phases," rooted in the numbers from one to ten of heaven and earth, and manifested in the categories of yin and yang odd and even. Though their names are connected, their actual contents differ.

故河圖之數重列五方，而洛書則平列九位。河圖之物，陰陽合得；而洛書則互為推移。其象之殊，即其取義之異；其物之別，即其致用之差。由是以合於河圖，則體用以全；以證於易，則變化以見。苟非聖人，焉足以明之哉。洛書象數，由河圖變化而來。其陽數自一而三，方位不變；自七而九，則互易矣。陰數則全與河圖易其方位。蓋陽體陰用，洛書為明用之圖，故陰數大易。

Therefore, the numbers of the Yellow River Chart are arranged in overlapping positions on the five cardinal directions—east, south, west, north, and center—with both the generating numbers and the completed numbers residing in the same direction. The Luo Writing, on the other hand, spreads the numbers out, distributing them across nine palace positions. The things associated with the Yellow River Chart are paired in yin and yang, fitting together mutually; the things associated with the Luo Writing, however, involve mutual shifting and exchanging of positions. Since the images differ, their meanings naturally differ as well; since the associated things differ, their applications naturally differ. When the Luo Writing and the Yellow River Chart are viewed together, both the essence and the application are complete. When used to verify the Zhou Changes, the principles of change become evident. Without the sages, who could explain this principle? The numerical patterns of the Luo Writing originate from the Yellow River Chart: for the yang numbers, from one to three, the positions remain unchanged; from seven to nine, their positions are exchanged. For the yin numbers, they are entirely exchanged in position with the Yellow River Chart. This is because yang represents the essence and yin represents the application, and the Luo Writing is originally a diagram that explains the concept of application. Therefore, the yin numbers undergo the greatest change.

然自其次序觀之，則一之與六，以重列變為先後平行；三之與八，四之與九，二之與七亦然，皆平行也。以一居北，而六在西北；三居東，而八在東北；九居南，而四在東南；七居西，而二在西南。其所合仍相得也。五之在中，本於中極不變之理，此所以允執厥中為至道也。體固如是，用亦不違，非中極之道，不足以喻之也。

From the perspective of numerical order: in the Yellow River Chart, one and six were originally located in the north, overlapping above and below, but in the Luo Writing they became positioned front and back in parallel. Similarly, three and eight, four and nine, and two and seven also changed from being stacked to being aligned side by side. Specifically, one is located in the central north, while six moves to the northwest; three is in the central east, while eight moves to the northeast; nine is in the central south, while four moves to the southeast; seven is in the central west, while two moves to the southwest. Although their positions have changed, their complementary relationship remains valid. As for five, it remains in the center, following the principle that the center is unchanging, which is also the reason why the phrase "uphold the middle path" from the Book of Documents, Great Yu's Mandate is regarded as the highest principle. The structure is like this, and the application cannot contradict it; without this principle of the central point, it would be impossible to explain.

就書象言之，數之變化在於動。以北方之一，東方之三，皆原位不動者，非不動也。先天之生化首為水，後天之生化首為木，其所變即在其位，故動而不動也。至南方之七，變而居西；西方之九，變而之南。以後天金火互用，與先天恰反其位，故動而易其地也。

In terms of the image of the Luo Writing, the changes in numbers all revolve around the concept of "movement." The number one in the north and the number three in the east appear to remain in their original positions without moving, but in reality, they are not truly stationary. The generation and transformation of the Earlier Heaven begin with "water," while those of the Later Heaven begin with "wood." The changes occur precisely through their steadfast adherence to their respective positions, hence movement that appears as stillness. As for the number seven in the south moving to the west and the number nine in the west moving to the south, this is because in the Later Heaven, metal and fire exchange their functions, which is the opposite of the Earlier Heaven's directional arrangement. Therefore, this is movement accompanied by a change in position.

以數之序言，則一三者順行北而東仍前，而七九者由西而南，則與前異，此由變化而分其用也。陰數之序，則東南之四，而西南之二，與東北之八，而西北之六，其序已與河圖反行；而其合乎陽數，則正相得。蓋陽由一三而七九分作兩途，一由北之東，一由西之南，以明四正之氣，猶相偶合也。而陰數則與之成逆行，一由東南之西南，一由東北之西北，亦分兩途，以與陽合。其所行之序雖變，而所合之數不差，蓋亦天地自然之變化，而成其用者也。

From the sequence of numbers, one and three move from north to east, following the original order of the Yellow River Chart; seven and nine, however, move from west to south, differing from the original order: this is precisely how differentiation occurs due to change, leading to their respective functions. The sequence of yin numbers is such that four from the southeast moves to two in the southwest, and eight from the northeast moves to six in the northwest, with their direction of movement now opposite to that of the Yellow River Chart; yet when they are paired with yang numbers, they still perfectly match. Overall, the yang numbers are divided into two groups: one group moves from north to east, and the other from west to south, indicating that the qi of the four cardinal directions remains paired in pairs. The yin numbers, moving in the opposite direction to the yang numbers, are also divided into two groups: one group moves from southeast to southwest, and the other from northeast to northwest, to be paired with the yang numbers. Although their sequence of movement has changed, the numbers obtained from their pairing remain exactly the same. This is also a natural change of heaven and earth, used to accomplish their functions.

夫陽之與陰，為萬物生化之本，有其一必有其二。如陽數順分而變位，陰數勢必逆分而變方，以便合陽而成其生化之用。故一之三、七之九，為生成數之經然；而四之二、八之六，為生成數之緯然。經緯相得，生成之功見矣。且合數之，自北而東，自西而南，陰陽之數，各得其半，即由兩以生四，兩儀生四象是也。陽由一三七九之一序，分為一三與七九兩繫；陰由四二八六之一繫，分而為四二與八六兩繫，以成其四也。

Yin and yang are the fundamental principles of the generation and transformation of all things. Where there is yang, there must be yin to correspond to it. Therefore, the numbers of yang proceed in order and divide into two lines to change their positions, while the numbers of yin necessarily reverse their order and divide into two lines to change their direction, so as to match with the numbers of yang and achieve the function of generation and transformation. The numbers from one to three and seven to nine form the 'jings' or longitudinal lines of the generating and completing numbers; the numbers from four to two and eight to six form the 'weis' or transverse lines of the generating and completing numbers. When the jings and weis interweave and correspond, the effects of generation become evident. If we combine them together, from north to east is one line, and from west to south is another line. Yin and yang numbers each occupy half, which is how the 'two principles' (two yi) give rise to the 'four images' (four xiang). This is exactly what the 'Great Treatise' of the 'Zhou Changes' (I Ching) says: 'The two principles give rise to the four images.' Originally, the numbers of yang are in the order of one, three, seven, and nine, now divided into the lines of one-three and seven-nine. Originally, the numbers of yin are in the order of four, two, eight, and six, now divided into the lines of four-two and eight-six. When combined, they form a total of four.

故陽有太陽少陽，陰有太陰少陰，則一與九為太陽，三與七為少陽，四與六為太陰，二與八為少陰。以在數之始終為太，中為少也。以此相分合，而變化成、生成見，萬物自是出，萬數自是成矣。合此兩繫之數觀之，為一八三四，此自北而止於東南也；為六七二九，此由西北而止於南也。兩數相錯而正相得，以符天地生成之用，陰陽均平之數故也。

Therefore, the yang is divided into "Taiyang" and "Shaoyang," while the yin is divided into "Taiyin" and "Shaoyin": one and nine are Taiyang, three and seven are Shaoyang, four and six are Taiyin, and two and eight are Shaoyin. The criterion for this division is that the numbers at the ends of the sequence are called "Tai," while those in the middle are called "Shao." According to this division and combination, change is formed, generation is manifested, and thus all things come into being, and all numbers are established. If we combine the two series of numbers: one, eight, three, four form a group, starting from the north and ending at the southeast; six, seven, two, nine form another group, starting from the northwest and ending at the south. These two groups are interwoven and precisely matched, which conforms to the function of heaven and earth in generating things. This is also because the numbers of yin and yang inherently require balance.

蓋左右兩行，亦陰陽之道路，二者必求其平均。左之八與三，右之七與二，雖原來火木生成之數，而二與八則互換其位以相合。若不換位，則三與二、七與八，皆相失，而生成之功不能見矣。故二八易位而後陰陽之數以平，生成之功不改，此則天地之自然之妙，不可不知者也。

The two rows on either side of the diagram represent the channels through which yin and yang interact. These two must be balanced. On the left, the numbers eight and three, and on the right, the numbers seven and two, are originally the numbers representing wood and fire, which are generative elements. However, in order for them to harmonize with each other, the numbers two and eight must be exchanged. If they are not exchanged, then three and two, as well as seven and eight, will not match, and the generative effect will not be evident. Therefore, after exchanging the positions of two and eight, the numbers of yin and yang become balanced, yet the generative effect remains unchanged. This is the subtle and ingenious aspect of the natural transformation of heaven and earth, which should not be overlooked.

因此互換，如是相對之位，皆合而成十，即一與九、三與七、二與八、四與六，莫不成土之成數。洛書中央用五而不見十，不知十之數，恰藏於八方，以相合而後得之。河圖之合皆五，洛書之合皆十，明五十為天地之心，土為天地之中、萬物之本，其義至深切矣。夫洛書之象，明用者也，天地大用，在此圖中見之。

Because of this exchange, any two opposite positions add up to ten: one and nine, three and seven, two and eight, four and six, all combining to form the number ten, which represents "earth." The center of the Luo Shu only uses five and does not show ten, so people think ten is absent from the chart. In fact, the number ten is hidden within the eight directions; it can only be obtained by combining the numbers of opposite positions. In the He Tu, the generating numbers and the formed numbers are paired, each separated by five and combined with it; in the Luo Shu, the numbers of opposite positions add up to ten. This shows that five and ten are the core of heaven and earth, "earth" being the central position of heaven and earth and the fundamental basis of all things. The meaning is profound. The Luo Shu diagram illustrates the concept of "use," the great function of heaven and earth, which can all be seen in this diagram.

即易之卦象，亦於此圖明之。南九北一，由乾坤變為離坎也；東三西七，由離坎變為震為兌也；東北之八、西南之二，由震巽變為艮坤也，而艮坤易其位焉；東南之四、西北之六，由兌艮變為巽乾也，而巽乾首明其用焉。此皆易象所自仿也。蓋河圖者體，合伏羲之卦，而含文王卦之變者也；洛書者用，合文王之卦，而合文王之卦，而存伏羲之卦之體者也。

Even the positions of the hexagrams in the Zhou Yi depend on this diagram. The nine in the south and one in the north result from the transformation of the Earlier Heaven trigrams, where Qian (Heaven) was originally in the south and Kun (Earth) in the north, becoming Li (Fire) in the south and Kan (Water) in the north in the Later Heaven arrangement. The three in the east and seven in the west come from the Earlier Heaven trigrams Li (Fire) in the east and Kan (Water) in the west, changing to Zhen (Thunder) in the east and Dui (Lake) in the west in the Later Heaven arrangement. The eight in the northeast and two in the southwest result from the Earlier Heaven trigrams Zhen (Thunder) and Xun (Wind) changing to Gen (Mountain) and Kun (Earth) in the Later Heaven arrangement, with Gen and Kun swapping positions. The four in the southeast and six in the northwest come from the Earlier Heaven trigrams Dui (Lake) and Gen (Mountain) changing to Xun (Wind) and Qian (Heaven) in the Later Heaven arrangement, where Xun and Qian first display their functions. All these are the sources from which the Zhou Yi hexagrams are derived. The He Tu (Yellow River Chart) governs the essence and corresponds with Fuxi's Earlier Heaven Trigrams, while also containing the seeds of movement for Wen Wang's Later Heaven Trigrams. The Luo Shu (Luo Writing) governs application and corresponds with Wen Wang's Later Heaven Trigrams, yet still preserves the essence of Fuxi's Earlier Heaven Trigrams.

二者必互觀之，方明其義。以天地之生化萬物，由一而眾，故由太極而兩儀，而四象，而八卦；即由二氣而五行，而九宮，皆由一而二，三而四，自少分多，自寡化眾，此生化自然之象，而圖書所示之例也。以生化之始，不離於一，故生化之眾，不失其中。有此中極，則千萬變化，不亂其序，此中央之五永不易者也。而其它象數，則隨氣數所至，二五分合而成其變。變成而天地之大用見，萬物之生化出。其理其事，固顯然如指掌矣！

The Yellow River Chart and the Luo Writing must be viewed together in order to understand their meaning. The generation of all things in heaven and earth begins from one and then produces many. Therefore, from the Taiji to the two principles, from the two principles to the four images, and from the four images to the eight trigrams; that is, from the two energies of yin and yang to the Five Phases, and then to the nine palaces, all proceed from one to two, from three to four, from few to many, from few to numerous. This is the natural manifestation of generation and transformation, which is exactly the pattern demonstrated by the Yellow River Chart and the Luo Writing. Since the beginning of generation does not depart from one, even though the generation is numerous, it never loses its central point. With this central point, myriad changes do not disrupt the order, which is why the central five remains constant. As for the images and numbers in other areas, they change according to the movement of the energies, arising from the combination and separation of yin and yang energies and the Five Phases. Once change occurs, the great function of heaven and earth is revealed, and the generation and transformation of all things spread out. The principles and facts in between are clear and distinct, as clear as pointing to one's own palm.

洛書言數，有明用者，有明變者，有與道同者，有與人事同者，大別之有三。（一）圖中之數與河圖異：河圖為五十五，洛書則四十五。此由天地生化，陰陽消長之數使然也。河圖言體，陰陽平均，此合乎道者也。洛書則重在用，用者以陰從陽，以陽統陰，陽主陰從，天包地而生化方就其序。故陽數二十五不變，陰數以三十變為二十，明陽道常長，陰道常消，而以立天地之極。

The numbers in the Luo Shu explain different aspects. Some are used to clarify function, some to clarify change, some connect with the heavenly way, and some connect with human affairs. Generally, they can be divided into three categories. First, the total number in the Luo Shu differs from that in the He Tu. The He Tu has a total of fifty-five, while the Luo Shu has forty-five. This is due to the numerical principles of the generation and transformation of heaven and earth, and the waxing and waning of yin and yang. The He Tu discusses the "body" or essence, with yin and yang equally balanced, which conforms to the heavenly way. The Luo Shu focuses on the "use" or application, which requires yin to follow yang and yang to govern yin. Yang is primary and yin is secondary, with heaven encompassing earth, allowing generation and transformation to proceed in order. Therefore, the total of yang numbers in the Luo Shu remains twenty-five, while the total of yin numbers decreases from thirty to twenty, indicating that the way of yang is constantly increasing while the way of yin is constantly decreasing, thereby establishing the standard of heaven and earth.

正陰陽之位，俾下毋僭上，小毋陵大，並育不害並生不賊，而全其用，以至無窮也。乃為陽位者五，為陰位者四，陽居四正，陰居四隅，陽正位中宮，陰環行四極，而後名正事順，體建用周。雖陰陽似失其平衡，實則如是方得其平衡也。蓋陰氣不可長，中極不可亂，以五之陽正立中宮，而四圍二氣，仍自平均，未嘗偏頗，此其為數以四十五為制也。

To properly arrange the positions of yin and yang, so that the lower does not exceed the upper, the weak does not oppress the strong, and they grow together without hindrance, coexist in mutual nourishment without mutual harm, thus preserving their functions to infinity. Thus, the positions of yang are five, and those of yin are four: yang occupies the four cardinal directions—east, south, west, and north—while yin resides in the four corners. Yang is located at the central palace, while yin circulates around the four extreme directions. In this way, the distinctions are clear, the principles are harmonious, the essence is established, and the functions are fully extended. At first glance, yin and yang may seem unbalanced, but actually, this arrangement achieves true balance. Because yin should not grow unchecked, and the central position should not be disturbed, five yang elements are placed in the central palace, while the yin and yang energies around the four directions remain balanced and impartial. This is the established principle of the Luo Writing, which totals forty-five.

（一）洛書之數，陰陽平列，而與河圖位異序殊。與河圖數同而象二者何也？則河圖明天地生成者，所生成為五行，其位限於五。又河圖明天地偶合者，其合以順逆，故序唯依陽順陰逆之例。洛書則由河圖而推其變化以極其用，所象在生成之後，自五行推至九宮，以明生化之序，由二五而可推至無窮也，故數位分而為九。

The numbers in the Luo Shu are arranged with yin and yang laid out side by side, differing from the He Tu in both direction and order. It is the same set of numbers, yet why do they appear in two different forms? Because the He Tu explains the origin of heaven and earth, and what is generated is the Five Phases, so its directions are limited to five. The He Tu also explains the mutual pairing of heaven and earth's yin and yang, with pairing methods that can be in order or reverse order, so its sequence follows the principle of yang moving in order and yin moving in reverse. The Luo Shu, however, is derived from the He Tu to show its transformations and exhaust its functions. The images it takes are after generation, expanding from the Five Phases to the Nine Palaces, to explain the sequence of generation and transformation, showing that from the two energies of yin and yang and the Five Phases, one can proceed to infinity. Therefore, the numbers are divided into nine.

又洛書明生化之例，本於二氣之交錯。二氣分合，生化以眾，則數序之行，亦循環往復以至無盡。而其序或順或逆，或移彼就此，或分此合彼，互相推移，成其變化，此亦天地生化自然之序，萬類消長一定之例，有不易而易，不變而變，而變仍不失，易仍不亂之道存焉。故與河圖同異也。

Furthermore, the Luo Shu explains the principles of generation and transformation, originating from the intermingling of yin and yang energies. These two energies continuously divide and combine, leading to an ever-increasing diversity of generation and transformation. Thus, the sequence of numbers operates in a cyclical manner, continuing endlessly. Its order sometimes proceeds forward, sometimes backward, sometimes moving elements from one side to the other, sometimes separating one side and merging it with the other, shifting back and forth, thereby producing change. This is precisely the natural order of generation and transformation in heaven and earth, the fixed pattern of the increase and decrease of all beings. Within it lies the principle that what is unchanging can become changed, what remains constant can undergo transformation, even when changed it does not lose its constancy, and even when transformed it does not disrupt its order. Therefore, the Luo Shu and the He Tu have both similarities and differences.

如陽數東北原位，以水木之生成，先後天之所始。言先天之生成者首水，以天之一氣切化也；言後天之生成者首木，以天之二氣再化也。故卦象以六為坤之用，定爻之數；以三為卦之數；以八之自乘，為全卦之數，皆取乎水木之數，以領先後天一切生成之象也。

For instance, the yang numbers remain in their original positions in the east and north, because the generation of water and wood marks the starting points of "Earlier Heaven" and "Later Heaven" respectively. The generation of "Earlier Heaven" begins with water, as water is produced from the first layer of heavenly qi. The generation of "Later Heaven" begins with wood, as wood is produced from the second layer of heavenly qi. Therefore, in the hexagram structure, the number six is used for the "Kun" trigram to determine the six lines in a hexagram. The number three is used for the three lines in a trigram. The number eight multiplied by itself gives sixty-four, which represents the total number of hexagrams. All these numbers are derived from water's one and six, and wood's three and eight, to unify the imagery of generation in both "Earlier Heaven" and "Later Heaven."

若西南之七九，則先天後天之生化各異。先天之火在南，數為七；金在西，數為九。而後天之九屬火非金，七屬金非火，二者恰易其數，故變其位。蓋火之與金本相剋也，非同水木之相生。既克則有勝有復，火之勝金於先天，則金必復於後天。若勝而不復，則生化將窮，更何後天變化可言哉。故在洛書火退而西，金進而南，恰得其反，以成其序。

As for the numbers seven and nine in the west and south, the generation and transformation of the Earlier Heaven and Later Heaven differ. In the Earlier Heaven, fire is in the south and corresponds to the number seven; metal is in the west and corresponds to the number nine. In the Later Heaven, however, nine belongs to fire rather than metal, and seven belongs to metal rather than fire. Thus, the numbers associated with these elements have exchanged places, and so have their positions. This is because fire and metal are naturally opposing, unlike water and wood which are mutually generating. Since they are opposing, there is a concept of 'victory' and 'recovery': in the Earlier Heaven, fire overcame metal, so metal must necessarily recover in the Later Heaven. If there were only victory without recovery, the process of generation and transformation would reach its end, and how could there be any change in the Later Heaven? Therefore, in the Luo Writing, the number seven, originally associated with fire in the Earlier Heaven, moves to the west, while the number nine, originally associated with metal in the Earlier Heaven, moves to the south. This is exactly the opposite of the Earlier Heaven, thus establishing its order.

蓋五行之生，火必因土而後生金。既互易其位，乃得受中央之土氣，而後不相剋而相生，生克之間，即在此易位數耳。且因變化之例，必二氣之平衡，且相得有合也。以火移西，以金移南，一則九與一對，一則七與三對，皆合十而受土氣，以自成後天之化。

According to the order of mutual generation in the Five Phases, fire must first generate earth, and then earth generates metal. After the numbers seven and nine exchange positions, they are exactly able to support the central earth energy. Thus, the originally opposing fire and metal transform into a mutual generation relationship. The distinction between mutual generation and mutual control lies precisely in this exchange of positions and numbers. Furthermore, following the principle of change, it is necessary to maintain balance between yin and yang energies and ensure they are compatible. Moving the number associated with fire to the west and the number associated with metal to the south, one side becomes nine and one facing each other, while the other side becomes seven and three facing each other. Both sides add up to ten and can support the central earth energy, thus completing the Later Heaven transformation on their own.

即以陰數言之，其變例亦同。以二之接七，而仍不失火之生成；以二之對八而合十，以受土氣，此二之必移西南與西七接也。其它四六八皆然。既以此互易，而後相得，則其原位必依此變易而後成用，此固自然之理也。

In terms of the yin numbers, the rules of change are the same. Two and seven connect with each other, yet the meaning of fire's generation is not lost; two and eight oppose each other to form ten, and they can also receive the earth's energy: this is why two must move to the southwest to connect with seven in the west. Similarly, the other numbers four, six, and eight are all like this. Since mutual exchange is necessary for compatibility, their original positions must be adjusted accordingly in order to achieve their functions. This is naturally the way things are.

（一）洛書中宮之數五，河圖之數十五，何也？則以河圖土之生成數全，陰陽之體，不可少也。洛書以明用為主，土之德在五，言五已賅十。前講河圖已詳其義。洛書之僅舉五者，又不獨以土德用五之例。蓋洛書明生化之變，為後天之象，非河圖可比。後天之例，以生化為用，生化之道雖本於五行，而非止於五行，故其象皆變河圖之原例，而成新例。

Third, the central palace of the Luo Shu contains only the number five, while the He Tu's central palace includes both five and ten, making fifteen. This is because the He Tu aims to fully list the "birth number" of earth, which is five, and the completed number ten. Yin and yang are both essential in their essence. The Luo Shu focuses mainly on illustrating function, and the virtue of earth is expressed through five, so mentioning five already includes ten. This point was explained in detail when discussing the He Tu earlier. However, the Luo Shu only presents five, not merely the principle that "earth's virtue is expressed through five." The Luo Shu explains the process of generation and transformation, which belongs to the "Later Heaven" pattern, and thus cannot be compared with the He Tu. In the Later Heaven pattern, the function of generation and transformation is emphasized, and although the way of generation and transformation originates from the Five Phases, it does not stop there. Therefore, all its patterns have changed from the original rules of the He Tu and established new ones.

後天者以生化無盡為用，故各方之數皆由內而外，由寡而眾以分合變化示生化者也。生化既眾，象數益繁，而並生不害、並育不亂者以有中極也。中極止於一，此數用五而去十，明其不二也。天地之道，一言可盡，為物不二，則生物不測。此即堯舜執中之道，以本天地之用，而見於洛書者也。

The concept of "Later Heaven" is based on the endless process of generation and transformation, so the numbers in each direction spread outward from the center, increasing from small to large, using division and combination to illustrate the process of generation and transformation. Since the process of generation and transformation is complex, the images and numbers also become increasingly intricate. Yet all things can grow together without conflict and be nurtured together without disorder, relying on the principle of "the central point." The central point is unique, so here only five numbers are used instead of ten, to indicate that the central point is singular and undivided. The way of heaven and earth can be fully expressed in one sentence. The "Zhongyong" says: "If a thing is not dual, then its ability to generate life is boundless." This is precisely the meaning of the transmission from Yao and Shun, "Yun zhi jue zhong," which originates from the function of heaven and earth and is manifested in the "Luo Book."

天地以五為中心，五行以土為根本，萬物萬事以中一為立極，皆自此象見之。以天道言之，則一切生化之數，不離於中五，而用以廣，德以大，萬物所倚，萬數所持，皆此五也。故曰：天地心，亦陰陽之中氣，五行之中道也。

Heaven and Earth take the number five as their center, the Five Phases take earth as their foundation, and all things and events take maintaining the center and unity as their highest principle. These can all be seen from the image of the Luo Writing. In terms of the Way of Heaven, all numbers of generation and transformation depend on the central five, its function is widely extended because of it, and its virtue is great because of it. What all things rely upon and all numbers depend on is this five. Therefore, it is the core of Heaven and Earth, the harmonious qi of yin and yang, and the upright path of the Five Phases.

易傳曰顯諸仁，藏諸用。此二語即釋洛書者也。洛書之中五，即仁也。而曰藏用者，則言洛書用五藏十也。夫陰陽二道，相倚而成用，而陰必藏，陽必顯。一藏一顯，其用始大。五與十皆土數，即土德也。一屬於仁陽也，一屬於智陰也。用仁而藏智，仁顯而智不顯。藏也者非去而不用，言藏之於內，不以顯也。

The Zhou Changes, Great Treatise says: "Manifest it in benevolence, conceal it in function." These two sentences can be used to explain the Luo Writing. The central number five in the Luo Writing is what is called "benevolence." Saying "conceal it in function" refers to the Luo Writing clearly using five but secretly containing ten. Yin and Yang depend on each other to achieve function, and Yin must be concealed while Yang must be manifest. One concealment and one manifestation allow function to be great. Both five and ten are numbers of earth, which is the virtue of earth: five belongs to benevolence, which is Yang; ten belongs to wisdom, which is Yin. Manifesting benevolence and concealing wisdom, benevolence is revealed externally while wisdom is not revealed. What is called "concealment" does not mean abandoning it, but rather keeping it within, not letting it appear externally.

蓋天下之道，必首德行。仁為人之全德，亦天地之全德也。若智者，以成仁之用也，不可獨用。仁顯其德，而智全其用，則用不顯而自大，是中庸成已成物之功，所謂不慮而中，不思而得者也，唯聖與至誠則之。以人之生本乎仁，仁之德無不全也，而智成之，即陰陽之道也。顯仁藏智，智在仁中，即扶陽抑陰之道也。

The principles of the world always begin with virtue. "Ren" is the complete virtue of a person, as well as the complete virtue of heaven and earth. As for "zhi" (wisdom), it is used to complete the function of ren, and cannot be used independently. Ren reveals its virtue, while zhi completes its function. Thus, although the function is not outwardly displayed, it naturally becomes great. This is the practice of "cheng ji cheng wu" (perfecting oneself and others) mentioned in the Zhongyong. It is also the state of naturally conforming to the middle way without deliberation and naturally attaining something without thinking. Only sages and those of utmost sincerity can achieve this. Human life originates from ren, and this virtue is present in all things. It is through zhi that this virtue is completed. This is precisely the way of yin and yang complementing each other. Making ren evident while concealing zhi, with zhi contained within ren, is the principle of "fu yang yi yin" (supporting yang and restraining yin).

此義則本於洛書。洛書顯五而藏十非無十也。四正四偶，所合皆十，即所謂藏也。藏之於內，而獨顯五，以明立極之義，實為天地微妙之道所見者也。天地之功，見於生成皆仁德也。不見其智，而功莫與大，此即能藏其智以成其用也。人若忘乎此義，不顯其仁而用智焉，是悖天逆道，無不敗矣，尚何成哉。故洛書用五之義至深切矣。洛書明變化之例，示生化之用，其所包者廣，此略舉其大者耳。要將河圖之象數，與之一一對參，而求其變化之跡，則可漸悟天地生物之則，聖人易教之心矣夫。

This principle is based on the Luo Writing. The Luo Writing reveals five but conceals ten, not lacking ten entirely. The sum of the numbers opposite each other in the four cardinal directions and the four corners is ten, which is called "concealment." By concealing ten within it, it only reveals five, thus expressing the meaning of establishing the central point. This is indeed a manifestation of the subtle way of heaven and earth. The achievements of heaven and earth are reflected in generating all things, which are all expressions of benevolence. Although its wisdom is not visible, its achievements are the greatest. This is precisely how wisdom is concealed to complete its function. If people forget this principle, and do not manifest their benevolence but instead rely solely on wisdom, they are going against the way of heaven and reversing the correct principles, and there is no way they can succeed, let alone achieve anything. Therefore, the Luo Writing's use of the number five is truly profound. The Luo Writing explains the principles of change and demonstrates the functions of generation and transformation, containing a vast range of content. Here, only the main points are briefly mentioned. Scholars should compare and study the images and numbers of the Heavens Chart with the Luo Writing, seeking the traces of change, and thus gradually understand the principles by which heaven and earth nurture all things, as well as the intentions of the sages in establishing the Zhou Changes (I Ching) as a teaching.

河圖負於龍馬，洛書呈於元龜，以其所出見在河洛也，故名河圖、洛書。圖之出雖以馬龜，象之征則符運數，蓋天地自然之象，顯於物者也。既出見於物，得聖人解之，以造成人文之始，而易象乃具。是河洛二圖者，天地之文顯於物，而用於人者也。

The Yellow River Chart appeared through a dragon horse, and the Luo Writing came through a great turtle; since they appeared at the Yellow River and Luo Water, they are called the Yellow River Chart and the Luo Writing. Although these charts emerged through a dragon horse and a divine turtle, the symbols they represent correspond with the numbers of the heavens and earth's vital energies. They are originally the natural phenomena of heaven and earth, merely manifested through specific objects. Once manifested through objects, they needed sages to explain them, thus initiating human civilization. The hexagrams of the Zhou Changes (I Ching) were thereby established. Clearly, these two charts, the Yellow River Chart and the Luo Writing, are manifestations of the principles of heaven and earth through objects, available for human use.

唯天地之神，能自成之，唯物顯之，唯人用之。蓋合天地人物四者之靈，而後見其功，成其名，以廣其德，著其道，其為物豈可輕言哉？觀易象之所本，六經之所仿，百度之所制，一切政教之所創，其為人文之袓，文化之源，固無他物可與方矣！

Only the mystery of heaven and earth can naturally produce it, only specific things can manifest it, and only humans can apply it. To combine the spirit of heaven, earth, human beings, and things, one can see its effectiveness and achieve its reputation, thus spreading its virtue and revealing its principles. Such a thing is not to be regarded lightly. The hexagrams of the Zhou Changes come from it, the Six Classics of Poetry, Book, Rites, Music, Changes, and Spring and Autumn Annals derive from it, all systems and institutions rely on it, and all political and educational measures originate from it. As the ancestor of human culture and the source of civilization, there is nothing else that can be compared with it.

圖書之象簡，而包舉天地之間，生成之德，變化之道，盡氣數之妙，示形神之全，固以一而賅萬，中而立極，有同易道者矣！其所明用，在順自然之序，而推其不息之功；在本生化之原，而溯其不二之道，猶天地之覆載，人物之生育，而莫外於至一至中之極者也。然考其用之大例，有數則焉：

The images of the Yellow River Chart and the Luo Writing are extremely simple, yet they encompass entirely the virtues generated between heaven and earth, and the principles of change. They exhaust the subtle aspects of the vital energy and demonstrate the completeness of form and spirit. Indeed, they unify all things through one principle, standing at the center and establishing the ultimate standard, which is exactly the same as the way of the Zhou Changes. Their purpose is to follow the natural order and investigate the continuous process of generation and renewal, and to return to the origin of creation and trace back to the single, ultimate Dao. This is like heaven covering and earth supporting, with people and things flourishing in between, all arising from the ultimate principle of "absolute unity and absolute centrality." Now, examining their major applications, they can be summarized as follows.

（一）河圖者，明位之用，位無動也；洛書者，明時之用，時有變也。河圖立天地之極，而見其體，是明位不動，有其生成之序也。洛書列天地之序，而著其變，是明時之時遷，有其復之情之也。二者大例，一體一用，一守中而立極，一循行而不窮，是天地生成始終，道德氣數往復遷變，可見可微者也。

The Yellow River Chart explains the function of "position," which is fixed and unmoving; the Luo Writing explains the function of "time," which is ever-changing. The Yellow River Chart establishes the principles of heaven and earth and reveals their essence, showing that although position is fixed, there is an inherent order of generation within it. The Luo Writing arranges the sequence of heaven and earth and highlights their changes, showing that although time is in constant movement, there is a cyclical pattern of return and reversal within it. These two great principles represent one as the main subject and the other as the main function; one remains centered and establishes the standard, while the other cycles continuously without end. The beginning and end of the generation of heaven and earth, as well as the ebb and flow of moral virtue and destiny, whether revealed or hidden, can all be understood from here.

（一）河圖者，明天地之生成也；洛書者，明萬物之變化也。河圖自陰陽二氣之生成，而五行出；洛書自五方之推遷，而九宮見。五行為萬物之本，數簡而位定；九宮為萬物之變，數繁而行周。此生化由簡而繁，氣數由正而變之例。故河圖之數，自一至十，不離五行，而成生成之母；洛書之數，自一至九，化分無盡，而明往復之理。

The second point is that the Yellow River Chart explains the origin of heaven and earth, while the Luo Writing explains the transformation of all things. The Yellow River Chart begins with the generation of yin and yang, thus revealing the Five Phases. The Luo Writing begins with the movement of the five directions, thus revealing the nine palaces. The Five Phases are the fundamental elements of all things, with simple numbers and fixed positions; the nine palaces represent the changes of all things, with numerous numbers and widespread movement. This is precisely the common pattern of generation moving from simplicity to complexity and the movement of qi and numbers moving from order to change. Therefore, the numbers in the Yellow River Chart range from one to ten, always connected with the Five Phases, becoming the mother of the generation of all things; the numbers in the Luo Writing range from one to nine, transforming infinitely, used to explain the principle of continuous cycles.

其例如：一六之水，則化為一與六之北，與西北二宮；四九之金，則變為九與四之南，與東南二宮；餘數皆然。雖水火之數不易而位移，火金之數互易而位改，在河圖可名為水火金木，在洛書則稱為四正四偶各宮。正猶易之兩儀，一變為四象，再化為八卦，其數已由合而分，其物亦由寡而眾。此天地生化自然之例，而易之所以為易也，若執河圖以釋洛書，則將滯而不通矣！

For example, in the Yellow River Chart, the numbers one and six both belong to water and are located in the north, but in the Luo Writing, one is placed in the north and six in the northwest. Similarly, in the Yellow River Chart, the numbers four and nine both belong to metal and are located in the west, but in the Luo Writing, nine is placed in the south and four in the southeast. The other numbers are also arranged in this way. Although the numbers representing water and fire remain the same but their positions change, and the numbers representing fire and metal are exchanged with their positions altered, in the Yellow River Chart they are called water, fire, metal, and wood, but in the Luo Writing they are simply referred to as the four cardinal directions and the four intermediate directions. This is similar to the Zhou Changes, which starts with the two principles (two yi), then transforms into the four images (four xiang), and further into the eight trigrams (eight gua). The numbers first merge and then divide, and the elements go from few to many. This is the natural pattern of generation and transformation in heaven and earth, and it is precisely why the Zhou Changes is called the "Book of Changes." If one rigidly uses the Yellow River Chart to explain the Luo Writing, there will be many obstacles and inconsistencies.

（一）河圖者：以數紀二五之本質；洛書者，以數名九宮之循環。河圖不動而自生成，洛書以動而形變化。河圖象天地初奠，物類自生之時；洛書象萬有具陳，氣數並行之例。其合於易，則圖如伏羲之卦，定位明序，而立其極；書如文王之卦，變化錯綜，而推其用。二者各有其所象，亦不外造化自然之理數。

Third, the River Chart uses numbers to record the essence of yin and yang and the Five Phases, while the Luo Square uses numbers to indicate the cyclic pattern of the nine palaces. The River Chart is unchanging and naturally arises, while the Luo Square emerges through movement and shows change. The River Chart represents the time when heaven and earth were just established and things naturally emerged; the Luo Square represents the time when all things were already arranged and the principles of qi and numbers proceeded in harmony. When paired with the Zhou Yi, the River Chart is like Fuxi's Earlier Heaven Trigrams, which establish directions and clarify order, thereby setting standards; the Luo Square is like King Wen's Later Heaven Trigrams, which display complex transformations, thereby deriving their functions. Each has its own symbolic representation, yet both conform to the natural principles and numbers of creation.

可征於物，可驗於形，可候於時令，可證於天地之文，可通於人物之生變遷者也。故河圖之象，不易而易，如天地之道也；洛書之象，易而不易，如天地之德也。就河圖推而上之，可明天地之自始；就洛書推而化之，可知萬物之將來。而天道以明，人道以建，天人以達，性命斯順；氣數不乖，行止斯定，此易之所以立教，為象天道以定人道者也。

They can be verified through specific objects, confirmed through form, observed according to seasons, verified through the patterns of heaven and earth, and understood through the changes of things and beings. Therefore, the imagery of the Yellow River Chart is "unchanging yet changing," akin to the way of heaven and earth; the imagery of the Luo Writing is "changing yet unchanging," akin to the virtue of heaven and earth. By following the Yellow River Chart upward, one can understand the beginning of heaven and earth; by following the Luo Writing downward, one can know the destination of all things. Thus, the way of heaven becomes clear, the way of humanity is established, heaven and humanity are connected, and nature and destiny are harmonious. The balance of qi and numbers is not violated, and movement and stillness become fixed. This is why the Zhou Changes (I Ching) can establish teachings, by following the way of heaven to determine the way of humanity.

夫河圖之數變，而洛書之象以成；其屬於天道者，萬物生化自然之象也；屬於人道者，則扶陽抑陰；中極不動，顯仁藏用，中和以成之義也。蓋天道遠，人道邇；天道精微，聖人則之；人道明易，眾人能之；必以人道為言，而後眾人可通天道也。河圖之屬天道者多，洛書則寓人道；以後天之世，唯以人道為急務也。然人生自天命，人道出於天道；非天道之外有人道，乃天道之見於人事，而宜取法者；故名之人道，明人之所當由者也。

The numbers of the Yellow River Chart once change, the images of the Luo Writing then take form. Among these, those belonging to the Way of Heaven are the images of the natural generation and transformation of all things; those belonging to the Way of Humanity are the meaning of "supporting Yang and restraining Yin," the central point remaining unmoved, "manifesting benevolence and concealing function," and achieving all things through harmony and balance. The Way of Heaven is distant, while the Way of Humanity is near; the Way of Heaven is profound and subtle, known only to the sages; the Way of Humanity is clear and easy to understand, accessible to all people. One must begin with the Way of Humanity, so that people may thereby reach the Way of Heaven. The Yellow River Chart mainly discusses the Way of Heaven, while the Luo Writing embodies the Way of Humanity, because in the Later Heaven world, the Way of Humanity is the urgent matter. However, human life comes from the Mandate of Heaven, and the Way of Humanity originates from the Way of Heaven. It is not that the Way of Humanity exists apart from the Way of Heaven, but rather that the Way of Heaven is manifested in human affairs, the part that should be followed by people. Therefore, it is called the "Way of Humanity," to indicate the path people should follow.

道路也；由之則可行；人生猶行路也，由道則全其生；大則治平之功，小則孝弟之事；遠則聖賢之德，近則日用之常；皆必由是而達焉。此人道之所以為重，而次於天道，以先於天道者也。洛書之象，由河圖而變；即由先天而為後天，亦即由天道而入人道；此可征之於其數也。

The original meaning of "Dao" is a path, and by following it one can proceed smoothly. A person's life is like walking, and by following the Dao one can preserve one's life. Whether it is great achievements in governing the country and pacifying the world, or small acts such as filial piety towards parents and respect for elder brothers in daily life; whether it is the virtue of sages and virtuous persons, or the routine of eating, drinking, and living, all must be achieved through this path. This is why the human Dao is regarded as important: in terms of order, it comes after the Heavenly Dao, but in practice, it precedes the Heavenly Dao. The diagram of the Luo Book originates from the He Diagram, meaning it transitions from the Earlier Heaven to the Later Heaven, from the Heavenly Dao to the Human Dao. This can be verified through its numbers.

五行雲者，非僅指水火木金土也，凡物與事之同列而有五者，皆是；亦如兩儀也；故在時，有春夏秋冬四季也；在地，有東南西北中央也；在人，有心肝脾肺賢也；在味，以酸鹹辛苦甘也；在音，有宮商角徵羽也；在德，有仁義禮智信也；在倫，有君臣父子兄弟夫婦朋友也；其類正多，要皆五行也。

The concept of "Five Phases" does not merely refer to the five elements of water, fire, wood, metal, and earth; any set of things that are grouped into exactly five categories falls under the scope of the Five Phases, just as "Two Principles" does not specifically refer to only two things. Therefore, in terms of seasons, there are spring, summer, autumn, and winter; in terms of geography, there are east, south, west, north, and the center; in terms of the human body, there are the five organs: heart, liver, spleen, lung, and kidney; in terms of taste, there are sour, salty, pungent, bitter, and sweet; in terms of music, there are the five tones:宫, 商, 角, 徵, 羽; in terms of virtue, there are the five constants: benevolence, righteousness, propriety, wisdom, and faithfulness; in terms of human relationships, there are the five bonds: ruler and subject, father and son, siblings, husband and wife, and friends. There are many such examples, and ultimately they all belong to the Five Phases.

行者，言其周流往復循環而行，不相害也；故一年四時象之，年以四時成歲，而土旺於四季；如河圖以水火木金定四方，而以五十之土立中極也；至洛書則方之四者變八，中之五者終不移，則可知天道之行，有化少為眾，變合為分之例；而中極不易也。去其十者，抑陰而扶陽也，顯仁而藏用也；此即人道所始仿也。

The character "行" refers to its flowing and circulating nature, moving in cycles without hindrance. Therefore, the four seasons of a year take their form from this principle: a year is formed by the four seasons, and "earth" (土) is strongest at the end of each season. Just as the Yellow River Chart uses water, fire, wood, and metal to establish the four cardinal directions, and uses five and ten to establish the central position, so too in the Luo Writing, the four directions become eight, yet the central five remains unchanged. From this we can see that the operation of heaven follows a general principle of transforming few into many and uniting into division, while the central remains constant. The Luo Writing omits ten, which is "restraining yin and supporting yang," and "manifesting benevolence while concealing its function," which is precisely the principle that human beings first emulated.

人之於生，有德業焉，有事功焉；不得徒生也。故天命之性以成其德，仁是也；天賦之知以立其功，智是也；人之以仁成性，則道成而生全；以智立功，則事成而名貴；二者人之所以為人也，然必顯其一；而藏其一，以合乎洛書之象，而契乎天地之德；若不能顯仁藏智，則有功無德，失主之本。

A person living in the world has virtue and learning, has achievements and accomplishments, and cannot live a life in vain. Therefore, Heaven gives a person his nature to accomplish his virtue, which is "ren" (benevolence); and gives a person his knowledge and ability to establish his achievements, which is "zhi" (wisdom). A person relies on ren to complete his nature, thus the Way is realized and life is preserved; relies on zhi to establish his achievements, thus affairs are accomplished and reputation is esteemed. These two aspects are precisely what make a person a human being. However, it is necessary to manifest one and conceal the other, in accordance with the image of the Luo Writing, and to conform to the virtue of Heaven and Earth. If one cannot manifest ren and conceal zhi, there will be achievements without virtue, losing the fundamental role of being the master.

若不顯仁而徒用智，則反未為本；離性日遠，去道日甚；不獨無以全生，必反因以賈禍。蓋智者，用也，末也，必有本體為之先焉；失其仁而唯智是尚，是舍本逐末，失體求用；無根之花，無源之泉，何以自全而成用哉。

If one does not manifest benevolence but relies solely on wisdom, this is reversing the order, taking the end as the beginning, moving further and further away from one's true nature and the great way. Not only will this fail to preserve life, but it will inevitably bring about calamity. "Wisdom" belongs to the function, to the secondary aspect; before it, there must be a fundamental principle as its foundation. To abandon benevolence and solely pursue wisdom is to discard the root for the branches, to seek function without the essence, like a flower without roots or a spring without a source. How can one preserve oneself and achieve function in such a case?

用者，言有所用也；有所主宰而後成其用也，非獨用可成功者；故顯仁藏用，示天地之道；必先立德，明人道之本；必先修已，其與中極不易之義，為易教並重者也。仁之德，即生成也；天地以生成為本，故人以仁為先。仁、人也；有仁斯有生，安有忘其仁，而能生者？即安有忘其生，而能致用也？故用者，為仁用也；為用以成其仁也。

The term "use" refers to application; one must first have a master principle before it can be effectively applied, and it is not sufficient to rely solely on use to achieve success. Therefore, the Zhou Changes say "manifest in benevolence, conceal in use," revealing the way of heaven and earth. Humans must first establish virtue in order to understand the fundamental principle of human conduct; they must first cultivate themselves, a principle that is equally emphasized in the teaching of the Zhou Changes as "the center does not shift." Benevolence is the virtue that generates all things; heaven and earth take generation as their fundamental principle, so humans should take benevolence as their primary concern. The character "仁" (benevolence) includes "人" (person), meaning that with benevolence there is life; how could there be life without benevolence? How could there be application without life? Therefore, "use" is used for the sake of benevolence, and it is through application that benevolence is fulfilled.

分言之，則有諸德之名；約言之，即仁也；用之屬智，亦為仁也；苟無仁，何以名其智哉？譬如其生且不省者，焉得為智？此夫子有予智不能中庸之嘆也！河洛二圖所重，在變化之例；洛書者，河圖之變；河圖者，天地之變。河圖以二氣之變，而五行出；洛書則五行之變，而九宮分，此易見者也。其中微妙難知者，則五行之數，本二氣之數；

When discussed separately, virtue includes various names such as benevolence, righteousness, propriety, wisdom, and faithfulness; but when summarized, it is simply the character 'ren' (benevolence). The wisdom used is actually also a form of benevolence; if there is no benevolence, how can it be called wisdom? For example, if a person has not even examined his own life, how can he be considered wise? This is precisely what Confucius lamented in the "Doctrine of the Mean," about how people think they are clever but cannot maintain the mean for even a month. The two diagrams, the "Yellow River Chart" and the "Luo Writing," focus on the principles of change. The "Luo Writing" is a variation of the "Yellow River Chart," and the "Yellow River Chart" itself is a variation of heaven and earth. The "Yellow River Chart" originates from the changes of yin and yang to produce the Five Phases, while the "Luo Writing" derives the nine palaces from the changes of the Five Phases. This is easy to see. However, the subtle and difficult part is that the numbers of the Five Phases originally come from the numbers of yin and yang.

而九宮之數，即五行之數；推之則萬物之數，莫非九宮之數，亦莫非五行之數，二氣之數也，溯而上之，則九而五而二，歸於太極之一；推而下之，則五而九，至於萬物，以達無窮；一本而萬殊，萬殊歸於一本，如布之經緯，網之綱目；其為數殊，為絲一也；故自太極以至無窮，為數雖殊，為氣無二；而數之殊者，非殊數也。

The numbers of the Nine Palaces are the numbers of the Five Phases; from this derivation, the numbers of all things are none other than the numbers of the Nine Palaces, none other than the numbers of the Five Phases, and none other than the numbers of the two energies of yin and yang. Tracing back, from nine to five, from five to two, ultimately returning to the unity of the Taiji. Moving forward, from five to nine, until all things, reaching infinity. One fundamental principle gives rise to myriad differences, and these myriad differences return to the one fundamental principle, just as a fabric has warp and weft, and a net has its main strands and its meshes. Although the number of strands varies, the threads that weave them are the same. Therefore, from the Taiji to infinity, although the numbers differ in myriad ways, the energies remain unchanging. The differences in numbers are not due to another set of numbers altogether.

數之自加減乘除也。故數殊而不殊，雖由萬物至於無窮，仍不外此一二三四五六七八九之數；不過有其分合變化而已。故數之殊者，數自殊之；非數外有數，則由氣之不二也。因氣不離陰陽，雖有錯綜生化之殊，仍不失其為陰陽；故氣無殊，數無殊；數以紀氣，氣之所至則數成，數之所見則氣達，氣數無殊用也。

The difference is merely the result of addition, subtraction, multiplication, and division within the same set of numbers. Therefore, numbers appear different but are essentially the same: even when derived from all things to infinity, they still do not go beyond the nine numbers one, two, three, four, five, six, seven, eight, and nine. They are only differentiated through their combination and separation. The difference among numbers arises from their own differentiation, not from another set of numbers outside this system. The origin lies in the oneness and non-duality of qi. Qi cannot be separated from yin and yang; although there are complex and varied processes of generation and transformation, they are ultimately yin and yang. Therefore, qi has no distinctions, and numbers also have no distinctions. Numbers are used to record qi: where qi goes, numbers take effect there; where numbers manifest, qi flows there. In terms of function, qi and numbers are essentially the same.

河洛者，明氣數之用，示天地萬物之始終也；果明其變例，則天下之氣數，皆可推而知之；以其用因變而後見也。設無所變。即無所用；果無變無用，天地已歸澌滅；更何河洛之圖存哉？唯其變多則用神，用神則天地無極；人物無盡，莫不在氣數之中；即莫能出此圖象之外，而後河洛二圖，乃為人之所必明，世之所必重者矣！

The Yellow River Chart and the Luo Writing are used to explain the function of qi and numbers, and to display the beginning and end of all things in heaven and earth. If one can truly understand the principles of their changes, then the qi and numbers of the world can all be calculated and known, because function is revealed through change. If there were no change, there would be no function; if there were truly no change and no function, heaven and earth would have long since perished, and how could the Yellow River Chart and the Luo Writing still exist? It is precisely because of the many changes that function becomes profound; because function is profound, heaven and earth have no end, and human beings and things continue endlessly. All of this is contained within the qi and numbers, and thus lies within the scope of these two diagrams. In this way, the Yellow River Chart and the Luo Writing are indeed something that every person must understand and every generation must value.

河圖與洛書異同之處，即氣數變之跡，與天地萬物生化之例；其所列雖僅此九宮之位，五行之名；而其類推，可至無盡；欲明其變，可就易象證之也；所須知者，河洛之變何自來？其氣數分合何所本？此則求明天地生成之序，人物生化之數，所必留意者也；茲試論之：

The differences and similarities between the Yellow River Chart and the Luo Writing are traces of the movement of qi and numbers, and they also serve as principles for the generation and transformation of all things in heaven and earth. Although they only arrange nine palace positions and the names of the Five Phases, by analogy and deduction, they can be extended infinitely. To understand their changes, one can refer to the hexagrams of the Zhou Changes. It is essential to first clarify: where does the change between the Yellow River Chart and the Luo Writing originate? What is the basis for their division and combination of qi and numbers? This is precisely what must be taken into consideration when trying to understand the sequence of the generation of heaven and earth, and the numerical principles of the birth and transformation of human beings and things. Now I will attempt to discuss this.

