The Hexagram of Completion

離下坎上。既濟：亨小，利貞，初吉終亂。彖曰：既濟亨，小者亨也。利貞，剛柔正而位當也。初吉，柔得中也；終止則亂，其道窮也。象曰：水在火上，既濟，君子以思患而豫防之。初九：曳其輪，濡其尾，無咎。象曰：曳其輪，義無咎也。曳輪，不速進也；濡尾，後其難也；險已濟，故雖艱無咎。

The lower trigram of the Hexagram of Completion is Li (Fire), and the upper trigram is Kan (Water). The Hexagram Statement says: Completion, smooth in small matters, favorable to uprightness; beginning is auspicious, but ending brings disorder. The Commentary on the Judgment says: The reason for the smoothness of Completion is that small matters are smooth. "Favorable to uprightness" is because the strong and the weak lines are in proper positions. "Beginning is auspicious" is because the line six in the second position is in the central position. "Ending brings disorder" is because its way has reached its limit. The Image Commentary says: Water above fire, properly used for cooking, this is the Hexagram of Completion. The gentleman takes this as a model, foreseeing difficulties and preparing in advance. The line statement of the first nine says: Holding back the chariot wheel, wetting the tail, no error. The Small Image Commentary says: Holding back the chariot wheel, in terms of principle, there is no error. Sima Guang explains: "Holding back the chariot wheel" means not rushing forward; "wetting the tail" means placing difficulties behind. The danger has already been crossed, so although there is hardship, there is no error.

六二：婦喪其茀，勿逐，七日得。象曰：七日得，以中道也。九三：高宗伐鬼方，三年克之，小人勿用。象曰：三年克之，憊也。六四：繻有衣袽，終日戒。象曰：終日戒，有所疑也。九五：東鄰殺牛，不如西鄰之禴祭，實受其福。象曰：東鄰殺牛，不如西鄰之時也；實受其福，吉大來也。上六：濡其首，厲。象曰：濡其首厲，何可久也。

The line statement for the second line says: A woman lost the curtain on her carriage, but there is no need to search for it, for it will be recovered after seven days. The small image commentary says: It will be recovered after seven days because the second line remains in the center. The line statement for the third line says: King Wu Ding of the Shang dynasty waged war against the Ghost People, and it took three years to conquer them, so one should not employ petty men. The small image commentary says: It took three years to conquer because it was extremely exhausting. The line statement for the fourth line says: A beautiful silk robe will eventually become a worn-out rag, so one must remain vigilant all day. The small image commentary says: Remaining vigilant all day is because there is some doubt in the heart. The line statement for the fifth line says: The eastern neighbor sacrifices oxen in a grand ceremony, but it is not as good as the western neighbor's simple spring sacrifice, for the latter truly receives the blessings of the divine. The small image commentary says: The eastern neighbor sacrificing oxen is not as good as the western neighbor's timely sacrifice; truly receiving the blessings of the divine is when great good fortune comes. The line statement for the top line says: The head is wet, there is danger and hardship. The small image commentary says: The head is wet and there is danger and hardship, how can such a situation last long?

坎下離上。未濟：亨，小狐汔濟，濡其尾，無攸利。彖曰：未濟亨，柔得中也。小狐汔濟，未出中也；濡其尾，無攸利，不續終也。雖不當位，剛柔應也。狐者，審於濟水者也。汔，幾也；幾濟而陷，猶未濟也。濡其尾無攸利，未出險中而力盡不繼也。

The lower trigram of the Hexagram of Not Yet Completed is Kan (Water), and the upper trigram is Li (Fire). The Hexagram Statement says: Not Yet Completed, it is smooth; a small fox is about to cross the river but gets its tail wet, which brings no benefit. The Commentary on the Judgment says: The reason why Not Yet Completed is smooth is because the yao in the fifth position, which is yin and in the central position, is properly placed. "A small fox is about to cross the river" means it has not yet escaped from danger; "its tail is wet, which brings no benefit" means it cannot complete the task. Although each yao is in an improper position, the yin and yang yao correspond with each other. Sima Guang explains: the fox is the most cautious animal when crossing water. "Qi" means approaching; it seems to have crossed but gets trapped, so it is still considered as not having crossed. "Its tail is wet, which brings no benefit" means it has not yet escaped from danger but has already exhausted its strength and lacks continued effort.

象曰：火在水上，未濟，君子以慎辨物居方。既濟、未濟反覆相承也。險難未濟，功業未成，故君子以矜慎之心辨物之宜，處之以道；如是則險無不濟，功無不成。無所復為，則又思未萌之患而豫防之，是以君子能康乂民物而永保安榮也。

The Great Image Commentary says: Fire on water, the two do not work together, this is the hexagram of Not Yet Achieved; the gentleman takes this as a model, carefully distinguishing things and placing them in their proper places. Sima Guang explains that the hexagrams of Already Achieved and Not Yet Achieved are successive and reciprocal. When the peril has not yet been crossed and the achievements have not yet been completed, the gentleman uses a cautious and careful mind to discern the appropriate places for things, and arranges them according to the right path; thus, no peril is too great to overcome, and no achievement is too difficult to attain. When there is nothing more to be done, one must again foresee potential future calamities and take preventive measures in advance. Therefore, the gentleman is able to govern the people and all things, maintaining long-term peace and honor.