洛書之數，因河圖而來；即萬物之生化，本天地五行所出；如五行生自二氣，即天地也；已見河圖。而九宮變自五行，即五方金木火水土也，則見洛書；而九宮雲者，非言九物，或九事也；以數盡於九，九宮足以包數之全；天下之物，盡在九數中，則莫逃乎九宮之外；故九宮者，萬物萬事之所隸屬，而萬數之所循環者也。

The numbers of the Luo Shu are derived from the He Tu, just as the generation and transformation of all things fundamentally originate from the Five Phases of heaven and earth. The Five Phases arise from the two energies of yin and yang, which represent heaven and earth. This principle is already shown in the He Tu. The nine palaces come from the Five Phases, which are the five elements—metal, wood, fire, water, and earth—located in the five directions. This aspect is demonstrated in the Luo Shu. The term "nine palaces" does not refer to nine separate things or nine different matters; since the number nine represents completion, the nine palaces are sufficient to encompass all numbers. All things in the world exist within the nine numbers, and none can escape the scope of the nine palaces. Therefore, the nine palaces form the framework to which all things belong, and they are also the place where all numbers cycle and operate.

無論生化之無盡，所推所衍，莫不盡於九數之中；由九而內則返於一，由九而外，則推至無量數；數雖無量，仍不外此九也；乾之用九，已盡天下生生之道；而大衍之用四十九，已極天下往來之數；其曰：大衍者，由中數之五，而十倍之也；衍者、推衍者：推其數之所至，而足以包舉一切數；故曰：大衍。以數之老陽在九，老陰在六；六九五十四，去中五，而得四十九；

No matter how infinite and boundless the transformations of all things may be, all calculations and deductions remain within the range of nine numbers. By contracting from nine inward, one returns to one; by expanding from nine outward, one reaches an immeasurable large number. Although the number is immeasurable, it still does not go beyond these nine numbers. The "Use of Nine" in the Qian hexagram of the Zhouyi has already explained the principle of continuous generation and transformation in the world. The passage in the Great Treatise says, "The great derivation consists of fifty numbers, but its use is forty-nine." This has already exhausted the numbers of all coming and going transformations. The term "great derivation" is called so because it comes from the central number five multiplied by ten. "Derivation" means deduction: investigating the limit that this number can reach, which is sufficient to include all numbers, hence it is called "great derivation." In terms of numbers, old yang is nine, old yin is six. Six multiplied by nine gives fifty-four. Subtracting the central five, we get forty-nine.

即大衍之用，此亦河圖洛書所有之數也；以其數之重在變也，則河圖之象變為洛書，所始在金火互易位也。以金之九，為先天數；若已變，則屬火；離代乾用，離為火；而乾為金，故其位隨乾離而易；此易見者也。

This is the number forty-nine used in the "Great Derivation" (dà yǎn), which is exactly the number found in both the Yellow River Chart (Hé tú) and the Luo Writing (Luò shū). Since these numbers emphasize the concept of change ("biàn"), the image of the Yellow River Chart transforms into that of the Luo Writing, beginning with the exchange of positions between metal and fire. The number nine originally belongs to metal in the Earlier Heaven (xiān tiān), but once it changes, it becomes associated with fire. This is because in the Later Heaven (hòu tiān), the Hexagram Li (Fire) replaces the Hexagram Qian (Heaven), and since Li represents fire and Qian represents metal, the position of the number nine changes along with the shift between Qian and Li. This is something that is easy to observe.

其間尚含深意，即以數之成，乃因氣之行；氣之行也，非置於一方而不動，必周流八方而無息；以位言之，則河圖之火與水對，金與木對；數隨五行之氣，而定其方，無所易也；若以時言之，則洛書北方之一，與東方之三，一屬太陽，一屬少陽；而後南方易以九，西方易以七；亦一太陽，一少陽；其位互易，而後正對；以其氣之既行，不復如河圖之初生也。

This contains a deeper meaning: numbers exist because qi is in motion; and since qi is in motion, it does not remain fixed in one direction but flows through all eight directions without ceasing. In terms of 'position,' the He Tu shows fire opposite water and metal opposite wood, with numbers determined by the Five Phases' qi and fixed in position without change. But in terms of 'time,' the Luo Shu has one in the north and three in the east, one belonging to the sun and the other to the young sun, so the south is assigned nine and the west seven, also belonging to the sun and the young sun. After their positions are exchanged, they become perfectly opposite. This is because qi is already in motion and circulation, no longer like the He Tu which only reflects the initial state.

河圖之氣，以陽生陰，以陰繼陽；故陽老於西方之九，而陰四繼之；陰老於北方之六，而陽一承之。陰陽互根於定位，而相得以合，而生成之功乃見，此其以氣之初生為象也；若在洛書，則陰陽已分，二氣環行；行者有序，太少必對；是以北方之一，南方之九；一始一終，皆太陽；東方之三，西方之七；一生一成，皆少陽也。

The qi of the Yellow River Chart arises from yang generating yin and yin receiving yang. Therefore, the yang number reaches nine in the west and becomes old, followed by the yin number four to take over. The yin number reaches six in the north and becomes old, followed by the yang number one to take over. Yin and yang mutually support each other in fixed directions, complementing and harmonizing with each other, thus producing effects. This is taking the form of qi in its initial state. In the Luo Writing, yin and yang have already separated, and the two energies circulate around. Since there is circulation, there must be order; the greater and the lesser must be paired accordingly. Therefore, one in the north and nine in the south, one is the beginning and the other is the end, both belonging to the sun; three in the east and seven in the west, one is the master of generation and the other is the master of completion, both belonging to the lesser sun.

陰氣亦然，東北之八，西南之二，皆少陰；西北之六，東南之四，皆少陰；兩兩相當，以周行於八方；而成一陰一陽之道，遂不可不易其南西金火之位也。此例可以一歲證之，春與秋對，冬與夏對；一寒一暑，相當其令；而一歲之氣，周而復始，如環無端，此其用之可明者也。故洛書之象，象後天已定之氣數；陰陽迭興，數位周流；以成其往來不息之德，不獨歲令然也；即一人之生，一日之晝夜；無不如是，皆以循環為率；此即洛書以明變化之用為象者也。

Yin energy is also the same: the eight in the Northeast and the two in the Southwest both belong to the Lesser Yin, and the six in the Northwest and the four in the Southeast are also called Lesser Yin (according to the system they should be Tai Yin). They correspond in pairs and circulate through the eight directions, thus fulfilling the statement in the Great Treatise, "One Yin and one Yang are called the Way." Therefore, the positions of the South and the West, which are Fire and Metal respectively, must be exchanged. This principle can be verified by the cycle of a year: Spring and Autumn are opposite, Winter and Summer are opposite, one cold and one hot each take their turn; and the energy of a year circulates continuously, like a circular ring with no beginning or end. This is the most easily understood aspect of its function. Therefore, the image of the Luo Writing represents the established Later Heaven pattern of energies: Yin and Yang alternate, numbers circulate without rest, thus forming an unceasing virtue. This is not only true for the cycle of the year, but also for a person's life and the day's night cycle, all following the principle of circulation. This is precisely why the Luo Writing takes its image to explain the function of change.

且數之既變，有數例焉；陽之合陽，則反為陰；陰之合陽，則化為陽；故二陽相遇，則成陽中陰；二陰相遇，亦為陰中陽；此在太少之外，更有陰陽也。是一與九對而成十，則九為陽，一為陽之陰；三與七對亦成十，則三為陽，七為陽之陰；陰數亦然。故四隅陰數，東北西南為陽，相對為陰；其所以然者，合則變，分則化也；後天之數多雜，無純陽純陰之物，以其不能生化也。

Furthermore, when numbers change, there are certain rules: when two yang numbers combine, they become yin; when a yang and a yin combine, they become yang. Therefore, when two yang numbers meet, they form yang with yin within it; when two yin numbers meet, they form yin with yang within it. This is another layer of yin and yang distinction beyond the Taiyang, Shaoyang, Taiyin, and Shaoyin. For example, one and nine combine to make ten. Nine is yang, and one is yang with yin within it. Three and seven combine to make ten. Three is yang, and seven is yang with yin within it. The same applies to yin numbers. Therefore, the four corners of the numbers, the Northeast and Southwest are considered yang, while their opposites are considered yin. This is because when numbers combine, transformation occurs; when they separate, change occurs. Later Heaven numbers are mostly mixed, with no purely yang or purely yin elements, because pure yang and pure yin cannot transform or change.

洛書之數，參伍錯綜，各有其分合之用；故變化無盡，不獨火金之易；即二八之易位，亦其例也；天地生成，全依此陰陽之摩蕩；而後萬物生化。世界悠久，以迄無窮，此所謂造化之機也。其行也，則以往來為則，循環不已，以成其生生不盡之功；即至誠無息之德也。故氣之陽者陰之，陰者陽之；天者下之，地者上之；左者右之，右者左之；相互以生，相交以成；不獨金火之互換也；

The numbers in the Luo Writing are interwoven in a complex manner, each having its own way of combination and separation, thus leading to infinite changes. It is not only the exchange between fire and metal; even the exchange between two and eight follows the same principle. The generation of heaven and earth entirely depends on such mutual interaction between yin and yang, allowing all things to be generated and transformed, and the world to continue endlessly. This is referred to as the key mechanism of creation and transformation. Its operation follows the principle of coming and going, circulating endlessly, thus achieving the endless generation of things. This is the virtue described in the Zhongyong as "the utmost sincerity has no cessation." Therefore, qi that is originally yang turns to yin, and qi that is originally yin turns to yang; what is in heaven descends, and what is on earth ascends; what is on the left moves to the right, and what is on the right moves to the left. They generate each other through mutual interaction and form each other through mutual crossing, not only involving the exchange between metal and fire.

故東南西北，四方之序；不似河圖，自一至九，九宮之數；不同五行，而後見後天之道，明世間之數。如河圖始於北，而洛書首東；河圖陰逆陽順，以一繫行；洛書均分二繫以往復，此皆二者同異，可資考證者也；蓋先天之象，由無入有；其始生也，因氣之動；後天則已生成之後，萬物隨之生化；

Therefore, the order of the numbers one to nine in the Luo Shu, arranged in the four directions east, south, west, and north, differs from that of the He Tu. The Luo Shu employs the numbers of the Nine Palaces, which differ from the arrangement of the Five Phases. This distinction reveals the principle of the Later Heaven and explains the numerical principles of the world. For example, the He Tu begins with the north, while the Luo Shu starts with the east. The He Tu has a single system of operation, with yin moving in reverse and yang moving forward, while the Luo Shu divides into two systems that operate reciprocally. These differences and similarities between the two can be used for reference and verification. The image of the Earlier Heaven arises from nothingness into being, beginning with a single movement of qi. The Later Heaven, however, occurs after generation, with all things continuously transforming and evolving.

氣之流行不息，數以變化不窮；其所以異者，皆自氣合之；而氣者，內徵於道，即理也；外徵於象，即數也；理數之間，不可過求其跡，以有神也；神御其用，故天地有主宰之數不易；而神不可測，以其微也；是陰陽之事，不可實之以物也。唯神通之，氣感之；固聖智之事也。以易言之，神而明之，存乎其人，言非易明也；而氣數之常變，吉凶生焉，禍福降焉，則盡人所當知也。

The movement of qi never ceases, and thus numbers change endlessly. The differences among them are all harmonized by qi. As for "qi," when examined internally according to the Dao, it is "li" (principle); when examined externally according to phenomena, it is "shu" (number). Between principle and number, one should not overemphasize their forms, for there is another "shen" (spirit) involved. The spirit governs their function, so there is a constant number that serves as the ruler in the world. However, the spirit itself is indescribable because it is too subtle. Therefore, the affairs of yin and yang cannot be fixed to a particular thing; they must be connected by the spirit and responded to by qi. This is the concern of sages and the most wise. Regarding the Zhou Yi, the Great Treatise says, "To grasp the spirit and make it clear depends on the person," which means this principle is not easily explained. As for the constant and changing aspects of qi and number, which give rise to good and bad fortune, and thus bring about blessings and misfortunes, these are things that everyone should know.

故逢其合，適其宜；去其逆，塞其空；為趨吉凶之道，不可不講；此數雖止於九，而用可千萬；物雖止於五，而道將無窮；如水之數，遇金而旺，遇火而尊，遇木而退；遇土而死；其道有窮通也；他行皆然；以數合之而自卜之，則吉凶無遁情，禍福有定數；不必求之人也。是故數之為用，合道明生者也；知數知生，順數順道；其所指者義精意切，惜乎人之不講，而不明聖人立教之旨，斯可慨矣！

Therefore, when encountering something that harmonizes with oneself, one should follow it; when encountering something suitable, one should seize it. One should avoid what is contrary to oneself and make up for what is lacking. This is the method to seek good fortune and avoid misfortune, which is something not to be neglected. Although numbers only go up to nine, their functions can be varied in countless ways; although things are only categorized into the Five Phases, their principles are endless. For example, the number of water, when encountering metal, becomes strong; when encountering fire, it attains its proper position; when encountering wood, it yields; when encountering earth, it declines and dies. Its path has both obstructions and smooth passages. The other four phases are also like this. By combining numbers with each other and using them for divination, good and bad fortune cannot be concealed, and calamity and blessing have a fixed destiny, without the need to consult others. Therefore, the function of numbers lies in conforming to the Dao and understanding the principle of generation. To understand numbers is to understand generation, and to follow numbers is to follow the Dao. The principles it points out are subtle and essential, yet people are unwilling to study them, thus failing to comprehend the purpose of the sages' teachings. This is truly lamentable.

古時象數，悉本河圖、洛書，是為易象之源。河圖負於龍馬，洛書呈於文龜；皆天地自然之象數，而聖人則之以演易；蓋所由來者遠矣！在天成象，在地成文，天地之象數，即由天地自呈於人前；神道之感應，為人道所昭彰；固上世常見之事。以地天猶通，神人時契；人習於道，無不通神；則神亦降其靈，資人以智，發人以道，非可異也；故圖書出，而人文以創；

In ancient times, the images and numbers were all based on the Yellow River Chart and the Luo Writing, which are the origins of the hexagrams in the Zhou Changes. The Yellow River Chart was brought forth by a dragon horse, and the Luo Writing was presented by a tortoise with cultural markings; both are natural images and numbers of heaven and earth. Sages took them as models to deduce the Zhou Changes. Their origin is indeed very ancient. The Great Treatise says, "In heaven, images are formed; in earth, forms are created." The images and numbers of heaven and earth were originally presented before people by heaven and earth themselves. Thesympathetic response of the divine path was manifested through human ways, which was common in ancient times. At that time, the qi of heaven and earth could still communicate, and the divine and human were constantly in harmony. People were familiar with the Dao, so none could not communicate with the divine. Thus, the divine descended its clarity, giving people wisdom and enlightening them with the great Dao, which was by no means surprising. Therefore, with the emergence of the Yellow River Chart and the Luo Writing, human civilization was thus established.

天地之道見，而人道以明；人之有文化教育，皆始於天地自然之象數文章；雖神而明之，存乎其人；而溯源探本，則有所自矣！故圖書者，易象之袓；欲明易象，必明圖書；如木本水源，不得其故；則枝流莫可究詰，是以夫子曰：「五十學易」，言由圖書以窮象數也。天五地十，五十為天地中心；

The way of Heaven and Earth becomes evident, and thus the way of human beings becomes clear. Human culture and education originate from the images and numbers of Heaven and Earth's natural phenomena and their principles. Although the Great Treatise says "to grasp the subtle and make it clear, it depends on the person," when tracing back to the source and exploring the root, there is always a beginning. Therefore, the Yellow River Chart and the Luo Writing are the ancestors of the hexagrams in the Zhou Changes. To understand the hexagrams of the Zhou Changes, one must first understand the Yellow River Chart and the Luo Writing. This is like a tree having roots and water having a source; if one does not clarify its origin, then the branches and streams cannot be pursued. Therefore, Confucius said in the Analects, "At fifty, one begins to study the Zhou Changes," meaning one should start with the Yellow River Chart and the Luo Writing to investigate the images and numbers. The Great Treatise mentions "Heaven is five, Earth is ten," and five and ten are the centers of Heaven and Earth.

天之道由此見，人道由此立。故五十為圖書之中數，猶易之太極也；太極在數曰一，在位曰中；在性曰至善，在氣曰純陽；為無始之始，萬有之宗；老氏之天下之母，即指此也；而其大包無外，廣盡萬類；故屬天地之中，亦天地所自成也。

The heavenly way is thus revealed, and the human way is thus established. Therefore, the numbers five and ten are the central numbers of the He Luo diagrams, just like the "Taiji" in the Zhou Changes. In terms of number, Taiji is called one; in terms of position, it is called the center; in terms of nature, it is called ultimate goodness; and in terms of energy, it is called pure yang. It is the beginning without a beginning, the master of all existence. The thing referred to by the Tao Te Ching as the "mother of the world" is precisely this. It is vast without boundaries, pervading all categories, thus belonging to the center of heaven and earth, and also the source from which heaven and earth naturally arise.

數雖自一至九，而其宗則五與十；五十分列，則乾坤定位；五十合用，則大衍成形；故曰五曰十，或五十，皆數之本體，其化則用也；乾用九，坤用六，九六為乾坤之用；乾數極於九九，坤數包於六六；人之數七，艮也；其數盡於七七，此大衍之用四十九，指人道也；

The numbers range from one to nine, but their master is five and ten. When five and ten are separated, the positions of Heaven and Earth are established; when five and ten are used together, the form of "the great derivation of numbers" is formed. Therefore, speaking of five, ten, or fifty, all refer to the essence of numbers, while their changes are called "use." The Qian hexagram has "use of nine," and the Kun hexagram has "use of six," with nine and six being the numbers used by Qian and Kun respectively. The number of Qian is limited to eight十一 (81), while the number of Kun is confined to thirty-six. The number of humans is seven, associated with the Gen hexagram. The number of humans ends at forty-nine, which is exactly the forty-nine used in "the great derivation of numbers," referring to the human way.

天地之道，由人而明；天地之數，由人而用；故大衍之數，以七七為用；而天地之數在其中矣。合則成用，分則為位；交錯則變化生，乘除則盈虛見；而其本始，莫外乎圖書之數也。河圖、洛書之象數，為自然象數；易之象數，則本圖書而推其變化之象數也；易與圖書有同異；但天地象數，終不外圖書所有者；

The principles of heaven and earth can only be explained through human effort, and the numbers of heaven and earth can only be applied through human effort. Therefore, the "Great Derivation Number" uses 49, which is seven times seven, as its basis, and the numbers of heaven and earth are included within it. When combined, they achieve function; when separated, they form positions. Through their intermingling, change arises; through multiplication and division,盈亏 (excess and deficiency) become apparent. Their origin lies entirely in the numbers of the Yellow River Chart and the Luo Writing. The images and numbers of the Yellow River Chart and the Luo Writing are naturally generated images and numbers. The images and numbers of the Zhou Changes (I Ching), however, are derived from the Yellow River Chart and the Luo Writing and further developed to show their transformations. The Zhou Changes and the Yellow River Chart and Luo Writing share similarities but also differences. However, the images and numbers of heaven and earth ultimately do not go beyond the scope already contained in the Yellow River Chart and the Luo Writing.

至其變化，雖推之無盡，仍不能有違於圖書之例；則由天地生成之數定，不可越也；自上而下，則二五賦形，而萬物以生；自下而上，則萬有歸一；由形返神；故圖書之數始一終九，五十在中；而二氣五行備具。其化生萬物，則以用言；以二五互交，推演為數；所謂二五構精是也。

As for their transformations, although they can be deduced infinitely, they still cannot violate the principles of the River Chart and the Lo Chart. This is because the numbers of heaven and earth have already been determined and cannot be exceeded. Looking from above, it is the interaction of yin and yang and the Five Phases that give form to things, thus generating all things. Looking from below, all things return to one, and from form they return to the spiritual. Therefore, the numbers of the River and Lo Charts begin with one and end with nine, with five and ten in the middle, thus completing the yin and yang and the Five Phases. As for their generation of all things, this must be understood in terms of application: through the interaction of the two energies and the Five Phases, numbers are generated, which is called "the combination of two and five to form essence."

故其數陽五陰五，陽以順行，陰以逆行；相交以生，相剋以變；而孤陰獨陽，則不生不變；易以乾坤交用，坎離相制；以成生克，而形變化；由數之用言，則陽者，一三七九順行，始一終九，其位在西；陰者，四二八六逆行，始四終六，其位始於西北；陽以九終交陰六，故陽數用九；陰數用六，九六相終始循環以生成變化；而五十主於中央，為天地中極；萬物樞紐。

Therefore, among these numbers, there are five yang numbers and five yin numbers: yang progresses in a forward direction, while yin moves in a reverse direction; they generate each other through mutual interaction and change through mutual control; if there is isolated yin or solitary yang, it cannot generate or change. The Zhou Changes uses the interaction of Qian and Kun, and the mutual restriction of Kan and Li, to form generation and control, thus revealing change. In terms of the use of numbers, the yang numbers are one, three, seven, and nine, progressing forward, starting from one and ending at nine, with the endpoint in the west; the yin numbers are four, two, eight, and six, moving backward, starting from four and ending at six, with the starting point in the northwest. When yang reaches nine, the terminal number, it meets the yin number six, so the yang number uses nine; the yin number uses six. Nine and six connect at their ends, continuing in a cycle to complete the process of generation and change. The numbers five and ten are central, serving as the axis of heaven and earth, and the key to all things.

此圖書象數之大概，即為易所本者；乾之用九，坤之用六；即準河圖之陰陽數也。觀河圖所列之數，作為環形；則一三七九，由北而東而南而西；而四二八六，則自西北而西南而東南而東北；亦環而終始，唯五十在中焉。

That is the general idea of the two diagrams, the River Chart and the Lo Square, which form the basis of the Zhou Yi. The "All Nines" in the Qian trigram and the "All Sixes" in the Kun trigram are derived from the yin and yang numbers in the River Chart. If the numbers in the River Chart are arranged in a circular form, then one, three, seven, and nine run from north to east, east to south, and south to west; four, two, eight, and six run from northwest to southwest, southwest to southeast, and southeast to northeast, also forming a circular pattern that connects head to tail. Only five and ten are located at the center.

洛書亦然，不過其用有異，由方圓不同也；由北之一，東之三，則以接西之七，南之九，皆陽數也；其陰數，則西北六，東北八，西南二，東南四；亦由東南之四，西南之二，接東北之八，西北之六，相環以終始，正如河圖；而五在中焉，其不同者，圖屬先天，書屬後天；一體一用，一位一成，一位一時。故洛書之數，以相交而行；而河圖則相貫也。洛書之位，以東南與西北易數，而河圖則順逆依序也。

The Luo Shu is also arranged in this way, but its function differs because one takes the square and the other the circle. By connecting the number one from the north, three from the east, seven from the west, and nine from the south, these are all yang numbers. As for the yin numbers, they are six in the northwest, eight in the northeast, two in the southwest, and four in the southeast. These also connect from the southeast four and southwest two to the northeast eight and northwest six, forming a circular sequence that links the beginning and end, just like the He Tu. The number five is in the center. The difference between the two is that the He Tu belongs to the Earlier Heaven and the Luo Shu to the Later Heaven; one is about the main body, the other about application; one discusses position, the other discusses formation; one emphasizes direction, the other emphasizes sequence. Therefore, the numbers in the Luo Shu run across each other, while the numbers in the He Tu run in a straight line. The Luo Shu swaps the numbers between the southeast and northwest, while the He Tu follows its original order, proceeding in a straight line or in reverse.

河圖之數，本於天地生成之象；蓋自無入有，首為太極；一氣既動，兩儀以分；兩氣相蕩，五行以具；故河圖象之，其數自一至十；分為陰陽，陽奇陰偶，各得其半；而生化之本，必基於二氣之和；五行之分，即由於陰陽之變；其生化也，以一陰一陽相合而成；

The numbers in the Yellow River Chart are based on the image of the generation of heaven and earth. Heaven and earth began from nothingness to become something, and first there was the "Taiji" (Supreme Ultimate). When the single vital energy suddenly moved, the "Two Principles" (Yin and Yang) were divided. When the two energies interacted and clashed, the "Five Phases" were fully established. Therefore, the Yellow River Chart takes its image from this process: its numbers range from one to ten, divided into two categories, Yin and Yang. Odd numbers represent Yang, and even numbers represent Yin, each occupying half. The fundamental principle of generation and transformation must be based on the harmony of the two energies, Yin and Yang. The differentiation of the Five Phases comes from the changes of Yin and Yang, and their generation and transformation are all achieved through the mutual interaction of one Yin and one Yang.

乃於是數中，以陰合陽，以陽合陰；天生則地成之，地生則天成之；故一至五為生數，六至十為成數；生成二數，各居陰陽之半；如將籌比算之，自左設陽籌，右之陰籌；則左數為一三五七九，右數為二四六八十，左右各半也；更將其配合之，為左設生數，右設成數；則左為一二三四五，右為六七八九十，亦各半也；皆以相得而合，而後有物生焉。

Thus, among these ten numbers, yin is paired with yang and yang is paired with yin: what is generated by heaven is completed by earth; what is generated by earth is completed by heaven. Therefore, the numbers one to five are called "sheng shu" (generative numbers), and the numbers six to ten are called "cheng shu" (completed numbers); the generative and completed numbers each account for half of yin and yang. If we use counting rods as an analogy: place yang rods on the left and yin rods on the right, then on the left we have one, three, five, seven, and nine, and on the right we have two, four, six, eight, and ten, with each side accounting for half. Alternatively, if we arrange the generative numbers on the left and the completed numbers on the right, then on the left we have one, two, three, four, and five, and on the right we have six, seven, eight, nine, and ten, again each side accounting for half. Only when these are paired and harmonized can things be generated.

故自左之一陽，合右之六陰，而水生成；左之三陽，合右之八陰，而木生成；自右之二陰，合左之七陽，而火生成；自右之四陰，合左之九陽，而金生成；更餘陽之五，合陰之十，而土生成，此為五行生成之次序也。其生與成，恰為相當之位；故其數相得，如一居左首，六居右首；

Therefore, the yang number one on the left pairs with the yin number six on the right, and water is generated; the yang number three on the left pairs with the yin number eight on the right, and wood is generated; the yin number two on the right pairs with the yang number seven on the left, and fire is generated; the yin number four on the right pairs with the yang number nine on the left, and metal is generated; the remaining yang number five pairs with the yin number ten, and earth is generated. This is the order in which the Five Phases are generated. The generating and forming numbers are exactly in corresponding positions, so the two numbers match perfectly: for example, one is placed in the first position on the left, and six is placed in the first position on the right.

故恰相得，猶子與午對也；是為配偶之定例也。因其位相當，而數相得；始有合，而見其生成之功；此一六居北，二七居南；三八居東，四九居西；五十居中，以既合而後同居；亦如人之夫婦也。故其位之相配以次，數之相得以序；雖有一二之殊，卻非父子，而為兄弟，不得視為水生火也。

Therefore, they fit perfectly, just like the Earthly Branches "Zi" and "Wu" which are opposite to each other, this is the established pattern of pairing. Because their positions correspond and numbers match, there is a union, and thus the effect of generation is seen. Thus, one and six dwell together 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: they first match with each other and then dwell together, just like the "husband and wife" in human society. Therefore, the matching of positions has its order, and the matching of numbers has its sequence. Although adjacent pairs differ by only one or two numbers, they are not father and son, but brothers, and should not be regarded as water generating fire.

然五行之數，亦為二氣之量數；如一六為水生成數，亦即水之量數；以陽一陰六，為其分也。其所差五數者，繫以五之前為生數，即生氣；其氣能生不主成，而成氣必自五以下；猶之日與夜也，非至日落，不得為夜；以生氣未盡，不見成氣；故一必與六合，不能與二三四五合也；一六既合，其次則屬二與七；二為陰，七為陽；二屬生，七屬成；陽多陰少，乃為火之成分；亦如水之一六合也，以下皆同。

However, the numbers of the Five Phases are also the measures of the balance between yin and yang. For example, one and six are the numbers that generate water, which are also the numbers representing the quantity of water: yang accounts for one part, yin accounts for six parts, which is the ratio of its composition. The difference between them is five, because the numbers before five are called "sheng shu" or life numbers, which refer to life qi; life qi can only generate but not complete. The completed qi must be counted from five onwards. This is similar to day and night: until the sun sets, it cannot be called night; until the life qi is exhausted, the completed qi will not appear. Therefore, one must combine with six, and cannot combine with two, three, four, or five. Once one and six have combined, the next is two and seven: two belongs to yin, seven belongs to yang; two belongs to generation, seven belongs to completion; yang is more and yin is less, which is the composition of fire. This is the same principle as the combination of one and six. The following combinations are also the same.

蓋五行之數字，包括數義；一示陰陽之成分，一示生成之先後次序，一示五行之量數，一示二氣之分合總數，一示二五之化成原數也；其義甚廣，而無不相通；實天地間至數，不得移易者也；如天一地二，謂之為陽陰次序可，謂之為天地氣分量數亦可；論五行生成，則次序也；論五行成分，則量數也；論生成次序，兼示陰陽量數；而以紀二五之精氣所行，與天地之形氣所積，莫不一致。

The numbers of the Five Phases contain several layers of meaning: one refers to the proportion of yin and yang, another refers to the order of generation, another refers to the quantity of the Five Phases, another refers to the total amount of yin and yang qi, and another refers to the original numbers from which the Five Phases and the two qi energies were generated. Its meaning is very broad, and all these layers are interconnected. It is truly the most fundamental numbers in the universe, unchangeable and immutable. For example, the "Heaven one, Earth two" mentioned in the Great Treatise says it can refer to the order of yin and yang, or it can refer to the quantity of heavenly and earthly qi. In terms of the generation of the Five Phases, it refers to the order; in terms of the composition of the Five Phases, it refers to the quantity; in terms of the order of generation, it also indicates the quantity of yin and yang. Using it to record the movement of the refined qi of the two energies and the accumulation of the forms and qi of heaven and earth, it is entirely consistent.

故河圖總數五十五，即由一六、二七、三八、四九、五十、相加之積；其屬天者二十五，即陽數之積；為最清輕之神，故居上而名天；其屬地者三十，即陰數之積；為重濁之精氣，故居下而名地；其實一陰一陽耳。其所間所差者五，此為元氣之未化者，雖在天地之中，卻非五十五數之內；

Therefore, the total number of the Yellow River Chart is fifty-five, which is the sum of each pair: one and six, two and seven, three and eight, four and nine, five and ten. Among these, the twenty-five belong to heaven, which is the sum of the odd numbers, representing the clearest and lightest divine energy, hence it is placed above and called heaven. The thirty belong to earth, which is the sum of the even numbers, representing the heavy and turbid vital energy, hence it is placed below and called earth. In the end, it is simply the interplay of one yin and one yang. The five in the middle, which is the difference between them, is the original energy that has not yet been transformed. Although it resides in the center of heaven and earth, it is not included in the total of fifty-five.

蓋可以名而無名，可以數而無數；故為中氣，即陰陽之間所差之數，然先天初見生化，無序可紀，無量可數；有差而無差，有積而無積；蓋以陽陰之異，祇在動靜之間；原同一氣，因其動靜，而後有始數可知；然未遽定也，必待五行次第生成；五十五數確定之後，始知其屬天者幾，屬地者幾；不可以後天之數。名先天之氣。

It can be named but has no fixed name, and can be counted but has no fixed number, so it is called "the middle qi," which refers to the number between yin and yang. However, at the very beginning when the Earlier Heaven first began to generate and transform, there was no order to record and no measure to count. Saying it has a difference, it actually has none; saying it has an accumulation, it actually has none. The distinction between yin and yang lies only in the movement and stillness; originally they were one qi, and only through the difference of movement and stillness did the first numbers become known. Yet at that time, the numbers were not yet fixed, and it was only after the Five Phases were generated in sequence and the total of fifty-five was determined that we could know how much belonged to heaven and how much to earth. Therefore, we cannot use the numbers of the Later Heaven to name the qi of the Earlier Heaven.

先天祇一團渾然之氣，分之為二；始為兩儀，然無量可數也；其為量者，乃五行生成之後，因而量之，始有其名；當初生之時，祇宜名曰：一陰一陽之化合；一、一也，六、亦一也；二、一也，七、亦一也；推之二十五與三十，初無異量，皆屬同氣；不過既分已久，生成已見；其氣已化，其行漸成；而後前之一中，變為有數可紀，有量可量；

The Earlier Heaven was originally a single mass of undivided energy. When it was divided into two parts, it was called the "Two Principles" or "Two Powers." But at that time, there was no measurable weight or quantity. The concept of weight and measure came into being only after the Five Phases were generated, and then it was used to determine their names. In the very beginning, it should be called the combination of one yin and one yang: one is a whole, six is a whole; two is a whole, seven is a whole. By this logic, twenty-five and thirty also originally had no difference in terms of quantity, as they all belonged to the same kind of energy. However, as the separation continued over time, the manifestations became evident, the energy changed, and its movement gradually took shape. It was only then that the originally undivided whole began to have numbers that could be recorded and quantities that could be measured.

如一六既成水，始有水成分可言；蓋以陰陽之偏，遂生差異之數；如冷與熱，升降異也，輕與重，上下殊也；於是有量有數，可以別其為何物；而物則因之更生他物，氣亦因之更化異氣，此後天數有一定者也。要知先天後天之分，本無多異；異者一有定，一無定；一有名有形，有象有數，故有定；一無名無形，無象無數，故無定；

For instance, when one and the Six Harmony become water, it is then possible to speak of the composition of water. Because yin and yang are unevenly distributed, differences arise: just as cold and heat represent upward and downward distinctions, and light and heavy represent being above and below. At this point, there is weight and number, allowing us to determine what kind of substance it is. And substances give rise to other substances, while qi transforms into other qi. This is why the Later Heaven numbers have a fixed standard. To understand the difference between the Earlier Heaven and the Later Heaven, there is not much difference in essence; the difference lies only in one being fixed and the other being unfixed: those with name, form, image, and number are fixed; those without name, form, image, or number are unfixed.

而介乎先後天之間，為初見生化之跡者；則可有可無之間，或定或否之類也；其象數，以上言之，先天也；以下言之，後天也；故其象數可量而不可量，可紀而不可紀；此以在上下之中，有無之界；如數之一，如位之中，如物之極是也。河圖之數亦如是，其數屬後天之始，其象屬初生之物；其氣仍純，其數仍簡，乃能為一切之母；故天地數止於十，而積之成五十五；其中之五十二數，即代示五十全數；而最中之五，即代示先天之中氣；

As for the section between the Earlier Heaven and Later Heaven, where the traces of generation and transformation first appear, it lies between existence and non-existence, belonging to a category that is both definite and indeterminate. Its images and numbers, when spoken of in relation to the Earlier Heaven, belong to that realm, but when spoken of in relation to the Later Heaven, they belong to this realm. Therefore, this section of images and numbers can be measured yet cannot be measured, can be recorded yet cannot be recorded. This is because it lies exactly in the middle between above and below, existence and non-existence, just like the number 'one' in numbers, the center 'zhong' in positions, and the extreme 'ji' in things. The numbers of the Yellow River Chart are also like this: its numbers belong to the beginning of the Later Heaven, its images belong to the initial stage of things. The qi is still pure, the numbers still simple, thus it can serve as the mother of all things. Therefore, the numbers of heaven and earth only go up to ten, adding up to fifty-five; among these, the numbers five and ten represent the full count of fifty. And the central number five represents the central qi of the Earlier Heaven.

先天中氣，本無五名；而名之五者，即由後天之五也；後天之五，亦主眾物，居中央，與先天同；故以其名先天之中氣。且因天地各五數，其積之差亦五，而生成之中數亦為五，天地之中心亦為五；故五者先後天之中位，亦先後天之中極；五為至中數，由其序言之，命曰一；由其量言之，命曰五；由其位言之，命曰極；由其方言之，命曰中；皆此數也。

The concept of the central energy in the Earlier Heaven originally did not have the name "five." It was given the name "five" by borrowing from the Later Heaven's five. The five in the Later Heaven also governs all things and resides in the center, which is the same as the central energy in the Earlier Heaven. Therefore, it was used to refer to the central energy of the Earlier Heaven. Moreover, both the heavenly numbers and earthly numbers each have five, and the difference between their accumulated totals is also five. The middle number generated by the Five Phases is also five, and the center of heaven and earth is also five. Thus, five is the shared central position and central extreme of both the Earlier Heaven and the Later Heaven. Five is the most central number: in terms of sequence, it is called one; in terms of quantity, it is called five; in terms of position, it is called extreme; in terms of direction, it is called center. All these refer to the same number.

故五者賅先後天之氣數，而獨立於其中者；且通先天中氣，立後天中極；謂之先天可，謂之後天亦可；以在後天直名曰土，實則土應有三個五；今僅曰中五者，即暗指先天之中氣矣！先天中氣，本無可名，無定居，無定方，無定形，無定數；而以五名之，以土位之，則以後天為主也，然此中氣，先後天同，而舉土亦可以代示中氣；因在後天五行，皆依於土而後成形；若無土，即無水火木金之質可見；

Therefore, the number five encompasses the qi of both the Earlier Heaven and Later Heaven, and stands independently between them; it connects upwards to the central qi of the Earlier Heaven and establishes downwards the central point of the Later Heaven. It can be said to belong to the Earlier Heaven, or to the Later Heaven. In the Later Heaven, it is directly called "earth," but originally, earth should have three fives. Now, when we refer to it as "middle five," it is implicitly pointing to the central qi of the Earlier Heaven. The central qi of the Earlier Heaven was originally nameless, without a fixed dwelling, direction, form, or number; using "five" to name it and "earth" to place it is a statement based on the Later Heaven. However, this central qi is essentially the same in both the Earlier and Later Heavens, so using "earth" can also represent the central qi. Because in the Later Heaven, the five elements all rely on earth to take form; without earth, the forms of water, fire, wood, and metal could not manifest.

是五行必賴土以成物，亦猶人物必賴中氣以為生；其義同也。如河圖中五，視為後天之數，則屬五行土之生數；若視為先天之氣，則屬中極之氣；故由河圖一變為洛書，僅留此中五不移；由河洛一變為八卦，則連此中五亦隱；所謂：「易無體」，即隱此中五；而將土之成數，暗附於四方，與洛書同；此皆示中極之地，為先後天中氣所在；而先後天所以變，而不離其宗；生化，而不失其本；皆賴有此中五也。

It can be seen that the Five Phases must rely on earth to accomplish all things, just as human beings and objects must rely on the central qi to survive. The principle is the same. For example, the number five in the center of the Yellow River Chart, if regarded as the Later Heaven number, belongs to the earth's generating number among the Five Phases; if regarded as the Earlier Heaven qi, it belongs to the central vital qi. Therefore, when the Yellow River Chart transforms into the Luo Writing, only this central five remains unchanged. When the River and Lake diagrams transform into the Eight Trigrams, even this central five disappears. The passage in the Great Treatise says, "The spirit has no fixed form and the Book of Changes has no definite body," where "no definite body" refers to hiding this central five and secretly assigning the earth's completed number to the four directions, following the same method as the Luo Writing. All this shows that the place of the central vital point is exactly where the central qi of the Earlier Heaven and Later Heaven lies. The reason why the Earlier Heaven and Later Heaven can change yet not depart from their origin, can generate and transform yet not lose their essence, is entirely due to the presence of this central five.

故天地之差止五，而大衍與天地之積之差亦五；此五彼五，與先天之中氣，後天土之生數，皆二而一也；能通而一之，始能明生化之源，造化之機；天人之道，道器之途；莫不豁然貫通焉！夫子講義，特提出此五，以為讀者告，其旨至深切矣！

Therefore, the difference between the numbers of Heaven and Earth is exactly five, and the difference between the "Great Derivation Number" and the total numbers of Heaven and Earth is also exactly five. The five here and the five there, together with the central qi of the Earlier Heaven and the generating number of Earth in the Later Heaven, may seem different, but they are actually the same thing. Only by integrating them can one understand the origin of generation and transformation, and the key to creation and change; the principles of Heaven and humanity, as well as the path of Dao and objects, will then all become clear. Confucius deliberately emphasized this number five in his teachings, with a very profound intention.

先天之氣，無形無名，因其動靜而後生成五行；故生之數五，成之數五，合為十；猶先天之一也。先天之一分為十，又分為陰陽各半；更由其生成次序，分為生成各半；故生之初為一屬陽，其次為二屬陰；其次為三為四為五，以奇偶而分屬陰陽；皆生之數也，然生者初見之氣，必賴成者而後成物；

The primordial qi is formless and unnamed, but because it has movement and stillness, it gives rise to the Five Phases. Therefore, the numbers of origin are five, and the numbers of completion are also five, making a total of ten. This ten is still the original "one" of the Earlier Heaven. The original one divides into ten, which then splits into yin and yang each comprising five. Following the order of generation, the numbers of origin and completion each make up half. Thus, the first to emerge is one, belonging to yang; the second is two, belonging to yin; then three, four, and five, which are divided between yin and yang according to their odd and even nature. These are all numbers of origin. However, what is called "generation" is merely the initial qi, which must rely on "completion" in order to form actual things.

故初成者六，屬地陰；其次七，屬陽；其次八九十，亦以奇偶而分陰陽，其次序恰與生數相得；故一與六合，二與七合，三與八合，四與九合，五與十合；而其生或成，亦以陰陽各得其一為序；故一六為水，則陽生而陰成之；二七為火，則陰生而陽成；其下木金亦然。至五與十，又屬陽生陰成；則陽占生者多之，陰居成者眾；以此為後天生化之大則，即必先陽而後陰也。

Therefore, the first to be formed is six, which belongs to the earth and is yin; next comes seven, which belongs to yang; then eight, nine, and ten follow, each assigned to yin or yang according to their odd or even nature, and their order exactly matches the sequence of the generating numbers. Thus, one combines with six, two with seven, three with eight, four with nine, and five with ten. Whether in generation or formation, the order is always that yin and yang each take one position: one and six are water, with yang generating and yin forming; two and seven are fire, with yin generating and yang forming; the same applies to wood and metal. As for five and ten, they are also yang generating and yin forming. In this way, yang predominates in the 'generating' aspect, while yin predominates in the 'forming' aspect. This becomes the great principle of the later heaven's transformation and generation, which necessarily follows the order of yang first and then yin.

此生成之次序共五，而陰陽不等，其意實為深微；果將此中數提出，而不與四方之數並列，則陰陽始平。土雖為五行之一，且居生成之終；卻能獨承先天之氣，而為後天之根；其兼備五行之數，合陰陽之德者，實有自也；故自五行生成之後，其數已定，其量始明；而其為二氣之差，亦恰此五；因其兼備先後天之氣，而包含陰陽之德；恆能齊所不齊，足所不足；而在後天之五，等於先天之元氣；

The sequence of generation consists of five groups, yet the numbers of yin and yang are not equal, and the intention behind this is profound and subtle. If the central group of numbers is taken out and not placed among the four directions, then yin and yang will be balanced. Though earth is only one of the Five Phases and is placed last in the sequence of generation, it alone can receive the qi of the Earlier Heaven and becomes the foundation of the Later Heaven. It is able to encompass the numbers of the Five Phases and conform to the virtues of yin and yang, which has a definite reason. Therefore, after the Five Phases have been generated, their numbers are already determined, and their proportions become clear. The difference between the two qi of yin and yang also corresponds exactly to this number five. Because it encompasses the qi of the Earlier and Later Heavens and includes the virtues of yin and yang, it is able to harmonize the uneven and make up for the deficiency. The number five in the Later Heaven is equivalent to the original qi of the Earlier Heaven.

作陰陽之中樞，物所資生，人所資育，初無限量；故在河洛之象，獨以之置於中央，而不與他數並列。且陰逆陽順之序，他數皆易其次，獨中五之次不移；明其為後天之極，即先天之精也；以數量言，屬後天者，本有多寡之殊，輕重之別；在先天則無殊無別，以皆一氣也；

It serves as the central axis of yin and yang, through which all things are generated and humans are nurtured. It has no limits. Therefore, in the diagrams of the Yellow River Chart and the Luo Writing, it is placed alone in the center, not listed together with other numbers. Moreover, in the order where yin moves against and yang moves in accordance, other numbers change their positions, but the central number five remains unchanged. This indicates that it is the ultimate point of the Later Heaven, which is also the subtle essence of the Earlier Heaven. In terms of quantity, those belonging to the Later Heaven have distinctions of more and less, light and heavy; but in the Earlier Heaven, there are no distinctions, since they are all the same kind of qi.

後天之異，而必求其同，則亦唯此五是賴；其所差者亦恰是此五數，果欲齊其不齊，足其未足，亦唯以此劑之；此由後天觀測者也，苟明乎五行生成，原由二氣之有多寡輕重；若其無也，則所生同一物矣！故所生之異，在乎數之不同；而其不同，即所差之五。

In the Later Heaven, differences have already arisen, yet one must seek unity within these differences, which can only be achieved through the number five. The difference between them is precisely this number five. If one wishes to harmonize the uneven and make up for the lacking, it can only be done by using this number five to adjust. This conclusion is drawn from observing the Later Heaven. To understand the generation of the Five Phases, we must recognize that they arise from the interaction of yin and yang energies, which vary in quantity and weight. If there were no such variations in quantity and weight, then only one thing would be produced. Therefore, the reason different things are generated is due to differences in number, and this difference is exactly the number five.

如以此中五調劑之，固可齊一；此係後天之例。以一陰一陽，而後為道。故河洛之後，變為大衍；其數始齊，若在河圖，猶陽少陰多；變為洛書，則陰少陽多；皆不齊。待易大衍，截長補短，而成各半之數；然大衍與河洛所差，亦皆此五數；以其恰合於中數，為陰陽之樞；故少則可加之。多則可減之；以歸於齊一。若其它數，則不得加減之也；

If we use this central five to adjust, it could make everything harmonious, which is the usual practice in the Later Heaven. It is necessary for yin and yang to be paired, only then can it be called the Dao. Therefore, after the Yellow River Chart and the Luo Writing, it became the "Great Derivation Number," and the numbers became complete. In the Yellow River Chart, there is still more yin than yang; when it became the Luo Writing, it turned into more yang than yin: neither is balanced. It is only when the Great Derivation Number of the Zhou Changes adjusts by taking from the long and adding to the short that the numbers become equal, with equal parts of yin and yang. However, the difference between the Great Derivation Number and the numbers of the Yellow River Chart and the Luo Writing is also this five. Because it exactly matches the central number, being the pivot of yin and yang, it can be added to when there is a deficiency, or subtracted from when there is an excess, thus achieving harmony. If another number were used, it could not be adjusted so freely.

河圖之數，原象也；洛書之數，變象也；大衍之數，例象也；言為後天生化之例，包含天地之數，而得陰陽之平者也；故日：大衍。衍者，演也；與古道字術近，即一陰一陽之謂道，由此而演其用，以明生化之例耳；故齊者，人齊之；演者，人演之；以便於推算耳。如歷之制閏，與歲月相齊也。

The numbers of the Yellow River Chart represent the original forms, while the numbers of the Luo Writing represent changing forms. The "Great Derivation" numbers represent the principles of regulation. By "principles of regulation," it means that it serves as the general rule for the later heaven's generation and transformation, encompassing the numbers of heaven and earth and achieving the balance of yin and yang. Therefore, it is called "Great Derivation." "Derivation" refers to deduction and inference, which is similar to the ancient usage of the term "Dao." This is the meaning of "One yin and one yang is called Dao" from the Great Treatise: by deducing its function, it is used to clarify the principles of generation and transformation. Therefore, when it says "alignment," it refers to the human making it aligned; when it says "derivation," it refers to the human deducing it. This is done for convenience in calculation, just as the calendar sets intercalation months to align the seasons with the years and months.

且大衍之數雖五十，而用則四十九；此中妙義，亦多未知；蓋本於象也。五十之象，雖陰陽各半；而其中一數，為二者共有；亦中數也。故用數止四十九，以陰陽分別數之，則各得二十五；若合數之，則各止二十四又半；故其用祇宜於合，不宜於分；苟分用時，則當更減去一數；即中數之一。而各二十四，於是陰陽之數始平均；

Furthermore, the "Great Derivation Number" is fifty in total, but only forty-nine is actually used. The profound meaning behind this is not well understood by most people. In fact, it is based on symbolic representation. The number fifty, although seemingly representing yin and yang each taking up half, includes one number that is shared by both yin and yang, which is the central number. Therefore, the number used in practice is forty-nine. If yin and yang are counted separately, each gets twenty-five; but when counted together, each only has twenty-four and a half. Therefore, its use is more appropriate when combined rather than divided. If it is to be used separately, one should subtract the central number, which is one, so that yin and yang each have twenty-four, making the numbers balanced.

若一歲之月十二，氣侯二十四；以合日之行度，而月之三旬，有晦朔望上下弦，亦見月光者，止二十四日；上半月十二日，下半月十二日；為得日照時，餘日則無光；是陽之合於陰，亦止二十四，與陽之度數同；雖河圖象陰陽之數，共五十五；而至大衍之用，僅四十九；及其分用時，則止四十八；此由先天易為後天數之差也。

For example, a year has twelve months and twenty-four solar terms, used to correspond with the sun's movement. Within a month, there are three ten-day periods, with new moon, full moon, and the waxing and waning phases. Only twenty-four days in a month actually have moonlight: twelve days in the first half and twelve days in the second half, when the moon is illuminated by the sun. On other days, there is no light. This shows that yin and yang combine to form only twenty-four days, matching the measure of yang. Although the Yin-Yang numbers represented by the Yellow River Chart total fifty-five, in the actual process of the Great Derivation, only forty-nine are used. When they are further divided, only forty-eight remain. This is precisely the numerical difference caused by the transition from the Earlier Heaven to the Later Heaven.

其差者，因欲齊其不齊，足其未足；故恆截長補短，以劑於平；此後天之數，以平為歸；而陰必後陽，天必包地；日必先月，女必順男；此皆後天一陰一陽之道，由河圖變易而來者。河洛之數，則異乎是；天地之數不齊，陰陽之象各異；為其初化，各物未具；數量猶混，不如後天之朗然若定；規然不移者也。

This is why there are these differences; it is to adjust the uneven, to supplement the deficient, so that things may be balanced by taking from the long to make up for the short. The later heaven numbers aim at balance, so yin must necessarily follow yang, heaven must necessarily encompass earth, the sun must necessarily precede the moon, and women must necessarily obey men. All these are the principles of yin and yang in the later heaven, derived from the changes in the Yellow River Chart. The numbers of the He Luo are different: the numbers of heaven and earth are not uniform, and the images of yin and yang differ. At that time, things had just begun to take form, and all things were not yet complete, so the numbers and measures were in a confused and undifferentiated state, unlike the clear, definite, and fixed numbers of the later heaven.

故在河圖之時，一六同級，二七等觀；三八如鄰，四九若親；五十為偶，皆自相得；不多不少，而以成其五行也；若既生成五行，次序已明，數量以定；始得其所差，而辨其數；再因其中數，而求其齊；於後天陰陽之道始明，生化之機乃定；故自河圖一變為洛書，再變為大衍；其數同而不同，與自太極兩儀四象八卦之變易，其例正同；八卦定而後後天之象見，大衍用而後後天之數明；

Therefore, in the stage of the Yellow River Chart, one and six are placed on the same level, two and seven are treated equally, three and eight are like neighbors, four and nine are like close relatives, and five and ten are paired as spouses. Each pair is matched appropriately, neither too many nor too few, thus forming the Five Phases. When the Five Phases have already been generated, their order is clear, their numbers fixed, then their differences can be discerned, and their quantities can be distinguished. Then, by relying on the central number, unity can be achieved. At this point, the principle of later Heaven yin and yang becomes clear, and the pivot of generation and transformation is established. Therefore, from the Yellow River Chart, it changes into the Luo Writing, and then into the "Great Derivation Number," whose numerical appearance seems the same but is actually different. This is consistent with the evolution from "Taiji" to "Two Principles," then to "Four Symbols," then to "Eight Trigrams." Only after the Eight Trigrams are established does the image of later Heaven appear; only after the Great Derivation Number is applied does the number of later Heaven become clear.

本末始終，各有所紀；通而一之，推而化之；則數不盡數，象不盡象；是在精研其自來，而貫澈其有無耳。至於五行之生成，與夫先天元氣之初化；何以如是生成？及天地之數，何以分生與成。是皆造化之階，為自無入有經歷之級；其理微，其義深；初非一二言所可盡，茲就大略言之：夫先天之氣，光明純潔，密緻剛健；凝然不動，晶然透澈；本無可名，無可形；

The beginning and the end, the root and the branch, each have their own records; when they are connected as a whole and extended with transformation, the numbers are not limited to the existing ones, and the images are not confined to the present ones. The key lies in carefully studying their origins and thoroughly understanding their existence and non-existence. As for how the Five Phases are generated, how the original qi of the Earlier Heaven first came into being, why it takes precisely this form of generation, and why the numbers of heaven and earth are divided into birth numbers and completed numbers, these are the steps of creation, the stages from nothingness to experience, whose principles are subtle and meanings profound, not something that can be fully explained in a few words. Now I will briefly explain. The qi of the Earlier Heaven is bright, pure, dense, strong, still, clear and transparent, originally nameless and indescribable.

乃因含有熱性，溫氣氤氳，光流渾圓；以成其動，動則氣搖；先熱乃布，布則氣分；於是渾圓者漸漸變化，光明者漸漸暗然；此由動而生變，即由一而成兩之機也。故無極而太極，直一氣之轉移；動則有靜，陰陽始分；陰為陽化，陽為陰復；二者相施，兩儀乃判；其始判也，一陰一陽，猶甚純簡；以旋迴之故，交合乃成；故陰陽漸離，其氣時接；此則四象之漸成也。

Because it contains warmth, the warm energy becomes diffused and misty, with light flowing smoothly and circularly, thus creating movement. Once movement begins, the energy begins to stir and fluctuate. The warmth spreads out first, and once it spreads, the energy differentiates. Thus, what was originally round and unified gradually begins to change, and what was originally bright gradually turns into darkness. This is the process of change caused by movement, which is the beginning of transformation from one into two. Therefore, the transition from "wuji" (formless) to "taiji" (primordial energy) is merely a transfer of the same energy; when there is movement, there must be stillness, and thus yin and yang become distinct. Yin arises from yang, and yang arises from yin, and the two alternate and interact, leading to the division of "liang yi" (two principles). At the moment of their initial division, yin and yang were still pure and simple. Due to their rotation and intermingling, they combine to form a union, and thus yin and yang gradually separate, yet their energies constantly connect: this is the process by which the "si xiang" (four images) gradually take shape.

其太陽太陰，全然兩儀之象，是為水火之生；太者，言其大也；然非純陰陽也，以各得其多者為名；故水為天生地成，火為地生天成；斯為兩儀之後，四象之初；太陰太陽之所象也。繼之者，則少陽少陰，亦出於兩儀；而其所得者少，所成者弱，是為木與金；此木亦天生地成，金亦地生天成；四者既具，生成之氣未盡，於是土乃成焉。故土者、生成之末，而備兩儀之精；全後天之象；接先天之氣；此其生成之序也。然亦非如此簡單者，蓋氣蕩無停，精流不見；生機既啟，成數斯應；

Among them, "Taiyang" and "Taiyin" fully inherit the image of the two principles, and what they generate are water and fire. The term "Tai" means that they possess a large share. However, they are not purely yin or purely yang; they are named according to the principle that dominates more. Therefore, water is born of heaven and formed by earth, while fire is born of earth and formed by heaven. This is the essence represented by Taiyin and Taiyang, which comes after the two principles and before the four images. Then come "Shaoyang" and "Shaoyin," which also originate from the two principles, but they possess a smaller share and weaker force, resulting in wood and metal. Wood is born of heaven and formed by earth, while metal is born of earth and formed by heaven. Once these four elements are in place, the generating qi has not yet been fully exhausted, so earth is subsequently generated. Thus, earth comes last in the order of generation but encompasses the essence of both principles, completing the Later Heaven image and receiving the qi of the Earlier Heaven. This is the order of their generation. However, the actual situation is not so simple: qi is constantly stirring and never ceasing, while the essence flows continuously and invisibly; once the vital force is activated, the numbers of generation respond accordingly.

天生於上，地乃應之；地生於下，天乃應之。以兩儀初分，力足精強，行走至速，各含生機，均有成德，此生彼成。如電與雷，不差毫黍。其分之為氣者十，生成各半，以與陰陽奇偶，相見而合。故水之生於陽也，而陰成之；火之生於陰也，而陽成之，其所應至捷也。

Heaven's energy first arises above, and Earth responds below; Earth's energy first arises below, and Heaven responds above. This is because when the two principles were first divided, the energies of yin and yang were strong, pure, and vigorous, moving very quickly, each containing the function of growth and each possessing the virtue of completion. Therefore, when one side begins to arise, the other side immediately completes it, as swift as lightning and thunder following each other without the slightest delay. The energies derived from the two principles total ten numbers, with the "generative numbers" and "completing numbers" each taking up half, exactly matching the odd and even numbers of yin and yang to combine. Thus, water is generated by yang energy but completed by yin energy; fire is generated by yin energy but completed by yang energy—when one side begins to arise, the other side's response arrives immediately.

然陽者，所生必陰；陰者，所生必陽。陽者下，而陰者上；陰者熱，而陽者涼；皆以動而變，得其反也。故天動生水而流於地，地乃成之；地動生火而炎於天，天乃成之。皆氣變自然而合，初無為之序，而自成序也。

However, what is produced by yang must belong to yin, and what is produced by yin must belong to yang. Yang is originally above, yet the water it produces flows downward; yin is originally below, yet the fire it produces rises upward. Yin is naturally cold, yet fire is hot; yang is naturally hot, yet water is cool. This is because once the qi is activated, it must change, and the result of this change is precisely its opposite. Therefore, when heaven activates, it produces water, which flows down to the earth, and the earth completes it; when the earth activates, it produces fire, which rises upward to the heaven, and the heaven completes it. All these are the natural transformations of qi that then come together. Initially, there was no one to arrange an order, yet an order naturally formed.

水火既生，其氣已弱，故木為陽之微，金為陰之微，氣自至焉。生成既眾，強弱皆見；精復其始，德返於初。於是土乃生成，而得氣獨全，以其值氣之復也。土生於天，成於地，與先天初生同，而土質厚德凝，為後天萬有之本。其氣全，其數中，此五行所獨有者，亦萬物所同母。

After water and fire have been generated, the sharpness of the two energies has already weakened, so the wood that comes next is merely a faint remaining yang energy, and metal is merely a faint remaining yin energy. This is the natural decline of energy. When the number of generated elements has become numerous, the differences in their strength become apparent, and the refined energy returns to its original state, while the virtue reverts to its source. At this time, earth is generated, receiving a complete energy, because it coincides with the moment when the energy returns to its original state. Earth is generated by heaven and formed by earth, which is the same as the original way of generation in the Earlier Heaven. However, earth has a heavy quality and a concentrated virtue, becoming the fundamental basis for all existence in the Later Heaven. Its energy is complete, and its number is in the center — this is unique to earth among the Five Phases, and it is also the common mother of all things.

故其用周於天地，利於四行；雖在生成之終，卻居後天之首，乃位中央而數中極。此其生化之妙，有非人之所能知；而後天生化無窮，莫不本於此土者，其得氣固不同也。先天生化之序，至土而止；而後生化之功，自土而成。是為先後始終之樞，恰當道器上下之紐，其為此世界之所貴者，自過於一切矣！

Therefore, the function of earth extends throughout heaven and earth, and it can benefit the four other elements, water, fire, wood, and metal. Although it comes last in the order of generation, it holds the first position in the Later Heaven, located in the center, and occupies the middle number. The subtlety of this process of generation and transformation is not something humans can fully comprehend. Yet the process of transformation in the Later Heaven is endless, and nothing is not based on earth, because the qi it receives is fundamentally different from the other four elements. The order of generation in the Earlier Heaven ends with earth; the function of transformation in the Later Heaven begins with earth. Thus, earth becomes the hub connecting the Earlier Heaven and the Later Heaven, linking the beginning and the end. It is precisely situated at the junction between the ultimate principle of "Dao" and the physical "qi" of things. Its value in this world naturally surpasses all others.

故先後天之生化次序，均不同也，而皆以土為貫通之機。舍土則不獨後天之生化不成，既先天之生成，亦無由竟其用。故言後天與先天同異，必自土溯其根源；此天地萬物，莫不依土而後生存變化也。

Therefore, although the sequence of generation and transformation in the Earlier Heaven and the Later Heaven differ from each other, both take earth as the key element connecting the two ends. Without earth, not only can the transformation in the Later Heaven not be completed, but the generation in the Earlier Heaven also cannot fully realize its function. Therefore, whenever one discusses the similarities and differences between the Later Heaven and the Earlier Heaven, one must trace back to earth as the root. All things in heaven and earth depend on earth to exist and to change.

五行之氣，水本太陰，而根於陽；火本太陽，而根於陰；以所生之屬與所成異也。故水火木金，皆陰體陽用，陽體陰用；唯土則兼陰陽體用，以得氣全也。氣始動為陽生陰，既復則仍返於陽；氣之初行，為陰隨陽，既定則仍抱於陰。

In terms of the Five Phases, water originally belongs to 'Taiyin' but its root is in the yang; fire originally belongs to 'Taiyang' but its root is in the yin. This is because the aspect that generates it and the aspect that completes it belong to different energies. Therefore, the four phases of water, fire, wood, and metal all have yin as their substance and yang as their function, or yang as their substance and yin as their function, with substance and function on opposite sides; only earth possesses both yin and yang as its substance and function, because it receives a complete energy. When the energy first begins to move, it is yang that produces yin; when it returns, it still reverts to yang. When the energy first starts to flow, yin follows yang; when it becomes stable, it is still embraced by yin.

土之生成數，雖有陰陽，而五則備二氣；十又五之倍，亦陽之所用。故其體用兼二氣，以為後天之母，四氣之長。五行雖分，莫不依土而生變化；是土者，直二氣之精，五行之本，萬物之源也。按之易卦，以艮為土，故曰：「成始成終」。以居先天生成之終，為後天生化之始；在後天卦位，艮與坤對，在連山易序，艮為首位，即洛書之象。二八易位，亦以艮坤相易，以明後天之土代地之用，為生化之本也。

The numerical values associated with earth, known as the generating number five and the completing number ten, also belong to yin and yang—five is yang and ten is yin. However, the number five itself already contains both yin and yang energies. Since ten is a multiple of five, it also belongs to yang. Therefore, earth possesses both yin and yang energies in its nature and function, making it the mother of all things in the later heaven system and the master of the four seasons. Although the five elements are divided into five, none of them can change without earth. Thus, earth is the essence of yin and yang, the foundation of the five elements, and the origin of all things. According to the hexagrams of the Book of Changes, the hexagram Gen is associated with earth. Therefore, the Commentary on the Hexagrams refers to Gen as the hexagram of "beginning and end." This is because Gen is at the end of the sequence of generation in the earlier heaven system, and also the beginning of generation in the later heaven system. In the later heaven hexagram positions, Gen and坤 are opposite each other. In the sequence of the Linked Mountains Changes, Gen is the first hexagram, which corresponds to the image of the Luo Writing. In the Luo Writing, the numbers two and eight have exchanged positions, which also corresponds to the exchange of Gen and坤. This indicates that in the later heaven system, earth has taken over the role of the earth element, becoming the fundamental source of all generation and transformation.

夫艮卦屬土，而異於坤之地也，乃能代坤之用，履地之位；其因氣之異，德之充也。在先天艮為山象，居西北隅；在後天則移東北，與坤對位，而其原位為乾所居。明後天之土，即先天之坤，足與天同功，與地同德，此連山易所以推為首也。後天之艮，當坎震之交，明生化之源；其成萬物終始者，即以其能代地而配天也。故艮在後天，非僅山之象，實土之總名也。

The Geng hexagram, although belonging to the earth element, differs from the Kun hexagram representing the earth. Because of this difference, it is able to take on the role of Kun and occupy the position of the earth. This is due to the distinct nature of the qi it possesses and its fullness of virtue. In the Earlier Heaven arrangement, Geng takes the image of a mountain and occupies the northwest corner. However, in the Later Heaven arrangement, Geng moves to the northeast, facing opposite the Kun. Its original position in the northwest is taken by the Qian hexagram. This shows that the earth in the Later Heaven is actually the Kun of the Earlier Heaven, capable of sharing the function of heaven and the virtue of the earth. This is why the Linked Mountains Changes places Geng as the first hexagram. In the Later Heaven arrangement, Geng is located at the junction of Kan and Zhen, indicating the source of generation. It is able to accomplish the beginning and end of all things because it can both replace the earth and harmonize with heaven. Therefore, in the Later Heaven, Geng is not merely a symbol of a mountain, but the general term for earth.

既以山言，亦對海洋而論，以出海面也。故其代地之德，多見於陸，而其象繫大陸也。因地之用，有陸水之別；而土之德，則見於陸；即水亦陸所載所防，而後成其用也。故五行之水，受制於土；而八卦之坎，與艮連居；其義至深切矣。

Since "mountain" is used to represent the trigram Gen (Geng), then mountain is also relative to the ocean, because mountain rises out of the sea surface. Therefore, the virtue displayed by Gen in place of earth is mostly manifested on land, and its image is actually the continent. The function of earth originally has a distinction between land and water, and the virtue of soil is only manifested on land; even water needs land to carry it and to build dikes before it can fulfill its function. Therefore, in the Five Phases, water is restrained by soil; in the Eight Trigrams, the position of Kan is adjacent to Gen—this meaning is extremely profound.

土之在後天，實為一切主，無論何物，莫不因地以為生化；即空中之氣，亦附於地面而後殖；其它有形之物無論矣！凡生在天地間者，無能離土以存以變；不獨人物之生也，即植物等或無生之物，亦必賴土以存以變。此可以見土之德，為造化之本源所寄，亦即氣數之根株所在；故土之數五，實為萬數之基。

In the Later Heaven, earth is indeed the master of all things. Whatever exists, whether it is something tangible or intangible, depends on the earth for its growth and transformation; even the air in the sky needs to rely on the ground to flourish and multiply, let alone other physical substances. All things existing between heaven and earth cannot exist or change without the earth. This is not only true for humans and animals, but also for plants and even inanimate objects. Therefore, the virtue of earth is the place where the origin of creation is entrusted, and it is the root of both qi and numbers. Hence, the number of earth is 'five', and this five is indeed the foundation of all numbers.

而足通天地之用，為人物之權衡；是五者，等於一，言其用廣，而能通一切數也。在河圖證之，一六居北，二七居南，三八在東，四九在西，五十處中；四方之數，均仰中央，而其差皆此五；已可見此中數所寓，即中氣所存。

The number five is sufficient to encompass the functions of heaven and earth, becoming the standard for measuring people and things. Saying 'five equals one' refers to its wide range of applications and its ability to integrate all numbers. Using the Yellow River Chart as evidence: one and six are 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. The numbers of the four directions all depend on the center, and the difference between each pair of numbers in the directions is exactly five. From this, it is evident that the number in the center embodies the essence of the 'central vital force'.

又以陰陽順逆言之，一三七九，由北而西；四二八六，由西反北；兩者循環，以相終始；五獨居中，以運其樞，不隨之移易。十以二五，亦同在中，皆氣之妙用，數之妙合也。故陰數皆逆，而十不動；由先天之本序言，則二四六八應為次，今以行之逆，故變四為首，六為終。

Looking at the progression and retrogression of yin and yang: the yang numbers one, three, seven, and nine move from the north to the west in sequence; the yin numbers four, two, eight, and six move from the west back to the north in reverse. They cycle continuously, mutually marking the beginning and end. Only the number five remains in the center, rotating as the central hub, not shifting with the numbers of the four directions. Ten is two fives, so it also remains in the center. These are the subtle workings of qi and the harmonious combination of numbers. Therefore, although the yin numbers generally move in reverse, the number ten remains stationary. Following the original order of the Earlier Heaven, the yin numbers should be arranged as two, four, six, and eight in sequence; but because they move in reverse, they now start with four and end with six.

六者為陰數始終之數，在成數為始，在用數為終。陽始一終九，陰始四終六；展轉相合，皆為五；亦即中數所寄，中氣所存也。一四同行，至九六相交；莫非五數，以明中氣之無不通也。五行之數，固如上述；先天後天各殊，即其方位，亦有此異。當五行之初見於數也，雖有南北東西之分，實則所指屬虛空之象。如以中國論，自當北為水，南為火，木居東，金居西，而土在中央；若合天下言之，則有不然。

Six is the number that combines both the beginning and the end within the yin numbers. In the "cheng shu" (completed numbers), it comes first, but in the "yong shu" (used numbers), it comes last. The yang numbers start from one and end at nine, while the yin numbers start from four and end at six. When these are paired together, the result always relates to the number five—adding one and four gives five, and adding nine and six gives fifteen, which is still a multiple of five. This is the place where the central number is embodied and where the central qi (vital energy) resides. The yang number one and the yin number four begin together and continue until nine and six meet, with no point failing to conform to the number five, showing that the central qi is present everywhere. The numbers of the Five Phases are as described above. The Earlier Heaven and Later Heaven differ, and so do their directions. When the Five Phases first appeared in terms of numbers, although they were assigned to the directions north, south, east, west, and center, they actually referred to the atmospheric phenomena in the void, not to specific places on the earth. If we consider China specifically, the north is associated with water, the south with fire, the east with wood, the west with metal, and the center with earth. But if we consider the whole world, this may not necessarily be the case.

蓋赤道南，則反其寒熱方位矣！此理原易明，蓋所云方位者，為其氣之所宜也。今以土為本，土之所在，當以大陸屬之。則凡赤道以北，大陸為多，而南則少；故當以北溫帶為中央，而順是以次南北焉。若果赤道南之大陸，則正與北反，即宜以南之北，當北之南，而反其五行之位。

Because in the southern hemisphere, the positions corresponding to cold and heat are exactly reversed. This principle is not hard to understand: what is meant by direction refers to the suitability of the qi, not to fixed directions on a map. Now that we take earth as the foundation, the place where earth resides should be considered as the continent. Since there is more land in the northern hemisphere than in the southern, the north temperate zone should be regarded as the center, and then the south and north should be determined accordingly. If we are discussing the continent in the southern hemisphere, the situation is exactly opposite to that in the northern hemisphere. Therefore, the northern part of the southern hemisphere should be regarded as the southern part of the northern hemisphere, and the five elements' directional arrangement should be completely reversed.

蓋河圖五行，本無定方，僅有定位。上火下水，左木右金；若在北溫帶，則下為北，上為南；若移南溫帶，則下為南，上為北。此固就所居地而定，不過水與火對，金與木配，乃不易耳。更推言之，水雖居北，而中國北方皆陸；火雖在南，而中國南方多水；東方亦為水居，西方則多高地；是即按之吾國，亦難以物質求之。

The Five Phases listed in the Yellow River Chart originally had no fixed directions, only fixed relative positions: fire is above, water is below, wood is to the left, and metal is to the right. If one is in the Northern Temperate Zone, the bottom of the chart would correspond to north and the top to south; if moved to the Southern Temperate Zone, the bottom would correspond to south and the top to north. Although directions depend on the location, the relationship that water and fire are opposite, and metal and wood are compatible, remains unchanged. Going further down: although water is said to be in the north, China's northern region is mostly land; although fire is said to be in the south, China's southern region is actually water-rich; the east is where the sea lies, while the west is mostly highlands and mountains. This shows that even when checking against China's geography, it is difficult to confirm the specific substances corresponding to the Five Phases' directions.

況水雖屬陰，而根於陽；火雖屬陽，而根於陰；是寒熱亦未盡水火之體用。木在山多，金出水內；東海無森林之地，西陲少金石之丱；則東西以配木金，亦非一定之理。故五方雲者，乃就氣而言；就先天之氣言，與一歲所合同；初非一一按之實物也。

Moreover, water though belonging to yin has its root in yang, and fire though belonging to yang has its root in yin. This shows that using only the terms cold and hot is insufficient to fully explain the nature and function of water and fire. Trees often grow on mountains, and metal is commonly found in water; the eastern sea area has no forests, and the western frontier has few mineral deposits. Therefore, associating the east with wood and the west with metal is not an unchanging principle. Hence, the concept of the five directions is based on qi, specifically the qi of the Earlier Heaven, which corresponds with the seasonal changes of cold and heat. Originally, it was not intended to match each direction with specific physical objects.

不然，春溫秋涼，冬寒夏熱，皆氣之變耳；物或隨之或否，不得以物執其說也。然若謂此言無定，而不信五行之說，則不可，蓋五行正同於二氣，無地無時不見之，其分別亦至明晰。如水之流下，火之炎上，與春夏之溫熱，秋冬之涼寒，皆一定不移者。雖至何地何時，仍可驗者；故其分別，得氣之殊，成象之異；實有至理，毫無可疑，不過學者宜會通其意，勿泥其辭。

If we do not look at it this way, then the warming in spring, cooling in autumn, severe cold in winter, and extreme heat in summer would merely be changes in qi; specific things may change with it or not, and we cannot rigidly apply this theory to individual things. However, if we reject the theory of the Five Phases simply because their positions are not fixed, that would be wrong. The Five Phases are just like yin and yang; they are present everywhere and at all times, and their distinctions are very clear. For example, water always flows downward, fire always rises upward, spring and summer are always warm and hot, and autumn and winter are always cool and cold. These are all unchanging; they can still be verified anywhere and at any time. Therefore, the Five Phases have distinct differences because they are influenced by different kinds of qi and form different appearances. There is real principle here, without any doubt. The scholars should understand its meaning thoroughly and not be stuck to its literal words.

貫徹其精，勿執其表；則天地之大，日月之明；山川之遙，草木之庶；無不可候其氣數，而得其類別也。故言五行，重在其生化之功，而探研生克之理；以求其象數，通乎天道耳。近世科學漸已近於是理之討論，果假以時日，讀吾中土之書，精以求精，自有會歸一途之日；

To grasp its essential meaning, one should not be fixated on its superficial aspects. In this way, the vastness of heaven and earth, the brightness of the sun and moon, the remoteness of mountains and rivers, and the abundance of grass and trees, none of these would be beyond the ability to perceive their qi and numbers, thus determining their categories. Therefore, when discussing the Five Phases, the key lies in understanding their function of generation and transformation, and then exploring the principles of mutual generation and mutual control. Through this, one can seek out their symbolic representations and numerical patterns, connecting them to the heavenly way. Modern scientific discussions have gradually approached this principle; if researchers continue to study our traditional texts with diligence and refinement, they will eventually reach the same conclusion through different paths.

蓋五行之說，乃古人探本生化之源；格物致知，窮理盡性；通天地鬼神之道，立人生修養之方；順吉凶禍福之常，為日用起居之則；固與科學之義同，初非惝況無據之談，迷離莫詰之論。故中國一切文物制度，無不准是而成；人倫綱紀，世道規範；以及醫卜之技，言行之箴；政教所成，禮法所制；初無不由是而出，所謂規法是也。

The theory of the Five Phases is originally a study by ancient people to trace the origin and investigate the fundamental principles of generation and transformation. It is like the saying in the "Great Learning" that "investigate things to gain knowledge," and like the saying in the "Book of Changes · Explanation of the Trigrams" that "exhaust the principles and fully understand the nature," it connects the principles of heaven and earth and spirits, establishes methods for personal cultivation, follows the regularities of good fortune and misfortune, and sets guidelines for daily life. This is fundamentally consistent with the purpose of science, and is not mere empty talk without foundation or obscure and indeterminate metaphysical speculation. Therefore, all cultural and institutional practices in China were established according to this principle: human relationships and social order, moral standards, as well as medical and divination techniques, guidelines for speech and action, achievements in politics and education, and the formulation of rites and laws—all originated from this—this is what is called "rules and standards."

如天文之軌度，地理之紀程；各有規矩方圓，以應乎二五氣數；故欲深通古時文化，必先自易探索；而易之仿始河洛圖書，以準天地之道，明鬼神之德；其精義入神，初非言文所盡；今所論者，尚其大略耳；望世之讀者，更由是以深求之；庶乎有通於古，有造於今；而不獨中國文化之得傳，無負聖人之教矣！

For example, the measurements of celestial orbits and the methods of recording distances on earth each have their own rules and standards, used to correspond with the principles of yin and yang and the numbers of the Five Phases. Therefore, to deeply understand ancient culture, one must first start with the Book of Changes to explore its principles. The Book of Changes was modeled after the Yellow River Chart and the Luo Writing, used to accurately grasp the way of the heavens and earth's movement, and to clarify the virtues of the transformations of ghosts and spirits. The subtle and profound aspects of it are not fully expressible through words and texts. What is discussed today is only a general overview. I hope that readers of the world will pursue further understanding from here, so that they can both comprehend the ancients and benefit the present generation. In this way, not only will Chinese culture be passed down, but also the earnest efforts of the sages in establishing teachings will not be in vain.

又曰：天地之間，萬物並生；而所憑者，多在地土；則以土為後天生化之母，備五行之氣，而為兩儀之所合化也。其德全而用宏，居中而運眾；雖天之高，星辰之遠；日月之明，風雨之降；寒暑之往復，關於天時氣候者，若不在地；而莫不自地見其用也。

It is also said that all things grow together in the space between heaven and earth, and most of them rely on the earth. This shows that the earth is the mother of all things generated in the Later Heaven, possessing the energies of the Five Phases. It is formed from the union of the two principles. The earth's virtue is complete and its functions are great, residing in the center and governing all things. Although heaven is high, the stars are far away, and the brightness of the sun and moon, the falling of rain and wind, the coming and going of cold and heat, these are all phenomena of heaven and climate, which seem not to be on the earth. Yet none of them can manifest their effects without the earth.

地者，萬物之中樞；為一切氣數之機衡，生變之爐冶；而人亦隨之生長死沒，至於無窮；故後天之土，雖居五行之末，實策生化之源。而本數則五，故其用亦五；以五應天，則天數成，此十乾之為二五也；以五應時，則時令備，此歲序之分為五時也。

The earth is the central hub of all things, the mechanism and scale for the movement and transformation of qi and numbers, the furnace where generation and change occur. Humans also grow and die in accordance with it, in an unending cycle. Therefore, although the Later Heaven's earth element is placed last among the Five Phases, it actually controls the source of generation and transformation. The number of earth is five, so its application follows the number five: using five to correspond with heaven, the numbers of heaven become complete, which is why the ten heavenly stems are divided into two fives; using five to correspond with the seasons, the sequence of the year becomes complete, which is why the annual cycle is divided into five periods.

在地則有五方，在人則有五臟；在行則有五德，在聲則有五音；在色則有五色，在味則有五味；凡由天地人物生化之物，接觸之事；莫不以五類別之。則以氣之所成，數之所至，莫不本於土，而同為五行之象也；五行雲者，言氣之運行無息，而有度也；故五行之位定，而方無定。

On the earth there are five cardinal directions: southeast, northwest, center, and the four cardinal directions. On the human body there are five internal organs: heart, liver, spleen, lung, and kidney. In terms of moral virtues, there are five virtues: benevolence, righteousness, propriety, wisdom, and faithfulness. In terms of musical tones, there are five tones: palace, commercial, angle, zheng, and yu. In terms of colors, there are five colors: green, red, yellow, white, and black. In terms of flavors, there are five tastes: sour, bitter, sweet, pungent, and salty. All things generated by heaven and earth, and all matters encountered, are classified using the number five. This is because the formation of qi and the limits of numbers all have earth as their foundation, and they all represent the manifestations of the five phases. The term 'five phases' refers to the continuous movement of qi without cessation, and the movement follows its own order. Therefore, the positions of the five phases are fixed, but the directions they correspond to are not fixed.

言五者氣自消長，不居一方，而其本位則不易也。如水流下，火炎上，其不變也；若以其所在言，則無定；如水可居山之高原，火可入地之洞穴；其所異者，水不能炎上，火不能流下，以非其性也。故五方之地，恆隨土而定，初非必南火而北水也；且方位者，本天空而言；以皆氣也，不可以形論；故天空之氣，流行不息，而五行隨之。

This passage explains that the Five Phases have their own natural rise and decline, and they are not fixed in any one direction. However, their inherent positions remain unchanged. For example, water naturally flows downward and fire naturally rises upward, and this is constant. But the specific locations where they are found are not fixed—water can be on a high mountain plateau, and fire can be in a cave beneath the earth. What truly cannot change is that water cannot rise upward and fire cannot flow downward, as that would contradict their nature. Therefore, the five directional regions are always determined by the presence of earth, and it is not necessary for the south to always belong to fire or the north to always belong to water. Moreover, the concept of direction is based on the sky; since they are all forms of qi, they cannot be determined by physical forms. The qi in the sky flows continuously, and the Five Phases follow its movement.

如人身之氣也。人身雖以五臟配五行，心居上而賢居下，肝居左而肺居右，脾在中央；一如河圖之位，但考其實非定也。蓋所配者氣之流行，用之主管，非謂物質之偏處一方，不相涉也；故一身之中，氣血周流，無處不至；則五藏之氣，循環全體，無部不連；故曰五行，而不曰五物；正以其運行不定方，非物之可擬也。

This is similar to the vital energy in the human body. Although the body uses the five internal organs to correspond with the Five Phases—heart above and kidney below, liver on the left and lung on the right, spleen in the center—this is exactly like the directions in the Yellow River Chart. However, upon closer examination, this correspondence is not fixed. What is actually being matched is the movement of energy and the functions it governs, not that each organ is fixed in one position and does not interact with others. Therefore, in the body, the vital energy and blood circulate throughout, reaching everywhere; the energies of the five internal organs circulate throughout the entire body, with no part left disconnected. That is why it is called the Five Phases rather than the Five Things, because its movement has no fixed direction and cannot be compared to tangible objects.

其歲時聲色等，雖分五類，恆有兼體；氣之所至，體用見焉；故五行之名，亦大略耳。按之佛經，則為四大；地水火風，分屬一體；其象同於易之四正。而地當土，風當木，合之水火，似少金位。然風亦作氣解，與乾金同德；且佛以金剛為佛體，而西方為佛土；是其以金為至堅至淨，非色非空，正與純陽之乾同象；則四大之外，仍有金也。合之中國河圖之象，易卦之位，小異大同。此可以廣五行之解，而證五位之說也；蓋佛生印度，未聞中國之學；而言若是，足見五行之分類，實造化自然生成，非古人為之名也；故五行之說，通於一切，而其德用，尤推於無窮也。

As for things like seasons, sounds, and colors, although they are divided into five categories, they often coexist with each other. Where the energy flows, both the form and function manifest there. Therefore, the term "Five Phases" is merely a general classification. Comparing it with Buddhist scriptures, Buddhism speaks of the "Four Great Elements": earth, water, fire, and wind, each belonging to a single entity. Their corresponding images are equivalent to the four cardinal trigrams in the I Ching. Among them, earth corresponds to soil, wind corresponds to wood, and adding water and fire, it seems that metal is missing. However, "wind" can also be interpreted as air, which is similar to the metal quality of the Qian trigram. Moreover, Buddhism uses "diamond" to symbolize the Buddha's essence, and the west is considered the Buddha's land. This shows that Buddhism regards metal as something extremely firm and pure, neither material nor empty, which corresponds exactly to the pure yang nature of the Qian trigram. Therefore, even outside the four great elements, there is still metal. When combined with the imagery of the Yellow River Chart and the trigram positions of the I Ching, differences may exist in minor aspects, but the overall meaning is the same. This broadens our understanding of the Five Phases and confirms the concept of the five positions. The Buddha was born in India and had not heard of Chinese learning, yet his teachings coincidentally align with this. This clearly shows that the classification of the Five Phases is naturally generated by the universe, not an arbitrary name invented by ancient people. Therefore, the theory of the Five Phases can unify all things, and its virtues and functions extend infinitely.

要知五行之分，固在氣之分合，生化之原質；而其用則在於生制之性，以後天生化，非二氣之合，不能成其生；非二氣之變，不能成其化；五行之性，有生有制，而後見其功用。故水遇土則塞，遇火則克，遇金則悅，遇木則竭；金火土木亦然，各有所生，有所制；則各有所愛，有所畏；於是展轉推衍，以盡其性，而成其德。

To understand the distinctions of the Five Phases, it is essential to recognize their differences in terms of the division and combination of qi, and their original material for generation and transformation. However, their function lies in the two properties of "mutual generation" and "mutual control." Because the later heaven's transformation requires the combination of yin and yang energies to achieve "generation," and the movement of these two energies to achieve "transformation." The Five Phases have both generating and controlling properties, and their functions are thus revealed. Therefore, water meets earth and is blocked, meets fire and is controlled, meets metal and is harmonious (since metal generates water), and meets wood and is dried up. Metal, fire, earth, and wood are also each able to generate and control others, thus each has what it loves and fears. In this way, they are continually extended and developed, fully expressing their inherent nature, and thus achieving their respective virtues.

於是萬物以生以育，以化以滅；循環往復，莫可究詰；於是造化之功見，而世界以立；為盛衰因果，繁枯消息；以竟二氣分合之用，而達天地生成之德；皆由此生制而來者也。故其氣往來不息，其數乘除不盡；其為萬物稟受之本，生死之機；禍福吉凶之源，妖祥順逆之則；無鉅細、遠近、多少、美醜、之倫類，必皆緣此以為例；無賢愚、老幼、動靜、之性情，必皆因此以為範；故天地以之成度，人物以之成紀；世界以之成用，宇宙以之成法；神鬼以之成德，形氣以之成行；上下今古，精粗鉅細，咸在其生制之中。

Thus all things are generated, nurtured, transformed, and extinguished, cycling endlessly without end; thus the function of creation and transformation becomes evident, and the world is established. All the causes and effects of prosperity and decline, the waxing and waning of flourishing and withering, are accomplished through the interaction of the two energies of yin and yang, expressing the virtue of the generation and transformation of heaven and earth—everything comes from the mechanism of mutual generation and mutual control. Therefore, this energy flows ceaselessly, and this system of numbers and calculations is endless. It is the fundamental principle received by all things, the pivot of life and death, the source of fortune and misfortune, good and evil, and the standard for strange phenomena and auspicious signs. Whether large or small, near or far, much or little, beautiful or ugly, all must follow this principle. Whether wise or foolish, old or young, active or still, all must follow this model. Thus heaven and earth operate according to this measure, human beings follow this code, the world functions through this, the universe establishes its law, spirits and ghosts achieve their virtue, and form and energy move according to this. All things above and below, past and present, refined and crude, great and small, are all encompassed within this mechanism of mutual generation and mutual control.

而後數命以成，氣象以明；智者察之，以為通道；愚者順之，以為安生；聖人著其象於卦，示其用為易，以立為教，而詒天下後世，是易之所述，本於河圖；而其所擬，莫外於五形生制之例；此凡習易者所當先知也。

With this system, numbers and destiny could take shape, and the principles of qi and phenomena could become clear. The wise observe it to understand the great way; the dull follow it to settle their livelihoods. The sages recorded its phenomena in the hexagrams and demonstrated its applications in the Book of Changes, establishing it as a teaching for moral cultivation and passing it down to future generations. Therefore, what the Book of Changes discusses originates from the Yellow River Chart, and what it imitates does not go beyond the principles of the Five Phases and their generating and overcoming relationships—this is what all those who study the Book of Changes should first understand.

蓋易之卦，雖始為八，終為六十四；而其本，則兩儀也，五行也，及其分合與生制也。故卦有性，不外陰陽；卦有德，不外水火木金土；卦有用，不外五行生制；二氣分合，以此卦象全演自河圖者。而卦納甲、納音、納辰、各例，尤為推五形之制，而盡其用；本二氣消長，而竟其功；至詳且明也。此習易必先習河洛圖，而明卦必先明納甲、納辰，納音者，良有以也。

The hexagrams of the Book of Changes, although they began with eight and eventually developed into sixty-four, fundamentally rely on the two principles, the Five Phases, and their interactions of mutual generation and mutual control. Therefore, hexagrams have a nature that does not go beyond yin and yang; they have a virtue that does not go beyond water, fire, wood, metal, and earth; and they have a function that does not go beyond the mutual generation and mutual control of the Five Phases and the division and combination of the two principles. This shows that hexagram images are entirely derived from the Yellow River Chart. The systems of "Najia" (纳甲), "Nayin" (纳音), and "Nachen" (纳辰) in hexagrams, especially in the process of exploring the constraints of the Five Phases and exhausting their applications, follow the waxing and waning of the two principles to fully implement their functions, explaining things in a very detailed and clear manner. Therefore, studying the Book of Changes must first study the Yellow River Chart and the Luo Writing, and understanding hexagrams must first understand Najia, Nachen, and Nayin. This is for a very good reason.

五行生剋之理，由於氣之分合；氣有消長，則用有生殺；以後天生萬物並生，必有所制；否則獨亢，反生為害；故有制使之不亢，而後成其生化。如水得土，則無泛溢之害；火得水，則無焚燎之災；而後水火之用見，利多而害少，故物得其益；此造化之妙用，亦本氣自然者也。

The principles of mutual generation and mutual control among the Five Phases arise from the division and combination of qi. Qi has both decline and growth, so its effects have both creation and destruction. In the Later Heaven, all things grow together, but there must be some regulation; otherwise, one aspect would become overly dominant, turning what was beneficial into a disaster. Therefore, there must be control to prevent excess, only then can generation and transformation be achieved. For example, water is contained by earth, thus avoiding flood disasters; fire is restrained by water, thus avoiding burning calamities. In this way, the functions of water and fire become evident, bringing more benefits and fewer harms, and all things thus gain advantage. This is the subtle workings of nature, and also the natural state of qi itself.

河圖之象，以當相生者相接，相剋者相對；而明其承制之義。知其對偶，非仇則愛；蓋相當不讓則仇，相得有合則愛；即以剛柔為辨也。剛遇剛則仇，柔遇剛則愛；故其承制，皆以相剋而成其用；如水與火，木與金，皆得其所制為助；以其克之，所以助之；雖抑其勢，實成其道；故相對若仇，而相得為婚；其成生化，全在於此。

The imagery of the Yellow River Chart arranges the mutually generating pairs adjacent to each other and the mutually controlling pairs opposite to each other, to indicate the meaning of "continuation and restraint." It is evident that any pair of opposites is either mutually hostile or mutually harmonious: when forces are equal and neither yields, they become hostile; when they complement each other and work well together, they become harmonious. The criterion for distinguishing between these is the quality of hardness and softness. Hardness meeting hardness leads to hostility, while softness meeting hardness leads to harmony. Therefore, the relationships of continuation and restraint are all achieved through mutual control: for example, water and fire, wood and metal, all benefit from the presence of the element that restrains them. It is precisely because they restrain one another that they actually help each other; although they suppress each other's strength, they actually enable each other's development. Thus, although opposites appear as enemies, when properly balanced they become partners—this is the reason why generation and transformation can take place.

故五行之運用，必合其生克之情而後見；河圖如是，卦象亦然；八卦之位，亦以對偶承制而盡其用。甲子亦如是。故子午卯酉，分合水火木金之位；而甲丙庚壬四剛亦如之，皆以相接相對，各成生克之用者也。

Therefore, the practical application of the Five Phases must take into account both mutual generation and mutual control. This applies to the Yellow River Chart as well as to the trigrams: the eight trigrams are positioned based on mutual opposition and mutual restriction, thereby fully expressing their functions. The heavenly stem and earthly branch combination Jiazi is also the same. Thus, the earthly branches Zi, Wu, Mao, and You each occupy the positions of water, fire, wood, and metal respectively, and they pair and combine with each other. Similarly, the four heavenly stems Jia, Bing, Geng, and Ren, which are all strong and yang, also rely on their adjacency and opposition to achieve the effects of mutual generation and mutual control.

五行之名固有定，其氣仍時通；故其用時相為助，而成其生成之數，亦恆以為用；如內經等書，以數紀用是也；在水火木金，多取地數；土則取天數，亦以其獨異也；土之生數五，成數為二五；生數實賅成數，而五又中數；故獨取之以明其用，其旨實深矣！

The names of the Five Phases are fixed, but their energies are always interconnected. Therefore, in practical applications, they often assist each other, thus achieving their respective generating numbers, which are also frequently used. Works like the Yellow Emperor's Inner Canon use numbers to record the applications of the Five Phases. For the four phases of water, fire, wood, and metal, the earth numbers are usually taken; for earth, the heavenly numbers are used, because earth is inherently unique. The generating number of earth is five, and the forming number is two fives (i.e., ten). In fact, the generating number already includes the forming number, and five is also the central number. Therefore, using a single five to indicate its application contains profound meaning.

易傳曰：「易有太極，是生兩儀，兩儀生四象，四象生八卦。」此言易卦所自始也。易卦有八，而本於四象之分。四象者：太陽、太陰、少陽、少陰也。陰陽太少，雖有四象，而本於兩儀之化。兩儀者陰陽也。陰陽雖有兩儀，而本於太極之所生。太極者至極也。言天地萬物莫不有始，始於太極。由下而溯其源，至斯已極，故曰太極。

The *Great Treatise* of the *Commentaries on the *I Ching* says: "The *I Ching* has the Supreme Ultimate, from which the two principles arise; the two principles give rise to the four images; the four images give rise to the eight trigrams." This passage explains where the *I Ching* hexagrams originate. The *I Ching* has eight trigrams, but its origin lies in the differentiation of the four images. The "four images" refer to the Sun, the Moon, the Lesser Yang, and the Lesser Yin. Yin and Yang each have a major and a minor aspect, so although they form four images, they are rooted in the transformation of the two principles. The "two principles" are Yin and Yang. Although Yin and Yang are divided into the two principles, they are rooted in the Supreme Ultimate. The term "Supreme Ultimate" means the ultimate limit. This means that all things in heaven and earth have a beginning, and this beginning is the Supreme Ultimate. If we trace its origin upward, we reach this point, hence it is called the "Supreme Ultimate."

言無極也。太極之始，陰陽未分，兩儀未生，純然一氣，精神光明，為無始之始，無生之生。真體圓靈，氣周道凝，德至玄玄，神至冥冥，光合息醇，悠然至清，不可物擬，不可言名，名之太極。立生之根。此太極之象，為自無之有，太初之母，萬有之宗，一氣之原也，故曰太極。

Speaking of "Taiji" is equivalent to speaking of "Wují." In its initial state, yin and yang had not yet been differentiated, and the two principles had not yet emerged; it was simply a pure mass of qi: spirit and light, an origin without beginning, a birth without origin. Its true nature is perfectly round, subtle, and profound. The qi flows continuously while the Dao gathers together; virtue reaches the level of being profoundly mysterious, and spirit reaches the depth of being obscure and unfathomable. Light and qi combine to rest and nourish in a thick and pure manner, remaining tranquil and extremely clear, beyond the ability of any specific thing to compare, and beyond the ability of words to name. Therefore, it iswith difficulty called "Taiji." It establishes the root for all life. This is the image of Taiji: moving from non-existence to existence, it is the mother of the primordial beginning, the master of all things, and the origin of a single qi, hence it is called Taiji.

言其至極，無可上進，無可分移，而不得以名稱，以象類者也。夫天地萬物，同斯氣也，同斯生也，同斯運行不息也，同斯有守有立也，而皆太極始。以太極能生也，有始也，運行不息也，守中立極不二也，故為天地萬物之母，氣數之祖，生成變化之大本也。言其遠不可知，言其可知，則太極而已；言其外不可名，言其可名，亦太極而已。天地尚自太極生成，況其下者乎。故欲窮生化之源，氣數之根，必自太極始。太極者固萬有之宗，而言易必以太極啟其端也。

It is called "the Ultimate" because there is nothing higher to reach, and it cannot be further divided or moved. Therefore, it cannot be named or classified by objects. Heaven, earth, and all things are all composed of this qi, all originate in this way, all operate ceaselessly, all hold on and establish themselves in this manner, and all begin with the Taiji. Since Taiji can generate, has a beginning, operates ceaselessly, maintains the center and the ultimate, and remains consistent, it is the mother of heaven and earth and all things, the ancestor of qi and numbers, and the great root of generation and transformation. If we speak of something distant, it is unknowable; if we speak of something knowable, it is Taiji. If we speak of something external, it is unnamed; if we speak of something named, it is still Taiji. Even heaven and earth originate from Taiji, so how much more so everything beneath heaven and earth? Therefore, to investigate the origin of generation and transformation, and the root of qi and numbers, one must necessarily begin with Taiji. Taiji was originally the sovereign of all things, so when discussing the Book of Changes, one must necessarily start with Taiji.

易之始也，伏羲之一畫，即太極也。為體一，為氣純，無數之可紀，無象之可象，而紀之以一，象之以一，言數之始象之初也。故易之卦象，即自一始，蓋示太極者也。太極之為象，雖僅此一畫，其氣雖純，而有動靜之用；其精雖凝，而有生化之功；其初雖一，而其既動則有所生，既生則有所變。

The beginning of the Book of Changes (Yi) is the single line drawn by Fuxi, which is the Taiji. In terms of its essence, it is one; in terms of its qi, it is pure. It has no number to record it and no form to represent it, yet it is recorded with the number 'one' and represented with the image 'one', signifying the beginning of numbers and the initial form. Therefore, the hexagrams of the Yi begin with 'one', precisely to represent the Taiji. Although the Taiji as an image is only this single line, and its qi is pure and unified, it contains the functions of movement and stillness; although its essence is settled and definite, it contains the functions of generation and transformation; although it starts as one, once it moves, something is generated, and once generated, there is change.

故一之動也而二生，靜也而一復。一者為陽，二者為陰，兩儀乃生焉。兩儀者太極之初變也。太極以氣之動靜，精之生化，動者自生，靜者自化，生者為陰，化者為陽。陰陽既分，其氣斯變。前之一者變而二矣，前之太極者變而兩儀矣。故易自太極生兩儀。然兩儀雖生自太極，非如後來之生化有父母也，乃自至極之元氣動盪而生。

Therefore, when "one" moves, it gives rise to "two," and when it is still, it returns to "one." "One" belongs to yang, "two" belongs to yin, and thus the two principles (yin and yang) are generated. The two principles are the first transformation of the Taiji. The Taiji, through the movement and stillness of qi, and the generation and transformation of essence, naturally produces the moving aspect and the still aspect; the produced aspect is yin, and the transformed aspect is yang. Once yin and yang have been separated, qi then changes accordingly. The original "one" becomes "two," and the original Taiji becomes the two principles. Therefore, the Book of Changes (Yi Jing) originates from the Taiji generating the two principles. However, although the two principles arise from the Taiji, they do not have a father and mother as in later generations of generation and transformation, but rather arise from the movement within the ultimate primordial qi itself.

因其有動則有靜，動靜異也。異則有別，而後生化見也。雖生化而仍由一氣之變，非生自二氣也；雖化而成兩儀之名，其始仍為一體也。故曰易有太極是生兩儀。言兩儀之生，生自一氣，而兩儀未生之前，固渾然一太極也。是生雲者，言自是始生也。明示兩儀之生，為生化之初始；而太極之變為兩儀，實生化之初見其用，以溯天地生成之本，人物化育之源也。

Because there is movement, there is stillness; movement and stillness are different from each other. Differences lead to distinctions, and thus the process of generation and transformation becomes evident. Although it is called generation and transformation, it is still merely the movement of a single qi, not arising from two separate qis. Although it is said to produce the concept of "two principles" (liang yi), it was originally a single whole. Therefore, the Great Treatise says, "The Book of Changes has the Supreme Ultimate (Taiji), from which the two principles (liang yi) arise." This means that the generation of the two principles comes from the movement of a single qi, and before the two principles were generated, the Supreme Ultimate was originally a unified whole. The phrase "is born from" indicates the beginning of this process. It clearly tells us that the generation of the two principles is the first step in the process of generation and transformation; and the transformation of the Supreme Ultimate into the two principles is the first manifestation of the process of generation and transformation, from which we can trace back to the fundamental origin of the heavens and earth and the source of the transformation of human beings and creatures.

故曰是生。凡古文是字有自此作始之義，且言其本能也。世界生物，莫不自陰陽之和生化，唯兩儀始生，則太極之一氣所化。由其有動靜，動靜亦陰陽也。不過一氣之動靜，而成兩體之陰陽。老氏所謂一生二者即指此也。夫太極之初，固渾然元氣，無形無質，無色無象者也。然以其元氣，有其光焉。光生熱，熱生動，動則有生。光者元氣之體，熱與動者，元氣之用，生者用之見也。

Therefore, it is said, "It comes into being." In ancient texts, the character "是" always implies "beginning from here," and also indicates that this is its inherent ability. All living things in the world come into being through the union of yin and yang; the only exception is the initial emergence of the two principles, which arose from the qi of the Taiji by itself. Because it contains movement and stillness, and movement and stillness themselves are yin and yang. When a single qi moves and stills, it becomes the yin and yang of two forms. What the "Dao De Jing" refers to as "one gives rise to two" is precisely this. Originally, the Taiji was a pure, undifferentiated qi, without form, substance, color, or image. Yet since it is qi, it has light; light gives rise to heat, heat gives rise to movement, and once there is movement, there is generation. Light is the essence of the original qi, heat and movement are its functions, and "generation" is the manifestation of these functions.

元者仁也。仁之德，以生為用，故元氣以生化為本。動而有生，生而陰陽出。此元氣自然之德，流行不息，而後陰陽之象，往復無窮。一生永生，一化眾化，而天地以成，人物以育。生之化之，日益以盛，固元氣之德所見，亦造化之功所徵者也。

"Yuan" is "Ren." The virtue of Ren is characterized by nurturing and generating, so the essence of Yuan Qi is fundamentally about generation and transformation. Once there is movement, there is generation, and once there is generation, yin and yang emerge. This is the natural virtue of Yuan Qi, which flows continuously, and thus the phenomena of yin and yang recur endlessly. Once generation occurs, it continues forever, and once transformation takes place, it produces countless transformations, thereby forming the heavens and earth, and enabling humans and things to be nurtured and developed. This continuous generation and transformation, growing more prosperous day by day, is clearly the manifestation of Yuan Qi's virtue, and also the proof of the workings of creation and transformation.