初六：濡其尾，吝。象曰：濡其尾，亦不知極也。九二：曳其輪，貞吉。象曰：九二貞吉，中以行正也。六三：未濟，征凶，利渉大川。象曰：未濟征凶，位不當也。九四：貞吉悔亡，震用伐鬼方，三年有賞于大國。四者，卦體變革之際，故否、睽、未濟之象皆云志行也。

The line statement for the first line says: The tail is wet, there is regret. The Small Image Commentary says: The tail is wet because it does not know its limit. The line statement for the second line says: Hold back the chariot wheel so that it does not move too quickly, upholding the correct path brings good fortune. The Small Image Commentary says: The second line brings good fortune by upholding the correct path because it practices the correct path in the middle. The line statement for the third line says: The matter has not yet succeeded, to act hastily would be dangerous, it is appropriate to cross a great river. The Small Image Commentary says: To act hastily before the matter is completed is dangerous because the position occupied is inappropriate. The line statement for the fourth line says: Upholding the correct path brings good fortune and regret disappears; exerting strength to attack the ghostly people, after three years, receives a reward from a great state. Sima Guang explains: The fourth line is the boundary where the structure of the hexagram changes, so the Small Image Commentaries of the fourth lines in the hexagrams of Guai, Wei Ji, and Wei Ji all say "the will is carried out."

六五：貞吉無悔，君子之光，有孚，吉。象曰：君子之光，其暉吉也。五雖未濟，以柔居中，又有文明之徳，能任賢以濟難，故曰君子之光。光輝著明，為物所信，則吉從之矣。上首也，下尾也；初不知極，上不知節，皆入於險，其揆一也。上九：有孚于飲酒，無咎，濡其首，有孚失是。象曰：飲酒濡首，亦不知節也。

The line statement of the fifth line says: To maintain the correct position brings good fortune without regret; this is the radiance of the gentleman, with sincerity in heart, bringing good fortune. The small image commentary says: The radiance of the gentleman brings good fortune because its light shines outward. Sima Guang explains: Although the fifth line is in the stage of things not yet completed, it resides in the central position with flexibility and virtue, and is capable of employing the virtuous to resolve difficulties, hence it is said "the radiance of the gentleman." The radiance is bright and clear, winning the trust of all things, thus good fortune naturally follows. The top line is the beginning, and the first line is the end; the first line does not know limits, and the top line does not know restraint, both ending in peril, the principle is the same. The line statement of the top line says: To drink with sincerity and enjoy oneself does not lead to error; but if one becomes so immersed that one's head is wet, even with sincerity, one loses the correct path. The small image commentary says: Drinking until one's head is wet is also due to lack of restraint.

繫辭上。繫辭雜記前聖及孔子解易之語，上下以簡帙重大，故分之。天尊地卑，乾坤定矣：言天地設位，則易已著。卑髙以陳，貴賤位矣。動靜有常，剛柔□矣：天地萬物皆有卑高，故易之六位亦有貴賤。

This is the Upper Classic of the Xici (Great Treatise). Sima Guang explains that the Xici chapter records the words of previous sages and Confucius explaining the Zhou Yi. Because the bamboo slips were too numerous and heavy, they were divided into upper and lower parts. "Heaven is above and exalted, Earth is below and humble, thus the positions of Qian and Kun are established": this means that once the positions of Heaven and Earth are set, the principles of the Yi (Book of Changes) become evident. "Humble and exalted are arranged in order, thus the positions of honor and humility are established; movement and stillness each have their regularity, thus the distinctions of strength and flexibility are clear (the original text here is missing one character)": since all things in heaven and earth have distinctions of high and low, the six lines of the Yi hexagrams also have distinctions of honor and humility.

方以類聚，物以群分，吉凶生矣：方，道也。道同則類聚，志異則群分；同則相愛，異則相惡；愛惡相攻而吉凶生，易皆則之。在天成象，在地成形，變化見矣：象有隠見，形有死生，猝變漸化，互相推移，易皆效之。

"Classification by category brings about gathering, and grouping by kind leads to division, thus producing fortune and misfortune." The term "fang" refers to the Way. When the Way is the same, similar things gather together; when the mind differs, they form separate groups. Similarity leads to mutual affection, difference leads to mutual dislike; affection and dislike clash, thus producing fortune and misfortune. The Zhou Changes take their model from this. "In the heavens, the forms of sun, moon, and stars are formed; on the earth, the forms of mountains, rivers, moving creatures, and plants are formed; thus change becomes evident." Celestial phenomena have hidden and revealed aspects; terrestrial forms have life and death. Some change suddenly, others transform gradually; they shift and replace each other, and the Zhou Changes follow these phenomena.

是故剛柔相摩：日月寒暑，一往一來。八卦相蕩：出震成艮，迭相推蕩。鼓之以雷霆，潤之以風雨，日月運行，一寒一暑：日舒月疾，一南一北，而寒暑生焉，此皆變化之道。乾道成男，坤道成女：乾坤變化，萬物自成。乾知大始，坤作成物：知猶主也，萬物始生者乾之所主，終成者坤之所為也。

"Therefore, the hard and the soft interact and refine each other," just like the sun and the moon, cold and heat, one going away and the other coming. "The eight trigrams interact and stimulate each other": starting from the Zhen trigram and ending with the Gen trigram, they successively push and stimulate each other. "Using thunder and lightning to move them, using wind and rain to nourish them; the sun and moon move, one cold and one hot": the sun moves slowly, the moon moves quickly, one leans south, the other leans north, thus cold and heat are produced, all of which are the principles of change. "The Qian trigram forms the male, the Kun trigram forms the female": when Qian and Kun change, all things naturally come into being. "Qian governs the creation of all things, Kun is responsible for completing all things": "knowing" means governing; the beginning of the generation of all things is governed by Qian; the final completion is accomplished by Kun.

乾以易知，坤以簡能：一以貫之，故曰易簡；乾言易，坤言簡。易則易知，簡則易從：情無幽險故易知，事不煩苛故易從。易知則有親，易從則有功：難知則人不親，難從則功不成。有親則可久，有功則可大：輔之者眾故可久，日滋月益故可大。可久則賢人之徳，可大則賢人之業：凡勝人者皆謂之賢。

"Heavenly Stem Qian governs creation through simplicity and ease, and Earthly Branch Kun achieves all things through simplicity and clarity." They are both explained by the same principle, hence called "Yi Jian" (simplicity and ease). On the side of Qian, it is "Yi" (ease), and on the side of Kun, it is "Jian" (simplicity). "Ease is easily understood, simplicity is easily followed": the mind and actions have no hidden or treacherous intentions, hence easily understood; affairs are not complicated or overly detailed, hence easily followed. "Ease in understanding brings people to attach themselves, ease in following leads to establishing achievements": if difficult to understand, people do not attach themselves; if difficult to follow, achievements cannot be made. "Being attached to brings longevity, achieving brings expansion": with many helpers, longevity is achieved; through continuous accumulation and growth, expansion is achieved. "Longevity is the virtue of the virtuous, expansion is the career of the virtuous": anyone who surpasses the ordinary is called "virtuous."

勿簡而天下之理得矣：天下之理不能出乾坤之外。天下之理得而成位乎其中矣：此言聖人上觀於天，下觀於地，中觀萬物而作易也，易道始於天地，終於人事。右第一章。

"The way of simplicity and ease is established, and the principles of the world are all understood": the principles of the world do not go beyond the two trigrams Qian (Heaven) and Kun (Earth). "When the principles of the world are understood, a person establishes his position within heaven and earth": this means that the sages observed the heavenly phenomena above, the earthly forms below, and the myriad things in the center, thus composing the Zhou Changes (I Ching). The principles of the Changes (I Ching) begin with heaven and earth and ultimately conclude with human affairs. This is the first chapter.

聖人設卦觀象：聖人窮理盡性以至於命，欲立有於無，統眾於寡，故設卦以觀萬物之象。繫辭焉而明吉凶：八卦成列，以盡天下之象，因而重之，變化備矣，猶未得與眾共之，故聖人復繫以爻彖之辭，明言吉凶以告。剛柔相推而生變化：爻彖所言者，有形之常道，猶未足以窮無形之神理，故復以剛柔相推，極變化之數，而占事知來。

"Saints established hexagrams and observed their images": Saints thoroughly investigated principles and fully understood nature, thus comprehending heavenly mandate. They wished to create "being" from "non-being," using few to encompass many, so they established hexagrams to observe the forms of all things. "Attaching statements to explain auspiciousness and misfortune": The eight trigrams arranged in lines have already exhausted all forms of things in the world; further combining them in pairs, their transformations become complete. Yet this was still not enough to share with the people, so the saints attached line statements and zhuang statements, clearly explaining auspiciousness and misfortune to inform people. "Hard lines and soft lines shift and interact to produce change": The statements of lines and zhuang explain tangible principles, yet they are insufficient to exhaust the subtle and mysterious principles. Therefore, they use the shifting interaction of hard and soft lines, fully exploring the numerical principles of change, to inquire about matters and foresee the future.

是故吉凶者，失得之象也；悔吝者，憂虞之象也：得之為吉，失之為凶；失而知悔，凶中之吉也；得而可恥，吉中之凶也；事雖小而皆可憂虞。變化者，進退之象也：天地萬物皆有消息盈虛。剛柔者，晝夜之象也：一往一來，迭為賓主。六爻之動，三極之道也：天地人至極之道。

Therefore, good fortune and misfortune symbolize loss and gain; regret and hesitation symbolize worry and doubt. To gain is good fortune, to lose is misfortune; losing but knowing regret is good fortune within misfortune; gaining but causing shame is misfortune within good fortune; even small matters are worth worrying and being cautious about. "Change symbolizes advancement and retreat": all things in heaven and earth have phases of decline, growth, fullness, and emptiness. "Strength and softness symbolize day and night": one goes away and the other comes, taking turns to be dominant. "The movement of the six lines embodies the principles of the three fundamental aspects": that is, the fundamental principles of heaven, earth, and humanity.

是故君子所居而安者，易之序也；所樂而玩者，爻之辭也。是故君子居則觀其象而玩其辭，動則觀其變而玩其占：序，上下終始之序；動，謂有所興為。是以自天佑之，吉無不利。右第二章。

Therefore, the gentleman bases his self-cultivation and life purpose on the order of the Book of Changes, and delights in the words of each line. Thus, when the gentleman is at rest, he observes the images of the hexagrams and delights in their words; when he acts, he observes their changes and delights in their divinatory judgments. The term "order" refers to the sequence of beginning and end; the term "movement" refers to taking action. "Therefore, from the heavens comes protection, which is auspicious and without adverse consequences." This is the second chapter.

彖者，言乎象者也：物之本體。爻者，言乎變者也：變化云為。吉凶者，言乎其失得也：得道則吉，失道則凶。悔吝者，言乎其小疵也：事之可憂虞者也。無咎者，善補過也。

"The Tuangeng is about the image of a hexagram": it refers to the essence of things. "The line statements are about change": they discuss transformation and action. "Good fortune and misfortune are about gain and loss": following the Dao brings good fortune, while departing from the Dao leads to misfortune. "Regret and meanness are about minor faults": they refer to matters worth worrying about and being cautious of. "No blame is about being good at making amends": it means being skilled in correcting mistakes.

是故列貴賤者存乎位，齊小大者存乎卦：陰幽禍惡為小，陽明福善為大。辯吉凶者存乎辭，憂悔吝者存乎介震，無咎者存乎悔。是故卦有小大，辭有險易，辭也者，各指其所之。右第三章。示人吉凶大趣，使人引而伸之。

"Therefore, the arrangement of importance lies in the yao positions, and the distinction between small and great lies in the structure of the hexagram." Darkness, calamity, and evil belong to "small," while brightness, blessings, and goodness belong to "great." "The discernment of good and bad fortune lies in the hexagram and yao statements, while worry and regret arise from subtle boundaries and fear. The ability to avoid error lies in repentance. Therefore, hexagrams have both small and great aspects, and statements have both dangerous and easy aspects; the so-called statements each indicate the direction they are heading toward." This is the third chapter. Sima Guang explains that this chapter is intended to guide people in understanding the general tendencies of good and bad fortune, allowing them to deduce further from there.