故太極者，主生化之樞，為天地萬物之母；而溯世界之初始，則固來自渾然之一氣也。是曰氣化。氣化作始，形化繼之。既有陰陽，則生化者自二氣之和合而後成。故有兩儀，乃生四象；有四象，乃生八卦。即猶河圖自二氣而生五行，洛書自五行而變九宮。老氏所謂二生三、三生萬物者是也。

Therefore, the Taiji controls the fundamental mechanism of generation and transformation, serving as the mother of all things in heaven and earth; if we trace back to the original beginning of the world, it originally came from a single, undifferentiated qi. This stage is called "qi transformation." Once qi transformation begins, "form transformation" follows. Since there are already yin and yang, all subsequent generation and transformation depend on the harmonious combination of the two energies. Therefore, with the two principles (two yi), the four images (four xiang) arise; with the four xiang, the eight trigrams (bagua) emerge. This is analogous to the Yellow River Chart (He Tu), which arises from the interaction of yin and yang qi to produce the Five Phases, and the Luo Writing (Luoshu), which arises from the Five Phases to form the nine palaces. The statement in the "Laozi" that "two produce three, three produce all things" refers precisely to this process.

陰者承陽，陽者包陰，二氣環行，乃見生成，此亦氣之自然，數之自合者也。故易之卦象，自□之象，生□與□之兩儀，更生□□□□之四象，更由是推之，而生□之八卦焉。皆氣數自然化合而生成者，而其自出則太極也，即一也。圖而象之，則為O，此示渾然之氣也。以其既具動靜也，則為□，示已生兩儀也。世傳之圖，有末盡合，應以此二圖為則：一圖則太極之象，純淨光明；二圖則動靜生陰陽之象，黑白環抱。如是可見太極之體，及所兩儀之象也。

Yin follows Yang, and Yang encompasses Yin; the two energies circulate and intermingle, and the function of generation becomes apparent. This is the natural result of the energies and the natural harmony of numbers. Therefore, the hexagrams of the Book of Changes originate from the single line of the Taiji, producing the two principles of Yang and Yin; from these two principles, the four images of the sun, the lesser Yin, the lesser Yang, and the greater Yin are generated; and from these, the eight trigrams are derived. All of these are naturally formed by the combination of energies and numbers, and their origin is the Taiji, which is simply 'one'. If we draw a diagram to represent it, the Taiji is a clear and empty circle, symbolizing the undivided primordial energy; since it already contains movement and stillness, it is then drawn as a circle with black and white embracing each other, indicating the emergence of the two principles. The Taiji diagram commonly found in the world is not entirely accurate, and should be based on these two diagrams: the first represents the original form of the Taiji, pure and luminous; the second represents the emergence of movement and stillness, with black and white embracing each other. Only then can we clearly see the essence of the Taiji and the images of the two principles it generates.

夫易象者言天地既生之後者也。取象自太極以下，而八卦也，六十四卦也，三百八十四爻也，皆兩四象既生之後之事物也。重在既變之象，故名曰易。易變易也，而易有太極一語，即明示所自始也。易字不必指書名，當以卦象變易之義釋之。

The "Xiang" (images) of the "Yi" (Book of Changes) refer to things that have already come into being after heaven and earth were formed. It takes images from the Taiji (Supreme Ultimate) downward: the Eight Trigrams, the sixty-four hexagrams, and the three hundred and eighty-four lines are all about things that arise after the two principles and the four images have been generated. The focus is on the images that have already changed, hence the name "Yi." "Yi" means change; the phrase "Yi has the Taiji" clearly indicates where this change begins. Therefore, the character "Yi" should not be interpreted as the name of a book, but rather understood as referring to the changing nature of the hexagrams.

有字不可屬於易經解，當以自無入有之義釋之。蓋言易之言變易也，必自其變所始考之。言變者必徵於有物之初，而始有者即變之始見也，則太極者即萬有之始，亦萬變之宗。故言變易，而明變化之源；言自無入有，自當溯太極而為全易之根本。則易有太極一語，其意義至深切著明也已。若視為易經有太極，則不合矣。

The character 「有」 should not be understood as meaning 「there is」 in the sense of 「the Book of Changes contains a Taiji」. Instead, it should be interpreted as meaning 「from non-existence to existence」. Since the study of the Book of Changes focuses on change, one must examine the starting point of this change; and since change must be verified through the initial emergence of all things, the first 「existence」 is precisely the first manifestation of change. Therefore, Taiji is the beginning of all existence and the sovereign of all change. To discuss change, one must clarify its origin; to discuss the transition from non-existence to existence, one must trace back to Taiji and regard it as the fundamental principle of all Book of Changes studies. In this way, the phrase 「The Book of Changes has Taiji」 carries profound and clear meaning. If it is understood as 「the Book of Changes contains a Taiji」, it becomes incoherent.

太極非物也。言易雖自伏羲，而太極之有象，則天地之先也，故太極不得視為易所有無者也。要知太極之象，傳之久矣。伏羲時畫之為一，無此圖也。後聖漸由伏羲之一，演之為圓圈，以示其體；又有由圓圈之象，演之為□，以明為用，即中字所自出也。

The Taiji is not an object. Although the Book of Changes began with Fuxi, the image of Taiji existed before heaven and earth, so it should not be regarded as something optional within the Book of Changes. One must understand that the image of Taiji has been passed down for a long time: during Fuxi's time, it was simply drawn as a horizontal line, without the diagram we have today. Later sages gradually inferred a circle from Fuxi's single line, using it to represent its essence. Others further deduced the shape of a circle with a central mark from the circular image, using it to indicate its function. This is the origin of the character 'zhong' (center).

後更演之為黑白交互之象，以明兩儀既生，二氣之周流不盡，而以證天地生化之序，乃合易象八卦之圖，此今世所傳之太極圖也。圖之為象，在明其體用。黑白之圖，有用遺體，尚非全也。必先有渾圓明澈之圖，以象其本來元氣；合以黑白交環之圖，以象其動靜生陰陽；於是體用皆全，變化自見。

Later, it was further developed into a diagram with black and white interwoven, used to indicate that the two principles have emerged and that the energies of yin and yang flow endlessly. This was also used to verify the sequence of generation and transformation in the universe. Thus, it was combined with the diagram of the eight trigrams from the Book of Changes, forming the Taiji diagram that is now widely circulated. The purpose of creating such a diagram is to clarify its essence and function. The diagram with black and white interwoven only shows the function but omits the essence, so it is not yet complete. One must first have a diagram that is perfectly round and clear, symbolizing its original vital energy; then combine it with the diagram of black and white interwoven, symbolizing the emergence of yin and yang from movement and stillness. In this way, both essence and function are fully represented, and the principles of transformation naturally become evident.

如易之卦象，自□生□，自□生四象八卦，皆有序也。若不循序觀之，則不知八卦所來，又何以明卦象之體用與變乎。故□者太極也，□者兩儀也，八卦皆自是生化者也。古人言文尚簡，況當畫卦之時，尚無文字，所有之象，僅八卦與六十四卦。雖有太極之象，而未有圖，以未以列於卦象前後，不過口授之後人，知其有所始耳。迨文王之後，諸聖人之言，皆筆之書。

Just like the hexagrams in the Book of Changes, the trigrams arise from the single line of the Taiji, which gives rise to the two yao, yin and yang. From these two yao come the four images and the eight trigrams, and everything follows a certain order. If one does not look at them in order, one would not understand where the eight trigrams come from, and how could one then comprehend the nature, function, and transformations of the hexagrams? Therefore, that single line is the Taiji, the yin and yang lines are the two principles, and all the eight trigrams arise from here. The ancients valued simplicity in their writing, and at the time of drawing the trigrams, there were no written characters. All the images were only the eight trigrams and the sixty-four hexagrams. Although they had the image of the Taiji in mind, they did not draw a diagram, nor did they place it before or after the hexagrams. They simply passed it down orally to later generations, so that people would know that the hexagrams have a beginning. Only after King Wen, did the words of the sages become written.

不獨易之象義，有其文言釋之；即河洛太極之圖象，亦有傳序以解之。此係傳中有易有太極之語也。蓋恐後人不知易卦所自始，而忘其本，故特述先聖之言，而繫辭以傳之耳。繫傳者謂繫於辭以為傳授，以易象之未備，恐先人口傳不垂久遠，故繫之辭，為之傳，言猶繫之於易，使毋遺耳。

Not only do the images and meanings of the Book of Changes (Yi) have explanations from the Wenyan Zhuan, but even the images of the Yellow River Chart (He Tu), the Luo Writing (Luoshu), and the Taiji also have explanatory texts such as commentaries and prefaces. The reason why the "Great Treatise" (Xici Zhuan) contains the phrase "The Yi has the Taiji" is because of this. It was probably to prevent later generations from forgetting the origin of the Yi hexagrams and thus losing their fundamental principles. Therefore, the sayings of the ancients were recorded and attached to the text for transmission. The term "xi zhuans" refers to attaching explanations to the text for the purpose of transmission. Since the images of the Yi were not yet complete, and there was a fear that oral transmission would not be enduring, they attached words and composed commentaries, thereby securing these principles to the Yi and preventing them from being lost.

天地之前，一氣所凝，固無物也。天地即判，萬物續生，仍氣之所周流。故盈天地者物也，運天地者氣也。氣化而物生，氣化自太極始，太極者氣之主宰，其生化之序，則見河洛二圖。陰陽並行，生化無垠。曰陰陽者，以太極氣化之次序也。太極之初，元氣純陽，不可分陰陽也。元氣胚動，乃生陰焉。動則陰生，靜則陽復；氣因動化，生以動成；故太極初生為陰氣。而其後動靜往復，二氣始分。此陰在陽先之義，非有所輕重也。至其既化，二者並行，陽主陰從，剛先柔後，則陰統於陽，天包乎地，此有生之序，不可亂也。

Before the separation of heaven and earth, there was only a single qi凝聚, and there were no specific things. Once heaven and earth were separated, all things arose successively, still relying on the circulation of this qi. Therefore, what fills the space between heaven and earth is "things," while what moves heaven and earth is "qi." When qi changes, things arise; and the process of transformation begins with the Taiji, which is the master of qi. The order of generation and transformation is reflected in the two diagrams, the Yellow River Chart and the Luo Writing. Yin and Yang operate together without contradiction, leading to boundless generation and transformation. The reason we talk about "yin and yang" is because this precisely reflects the sequence of transformation of the Taiji qi. At the very beginning of the Taiji, the original qi was purely yang and could not yet be distinguished as yin and yang. Only when the original qi began to stir like an embryo did yin emerge. Movement produces yin, stillness returns to yang; transformation occurs through movement, and generation is completed through movement. Therefore, the first thing to arise from the Taiji was actually yin qi. After that, the alternation of movement and stillness led to the formal separation of the two qi, yin and yang. The saying "yin precedes yang" refers to this, not implying that yin is more important than yang. Once the transformation is complete, both yin and yang operate together, with yang as the main and yin as the subordinate, hardness preceding softness, and thus yin is subordinate to yang, heaven encompasses the earth—this is the order of things in the process of generation, which cannot be reversed.

故太極之後，河洛之象乃見。天地為兩儀之大者，天生則地成，地生則天成，天地合精，生成乃見，非如太極之氣化也。故兩儀分合，五行以出；五行往來，九宮以分；五行九宮，即易之四象八卦也。故卦有氣，有數，有位，有時，有其名類，有其變化，皆由氣之所至，生化自然之序。然生化雖眾，不得離於陰陽，以氣化之後，必因陰陽之化合而後生也。

Therefore, after the Taiji, the images of the Yellow River Chart and the Luo Writing became apparent. Heaven and Earth are the greatest pair among the two principles: Heaven gives birth to Earth, and Earth gives birth to Heaven. When the vital energies of Heaven and Earth interact, the process of generation becomes evident, which is different from the simple transformation of Taiji. Thus, the division and union of the two principles give rise to the Five Phases. The movement and interaction of the Five Phases lead to the establishment of the Nine Palaces. The Five Phases and the Nine Palaces correspond to the Four Symbols and the Eight Trigrams in the Book of Changes. Therefore, the trigrams have qi, numbers, positions, and times; they have their names and categories, and their transformations. All these are results of the movement of qi, forming a natural order of generation and transformation. However, although the processes of generation and transformation are complex, they all depend on yin and yang. After the transformation of qi, it must rely on the union of yin and yang to produce things.

天地絪縕，萬物化生，此造化之序可紀者也。自太極以一氣而分為兩儀，其德在生，德流氣薄，生生不已。太極為有生之祖，兩儀為有生父母，皆氣之自至也。氣之自至，是謂之道，以其循環往來不相害，消長盈虛不相亂，而以成其德也。唯道有德，道不可見，其德顯焉。兩儀之德在生，即其道之見也。道以成其生為先，人之成道者，長生而生物，此即順道致德之土也。故道出於太極，見於兩儀，成於仁，全於性，唯合乎道也。

The Great Treatise says, "Heaven and Earth blend together, and all things thus become pure and harmonious." This refers to the blending of the two energies of Heaven and Earth, from which all things are generated. In the process of creation, there is an order that can be recorded. The Taiji (Supreme Ultimate) divides into the two principles (Yin and Yang) with a single breath; its virtue is "to give birth." When virtue spreads and energies meet, there is continuous generation. Taiji is the ancestor of all life, and the two principles are the parents of all life, all naturally arising from the movement of energy. When energy naturally arises, this is called the Dao. Because it circulates and interconnects without hindrance, and expands and contracts without disturbance, it achieves its virtue. Only the Dao has virtue; the Dao itself is invisible, but its virtue reveals it. The virtue of the two principles is "to give birth," which is the manifestation of their Dao. The Dao's primary function is to nurture and sustain life. When a person attains the Dao, he can achieve longevity and nurture all things, which is realizing the foundation of virtue by following the Dao. Therefore, the Dao originates from Taiji, manifests in the two principles, is realized in benevolence, perfected in nature, and everything depends solely on conformity with the Dao.

人生之性，受於中氣，亦太極之元氣，生而有之。全性則全生，成仁則成性。生全仁成，純乎道也，故歸於太極，復於真境，是謂得道。故曰道者返本復始者也。本始者太極也，返而復之，純於元氣之體矣。

Human nature is inherited from the "central qi," which is the original qi of the Taiji. It is present from birth. To preserve one's nature is to preserve life; to achieve benevolence is to realize one's nature. When life is preserved and benevolence is achieved, one fully aligns with the Dao, thus returning to the Taiji and the original state. This is called "achieving the Dao." Therefore, the Dao refers to returning to the root and the origin. This root and origin are the Taiji. Returning to the past and reverting back is purely the essence of the original qi.

是故易之言教也，以道為本，聖人立卦象，將以明道也。道之始乎太極，運行於二氣，調和於五行，以應萬物萬事，而成其德；以守中立極，而全其性。雖依象以稽數，而判其吉凶；依數以言命，而明其順逆；而莫非指人以道，俾克全生以返本復始也。故易之言為道言也。易之象，原始要終，為教人各正性命也。故必推原道之所自，人生之源，氣之所運，數之所合，以定其所宜，而為人立其則；以辨其所至，而示人所有修。必以天道為之準繩，人道為之綱紀，盡人以合於天，致力修養，以全生適性，立德成道。

Therefore, the teachings of the Book of Changes are based on the "Dao." The sages established hexagrams precisely to explain the Dao. The Dao originates from the Taiji, operates within the two energies of yin and yang, harmonizes within the Five Phases, and is used to deal with all things and accomplish its virtue. It also preserves human nature through the practice of maintaining the center and upholding the ultimate principle. Although the Book of Changes uses hexagrams to examine numbers, thereby judging good and bad fortune; uses numbers to discuss fate, thereby explaining favorable and adverse conditions, ultimately, everything is aimed at guiding people to understand the Dao, so that they may preserve their lives and return to their original nature. Therefore, all the words of the Book of Changes are words about the Dao. The hexagrams of the Book of Changes "trace the origin and consider the end," aiming to teach people to properly regulate their nature and destiny. Therefore, it must investigate from where the Dao originates, where the source of human life lies, how the vital energy flows, and how numbers correspond, thereby determining what is appropriate and establishing standards for people. It also clarifies where people will go, thus guiding them on what they should cultivate. It certainly uses the heavenly Dao as a standard and human conduct as a framework, doing everything humanly possible to align with the heavenly Dao, striving for self-cultivation, thus preserving life, harmonizing with one's nature, establishing virtue, and achieving the great Dao.

此易有太極一節之大旨也。夫太極固示人以象矣：渾圓無名，虛然光明，凝然周流，悠然長存；氣行不息，德徵廣生；數紀太一，道在用中。固已純精至神，為天地先；周環太和，為萬物宗。其所象者，道之體用；而人之所見者，德之玄玄。仁智隨所識而得，生成隨所遇而合，無大無小，莫能外內。況參以河洛之圖，證以乾坤之卦，大哉至矣，其義有不可盡矣。

This is the general meaning of the section "The Book of Changes has the Taiji." Taiji originally reveals itself through symbolic images: it is complete and perfect, beyond description, with light existing in emptiness, and movement within stillness. It is remote yet enduring; its qi flows ceaselessly, and its virtue manifests in the vast nourishment of all beings. In terms of numbers, it is recorded as "Taiyi," and in terms of the Way, it is realized as "Yongzhong" (acting in the center). It is already pure and divine, existing prior to heaven and earth. It circulates and surrounds, reaching a state of calm harmony, and is the master of all things. It symbolizes the essence and function of the Way, but what humans can see is only the profound and mysterious virtue. As the Great Treatise says, the wise see wisdom, and the benevolent see benevolence; each person understands it according to their own perception, and the principle of generation is verified according to their own circumstances. Whether it is great or small matters, none can go beyond it or separate from it. Moreover, by referring to the Yellow River Chart and the Luo Writing, and verifying through the Qian and Kun trigrams, it is truly vast and profound, with meanings that are inexhaustible.

故易之象始於斯也。且易之言易，以不易明易，易明不易。溯始迄終，則天地推於無盡；返本復始，則萬歸於一原。太極主其始矣，而終亦盡於是。蓋以不易之元氣，而主變易之陰陽；生生不窮，而真體常存；行行不息，而中極永在。此所以為道之象也。天地尚自此出，而師其用，況其下者乎。故物物有極，事事有中，中極之德，即性命之所見；此中和之功並覆載，而仁智之德同天地也。

Therefore, the image of the Book of Changes begins here. Moreover, the Book of Changes discusses change, using "unchanging" to explain "change," and using "change" to explain "unchanging." Starting from the beginning and proceeding to the end, heaven and earth are unfolded endlessly; returning from the end to the beginning, all things are traced back to the same origin. The Supreme Ultimate governs this beginning, and the end also returns to it. This is because it uses the unchanging vital energy to govern the ever-changing yin and yang: it produces endlessly, yet the true essence remains constant; it moves ceaselessly, yet the central point remains unmoved. This is precisely why it can serve as the image of the "Way." Even heaven and earth arise from here and must follow its usage; how much more so those things below heaven and earth? Therefore, each thing has its own Supreme Ultimate, and each matter has its own center; this "central Supreme Ultimate" virtue is where nature and destiny are manifested. This function of harmony in the center can be compared with the carrying and supporting of heaven and earth, and this virtue of benevolence and wisdom can be equal to heaven and earth.

易傳日：「分陰分陽，迭用柔剛。」可以明太極之道矣。夫易自太極立其極，而以乾坤代名其兩儀，萬物皆自陰陽生，故全易卦爻，皆自乾坤出。乾坤者，天地也，父母也；其德則剛柔也，仁義也；其功則生成也，覆載也。何莫非陰陽之道所見耶。欲明道而知太極，必自易始，易固演太極而賅河洛之象者也。

The "Sayings on the Hexagrams" from the "Commentaries on the Book of Changes" says: "Divide yin and divide yang, alternately using softness and strength." From these two sentences one can understand the principle of the Taiji. The "Book of Changes" establishes its "extreme" from the Taiji, then uses the hexagrams Qian and Kun to represent the two principles (wuxing). All things arise from yin and yang, so all the hexagrams and lines in the entire "Book of Changes" originate from Qian and Kun. Qian and Kun represent heaven and earth, which are also the parents; their virtues are strength and softness, benevolence and righteousness; their contributions are generation and completion, covering and bearing. Which of these is not a manifestation of the way of yin and yang? To understand the Dao and recognize the Taiji, one must start with the "Book of Changes"; the "Book of Changes" itself is a book that deduces the Taiji and encompasses the images of the Yellow River Chart and the Luo Writing.

此文講太極要義，以舉其大者言之耳。太極圖象，秦後儒者失傳，唯道家存之；至宋時傳於周濂溪氏，而後儒者亦得有之。時以門戶之見，沿習之深，訛毀者大有人在；徒以易傳有易有太極一語，無能根本推翻之也。

This article discusses the essential principles of the Taiji, merely highlighting its main aspects. The image of Taiji was lost by the Confucian school after the Qin dynasty, but was preserved by the Daoist school. It was passed down to Zhou Dunyi (Zhou Lianxi) in the Song dynasty, after which the Confucian scholars regained possession of it. At that time, due to the prejudice of sectarianism and deeply rooted traditions, many people spread errors and criticized it. However, they could not completely refute it because the "Book of Changes" contains the phrase "The Book of Changes has Taiji."

然周所傳，雖名「太極圖」實則太極已生兩儀之象，非太極之體也；後人有演為一圈者，有為黑白相互，中藏一小圓圈者；取意固善，然尚非全體；以太極之初本無極，由無入有，必有其象；如河圖之與洛書，由二五變為九宮；其圖不能混為一也。必先示太極之體，渾然元氣之時；再示其動靜之用，陰陽生化之象；方可由圖見天地生成之序，陰陽未判之先也。

However, the diagram transmitted by Zhou Dunyi, although called the "Diagram of the Supreme Ultimate," actually depicts the image after the Supreme Ultimate has already produced the Two Principles (Yin and Yang). It is not the original form of the Supreme Ultimate. Later people have interpreted it as a circle, or as black and white intermingling with a small circle in the center. Although their intention is correct, they have not fully captured the complete whole. Because the Supreme Ultimate originally began as "the Limitless" (wuji). From nothingness to existence, there must be an image to represent this transition. Just as the Yellow River Chart (He Tu) and the Luo Writing (Luoshu), which combine the numbers two and five to form the Nine Squares (jiugong), the two diagrams cannot be confused. Therefore, one must first draw the original form of the Supreme Ultimate, which is the moment when the primordial qi is undifferentiated and unified. Then one must depict its dynamic and static functions, which represent the image of the generation of Yin and Yang. Only in this way can one see from the diagram the sequence of the generation of heaven and earth, as well as the scene before Yin and Yang were differentiated.

故夫子命作二圖以象之，一圓圈渾然明淨，此其體也；一黑白交互，二氣流行，此其用也。體用既全，始終在目；自易探造化究竟，而明曉由無入有之景象也。夫太極氣之所化，全為自然生化之物。因其氣之有動靜。而後陰陽分；初則一氣而已，二氣既判，生物無窮而此太極之象，仍如故也；蓋前者先天之氣，後者後天之體；後天之生化，即後者之所主；而先天之氣，仍存其中也；習道者由後天陰陽之體，漸復於先天元氣之時；當依此圖證之。苟在生時。百體俱用；情識未除，不能逃於陰陽往復之道；即在生滅輪迴之中，是後圖二氣互為消長之象。

Therefore, the Master (Confucius) ordered the drawing of two diagrams to illustrate this: one is a perfectly clear and round circle, representing its 'body'; the other is a diagram with black and white alternating, showing the mutual flow of the two energies, representing its 'function'. With both body and function complete, the beginning and end become clear, making it easy to investigate the principles of creation and understand the transition from non-existence to existence. The Taiji is formed from qi, and everything is a natural product of generation and transformation; because qi has movement and stillness, yin and yang then separate. Initially, it was just a single qi, but when the two energies divided, the things produced were endless, while the image of Taiji itself remained unchanged. The first diagram represents the Earlier Heaven qi, and the second diagram represents the Later Heaven body; the generation and transformation of the Later Heaven is governed by the second diagram, while the Earlier Heaven qi still exists within it. Those who practice the Way should gradually return from the Later Heaven yin and yang body to the state of the original qi of the Earlier Heaven, by referring to these two diagrams. As long as a person is still alive, all parts of the body are in action, and emotions and consciousness have not been completely eliminated, so they cannot escape the law of the mutual transformation of yin and yang, and remain in the cycle of birth and death—this is precisely the image of the mutual increase and decrease of the two energies in the second diagram.

若果屏除物好，絕制情識；充其性靈，致於中和；則由後天返於先天，即前圖渾然光明之象；所謂返本復始。原始要終之道，皆在此二圖中驗之；其義固重在明道者也。夫子此文，抉易教之微，指修道之要；非僅釋易有太極之文義已也，讀者當三復焉。

If one can truly eliminate desires for external things, cut off disturbances from emotions and thoughts, enrich one's spiritual nature, and reach a state of harmony, then that is returning from the Later Heaven to the Earlier Heaven, which is the image of the first diagram, a state of pure and bright unity. The principle of "returning to the source and beginning again" and "origin and end are fundamental" can all be verified in these two diagrams. This shows clearly that the essence lies in explaining the path of cultivation. The Master's article removes the subtle aspects of the teachings of the Book of Changes, points out the key to cultivation, and is not merely explaining the literal meaning of the phrase "the Book of Changes contains the Taiji." Readers should contemplate it repeatedly.

夫子前講易本河洛圖象，不止言取其象而制為易之卦象也；實則取其象，以立修道之教耳。蓋「道」字本無名之名，修道更難以言文明其方；必因圖象而指示之，乃得悟其本原，及其歸著處。而圖象則自河洛始，河洛圖象，以變者示人不變，不變者示人變；一靜一動而陰陽生，一順一逆而生成見；皆本道以明道，明之即以教人修之也。故觀河洛圖象，重在動靜之間，順逆之序；更重在以天道立人道，以人道順天道；天人之相成者道，聖人之立教者亦道；道無二用，用之於身則成已；用之於人物，則成人成物；皆一以貫之，皆自河圖象始終之也。

The Master previously explained that the origin of the Book of Changes lies in the images of the Yellow River Chart and the Luo Writing. It is not merely about using their images to create the hexagrams of the Book of Changes, but actually using their images to establish the method of cultivating the Way. Because the term "Way" itself is nameless, the path of cultivating the Way is even more difficult to explain with words and characters. It must rely on images to guide people, so that they can understand its origin and ultimate destination. And the images begin with the Yellow River Chart and the Luo Writing: the images of the Yellow River and Luo Writing use the changing parts to indicate the unchanging, and the unchanging parts to indicate the changing. One still and one moving gives rise to yin and yang; one following and one opposing reveals the principle of generation. All of this is based on the Way to explain the Way, and explaining the Way is also teaching people how to cultivate it. Therefore, when observing the images of the Yellow River and Luo Writing, the focus should be on the relationship between movement and stillness, and the order between following and opposing. More importantly, it is about establishing human conduct based on the Way of Heaven and aligning human conduct with the Way of Heaven. Heaven and humanity mutually complete each other through the Way, and the sages who established education and guidance also relied on the Way. The Way has only one use: applying it to oneself is "perfecting oneself," applying it to others and things is "perfecting others and things," and both can be consistently applied, and both can be found throughout the images of the Yellow River Chart.

故修道之教，不外於河洛之圖；而聖人之道，不殊於天地之數；由其淺言之，則為人之事；由其深言之，則成道之功；易傳曰：「仁者見之為仁，智者見之謂智。」此語已盡河洛之義，一部易經如是，六經亦如是；除是外，更無他語足以盡之也。故道無大小，無遠近；人自見之，若推而言之；妄者謂之妄，愚者謂之愚；人自妄愚，何咎乎圖象也？

Therefore, the teachings of cultivating the Way do not go beyond the two diagrams, the Yellow River Chart and the Luo Writing, and the Way of the sages is no different from the numbers of heaven and earth. On a shallow level, it concerns matters of being a person and dealing with the world; on a deeper level, it is the practice of attaining the Great Way. The Great Treatise of the Book of Changes says: "The benevolent person sees it and calls it benevolence; the wise person sees it and calls it wisdom." This single sentence has already explained the meaning of the Yellow River Chart and the Luo Writing completely. The entire Book of Changes is like this, as are the six classics. There is nothing else that can summarize it. Therefore, the Way itself has no distinction of small or great, near or far; it all depends on how a person looks at it. If we take a broader view: the foolish say it is foolish, the ignorant say it is ignorant—that is the foolishness and ignorance of the person themselves, how can it have anything to do with the diagrams?

中國言道，以性理代之，此宋人言也；實則道字不止性理，凡天地之物，無不在道中生成往來，無一事不有道在，蓋天下物物事事，無不在氣中行運，而自然生成往來者也；此氣之名曰：「陰陽」。氣之用即道也，故曰：「一陰一陽之謂道」。天下物物事事不離陰陽，故不離道；非止性理名為道也，氣之所行，不獨生物；即木石之類，無知無情者，皆有其氣，皆在道中也；如一室中，或桌几，或書畫，或玩好之物，皆在自然中位置；或主或客，或畜類，或蟲蟻，出入住息，皆在自然中游走去住，皆有其道也。

The Chinese concept of "Dao" was replaced by the Song scholars with "Xingli" (principles of nature and mind), which was their way of expressing it. In reality, the term "Dao" is not limited to "Xingli": everything in the universe is generated and interacts within the Dao. Since all things in the world operate through the movement of Qi (vital energy), they naturally come into being and interact. The movement of Qi is called "Yin and Yang," and the function of Qi is Dao. Therefore, the Great Treatise says: "The alternation of Yin and Yang is called Dao." Since all things in the world depend on Yin and Yang, they also depend on Dao, and it is not only "Xingli" that can be called Dao. The movement of Qi is not limited to living beings; even things like grass, trees, soil, and stones, which are without consciousness and emotion, also have their own Qi and are included within Dao. For example, in a room, tables, paintings, and decorative objects are naturally placed in their respective positions. The owner, the guest, the domestic animals, and even insects enter, stay, and rest naturally, moving and staying as they please. All of these have their own Dao.

因天地成於此一陰一陽之道，則自天地以下，無大細，皆不得離道以生成往來；故道者，氣之道，猶車之軌也；有車必有軌，有氣必有道；同此氣，即同此道；太極者，氣之所始，道之所自；言道而不溯太極，譬如行路而忘所自至地，徘徊歧路而已；故言道必先明太極之用，既明太極，則性理在其中矣！所謂知其原，則流易測；得其本，則枝葉易探；此言道者所當知也。儒者言道莫先於易，易自太極出，則欲習道者，可不先求之太極哉！

Since heaven and earth are composed of the principle of "one yin and one yang," everything below heaven and earth, regardless of its size, cannot separate from the principle to come into being and interact. Therefore, the "Dao" is the path that qi follows, just as the tracks are the path that a cart follows: if there is a cart, there must be tracks; if there is qi, there must be a Dao. Since qi is the same qi, the Dao is also the same Dao. The Taiji is the beginning of qi and the origin of the Dao. If one talks about the Dao without tracing back to Taiji, it is like a traveler who forgets where he started from and can only wander around at a crossroads. Therefore, to talk about the Dao, one must first understand the function of Taiji; once the function of Taiji is understood, the nature and principles are naturally included within it. This is what is meant by knowing the source makes the tributaries easy to measure, and grasping the root makes the branches easy to trace—this is what those who talk about the Dao should know. The Confucian scholars who talk about the Dao have nothing more fundamental than the Book of Changes; and the Book of Changes itself originates from Taiji. Therefore, how can those who wish to study the Dao not first seek it from Taiji?

又曰：陰陽動靜原相根，而動為陽則陰生焉，靜為陰則陽復焉；初無一刻之停，祇見消長之氣；故動則陽生陰，靜則陰生陽；如人坐功，以動屬陽，而情見即生陰；返於靜，則性見而陽復；二者斯須之間，往復之運，非瞭然二事也；果動矣，必由陽生陰；靜矣，必仍返於陽；此理自然而然者，以含有往復消息之義，足以明太極之氣無一時停住，陰陽來去有相根之妙；即天地間二者之相應，正如是也。

It is also said that yin and yang, and movement and stillness, are originally interdependent. Movement belongs to yang; within the movement of yang, yin arises. Stillness belongs to yin; within the stillness of yin, yang returns again. There is no moment of pause in this process; only the alternation of the qi of decrease and increase can be observed. Therefore, when there is movement, yang gives rise to yin; when there is stillness, yin gives rise to yang. For example, when a person practices meditation: the arising of thoughts and activities belong to yang; but once emotions begin to appear, yin follows. When returning inward to stillness, the true nature is revealed, and yang returns again. These two aspects alternate rapidly within an extremely short moment, and are not separate events. If there is indeed movement, it must be that yang gives rise to yin; if there is indeed stillness, it must still return to yang. This principle is natural and spontaneous, containing the meaning of mutual increase and decrease, which can explain why the qi of the Taiji (Supreme Ultimate) never stops, and why the coming and going of yin and yang have a profound interdependence. The mutual correspondence between yin and yang in the universe is precisely like this.

以陽為主，則陰從之；以陰為母，則陽生焉；非截斷可比。如靜坐至極，神氣活潑；靈光周迴，即動也；然非動之動，乃靜生動也；故曰陽復。太極之成兩儀，即由此動，而分為陰陽；若未動，固無二名；動則陰生，即此義也。凡易理象氣之流行者，若以不動者擬之，則失易義矣！易者，變易也；變易者，即流行無住之義；陰陽互抱，初無可截為二者，詳細體會之自明。

The principle of yin and yang is such that yang is the main force, and yin follows it; yin is the mother, and yang arises from it. This cannot be viewed as something that can be completely separated. For example, when one sits in stillness to the extreme, the spirit and energy become active, and a luminous glow circulates throughout the body. This is called "movement" or "action." However, this movement is not movement arising from movement, but movement that arises from stillness, hence it is called "yang returning." The Taiji (Supreme Ultimate) becomes the two principles (yin and yang) precisely because of this movement; if there were no movement, there would originally be no names of yin and yang. The idea that movement gives rise to yin is exactly this meaning. All the flow of qi symbolized by the principles of the Yi (Book of Changes) cannot be compared to static things, or else the original meaning of the Yi would be lost. "Yi" means change; change means continuous flow without stopping. Yin and yang embrace each other, and they cannot be completely divided into two separate parts. If one carefully reflects on it, one will naturally understand.

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.

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.

故立卦，而萬物萬事皆自卦中出；天地尚不外是，況其下者乎？故卦者卦也，言以一而卦眾也。懸則以測物，謂之卦；卦立，則物物事事皆得依則以測之，故能周知無窮。八卦之序，乾一、兌二、離三、震四、巽五、坎六、艮七、坤八；自乾至震，自巽至坤，分為左右，而仍成圓形，以二氣之往來相續，循環無已也。乾坤對列，六子成行，以明陰陽之有所屬，而升降之有次也。

Therefore, once a hexagram is established, all things in the universe emerge from it. Even heaven and earth do not go beyond this scope, let alone the things beneath heaven and earth. Therefore, the term "hexagram" refers precisely to the meaning of encompassing a multitude of things with a single hexagram. To suspend the principles and measure things by them is called a hexagram. Once a hexagram is established, all things can be measured according to this principle, thus enabling the comprehensive understanding of infinite matters. The order of the eight trigrams is: Qian (Heaven) one, Dui (Lake) two, Li (Fire) three, Zhen (Thunder) four, Xun (Wind) five, Kan (Water) six, Gen (Mountain) seven, Kun (Earth) eight. Counting from Qian to Zhen forms one sequence, and from Xun to Kun forms another sequence, dividing them into left and right sides, yet together they form a circle. This is because the dual forces of yin and yang continuously flow and cycle without end. Qian and Kun are paired opposite each other, and the six subsidiary trigrams follow in sequence, illustrating how yin and yang each have their proper place and order of ascent and descent.

故一二三四之序，乃位次也；必求於象之變化，始見氣之進退。如自下而上，則震者坤所變；自上而下，則巽者乾所化，其序不同，亦相當也。蓋陰陽二者，往來不已，初非泥於一地也；升降有時，初非限於一日也。故時位不同序，升降往來不同道，消長進退不同途，各以所宜而自至焉。卦象亦如之，故以兌次乾，言兌之上既復，即歸於乾；

Therefore, the numbers one, two, three, and four refer to the order of positions; one can only understand the movement of qi by observing the changes in the hexagram. For example, looking from the bottom up, "Zhen" comes from "Kun"; looking from the top down, "Xun" comes from "Qian": the direction of the numbers differs, yet their positions remain corresponding. Since yin and yang qi continuously move and change, they do not remain fixed in one place; their rising and falling occur at specific times and are not limited to a single day. Therefore, time and position do not share the same order, rising and falling do not follow the same path, and growth and decline do not proceed along the same route; each follows its own appropriate way to reach its destination. Hexagrams are the same, so "Dui" is placed after "Qian," meaning that once the top line of "Dui" returns to its original position, it reverts to "Qian."

以巽隨乾，言乾之初初變，即成為巽。一來一往，一進一退，各有序也。由兌溯離，可見其升之道；由巽推坎，可見其去之途，其相次亦有定也。坤之與震艮亦然，不可泥一二之序，而執於一偏；必通各象之形，而尋其所至。此八卦位序所賅之義，實至精深也。

The trigram Xun follows Qian immediately, meaning that the first line of Qian changes to become Xun. One goes and comes, advances and retreats, each with its own order. From Dui tracing back to Li, we can see the path of rising yang energy; from Xun extending to Kan, we can see the path of retreating yang energy: their sequence before and after is equally definite. The positions of Kun, Zhen, and Gen are also like this; one should not be rigid about the numbers one, two, etc., and fixate on one side. Instead, one must observe the forms of the images of all the trigrams to find out where they have actually arrived. The principles contained in the positions of the Eight Trigrams are indeed extremely profound.

陽之進者，為陰之退；陰之長者，為陽之消，此易見者也。皆定於三畫，故有多必有少，有減必有加，其象所具，則數之所計也。故坤納艮之陽而變震，震之初爻，即乾之下；乾氣初見，坤氣即潛；此震卦之象，示由靜初動，由陰生陽之機。其象既明，其氣亦昭；觀其所變，即得其所示之義矣！不獨震也，餘卦皆然。

When yang advances, yin retreats; when yin grows, yang diminishes. This is easy to observe. All of this depends on the arrangement of the three lines. Where there is more, there must be less; where there is reduction, there must be addition. What is contained in the hexagram is precisely what is calculated by numbers. Therefore, the yang line that is incorporated into the hexagram of Kūn becomes the hexagram of Zhèn. The first line of Zhèn is exactly the lower line of Qián. As the yang energy of Qián begins to appear, the yin energy of Kūn retreats secretly. This is the image of Zhèn, which shows the moment when stillness turns into movement and yin gives rise to yang. Once the image is clear, the energy becomes evident. By observing where the change occurs, one gains the meaning that the hexagram aims to convey. Not only does Zhèn follow this pattern, but all other hexagrams do as well.

故來往有途，進退有道；以成環行，永無斷絕。此始彼終，非真始終也，為便於紀錄，謂之始終耳。如春去夏來，秋往冬至，此一歲之始終，為紀歲也；實則冬去春復來，日月何嘗有所始終哉？彼八卦之交遞亦猶是也。故泥其跡則不達，通其意則皆知；氣行無垠，數至有紀；必旁通各象而會歸之，方得聖人立卦之心，與河洛圖書相合之義耳。

So coming and going have their own paths, advancing and retreating have their own principles, thus forming a circular movement that never ceases. This side is considered the beginning, that side the end, but there is no real beginning or end. It is only for convenience of record that they are called beginning and end. For example, spring goes and summer comes, autumn passes and winter arrives; this is the beginning and end of a year, established for the purpose of recording years. In reality, after winter comes spring again, and the sun and moon never truly have a beginning or an end. The alternation of the Eight Trigrams is also like this. Therefore, clinging to its surface traces will not lead to understanding, but grasping its meaning will bring clarity. The movement of qi has no boundaries, but the numbers have their order and structure. Only by comprehending the images of all the trigrams and integrating them can one understand the original intention of the sage in establishing the trigrams, as well as the connection between them and the Yellow River Chart and the Luo Writing.

夫卦之用以測物，必自物之既生始；物物事事所自生成者三，天地人是也。故卦之爻三，既仿河圖中之三五也。然生成必自二氣之合化，孤陰獨陽不克生化也；必合陰陽，而後生成之功始見；必列陰陽，而後事物之情始明。此三爻之卦必重，重而後竟其用也，亦即河圖、洛書四方之數，以一陰一陽交合成象之義。故卦之體三爻，而成用，則六爻也。

The use of hexagrams is to measure and understand things, and measurement must begin after things have already come into being. All the factors that enable things to be generated are three, namely heaven, earth, and humanity. Therefore, hexagrams have three lines, which is exactly imitating the number 'three' and 'five' in the Yellow River Chart. However, generation must come from the combination of yin and yang energies. A single yin or a single yang cannot generate by themselves; it is only when yin and yang meet and interact that generation occurs. It is only when yin and yang are combined that the forms of things become clear. Therefore, a three-line hexagram must be overlapped, and only after overlapping can its full function be exhausted. This is also the meaning of the Yellow River Chart and the Luo Writing, where the numbers of the four directions are formed by the mutual combination of one yin and one yang. Therefore, the 'body' of a hexagram is three lines, but to achieve its 'function', it must be six lines.

天有陰陽，地有柔剛，人有仁義；皆二氣相間，以生成事物，而見其情性者也，名之日道，言物物事事必由者也。天地人之合，而二氣行止於其間，故卦象以六爻分象之，而變化亦因之生矣！六爻之卦所自成者以此。原夫天下之物事，莫不以陰陽之從違，為有無生化之本；陰者求陽，陽者求陰，合而有得，生化無盡，則前之孤獨者，至此必偶；而前之三爻者，至此必重。此重卦之立，亦本乎生化自然所至者也。

Heaven has yin and yang, earth has softness and firmness, and humans have benevolence and righteousness; these are all manifestations of the intermingling of yin and yang energies, used to generate things and reveal their nature. This is called "the Dao," referring to the principle by which all things must follow. Heaven, earth, and humanity converge, and the two energies operate within them, so the trigrams use six lines to represent them, and change arises accordingly. The formation of hexagrams with six lines is due to this reason. Investigating all things in the world, none exists without relying on the mutual following or opposing of yin and yang as the fundamental basis for existence and transformation: yin requires yang, and yang requires yin, combining to gain from each other, thus generation and transformation have no end. Therefore, what was originally single becomes paired, and what was originally three lines becomes doubled. Hence, the formation of compound hexagrams is also based on the natural tendency of generation and transformation.

如乾之三爻也，無所謂生成，故無所謂物事，不過以象天之元氣而已。若推其生成，象其物事，則必加其所行止之象，而仿其氣之動靜，名其數之奇偶，以盡其生化之用，則三爻之乾，即重為六爻矣！動靜之所別，行止之所殊，而後可記可名，不復渾沌；而氣之所至，亦悠然見之於數矣！

For instance, when "Qian" (Heaven) consists of only three lines, it cannot be said to have generation or to represent anything, but merely symbolizes the primordial qi of Heaven. If we wish to investigate its generation and to manifest its representation, we must add the images of its movement and stillness, imitate the movement and stillness of its qi, and indicate the odd and even numbers to exhaust its function of generation and transformation. In this way, the three lines of "Qian" become six lines. Only when movement and stillness are distinguished, and movement and rest differ, can it be recorded and named, no longer a confused whole; and the extent to which the qi reaches can then be clearly manifested through numbers.

如乾卦既為六爻，已由陽而生陰，奇而成偶；前之三九為奇者，今已六九為偶；奇之為陽者，今已偶之為陰矣！此孚於二氣之妙用，生化之大則，莫之為而為，莫之致而至者也。蓋陽動必生陰，體陽者必用陰；乾雖純陽之氣，若既動矣，亦當生陰；既用矣，必當有陰，不必其變也。以三爻之重，逐換奇為偶，非爻之變，其數之自易也。

For example, the hexagram "Qian" (Heaven) has already become a hexagram of six lines. It has already generated yin from yang, and transformed from odd to even: previously, three lines of nine multiplied together gave twenty-seven, an odd number; now, six lines of nine multiplied together give fifty-four, an even number. Previously, because it was odd, it belonged to yang; now, because it is even, it belongs to yin. This conforms to the subtle workings of yin and yang and the great principle of generation and transformation. It is "without anyone doing it yet it is accomplished, without anyone prompting it yet it is achieved." Because yang once moves, it must generate yin; something that belongs to yang must use yin. Although "Qian" is purely yang, once it moves, it should generate yin; once it is used, it must contain yin, without needing the line markings to actually change. Simply doubling the three lines into six lines sequentially changes odd into even: this is not the lines changing, but the number itself changing.

乾卦如是，餘卦亦然，故體用不同，動靜各異；因其異，而氣乃見，數乃明；生成之功，乃得而言；事物之類，乃得而辨，則六爻重卦者，實易道之本，而言易者所必知者也。重卦之爻六，因而變化以成六十四卦，即八自乘數也；六爻之變為三百八十四爻，因而變化以成四千九十六，即六十四之乘數，皆自變出。故六爻重卦，為極卦之變，而窮象之用也。

The hexagram Qian is like this, and all other hexagrams are the same. Therefore, the essence and function differ, movement and stillness vary; precisely because of these differences, qi becomes apparent and numbers become clear; the process of generation has something to say, and the classification of things has a method to follow. Thus, the hexagram with six lines is indeed the fundamental principle of the Way of the Book of Changes, something essential for those who study the Book of Changes. The hexagram has six lines, thus generating the sixty-four hexagrams through change, which is the square of eight; the six lines each change, forming three thousand eight hundred and forty lines, thus generating four thousand and nine十六, which is the square of sixty-four—these are all derived from change. Therefore, the hexagram with six lines pushes the change of the hexagram to its extreme and exhausts the function of the images to the very end.

伏羲之初創時，由八卦之三爻，易為六爻，八卦之用以見；由六爻之變，成六十四卦，而八卦之變以明；若再推之，則變者愈多，為用愈廣，其所以測事物者，亦無盡矣！故卦之體止於八，而變則無盡，則由於六爻之重卦也。其所仿者，河圖之數，易為洛書；二氣分合，化成萬類，皆以數之變，而象以成，類以眾也。易卦之象，三爻者，陰陽自純，而六爻則交錯矣！

Fuxi originally created the Eight Trigrams, and changed the three lines of each trigram into six lines, thus making the function of the Eight Trigrams evident. Then, by the movement of the six lines, the sixty-four hexagrams were formed, and the changes of the Eight Trigrams became clear. If we continue to derive further, the changes would become even more numerous, and their applications would be even broader. Using them to measure things would have no end. Therefore, the "body" of the hexagrams stops at eight, but their "changes" have no end, because of the repeated hexagrams with six lines. It imitates the transformation of numbers from the Yellow River Chart to the Luo Writing: yin and yang energies have both separation and union, giving rise to myriad things. This is all due to the movement of numbers, which allows images to be formed and categories to become numerous. In terms of the images of the Book of Changes, the three-line trigrams still have pure yin and pure yang, but in the six-line hexagrams, they have become intermingled and mixed.

三爻者，生化未見；而六爻，則分明矣！六爻之卦，繫後天之象，蓋氣已動，而形亦成，數已繁，而用亦廣，非復單純之象可比；則觀象以辨物，徵數以卜事者，必於爻求之，且必於重卦之爻求之也。三爻之象天地人也，為數甚簡；六爻則天在上，地在下，人居中，各得二爻，其數已繁。由下而上，地居其始；由上而下，天處其顛；人在中央，得二氣之和。

The third line of a trigram, the trigram itself, has not yet shown its transformation; but in the case of a hexagram, the lines are clearly visible. A hexagram belongs to the Later Heaven configuration, because at this point the energy has already begun to move, the form has already been established, the numbers have become numerous, and the application has become extensive. It is no longer comparable to a simple image. Therefore, to observe the images in order to distinguish things and to use numbers in order to predict events, one must look at the lines, and specifically at the lines of the compound hexagram. A trigram represents heaven, earth, and humanity, with a simple number of lines; but a hexagram has heaven above, earth below, and humanity in the middle, with each of the three elements occupying two lines, making the number of lines more complex. Looking from below, earth is at the beginning; looking from above, heaven is at the top; humanity is in the center, receiving the harmonious influence of yin and yang energies.

故爻六而氣仍二，天氣上行，地氣下降；一卦之例，正如八卦之方位圖。故乾氣自初至五，為乾之正位，即九五也；坤氣自上至二，為坤之正位，則六二也。陽者陰用，陰者陽用，陰陽交用者也。

Therefore, although there are six lines, the energy remains just two streams: the heavenly energy ascends upward, and the earthly energy descends downward; the structure within one trigram is exactly like the directional diagram of the eight trigrams. Thus, the energy of Qian ascends from the first line to the fifth line, which is Qian's central position, known as 'nine five'; the energy of Kun descends from the top line to the second line, which is Kun's central position, known as 'six two'. Yang is used with Yin, and Yin is used with Yang; Yin and Yang are interdependent in their use.

故天氣下行，而地氣上達，人在其中也；卦之有爻，以紀數也；爻之有象，以明氣也；重卦之爻，二氣或備；六爻之用，八卦俱全；陽奇陰偶，天往地來；故在下為初，在未為上；初以明時之始，上以紀位之高；皆氣之所至、所行、所進、所退也。故卦爻六，而所象甚多；類雖三，而所用無盡也。

Therefore, the heavenly qi descends, and the earthly qi ascends, with humans in the middle. The lines in the hexagrams are used to record numbers; the lines have images to explain qi. The lines in the compound hexagrams contain both yin and yang qi in general; the functions of the six lines include all the meanings of the eight trigrams. Yang is paired with odd numbers, and yin with even numbers; the heavenly qi descends, and the earthly qi ascends. Therefore, the line at the very bottom is called "Chu" (Initial), and the line at the very top is called "Shang" (Upper): "Chu" indicates the beginning of time, and "Shang" records the lofty position. These all show the movement, arrival, advancement, and retreat of qi. Thus, although there are only six lines in a hexagram, they can represent a great variety of things; although the three principles (Heaven, Earth, and Humanity) are only three categories, their functions are endless.

文王八卦，世所稱為後天卦象者，即今本易經所傳，以別於連山歸藏，故曰周易。其八卦方位次序，與伏羲者不同，易傳帝出乎震一節，即指明其位次也。其位次之定，亦由於太極圖及洛書之象，合伏羲卦而互闡其用也。蓋伏羲之卦，位次依於河圖；文王之卦，位次仿於洛書；一體一用，一天一人，其異者正其變化之跡，其變者正其自然之象，初非文王故異之而變之也。

King Wen's eight trigrams, commonly referred to as the Later Heaven trigrams, are the system found in the currently transmitted version of the Classic of Changes. This system is distinguished from the Lianshan and Guicang, hence it is called the Zhou Yi. The arrangement and order of the trigrams in the Zhou Yi differ from those in Fuxi's system. The passage "The Emperor arises from Zhen" in the Sayings on the Trigrams section of the Commentary on the Changes explains precisely the positional sequence of the Zhou Yi trigrams. The determination of these positions is based on the Taiji diagram and the image of the Luo Book, combined with Fuxi's trigrams to elucidate their functions. Generally speaking, Fuxi's trigrams are based on the He Tu, while King Wen's trigrams follow the pattern of the Luo Book: one belongs to "body" and the other to "function"; one emphasizes heaven, the other emphasizes humanity. The differences between the two are the traces of transformation; their changes are the expressions of nature, not because King Wen deliberately sought to differ from Fuxi and made intentional alterations.

文王之卦，原伏羲所制，八卦及六十四卦，六爻及三百八十四爻，皆無異也，其所異者，方位次序而已。因方位之異，而見主客之殊；因次序之異，而見生化之別；無非就天人之間，事物之內，盡其情狀，推其始終，以象之於卦，而足為推測之用耳。故位次之不同，乃卦之自變，文王不過因而演之，以成易耳。他如連山歸藏，亦如此例，各以不同而征其變，以變而成其易而已。

King Wen's hexagrams were originally established by Fuxi: the eight trigrams and the sixty-four hexagrams, the six lines and the three hundred and eighty-four lines, are all the same. The difference lies only in their positions and order. Because of different positions, the distinction between the main and the guest becomes apparent; because of different order, the difference between origin and transformation is shown. This is simply a complete description of the situations between heaven and humanity, and within things and events, making clear their beginning and end, and then taking the form of hexagrams so that they may be used for divination. Therefore, the difference in positions is actually the change of the hexagram itself, and King Wen merely followed this change and explained it, thus composing the Book of Changes. Other works such as the Lianshan and Guicang are similar examples, each using different arrangements to verify their changes, relying on this 'change' to become their own respective Books of Changes.

夫易固取變易為旨者，則推異致變，亦伏羲易之所有。而人事變易無窮，一易之象，無以盡之，則雖屢變屢異，既為易道所包者，自可順其然，而推衍其新。蓋後天之事物日繁，氣數日變，而易亦象之，以成後天之卦也。故卦之方位，非前之地位；次序非前之交代；其各類以殊，道路以別。觀文王之制，即可見後天與先天之不同也。夫先天八卦以乾坤居上下，而後天則易以離坎；先天以日月列東西，而後天則易以震兌；而乾坤反在其則，與巽艮同處於隅者、何也？

The Book of Changes originally focuses on "change," so seeking differences and causing change is something inherent in Fuxi's Book of Changes. Since human affairs are ever-changing and endless, a single set of hexagrams in the Book of Changes cannot fully express all these changes. Therefore, even though changes occur repeatedly and differences arise continuously, as long as they remain within the scope of the principles of the Book of Changes, one can naturally derive new forms by following the natural course. As later phenomena become increasingly complex and the transformations of qi become more frequent, the Book of Changes also takes on new symbolic forms, thus forming the later hexagrams. Therefore, the positions of the hexagrams are no longer as they were before, and their order is no longer the same as before; their categories have changed, and their paths have diverged. By looking at King Wen's arrangement, one can clearly see the differences between the later and earlier hexagrams. In the earlier hexagrams, Heaven and Earth occupy the top and bottom positions, but in the later hexagrams, they are replaced by Fire and Water. In the earlier hexagrams, the Sun and Moon are placed in the east and west, but in the later hexagrams, they are replaced by Thunder and Lake. Heaven and Earth even retreat to the corners, alongside Xun and Gen—why is this so?

蓋即後天之氣數然耳。後天者，本生生不息之例，為變化不居之規；不息則位無定方，行無定所；不居則氣有消長，數有盈虛，與先天者自異其趣矣。以先天之氣，變為後天事物，則體用自殊。如後天之二氣，以水火為主，水火代乾坤大用，為五行之首，為陰陽主器，司萬物之生，故坎離二卦為上下正位，示後天生化之本源，如先天之乾坤也。且先天之氣純，一交而分後天，則相錯以行，相和以化，不可劃為二也。

This is precisely due to the later heaven's qi numbers. The so-called "later heaven" is essentially the common principle of continuous generation and the ever-changing rules: because it is unceasing, there is no fixed direction or place for its movement; because it is ever-changing, the qi has both decline and growth, and the numbers have both fullness and emptiness, differing from the natural principles of the earlier heaven. When the qi of the earlier heaven transforms into the things of the later heaven, the nature and function naturally differ. For example, the yin and yang qi of the later heaven are mainly water and fire: water and fire take the place of heaven and earth to perform their great functions, occupying the first place among the five phases, serving as the main tools of yin and yang, governing the growth of all things. Therefore, the two trigrams "Kan" (Water) and "Li" (Fire) occupy the upper and lower central positions, showing the origin of later heaven's generation and transformation, just as the trigrams "Qian" (Heaven) and "Kun" (Earth) do in the earlier heaven. Moreover, the qi of the earlier heaven is pure and unified. Once it is differentiated through interaction to become the things of the later heaven, it runs in a mixed manner and harmonizes in generation and transformation, and can no longer be clearly divided into two separate parts.

如水火為陰陽合體，水以陽合於陰，火以陰藏於陽，其成固非純。而水以體陽用陰，故坎屬陽而在下；火以體陰用陽，故離屬陰而居上；其行固交錯以推演之也。故連歸之後，文王又重演之，得文王之易，而伏羲之卦象更明。以用能昭體，人能合天，其義一貫，其道互證，而其象數變化，尤能全始終。

For instance, water and fire are both composite entities formed by the union of yin and yang: water is formed by yang entering into yin, while fire is formed by yin being concealed within yang. Their composition is inherently not pure. Water has a yang nature in its substance but a yin nature in its function, so the trigram "Kan" (Water) is classified under yang but is placed below; fire has a yin nature in its substance but a yang nature in its function, so the trigram "Li" (Fire) is classified under yin but is placed above. Their operation is inherently interwoven and interdependent. Therefore, after the books of "Lianshan" and "Guicang", King Wen reinterpreted them and developed the "Yi" (Book of Changes) of King Wen. As a result, the hexagrams of Fuxi became even clearer. This is using function to reveal essence, using human affairs to connect with heavenly principles. The meanings are consistent, and the reasoning mutually supports each other. The changes in images and numbers are especially able to connect from beginning to end.

一本末，足以探天下之繁賾，極事物之常變者也。故以先天名伏羲之易，後天名文王之易，示雖有異，不過先後之分。其如一人亦有先後天，事物皆然，則先後天之易，猶一易也，何可異視之耶？文王卦位次之變自伏羲卦者，由於先天之氣數，因動靜往來而生變化，如河圖之象，因五行之交代而生變化也。故河圖易而洛書成，先天卦易而後天卦見，其例然也。

Unifying the beginning and the end is sufficient to explore the complexity and depth of the world, and to exhaust the normal and abnormal states of things. Therefore, the Book of Changes attributed to Fuxi is called Earlier Heaven, and the Book of Changes attributed to King Wen is called Later Heaven, indicating that although they are different, they are merely a matter of earlier and later. This is like a person having both an Earlier Heaven and a Later Heaven; all things are the same. Thus, the Earlier Heaven Book of Changes and the Later Heaven Book of Changes are actually the same Book of Changes; how can they be regarded as two separate things? The reason why King Wen's arrangement of the hexagrams changed from Fuxi's is because the qi of the Earlier Heaven changes due to movement and stillness, coming and going. It is similar to the image of the Yellow River Chart changing into the Luo Writing due to the alternation of the Five Phases. Therefore, the Yellow River Chart changes into the Luo Writing, and the Earlier Heaven hexagram changes into the Later Heaven hexagram, following the same pattern.

先天之象，陰陽始判，天地始位，氣動而升，形定而降。乾坤定位於上下，日月交行於東西，陽由地升而為震，陰自上降而成風；澤則近天，以示陽之近極；艮則近地，以明陰之將盈；其位定而次明也。定則不變，明則不化；不變則窮，不化則滅，而天地將息，事物何生？此先天之氣數，必由窮而變，明而通，生而繼滅，化而繼盡，以太極之運，本不息也。

The image of the Earlier Heaven shows the stage when yin and yang were just beginning to differentiate and heaven and earth were just beginning to be established: when the qi moves, it rises; when the form is fixed, it descends. Heaven and Earth are positioned at the top and bottom, while the sun and moon move across east and west. Yang qi rises from the earth, becoming "Zhen" (Thunder), and yin qi descends from above, becoming wind, which is "Xun" (Wind). The marsh is near heaven, showing that yang has approached its extreme; "Gen" (Mountain) is near the earth, indicating that yin is about to be full. When positions are fixed, the order becomes clear. However, once fixed, there is no change; once clear, there is no generation. No change leads to exhaustion, no generation leads to extinction. If heaven and earth were to stop, where would things come from? Therefore, the qi of the Earlier Heaven must necessarily arise from exhaustion to bring about change, from clarity to seek communication, and from extinction to bring about life, and from exhaustion to bring about transformation—because the movement of the Taiji never ceases.

天地之氣，原貴生也，故不息以行其位，而性使然也。水性流下，故就地；火性炎上，故親天；故天火為同人，水地為比。且其致用，則水以體陽宜上升，火以體陰宜下濟，如天道尊而下，地道卑而上，故水火為既濟，火水為未濟，皆以其所得於二氣者交錯，所行於天地者同化，而足以為萬物生化之本，代乾坤上下之用也。此後天八卦方位，皆定於坎離，不復同於先天矣。夫坎離既主後天之位，為全易之宗，則猶先天之乾坤，為諸卦之主，已無疑矣。

The vital energy of heaven and earth naturally values "generation" as its essence, thus continuously moving in their respective directions, which is inherent to their nature. Water flows downward, so it tends toward the earth; fire ascends, so it adheres to heaven. Therefore, when heaven is above and fire below, it forms the hexagram of "Union"; when water is above and earth below, it forms the hexagram of "Following." Regarding their initiating transmission, water, though belonging to yang, should rise, and fire, though belonging to yin, should descend. Just as the heavenly way, though exalted, gives downward, and the earthly way, though humble, receives upward; thus, when water is above and fire below, it forms the hexagram of "Already Completed," and when fire is above and water below, it forms the hexagram of "Not Yet Completed." This is because they receive exactly the right intermingling from the two primordial energies, yin and yang, and their movement in the world is exactly harmonized, thus becoming the fundamental force for the generation of all things, taking the place of heaven and earth in their roles of above and below. This is why the later heaven trigrams are all determined by kan and li, not the same as in the earlier heaven. Since kan and li now govern the later heaven directions and become the main trigrams of the entire Book of Changes, they are like the earlier heaven's qian and kun, the rulers of all hexagrams, which is without doubt.

而先天日月之象、東西之行，今既以坎離象水火而代天地，則必易以震兌，而指日月之升降，明陰陽之道路。在先天以天言，則為東西；在後天以人言，則為左右。先天之日月升降，即後天之晝夜往來。故震在東方，示日所生為陽所始；兌居西方，示月所出為陰所行。在一日為旦夕之分，在一年為春秋之別。

In the Earlier Heaven arrangement, the images of the sun and moon are represented by the trigrams Li (Fire) and Kan (Water), positioned east and west respectively, symbolizing their rising and setting, traversing the east-west path. Now, in the Later Heaven arrangement, the trigrams Kan (Water) and Li (Fire) are used to symbolize water and fire, taking the positions of Heaven and Earth instead. The original positions indicating the sun and moon in the east and west are thus left vacant, and the trigrams Zhen (Thunder) and Dui (Lake) are used instead to indicate the rising and setting of the sun and moon, thereby marking the channels of yin and yang movement. In the Earlier Heaven arrangement, the discussion is from the perspective of Heaven, hence the terms east and west. In the Later Heaven arrangement, the discussion is from the human perspective, hence the terms left and right. The rising and setting of the sun and moon in the Earlier Heaven arrangement correspond to the alternation of day and night in the Later Heaven arrangement. Therefore, the trigram Zhen is placed in the east, indicating the birth of the sun, which is the beginning of yang energy; the trigram Dui is placed in the west, indicating the emergence of the moon, which is the beginning of yin energy. This distinction between rising and setting divides a day into morning and evening, and a year into spring and autumn.

而以五行言之，則震為東方之木，兌屬西方之金。木生火而相親，則陽升之道；金生水而相近，則陰降之途。既以水火主生化之中樞，自當以金木司生化之相位。此震兌在後天居左右之地，代日月之明，本陰陽升降之機，為天地生殺之宰。而與先天之象，以變而殊、化而易者，正由後天五行之氣、萬物之生化，自然而然，自至而成，其方位次序遂依此而見矣。

If we consider the Five Phases, "Zhen" (Shock) belongs to the Eastern Wood, and "Dui" (Lei) belongs to the Western Metal. Wood can generate fire, which is closely related to fire, and this is the path of ascending yang energy; Metal can generate water, which is close to water, and this is the path of descending yin energy. Since the Later Heaven has already used the trigrams of water and fire as the central elements of generation and transformation, the positions that support them naturally should be entrusted to the phases of Metal and Wood. This is why "Zhen" and "Dui" occupy the left and right positions in the Later Heaven trigram arrangement: they take the place of the sun and moon to illuminate, and they themselves are the pivot of yin and yang rising and falling, thus becoming the masters of growth and decline in the universe. As for why the Later Heaven image differs from the Earlier Heaven and must be changed, it is because the Later Heaven operates through the energies of the Five Phases, within which all things grow, develop, and mature naturally, and thus the directions and order become evident.

河圖之易為洛書，由五行化為九宮，此自然變化所至者也。先天卦之變後天亦如是。以先天之卦，分陰分陽，統於乾坤；而後天之卦，則陰陽交錯，或老或少，升降往來，或多或少，而統於四正，即坎離震兌也。四卦應四象，而推演之，以加於四隅，象氣之多寡、數之進退，而仍附於四正。以其數不止四，卦則演為八，猶陰陽之復分陰陽也。故八卦出於四象。

The transformation of the Yellow River Chart into the Luo Writing is due to the transformation of the Five Phases numbers into the numbers of the Nine Palaces, which is a result that naturally occurs. The change from the Earlier Heaven trigram positions to the Later Heaven trigram positions follows the same principle. In the Earlier Heaven trigrams, yin and yang are completely separated, and all are subordinated to the trigrams Qian and Kun. In the Later Heaven trigrams, yin and yang intermingle; some are old and some are young, with the movement of qi having more or less. All are subordinated to the four cardinal directions, which are the trigrams Kan, Li, Zhen, and Dui. These four trigrams correspond to the Four Symbols. From them, further trigrams are added to the four corners to represent the quantity of qi and the advance and retreat of numbers. These corner trigrams still depend on the four cardinal trigrams. Since the numbers to be expressed are not limited to four, the trigrams develop from four to eight, just as yin and yang are further divided into yin and yang. Therefore, the Eight Trigrams arise from the Four Symbols.

而四隅之卦，本於四正也。四隅之卦乾坤巽艮，在先天為正位，與老陰少陽，所象重要；而在後天，則繫坎離震兌之所分化，以明氣之往來、數之大小而已，故反置於隅位，不似先天之重要矣。蓋天地生化有主宰，氣數有權衡，當位者貴，逢時者宜。坎離震兌，位當時逢，其綱領全易，如一歲之四時、天下之四方，為拄持全體者也。而乾坤巽艮，則其節目，附庸於四正者，故處於隅位，而當於閒時，其取象自異於先天也。

The four corner trigrams are actually derived from the four main trigrams. The trigrams Qian, Kun, Xun, and Gen, which later occupy the four corners, originally held central positions in the Earlier Heaven arrangement, paired with images such as "old yin" and "young yang," and symbolized significant meanings. However, in the Later Heaven arrangement, they become subordinate branches of Kan, Li, Zhen, and Dui, used to explain the movement of qi and the magnitude of numbers. Therefore, they are placed in the four corners, no longer occupying central positions as in the Earlier Heaven. The generation and transformation of heaven and earth have their master, and the balance of qi and numbers has its measure: those in proper positions are esteemed, and those in accordance with the season are appropriate. Kan, Li, Zhen, and Dui are both in proper positions and in harmony with the season, capable of encompassing the entire Yi hexagram, like the four seasons of a year or the four directions of the world, forming the main framework. Qian, Kun, Xun, and Gen, on the other hand, are merely details subordinate to the four main trigrams, thus occupying the four corner positions, serving only during the transitional periods between the four seasons. The images they represent naturally differ from those in the Earlier Heaven.

先天以乾坤為主，故二者獨尊；後天以四正為綱，故餘者賤。道有輕重，物有先後。不獨後天之乾坤，非先天比，且所象者亦異於先天，猶洛書之數雖同河圖，而其名類已非河圖之舊。故乾坤在先天為全易主體，在後天則僅一枝節之用，與巽艮同觀。人或疑其退處一隅為不倫，或意其甘退讓為自卑，皆誤也，皆不明後天卦象所取義全異者也。夫後天之乾坤，為本五行之物，推演而得之象，與各卦象同，非復統二氣之乾坤矣。

The trigrams of Heaven and Earth hold a primary position in the Earlier Heaven arrangement, thus occupying a unique status. In the Later Heaven arrangement, the four cardinal trigrams serve as the main framework, and the other trigrams take a subordinate position. The principles have inherent distinctions of importance and sequence. Not only do the trigrams of Heaven and Earth in the Later Heaven arrangement fall far short of those in the Earlier Heaven, but their symbolic meanings are also different. Just as the numbers in the Luo Writing are the same as those in the Yellow River Chart, their names and classifications have changed. Therefore, the trigrams of Heaven and Earth in the Earlier Heaven are the core of the entire Yi system, while in the Later Heaven they have only a secondary role, and should be treated together with the trigrams of Wind and Mountain. Some people doubt that the trigrams of Heaven and Earth being placed in a corner is improper, while others think they willingly step down and take a humble position. These views are incorrect, as they fail to understand that the meaning of the Later Heaven trigrams has completely changed. The trigrams of Heaven and Earth in the Later Heaven are derived from the Five Phases and are of the same nature as the other trigrams, no longer representing the overarching trigrams of yin and yang.

後天二氣之主，以水火當之。水火之外，則皆升降往來之象。乾在西北，坤處西南，其象不過陰陽升降之跡、水火往來之道耳。後天之用，以事物為主，不限於氣，而氣行有形，氣至有質，所象有物，非空言天地也。故後天乾坤，自水火之升降、陰陽之往來，而見其所象之物，不可與先天乾坤等量齊觀。

Later Heaven's yin and yang energies are governed by the trigrams of Water and Fire; the other trigrams merely symbolize the rising and falling movements. The trigram Qian (Heaven) is located in the Northwest, and the trigram Kun (Earth) is located in the Southwest. They merely represent the traces of yin and yang rising and falling, and the channels through which water and fire move. Later Heaven studies focus on concrete things rather than abstract energies; when energy moves, it takes shape; when energy arrives, it takes form. What is symbolized are real objects, not empty talk about heaven and earth. Therefore, the trigrams Qian and Kun in Later Heaven should be understood from the rising and falling of water and fire, and the movement of yin and yang, to see the concrete things they symbolize. They should not be compared directly with the trigrams Qian and Kun in Earlier Heaven.

若不明此義，而仍視如先天，則將坎離混觀，而亂其序；抑將天地顛倒，而失其真，則何以明文王卦位哉？故乾坤巽艮之在後天，正同先天之震巽艮兌，其位序既易，其象數隨殊。此即先後之分、體用之別。學者不可執於名而忘其實，滯於象而遺其位，混先後天而一之，使體用不彰，變化不明，而無以探易之蘊也。

If one does not understand this principle, and continues to view the Later Heaven's Qian and Kun with the perspective of the Earlier Heaven, they will confuse them with Kan and Li, thereby disrupting the order of the Later Heaven; even more so, they may reverse the positions of Heaven and Earth, losing the true nature of the Later Heaven's卦 positions. Then how can one explain King Wen's卦 positions? Therefore, the positions of Qian, Kun, Xun, and Gen in the Later Heaven correspond exactly to the positions of Zhen, Xun, Gen, and Dui in the Earlier Heaven: once the positions have changed, the images and numbers associated with the卦 also differ. This is precisely the distinction between the Earlier Heaven and Later Heaven, as well as the difference between the essential nature and the function. Those who study the Book of Changes should not be rigid in their attachment to the names of the卦 and forget their actual meaning, nor should they be stuck in the images of the卦 and neglect their positions. They must not confuse the Earlier Heaven and Later Heaven as one, leading to confusion between the essential nature and function, and making the changes unclear. In that case, one would be unable to explore the profound essence of the Book of Changes.

文王卦位，以後天二五之氣，分佈天地間而不息。為陽者求於陰而成生育，為陰者近於陽見變化。故繫以分，類以別，正如洛書之數，陰陽次序，分為兩繫，奇偶之數，交錯以行，不似河圖之一氣相環，終始相屬也。蓋動愈久，則變出愈多；生日眾，則類分日繁，有必至之勢也。

King Wen established the positions of the hexagrams by distributing the Later Heaven "two and five" energies—yin and yang energies and the Five Phases energies—throughout the heavens and earth, which continuously move. Those belonging to yang must seek yin in order to achieve generation and reproduction; those belonging to yin must approach yang in order to manifest transformation. Therefore, the hexagrams should be classified systematically and distinguished by categories, just as the numbers in the Luo Writing divide yin and yang in sequence into two series, with odd and even numbers alternating, unlike the Heavens Chart which has a single energy circulating continuously from beginning to end. Generally, the longer the movement continues, the more changes it produces; the more things generated, the more complex the categories become, which is inevitable.

文王之卦，既以坎離震兌分列四柱，則乾坤巽艮自隨之而各屬其類。因後天事物，以形為主，形氣所成，以方為定，二五所生，隨其類而位於一方：水從北，火歸南，木在東，金居西，土行中央而運四季，各有其序也。水與金接，火與木連，風木相依，水天一氣，山土成地而載萬物，相生則承其氣，相制則抗其位，各有其次也。

King Wen arranged the trigrams Kan, Li, Zhen, and Dui as the four main pillars. Consequently, Qian, Kun, Xun, and Gen naturally fell into their respective categories. Since Later Heaven is based on physical forms, all things composed of form and qi must be determined by direction; the things generated by yin and yang and the Five Phases are thus placed in specific directions according to their categories: water belongs to the north, fire to the south, wood to the east, metal to the west, and earth in the center, circulating through the four seasons. Each has its own order. Water and metal connect with each other, fire and wood are linked, wind and wood are interdependent, water and heaven share the same qi, and mountain and earth form the land to support all things. Those that mutually generate receive each other's qi, while those that mutually control oppose each other in position, each following its own order.

故先天乾為天，包舉宇宙，後天則屬金，建位西北；先天坤為地，載育群倫，後天則屬土，序次西南。南為離火，與土相生；北為坎水，與乾相得。而西方之兌屬金，亦生自土而類於乾。艮為山，為氣之終，與土同類，而水泉潛焉。震為木之生地，木雖生於水，必得土之培，故自山出。巽亦木也，風之所見；風亦氣也，火之所燃。其性相宜，其位相接，故成環也。

Therefore, the Qian hexagram of the Earlier Heaven represents Heaven, encompassing the entire universe; in the Later Heaven, it belongs to the Metal element and is located in the Northwest. The Kun hexagram of the Earlier Heaven represents Earth, nurturing all creatures; in the Later Heaven, it belongs to the Earth element and is situated in the Southwest. The South is Li fire, which generates Earth; the North is Kan water, which generates Metal and thus harmonizes with the Metal of Qian. The Dui hexagram in the West also belongs to Metal, and is generated by Earth, thus being similar to Qian. The Gen hexagram represents mountain, the end of the movement of qi, and is similar to Earth, with underground springs hidden within it. The Zhen hexagram represents the place where wood grows; although wood is generated by water, it must be cultivated by Earth, so it grows from the mountain. The Xun hexagram also belongs to wood, being the place where wind manifests; wind is qi, which is what fire relies on to burn. These hexagrams are harmonious in nature and adjacent in position, thus forming a circular connection.

水為火仇，金為木敵，土受木制，金被火刑，水逢土掩，氣為風搖，相異其性，相抗其位，相制其能，相隔其次，故成錯也。環則氣順生成，錯則氣變化見。分則為四為八，推之無盡；合則為五為二，返之太極。此固後天自然之象，亦文王卦位次之所定也。

Looking at it in reverse: water is the enemy of fire, metal is the master of wood, earth is subdued by wood, metal is melted by fire, water is buried by earth, and qi is disturbed by wind. Their natures are opposite, their directions are opposing, their functions are mutually restraining, and their sequences are mutually separated, thus forming a situation of mutual crossing. The aspect where they form a continuous loop allows qi to flow smoothly and generate all things; the aspect where they cross each other allows the transformation of qi to be revealed. Separately, they are the Four Symbols and the Eight Trigrams, and their derivation has no end; together, they are the Five Phases and the Two Principles, and their return leads back to the Taiji. This is naturally the state of Later Heaven, and it is precisely the basis for the order of the hexagrams as established by King Wen.

且文王卦，為推伏羲卦之用，而盡其變也，即本先天氣數，推至後天事物，以求其遞嬗之跡也。故伏羲卦位次為易之體，文王卦位次為易之用。因用得體，因體得用，原無二致，則伏羲卦之位次，即文王卦之前身；而文王卦之位次，即伏羲卦之變象。二者一而二也。由其異以求其同，知其同以辨其異，此習易者之所先務，而不可不通之為一，以明其旨之所在，與象之所示也。

Furthermore, the positions of the hexagrams in the Book of Changes attributed to King Wen were intended to expand the function of the hexagrams from Fuxi, pushing their transformations to their ultimate extent. This was done by following the qi and numbers of the Earlier Heaven and proceeding all the way to the Later Heaven's specific phenomena, in order to trace the mutual transformation between the two. Therefore, the positions of the hexagrams from Fuxi represent the essence of the Book of Changes, while the positions of the hexagrams from King Wen represent its function. From function one can perceive the essence, and from the essence one can understand the function; the two are essentially the same. The positions of the hexagrams from Fuxi are the original form of the hexagrams from King Wen, and the positions of the hexagrams from King Wen are the manifested form of the hexagrams from Fuxi. It is acceptable to regard them as one or as two. One should first seek the commonality from their differences and then distinguish their differences based on their commonality. This is the primary effort required for those studying the Book of Changes. Only by integrating the two can one understand the fundamental principles and the meanings conveyed by the hexagrams.

如文王八卦之序自震始，與伏羲似同，而一則出於坤，為陽始生；一則變於艮，為陽已動，是不同也。蓋先天之氣，一六為水，三八為木，其序同也；後天之物，因土制水，因水生木，其用殊也。故甲乙為木，必得壬癸之生源，而甲已化土，方成生化之大用。若徒水不生木也，有土以培之，有山以蓄之，則水用見，而木道成，此後天之序，有異於先天，

For example, the order of the trigrams in the King Wen's arrangement starts with Zhen, which appears similar to the trigrams in Fuxi's arrangement. However, one originates from Kun, indicating the initial emergence of yang energy, while the other comes from Gen, indicating that yang energy has already begun to move, thus making them different. The Earlier Heaven arrangement discusses energy: one and the Six Harmonies form water, three and eight form wood, and the order is the same in both cases. The Later Heaven arrangement discusses things: it requires earth to control water and water to nourish wood, resulting in different functions. Therefore, the heavenly stems "Jia" and "Yi" belong to wood, but they must be supported by the water stems "Ren" and "Gui" as the source for their growth. Furthermore, "Jia" combines with "Ji" to form earth, enabling the full function of generation and transformation. If there is only water, it cannot alone produce wood; there must be earth to cultivate it and mountains to contain it, allowing the function of water to be revealed and the growth of wood to be completed. This is why the order in the Later Heaven differs from that in the Earlier Heaven.

而震坤之位，有殊於前象者也。先天生化本乎氣，故五行順序；後天生化存乎形，故五行錯行。一年之序之自春始，一日之氣自寅見，一地之氣自東起，故後天以震司動令也。動者自靜出，則震必自艮出。艮者止也。由動而止於靜，此艮為氣之終；由靜而漸於動，則艮又氣之始。故艮者始終之地。先天以艮入地，後天以艮出水，故艮之先後天，皆為終始之樞，而在後天尤至顯也。

This is why the trigrams Zhen (Thunder) and Kun (Earth) differ in their positions between the Earlier Heaven and Later Heaven arrangements. In the Earlier Heaven arrangement, the process of generation and transformation is based on qi, so the Five Phases are arranged in the order of mutual generation. In the Later Heaven arrangement, the process of generation and transformation occurs in form, so the Five Phases intermingle and move in a different sequence. The order of a year begins with spring, the qi movement of a day begins at the hour of Yin, and the qi flow of a region begins from the east, hence the Later Heaven uses the trigram Zhen to govern the time of movement. Since all movement originates from stillness, the trigram Zhen must arise from the trigram Gen. Gen signifies stopping: movement leads to stopping in stillness, so Gen is the end of qi; stillness gradually leads to movement, so Gen also becomes the beginning of qi. Therefore, Gen is the meeting point of beginning and end. In the Earlier Heaven arrangement, Gen is placed at the point of entering the earth, while in the Later Heaven arrangement, Gen is placed at the point where water qi emerges from the earth. Thus, Gen serves as the hub between beginning and end in both the Earlier Heaven and Later Heaven arrangements, and this is especially evident in the Later Heaven.

東北之方，正生機所息，如春之先、冬之盡也；山土之中，正生物之所始，如木之根、草之荄也。故艮者，萬物之所資以生育者也。其同者則為坤，故與抗位，然後天之序分相次也。以升降言，則坤艮相對；以出入言，則巽艮相當。巽為風木，草也，氣也。草木之出於地，已異於艮之根荄；風氣之流於空，卻近於乾之金氣，故與乾對，而同艮比。

The northeast direction is where vitality lies hidden and rests, much like the period before spring arrives or just before winter ends; in the soil of the mountains, it is where living things begin to sprout, similar to the roots of trees and the overwintering roots of wild grass. Therefore, the Gen trigram represents the foundation upon which all things rely for growth and development. The Kun trigram, which also belongs to earth, is paired with Gen, and they are placed opposite each other, facing each other, which is the arrangement of order in the Later Heaven. In terms of rising and descending, Kun and Gen are opposite; in terms of entering and exiting, Xun and Gen correspond. Xun represents wind and wood, as well as grass and qi. Grass and trees emerging from the ground have a form different from the roots and overwintering roots that Gen represents; wind moving through the void is closer to the metal qi of the Qian trigram, so Xun is opposite Qian and is adjacent to Gen.

乾為氣，若天空之氣，與水一類，化而為水，凝而為金，位在坎兌間，則西與北之相生也。次於西北方，則淨土之天所在也。佛稱淨土在西方，而佛身金剛不壞，佛相非空非色，其義與乾象同。佛言四大，地水火風，獨少金，而以西方淨土為佛地，亦與五行之言一也。故乾為天，而性屬金，而以西北，與巽對。

The trigram Qian represents qi, just like the atmospheric qi in the sky, and belongs to the same category as water: when dispersed it becomes water, and when condensed it becomes metal. Its position is between Kan and Dui, exactly where the western and northern regions of metal and water interact through mutual generation. It is placed in the northwest, which is considered the location of the "Pure Land Heaven." Buddhism says the Pure Land is in the west, and also describes the Buddha's body as being like a diamond, indestructible, and the Buddha's form neither empty nor material, which aligns with the imagery of the Qian trigram. Buddhism speaks of the "Four Great Elements," listing earth, water, fire, and wind, but omitting metal, yet it designates the western Pure Land as the Buddha's realm, which coincides with the Five Phases theory. Therefore, the Qian trigram represents heaven, and its nature belongs to metal, placed in the northwest, facing the Xun trigram in the southeast.

以用言，則與坤對。坤司載物，乾司覆物。坤為生，乾為化。乾知大始，坤代有終，皆功用之相當也，故位相比。此亦先後天之同異也。在五行生制中，萬物生化以成，固氣之所推蕩也。八卦之分五行以象物，因二氣生降消長，以象生化之跡，而以後天之卦為最明顯。

If we consider their functions, Qian and Kun are opposites: Kun is responsible for supporting all things, while Qian is responsible for covering all things; Kun governs generation, and Qian governs transformation. The "Great Treatise" of the Upper Canon says, "Qian knows the beginning of great things, and Kun completes the formation of things." Here the meaning is that Qian initiates the beginning of all things, while Kun continues the process so that things have an end. These are aspects of their functions that are mutually corresponding, hence the two trigrams are adjacent in position. This is also an example of the relationship between Earlier Heaven and Later Heaven, which are both the same and different. In the operation of mutual generation and mutual control among the Five Phases, all things are successively generated, and this is the result of the movement and agitation of qi. The Eight Trigrams are assigned to the Five Phases to symbolize specific things, following the rise and fall, increase and decrease of the two energies, yin and yang, to indicate the trajectory of generation and transformation. This is most clearly reflected in the Later Heaven arrangement of the trigrams.

蓋先天之卦，為示氣之本體，與其行至之序，非如後天均可按之事物也。後天卦象，全體生化，有行至之序，有變遷之跡，有相生制之象，有相循環之式。故分觀之，則一節一方之物；合觀之，則全部全體之事，均貫通者也。

The earlier heaven trigrams are meant to show the essence of qi and the order in which it moves and reaches. Unlike the later heaven trigrams, they do not correspond to specific things that can be verified in every aspect. The later heaven trigrams encompass the entire process of generation and transformation: they include the order of qi movement and the path of change, as well as the images of mutual generation and mutual control, and the pattern of continuous cycles. When viewed separately, each trigram corresponds to a specific season and direction; when viewed together, they represent the whole and overall principles, with everything interconnected.

如先天之卦，天地水火對列，山澤風雷抗居，其氣佈於兩間，其數分於萬物，而不相聯接也，故分為二，以屬於乾坤。後天則不然，以水火為主，金木為輔，四隅相錯，皆相接也。因後天之象，由合而分，本無窮盡，雖本先天一氣，可統於陰陽，而應五行生化，可變為萬用。故水火司乾坤之用，金木助陰陽之功，功用以全，物事以備。

For example, in the Earlier Heaven hexagrams, heaven and earth, water and fire are paired opposite each other, mountain and marsh, wind and thunder are opposed to each other. Their qi is distributed throughout heaven and earth, their numbers are allocated among all things, yet they are not connected to each other. Therefore, they are divided into two groups of yin and yang, each group belonging to Qian and Kun. However, in the Later Heaven, it is different: water and fire are the main elements, metal and wood are the auxiliary ones, and the four corner hexagrams are interwoven among them. They are all connected to each other. Because the image of Later Heaven comes from combination and then division, it has no end. Although it originates from the single qi of Earlier Heaven and can be summarized under yin and yang, once it is applied to the generation and transformation of the Five Phases, it can produce countless uses. Therefore, water and fire take on the functions originally belonging to Qian and Kun, while metal and wood assist yin and yang in completing their tasks, thus making the functions complete and things fully established.

在先天以元氣為貴，故乾包坤；而後天以生化為先，故陰先陽，此離上坎下，與乾上坤下各不同也。生化之用，以陽求陰，得陰始生，陽不獨生也，故曰陰陽。而上離下坎，離陰以代乾，坎陽以代坤，陰陽互濟，生化乃見，此實天下至理，萬物大本，而後天卦象位次之要義也。

In the Earlier Heaven arrangement, primordial qi is considered most important, hence the Qian trigram encompasses the Kun trigram. In the Later Heaven arrangement, generation and transformation take precedence, so yin comes before yang—this is why in the Later Heaven arrangement, the Li trigram is above and the Kan trigram is below, opposite to the Earlier Heaven arrangement where Qian is above and Kun is below. The function of generation and transformation is that yang seeks yin; only by obtaining yin can something be generated. Yang alone cannot produce offspring, so it is called "yin and yang." Thus, the upper position is occupied by the Li trigram, which has an outer yang and an inner empty space containing yin, taking the position of Qian as yin; the lower position is occupied by the Kan trigram, which has an outer yin and an inner solid space containing yang, taking the position of Kun as yang. Yin and yang support each other, enabling generation and transformation to manifest. This is truly the highest principle in the world, the fundamental basis of all things, and the most important meaning behind the arrangement of Later Heaven trigrams.

若仍如先天之象，則生化不成，氣數不續，道之窮也。窮則必變，變則後天之象見，此文王之卦，必繼伏羲而明，而離坎之位必代乾坤而立者也。物變必因陰陽之交，事變必因氣數之易，天地尚不得不變，況下者乎。後天者變象也，變於先天，而成現在之象，故人道存焉。人道以為主，則乾坤退用，此離坎屬人，為後天位次之樞，而主八卦之用也。學者當思之。

If the trigrams remained as in the Earlier Heaven, generation and transformation would not be completed, and the cycle of qi and numbers would not be continued. This is when the Dao reaches its end. When the Dao reaches its end, transformation is inevitable. Once transformed, the Later Heaven trigrams appear. This is precisely why King Wen's trigram positions must follow Fuxi and clarify them, and why the positions of Li and Kan must replace Qian and Kun. All changes in things are due to the meeting of yin and yang; all changes in affairs are due to the transformation of qi and numbers. Even heaven and earth cannot avoid change, so how much more so can the myriad things under heaven and earth? The Later Heaven trigrams are the trigrams after transformation; they come from the Earlier Heaven and form the appearance we now see. Thus, the human Dao exists within them. Since the human Dao is the main focus, Qian and Kun take a secondary role. Therefore, the trigrams Li and Kan belong to humanity and become the central points of the Later Heaven order, governing the functions of the eight trigrams. Those who study the Book of Changes should thoroughly understand this.

六十四卦，自八卦出，無論伏羲文王一也；其次序自伏羲八卦方位定，無論先後天一也。唯六十四卦，有本宮次序，有本卦次序，有相錯次序，有相和次序，各以其變化而定。本宮者，分乾坎艮震巽離坤兌八宮，各八變，成六十四卦，此序卦之自生也。

All sixty-four hexagrams are derived from the eight trigrams. Whether it is the Yi of Fuxi or the Yi of King Wen, there is no difference in this regard; their order also depends on the arrangement of the eight trigrams of Fuxi, whether earlier Heaven or later Heaven, and this is also without difference. However, the arrangement of the sixty-four hexagrams has several systems: there is the "order within the palace," the "order of the primary hexagram," the "order of mutual opposition," and the "order of mutual harmony," each determined by the particular method of change adopted. The "order within the palace" divides the sixty-four hexagrams into eight palaces: Qian, Kan, Gen, Zhen, Xun, Li, Kun, and Dui. Each palace undergoes eight changes, resulting in the sixty-four hexagrams. This is a method of arrangement that arises naturally from the hexagrams themselves.

本卦者，亦依八卦之生化，而以乾兌震離巽坎艮坤之序，分屬一卦，以成八屬，此明卦氣之消長為循環也。相錯者，以卦之交錯，分乾坤坎離震艮巽兌，相交錯而成行，以循環而為序，即《周易》上下經之序也。

The order of the primary hexagrams is also arranged according to the generation and transformation of the eight trigrams. Following the sequence of Qian, Dui, Zhen, Li, Xun, Kan, Gen, and Kun, all hexagrams generated from a particular trigram are grouped under that trigram's name, forming eight categories. This is used to explain the continuous cycle of the hexagram energies. The sequence of alternating trigrams is determined by the mutual crossing of trigrams. The trigrams Qian, Kun, Kan, Li, Zhen, Gen, Xun, and Dui are separated and arranged alternately in rows. The order is determined by the cyclic pattern, which establishes the sequence of the upper and lower parts of the Zhou Changes.

相和者，亦卦之交錯，合其體用，明其常變，和先後天之例，一伏羲文王之序，並及《連山》《歸藏》之成規，與本宮本卦參照而為序者，即《雜卦傳》之序也。蓋卦變本多，變必有例，易以明變，則一變有一序也。以此四者舉其凡，若盡其變，尚不止耳。

The concept of harmony and sequence also involves the intermingling of hexagrams, but it goes further by combining the essence and function together, clearly indicating both the constant principles and the changes. It harmonizes the Earlier Heaven and Later Heaven systems, unifies the two arrangements of Fuxi and King Wen, and takes into account the old practices of the books of Continuous Mountains and Returning Concealment. It also refers to the sequences of the original palace and the primary hexagram to determine the order. This is the order used in the "Zagua Transmission." Generally speaking, hexagrams naturally have many variations; whenever there is change, there must be a corresponding system. The Book of Changes is precisely used to explain change, so each variation produces a different pattern, and thus there is a corresponding order. Here four examples are given only as a general idea; if all variations are to be fully covered, there would be more than these.

六十四卦既由八卦出，八卦之序已有不同，則六十四卦之序，自分多類。不過後天易象重在交錯，二五流行，無不交互，天下萬類無非錯行，合則以生，分則以化，推之不盡，用之不窮，則當以文王所序之例為主，以能象現在之事物，而可推諸往來之氣數也。其它各例，以備參考，俾知序變則用殊，易道不窮，則變例無盡。

The sixty-four hexagrams arise from the eight trigrams, and since the eight trigrams themselves have an order of Earlier Heaven and Later Heaven, the order of the sixty-four hexagrams naturally divides into many categories. However, the Later Heaven arrangement of the Book of Changes focuses on intermingling: the energies of yin and yang and the five phases constantly flow and interact everywhere, and all things under heaven are intermingled. When combined, they give rise to existence; when separated, they undergo transformation. This process continues endlessly, and its application is inexhaustible. Therefore, we should take the system established by King Wen as the main reference, because it can symbolize current realities and be used to calculate the flow of energies. Other systems should be left as references, so that people may understand that when the order changes, its function also changes. The Way of the Book of Changes is boundless, and so too are the systems of change.

有後聖者出，推而廣之，亦足與文王易同，則變例之存，將有待於推闡，不獨溯源探本已也。文王所定六十四卦次序，大別之為上下篇，而上篇統於乾坤坎離，下篇統於震艮巽兌，此大略也。其實皆相錯交互，明氣之周流，二氣消息往復無已，自為環行，繫後天自然之象。

If there were a sage in later generations who could elaborate and expand upon these systems, they would be sufficient to stand equal with the Yi of King Wen. This shows that preserving these variations is left for later scholars to explore and clarify, not merely for tracing back to the origin. The order of the sixty-four hexagrams established by King Wen is generally divided into upper and lower parts: the upper part belongs to Qian, Kun, Kan, and Li, while the lower part belongs to Zhen, Gen, Xun, and Dui. This is a general classification. In reality, both upper and lower parts are interwoven and contain each other, used to illustrate the continuous flow of qi. The mutual rise and fall, movement and return of yin and yang energies have no end, naturally forming a circular movement, which is precisely the natural phenomenon of the Later Heaven.

由先天既變，氣隨形化，數隨事見，天道存於人物，化育寓於時位，皆莫為而為，莫致而至，以繼往啟來，垂今鑑古，無不符合，故為易之主體，而見卦之大用也。上篇三十，首乾坤而終坎離，明先後天之卦象異主，坎離即以代乾坤，為宇宙之樞機，運陰陽之中極，而天地間萬物從此生化也。

Since the Earlier Heaven transformed into the Later Heaven, the vital energy has changed along with forms, and numbers have manifested along with things. The heavenly way resides within people and objects, and the nurturing and transformation are contained within seasons and directions. All of this happens naturally without deliberate effort, without intentional invocation, and naturally comes to be. It connects the past with the future, guides the present, and reflects upon the ancients, with nothing failing to correspond. Therefore, the sequence established by King Wen became the main body of the Book of Changes, and the great function of the hexagrams is thus evident. The upper section contains thirty hexagrams, beginning with Qian and Kun and ending with Kan and Li, clearly indicating that the rulers of the Earlier Heaven and Later Heaven hexagram systems have changed: Kan and Li have replaced Qian and Kun, becoming the key elements of the universe, operating at the center of yin and yang, and from here all things in the universe between heaven and earth begin to grow and flourish.

下篇首咸怛，終既未濟，即本上篇乾坤坎離交錯，而成人類之萬事萬象，以震艮巽兌縱橫其間，明事物之迴環曲折，無窮無盡。人主其中，以代天地，並化育，為世界開化，為物類建極，以成天地人三才之德，而全易卦六爻之用。此下篇三十四卦始終，與上篇大同，皆以乾坤起，坎離終，而更交錯之也。

The lower section begins with the hexagrams "Xian" and "Heng" (the latter originally written as "Da"), and ends with "Ji Ji" and "Wei Ji." This structure continues from the interweaving of Qian and Kun, Kan and Li in the upper section, thereby forming the myriad phenomena of the human world. Then the hexagrams Zhen, Gen, Xun, and Dui are interwoven throughout to illustrate the endless cycles and twists of things. Humans dwell amidst all these, taking the role of heaven and earth, participating in the process of nurturing and transforming all things. They bring civilization to the world and establish standards for all creatures, thus achieving the virtue of the three elements—Heaven, Earth, and Humanity. This also completes the full function of the sixty-four hexagrams. The overall structure of the thirty-four hexagrams in the lower section is similar to that of the upper section, both beginning with Qian and Kun and ending with Kan and Li, but the interweaving is more complex.

蓋後天之象異先天者，以多變也。變因於交錯，而天地既判，人物已繁，往來其中者，形與氣也。司形者數，司氣者神；神主於隱，數行於顯，於是一者分為二矣。先天一氣，同屬乾坤，雖二仍一，以氣同也；後天之變，乾坤分居，坎離代用，形氣並具，二者乃分。

Later Heaven differs from Earlier Heaven, primarily because of the multiplicity of change. Change arises from interaction, and once heaven and earth have been separated, human beings and things have become numerous. What moves among them is no more than the two aspects of "form" and "vital energy." The aspect of form is governed by numbers, while the aspect of vital energy is governed by spirit; spirit resides in the subtle and hidden, while numbers operate in the manifest and clear. Thus, what was originally unified splits into two. Earlier Heaven consists of a single vital energy, unified under the governance of Qian and Kun, though it is said to be two trigrams, they are still one in essence, because they share the same vital energy. After the change of Later Heaven, Qian and Kun retreat to the four corners and occupy two positions, while Kan and Li take over their functions. Form and vital energy coexist, and thus the division into two is truly established.

故後天統於水火，分於木金，而同寓於土，非復先天二氣之一源，生化盡於乾坤，周迴歸於陰陽，其象簡，其數單，而明顯易見，純一易名也。故後天之卦，必以交錯為用，愈交愈生，愈錯愈化，生化日眾，交錯益多。此六十四卦，雖大類統於水火，屬於四正，而其往復之跡、消息之機，無不縱橫如織，迴環若輪也。此文王六十四卦定序之義也。

Therefore, the Later Heaven system is governed by water and fire, distributed among wood and metal, and jointly resides in earth. It is no longer like the Earlier Heaven, where yin and yang arise from the same source, and all processes of generation and transformation belong to Heaven and Earth, circulating in a cycle and returning to yin and yang. The image of the Earlier Heaven is simple, with a small number of elements, clearly visible, purely unified, and easy to name. The hexagrams of the Later Heaven, however, must be used through their interweaving: the more they intersect, the more things they generate; the more they differ, the more transformations they produce. The processes of generation and transformation increase day by day, and the intersections become more intricate day by day. Therefore, these sixty-four hexagrams, although generally categorized under water and fire and belonging to the four cardinal directions, their reciprocal movements and the mechanisms of their waxing and waning are all like the crossing threads of a loom, or the turning of a wheel. This is the intention of King Wen in establishing the order of the sixty-four hexagrams.

文王六十四卦次序，雖因交錯，而因異本宮本卦之序，而其取法者，則仍乾坤對列之八卦位次也。蓋乾坤對列之位次，雖屬先天卦象，究為卦象本體，不得棄之而別取法也。若上離下坎之象，雖名後天位次，其為用祇與本宮本卦之序相證，而非文王六十四卦序所本也。

King Wen's sequence of the sixty-four hexagrams, although different from the sequences of the original trigrams and the primary hexagram due to the principle of mutual crossing, still follows the fundamental arrangement of Heaven above and Earth below, with the eight trigrams paired accordingly. Although the arrangement of Heaven above and Earth below belongs to the Earlier Heaven diagram, it is the essential position of the trigrams and cannot be abandoned for another basis. As for the diagram with Fire above and Water below, although it is called the Later Heaven arrangement, its function is only to corroborate the sequences of the original trigrams and the primary hexagram, and it is not the fundamental basis for the sequence of the sixty-four hexagrams. In other words, King Wen changed the positions of the eight trigrams, but in the sixty-four hexagrams he returned to the fundamental principle of Heaven above and Earth below. The positions can change with time, but the essential nature cannot change along with the positions, otherwise change would lose its reference point, and the mutual crossing and arrangement of the sixty-four hexagrams would be impossible.

此其異者，以先天之至後天，因其變，變有其例，因於體用，體此而用則彼，體先而用則後。文王八卦位次，仿自伏羲八卦，而與本宮本卦之序相應，一先一後，一體一用也。二者同出異用，一常一變，常者不變，故其用能變，變而不失其常。若體已變，則何以用變？以變為變，將不復知有常矣，則易道亂，亂則何以神其用哉？故變者本於不變，而後天必本於先天也。

The difference between them arises because moving from the Earlier Heaven to the Later Heaven necessarily involves a transformation, and this transformation follows a specific pattern, which depends on the relationship between form and function: taking one set as form, another set becomes function; taking the Earlier Heaven as form, the Later Heaven becomes function. The arrangement of King Wen's eight trigrams is modeled after Fuxi's eight trigrams, and it corresponds with the sequence of the original trigrams and the primary hexagram, one preceding the other, one as form and one as function. Both originate from the same source but serve different purposes; one is constant, the other is changeable. The constant aspect remains unchanged, so the changeable aspect can change; even though it changes, it does not lose its constancy. If the original form itself were to change, then what would the function rely on to change? Changing by means of change would lose the constant, and the Way of the Book of Changes would become chaotic; once it is chaotic, how could its function become profound and mysterious? Therefore, change must be based on constancy, and the Later Heaven must be based on the Earlier Heaven.