易與天地準，故能彌綸天地之道：與天地準，與天地相似。孔穎達曰：彌綸，彌縫補合，經綸牽引也。仰以觀於天文，俯以察於地理，是故知幽明之故：天文地理皆不能離陰陽五行，以其所見揆所不見，則知幽明之理一也。原始反終，故知死生之說：物有始必有終，人有生必有死。

"The Book of Changes is equal to the heavens and earth, so it can comprehensively unify the way of the heavens and earth": what is meant by "being in accordance with the heavens and earth" is that it is similar to the heavens and earth. Kong Yingda said: "Mi" means to mend and join together, and "lun" means to plan and manage. "Looking up to observe the patterns of the heavens and looking down to examine the patterns of the earth, thus understanding the hidden and the manifest": astronomy and geography both depend on yin and yang and the Five Phases; using the visible to infer the invisible, one understands that the principles of the hidden and the manifest are actually the same. "Investigating the beginning and seeking the end in reverse, thus understanding the principles of life and death": all things have a beginning and thus necessarily have an end; humans have birth and thus necessarily have death.

精氣為物，游魂為變，是故知鬼神之情狀。與天地相似，故不違。知周乎萬物而道濟天下，故不過：知周萬物，無所不知；道濟天下，無所不利；如此則何有過差。旁行而不流：旁行謂觸類而長之，不流謂既有典常。樂天知命，故不憂：知易則吉凶有命，惟天所授而樂之，夫復何憂。

"Essence and energy coalesce to form objects, while wandering spirits disperse and cause changes, thus understanding the nature of ghosts and spirits. The Book of Changes is similar to heaven and earth, so it does not contradict them. Its wisdom pervades all things, and its way benefits the world, thus there is no error." Wisdom pervading all things means nothing is unknown; its way benefiting the world means nothing is without advantage; thus, how could there be any error or mistake? "Extending widely without overflowing": "Extending widely" means understanding by analogy and deducing further; "not overflowing" is because it follows a constant principle. "Rejoicing in heaven's will and accepting one's destiny, thus having no worries": Understanding the principles of the Book of Changes, one knows that good and bad fortune are determined by heaven's will, and since it is bestowed by heaven, one rejoices in accepting it, so what is there to worry about?

安土敦乎仁，故能愛：介甫曰，安土謂不擇地而安之。光謂：仁者求諸已，不求諸人；安土敦仁，則內重而外物輕，乃能自愛。範圍天地之化而不過：範謂則效，圍謂周徧。曲成萬物而不遺，通乎晝夜之道而知：知陰陽通變，反覆無窮，則無所不知。故神無方而易無體：韓曰，神則陰陽不測，易則惟變所適。光謂：神者言其化，易者言其書。右第四章。

"Being content with one's current situation and being sincere in benevolence allows one to love others," said Wang Anshi, explaining that "being content with one's place" means not being selective about one's environment and being at ease wherever one is. Sima Guang said: the benevolent person looks inward rather than demanding from others; being content with one's current situation and sincere in benevolence makes the inner self substantial and external things light, thus enabling one to truly cherish oneself. "Modeling the nurturing that surrounds heaven and earth without error": "Fan" means to take as a model and emulate, and "wei" means to encompass thoroughly. "Winding and completing all things without omission, understanding the alternation of day and night without ignorance": understanding the principles of yin and yang transformation and the endless cycles of change, there is nothing one does not know. "Therefore, the mysterious is without fixed place, and the Book of Changes has no fixed form": Han Kangbo said, "Shen" refers to the unpredictable changes of yin and yang, and "Yi" refers to adaptation through change alone. Sima Guang said: "Shen" refers to its nurturing aspect, and "Yi" refers to the book itself. This concludes the fourth chapter.

一陰一陽之謂道：反覆變化，無所不通。繼之者善也：易指吉凶以示人，人當從善以去惡，就吉而避凶，乃能繼成其道。成之者性也：人之性分不同，因易而各有成功。仁者見之謂之仁，知者見之謂之知：仁者守其常分，知者應變不窮，易道兼而有之。

"When yin and yang alternate in operation, it is called the Dao": it constantly changes and pervades all things. "To follow it is to be good": The Zhou Changes indicate auspicious and inauspicious signs to people, and people should follow goodness and eliminate evil, pursue auspiciousness and avoid misfortune, thus following and achieving that Dao. "To complete it is to be nature": human nature varies, and through the Book of Changes, each person achieves their own. "The benevolent person names it benevolence, the wise person names it wisdom": the benevolent person maintains their constant nature, the wise person responds to change endlessly, and the Book of Changes encompasses both aspects.

百姓日用而不知，故君子之道鮮矣：物之於易，猶魚之於水，朝夕起居不離於其中而莫之能知，故夫知易之君子為少。韓曰：君子體道以為用也，仁知則滯於所見，百姓則日用而不知，體斯道者不亦鮮矣乎。顯諸仁，曲成萬物，藏諸用：韓曰，日用不知。鼓萬物而不與聖人同憂：振動之而無為。

"The common people use it every day but do not realize it, so those who truly understand the Way of the gentleman are few." All things relate to the Book of Changes just as fish relate to water; they live in water all day and night without ever knowing it. Therefore, those who truly understand the Book of Changes are indeed rare. Han Kangbo said: The gentleman comprehends the Great Dao and applies it; the benevolent and the wise each fixate on their own partial views, while the common people use it daily without awareness. Thus, how few are those who truly grasp this Dao? "It manifests in benevolence, subtly completes all things, and hides its function": Han Kangbo said, this is what is meant by "the common people use it daily without knowing it." "It stimulates all things without sharing the anxieties of the sage": it revives and stimulates all things, yet does not deliberately act.