世之習易者，以文王六十四卦不合其八卦位次，而其八卦位次恰與本宮之序同，有疑為不如是者。不知六十四卦者，全易之象，八卦亦在其中；文王六十四卦之序，即後天之象，與伏羲本宮卦序，正為體應，非可疑也。苟就六十四卦之象前後觀之，其氣消息，其數盈虛，其行往復，其道迴環，無不與伏羲八卦位次同，蓋可見其取法所自矣。

People who study the Book of Changes in the world notice that the arrangement of the sixty-four hexagrams in King Wen's system does not match the order of the eight trigrams he himself established, but instead exactly corresponds to the sequence of the hexagrams in his own palace. Therefore, they doubt that this should be the case. They do not realize that the sixty-four hexagrams encompass all the images of the Book of Changes, and the eight trigrams are already included within them. The sequence of the sixty-four hexagrams in King Wen's system is precisely the Later Heaven arrangement. It has a relationship of essence and response with the original sequence of the eight trigrams from Fuxi. There is nothing to doubt. If one carefully examines the sequence of the sixty-four hexagrams from beginning to end, one will find that the flow of energy, the waxing and waning of numbers, the movement back and forth, and the circular path all correspond exactly with the positions of the eight trigrams from Fuxi. The source of this system becomes clearly evident.

且六十四卦之序，不有數例在乎？試各按之，皆足以參證其用。以本宮言之，三變而後則屬對宮，七變為游魂，八變為歸魂，仍本先天八卦方位者也。蓋變多必因交錯，氣交數錯，變乃無盡。後天以變為主，固必取交錯之例。交錯以對位為主，以旁行為輔；對位為交，旁行為錯。如乾之坤，對位也；之離坎，則旁行也。

Moreover, the order of the sixty-four hexagrams is not based on just one system; there are several different arrangements. If each is tested individually, each is sufficient to confirm its function. In terms of the sequence of this particular palace: after the third change, it moves to the opposite palace; the seventh change is called "you hun" (wandering soul), and the eighth change is called "gui hun" (returning soul). This still follows the positional arrangement of the Earlier Heaven Trigrams. The reason for the multitude of changes is due to the interweaving: when the qi (vital force) meets and the numbers shift, the changes have no end. The Later Heaven focuses on change, so it must adopt the system of interweaving. Interweaving is mainly based on "duiwei" (opposite position) and assisted by "pangxing" (side movement): "duiwei" is called "jiao" (meeting), and "pangxing" is called "cuo" (error). For example, moving from Qian to Kun is "duiwei"; moving from Qian to Li or Kan is "pangxing".

文王六十四卦序，其例正如此，故以乾坤為首，以既未濟為終，明後天之交錯，而象事物之生化也。夫本宮之序，終於歸妹，與此之終於未濟，其義亦可互參。傳曰歸妹女之終也，未濟男之窮也。乾道成男，坤道成女，男女即乾坤也，乾坤即天地也，天地即陰陽也。陰盡于歸妹，明體靜也；陽盡於未濟，明用動也。

King Wen's arrangement of the sixty-four hexagrams follows this system, beginning with the hexagrams Qian and Kun and ending with Ji Ji and Wei Ji, to illustrate the Later Heaven arrangement and symbolize the growth and transformation of things. The sequence of this particular set of hexagrams ends with Gui Mei, which can be cross-referenced with King Wen's sequence ending with Wei Ji. The "Xugua Zhuan" states, "Gui Mei signifies the end of women," and "Wei Ji signifies the end of men." The "Xici Shang Wen" says, "The way of Qian gives rise to masculinity, and the way of Kun gives rise to femininity." This shows that male and female correspond to Qian and Kun, Qian and Kun correspond to heaven and earth, and heaven and earth correspond to yin and yang. The termination of yin energy at Gui Mei indicates the principle of stillness, while the termination of yang energy at Wei Ji indicates the principle of action.

先天主靜，內陽外陰；後天主動，內陰外陽。故文王之序，以乾始，以未濟終，示陽氣之循環，為後天生化之本；而陽氣之終盡，為人物窮竭之時。此其取義，亦象天地自然之氣者也。況易者盡而無盡，窮而復通，以其循環也。天地為一大循環，終則有始，非不續也，故未濟窮而不窮。

The Earlier Heaven emphasizes stillness, with yang within and yin outside; the Later Heaven emphasizes movement, with yin within and yang outside. Therefore, King Wen's arrangement starts with the Qian hexagram and ends with the Weiji hexagram, illustrating that the cycle of yang energy is the fundamental principle of later heaven generation and transformation. When yang energy reaches its limit, it is also the time when both people and things reach their exhaustion. This meaning is also a depiction of the natural flow of qi in heaven and earth. Moreover, the Yi Jing discusses completeness that is not yet complete, and exhaustion that is not final, because it is inherently cyclical. Heaven and earth form a great cycle; reaching the end is also the beginning again, and it is not a complete interruption. Thus, although Weiji is named as the extreme, in reality it is not truly extreme.

卦象先後天之異，在方位與次序，夫子已詳言之。唯先後天各圖象，位次各不同者，以其氣數各有合也。伏羲八卦位序，為一切根本，其六十四卦則有數種；位序不同，名類斯異。文王八卦位序，自伏羲變來，其六十四卦，亦與伏羲者殊，然皆出於上乾下坤之八卦位序則同。蓋根本一，而變化無盡也。

The differences between the Earlier Heaven and Later Heaven diagrams are reflected in both direction and sequence. The Master has already explained this in detail. However, the reasons why the various diagrams of Earlier Heaven and Later Heaven differ in their positions and order are due to the different ways in which their energies and numbers are combined. The sequence of the Eight Trigrams of Fuxi is the foundation of all Yi diagrams. From this, sixty-four hexagrams can be derived, but there are several different arrangements. If the sequence differs, the names and classifications also change accordingly. The sequence of the Eight Trigrams of King Wen is derived from that of Fuxi. The sixty-four hexagrams derived from King Wen's sequence also differ from those of Fuxi. However, in the end, they all originate from the same fundamental sequence of Heaven above and Earth below in the Eight Trigrams. There is only one root, yet the variations arising from it are endless.

伏羲六十四卦，應以本卦之序為最明顯，即依乾、兌、離、震、巽、坎、艮、坤之一、二、三、四、五、六、七、八次序，而將本卦所變者，統屬之於一卦。如乾卦之下，兌乾、離乾、震乾、巽乾、坎乾、艮乾、坤乾各卦，即夬、大有、大壯、小畜、需、大畜、泰，皆屬之乾卦。

Fu Xi's sixty-four hexagrams are most clearly ordered according to the sequence of the Primary Hexagram. This sequence follows the Earlier Heaven order: Qian (Heaven) one, Dui (Lake) two, Li (Fire) three, Zhen (Thunder) four, Xun (Wind) five, Kan (Water) six, Gen (Mountain) seven, and Kun (Earth) eight. All hexagrams generated from a particular Primary Hexagram are grouped under that one. For example, under the Qian hexagram, all hexagrams with Qian as the Lower Trigram and Dui, Li, Zhen, Xun, Kan, Gen, or Kun as the Upper Trigram—namely, Gua, Da You, Da Zhuang, Xiao Xu, Xu, Da Xu, and Tai—are grouped under Qian. This grouping is because the Lower Trigram represents the inner and primary aspect, and the Earlier Heaven system discusses the generation of qi. Qi arises from within and moves outward, from below to above. Therefore, the Lower Trigram determines which hexagram is generated. The change of the Upper Trigram merely indicates the different objects encountered by this qi. Each of the eight trigrams leads eight hexagrams, and eight multiplied by eight gives exactly sixty-four, neither more nor less.

其次則兌卦，兌所合者，如履、兌、暌、歸妹、中孚、節、損、臨各卦，皆屬之。兌以下，如離、如震、如巽、坎、艮、坤各本卦所合者，依序列之，以為全易次序。因其由本卦所推，故名為本卦序；因其依先天八卦位次，故名為先天六十四卦序，或伏羲六十四卦序。

The next is the Dui trigram. All hexagrams that combine with Dui, such as the hexagrams of "Lǚ" (Following), "Dui" (Joy), "Kuí" (Strife), "Guī Mèi" (Return of the Maiden), "Zhōng Fú" (Faith in the Middle), "Jié" (Regulation), "Sǔn" (Loss), and "Lín" (Approach), are all classified under Dui. Following Dui, the hexagrams generated by combining with Li (Fire), Zhen (Thunder), Xun (Wind), Kan (Water), Gen (Mountain), and Kun (Earth) are also arranged in the same manner, sequentially. Together, they form the entire sequence of the Book of Changes. Because these hexagrams are derived from the primary hexagrams, this sequence is called "Primary Hexagram Sequence." Additionally, since it follows the order of the Earlier Heaven Trigrams, it is also referred to as "Earlier Heaven Sixty-Four Hexagram Sequence" or "Fuxi Sixty-Four Hexagram Sequence."

此種卦序，為圖有方，有圓，有平列，有豎立，其象雖殊，致用略一，而其別於他類者，順八卦之位次，示本卦之分合，無交錯之用，純先天之象。蓋其變化少，而生育之功不見，藉以定天地之位、辨氣數之差而已。故後人多不曉其意義，不過備易象之一格，而為他卦參證云爾。

This set of hexagram sequences can be drawn in various forms, such as square diagrams, circular diagrams, flat arrangements, or vertical arrangements. Although the forms differ, their general purposes are similar. Its distinction from other methods of arrangement lies in the fact that it follows entirely the order of the eight trigrams, only showing how the primary hexagram is divided and combined, without discussing the interweaving between hexagrams. It is a pure representation of the Earlier Heaven pattern. Because it contains fewer changes, it is not capable of demonstrating the function of generating all things. It can only be used to determine the directions of heaven and earth and to distinguish differences in the vital energies. Therefore, later generations mostly did not understand its meaning, treating it as a mere part of the Yi hexagrams, used only for mutual verification with other hexagram sequences.

又有本宮卦序者，則依文王八卦位次，而為各類；其卦變化，則依本宮對宮相交錯，及比類五卦，而推生各卦，皆為八變。如乾宮自乾起，初變為乾巽，次為乾艮，次為乾坤，次為巽坤，次為艮坤，次為離坤四，終為離乾，即乾、姤、遯、否、觀、剝、晉、大有各卦，依次序列，屬之乾宮卦。

There is another system called "the sequence of the trigrams within their respective palaces," which divides the trigrams according to the order of the King Wen trigrams. As for the transformation of the trigrams, they are generated by the interaction between the trigram of the palace and the trigram of the opposite palace, along with adjacent trigrams of the same type, resulting in eight transformations for each palace. For example, the palace of Qian starts with the Qian trigram: the first transformation is upper Qian and lower Xun, the second is upper Qian and lower Gen, the third is upper Qian and lower Kun, the fourth is upper Xun and lower Kun, the fifth is upper Gen and lower Kun, the sixth is upper Li and lower Kun, and the last is upper Li and lower Qian. That is, the trigrams of Qian, Gou, Dun, Po, Guan, Bo, Jin, and Dàyǒu are arranged in order, all belonging to the palace of Qian.

其次為坎宮，自坎以下，為節、屯、既濟、革、豐、明夷、師各卦，亦依變化之次序列，屬之坎宮卦。以下如震、如巽、如離、如坤、如兌，皆依後天八卦位次序列，以推生全易卦象者也。以其變由生於本宮，不似前之出於本卦者，故名本宮卦序，亦曰八宮卦序，或稱後天六十四卦序。然非與文王六十四卦序同，不過序列各宮，依文王八卦位次，其推生變化純先天例，有異文王後天交錯之序也，應仍屬之先天卦序之一種。

Next is the Kan Palace: starting from the Kan hexagram, the sequence proceeds to the hexagrams 《Jie》, 《Zun》, 《Ji Ji》, 《Ge》, 《Feng》, 《Ming Yi》, and 《Shi》, arranged in the order of their transformation. All these hexagrams belong to the Kan Palace. Continuing downward, the Zhen Palace, Xun Palace, Li Palace, Kun Palace, and Dui Palace are also arranged according to the positions of the Later Heaven Trigrams, used to generate all the images of the sixty-four hexagrams. Since these transformations originate from within each palace, unlike the previous method which involves combining hexagrams, they are called "hexagram sequences within the palace," also known as "eight palace hexagram sequence" or "Later Heaven sixty-four hexagram sequence." However, it is not equivalent to the sequence of the sixty-four hexagrams arranged by King Wen. It merely arranges each palace in the order of the eight trigrams of King Wen. The principles used for generating and transforming the hexagrams are purely based on the Earlier Heaven system, differing from King Wen's Later Heaven arrangement which involves interweaving. Therefore, it should still be considered a type of Earlier Heaven hexagram sequence.

此種卦序，有一定之例，即自本宮本卦起，三變而至對宮，七變而為對比宮，是曰游魂；八變由比宮仍還本卦，是曰歸魂。大凡八卦，依伏羲方位相對者曰對宮，相併者曰比宮。如乾與坤，離與坎，震與巽，艮與兌，對宮也；如乾與離，坤與坎，震與艮，巽與兌，則比宮也。

This sequence of hexagrams follows a fixed pattern: starting from the primary hexagram of the original trigram, the transformation reaches the third change and moves to the opposite trigram's palace, then at the seventh change it moves to the palace adjacent to the opposite one, and this transformation is called "you hun." When it reaches the eighth change, it returns from the adjacent palace back to the original hexagram, and this transformation is called "gui hun." In general, among the eight trigrams, two trigrams that are opposite to each other according to Fuxi's arrangement are called "dui gong," while two trigrams that are adjacent to each other are called "bi gong." For example, Qian and Kun, Li and Kan, Zhen and Xun, Gen and Dui are dui gong; while Qian and Li, Kun and Kan, Zhen and Gen, Xun and Dui are bi gong.

對宮不獨本卦位次相對，其變化位次皆相對。如乾變之巽，之艮，至坤，由離返乾，皆自上下行，由下返上；而坤則之震，之兌，至乾，由坎返坤，皆自下上行，由上返下。所至所行，恰相對也。

The hexagrams in opposite trigrams not only have their positions relative to each other, but also the positions they pass through during transformation are oppositely aligned. For example, the transformation of the Qian trigram first reaches Xun, then Gen, and finally Kun, and finally returns to Qian via Li. This path follows a route from top to bottom and then back from bottom to top. Meanwhile, the transformation of the Kun trigram first reaches Zhen, then Dui, and finally Qian, and then returns to Kun via Kan. This path follows a route from bottom to top and then back from top to bottom. The destinations and the paths taken are exactly opposite to each other.

其行各宮，而生變化，一宮所涉者五，不入者三。如乾涉巽、艮、坤、離，坤則涉震、兌、乾、坎，餘宮皆然，此其例也。蓋氣之變，必以動，變至三則易其位，至七則遊於比宮，八則歸於本宗。故一宮八卦，所交五宮，亦自然變化之序。此序之用，為納甲所本，於占法適宜，是先天用法，古人常取之以卜筮，至今猶傳，與後天卦序有相闡發也。

Changes move among the various palaces, and each palace is connected to only five others, with three palaces unreachable. For example, the Qian palace relates to Xun, Gen, Kun, and Li; the Kun palace relates to Zhen, Dui, Qian, and Kan; the same applies to the other palaces. This is the general rule. Change requires movement: after the third change, the direction shifts; after the seventh change, it moves to an adjacent palace; after the eighth change, it returns to its original palace. Therefore, the eight trigrams of one palace relate to five other palaces, following the natural order of change. This sequence is fundamental to the method of 'Najia' stem assignment, which is very suitable for divination. It belongs to the Earlier Heaven system, and ancient people often used it for divination, and it has been passed down to the present day. It can be used in conjunction with the Later Heaven sequence to explain each other.

此外有合一歲序者，亦有數種。如以八卦八宮分候四季者，以乾坤二宮分候十二月者，以六十四卦分候全歲、一卦六日七分者，其例詳各家書，皆傳自古，為曆數家所用，亦本先天卦象，推其變化，而應於歲時，無不合也。

In addition, there are also various systems that combine the trigrams with the seasonal changes of a year. For example, some use the eight trigrams divided into eight palaces to correspond with the four seasons, others use the Qian and Kun palaces to correspond with the twelve months, and still others distribute the sixty-four hexagrams throughout the entire year, with each hexagram governing six days and seven parts. These systems are thoroughly recorded in the writings of different scholars, and they have been passed down since ancient times, adopted by those who study calendars and mathematics. They all base themselves on the Earlier Heaven trigrams, deduce their transformations, and use them to correspond with the seasonal changes of the year, and they all match perfectly.

蓋卦象包羅無盡，其變化隨用而見，初非限於一例也。天文地理，日月度數，星辰躔次，山川里程，人物形體，皆有所象。神而明之，無不符合，固不僅象一事一物，亦不止象一時一世。果推而廣之，則宇宙之圖，今古之跡，天下之事，神形之倫，在大氣之中者，無不隨象而可征也。蓋氣者生化之本源，卦象氣也，則凡有生化者，舉不外於卦象，而視人之能明否耳。

The infinite variations contained in the hexagrams are not limited to a particular system; they manifest according to their application. The hexagrams can correspond to astronomical and geographical phenomena, the degrees of the sun and moon's movement, the positions of stars, the distances of mountains and rivers, and the forms of people and objects. As long as one can understand and explain them thoroughly, there will be no discrepancy. The hexagrams do not merely symbolize specific things or events, nor do they represent particular times or eras. If we truly expand their application, then the entire universe, the records of past and present, the affairs of the world, and all kinds of beings and forms existing within this great atmosphere can all be verified through the hexagrams. This is because qi is the source of generation and transformation, and the hexagrams symbolize precisely this qi. Therefore, all things that undergo generation and transformation are encompassed within the hexagrams, and the only difference is whether people can comprehend them.

文王之易，亦此一例，以後天之卦，象後天之氣，而推及變化所至而已。故易象一，而用無盡；一者本也，即伏羲八卦是也，餘皆其用。而所異則在次序，次序異，則象異；而象不因事物名，皆以氣數紀。先天之氣純數簡，故取象少，既伏羲八卦，已足為萬變之宗；後天之氣交數繁，故取象眾。

The Yi of King Wen is also one of these systems: using the Later Heaven trigrams to symbolize the Later Heaven qi, then deriving the various changes that this qi brings about. That is all. Thus, the origin of the Yi images is one, yet its functions are endless—the "one" is the root, that is the trigrams of Fuxi. All other arrangements are merely its applications. The differences among various arrangements lie only in the order: when the order changes, the images taken also change. However, the images are not named according to specific things, but are uniformly recorded by qi and numbers. The qi of the Earlier Heaven is pure and the numbers simple, so the images taken are few; with just the trigrams of Fuxi, they are sufficient to serve as the master principle for all changes. The qi of the Later Heaven is complex and the numbers intricate, so the images taken are numerous.

雖匯各序例，猶未盡其變，但歧途而同歸，仍不離一本之源。此無論為伏羲，為文王，為連、歸，為本宮本卦，六日七分，歲時星紀，種種例用，更無問其為出自先天後天，合自八卦六十四卦，皆一也，皆上乾下坤之八卦位次，所生所化耳。故伏羲八卦，為一切卦之母，因得名先天之象，其餘皆後天也。

Even if all the various systems of arrangement are gathered together, they still cannot exhaust its transformations; however, all paths lead to the same origin. Therefore, whether it is the Yi of Fuxi or the Yi of King Wen, whether it is the Lianshan and Guicang, whether it is the order of the palace, the order of the primary hexagram, the method of six days and seven parts, or the method of coordinating with the seasons, stars, and the calendar, all these systems and methods, let alone the question of whether they come from the Earlier Heaven or the Later Heaven, or whether they are derived from the Eight Trigrams or the sixty-four hexagrams — they are all the same thing, all derived from and transformed from the arrangement of the Eight Trigrams with Heaven on top and Earth below. Therefore, the Eight Trigrams of Fuxi are the mother of all hexagrams, hence named "the image of the Earlier Heaven." The rest are all considered Later Heaven.

然以伏羲六十四卦本卦之序，與文王者異，亦名之先天，猶日後天之先天也。若繩之八卦，則為後天；若較之文王各卦，則為先天。故以此別之，其實先天之象祇一，而克稱先天者，上乾下坤之八卦序耳。此為爭論先後天之重要處，故表出之，以袪世人之惑。

However, the order of the sixty-four hexagrams in Fuxi's system is different from that of King Wen, so it is called Earlier Heaven. This is like saying it is "Earlier Heaven within Later Heaven." If we measure it by the source of the Eight Trigrams, it already belongs to Later Heaven; but if we compare it with King Wen's hexagrams, it is considered Earlier Heaven. People distinguish between them in this way. In reality, there is only one true image of Earlier Heaven, and only the sequence of the Eight Trigrams with Heaven on top and Earth below qualifies as Earlier Heaven. This is exactly the key point of contention throughout history regarding Earlier and Later Heaven, so it is specially pointed out to eliminate people's doubts.

文王六十四卦次序，所取旨意，已見序卦傳，而所應知者，則其例也。其次序本於伏羲八卦方位，以往來交錯而成，而其連接者，皆相對也。以後天生化，必一陰一陽，交互而行，非如先天之陽行於陽，陰行於陰也。故文王六十四卦，取八宮各卦，分合而交錯之，本八卦位次，往復而對舉之，以成一陰一陽之道，而見天生地成之義。

The rationale behind the order of the sixty-four hexagrams in the Book of Changes, as explained in the "Sequence of Hexagrams" passage, is already clarified. Readers should also be aware of the arrangement principle. This sequence is based on the original positions of the eight trigrams attributed to Fuxi. Through their mutual interaction and alternation, each pair of consecutive hexagrams are opposites of each other. Because the later heaven's generative process necessarily involves the alternation of yin and yang, unlike the earlier heaven where yang moves only within yang and yin moves only within yin. Therefore, the sixty-four hexagrams of King Wen are derived by taking the eight trigrams and either separating or combining them to create alternations. According to the order of the eight trigrams, they are paired alternately to illustrate the principle stated in the "Great Treatise Upper Transmission" that "yin and yang together are called the Dao," thereby demonstrating the meaning of heaven's giving birth and earth's forming things.

凡各卦之有往者，必繼之以復；有上者，必對之以下；有奇者，必聯之以偶；有動者，必應之以靜。使本宮對宮相錯，比卦類卦相交，不限於八宮之序，不囿於本卦之次；而其次序，恰與八宮相證，不亂其數；恰與本卦相通，不乖其位，以後天自然之序也。天地人物，歲時日月，周行不息，動靜有度，皆如此序。

Whenever there is a hexagram indicating movement outward, there must be a following hexagram indicating return; whenever there is an upward movement, there must be a corresponding downward movement; whenever there is an odd number, there must be a connected even number; whenever there is an active element, there must be a corresponding passive element. In this way, the primary hexagram and its opposite hexagram interweave with each other, and adjacent hexagrams and similar hexagrams connect with each other. This arrangement is not restricted by the order of the eight palaces, nor is it bound by the sequence of the primary hexagram. Yet the resulting order coincides perfectly with the sequence of the eight palaces without disrupting their numerical arrangement, and it also harmonizes perfectly with the primary hexagram without contradicting its position. This is because this order is naturally established in the Later Heaven. The heavens and the earth, human beings, the seasons, days, and months all flow and circulate continuously, with movement and stillness each following their own rules, all conforming to this order.

故以卦象言，文王六十四卦，自乾坤起，以乾坤對舉，陰陽交行也；終於既未濟，以坎離互交，水火易位也。其中各卦，莫非此例，皆以比偶相及，對應相生，分之自成一卦，合之則為全序。

Therefore, in terms of the hexagram images, King Wen's sixty-four hexagrams begin with the hexagrams of Qian and Kun, pairing them together to signify the mutual interaction of yin and yang. They conclude with the hexagrams of Ji Ji and Wei Ji, allowing Kan and Li to intermingle, symbolizing the mutual exchange of water and fire. In between, each hexagram follows this pattern: they are all related to one another in pairs through adjacent pairings, and they correspond to each other in pairs to generate each other. Individually, each hexagram forms a complete hexagram on its own; collectively, they constitute the complete sequence of the entire text.

以卦雖六十四，而乾、坤、坎、離、頤、中孚、大小過八卦，獨不同象；其它五十六卦，皆反覆自為兩卦；則五十六卦，實二十八也。合之乾、坤、坎、離、頤、中孚、大小過八卦，共三十六卦，以應周天之數，而象萬物之類。

There are sixty-four trigrams in total, but eight of them, namely Qian, Kun, Kan, Li, Yi, Zhongfú, Da Guo, and Xiao Guo, are unique in that when they are viewed upside down, they remain the same. The remaining fifty-six trigrams each become another trigram when reversed, forming pairs of opposites. Thus, these fifty-six trigrams actually represent only twenty-eight distinct forms. Adding the eight special trigrams, there are a total of thirty-six trigrams, used to correspond to the degrees of the celestial circle and to symbolize the various categories of things in the world.

故其次序，以上下篇分括六十四卦，而皆統之於乾坤坎離；明天地為萬物之本，水火為二氣之宗，而合乎伏羲八卦方位四正之象也。故全易之序，皆以此四卦為主，反覆交互，上下錯綜，更以震、巽、艮、兌為用，縱橫應接，奇偶對生，以盡二氣之生化，而推五行之承制，蓋其旨意固如是也。

Therefore, this order uses the upper and lower parts to encompass the sixty-four hexagrams, and both parts are subordinate to the four hexagrams of Qian, Kun, Kan, and Li. This is to indicate that heaven and earth are the fundamental elements of all things, and water and fire are the masters of yin and yang energies. It also corresponds with the four cardinal directions of the eight trigrams in Fuxi's arrangement. Thus, the entire sequence of the Book of Changes revolves around these four hexagrams, allowing them to interact repeatedly and intermingle in a complex manner. The other four trigrams, Zhen, Xun, Gen, and Dui, serve as supplementary elements, interweaving and connecting with each other in all directions. Odd and even numbers are paired to exhaust the generation and transformation of yin and yang energies, and to demonstrate the relationships of succession and control among the five phases. This was the original intention.

至文王卦序之例，可得言者，則其卦之對舉，合之本宮卦序，必一與五世，二與四世，三與三世；游魂與游魂，歸魂與歸魂，皆不亂也。如屯蒙二卦對舉，屯為坎宮二世卦，蒙為離宮四世卦；又如同人大有二卦對舉，同人為離宮歸魂，大有為乾宮歸魂，是其所舉異宮，而仍同世也。

As for the arrangement of the hexagrams in the sequence of King Wen, there is another point worth noting: whenever two hexagrams are paired together, if we check them against the sequence of their respective trigrams, they must always be paired as first-generation hexagram with fifth-generation hexagram, second-generation with fourth-generation, and third-generation with third-generation. Similarly, wandering soul hexagrams are paired with wandering soul hexagrams, and returning soul hexagrams are paired with returning soul hexagrams, without any confusion. For example, the hexagrams Zun and Meng are paired together. Zun is the second-generation hexagram of the Kan trigram, while Meng is the fourth-generation hexagram of the Li trigram. Another example is the pairing of Tongren and Dayou. Tongren is the returning soul hexagram of the Li trigram, while Dayou is the returning soul hexagram of the Qian trigram. This shows that although the two paired hexagrams come from different trigrams, their generational positions remain consistent.

其次則乾、坤、坎、離常以對舉，以屬先天對宮也；震、巽、艮、兌或對舉，或比類，以屬於先天四隅卦也。又乾與坎，坤與離，或離與乾，坎與坤，亦比類連舉，以先天之乾坤，後天之坎離同位；先天乾以離為用，坤以坎為用，其位次相比並，有如比肩。

Next, the four trigrams Qian, Kun, Kan, and Li are often paired together, because in the Earlier Heaven arrangement they naturally belong to opposite trigrams facing each other. The four trigrams Zhen, Xun, Gen, and Dui are sometimes paired together or grouped by similarity, because in the Earlier Heaven arrangement they belong to the four corner trigrams. Additionally, Qian with Kan, Kun with Li, or Li with Qian, Kan with Kun, are also sometimes mentioned together as similar trigrams. This is because in the Earlier Heaven arrangement, the trigrams Qian and Kun correspond to the Later Heaven trigrams Kan and Li, which occupy the same position. In the Earlier Heaven arrangement, Qian uses Li, and Kun uses Kan, and these two trigrams are closely adjacent, standing side by side.

故其在後天有相對之象，有相類之象，亦猶乾與坤，坎與離也。震、巽、艮、兌亦然：震之於艮、於兌，巽之於兌、於艮，艮之於震、於巽，兌之於巽、於震，皆以比類連舉，如震與巽、艮與兌之對舉也。

Therefore, these four trigrams, when considered in the Later Heaven, have both opposing relationships and similar relationships, just like the relationship between Qian and Kun, or between Kan and Li. The trigrams Zhen, Xun, Gen, and Dui also follow this pattern: Zhen opposes Gen and Zhen opposes Dui; Xun opposes Dui and Xun opposes Gen; Gen opposes Zhen and Gen opposes Xun; Dui opposes Xun and Dui opposes Zhen. All of these can be paired as similar trigrams, just as Zhen and Xun, and Gen and Dui, are paired as opposing trigrams.

且在先天震巽為對，後天則震與兌對；先天艮兌為對，後天則艮與坤對；巽與乾對，其為比類者，在後天變對舉。故其序怛連舉也。又震與艮、巽與兌二卦獨舉，不以先後天對宮，為明四隅之卦，以交錯為先，以類及為重，不似乾、坤、坎、離四正之卦也。故其下篇序，震艮連及，巽兌並列，以先天方位次序，固如是對，而卦之性相同也。

In the Earlier Heaven arrangement, Zhen faces Xun, but in the Later Heaven arrangement, Zhen faces Dui; in the Earlier Heaven arrangement, Gen faces Dui, but in the Later Heaven arrangement, Gen faces Kun; Xun faces Qian. Previously, these were two trigrams adjacent to each other, but in the Later Heaven arrangement, they become pairs facing each other, so they are always mentioned together in the sequence of trigrams. Additionally, the pairs Zhen and Gen, Xun and Dui are mentioned separately and not paired according to the Earlier Heaven or Later Heaven opposite positions, to indicate that the trigrams in the four corners are primarily arranged in a crosswise manner and emphasize mutual relations, unlike the four cardinal trigrams Qian, Kun, Kan, and Li, which strictly adhere to opposite positions. Therefore, in the sequence of the next section, Zhen and Gen are mentioned consecutively, and Xun and Dui are arranged together: according to the Earlier Heaven positional order, they were originally facing each other, and moreover, the nature of the trigrams is similar to each other.

震艮一長男也，一少男；巽兌一長女，一少女；性類不殊，氣數可通。故其致用也順，為生也孚。風澤為中孚，澤風為太過；雷山為小過，山雷為頤；之四卦者，反覆不變，恰與乾、坤、坎、離同，其並舉有由來矣。

Zhen and Gen represent the eldest son and the youngest son respectively; Xun and Dui represent the eldest daughter and the youngest daughter respectively. Their nature and category are essentially the same, and their qi and numbers can communicate with each other. Therefore, when they function, they proceed smoothly without obstruction, and when they generate and nurture all things, they harmonize with each other. When Xun is above and Dui is below, it forms the hexagram Zhongfou; when Dui is above and Xun is below, it forms the hexagram Daguò. When Zhen is above and Gen is below, it forms the hexagram Xiaoguo; when Gen is above and Zhen is below, it forms the hexagram Yi. These four hexagrams remain the same when viewed upside down, just like Qian, Kun, Kan, and Li. This shows that they are intentionally paired together in the sequence of hexagrams.

又六十四卦，一往一復，無不相應，合之先天八卦方位，自可見也。如乾坤之後，繼以屯蒙，屯為水雷，蒙為山水。後天之用，始於震，終於艮，而藏機於坎。坎水以代坤，坤之氣見於坎，故坎陽體陰用。屯自水中陽出，蒙則山下水流；屯為往，蒙為復，一往一復，見氣之所化。

Furthermore, the sixty-four hexagrams alternate between movement and stillness, and none fail to correspond with each other; by comparing them with the positions of the Earlier Heaven Trigrams, this becomes evident. For example, after the Trigrams of Heaven and Earth come the hexagrams of Zhun and Meng. Zhun is composed of Kan above and Zhen below, representing the image of water and thunder; Meng is composed of Gen above and Kan below, representing the image of mountain and water. The function of the Later Heaven begins with Zhen and ends with Gen, with the key hidden in Kan. The water of Kan replaces the function of Kun, and the energy of Kun manifests within Kan, so Kan takes Yang as its essence and Yin as its function. Zhun represents the emergence of Yang energy from water, while Meng represents water flowing out from beneath the mountain; Zhun signifies movement, and Meng signifies return. Between movement and return, the manifestations of the vital energy become apparent.

陽動而陰靜，陰出而陽歸，故二卦對舉，而見一陰一陽之道。此後天生化之始，二氣往復之初，以交互而生，以循環而化。為卦止二，為象已多，天地之機以明，乾坤之用以啟，故繼乾坤而為六十四卦之首也。

Yang is active and Yin is static. When Yin energy moves, Yang energy returns. Therefore, the two hexagrams Zun and Meng are presented together, illustrating the alternating principle of Yin and Yang. This marks the beginning of later heaven generation and transformation, the first step of the reciprocal movement of Yin and Yang energies. They produce through mutual interaction and transform through continuous cycles. Although there are only two hexagrams, the symbolic meaning is already very rich: the mechanism of heaven and earth's operation is thus revealed, and the functions of Heaven and Earth are thus initiated. Therefore, they follow Heaven and Earth and are placed first among the sixty-four hexagrams.

雷之為物，動而為陽，靜而為陰，故出於地，而升於天。在後天，東方木也；木氣生於天，成於地；木數生於三，成於八。其本則天地也，其先則水火也；在先天水為始，而後天木為初。故傳曰帝出乎震，言萬物之始生也。然自出者，必有本；震之所本，坎也。

Thunder is a thing that, when active, belongs to Yang, and when still, belongs to Yin. Therefore, it arises from beneath the earth and ascends to the heavens. In the Later Heaven arrangement, Zhen (Thunder) is associated with the East, the direction of Wood. The vital energy of Wood originates in Heaven and takes form in the earth. The generative number of Wood is three, and its completed number is eight. Its root lies in Heaven and Earth, and its leading force is water and fire. In the Earlier Heaven arrangement, water is considered the beginning of all things, but in the Later Heaven arrangement, Wood is regarded as the starting point. Therefore, the "Commentary on the Hexagrams" says, "The Emperor arises from Zhen," referring precisely to the beginning of all things. However, wherever there is an origin, there must be a source; the fundamental basis upon which Zhen relies is Kan (Water).

坎為水，先天之始生，後天之根源；震自坎出，為先天化為後天之啟端，故屯卦為全易各卦之初始，象萬物之初生也。祇在卦爻求之，即可見矣。然生者必化，往者必復，此後天公例。既有屯，以象往生；自有蒙，以象復化。化於此者，即生於彼；往於昨者，必復於今。

The trigram Kan represents water, which is the beginning of all things in the Earlier Heaven and the origin of all things in the Later Heaven. The trigram Zhen arises from Kan, marking the starting point of the transformation from the Earlier Heaven to the Later Heaven. Therefore, the hexagram Zun is placed as the first hexagram in the entire Book of Changes, symbolizing the initial emergence of all things. By examining the lines of the hexagram, this can be clearly understood. However, whenever there is generation, there must also be transformation; whenever there is movement forward, there must also be return. This is the general principle of the Later Heaven. Since the hexagram Zun symbolizes forward movement and generation, there must naturally be the hexagram Meng symbolizing return and nurturing. What is transformed here will be generated elsewhere; what went out yesterday will surely return today.

此循環之定理。既有屯蒙以明其初氣，自有需訟以象其次數。氣數周流，生化無盡，而後萬物之象見，萬類之數明，其例固昭昭矣。就屯蒙卦言，在先天八卦，坤之左右，雷自水出，泉流山下。二者一自左上，一自右降，一升一降，仍還於原。坤用重坎，故用水不言地，明卦序之為後天也。

This is the principle of continuous cycles. Since the hexagrams Zhun and Meng explain the initial qi, there naturally exist the hexagrams Xu and Song to symbolize the subsequent qi numbers. Qi and numbers flow endlessly, generating and transforming without end, and thus the forms of all things become evident, and the numbers of all categories become clear. This system is inherently clear. Regarding the hexagrams Zhun and Meng, in the Earlier Heaven arrangement of the eight trigrams, they are positioned on either side of the Kun trigram: thunder arises from water, and spring water flows down the mountain. One rises from the left, the other descends from the right, ascending and descending, eventually returning to their original positions. Here, the Kun trigram uses the overlapping Kan trigram to function, so it only speaks of water and not of earth. This clearly indicates that this sequence of hexagrams belongs to the Later Heaven arrangement.

然後天者，仍出於先天，仍歸於先天，故需訟二卦，則一為水天，一為天水。坎本得乾陽為體，故游魂之卦，仍溯源於所生，而需訟之象，乃往復於乾坎也。需訟二卦，一為坤宮之游魂，一為離宮之游魂；坤之游魂，即乾宮之氣所化；離之游魂，即坎宮之氣所化，則需卦為乾坤二氣之交互，訟卦即離坎二氣之循環。

However, Later Heaven ultimately originates from Earlier Heaven and eventually returns to Earlier Heaven. Therefore, the hexagrams "Need" and "Song" represent the image of water above heaven below (upper Kan, lower Qian) and heaven above water below (upper Qian, lower Kan), respectively. The hexagram Kan originally takes the yang line of Qian in the central position as its body, so it belongs to the category of wandering souls. Hence, the images of "Need" and "Song" alternate between Qian and Kan. These two hexagrams are wandering souls of the K'un palace and the Li palace respectively. The wandering soul of the K'un palace is actually transformed from the qi of the Qian palace, and the wandering soul of the Li palace is transformed from the qi of the Kan palace. Thus, the hexagram "Need" represents the mutual interaction of the qi of Qian and K'un, while the hexagram "Song" represents the cyclic transformation of the qi of Li and Kan.

以水天合而為需，水上於天，即坎與乾交，而陽上升；以天水合而為訟，天下近水，即乾與坎交，而陽下降。一升一降，一往一復，自相偶也，故需與訟二卦對舉，恰相當其位，而氣數亦相得。

Water above and Heaven below form the hexagram Need, where water floats above Heaven, meaning the trigrams Kan (Water) and Qian (Heaven) meet, and the yang energy rises; Heaven above and Water below form the hexagram Suing, where Heaven descends close to Water, meaning the trigrams Qian and Kan meet, and the yang energy descends. One rising and one falling, one moving forward and one returning, naturally form a pair. Therefore, the hexagrams Need and Suing are presented together, their positions exactly corresponding, and their energies and numbers complement each other.

自先天八卦言之，乾與坎為比類，即後天之對位也。在後天坎代坤用，有似於泰否二卦，與晉明夷卦二卦相類。晉與明夷，一為火地，一為地火，為坤與離升降交互之卦。離在後天代乾，與泰否亦相似，又與既未濟亦相近也。蓋先天為泰否，後天為既未濟。

From the perspective of the Earlier Heaven Trigrams, Qian and Kan belong to adjacent trigrams of the same type. However, in the Later Heaven arrangement, they become opposite positions. In the Later Heaven, Kan takes the role of Kun, and this relationship is somewhat similar to the two trigrams Tai and Po. It is also comparable to the two trigrams Jin and Mingyi. Jin is the trigram of fire on earth, while Mingyi is the trigram of earth on fire; both are formed by the interaction of Kun and Li rising and falling. In the Later Heaven, Li takes the role of Qian, so these two trigrams are similar to Tai and Po, and also close to Ji Ji and Wei Ji. In summary, the trigrams Tai and Po are used to explain the Earlier Heaven, while Ji Ji and Wei Ji are used to explain the Later Heaven.

半先半後，則需訟與晉明夷也，皆乾坤坎離交錯往復之卦，即陰陽二氣交互升降之象也。故皆對舉以成序，仍本於八卦位次者也。需訟在八宮，以坤與離對；在八卦位次，以乾與坎合。對合之間，見其交錯之出於自然，明其生化之有其定序，不少差也。不獨其世同也，

As for the four hexagrams that are half belonging to the Earlier Heaven and half to the Later Heaven, they are the hexagrams of Need, Strife, Progress, and Bright Abundance. They are all composed of the trigrams of Heaven, Earth, Water, and Fire alternating and interchanging, which represent the image of the mutual rise and fall of the two energies of yin and yang. Therefore, they are paired in pairs to form sequences, still following the order of the eight trigrams. In terms of the eight palaces, Need and Strife are opposite between the Earth Palace and the Fire Palace; in terms of the order of the eight trigrams, they are paired between Heaven and Water. Between this pairing and combination, one can see that the interweaving is natural, and one can understand that the process of generation and transformation has a definite order, without any error. Moreover, the two paired hexagrams not only share the same worldly position,

凡此卦序，其例皆然，皆自氣數所至，生化所成，非故為之序也。故六十四卦之序，循環終始，一一相得；而八卦之用，往來升降，一一相當；初無不偶之處，亦無相逆之情。其相對舉也，正一陰一陽之道，後天生化之理然也。合之洛書，征之太極，自易明曉；至其續之義，見序卦傳者，不贅述也。

All the sequences of the sixty-four hexagrams follow this pattern: they are the results of the movement of qi and the natural process of generation and transformation, not deliberately arranged by anyone. Therefore, the sequence of the sixty-four hexagrams continues cyclically from beginning to end, with each hexagram complementing the others. The functions of the eight trigrams are interrelated in their movement and changes, being appropriate in every aspect; there is no place where any is isolated or mismatched, nor any instance of contradiction between them. The reason they are paired and presented in pairs is precisely in accordance with the saying "yin and yang together are called the Dao," which reflects the inherent principle of generation and transformation in the Later Heaven. Comparing them with the Luo Writing and verifying them with the concept of the Supreme Ultimate naturally makes this clear. As for the meaning of the sequence of hexagrams following one another, the "Sequence of Hexagrams" passage has already explained it, so there is no need to repeat it here.

周易之書，文王所作；易卦之象，伏羲所制。文王演之以盡其變，是為周易，故卦象一而用二，卦名同而用殊。以伏羲初制為先天象，文王復演為後天象，以此分別，體用斯明。

The book of Zhou Yi was composed by King Wen; the images of the hexagrams were created by Fuxi. King Wen elaborated upon Fuxi's hexagrams, exhausting their transformations, thus forming the Zhou Yi. Therefore, the images of the hexagrams are only one set, yet their functions are divided into two layers; the names of the hexagrams are the same, yet their uses differ. The hexagrams originally created by Fuxi are considered the Earlier Heaven images, while those re-examined and elaborated by King Wen are regarded as the Later Heaven images. By distinguishing them in this way, the relationship between their essence and function becomes clear.

然夫子刪訂六經，獨宗周易，而不及文王以前者，文王之作，足賅各易也。文王之易，雖屬後天，而先天存乎其中。人之生也，神存形中，言形而神在，以神之德，體物不遺也。先天之象亦然，先天以後天用，後天以先天神，先後並行，神用無極。故曰「神無方，易無體」，以體不見，由其而用見也。

However, the Master edited the Six Classics, and alone revered the Zhou Yi, without involving the Yi texts prior to King Wen, because King Wen's work was already sufficient to encompass all other schools of Yi. Although King Wen's Yi belongs to the Later Heaven, the Earlier Heaven exists within it. Just as when a person is alive, the spirit resides within the body; when speaking of the body, the spirit is within it, because the spirit's virtue pervades all things without omission. The images of the Earlier Heaven are also like this: the Earlier Heaven relies on the Later Heaven to manifest its function, and the Later Heaven relies on the Earlier Heaven to reveal its spirit. The two proceed together without contradiction, and the mysterious function has no end. Therefore, the Great Treatise of the Upper Transmission says, "The spirit has no fixed form, and the Yi has no independent form," precisely because the essence is invisible, so it must be revealed through its manifested function.

然體不可見，因而忘之，不可也；先天之象，不用可也，因而蔑之，不可也。故言後天必及先天，原始要終，易之道固如是；推來溯往，易之用亦當然。明乎先天，則知後天所出；明乎後天，則知先天所存。氣數不同，名類異致，雖猶木本與枝、水源與流，一脈所傳，而在既變之後，形神各別，理氣殊途，有一而不一、同而未同者在也。

Although this is the case, if we cannot see the essence, we should not forget it; although the images of the Earlier Heaven may be temporarily set aside, it is also wrong to therefore disregard them. Therefore, when discussing the Later Heaven, we must inevitably involve the Earlier Heaven, investigating the beginning and concluding at the end. The principles of the Book of Changes are inherently like this; inferring from the future and tracing back to the past, the application of the Book of Changes should also be like this. If we understand the Earlier Heaven, we will know where the Later Heaven comes from; if we understand the Later Heaven, we will know where the Earlier Heaven resides. The two differ in terms of qi and numbers, and in their names and categories. Although they are like the trunk and branches, the source of water and its tributaries, originating from the same root and passed down in succession, after transformation, form and spirit become separate, principles and qi take different paths, thus resulting in a situation where they are one yet not one, similar yet not entirely the same.

故言文王之易，必溯以前之易；習文王之卦，必本以前之卦。卦同而異，以用不同；易異而同，以體無異。故雖有同異，而不得不求其合也。合則通，通則神；不合不通，滯於物而失其神，將何以致易之用哉？故學者必將先後天二者氣與數之分，明晰無遺，再將二者之合，通貫無滯，庶可以因文王之作，探伏羲之制，即可由周易包括以前之易也。請將先後天卦象之同異者略述之。

Therefore, to discuss the Yi of King Wen, one must trace back to the earlier Yi; to study the hexagrams of King Wen, one must take the earlier hexagrams as the foundation. Although the forms of the hexagrams are the same, their meanings differ because of different applications; although the books of Yi differ, their essence is the same because their fundamental nature is not different. Therefore, although there are similarities and differences, one must strive to find a way to integrate them. Only when they are integrated can one understand clearly, and only when one understands clearly can one grasp the profound; without integration, one cannot understand clearly, and one remains stuck in specific things, losing the profound essence, and then how can one make use of the Yi? Therefore, those who study the Yi must first clearly understand the differences between the Earlier Heaven and Later Heaven in terms of qi and numbers, and then integrate their convergence without any obstruction, only then can one use King Wen's work to explore Fuxi's system, and also be able to use the Zhou Yi to encompass all previous forms of Yi. Below is a brief explanation of the similarities and differences between the Earlier Heaven and Later Heaven hexagrams.

先天八卦方位次序，與後天異。先天乾坤上下，離坎東西；震居坤左，巽在乾右；艮連坎坤，兌接離乾。此為相對，方位卦象皆相對也。乾陽坤陰，離陰坎陽，震艮皆陽，巽兌同陰；陰下陽上，陰上陽下；一陽與一陰對，二陽與二陰對，無相失也。

The arrangement and order of the Earlier Heaven Trigrams differ from the Later Heaven. In the Earlier Heaven, Qian is at the top and Kun at the bottom, Li is in the east and Kan in the west; Zhen is placed to the left of Kun, and Xun to the right of Qian; Gen is connected with Kan and Kun, while Dui is connected with Li and Qian. This forms a structure where each element is opposite to another. The positions and trigrams are paired oppositely throughout. Qian belongs to Yang, and Kun to Yin. Li has Yang outside and Yin inside, while Kan has Yin outside and Yang inside. Zhen and Gen both belong to Yang, while Xun and Dui both belong to Yin. When Yin is below, Yang is above; when Yin is above, Yang is below. A trigram containing one Yang is opposite to one containing one Yin, and a trigram with two Yangs is opposite to one with two Yins. There is no error in the pairing.

故其數為乾一、兌二、離三、震四，此左之行卦；巽五、坎六、艮七、坤八，此右之下行卦。而其本數，則與河圖同。其式為左右兩行，左則自下數，右則自上數：左為震一、離三、兌七、乾九，右為巽四、坎二、艮八、坤六。

Therefore, the sequence of the trigrams in the Earlier Heaven arrangement is Qian one, Dui two, Li three, Zhen four, which are the trigrams on the left row moving upward; Xun five, Kan six, Gen seven, Kun eight, which are the trigrams on the right row moving downward. As for their original numbers, they correspond with the Yellow River Chart. The diagram is divided into two rows, left and right. On the left, the numbers are counted from bottom to top; on the right, from top to bottom: the left row is Zhen one, Li three, Dui seven, Qian nine; the right row is Xun four, Kan two, Gen eight, Kun six. One should be careful to distinguish between "sequence numbers" and "original numbers": Qian one to Kun eight represent the order of arrangement, while Zhen one to Kun six correspond to the qi numbers assigned by the Yellow River Chart. The left row moves upward from bottom to top, symbolizing the generation of yang qi from the bottom upward, layer by layer; the right row moves downward from top to bottom, symbolizing the descent of yin qi from the top downward, layer by layer. The alternating ascent and descent of the two rows establish the dual opposition structure of the Earlier Heaven arrangement.

九 乾　　巽 四；七 兌　　坎 二；五；三 離　　艮 八；一 震　　坤 六

This is the diagram of the Earlier Heaven Trigrams, divided into five layers, with the trigrams arranged facing each other on the left and right sides. The top layer has Heaven (Qian) with the number nine on the left and Wind (Xun) with the number four on the right. The second layer has Lake (Dui) with the number seven on the left and Water (Kan) with the number two on the right. In the center is the number five alone. The fourth layer has Fire (Li) with the number three on the left and Mountain (Gen) with the number eight on the right. The bottom layer has Thunder (Zhen) with the number one on the left and Earth (Kun) with the number six on the right. The odd numbers on the left side, one, three, seven, and nine, are arranged from bottom to top as yang numbers. The even numbers on the right side, four, two, eight, and six, are arranged from top to bottom as yin numbers. The central number five represents the earth number and is not included in the Eight Trigrams but is hidden at the center of the diagram.

此即先天卦數，合河圖者也。以乾九坤六，為乾坤大用；左為陽數，一三七九，順行而上；右為陰數，四二八六，逆行而下；五在中央。以一合六為水，三合八為木，七合二為火，九合四為金，五為土，以成交互之則。一與四、三與二、七與八、九與六，皆成五，即中央所得之數也。故卦八而數九，中數暗藏，明卦之體不見，而寓於用也。

This is the numerical sequence of the Earlier Heaven hexagrams, in harmony with the Yellow River Chart. The great function of the hexagrams Qian and Kun is represented by the numbers nine and six respectively. On the left side are the yang numbers, one, three, seven, and nine, ascending in order; on the right side are the yin numbers, four, two, eight, and six, descending in order. The number five is in the center. One combines with six to form water, three combines with eight to form wood, seven combines with two to form fire, nine combines with four to form metal, and five itself is earth, thus forming a principle of mutual interaction. Now observe: one and four, three and two, seven and eight, nine and six, each pair differs by five, which is precisely the number in the center. Therefore, although there are eight hexagrams, there are nine numbers, with the central number hidden within. This indicates that the essence of the hexagrams is invisible and only manifests through their functions.

乾用九，坤用六，為用之最大者，以陽極於九，陰終於六。九六為乾坤之用，即全易之用，故以九六代卦之用。九與六合為十五，成中央土數，即體也。體以用見，故乾坤以下各卦之用，皆為五，不違其體；體一而用殊，八卦各有所用，而體則一。

Heavenly Stem Qian uses nine and Earthly Stem Kun uses six, which are the largest numbers among all the numbers used. This is because the yang number reaches its peak at nine, and the yin number ends at six. Nine and six are the numbers used by Qian and Kun, meaning they represent the entire use of the Book of Changes. Therefore, the Book of Changes uses nine and six to represent the application of lines. When nine and six are added together, they total fifteen, which exactly corresponds to the number of the central earth. This is the fundamental essence. The essence becomes evident through its function, so the numbers used in the hexagrams following Qian and Kun all reduce to five, without contradicting this fundamental essence. Although there is only one fundamental essence, the functions differ: each of the eight trigrams has its own function, yet the fundamental essence remains the same.

五在中央，名為中數。中者天下之大本，八卦皆自此出，萬物皆歸於中道，此數之妙，亦氣之所存也。數以紀氣，氣行無垠，周流無息，而不離其宗，即永繫於中也。中之氣，先天之真，八卦之氣，兩儀之象，八卦有物。

Five is located in the center and is called the "central number." The concept of center is the great foundation of the world. The Eight Trigrams all originate from here, and all things ultimately return to the middle path. This is both the profound mystery of numbers and the place where qi resides. Numbers are used to record qi. The movement of qi has no boundaries and flows continuously, yet it never departs from its origin, which is always connected to this central point. The qi located in the center is the true qi of the Earlier Heaven. The qi of the Eight Trigrams is the manifestation of the two principles, and the Eight Trigrams are the embodiment of things in the physical world.

故氣有二，而成生化；有升降消長，而成變化。真氣無形，獨居中央，無動無變；八卦有名有數，中氣無名，而數以用成。此即伏羲本河圖之象，制卦象也。卦八用九，而不以九卦者，為示中氣之先天，而有異乎他物也。然有物，則有此氣；卦雖八，而中氣仍在，其妙義可見矣。

Therefore, qi is divided into yin and yang, enabling the process of generation and transformation. There must be rising and falling, as well as decrease and increase, in order to achieve change. As for true qi, it has no form or trace, resides in the center, remains unmoving and unchanging. Each of the eight trigrams has its own name and number, but the central qi has no name, and only manifests through numbers. This is precisely the reason why Fuxi based the trigrams on the imagery of the Yellow River Chart. Although there are only eight trigrams, the use of numbers involves nine positions. The reason for not including the ninth trigram is to indicate that the central qi belongs to the Earlier Heaven, differing from other tangible things. However, as long as there is something, this qi exists within it. Although there are only eight trigrams, the central qi still exists, and the profound meaning is evident here.

後天八卦之象，方位次序，均與先天異，以先天之已變也。其象本於洛書，而成二五交錯之用，故離上坎下，震東兌西；乾居西北，坤處西南；巽在東南，艮移東北。離陰而在上，坎陽而就下；震木在東，如日之出；兌金在西，如月之升；乾以金而連兌，巽以木而接震，同類相親也。坤以地而守南隅，艮以土而歸北角，土氣分佈也。陰陽皆交互以成生化，五行有生制以為功用，以其後天之象，必由二五之交錯、氣數之升降往來，而後見其生化，成其功用也。

The Later Heaven Trigrams differ in their arrangement and order from the Earlier Heaven Trigrams, because the Earlier Heaven has already changed. The Later Heaven Trigrams are based on the Luo Writing, forming a pattern where yin and yang energies and the Five Phases interact. Thus, Li is at the top, Kan at the bottom, Zhen in the east, Dui in the west; Qian is located in the northwest, Kun in the southwest; Xun is in the southeast, Gen moves to the northeast. Li is originally yin but is placed at the top, Kan is originally yang but is located at the bottom; Zhen, belonging to wood, is in the east, like the sun rising; Dui, belonging to metal, is in the west, like the moon rising in the east; Qian, belonging to metal, is connected to Dui, and Xun, belonging to wood, is connected to Zhen, all showing affinity among similar elements. Kun, representing earth, stays in the southwest corner, and Gen, representing earth, moves to the northeast corner, showing the distribution of earth energy at the two opposite corners. Yin and yang must interact to achieve generation and transformation, and the Five Phases must generate and control each other to function properly. It is precisely because the Later Heaven Trigrams must go through the interaction of yin and yang and the Five Phases, and the rising and falling of energies, that they can manifest generation and achieve their functions.

四 巽　　離 九；三 震　　坤 二；五；八 艮　　兌 七；一 坎　　乾 六

This is the diagram of the Later Heaven Trigrams, also arranged in five layers with left and right facing each other: the topmost layer has Xun four on the left and Li nine on the right; the second layer has Zhen three on the left and Kun two on the right; the central position still has a five; the fourth layer has Gen eight on the left and Dui seven on the right; the lowest layer has Kan one on the left and Qian six on the right. Compared to the Earlier Heaven diagram, the left and right sides are now counted from bottom to top, yin and yang alternate, and the central five remains in the middle position unchanged.

由八卦之序數之，則為乾、坎、艮、震、巽、離、坤、兌，循環以行，牽引以用；而其本數，則為坎一、坤二、震三、巽四、乾六、兌七、艮八、離九，其式仿洛書也。坎為一，自下始，左右皆由下上，陰陽皆交互行，不似先天在左上右下，左陽右陰，兩相對待，而未交合也。

Following the order of the Later Heaven Trigrams, they are arranged as Qian, Kan, Gen, Zhen, Xun, Li, Kun, Dui, circulating and interacting with each other to exert their effects. As for the numerical sequence, it is Kan one, Kun two, Zhen three, Xun four, Qian six, Dui seven, Gen eight, Li nine, with the diagram pattern modeled after the Luo Writing. Kan is assigned the number one, starting from the very bottom, with both left and right sides counted upward from the bottom. Yin and Yang interact with each other in this arrangement, unlike the Earlier Heaven arrangement where the left side goes upward and the right side downward, with all the left side being Yang and all the right side being Yin, opposing each other without merging. The Later Heaven arrangement changes to have both sides moving upward together because all things have already been generated, with Yin containing Yang and Yang containing Yin. The Qi no longer flows separately on each side but is intermingled and rises together. Kan being at the very bottom and assigned the number one also signifies that all generation and transformation in the Later Heaven begin from water, the source.

後天之象，在生化之後，本已交合，故氣為同化，數為連生。自坎至巽，為左之四卦；自乾至離，為右之四卦。其數原以一二三四居左，六七八九居右，而其中二八易位，坤艮易方，故左則坎一、坤八、震三、巽四，右則乾六、兌七、艮二、離九，以成後天之數，合乎洛書者也。

The Later Heaven arrangement arises after the process of generation and transformation, as yin and yang have already combined. Thus, the qi is mutually assimilated, and the numbers are continuously generated. From Kan to Xun, there are four trigrams on the left; from Qian to Li, there are four trigrams on the right. Originally, the numbers should be arranged as one, two, three, and four on the left, and six, seven, eight, and nine on the right. However, the numbers two and eight have exchanged positions, and as a result, the trigrams Kun and Gen have also exchanged their positions. Therefore, the left side becomes Kan one, Kun eight, Zhen three, and Xun four, while the right side becomes Qian six, Dui seven, Gen two, and Li nine. This forms the Later Heaven numbers, which correspond exactly with the Luo Writing.

洛書之數，二在西南，與七連；八在東北，與三接。正符河圖之數。二七為火，轉為金，三八為木也。故後天卦數，下則坎一與乾六合，上則巽四與離九合，金水為橫也；左則坤八震三合，右則艮二與兌七合，木火為縱也。

The numbers of the Luo Shu are arranged so that two is in the southwest and connects with seven; eight is in the northeast and connects with three. This exactly matches the numerical principles of the He Tu: two and seven originally belong to fire, but in the Later Heaven they become metal, while three and eight belong to wood. Therefore, the numbers of the Later Heaven hexagrams have the lower part combining Kan one with Qian six, and the upper part combining Xun four with Li nine, with metal and water running vertically through the top and bottom. On the left side, Kun eight combines with Zhen three, and on the right side, Gen two combines with Dui seven, with wood and fire extending horizontally on both sides.

以在後天金火易位，變為水火上下；金木東西，而巽木仍連震，乾金仍接兌，離與坎對，水火相交；坤與艮偶，土地分化，土為四季之旺，分佈於四行中，故土在後天，得時最多，以成生化之本也。

Because in the Later Heaven the metal and fire have exchanged positions, water and fire now occupy opposite positions; metal and wood are separated east and west, while the wood of Xun remains connected to Zhen, and the metal of Qian remains connected to Dui. Li (fire) and Kan (water) face each other, thus water and fire meet. Kun (earth) and Gen (mountain) form a pair, and the earth splits into the other four elements. Earth is prosperous and strong in all four seasons, distributed among the other four elements, so earth receives the most seasonal influence in the Later Heaven, thus becoming the fundamental source of generation and transformation.

水火既濟，則萬物以生；雷澤歸妹，則萬物以化；有地山之謙，以行其令，厚其德，則萬物以成，而後後天之用可見也。且以乾六與巽四合十，則天風姤之象，示氣之媾遇也；以坎一與離九合十，則水火即濟之象，示氣之交濟也。

Water and fire combine to form the hexagram of "Perfect Union," from which all things are born; thunder and marsh combine to form the hexagram of "Return of the Wife," from which all things are transformed; further, earth and mountain combine to form the hexagram of "Humility," used to regulate the seasons and accumulate virtue, from which all things are formed. Only then is the function of Later Heaven fully revealed. Furthermore, in terms of numbers: the number six of Heaven and the number four of Wind add up to ten, which is the image of the hexagram "Meeting," indicating the meeting and union of qi; the number one of Water and the number nine of Fire add up to ten, which is the image of "Perfect Union," indicating the mutual assistance of qi.

震三兌七亦合十，坤八艮二亦合十，則謙與歸妹之象，示氣之通貫和好也。氣皆交和，用乃宏大；數皆錯列，功乃周密。而體以用見，神以功名，則中數之五與十，仍存其中矣。此後天八卦之象，全本乎洛書者也。

The trigram Zhen three and Dui seven add up to ten, and Kun eight and Gen two also add up to ten, which corresponds exactly to the images of the hexagrams Qian and Guimiao, indicating the flow and harmony of qi. When qi is fully integrated and harmonious, its function can be great; when numbers are interwoven, their effects can be thorough. The essence is revealed through function, and the marvelous is known through effect. Thus, the middle number five and ten remain hidden within all of this. This is the image of the Later Heaven Trigrams, fully based on the Luo Writing.

周易一書，文王所本於連山、歸藏者，而復推衍其變，以與伏羲之作相證也。故卦象不異，而序異焉。文王六十四卦序，雖參伍錯綜，往復循環，與本宮本卦之序異，而仍不變其宗。宗者伏羲八卦之序是也，伏羲八卦為各易根本，無論何易，皆由其序而推衍之，故連山、歸藏、周易三者，其所宗皆同。

The book of Zhou Yi was composed by King Wen based on the two earlier books of Lian Shan and Gui Cang, and he further elaborated on their transformations to verify the old system of Fuxi. Therefore, the hexagrams themselves remained unchanged, only their order was altered. Although the order of the sixty-four hexagrams in King Wen's arrangement is complex and interwoven, differing from both the original sequence of the trigrams and the sequence of the primary hexagrams, its main principle has not changed. This main principle refers to the sequence of the eight trigrams of Fuxi. The eight trigrams of Fuxi are the foundation of all schools of Yi. No matter which school of Yi, it is derived from this sequence. Therefore, the three books of Lian Shan, Gui Cang, and Zhou Yi all revere the same main principle.

即本宮本卦，及六日七分、十二闢卦之序，亦自伏羲卦序所變，初無異也，其所異者，為其用耳。用者合于時宜，孚於人事，本於天道，翕於鬼神，而無間隔也。故夏有連山，商有歸藏，周有周易，時之殊也。

Even the sequence of the primary hexagrams, the order of the primary hexagram, the method of six days and seven parts, and the sequence of the twelve trigrams are all derived from the sequence of Fuxi's hexagrams, and their origins are fundamentally the same. The difference lies only in their respective applications. What is meant by application is to conform to the needs of the times and the actual circumstances of human affairs, to take the heavenly way as the foundation, and to harmonize with the principles of the spirits and ghosts in the unseen realm, without any barrier. Therefore, the Shang dynasty had the "Lianshan" (Continuous Mountains), the Zhou dynasty had the "Guicang" (Return to the Hidden), and the Zhou dynasty had the "Zhouyi" (Book of Changes), which resulted from differences in the times.

有天地之序，日月之度，歲時之歷，人物之生，幽明之道，不相侔者，則卦用以變。故有本宮、本卦、六日七分、闢卦之異，及夫納甲、納辰、納音、運氣、占候之差也。蓋卦以象物事，物事不一，則卦用不同；而卦之為卦，仍止六十四，其應於變者，唯有異其序。序異則用殊，雖卦同，而為象不同。

The order of heaven and earth, the measured movement of sun and moon, the calendar of the seasons, the growth of things and beings, and the principles between the hidden and the manifest—all these differ from one another. Therefore, the use of hexagrams must adapt accordingly. Hence there are differences such as the sequence of the primary hexagram, the sequence of the original hexagram, the six days and seven parts, and the distinction of hexagrams. There are also various methods such as "Najia," "Nachen," "Nayin," "Guqi," and "Zhanhou." Hexagrams are originally used to symbolize things, and since things are not all the same, their applications naturally differ. However, there are only sixty-four hexagrams. To deal with these changes, the order of the hexagrams must be altered. When the sequence changes, their function also changes: although the hexagrams remain the same, the images they represent have become different.

故各序皆有其象，以致其用，非重複也，亦別有他易，而異於伏羲文王之制也。制羲之制最古，時世簡樸，事物純省，故為序者少異例，以不用也，遞降而時移世易，物繁事多，則必推其變，以窮其用。而後序之異例日加，為易亦日眾，此自然之理也。苟有賢者，能通其變，則卦序猶可推衍之以應於用，亦如文王之變連歸為周易也。

Therefore, each type of ordering has its own symbolic meaning and is used for its particular function, not redundant work. It can also be said to form another kind of Book of Changes, distinct from the old systems of Fuxi and King Wen. Fuxi's system was the most ancient, when the world was simple and things were straightforward, so there were few variations in the ordering, as they were not needed. As time passed and the world changed, things became more complex and numerous, and affairs more complicated, it became necessary to elaborate on their changes in order to exhaust their uses. After that, variations in the ordering increased day by day, and the books of Changes also grew in number day by day, which is a natural development. If there were a wise person who could understand these changes, the order of the hexagrams could continue to be extended to meet new needs, just as King Wen transformed the books of "Lianshan" and "Guicang" into the "Zhou Changes."

故周易，文王之制，周代之作，為孚有周政教之用，應當時事物之變也。三代之政教極於周，故夫子刪訂以周易為主。周鑑二代，崇五帝，明周之作，即足概以上之制；取周易，足以窺各易之用也。然周易之序，序周時之政教，即足概以上之制；取周易，足以窺各易之用也。然周易之序，序周時之政教，應事物之變者，以後有所傳者、亦可輔周易而廣其用。

Therefore, the Zhou Yi was composed by King Wen and is a product of the Zhou dynasty, intended to meet the needs of the political and educational policies of the Zhou dynasty and to deal with the changes of things at that time. The political and educational systems of the Xia, Shang, and Zhou dynasties reached their peak in the Zhou dynasty, so when the Master edited the classics, he took the Zhou Yi as the main text. The Zhou dynasty drew lessons from the Xia and Shang dynasties and revered the Five Emperors, showing that the works of the Zhou people were sufficient to encompass the systems of previous dynasties. Taking the Zhou Yi alone is enough to see the methods used in the various schools of the Yi. The order of the Zhou Yi reflects the political and educational policies of the Zhou dynasty and responds to the changes of things. If there were other transmitted versions later on, they could also assist the Zhou Yi and expand its applications. (This passage has repetitions, caused by transmission and copying in old editions, and is kept as it was.)

非僅限於周易也，故於各序之列，有由來者，亦宜習之，以廣易道，而神變化，此固夫子之微意也。本宮之序，以乾、坤、坎、離、震、巽、艮、兌相對之卦次。如乾本宮卦，一世為姤，二世為遯，三世為否，則變於坤，四世為觀，五世為剝，皆坤卦所變；六世游魂為晉，則乾附於坤；七世歸魂為大有，則乾反於乾。

It is evident that one need not limit oneself to the book of The Zhou Changes. Therefore, all sequences that have a source should be studied, to broaden the path of divination and enhance the transformations within it. This was the profound meaning that the Master did not explicitly state. The order of this system is arranged according to the pairs of trigrams: Qian and Kun, Kan and Li, Zhen and Xun, Gen and Dui. For example, in the Qian trigram section: the main trigram is Qian, the first generation trigram is Gou, the second is Dun, the third is Pinyin, and at this point it transitions into the domain of Kun. The fourth generation trigram is Guan, the fifth is Bo, both derived from Kun. The sixth generation is the wandering soul trigram Jin, at which point Qian has become attached to Kun. The seventh generation is the returning soul trigram Da You, and Qian returns to Qian.

自本卦至三世，屬本宮所變；自四世至五世，屬對宮所變；六為附於對宮，故曰游魂，言在外也；七為返於本宮，故曰歸魂，言歸本也。此本宮之序例，以本位與對位，相生相變，次第以成。七世而終必有始，往必有復，故三變而易對宮，七變而還本位，與其本卦成一宮。八卦雖屬一宮，已見交錯往還之象，非純一宮卦也。

From the primary hexagram to the third generation hexagram, the changes occur within the same palace; from the fourth generation hexagram to the fifth, the changes occur between the opposing palace. The sixth change is attached to the opposing palace, so it is called "youhun," meaning being away from the original position. The seventh change returns to the original palace, so it is called "guihun," meaning returning to the source. This is the general pattern of the palace sequence: the original position and the opposing position generate and transform each other in sequence. The seventh generation hexagram marks the end. Since there is an end, there must be a beginning; since there is movement, there must be return. Therefore, the change occurs to the opposing palace at the third generation, and returns to the original position at the seventh generation. Together with the primary hexagram, they form a complete palace. Although the eight hexagrams in one palace belong to the same palace, they already show an image of mutual movement and exchange, and are not purely hexagrams within one palace.

蓋既有生化，必有陰陽；陽合於陰，陰交於陽，生化始成；陽還於陽，陰還於陰，循環始見。本來天地萬物生化，固如是也。故卦序象之，其異乎周易者，則所交錯往復，僅限於相對二宮，而不及他卦。故其所象者，先天初化，萬物始生，二氣初調，五行未雜，其數簡，其氣純，與周易之錯雜循環者異矣。

Since there is generation and transformation, there must necessarily be yin and yang: yang and yin come together, yin and yang interact, and thus generation and transformation can take place; yang returns to its place, yin returns to its place, and the cycle becomes evident. The generation and transformation of all things in heaven and earth are originally like this. Therefore, the order of the hexagrams imitates this process; its difference from the Zhou Changes lies in that the alternating and returning movements are confined within the two opposing trigrams, without involving the other hexagrams. Therefore, it symbolizes the stage when the Earlier Heaven is just beginning to transform, when all things are just beginning to emerge, when the two energies of yin and yang first harmonize, and when the Five Phases have not yet become mixed: the numbers are simple, the qualities pure, differing from the complex and intertwined cycles of the Zhou Changes.

且本宮之序為縱，周易之序為橫。本宮八卦，為一宮卦屬，而不連他宮卦。如乾宮各卦，皆屬金，納甲納辰皆同乾卦；唯游魂屬艮，歸魂屬坤，不同乎乾，以其氣變，數亦易也。氣變則改其情，數易則殊其名，此必至者也；然其大用，仍不離其宗。故所取者，仍本宮內之所合卦；如晉取艮，則遯卦之所合；大有取坤，則否之所合，個二世三世之卦也。

In addition, the order of the trigrams in each palace is arranged vertically, while the order of the Zhou Changes is arranged horizontally. The eight trigrams in a single palace belong to the same category and are not connected with trigrams from other palaces. For example, all trigrams in the Qian palace belong to the metal element, and both "Najia" and "Nachen" also correspond to the Qian trigram. Only the "youhun" trigram belongs to Gen and the "guihun" trigram belongs to Kun, which differ from Qian, because when the qi changes, the numbers also change. When the qi changes, the nature of the trigram changes; when the numbers change, the name of the trigram changes, which is a natural occurrence. However, their main use still remains within the main trigram of their palace. Therefore, when taking symbolic meanings, the trigrams within the same palace are still used to match: for example, the hexagram "Jin" takes Gen, which corresponds to the hexagram "Dun"; the hexagram "Dayou" takes Kun, which corresponds to the hexagram "Po" — that is, the two trigrams corresponding to the second and third generations.

夫卦在後天，以下卦為主；而本宮卦以上卦為先。如姤卦乾上巽下，不從巽而屬乾，則以卦之變自下始也。乾之變初爻為陰，則成巽，而姤卦出，故以下卦明變也。二變則為艮，三變則成坤，四以後所變者，上卦各爻，故反以對宮為主，而坤不動也；迄七變歸魂，而始還於本來，

When a hexagram reaches the Later Heaven arrangement, the lower trigram is the main focus; however, the native hexagram takes the upper trigram as the primary element. For example, the hexagram Gou (Encounter) has the trigram Qian (Heaven) as the upper trigram and Xun (Wind) as the lower trigram. It is not classified under the Xun trigram group but under the Qian trigram group, because the change in the hexagram begins from the lower trigram. The first line of the Qian trigram changes from yang to yin, transforming the lower trigram into Xun, and thus the hexagram Gou appears. Therefore, the change is shown through the lower trigram. The second change transforms the lower trigram into Gen (Mountain), the third change transforms it into Kun (Earth); from the fourth change onwards, the changes occur in the lines of the upper trigram, so the opposite trigram group becomes the main focus, and the lower trigram Kun no longer changes. This continues until the seventh change, when it becomes a returning soul hexagram, and then it begins to return to its original form.

而後後天之用見，如大有一卦，乾在下，與前一二三世相孚；而乾卦之氣乃完，生化循環之用乃盡；其序之次第，皆自然而然，亦猶天地生化之序也。乾宮如此，他宮亦然，其例皆同，不待盡述。

Thus the function of the Later Heaven arrangement becomes evident. For example, in the hexagram "Great Possession," the trigram Qian returns to the lower position, harmonizing with the previous hexagrams of the first, second, and third generations. At this point, the energy of Qian is complete, and the cycle of generation and transformation is fulfilled. The order of these sequences is naturally formed, just as the order of generation and transformation in heaven and earth. This is the case with the Qian trigram, and similarly applies to all other trigrams, following the same pattern, so there is no need to elaborate further.

本卦之序，有方圓二圖，即世傳之先天六十四卦方圓圖，宋人所得於道家者，實古人所留傳也。其序一依伏羲八卦位次之數，既乾一、兌二、離三、震四、巽五、坎六、艮七、坤八，全與河圖數合。乾與坤對，一始一終；離與坎對，一來一往；餘卦順序，分陰分陽，以明氣之升降、數之消長也。

The sequence of the primary hexagram has two forms: the square diagram and the circular diagram, which are the well-known Earlier Heaven sixty-four hexagram square and circular diagrams. These were obtained by people of the Song dynasty from Daoism, but in reality they are remnants passed down from ancient times. The order follows entirely the numerical positions of the Eight Trigrams as arranged by Fuxi. That is, Qian is first, Dui second, Li third, Zhen fourth, Xun fifth, Kan sixth, Gen seventh, and Kun eighth. This sequence corresponds completely with the numbers of the Yellow River Chart. Qian and Kun are opposite to each other, one being the beginning and the other the end; Li and Kan are opposite, one coming and the other going; the rest of the hexagrams are arranged in order, divided into yin and yang, to indicate the rising and falling of qi and the waxing and waning of numbers.

自乾卦始，為一之一，屬乾卦者則為夬、大有、大壯、小畜、需、大畜、泰八卦。順序數之，則夬為兌乾合，為一之二；大有為離乾合，為一之三；大壯為震乾合，為一之四；小畜為巽乾合，為一之五；需為坎乾合，為一之六；大畜為艮乾合，為一之七；泰為坤乾合，為一之八。

Starting from the Qian Trigram, the first one is numbered one; the trigrams belonging to Qian are the Gua, Da You, Da Zhuang, Xiao Xu, Xu, Da Xu, and Tai. Following the order, Gua is composed of upper Dui and lower Qian, numbered two; Da You is composed of upper Li and lower Qian, numbered three; Da Zhuang is composed of upper Zhen and lower Qian, numbered four; Xiao Xu is composed of upper Xun and lower Qian, numbered five; Xu is composed of upper Kan and lower Qian, numbered six; Da Xu is composed of upper Gen and lower Qian, numbered seven; and Tai is composed of upper Kun and lower Qian, numbered eight.

是八卦皆屬乾卦所合而生者。乾之所生八卦，凡乾在下者，無論上卦何屬，皆歸乾，其次第則全依先天數；自一至八，一為乾、八為坤，相循環也，故皆相對。其次則兌卦所屬，自履始，為乾兌，為二之一。

These eight trigrams are all derived from the Qian trigram. The eight trigrams generated by Qian, whenever the lower trigram is Qian, regardless of which trigram is the upper one, are all classified under Qian. Their order follows the Earlier Heaven sequence, numbered from one to eight, with one being Qian and eight being Kun, forming a cycle from beginning to end, thus each pair is opposite. Next comes the group associated with the Dui trigram, starting with the Lu hexagram: Lu is upper Qian and lower Dui, numbered as the second trigram.

次為兌卦，為二之二；次為離兌之暌，為二之三；次為震兌歸妹，為二之四；次為巽兌之中孚，為二之五；次為坎兌之節，為二之六；次為艮兌之損，為二之七；次為坤兌之臨，為二之八。

Next is the hexagram "Dui" (Joy), with both lines being Dui, numbered 2.2; below it is the hexagram "Kui" (Strife), with upper Li and lower Dui, numbered 2.3; below that is the hexagram "Gui Mei" (Return of the Wife), with upper Zhen and lower Dui, numbered 2.4; below that is the hexagram "Zhong Fu" (Sincerity), with upper Xun and lower Dui, numbered 2.5; below that is the hexagram "Jie" (Regulation), with upper Kan and lower Dui, numbered 2.6; below that is the hexagram "Sun" (Loss), with upper Gen and lower Dui, numbered 2.7; below that is the hexagram "Lin" (Approach), with upper Kun and lower Dui, numbered 2.8.

是八卦皆屬兌卦所合而生者，故為兌卦屬；而其數以兌屬先天數二，故皆統於二，猶乾所統於一也。以下各卦皆依此例，以迄於坤卦，為八之八，而殿六十四卦焉。

These eight trigrams are all derived from the Dui trigram, so they all belong to the category of Dui; as for their numbering, since Dui is the second in the Earlier Heaven sequence, this group is all classified under number two, just as the Qian trigram group is classified under number one. The following trigrams follow the same pattern, continuing up to the Kun trigram, which is numbered eight within the eighth group, concluding the entire sequence of sixty-four trigrams.

乾始坤終，乾一坤八，氣數相得，而成全易之序，為圖或方或圓皆同也。蓋此卦序，純本先天之象，以明天地物事之序，有所定也。位有定方，至有定時，上下有次，左右有紀，升降有度，往復有制，不相差於黍粒，不相失於毫毛。故其致用不同後天，而異乎周易之序，且不同先天生化之例，而異乎本宮各卦之序。

The trigrams begin with Qian (Heaven) and end with Kun (Earth), with Qian occupying the first position and Kun the eighth. The interaction between qi (vital energy) and numbers establishes the entire sequence of the Yi (I Ching). Whether drawn as a square or circular diagram, the principle remains the same. This sequence of trigrams is purely based on the Earlier Heaven pattern, used to explain the ordered nature of heaven, earth, and all things. Directions have fixed positions, arrival has fixed times, up and down have fixed order, left and right have fixed rules, ascent and descent have fixed measures, and movement and return have fixed limits. There is no deviation as small as a grain of millet or a hair's breadth. Therefore, its application differs from the Later Heaven system, and it differs from the sequence in the Zhou Yi. It does not follow the model of the Earlier Heaven's creation and transformation, so it also differs from the sequence of trigrams within the same palace.

其象之所指，為明先天之物與事，俾知氣數之本源，而得生化之初象。方以象地，圓以象天，天地既立，萬有斯定。故其制為道家所重，實足以探先天之奧，明無為之道，超形跡之上，達天人之源者，惜乎世人未知其用耳。

This diagram illustrates the principles of the Earlier Heaven, explaining the origins of qi and things, so that people may understand the fundamental source of generation and transformation. The square diagram symbolizes the earth, while the circular diagram symbolizes the heaven. Once heaven and earth are established, all things follow accordingly. Therefore, this system is highly valued by Daoists, as it is indeed capable of exploring the mysteries of the Earlier Heaven and elucidating the way of non-action. It can transcend physical forms and directly reach the common origin of heaven and humanity; the regret is that people do not understand its use.

本卦序與本宮序，二者有可印證處。如本卦乾卦所生八卦，夬、大有、大壯、小畜、需、大畜、泰諸卦，合之本宮，則僅本卦之乾，與歸魂之大有，屬乾宮；

The sequence of the primary hexagrams and the sequence of the native hexagrams can be cross-referenced with each other. For example, among the eight trigrams generated from the Qian hexagram in the sequence of primary hexagrams—such as Gua of Guai, Da You, Da Zhuang, Xiao Xu, Xu, Da Xu, and Tai—it is only the primary hexagram Qian and the returning soul hexagram Da You that truly belong to the Qian palace when checked against the sequence of the native hexagrams.

合之本宮，則僅本卦之乾，與歸魂之大有，屬乾宮；其泰、大壯、夬、需四卦，則屬對宮坤宮；其小畜、大畜二卦，則一屬巽宮，一屬艮宮。是八卦分屬四宮也。而所屬者，仍與本宮之例合。如對宮四卦，原由本宮變；乾坤對變，原定例也。

In the "Primary Hexagram Sequence," the eight trigrams generated by the Qian hexagram are compared with the "Primary Palace Sequence." Only the Qian hexagram itself and the returning soul hexagram Dali belong to the Qian palace. The four hexagrams Tai, Da Zhuang, Guai, and Xu are all assigned to the opposite palace, Kun palace. The two hexagrams Xia Xu and Da Xu are assigned to the Xun palace and Gen palace respectively. This shows that these eight trigrams belong to four different palace groups. However, their assignments still conform to the general rule of transformation within the same palace: the four hexagrams that are assigned to the opposite palace were originally generated from their own palace. Qian and Kun are opposite palaces that transform into each other, which is a fixed rule established in the arrangement of the eight palaces.

大小畜二卦，雖非本對宮，而小畜由巽合，即本宮一世之所變；大畜與艮合，即本宮二世之所變。本宮一世為姤，亦變巽也；二世為遯，亦變艮也。卦雖不同，所合之例仍同。

The hexagrams Xiao Xu and Da Xu, although not derived from the opposite trigram of Qian, are formed by the combination of Qian with Xun for Xiao Xu, corresponding to the first generation hexagram of the Qian palace; and by the combination of Qian with Gen for Da Xu, corresponding to the second generation hexagram of the Qian palace. The first generation hexagram of the Qian palace is Gou, whose lower trigram is Xun; the second generation hexagram is Duan, whose lower trigram is Gen. Therefore, although the names of the hexagrams are different, the principle of their combination remains consistent.

故本宮乾宮八卦，由對宮與對宮合變者，亦四卦；與巽艮合變者，亦二卦。是與本卦之變例，異而不異也。坤卦亦然，所屬八卦除本宮外，亦屬乾宮者四卦，屬震兌二者二卦，與本宮之變例皆同。

Therefore, among the eight trigrams governed by the Qian trigram, those transformed through the opposite trigram Kun and those combined with the opposite trigram are exactly four trigrams; those combined with Xun and Gen produce exactly two trigrams. This shows that the rules of change in the "primary hexagram sequence" and the "governed trigram sequence" appear different but are actually the same. The Kun trigram is also the same: among the eight trigrams generated by Kun, excluding those still belonging to the Kun trigram group, four trigrams are assigned to the opposite trigram group Qian, and two trigrams are assigned to the Zhen and Dui trigram groups, which completely conform to the transformation rules of the Kun trigram group.

故卦雖殊，氣之所合不殊也。乾之氣由西下，而與對宮坤合；坤之氣由東上，而與對宮乾合。無論何序，其例不差，蓋天地陰陽之氣，原來如是也。凡本卦各卦，皆以陰陽升降，本對合化，而生各卦，其例不亂，故其序有定，如指與臂；其象有數，如線串珠；無或差池，無少凌亂。

Therefore, although the names of the hexagrams differ, their essential nature remains the same. The energy of Qian comes from the west and descends, thus combining with Kun in the opposite direction; the energy of Kun rises from the east, thus combining with Qian in the opposite direction. No matter which sequence of hexagrams is used, this principle remains correct, because the yin and yang energies of heaven and earth naturally operate in this way. All the hexagrams in the 'Primary Hexagram Sequence' arise through the interaction of yin and yang rising and falling, and the combination of the original hexagram with its opposite. The order is perfectly consistent. Therefore, its sequence is fixed, like fingers connected to the arm in a natural way; its hexagram images are definite, like beads strung on a thread, orderly and without any disorder or confusion.

不過本卦之序，明先天之真，由下而上，以返本復始，故其卦以下卦為主；本宮序則為明後天之象，由內而外，溯源達流，故其卦以上卦為本。一自下而上，一自上而下，其變化次序不同耳。

The "primary hexagram sequence" aims to reveal the truth of the Earlier Heaven, taking the direction of moving upward from the lower to return to the source and start anew, so when arranging the hexagrams, the lower trigram is taken as the main one. The "primary palace sequence" aims to reveal the image of the Later Heaven, taking the direction of moving outward from the inner to the outer, from the source to the end, so when arranging the hexagrams, the upper trigram is taken as the basis. One goes from bottom to top, the other from top to bottom; the difference between them is merely the direction of the order of change.

苟細按之，自得其故。如為人事吉凶，物理變化，則本宮之序，便於用也；如為天道往復，元氣動靜，則本卦之序，得其真也。故術家卜筮，必取本宮飛伏納甲之圖；而道家修恃，必重本卦方圓合數之象。皆易中精妙，非淺識可得；此不過舉其大要，以明其用耳。

As long as one carefully investigates, the underlying reasons will naturally become clear. If one wishes to predict the fortune or misfortune of human affairs or the changes in the principles of things, using the 'Sequence of the Palace' is most convenient. However, if one aims to observe the cyclical movement of heaven's path and the dynamic stillness of the vital energy, then the 'Sequence of the Primary Hexagram' is most accurate. Therefore, in divination, practitioners of numerology and divination must use the 'Flying and Hidden' and 'Najia' diagrams of the Palace. Meanwhile, those engaged in Daoist cultivation must emphasize the hexagrams of the Primary Hexagram, both the square and circular diagrams, which conform to the numerical principles. These are the subtle aspects of the Book of Changes, not something that can be understood by those with shallow insight. Here, only the main points are mentioned to illustrate their respective uses.

易之合歲時者，有闢卦序、有六日七分、歲象序。闢卦者，以乾坤二宮卦，除游魂歸魂二卦外，分配十二月：自四月起乾，五月乾之一世姤，六月二世遯，七月三世否，八月四世觀，九月五世剝；十月則為坤，十一月坤之一世復，十二月二世臨，正月三世泰，二月四世大壯，三月五世夬。周而復始，以象二氣之流行，明寒暑之迭更也。

In the Book of Changes, there is a sequence of hexagrams corresponding to the seasonal changes of a year, known as the "辟卦序" and the "six days and seven parts" "岁象序." The term "辟卦" refers to selecting hexagrams from the乾 and坤 trigrams, excluding the two additional hexagrams of wandering soul and returning soul, and assigning them to the twelve months. Starting from the fourth month with the乾 trigram, the fifth month corresponds to the first generation hexagram of the乾 trigram, Guo; the sixth month corresponds to the second generation hexagram, Duan; the seventh month corresponds to the third generation hexagram, Pí; the eighth month corresponds to the fourth generation hexagram, Guan; the ninth month corresponds to the fifth generation hexagram, Po. The tenth month corresponds to the坤 trigram, the eleventh month corresponds to the first generation hexagram of the坤 trigram, Fu; the twelfth month corresponds to the second generation hexagram, Lin; the first month corresponds to the third generation hexagram, Tai; the second month corresponds to the fourth generation hexagram, Da Zhuang; the third month corresponds to the fifth generation hexagram, Guai. This cycle repeats, symbolizing the movement of yin and yang energies and explaining the alternation of cold and hot seasons.

另有分各月屬春夏秋冬四時，而分各宮分配之者，即以震巽二宮分配四孟月，離坎二宮分配四仲月，艮兌二宮分配四季月，而循環交錯，以周一歲，與十二闢卦相應。其取義蓋本周天之數，三百六十；天地主其綱，則半為天，半為地，各得百八十；故以乾坤二宮之卦，分主冬夏。自已至戌，屬天氣，即乾主之；自亥至辰，屬地氣，即坤主之；而更以六子，分象四季之氣。

There is another method of arrangement which assigns each month to one of the four seasons, spring, summer, autumn, and winter, and then distributes them among the eight trigrams: the trigrams Zhen and Xun are assigned the four "first months" (孟月), the trigrams Li and Kan the four "middle months" (仲月), and the trigrams Gen and Dui the four "last months" (季月). This cycle completes a full year and corresponds with the twelve trigrams of the heavenly stem. The reasoning behind this method is based on the number of days in a year, which is 360. The heavens and earth each govern half of this number, 180 each. Therefore, the trigrams Qian and Kun are used to govern the winter and summer ends respectively. From Si to Xu, the half-circle belongs to the heavenly energy, governed by Qian; from Hai to Chen, the half-circle belongs to the earthly energy, governed by Kun. Then, the six sub-trigrams generated from Qian and Kun are used to symbolize the energies of the four seasons.

震巽為長，乾坤之長男長女，故震配春夏二孟月，即正月四月；巽配秋冬二孟月，即七月十月。坎離為中男中女，故配四仲月，即二五八十一月；艮兌為少男少女，故配四季月，即三六九十二月。如是乾坤二宮總主一歲，猶二氣之升降消息也。

Zhen and Xun are the eldest son and eldest daughter born from Qian and Kun, so Zhen is paired with the first months of spring and summer, that is, the first and fourth months; Xun is paired with the first months of autumn and winter, that is, the seventh and tenth months. Kan and Li are the middle son and middle daughter, so they are paired with the second months of the four seasons, that is, the second, fifth, eighth, and eleventh months; Gen and Dui are the youngest son and youngest daughter, so they are paired with the last months of the four seasons, that is, the third, sixth, ninth, and twelfth months. In this way, the two trigrams Qian and Kun oversee the whole year, just as the rise and fall of yin and yang energies.

震巽六子分主四時，猶五行之分合生化也。故一年三百六十餘日，合之於六子之爻，亦三百六十爻；乾坤二宮，則合十二月。雖綱目交錯，日月代嬗，若不相接，實則後天二五生化，固交錯而行，代嬗以成，非復先天之單純也。故卦象往復，爻象錯雜；氣數相間，循環無盡。雖以一歲為例，非限於歲月也。

The six subordinate trigrams, such as Zhen and Xun, govern the four seasons, just as the Five Phases interact through generation, transformation, and mutual restriction. Therefore, the 365 days of a year correspond exactly to the 365 lines of the six subordinate trigrams. The two main trigrams, Qian and Kun, correspond to the twelve months. On the surface, the main and subordinate trigrams appear to be interwoven, with the sun and moon alternating, seeming disconnected. In reality, the Later Heaven's transformations depend on the interaction of yin and yang and the Five Phases, the "two and five," which alternate and succeed each other. This is different from the Earlier Heaven, which is simpler. Thus, the trigrams have movement and return, the lines are varied and complex, the qi and numbers alternate, and the cycle has no end. Although this passage uses the year as an example, it is not limited to the year.

本來卦象，無所不包；其序既殊，其用自異。而一歲氣數，恰符周天之數；日月推行，恰符陰陽消息之度。遠者可譬於近，難者可喻於易；就其簡明者衍之，足以推於精微，極於高深；非日六十四卦，專為歲序用也。故此歲序之易，亦言易之一例，有不可不知者焉。

The images of the hexagrams originally encompass everything, but since their sequences differ, their uses naturally vary. The cycle of a year precisely corresponds to the number of the celestial circle, and the movement of the sun and moon exactly matches the measure of the waxing and waning of yin and yang. Far things can be compared with near ones, and difficult things can be explained by simple ones. By following this clear cycle of a year, one can extend it to reach subtle and profound understandings. This does not mean that the sixty-four hexagrams were specifically created for the sequence of the years. Therefore, this "annual sequence" section of the Book of Changes is merely one example of interpreting the Book of Changes, yet it is essential for those studying the Book of Changes to understand.

六日七分歲象序者，以全易六十四卦分配一歲，而將坎離震兌四卦，當二至二分：震主春分，離主夏至，兌主秋分，坎主冬至，謂之四正。餘六十卦，以每月五卦，一卦主六日七分。因一歲三百六十五日又四分一，則卦六十合三百六十爻；每日八十分，一卦合六日七分，恰當一歲之數。

The concept of "six days and seven parts" in the annual sequence of the heavenly phenomena refers to the distribution of all sixty-four hexagrams throughout the year. The four trigrams Kan, Li, Zhen, and Dui correspond to the solstices and equinoxes: Zhen governs the spring equinox, Li governs the summer solstice, Dui governs the autumn equinox, and Kan governs the winter solstice, known as the "four cardinal" trigrams. The remaining sixty hexagrams are divided monthly, with each hexagram governing five days and seven parts. Since a year consists of 365 and 1/4 days, the sixty hexagrams together total 360 lines. Dividing a day into eighty parts, each hexagram corresponds to six days and seven parts, exactly matching the number of days in a year.

其氣始於中孚，其時始於冬至之月。由復至咸，共半歲，為八十八陽爻，九十二陰爻；自姤至中孚，亦半歲，為八十八陰爻，九十二陽爻，恰當百八十爻，而主陰陽寒暑之數。而中孚至復，咸至姤，恰得六日七分，定為例，實天時之度數，自然之序也。

This set of hexagram sequence begins with Zhongfú hexagram, and the corresponding season starts from the month of Winter Solstice. From Fu hexagram to Xian hexagram is half a year, containing eighty-eight yang lines and ninety-two yin lines; from Guo hexagram to Zhongfú hexagram is also half a year, containing eighty-eight yin lines and ninety-two yang lines. Each of them exactly consists of one hundred and eighty lines, used to govern the measure of yin and yang, cold and heat. From Zhongfú to Fu, and from Xian to Guo, the interval is exactly six days and seven parts, which is established as a general rule. This is indeed the measure of heaven's time, a natural order.

卦以交錯，爻以次第；一升一降，一往一復；象氣之周行，後天生化之例也。故其序可以紀歲候時，可以占天驗氣；即四正之卦，分管四時，以候四氣；春夏秋冬有其序，生長收藏有其令；木以長春，火以長夏，金以長秋，水以長冬；五行不失其常，二氣不亂其道；以往復循環無盡，而消息進退可見；其易之傳，蓋已久矣！

The trigrams interconnect with each other, and the lines connect in sequence, rising and falling, moving forward and returning, symbolizing the circulation of qi. This is the principle of generation and transformation in the Later Heaven. Therefore, this sequence of trigrams can be used to record years and observe time, and to predict celestial phenomena and detect the movement of qi. Take the four cardinal trigrams, which govern the four seasons, and are used to measure the qi of each season: spring, summer, autumn, and winter each have their order, and growth, flourishing, harvesting, and storage each have their proper time. Wood thrives in spring, fire is vigorous in summer, metal is mature in autumn, and water is stored in winter. The Five Phases do not deviate from their regular course, and the two energies of yin and yang do not disorder their principles. Because this process of rising and falling, circulating and returning has no end, the waxing and waning, advancing and retreating are clearly visible. This system of the Book of Changes has been passed down for a very long time.

蓋自黃帝造甲子，曆數漸明；堯舜之時，曆象尤備。其制仿於易卦，本於河洛之圖，合於日月之紀，非率爾之作也。《易傳》曰：「懸象著明，莫大乎日月。」日為陽，月為陰；後天之離坎，代先天之乾坤，故歲象以坎離為主，當冬夏二至。冬至為陽生陰消，夏至陰生陽消。

Since the Yellow Emperor established the Jiazi system, the calendar became gradually clear; by the time of Yao and Shun, the system of observing celestial phenomena and setting the time was especially complete. These systems were modeled after the trigrams of the Book of Changes, based on the Yellow River Chart and the Luo Writing, and in harmony with the cycles of the sun and moon, not made up arbitrarily. The Book of Changes, Great Treatise Upper Transmission says: "The suspension of celestial phenomena and their clear manifestation, nothing is greater than the sun and moon." The sun belongs to yang, the moon to yin; in the Later Heaven arrangement, the trigrams Li and Kan replaced the trigrams Qian and Kun from the Earlier Heaven. Therefore, the sequence of the "Annual Phenomena" trigrams takes Kan and Li as its main trigrams, corresponding to the two extremes of the solstices. The winter solstice marks the beginning of yang energy and the gradual decline of yin energy, while the summer solstice marks the beginning of yin energy and the gradual decline of yang energy.

實一歲寒暑之樞機，而四時氣候之中宰。震司春分，如日之升；兌司秋分，如月之上；為陰陽之管鑰，實歲時之道路。皆為氣數所至，而象最明。以之合時令，則足為歷家之所法；以之體天道，則足為生化之模範。

These two solar terms are indeed the key points of the year's cold and heat, as well as the central governing forces of the four seasons' climate. The Zhen trigram governs the spring equinox, like the sun just rising; the Dui trigram governs the autumn equinox, like the moon waxing. They are the keys to the entry and exit of yin and yang, and the channels through which the annual cycle operates. These are the natural results of the flow of qi, and the trigrams clearly manifest these phenomena. Using them to coordinate with the seasons provides a reliable basis for those who compile calendars; using them to understand the heavenly way offers a model for the operation of generation and transformation.

蓋其序之取義，雖近闢卦，而尤善焉。不過闢卦法乎先天，故以乾坤二宮，為一歲之綜；而歲象法乎後天，故以坎離四正，為一歲之綱。先天乾坤對位，主於上下，此伏羲八卦之序；後天坎離震兌分主四正，此文王八卦之序。二者各有取義，而後者最宜於後天之用，以所象無不交錯往復，所配皆以消長平均，以合一陰一陽之道，而能會通日月之行也。

This sequence of hexagrams is similar in meaning to the method of dividing the trigrams, but it is more comprehensive. The method of dividing the trigrams follows the Earlier Heaven arrangement, using the trigrams Qian and Kun to represent the whole year; the annual pattern follows the Later Heaven arrangement, using the four cardinal trigrams Kan, Li, Zhen, and Dui as the framework for the year. In the Earlier Heaven arrangement, Qian and Kun are opposite each other and govern the upper and lower positions, which is the order of the Eight Trigrams of Fuxi. In the Later Heaven arrangement, Kan, Li, Zhen, and Dui each govern the four cardinal directions, which is the order of the Eight Trigrams of King Wen. Each has its own meaning, but the latter is more suitable for practical use in the Later Heaven system, because the trigrams it uses are interwoven and reciprocal, and the paired seasonal periods are balanced in their waxing and waning, conforming to the principle in the Great Treatise that "the way is characterized by the interplay of yin and yang." Thus, it can integrate the movement of the sun and moon.

故中國之曆法，實本此序；而後人以之占筮，亦無不驗。其為易之精妙，亦足與《周易》相證；即合之其它各易，不問為先天後天，亦無不貫通。要以後人多不明其用，忽其旨趣；門戶之見，以責難之；方技之辭，以鄙夷之；遂使上古流傳之易，反為俗人所訛，豈不惜歟！

Therefore, the Chinese calendar is actually based on this sequence of hexagrams; later people used it for divination, and it never failed to be accurate. Its refined aspects in the study of the Yi (Book of Changes) are sufficient to corroborate the Zhou Yi; even when applied to other schools of Yi methodology, whether earlier Heaven or later Heaven, it is fully consistent. Alas, most later people do not understand its use and overlook its meaning: some criticize it with narrow-mindedness, while others belittle it as mere words of the alchemists and look down upon it. Thus, the Yi methodology passed down from ancient times has been wrongly transmitted and misunderstood by the common people. Is this not regrettable?

周易之用，在乎人之誠，不必一例。如周易之序，固為周時太卜所司；而太卜所用，兼及連、歸，不限文王之易也。則可知易之為用，不以序為限；但有是序，即有是變；有是變，即有是用。伏羲之易，有伏羲之用；文王之易，有文王之用。夫子合二者而作雜卦序，即夫子之易，亦有夫子之用也。

The function of the Zhou Yi lies entirely in the sincerity or lack of sincerity of those who use it, and there is no fixed pattern that remains unchanged. Just as the sequence of hexagrams in the Zhou Yi was originally managed by the official "Tai Bu" in the Zhou dynasty; yet the Tai Bu also used the Lian Shan and Gui Zang, not limited to the Yi of King Wen alone. From this we can see that the function of the Yi is not restricted by any particular sequence of hexagrams: there is such a sequence, there is such a change; there is such a change, there is such a method of use. The Yi of Fuxi has its own method of use; the Yi of King Wen has its own method of use. Confucius combined the Earlier Heaven and Later Heaven sequences to compose the Zage sequence, showing that the Yi of Confucius also has its own method of use.

推之連山之易，有連山之用；歸藏之易，有歸藏之用；八宮之易，有八宮納甲之用；歲象之見，有六日七分之用，分而言之，各有其用；合而通之，則易之用，廣無不包，變無可窮；而能通之為一者，則見天地之心；斯非聖知不克也！就其最簡易者，則但執一易；審其象，參其數，列其圖；而合其先後天，明其辭而衍之經與傳，則亦可以得易之用矣！

From this, we can extend further: The Book of Linked Mountains has its own usage, and the Book of Return and Concealment has its own usage; the eight palaces of the Book of Changes have the method of "eight palace stem assignment"; the annual phenomena of the Book of Changes have the method of "six days and seven parts." When considered separately, each has its own use; when combined and integrated, the function of the Book of Changes is vast and all-encompassing, its transformations numerous and endless. Only those who can integrate them into one can see the heart of the continuous generation of heaven and earth, something that cannot be achieved without the wisdom of a sage. If one starts from the simplest approach, then one may just fix upon a single Book of Changes: examining its hexagrams, investigating its numerical principles, arranging its diagrams, and combining them with the Earlier Heaven and Later Heaven views. Clarifying its hexagram line statements, and deriving the commentaries from the classics, one can also attain the function of the Book of Changes.

故易之種類雖眾，精其一者，能通其餘；若一而未精，雖多奚益？目迷於象數之異，手迷於圖表之繁，能紀其粗，而遺其精；逐其物、忘其神；則為易百年，曾不得易道之一二；此後世有掃象之說也。

Therefore, although the types of the Yi are numerous, mastering just one can lead to understanding the rest through analogy; if one does not master even one, how can learning more be of any benefit? The eyes are confused by the differences among various schools of imagery and numbers, and the hands are tangled by the complexity of different charts. One remembers only superficial details but misses the essential core; chasing external phenomena while forgetting the inner principles. Thus, studying the Yi for a hundred years would still yield only a fraction of its true meaning. This is the root cause of the later saying "sweeping away images."