盛徳大業至矣哉！富有之謂大業：廣大悉備。日新之謂盛徳：其益無方。生生之謂易：形性相續，變化無窮。成象之謂乾：見乃謂象，乾知大始。效法之謂坤：制而用之謂之法，坤作成物。極數知來之謂占：錯綜其數，遂知來物。通變之謂事：物各居其所則無事。陰陽不測之謂神：可測則不為神。

Its great virtue and vast endeavors are truly ultimate. Being all-encompassing is called great undertaking. Renewing every day is called great virtue; its increase has no fixed place. Continuing to produce without end is called change; the form and nature succeed each other continuously, and change has no end. That which forms images is called Qian; only when it appears can it be called an image, and Qian governs the creation of all things. That which takes shape by following the pattern is called Kun; making and using it is called "pattern," and Kun is responsible for shaping all things. To reach the limit of the divining numbers and foresee the future is called divination; by combining and interweaving those numbers, one knows what is to come. To understand change is called affairs; when all things are in their proper place, there are no more affairs. The transformation of yin and yang is unpredictable, and that is called spirit; what can be measured is not spirit.

夫易廣矣大矣，以言乎逺則不御：莫之止。以言乎邇則靜而正：靜謂寂然不動，正謂貞夫一。以言乎天地之間則備矣：百物不廢。夫乾，其靜也專，其動也直：陽能制陰，陰不能制陽，故陽之動靜得以專直。是以大生焉：大可以兼廣。夫坤，其靜也翕，其動也闢：收斂發生，和而不唱。是以廣生焉：廣不可以兼大。

The Book of Changes is truly vast and profound: when viewed from afar, it has no limits; nothing can hinder it. When viewed from near, it is quiet and upright. What is meant by "quiet" is stillness and immobility; what is meant by "upright" is adherence to one principle. When viewed from the space between heaven and earth, it encompasses everything; nothing is left out. The trigram Qian, when still, is focused and unified; when active, it is upright and just. Yang restrains Yin, but Yin cannot restrain Yang, so Yang's stillness and activity can both be focused and upright. Therefore, there arises the concept of "greatness," which can encompass "vastness." The trigram Kun, when still, is reclusive and closed; when active, it is expansive and open. One contraction and one expansion, merely responding without leading. Therefore, there arises the concept of "vastness," which cannot encompass "greatness."

廣大配天地，變通配四時，陰陽之義配日月，易簡之善配至徳。子曰：易其至矣乎！夫易，聖人所以崇徳而廣業也：法易簡以成久大。知崇禮卑，崇效天，卑法地，天地設位而易行乎其中矣：易所以通成知禮之功。成性存存，道義之門：人各有性，易能成之，存其可存，去其可去，道義之門皆由此塗出。右第五章。

"The vast and great matches with heaven and earth, change and adapt match with the four seasons, the meaning of yin and yang matches with the sun and moon, and the simple and easy virtue of the Book of Changes matches with the highest virtue. Confucius said: 'The Book of Changes is perhaps the ultimate.' The Book of Changes is used by the sages to promote virtue and expand endeavors": this is to follow the way of "easy and simple" to achieve enduring and vast achievements. "Wisdom should be lofty, rites should be humble; the lofty follows heaven, the humble follows earth; heaven and earth set the positions of high and low, and the Book of Changes operates within them": the Book of Changes is precisely used to connect and achieve the two aspects of "knowledge" and "rites." "To realize human nature and make it endure forever, this is the gate of righteousness": each person has their innate nature, and the Book of Changes realizes it; what should be preserved is preserved, what should be removed is removed, and the gate of righteousness opens through this path. This is the fifth chapter.

聖人有以見天下之賾，而擬諸其形容：賾者，精□之極致，人莫之見，聖人必有以見之，立形於無形而為卦。象其物宜，是故謂之象：物之質性各有宜。聖人有以見天下之動，而觀其□通，以行其典禮：動雖萬變，必有可□之地、可通之道；典禮猶法度。繫辭焉以□其吉凶，是故謂之爻：合其法度則吉，違之則凶。

The sage is able to perceive the most profound and intricate aspects of the world and to liken them to their forms and appearances. The term "赜" refers to something extremely subtle and refined, which ordinary people cannot see, but the sage has the ability to perceive it, establishing images in the invisible and drawing the hexagrams. "To symbolize the proper form of things, hence called 'xiang'" means that each thing has its own appropriate nature. "The sage is able to observe the changes of all things under heaven and to examine their points of convergence and connection, thus promoting rituals and institutions": although changes are numerous and complex, there must be points where they can be united and paths through which they can be connected; "rituals" correspond to rules and regulations. "To attach words to judge its fortune or misfortune, hence called 'yao'": if it conforms to the rules it is auspicious, if it violates them it is inauspicious.

賾者，至理幽□無形者也，故聖人立象，所以謂之形容也。□通，交衢也；典禮，法則也。聖人以一類萬，以要知繁，故謂之爻。爻者，群動之交也。言天下之至賾而不可惡也，言天下之至動而不可亂也：有條而不紊。擬之而後言：擬之於易。議之而後動：議之於易。擬議以成其變化：成其龍徳。

Sima Guang explained that "赜" refers to the highest principles that are hidden and without form. Therefore, the sage established the hexagrams in order to give them a form and description. "Will and communication" is like a crossroads where many paths meet; "rituals and norms" are the rules. The sage uses a single principle to encompass all things, and uses simplicity to grasp complexity, hence it is called "yao." "Yao" is the meeting point of many changes. "Speaking of the most profound and intricate principles without causing aversion, and speaking of the most complex changes without causing confusion": because it is orderly and not chaotic. "First comparing and then speaking": is to use the Book of Changes as a comparison. "First considering and then acting": is to use the Book of Changes as a consideration. "Achieving its changes through comparison and consideration": is also achieving the virtue of the dragon.

“鶴鳴在陰，其子和之；我有好爵，吾與爾靡之。”子曰：君子居其室，出其言善，則千里之外應之，況其邇者乎？居其室，出其言不善，則千里之外違之，況其邇者乎？言出乎身，加乎民；行發乎邇，見乎逺。言行，君子之樞機，樞機之發，榮辱之主也。言行，君子之所以動天地也，可不慎乎？

The Great Treatise cites the line statement of Zhongfu hexagram Nine in the Second: "A crane calls in the mountain shade, and its young cranes respond in harmony; I have a cup of fine wine, and I wish to share it with you." Confucius said: A gentleman resides in his own house. If his words are good, people a thousand miles away will respond, let alone those nearby. If his words are not good, people a thousand miles away will turn away, let alone those nearby. Words originate from oneself and affect the people; actions begin nearby and are seen far away. Words and deeds are the door hinges and the crossbow mechanism of a gentleman. Once the door hinge or crossbow mechanism is set in motion, honor and disgrace depend on it. Words and deeds are what a gentleman uses to move heaven and earth; how can they not be cautious?

鶴鳴子和，誠信發於中，無幽而不應。樞機謂得失至要，言行動天地，而況於人。“同人先號咷而後笑”：中直求合，同之者寡，故先憂；聖賢相值，天下大同，故後喜。子曰：君子之道，或出或處，或黙或語：跡不必同。二人同心，其利□金：二人心同，至堅可□，況於眾多。同心之言，其臭如蘭：志同言合，芬芳條暢。右第六章。

Sima Guang explained that when a crane calls, the small cranes respond because sincerity comes from the heart, and even in the most hidden places, there is no failure to respond. "The pivot and mechanism" refers to the most critical point of gain and loss; words and deeds that can move heaven and earth, how much more so can they move people. The "Great Treatise" cites the "Line Statement" of the "Same People" hexagram's "Nine in the Fifth" line, "Same People first weep and then laugh": the "Nine in the Fifth" maintains the middle and uprightness, seeking harmony with others. At first, few agree with him, so he is first sorrowful; later, when sages meet and the world becomes harmonious, he is later joyful. "Confucius said: the way of a gentleman in dealing with the world is sometimes to take office and sometimes to retreat, sometimes to be silent and sometimes to speak": external actions need not be the same. "When two hearts are in harmony, their sharpness is enough to cut through metal (the original text here is missing one character)": when two hearts are in harmony, even the hardest things can be cut through, how much more so when many hearts are in harmony. "The words of a person with the same heart have the fragrance of orchids": when hearts are the same and words are in harmony, they are fragrant and smooth. The above is Chapter Six.

“初六：藉用白茅，無咎。”子曰：茍錯諸地而可矣，藉之用茅，何咎之有？慎之至也。夫茅之為物薄，而用可重也；慎斯術也以往，其無所失矣。必言初六者，見其以柔處下；薄言易有，用可重，可以供神明。

The Great Treatise cites the Line Statement of the Great Excess hexagram's Six at the Beginning: "Using white reed grass as a mat, there is no blame." Confucius said: If it were simply placed on the ground, that would suffice; yet they use white reed grass as a mat, so what could possibly be wrong? This shows extreme caution. Reed grass itself is very humble, yet its use can be of great value; if such cautious behavior is carried through, there will be no mistakes. Sima Guang explained: The Great Treatise specifically mentions "Six at the Beginning" to show that it is a soft and yielding line in a low position. What is meant by "thin" is that it is easily obtainable everywhere; what is meant by "can be valuable" is that it can be used to offer sacrifices to the spirits.

“勞謙君子，有終吉。”子曰：勞而不伐，有功而不徳，厚之至也，語以其功下人者也。徳言盛，禮言恭；謙也者，致恭以存其位者也。“勞謙君子，有終吉”：雖有功勤，不謙則不能保其終。“徳言盛，禮言恭”：徳愈盛，禮愈恭。“致恭以存其位”：保其富貴。

The Great Treatise cites the line statement of the卦 of Humility, line nine three: "A virtuous man who labors humbly will have a favorable ending." Confucius said: having merit without boasting, having achievements without claiming virtue, this is the extreme of sincerity and modesty; it refers to those who still remain in a lower position despite their merits. Virtue should be spoken of as great, ceremony should be spoken of as respectful; what is meant by humility is to show extreme respect in order to preserve one's position. Sima Guang explained: "A virtuous man who labors humbly will have a favorable ending" means that even though one has exerted effort and achieved merit, if one is not humble, one cannot preserve a good ending. "Virtue is spoken of as great, ceremony is spoken of as respectful" means that the greater the virtue, the more respectful the ceremony. "Expressing respect to preserve one's position" means preserving one's wealth and rank.

“亢龍有悔。”子曰：貴而無位：仁不能守，是為無位。髙而無民：眾心不附，是為無民。賢人在下位而無輔：雖無道而有賢人為輔，猶可以不亡；今在下位，是無輔也。是以動而有悔也：守靜猶愈。

The Great Treatise cites the Line Statement of the Qian hexagram's Nine at the Top: "A dragon soaring high brings regret." Confucius said: "Being in a high position without an actual office." Sima Guang explained: "If one cannot maintain benevolence in that position, it is as if there is no position at all." "Being in a high position without the people's support." If the people's hearts are not close, it is as if there are no people. "A virtuous person is in a low position but does not come to assist him." Even if the ruler is unjust, as long as there are virtuous ministers to assist, it may still avoid ruin; now, the virtuous are in low positions and do not come to assist, which means there is no assistance. "Therefore, any action brings regret." It would be better to remain quiet and still.