夫易之本在象，而掃之，將何以見易？豈非以世人之馳於外，而遺其內；求其未，而棄其本歟！故習易者，必先去其蔽，所敝者，多而不精，博而不深；能於貌，而不及於神；以為能通習，而不知無一得也。

The fundamental aspect of the Book of Changes lies in 'image' or 'symbol'. If one clears away the images, what else is there to see in the Book of Changes? This is precisely because people have been blindly seeking outwardly and have lost their inner essence, chasing superficial details while abandoning the root. Therefore, those who study the Book of Changes must first remove their obstructions. These obstructions refer to learning a lot but not mastering it, exploring widely but not deeply; merely imitating the surface without reaching the profound meaning; believing oneself to have fully integrated and understood, yet actually achieving nothing.

故各易之序，夫子不錄；僅取文王者著為經，而集其它關乎易理者，述之為傅；做學者知所宗，而不紛其智，知所本，而不亂其思；庶由一以通其餘，由易以達事難，由近以賅其遠；則習之有成，而易道亦不荒塞；此則夫子刪易之微旨也。

Therefore, the various sequences of hexagrams in different schools were not all collected by the Master. He selected only one sequence from King Wen and established it as the "Classic," while gathering other materials related to the principles of the Book of Changes and compiling them into the "Commentaries." This was to enable those studying the Book of Changes to know what to revere, so their thoughts would not become confused, and to know what to rely on, so their reasoning would not become disordered. In this way, one could start from one comprehensive principle and extend it to all others, proceed from the easy to the difficult, and from the near to the distant. By following this path, one could achieve mastery, and the teachings of the Book of Changes would not be neglected or blocked. This is the profound intention of the Master in editing the Book of Changes.

夫易之致用，非為卜筮也；若為卜筮，則巫祝在，夫子不以之首六經也；夫子以易為六經之首者，以其用明天人之道，類萬物之情；定日月之行，奠山河之度；可以致治平之業，可以正性命之功；可以四達神鬼之情；可以敷教化之德；故其用在此，而不為卜筮也。

The usefulness of the Book of Changes lies not in divination. If it were solely for divination, there would be others, such as the shamans and diviners, who would handle that. Confucius would not have placed the Book of Changes first among the Six Classics. Confucius placed the Book of Changes first among the Six Classics because its function is to clarify the communication between heaven and humanity, to classify and compare the nature of all things; to determine the movement of the sun and moon, to establish the measurements of mountains and rivers; to achieve the affairs of governing the country and pacifying the world, to correct the cultivation of human nature and the attainment of destiny; to understand the hidden feelings of ghosts and spirits, and to spread the virtue of teaching and moral cultivation. Its usefulness lies here, not in divination.

然卜筮亦易所固有，卦爻之辭，吉凶之占；悔吝之途，君子小人之道；皆著於象數，徵於言文；苟按其數而卜之，因其辭而決之；則所謂易逆數也。通變化而行鬼神者，皆在傳中揲卦之法，可見之也；故經不備者，傳則補之；經取其約，約而后尊；傳取其博，博而後宏。

But divination is indeed an inherent part of the Book of Changes: the hexagram statements, line statements, the determination of fortune and misfortune, the tendencies of regret and hardship, and the paths of the gentleman and the petty person—all rest upon the images and numbers, and are verified in the textual expressions. If one divines by following the hexagram numbers and makes decisions based on the line statements, this is what the "Commentary on the Hexagrams" refers to as "the Book of Changes is about inverse numbers." As for the principles of continuous transformation and the operation of spirits and ghosts, these are evident in the method of "casting yarrow stalks to form the hexagram" described in the "Great Treatise." Therefore, the classic text does not cover everything, and the commentaries supplement it. The classic is concise, and only through conciseness does it become dignified; the commentaries are comprehensive, and only through comprehensiveness do they become grand.

用宏而道尊，則易之精粗皆備；故傳所舉者，有各易之例；凡連山歸藏之類，八宮歲象之圖；上自先天，旁及河洛，無不徵取，以為周易之輔，而明易道之大也。故讀經則專文王之制，雖伏羲之序不列；讀傳則必廣搜各易之圖，而不限於一種；此講易時必旁及各序也。

The scope of application is vast and the principles are dignified, encompassing both the subtle and the superficial aspects of the Book of Changes. Therefore, the "Commentaries on the Book of Changes" include the systems of various schools of the Book of Changes: all kinds of diagrams such as the Eight Trigrams and the annual phenomena, tracing back to the Earlier Heaven trigram positions, and extending to the Yellow River Chart and the Luo Writing, are all cited and adopted as auxiliary materials for the Zhou Changes, to demonstrate the vastness of the principles of the Book of Changes. Therefore, when reading the classics, one should focus solely on the system of King Wen, even excluding the trigram sequence of Fuxi. However, when reading the commentaries, one must widely collect the diagrams of various schools of the Book of Changes, not limited to one system. This is why, when discussing the Book of Changes, it is necessary to refer to various trigram sequences.

人或疑其言之雜，不知正欲其雜也；人或謂異於經文，不知正求其異也；雜則變例多，而用可廣；異則分類明，而道可通；此傳之本旨，夫子訂易之徵意也。故傳中之辭，各不相類；方位次序各不同；名類上下各不一，其所以然者，各易之原制如是也。

Some people doubt that the "Commentaries on the Changes" are too miscellaneous, but they do not realize that it is precisely meant to be miscellaneous. Others say that the commentaries are inconsistent with the classic text, but they do not understand that it is precisely meant to be inconsistent. Being miscellaneous allows for a greater variety of flexible applications, making it more useful; being inconsistent allows for clear categorization, enabling the principles to be fully understood. This is the true intention of composing the commentaries, as well as the profound purpose of Confucius in establishing the study of the Changes. Therefore, the words in the commentaries are not similar to each other, their positions and orders differ, and their titles and arrangements are also inconsistent. This is because the original forms of the Changes themselves were inherently varied.

各易皆可用於卜筮，而周易最善；其次則八宮納甲法，其次則歲象六日七分術；而伏羲先天本卦方圓序，則為示修養之道，明先天之氣；若用於卜筮則淺矣！然亦能通，不過難測耳；至俗傅各種卜易法，皆由數者變化而來，有當有未當也；與周易等者，前有連山、歸藏，後有夫子雜卦；皆以卦爻象數為本，不取甲辰，不用日月；其道簡而理微，人多難知；故卜者不用，而好八宮與歲象術；其實理數一也，苟通者無所忤焉。

All schools of divination using the Yi can be used for divination, among which the Zhou Yi is the most complete; next comes the method of the Eight Palaces with the stem assignment, and then the method of the annual cycle and six days and seven parts. As for the square and circular diagrams of the Fuxi Earlier Heaven primary hexagram, they were originally used to indicate the way of cultivation and to clarify the primordial qi. If they are used for divination, they become superficial; however, they can also be used, though it is difficult to measure. As for various methods of divination that are popular among the common people, they all originate from the above-mentioned schools, some being appropriate and some not. Those that can be compared with the Zhou Yi include the Lianshan and Guicang, and later the Zazha by the Master, all of which take the hexagram lines and numbers as their foundation, not using the heavenly stems and earthly branches, nor the sun and moon. Their methods are simple but their principles are subtle and profound, so they are not easy to understand for ordinary people. Therefore, diviners do not use them, but prefer the methods of the Eight Palaces and the annual cycle. In reality, the principles and numbers are the same. If one truly understands them, using any of these methods will not feel contradictory.

做周易之卜，古之史傳常見其例；其應甚靈，豈古可用，而今不宜哉？蓋用之在人，能誠而通神者，何易不可靈？否則雖俗淺之術，亦不得其效；故易之用，不在序之異也；序之所異，不為卜也；其理見前，可以知矣。周易之精，在以後天之物象，明先天之氣數；一卦一爻，各有所象，而貫通先後天，以明其變化；故不枝不離，而獨來獨往；為最宜於時中之道，合於戒慎之教也。

Divination using the Zhou Yi is commonly found in ancient historical records, and its predictions are very accurate. How could it be that ancients could use it, yet modern people should not? Actually, the key lies in the person using it: if one is sincere and communicates with the divine, then which divination method would not be effective? Otherwise, even using secular and simple methods would not work. Therefore, the function of the Zhou Yi does not lie in the differences of its hexagram sequences. The differences in the sequence of hexagrams were not originally intended for divination, as this reasoning has already been explained earlier, and now it should be clear. The profound aspect of the Zhou Yi lies in using later heaven phenomena to explain the earlier heaven principles of qi and numbers. Each hexagram and line has its corresponding image, and it can connect both earlier and later heaven, clearly explaining the changes within. Therefore, it does not branch out into irrelevant matters, nor does it depart from the fundamental principles. It moves independently and freely, most in line with the principle of "timeliness and moderation" and also conforms to the teaching of "caution and reverence."

以文王作此，正囚辱之時；憂天下之亂，存革正之心；鑑前人之敝，立新教之意；故其辭巽而決，其旨正而中，其道極變化，而仍守常度；其志攘暴亂，而先重仁德，故與夫子中庸之教，修道戒慎為本；忠恕時中為用，立誠復始為成，其義正同。

Because King Wen composed this Book of Changes while he was imprisoned and humiliated, he was concerned about the troubles of the world and had the determination to reform corrupt governance and restore proper order. Taking into account the accumulated evils of previous generations, he intended to establish a new teaching. Therefore, his words were humble yet resolute, his principles upright and moderate; his doctrines reached the utmost of change yet remained within the constant path; his aspirations aimed to eliminate tyranny, yet he first valued benevolence. This aligns perfectly with the teachings of the Master's Doctrine of the Mean, which takes cultivating the Way and being cautious as its foundation, practicing loyalty, forgiveness, and timely moderation as its functions, and establishing sincerity and returning to the original nature as its achievement.

夫子取之以繼堯舜之傳，而明文武之治，即所謂祖述憲章者，易經居其首也，中庸之書，繼易而作；皆言事而歸於道，言人而歸於天，原怡返終，正其性命，明物達情，通其精粗；故言博而約，辭詳而明；為古聖心傳之所存，而儒家至教之所寄也。後之學者當加意焉！

The Master took up the Zhou Yi, aiming to carry forward the heart method passed down from Yao and Shun, and to clarify the governance principles of King Wen and King Wu. This is exactly what the Zhongyong says: "Following the path of Yao and Shun, and establishing the model of Wen and Wu." The Yi Jing stands at the beginning of this. The Zhongyong itself was written in succession to the Yi. Both deal with matters and return to the Dao, with people and return to Heaven; they trace back to the origin and seek the ultimate, correct human nature and life; they clearly observe all things and understand the nature of things, integrating the subtle and the obvious. Therefore, their writings are extensive yet concise, their expressions detailed yet clear. This is where the sacred heart tradition of the ancients is preserved, and where the highest teaching of Confucianism is entrusted. Later scholars should focus on this aspect.

夫子刪定六經，取文王之易為首，同於《尚書》，為三代以上之遺；於此可見二帝三王之政教，神農伏羲之制作也；而不取《連山》《歸藏》，及伏羲神農之易，獨採文王者，為文王之易，即各家之所傳；傳至文王變例已多，易道更明，易習易知也。伏羲神農堯舜之時，有象無文，有文未備；《連山》《歸藏》之易，有文異義，有變未全；唯文王之易，象仍古昔，文備義明；變推新例，體具用昭；故言易至文王，為最宜於時之制，而易道亦更發皇光大矣！

Confucius compiled the Six Classics, placing King Wen's Book of Changes first, just as the Book of Documents is arranged, both being ancient traditions passed down from the Xia, Shang, and Zhou dynasties. From these texts, one can see the political and educational practices of the two emperors, Yao and Yu, and the three kings, Xia Yu, Shang Tang, and Zhou Wen Wang, as well as the inventions of Shen Nong and Fuxi. He did not adopt the books of Lianshan and Guicang, nor the Book of Changes attributed to Fuxi and Shen Nong, but only used King Wen's version, because King Wen's Book of Changes had already integrated the teachings of various schools. By the time it reached King Wen, the system of change was already well developed, the principles of the Book of Changes were clearer, and it was easier to learn and understand. In the time of Fuxi, Shen Nong, Yao, and Shun, there were hexagrams but no written explanations, and even if there were explanations, they were incomplete. The two books of Lianshan and Guicang had written explanations but their meanings differed, had examples of change but were not comprehensive. Only King Wen's Book of Changes maintained the ancient method of hexagrams, had complete written explanations, clear principles, and further developed new examples of change, making its system complete and its functions clearly evident. Therefore, when discussing the Book of Changes, it was only when reaching King Wen that it fully aligned with the contemporary system, and the principles of the Book of Changes were thus further promoted and expanded.

此夫子序易，以周易為本者也；然周易雖善，舊制亦不可盡棄；伏羲之作，固為易之源，不可不知；即神農堯舜夏商之易，亦不可不明；則將其說備載於傳，繫之於經，故曰繫辭。而以證諸經文，廣其變，推其用也。

This is the reason why the Master arranged the Book of Changes with the Zhou Yi as its foundation. However, although the Zhou Yi is excellent, the old system cannot be entirely discarded: Fuxi's creation is indeed the origin of the Yi, and it is essential to know it; even the Yi of Shen Nong, Yao, Shun, and the Xia and Shang dynasties should not be overlooked. Therefore, these views were thoroughly recorded in the "Transmission" and attached beneath the classic text, hence called the Great Treatise, to verify the classic text, expand its variations, and elaborate on its applications.

故有先天乾坤上下之位序，為伏羲之遺，即天地定位一章所述也；有日月成歲，合乎天行之序，即揲蓍求卦象一歲之一章所述也；有納甲應爻，分宮飛伏之序，即出震齊巽，先甲後甲各所述也；有日月代行，水火上下之序，即後天卦位，三索得男女各節所述也。

Therefore, the transmission contains the earlier heaven arrangement where Heaven is above and Earth is below, which is the old system left by Fuxi, as discussed in the chapter "Heaven and Earth are positioned" of the "Discourse on Hexagrams"; the sequence of hexagrams formed by the movement of the sun and moon completing a year, conforming to the movement of heaven, is explained in the chapter "Divination with the Yarrow Stalks, the day of the appointed period" of the Great Treatise; the assignment of heavenly stems to lines and the sequence of hexagrams involving division of palaces and flying and hiding lines is discussed in the "Discourse on Hexagrams" chapter "The Emperor arises from the震 (Thunder) and harmonizes with the巽 (Wind)" and the text mentioning "three days before the Jiā day and three days after the Jiā day"; the sequence of hexagrams showing the mutual movement of the sun and moon and the mutual assistance of water and fire above and below is explained by the later heaven hexagram positions and the sections in the "Discourse on Hexagrams" titled "Three searches result in male and female."

其它如地代有終，《歸藏》之羲也；艮為終始，《連山》之義也；方圓之圖，伏羲之制也；納甲納音，黃帝之制也；歲象闢卦，神農之制，及於堯舜，而更推衍者也；九宮五行，五運六氣，河洛之遺，及於黃帝，而更發明者也。

Other expressions such as "the earth path signifies the end" reflect the meaning of the book of Guizang; "Geng signifies the beginning and the end" reflects the meaning of the book of Lianshan; the square diagram and the circular diagram were created by Fuxi; the system of Na Jia and Na Yin were established by the Yellow Emperor; the system of annual phenomena and the method of dividing trigrams were developed by Shen Nong, and later refined during the time of Yao and Shun; the nine palace system of the Five Phases and the theory of the Five Movements and Six Qi were remnants left by the Yellow River Chart and the Luo Writing, and were further elaborated during the time of the Yellow Emperor.

故易者成於各聖，傳於千古，而其義備於傳，以與周易證明也。夫子猶以為未足，更合伏羲文王之作，先後天之象，各家之制，而成雜卦傳；雜者合也，合各種而一之，以見其會通一貫之義也；故以之終諸書，而成夫子之易，是易雖取文王，而仍包各書，夫子之作亦附焉，此讀者所宜知也。

Therefore, the book of Change (Yi) is a work completed by sages of all generations and passed down through the ages. Its principles are fully explained in the "Transmission" (Zhuan), used to verify the Zhou Yi. Confucius still found it insufficient, so he combined the works of Fuxi and King Wen, the earlier and later heavenly diagrams, and the systems of various schools, to compose the "Miscellaneous Diagram Transmission" (Zagua Zhuan). "Miscellaneous" means combination, bringing together various elements into one, to show their unified meaning. Hence, it is placed at the end of the various chapters, completing Confucius' own version of the Yi. This shows that although the Yi is taken from King Wen's school alone, it still includes the works of other schools, and Confucius' own writings are also included. This is something those who study the Yi should know.

易之致用，一而已；一者道也，故各易，皆為明道用；無論為伏羲，為文王，為先天後天，為《連山》《歸藏》，皆不離於道；然道自一，何以各易不同？則為明道之方，有不同耳，道本無方無體，人之求之也，則有其方，以悟其體；是猶行路，或車或馬或步行，其行一也；所以行不同也，故各易各有其方，以明其用。

The function of the Book of Changes ultimately comes down to one thing, which is the Dao. Therefore, all schools of the Book of Changes are established to explain the Dao. Whether it is the Book of Changes of Fuxi, the Book of Changes of King Wen, whether it is Earlier Heaven or Later Heaven, whether it is the Book of Continuous Mountains or the Book of Returning Concealment, none of them deviate from the Dao. However, the Dao is originally one, so why do the various schools of the Book of Changes differ? This is only because the approaches to explaining the Dao differ. The Dao itself has no place or form, and in order to seek it, people must have a path or method to understand its essence. This is like traveling, whether by carriage, horseback, or on foot; the act of traveling is the same, but the methods differ. Therefore, each school of the Book of Changes has its own approach, to demonstrate its function.

在太上之時，道至簡，事至略；人樸物醇，生計至易；故象之者，亦直樸無文，而見道亦真；其後則漸降漸變，漸繁而文；而象之者，隨之而異；故易自古入今，自簡趨繁，人事使然；道之為道，固未改也。故一易之用，為應時之需；時之不居，易亦必變，此易之所以為易也。

In ancient times, principles were extremely simple, affairs were very straightforward, people's hearts were pure, things were naturally sincere, and livelihood was very easy. Therefore, the images used in the hexagrams were direct and unadorned, yet they truly reflected the way. Later, as the world's customs gradually declined and changed, things became more complex and more elaborate, and the images used in the hexagrams also changed accordingly. Therefore, from ancient times to the present, the Book of Changes has evolved from simplicity to complexity, which is due to human affairs. However, the way itself has never changed. Therefore, every use of the Book of Changes is to meet the needs of its time. Since circumstances never stop, the Book of Changes must also change accordingly. This is precisely why it is called the "Book of Changes" (Yi), meaning change.

伏羲之易，名為先天，義為修道，政尚虛靜，教崇純樸，其時然也；神農黃帝以迄堯舜，生息日眾，世事日新；政日以備，教日以詳；善惡以明，吉凶斯判；故其易亦由簡而繁，其用由純而雜；堯舜之後，文勝於質，政明於教；禮備於德，事增於物；變化既多，氣數以分；於是三代之易，更張其舊，名適時宜，以為新制。

Fuxi's Book of Changes is called "Earlier Heaven," and its meaning lies in cultivating the Way. In terms of governance, it values emptiness and quietude; in terms of education, it values simplicity and purity. That was the situation of the time. From Shen Nong and the Yellow Emperor down to Yao and Shun, the population grew increasingly numerous, and worldly affairs became more and more new. Orders became more and more complete, and education became more and more detailed. Thus, good and evil became clearly distinct, and auspicious and inauspicious became clearly separated. Therefore, the Book of Changes at that time changed from simple to complex, and its use changed from pure to mixed. After Yao and Shun, ornamentation surpassed simplicity, and orders surpassed education. Rituals were complete compared to virtue, and affairs outnumbered objects. With many changes, the destiny and fortune thus differentiated. Therefore, the Book of Changes of the Xia, Shang, and Zhou dynasties altered the old system, established new names to suit the times, and became a new system.

至文王而變益異，時勢既迫，事物乃非；道晦不明，教亡不復；政失其紀，俗失其常；善不敵惡，吉不侔凶；君子道消，小人在位；易道至是窮矣！窮則必變，敝則必革；此湯伐桀之時也；文王師之，以變為新易，而寓教於卦象焉；故周易者，革舊改新，正教明道者也。

By the time of King Wen, the changes became even more different: the situation had become urgent, things had already changed beyond recognition; the Way was obscured and unclear, education had declined and could not be restored; government orders had lost their order, and customs had lost their proper course; good could not overcome evil, and good fortune could not surpass misfortune; the Way of the gentleman had receded, while petty men occupied high positions; at this point, the Way of the Changes had reached its limit. When something reaches its limit, it must change, and when something is in disrepair, it must be reformed, just as was the case when Tang of Shang attacked Jie of Xia. King Wen took the example of Tang, using the method of change to create a new Changes, entrusting education in the images of the hexagrams; therefore, the book of The Zhou Changes is precisely a book for eliminating old evils, establishing new laws, rectifying education, and explaining the great Way.

當時晦塞，值身窮因，而欲為此挽回教政，光復道德，其非易事。蓋可知矣。故其為象曲折反覆，為辭宛委丁寧；一變前日之作，而成獨有之制；此其與伏羲之舊大殊，與連歸之辭亦異；而成一後天之易也。

At that time, the world was dark and obstructed, and King Wen himself was in a difficult situation. Yet he wished to use this book to restore moral teachings and political orders, and revive virtue. How difficult this must have been, one can easily imagine. Therefore, the hexagrams he selected were intricate and complex, and the accompanying texts were subtle and repeated for emphasis. He completely changed the previous style, creating a unique system. This is why it differs greatly from Fuxi's original system, and also differs from the wording of the "Lianshan" and "Guicang," thus becoming its own form of Later Heaven Yi.

蓋文王之易，與時相宜；後天者，奉時也；本無先後天之名，以別於伏羲，故曰後天；以能奉天時，故曰後天；其實易一也，用異耳；若分先後，則文王以前者，皆宜先之；伏羲以後者，皆宜後之；而獨先伏羲後文王者，以二易足盡易之體用耳。

King Wen's Yi is in harmony with the times. The term "Later Heaven" refers to following the heavenly timing. Originally, there were no names like "Earlier Heaven" or "Later Heaven." These terms were introduced to distinguish King Wen's Yi from Fuxi's Yi. It is called "Later Heaven" because it follows the heavenly timing. In reality, there is only one Yi, differing only in its application. If we were to divide based on time, everything before King Wen should be considered Earlier Heaven, and everything after Fuxi should be Later Heaven. However, Fuxi is regarded as Earlier Heaven and King Wen as Later Heaven because the Yi systems of these two sages have already fully explained the nature and application of Yi.

若推而言之，則連、歸各易，皆後天也；以其明伏羲之變，同於周易也；不過歸藏出，而連山亡；周易成，而歸藏息；時之既易，易亦隨之，由歷代之文物考之，則連歸可備參證；若以時之宜，變之極，明易之道，為後世之則；則唯周易足與伏羲表裡，取周易而他易其中矣！此夫子以周易為輕，而博搜各易之義為傳也。

If we generalize, the Yijing of the Lianshan and Guicang schools are also considered Later Heaven, because they all explain the changes of Fuxi's Yijing, which is the same as the Zhou Yijing. The only difference is that when the Guicang appeared, the Lianshan disappeared; and when the Zhou Yijing was established, the Guicang ceased to exist. As times changed, the Yijing also changed. From historical relics, the Lianshan and Guicang can still serve as references. But if we consider which Yijing is most suitable for the times, fully explains the changes, and adequately demonstrates the principles of the Yijing to serve as a model for future generations, then only the Zhou Yijing corresponds with Fuxi's Yijing in both form and essence. Therefore, the Master took the Zhou Yijing as the main text and widely collected the meanings and interpretations from other schools to compose the "Commentaries."

周易之用，為救時明道，而本於易之原旨；易者以六爻三極，合天地人者也；天道陰陽，居上兩爻；地道剛柔，居下兩爻；人道仁義，居於中央；此名三極，以人道為綱。故三四爻，人之位，善惡之門，吉凶之途，皆在是焉；人為天地之中，道之所存，時之所依；教政所出，生化所成。

The purpose of The Zhou Changes is to correct current evils and clarify the great way, and its fundamental principle still comes from the original meaning of the Book of Changes. The term "Easy" refers to dividing the six lines into "three extremes," combining heaven, earth, and humanity into one. The heavenly way is yin and yang, located in the upper two lines; the earthly way is strength and softness, located in the lower two lines; the human way is benevolence and righteousness, located in the middle two lines. This is called "three extremes," with the human way as the main point. Therefore, the third line and the fourth line are the positions of human beings, where the gate of good and evil and the path of fortune and misfortune lie. Humans are situated in the middle of heaven and earth, which is the place where the way resides, the place where time relies upon, and also the source from which teachings and commands arise, and the origin from which life is nurtured and cultivated.

故天地之道，依人而明，時之敝，依人而新，教政之失，依人而復振；仁義之不講，時之亂也；教政之不明，人之責也；唯人能理亂救亡，正失止敝。故聖人則之，以負其任；而文王適逢之，乃明易之變，而濟道之窮；以教寓於象，而濟道之窮；以教寓於象，以心存於卦。

Therefore, the way of heaven and earth relies on people to be made clear, the corruption of the times depends on people to be renewed, and the mistakes in education and government depend on people to be restored. Not speaking of benevolence and righteousness is the disorder of the times; unclear education and government is the responsibility of people. Only people can rectify calamities, save from peril, correct mistakes, and prevent evils. Thus, sages emulate heaven and earth, taking up this responsibility. King Wen just happened to live in such an era, so he explained the changes of the Book of Changes, using it to relieve thepredicament of the Dao; he寄托 education in the hexagrams and placed his mind in the hexagram figures.

故其易與前異者，應夫時也。道之不明，時之所為；時之不回，則人心失所主，而變生焉；變之亂者，時之咎也；變之治者，人之功也；人應時而為變，變乃通，通乃道；故道在時，而聖人乃能用時；用時變時，是曰時中；道之存也，時之隆也，則守其常；道之晦也，時之汙也，則達其變；唯變乃復於中道，而道乃明。

Therefore, his Book of Changes differs from before, precisely to correspond with the times. The reason the Way is not clear is due to the times; if the times do not change, people's minds will lose their guidance, and chaos will arise. Chaos caused by change is due to the times; order achieved through change is due to human effort. When people adapt to the times and make changes, change leads to communication, and communication brings harmony with the Way. Therefore, the Way exists in the times, and only the sage can skillfully use the times. Being able to use the times and change the times is called "the middle of the times." When the Way still exists and the times are favorable, one should maintain the constant; when the Way is obscured and the times are corrupt, one should adapt and change. Only through adapting and changing can one return to the middle path, and the Way can be made clear.

聖人在因時明道，非守死而忘時也；乃因時而變之，以存亡正失也。故文王之易在於是，其意若曰：伏羲之易，經常之道，不可變也；時無明之者，易乃日晦；必以變而新之，則前者益光大；其義取在革卦，革以去故，言去時之汙也；而其用取之鼎卦，鼎取新也，言新易之道，而光大伏羲之制也。

The sage values adapting to the times in order to explain the great way, not rigidly adhering to old methods while ignoring the times. Instead, he follows the times to make changes, thus preserving what is about to perish and correcting what has already been lost. King Wen's approach to the Book of Changes is precisely this. His meaning seems to be that Fuxi's Book of Changes represents a constant way, which should not be altered. However, because at that time no one could explain it clearly, the principles of the Book of Changes gradually became obscured. Therefore, change was necessary to renew it, and the old methods became even more prominent. Hence, he drew the meaning from the "Revolution" hexagram, "Revolution" meaning removing the old, referring to eliminating the corruption of the times; and he used the "Tripod" hexagram, "Tripod" symbolizing renewal, referring to establishing new regulations for the Book of Changes, thus expanding upon Fuxi's original system.

故其序以往復循環為則，以吉凶相對，善惡相當；明世道之無往不復，而人心無時不動；必以善制惡，以新革故，以成循環之數，而復歸於道；此則文王之易所以異也。夫連、歸遞嬗，夏商異代；其政教不一，制度各殊，故文王因之；而鑑於二者，成其新作，存其所長；尤能揭二代之善制，合兩易之成規；以開有周之政教，為盡美盡善之禮樂制度；此夫子有從周之嘆也！

Therefore, the sequence of hexagrams in The Zhou Yi follows the principle of reciprocity and cyclical repetition, making good and bad relative to each other, and virtue and evil corresponding to one another, thereby demonstrating that the world's course has no irreversible direction, and human hearts never remain still for a moment. It is necessary to use virtue to overcome evil and to renew the old with the new, in order to fulfill the fixed destiny of the cycle, and thus return to the Dao. This is precisely what makes the Yi of King Wen different from others. The Lian Shan and Gui Zang came one after another, each representing a dynasty, with the political and educational systems of the Xia and Shang dynasties differing, and their institutions varying. King Wen inherited these, observed them critically, and composed his new Yi, preserving their strengths. Moreover, he was especially able to reveal the good laws of the Xia and Shang dynasties, blending the established practices of both Yi texts, to establish the political and educational systems of the Zhou dynasty, creating a perfect system of rites and music. This is why the Master expressed his lament, "I follow the Zhou."

故文王之易，為易道之大明；其旨在變，變以復道；乃宜於時之敝，道之衰，教之亡，政之失也；故夫子獨取之，以鑑於周道之微；春秋之亂，非重新易教，不克以復堯舜文王之道，而續伏羲神農黃帝之德也。其意見於雜卦焉，苟有明哲之主，而取用之；以新政教，振仁義；以盡人道，合乎天地之原旨；而因時推變，以孚革故鼎新之義；則文武之治，周初之禮樂制度，固當復見於世。

Therefore, King Wen's Book of Changes represents the great illumination of the Way of Change; its purpose is 'change,' which aims to return to the Dao. It is especially suitable for times of disorder, when the essence of the Dao is declining, moral teachings are lost, and political orders are disordered. Hence, the Master alone chose this Book of Changes, for he saw that the Zhou Way was declining and the Spring and Autumn period was chaotic. Without reviving the teachings of the Book of Changes, it would be impossible to restore the Way of Yao, Shun, and King Wen, and to continue the virtues of Fuxi, Shen Nong, and the Yellow Emperor. This meaning is expressed in the Miscellaneous Hexagrams. If a wise ruler were to adopt and apply it, using it to renew politics and education, to revive benevolence and righteousness, to fulfill human conduct, to align with the fundamental principles of heaven and earth, and to implement changes in accordance with the meaning of renewal and transformation, then the governance of King Wen and King Wu, and the rites and music of the early Zhou dynasty, could indeed be restored in the world.

則夫子老安少懷之志，大同之願，時中之智，皆將見於行事，非復微言之擬，文章之可知而已；觀夫《雜卦傳》末云：「君子道長，小人道消。」云云，蓋已自言其效，或者他日必驗於世；時乎時乎，吾知之矣！運之流行，寧無極乎！請留吾言，以待後人之證之也。

Then the Master's aspiration of "the elderly may be given peace, the young may be cherished," his wish for universal harmony, and his wisdom of maintaining balance at all times will be realized in actual deeds, no longer merely as comparisons in subtle words or things that can only be inferred from writings. Looking at the closing remarks of the "Zagua Transmission" which say "the way of the gentleman prevails, the way of the petty person declines," we can see that the Master himself has already spoken of the manifestation of these truths. Perhaps one day they will surely come to pass in the world. Oh, the times! I am fully aware! How could the flow of destiny have no end? Let me leave these words for future generations to verify.

易道兼體用，統神形者也；先天卦象，可用以釋道之真體；而明神天之德，成誠明之功；後天卦象，可用以釋道之大用；而明人物之生，成位育之德；合而言之，則內聖外王之道，大學之修齊治平，中庸之中和誠明，莫不在易中也！智者見之謂智，仁者見之謂之仁；以道無大小，所見者有大小耳。

The principles and applications of the Way are both embodied in the Book of Changes, encompassing both the spiritual and the physical. The trigrams of the Earlier Heaven can be used to explain the true essence of the Way, thereby elucidating the divine and the virtue of Heaven, achieving the practice of 'sincerity and clarity'. The trigrams of the Later Heaven can be used to explain the practical applications of the Way, thereby elucidating the transformation of human beings and things, achieving the virtue of participating in the workings of Heaven and Earth, and cultivating all things. In summary, the path of inner sagehood and outer kingship, the Confucian ideals of self-cultivation, family management, state governance, and world peace, as well as the doctrine of the Mean concerning harmony and sincerity, are all found within the Book of Changes! The wise see it and call it wisdom, the benevolent see it and call it benevolence; for the Way itself has no small or great, only the perspective of individuals varies.

易之初，有象無文；象則隨人所解，文則泥於一詮；故以象用，而不重文字也；易之後，兼象與文；象存其真，文釋其例；二者並重，則後天物事可見；從文明象，則先天性亦知；故易在後天藏體於用，猶寓神於形也。

At first, the Book of Changes had only trigrams without textual explanations; the trigrams could be interpreted freely, but the text could easily become fixed in a single interpretation. Therefore, at that time, people used the trigrams rather than focusing on the words. Later, both trigrams and text existed together: the trigrams preserved their true nature, while the text explained their principles. Both were given equal importance, allowing later phenomena to be understood. Through the text, one could grasp the trigrams, and thus understand the principles of the Earlier Heaven. Therefore, in the Later Heaven, the essence is hidden within the application, just as the spirit is embodied in the form.

以人言之，其未生也，無神形可分；迨其既生，形著神隱，神在形中，未嘗無也；神主其真，形達其用；知覺運動俱全，而生育以見焉；易之為用亦然，卦爻形也，氣神也；明其卦爻，得知其氣；知氣始終，得知生化；故必從象求之。

Taking a person as an example, when a person has not yet been born, the spirit and form cannot be distinguished; but once born, the form becomes apparent while the spirit becomes hidden, yet the spirit exists within the form. The spirit governs its true essence, and the form expresses its function; with perception and movement fully present, the ability to produce offspring is also manifested. The function of the Book of Changes is similar: the trigrams are the form, and the qi is the spirit. Understanding the trigrams allows one to know the qi; knowing the beginning and end of the qi enables one to understand the process of generation and transformation. Therefore, one must seek from the "image" or "form."

一卦一爻，象也；合數卦爻，亦象也；總六十四卦，三百八十四爻，無非象也；皆有其氣，則皆有其神。故一易有一易之序：序之異者，象之異；象之異者，氣之異；氣之異者，神之異；神之異者，用之異；用之異者，生與化也，消與息也，往與復也，去與來也，變與不變，靜動也，生與無生，成敗也，吉凶悔吝之事也，從逆反側之道也，上下終始之行也，大小分合之情也。

A single trigram and its line represent an image; when several trigrams and their lines are combined, they also represent an image. In total, the sixty-four trigrams and the three hundred and eighty-four lines all represent images. Since each has its qi, they also have their spirits. Therefore, each type of Yi has its own sequence of trigrams: the sequence differs because the images differ; the images differ because the qi differs; the qi differs because the spirits differ; the spirits differ because the applications differ. By application differing, we mean the differences between generation and transformation, decline and cessation, movement and return, going away and coming back, change and unchange, stillness and motion, existence and non-existence, success and failure, and matters of good fortune, regret, and hardship. It also refers to the differences between following and opposing, right and left, the beginning and end of above and below, and the differences of size, separation, and unity.

而皆歸於陰陽，辨於五行；存於二氣，通於微顯；孚於人天，以究其性情；探其數命，而致其德；立其道，此易之大用。有各易，而無不通；用各象，而無不達者也；智者察同，昏者察異；異其初，同其終也；何哉？為其不越於道耳。道之用或有異，其本大同；易雖多種，原始反終，則歸於一；一者道也，故曰：易以道陰陽，言由陰陽而歸於道；二者為一，此則易之真用也。

All these things are reduced to yin and yang, and distinguished by the Five Phases; they exist within the two energies of yin and yang, and run through both subtle and manifest aspects; they harmonize between human beings and heaven, used to investigate the nature of all things, explore their numbers and destinies, thus cultivating virtue and establishing the Way. This is the great use of the Book of Changes. Although there are many schools of the Book of Changes, none are completely separate; although the images used may differ, none are entirely unconnected. The wise see their commonality, while the dull see their differences; in fact, although they may initially seem different, they ultimately converge. Why is that? Because none of them go beyond the scope of the Dao. The application of the Dao may vary, but its fundamental nature is largely consistent. Although the Book of Changes has many forms, tracing its origin and returning to its end, it still comes back to one; this one is the Dao. Therefore, the "Zhuangzi · Tianxia" says, "The Book of Changes uses the Dao of yin and yang," meaning that it leads from yin and yang back to the Dao; uniting yin and yang into one is the true use of the Book of Changes.

夫子以周易為本，而於各易略採其一二，列之於傳，明易之為用無二也；文王之易，所異於眾者，為其取象；極變化之例，明循環之道；言無道無往不復，而人事應之；人事無處不交，而天道順之；如人物生化，此往復也；氣候遞嬗，此交錯也；有陽必有陰，有陰必有陽，此交錯也；陰窮則陽生，陽盡則陰息，此往復也。

The Master took The Zhou Changes as the foundation, and included a few points from various schools of the Yi into the "Transmission," to show that the function of the Yi is the same. The unique aspect of King Wen's Yi lies in its use of images: it pushes the principles of change to their extreme and clearly explains the cycle. It says that the heavenly way has no going forward without returning, and human affairs correspond accordingly; human affairs have no place without interaction, and the heavenly way follows accordingly. For instance, the continuous generation and transformation of things and objects is called "reciprocal movement"; the alternating changes of climate are called "interweaving." Where there is yang there must be yin, and where there is yin there must be yang, this is interweaving; when yin reaches its limit, yang arises, and when yang reaches its limit, yin grows, this is reciprocal movement.

日往則月來，寒往則暑來；一交一錯，而成紀焉；冬盡則春回，夜盡則朝回；一往一復，而成度焉；不得有失，有數可數；不得有差，有氣可候；天道如是，萬物亦然；故今之是者，昨之非；往之得者，來之失；此成則彼敗，早生則晚殺。

As the sun sets, the moon rises; after the cold comes the heat, alternating in order to establish a pattern; when winter ends, spring returns; when night ends, day comes again, alternating to form a measure. There will be no mistakes, because there is a number that can be calculated; there will be no errors, because there is a qi that can be observed. The way of heaven is like this, and all things are the same. Therefore, what is considered correct today was thought incorrect yesterday; what was gained before will be lost later; where one side thrives, the other declines; what grows in the morning withers in the evening.

有見於前，必應於後；有開於舊，必復於新；日久則移，風久則改；滿者則傾，中者則側；昔之壯者今則老，今之微者後則盛；盛衰倚伏，成敗推移；吉凶無定時，悔吝無定位；生死相續，榮枯相聯；莫不自成循環往復之象，自合交錯來去之數；象數如是，卦乃應之；故文王之易，純取此義，而異乎各易也。

What is revealed at the beginning will surely be fulfilled later; what is opened in the past will surely be continued in the present. When time is long, there will be change; when customs are long established, they will change. When fullness is reached, there will be collapse; when centered, there will be deviation. What was once strong now becomes old; what is now weak will become strong in the future. Prosperity and decline depend on each other; success and failure shift from one to the other; good fortune and misfortune have no fixed time; regret and hardship have no fixed position; life and death follow each other continuously; glory and withering are connected. Nothing is not naturally formed in a cycle, naturally conforming to the numbers of mutual interaction and movement. Since the images and numbers are like this, the hexagrams will correspond accordingly. Therefore, King Wen's Book of Changes purely takes this meaning, hence differing from the interpretations of other schools.

夫文王作易，有為而作之也；當商紂無道，湯德既衰；暴政虐民，汙吏乾位；時非俗敝，上下交困；天怒民怨，神鬼同愁；文王身在憂囚，處地艱險；救民之志未已，切膚之痛且深；鑑諸天道之推遷，欲期人事之改革；故明志於易，易者變易也，言當變易之際，必有以處變易之道，而成變易之功。時之變易，即天之變易；天之變易，則人事不得不變易之，以順承天。

King Wen composed the Book of Changes with a specific purpose in mind. At that time, King Zhou of Shang was tyrannical and lawless, and the virtue of King Tang of Shang had already declined. Oppressive government harmed the people, and corrupt officials occupied high positions. The world was unjust, morals were deteriorating, and everyone was in distress. Heaven was angry and people were resentful, even the spirits and ghosts felt sorrow. King Wen was imprisoned in hardship and faced dangerous circumstances; his determination to save the people never ceased, and his deep suffering was especially intense. He observed the changes in the heavenly way, hoping for reform in human affairs, so he expressed his aspirations in the Book of Changes. "Yi" means change; it refers to the necessity of having methods to deal with change in order to achieve the effectiveness of change. The change of circumstances is the change of heaven; when heaven changes, human affairs must also change accordingly, to conform to the will of heaven.

故其取義重於鼎革二卦，而明變足以適道；撥亂反正，足以順天應民；故明易之道，以寓其教，而在以天時示人事之則；如秋冬肅殺，萬物皆殘；若不易以春和，則生機且息；如子夜暗澹，萬物同昧，若不易以朝陽，則大道莫明；此皆天之必變易者，而人事亦當應之；故卦象重在明變，變則通，通則道，而往復循環者，變之所由來；交錯消息者，變之所自至。

Therefore, King Wen particularly emphasized the hexagrams of "Ding" (Cooking Vessel) and "Ge" (Revolution), to illustrate that change is sufficient to conform to the Way. To rectify chaos and restore order, it is enough to align with the will of Heaven and respond to the people's will. Therefore, he explained the principles of the Book of Changes, embedding moral education within it. The key point lies in using heavenly timing to demonstrate the principles of human affairs: for example, in autumn and winter, when all things wither and decay, if they are not transformed into the warmth of spring, vitality would be cut off; or at midnight, when all things are dark and obscure, if they are not transformed into the brightness of morning, the Great Way would remain hidden. These are all natural changes that Heaven necessarily undergoes, and human affairs should correspond accordingly. Therefore, the hexagrams focus on elucidating "change": only through change can things become unblocked, and only when unblocked can they conform to the Way. The cyclical alternation is the source of change, while the intermingling and waxing and waning are the manifestations of change.

故綜論卦象之旨，不過明易之為易，而推衍其變；以教天下後世，知道在變；則變為道，不復以天不變，道不變為言；蓋變者、變而復於不變，非永變不亡也；故變亦道也。試當桀紂之時，果無湯武之變？天下尚有人類乎？故其變，天也；天之宜變，則變為天，豈悖天哉？故易道至文王為一大變，自商湯至紂，為數之窮，窮則變耳；而夫子之時，周德既衰，諸候僣竊；人民塗炭，政教乖違；以易言之，毋亦應變之世乎！故夫子取其義也。

Therefore, the overall purpose of discussing the hexagram images is merely to clarify why the Book of Changes is called the Book of Changes, and to explore its transformations, using them to instruct future generations. One should understand that "the Way" lies in change, so change itself is the Way, and one should not cling to the notion that "heaven remains unchanged, and so does the Way." For change is change that returns to unchangeable order; it is not an endless change without end. Thus, change itself is part of the Way. Consider the time of King Jie of Xia and King Zhou of Shang: if there had not been the reforms of King Tang of Shang and King Wu of Zhou, would there still be human beings in the world? Clearly, that reform was in accordance with heaven's will. Since heaven itself required change, that change was in harmony with heaven, how could it be considered a violation of heaven? Therefore, the Way of the Book of Changes underwent a great transformation in the hands of King Wen. From King Tang of Shang to King Zhou of Shang, the era had reached its end, and when an era reaches its end, change is inevitable. And the time when Confucius lived, the virtue of the Zhou dynasty had already declined, the feudal lords acted beyond their proper roles, and the people were suffering in misery, with political and moral order disrupted. In terms of the Book of Changes, was this not also a time that required change? Hence, Confucius adopted the meaning and intent of King Wen.

夫周易之用，雖重明變，亦非有背於伏羲之旨；伏羲之易，重常道，以道為本，而人事隨之；其用主常。文王之易，以用為本，其羲主變；然二者一也，一由上而下，一由下而上；文王以人事明天道，其終亦歸於天道；故變而不失其常，其卦序始乾坤，終坎離；始咸恆，終既未濟；仍以伏羲之序為本。

The Zhou Changes focus on explaining change, yet they do not contradict the purpose of Fuxi's approach. Fuxi's Yi emphasizes the constant way, taking the Dao as its foundation, with human affairs following accordingly; its use is based on "constancy." Wen Wang's Yi takes utility as its foundation, with its meaning centered on "change." However, the two are actually one, differing only in direction: one proceeds from above to below, the other from below to above. Wen Wang used human affairs to explain the heavenly Dao, ultimately returning to the heavenly Dao, so although it involves change, it does not lose its constancy. Its sequence of hexagrams begins with Qian and Kun, and ends with Kan and Li; the lower part of the sequence begins with Xian and Heng, and ends with Ji Ji and Wei Ji: it still follows the original sequence of Fuxi's hexagrams.

乾坤定位，故首上經；坎離代用，故終上經；乾坤交錯，故咸恆首下經；坎離往來，故既未濟終下經；合而言之，仍以乾坤為經，坎離為緯，與伏羲卦象同；分而言之，則多一交錯之用，即所以見其變也。

Heaven and Earth establish the positions of the universe, so they are placed first in the Upper Classic; Kan and Li take the place of Heaven and Earth and come into use, so they are placed last in the Upper Classic; Heaven and Earth intermingle to form Xian and Heng, so Xian and Heng are placed first in the Lower Classic; Kan and Li move back and forth to form Ji Ji and Wei Ji, so Ji Ji and Wei Ji are placed last in the Lower Classic. When viewed as a whole, it still takes Heaven and Earth as the main axis and Kan and Li as the cross axis, the same as Fuxi's hexagrams; when viewed separately, there is an additional layer of intermingling, which precisely demonstrates its 'change'.

既未濟坎離二卦交錯，以終全易；而取未濟，不用既濟者；明人事雖合終分，雖交終離；以復於先天之不生不滅，猶本天道立言，為天道由無入有；雖人事紛紜，時時交錯，及其至也，終返其本來，有仍歸無；如首之乾坤定位，上下不侔；而終未濟之水火不相射，即伏羲八卦位次也；水自下，火自上；水火相離，天地大定；此由有反無之道，而不生不滅之觀；至此生機已息，天地終老；萬物入定，世界將傾。

The hexagrams Ji Ji and Wei Ji are the intermingling of the trigrams Kan (Water) and Li (Fire), used to conclude the entire Book of Changes. The final position takes Wei Ji rather than Ji Ji to indicate that although human affairs may seem to converge at the end, they still require separation, and although things may appear to intersect at the end, they still need to part, returning to the state of the Earlier Heaven, which is without origin or cessation. This still follows the principle of the heavenly way: the heavenly way proceeds from non-existence to existence; although human affairs are complex and constantly intersect, when they reach their extreme, they ultimately return to their original state, with existence returning to non-existence. Just as the beginning sees Qian (Heaven) and Kun (Earth) establishing their positions, with upper and lower not being equal, the end sees Wei Ji, where water and fire do not interact, which is exactly the arrangement of the eight trigrams of Fuxi. Water naturally flows downward, fire naturally rises upward; water and fire are separate from each other, and thus heaven and earth become fully established. This is the path returning from existence to non-existence, and it is the contemplation of non-origin and non-cessation; at this point, vitality has ceased, heaven and earth eventually age, all things enter into stillness, and the world is about to collapse.

故全易之數，至此乃終；而出於乾坤者，仍歸之乾坤；成於陰陽者，仍分於陰陽；坎離不交，而一切同歸於盡；此未濟一卦，為天地大結束；而由生化言之，為生化之氣絕；由修持言之，則因緣之業淨；瞭然無礙，闊然無罣，空然無存；是則無聲無臭之時，而將同於上天之載；故曰大終，以人事無可再續也。

Therefore, all the numbers of the Book of Changes come to an end here. Those originating from Qian and Kun return to Qian and Kun; those formed by yin and yang are again separated back to yin and yang; Kan and Li no longer intersect, and everything returns to complete extinction. This hexagram, Without Completion, represents the great end of heaven and earth. In terms of generation and transformation, it signifies the interruption of the vital energy of generation and transformation; in terms of cultivation, it signifies the purification of karmic conditions: clear and unobstructed, vast and free from attachments, empty and without anything to retain. This is precisely the state described in the Zhongyong as "without sound and without smell," approaching the state of what heaven carries. Hence, it is called "Great End," because human affairs can no longer be continued.

夫人事既盡，易義自終；既無生化可言，更何交錯之跡；故曰：未濟。明其濟則為生，未生將何用哉？文王之易，主於用者也；未濟用窮，故全易至此盡矣；果有續者，則再來天地，仍循環於初始之乾坤，則又一太極矣！

Human affairs have already been fully exhausted, so the principles of the Book of Changes naturally come to an end; there is no more generation and transformation to speak of, and where would the traces of interaction be? Therefore it is called "Not Yet Completed." To understand "completion" means to bring about life, but if life has not yet come into being, what can be used? King Wen's Book of Changes focuses on "use," and "Not Yet Completed" signifies that the use has reached its limit. Therefore the entire Book of Changes ends here. If there were a continuation, it would be another cycle of heaven and earth, returning once again to the original Heaven and Earth, thus forming another Taiji.

此義與先天卦象，自乾至坤，各不相離，正同，如本宮卦，大終於歸妹，其羲亦然；以歸妹之象，地氣已盡；天地分離，與未濟之乾氣盡；水火分離，皆孤陰陽之象也；故傳曰：「未濟男之窮也，歸妹女之終也。」言此二卦，為二氣之大終；終則生化息，而易道盡；易以道陰陽，陰陽既盡，更何易道之存？故易之終，必終於二卦也。

This principle corresponds exactly with the earlier heaven trigrams from Qian to Kun, where each trigram is interconnected. For example, the native trigram of each of the eight palaces ends with Guimiao, and the meaning is similar: in the trigram Guimiao, the earth energy has reached its limit, causing the separation of heaven and earth; this is similar to the trigram Weijì, where the heavenly energy has reached its limit, causing the separation of water and fire. Both are examples of isolated yin and yang. Therefore, the "Zagua Zhuan" says, "Weijì signifies the exhaustion of the male; Guimiao signifies the end of the female." This means these two trigrams represent the ultimate conclusion of yin and yang energies. When the process of generation and transformation stops, the way of the Book of Changes also reaches its end. Since the Book of Changes is about yin and yang, once yin and yang have reached their limits, what remains of the way of the Book of Changes? Therefore, the end of the Book of Changes must necessarily conclude with these two trigrams.