“不出戸庭，無咎。”子曰：亂之所生也，則言語以為階。君不密則失臣：忠臣不親。臣不密則失身：陷於罪戮。幾事不密則害成，是以君子慎密而不出也：事未動而先露則無功。

The Great Treatise cites the Line Statement of the first line of the节卦: "Not leaving the gate or courtyard, no blame." Confucius said: The origin of calamity often begins with words. "If a ruler is not cautious in keeping secrets, he will lose his ministers"—Sima Guang explained: loyal ministers will therefore not be close to him. "If a minister is not cautious in keeping secrets, he will lose himself"—he will fall into punishment and death. "If confidential matters are not kept secret, they will cause harm, so the gentleman is cautious and keeps secrets without easily speaking them out"—if things have not yet begun to take effect but are already revealed, there will be no success.

子曰：作易者其知盜乎：知盜之情。易曰“負且乘，致寇至”，負也者，小人之事也；乘也者，君子之器也；小人而乘君子之器，盜思奪之矣：徳薄位尊，必不能守。上慢下暴，盜思伐之矣：上慢下暴者，慢其上而暴其下也，慢上暴下皆所以致伐禍也。

Confucius said: The person who composed the Zhou Yi must have understood the psychology of thieves. Sima Guang explained: This refers to his understanding of the actual situation of thieves. The Zhou Yi explains the hexagram Six in the Third, which says, "Carrying goods but sitting in a carriage, inviting bandits." Carrying goods is the work of the petty person; using a carriage is the tool of the gentleman. When the petty person sits in the gentleman's carriage, thieves will come to seize it. Sima Guang explained: Those who have shallow virtue but hold high rank will surely not be able to hold on. "Being disrespectful to superiors and cruel to subordinates, thieves will come to attack him": what is meant by "being disrespectful to superiors and cruel to subordinates" is being disrespectful to those above and cruel to those below. Those who are disrespectful to those above and cruel to those below are sufficient to invite calamity.

慢藏誨盜：守國不謹則敵人取之，立身不謹則禍辱乘之。冶容誨淫：先自敗然後人敗之。易曰“負且乘，致冦至”，盜之招也。右第七章。

"Being careless in guarding wealth and property is like inviting thieves." If one is not careful in defending the country, enemies will invade; if one is not careful in personal conduct, calamity and disgrace will enter easily. "Being overly seductive in appearance is like inviting lust." It is always oneself who first ruins oneself, and then others take advantage. Therefore, the I Ching says, "Carrying burdens and riding in a carriage, leading to the arrival of bandits," for those strong bandits are precisely what one has invited. This is Chapter Seven.

大衍之數五十，其用四十有九：闗子明曰，數兆於一，生於二，極於三，此天地人所以立也。地二天三合而為五，其一不用者，六來則一去也，既成則無生也。有生於無，終必有始，既有則無去矣，既終則始去矣。五位皆十，衍之極也，故曰大衍。

The number of great derivation is fifty, but only forty-nine are actually used. Guan Ziming explains that numbers originate from "one," are generated from "two," and reach their limit at "three," thus establishing the three elements of heaven, earth, and humanity. The earth number two and the heaven number three combine to make five. One stalk of chrysanthemum is not used because when "six" comes, "one" is subtracted, and once formed, it does not generate again. "Being" arises from "non-being," and if there is an end, there must be a beginning. Since there is already "being," "non-being" retreats; since there is already an end, the beginning also retreats. Each of the five directions has ten units, which is the limit of derivation, hence it is called "great derivation."

光謂：易有太極，一之謂也。分而為陰陽，陰陽之間必有中和，故夫一，衍之則三而小成，十而大備。小衍之則為六，大衍之則為五。一者，數之母也；數者，一之子也。母為之主，子為之用。是故小衍去一而為五行，大衍去一而為揲蓍之數。

Sima Guang said: The "Taiji" in the Book of Changes refers to "one." When "one" is divided, it becomes yin and yang, and between yin and yang there must be harmony and balance. Therefore, this "one," when extended in a small way, becomes "three," and when extended in a large way, becomes "ten." In a small extension, it leads to "six," and in a large extension, it leads to "five." "One" is the mother of numbers, and all numbers are the sons of "one." The mother is the master, and the sons are the applications. Therefore, when small extension removes one "one," it becomes the numbers of the Five Phases. When large extension removes one "one," it becomes the forty-nine numbers used in the divination with yarrow stalks.

分而為二以象兩，掛一以象三，揲之以四以象四時，歸竒於扐以象閏：奇者，四揲之餘；扐者，不用之數。五歲再閏，故再扐而後掛：左右手之扐，皆合於所掛之一。天數五：韓曰，五奇也。地數五：韓曰，五耦也。五位相得而各有合：生成相合，為水火木金土。

Divide the chrysanthemum grass into two bundles to symbolize the two principles of Heaven and Earth, and hang one bundle to symbolize the three elements. Count the bundles in groups of four to symbolize the four seasons, and place the remaining sticks between the fingers to symbolize the leap month. The term "qi" refers to the remainder after counting in groups of four. The term "tuo" refers to the part temporarily set aside. Since there are two leap months in five years, the remainders from both hands should be combined and added to the hanging bundle. The "Heavenly numbers" consist of five, as explained by Han Kangbo, meaning the five odd numbers. The "Earthly numbers" also consist of five, as explained by Han Kangbo, meaning the five even numbers. The five directions correspond to each other and are paired accordingly. The generating numbers and the formed numbers are paired to form water, fire, wood, metal, and earth.

天數二十有五，地數三十，凡天地之數五十有五：皆積數。此所以成變化而行鬼神也。乾之策二百一十有六：老陽一爻九揲三十六策，少陽七揲二十八策，獨舉老，取其變。坤之策百四十有四：老陰六揲二十四策，少陰八揲三十二策。凡三百有六十，當期之日；二篇之策萬有一千五百二十，當萬物之數也。

"The total of the heavenly numbers is twenty-five, and the total of the earthly numbers is thirty, making a total of fifty-five for heaven and earth combined." These are the total numbers obtained by adding them up. "This is the reason for the generation of change and the operation of ghosts and spirits. The number of stalks used in the divination for the Qian hexagram is two hundred and sixteen." The old yang line is nine, and nine multiplied by four gives thirty-six stalks. The young yang line is seven, and seven multiplied by four gives twenty-eight stalks. Here only the old yang is mentioned because it is the one that can change. "The number of stalks used in the divination for the Kun hexagram is one hundred and forty-four." The old yin line is six, and six multiplied by four gives twenty-four stalks. The young yin line is eight, and eight multiplied by four gives thirty-two stalks. "The total number of stalks for the Qian and Kun hexagrams combined is three hundred and sixty, which corresponds exactly to the number of days in a year. The total number of stalks used in the divination for the upper and lower parts of the Zhou Changes is eleven thousand five hundred and twenty, which corresponds exactly to the number of all things."

是故四營而成易：自分而為二，至歸奇於扐。十有八變而成卦：三變而成一爻，八卦而小成。引而伸之，觸類而長之，天下之能事畢矣：萬物所能之事皆畢。顯道神徳行，是故可與酬酢，可與佑神矣。右第八章。

"So after going through four procedures, one transformation is completed": starting from dividing the chrysanthemum grass into two bundles until the remaining stalks are held between the fingers. "After eighteen transformations, one hexagram is formed": three transformations form one line, and the formation of the eight trigrams is considered a minor completion. "Extending this principle, and inferring from similar cases, all things that can be done under heaven are included within it": all actions that things can perform are fully encompassed. "It reveals the Dao, making virtue mysterious and profound, so it can be used to respond to people and assist the workings of the divine." This is the eighth chapter.

子曰：知變化之道者，其知神之所為乎：神之所為，變化不測，惟易能知之。易有聖人之道四焉：以言者尚其辭：繫辭以盡言。以動者尚其變：君子動靜效易變化。以制器者尚其象：若舟楫杵臼之類。以卜筮者尚其占。

Confucius said: Those who understand the principle of change probably also understand the workings of the divine. Sima Guang explained: The workings of the divine are changeable and unpredictable, and only the Zhou Changes can comprehend them. "The Zhou Changes contain four aspects of the sage's way: those who speak value its words" — the words are used to express fully the meaning. "Those who act value its changes" — the gentleman's every movement and stillness follows the changes of the Zhou Changes. "Those who make objects value its symbolic images" — for example, boats, oars, mortars and pestles. "Those who use divination value its judgments."

是以君子將有為也，將有行也：為、行所以異。問焉而以言，其受命也如向，無有逺近幽深，遂知來物，非天下之至精，其孰能與於此？參伍以變，錯綜其數，通其變，遂成天地之文：天有三辰五星，地有三正五行。極其數，遂定天下之象，非天下之至變，其孰能與於此？

Therefore, when a gentleman is about to take action or make a move, Sima Guang explains that "to act" and "to act out" are distinct. "One consults the Book of Changes and seeks guidance through words; it responds as swiftly as an echo. Whether distant or deep, one can thus know what is to come. If it is not the most subtle thing in the world, who could reach such a level? By intricately interweaving and transforming its numbers, it connects with its changes, thus forming the brilliance of the world. There are the three celestial bodies, the five planets in the sky, and on the earth, the three correct calendars and the five elements. By exhausting its numbers, one can determine the forms of all things. If it is not the most changeable thing in the world, who could reach such a level?"

易無思也，無為也，寂然不動，感而遂通天下之故，非天下之至神，其孰能與於此？夫易，聖人之所以極深而研幾也。惟深也，故能通天下之志：達物情。惟幾也，故能成天下之務：幾者，動之□，慮之於□，則事無不濟。惟神也，故不疾而速，不行而至：感而遂通天下之故。子曰易有聖人之道四焉者，此之謂也。右第九章。

"The Book of Changes has no thoughts, no actions, is quiet and still; once it responds to something, it connects with all events throughout the world. If it is not the most mysterious thing in the world, who could reach such a level? The Book of Changes is precisely what the sage uses to explore the profound and investigate the subtle. Because it is profound, it can understand the aspirations of people throughout the world." — this is understanding the actual situation of all things. "Because it is subtle, it can accomplish all affairs under heaven." — "Ji" refers to the initial signs of change (the original text is missing one character here); considering things at the initial signs ensures that nothing cannot be accomplished. "Because it is mysterious, it does not need to hurry and yet naturally becomes swift, does not need to move and yet naturally arrives." — because once it responds, it connects with all events throughout the world. "Confucius said the Book of Changes contains four aspects of the sage's way, which are exactly these." This is the ninth chapter.

天一，地二，天三，地四，天五，地六，天七，地八，天九，地十：此天地自然之數，所以成變化而行鬼神。子曰：夫易何為者也？夫易開物成務，冒天下之道，如斯而已者也。是故聖人以通天下之志，以定天下之業，以□天下之疑：開物，專示吉凶；成務，成天下之務；冒天下之道，包而有之。

"The heavenly numbers are one, two, three, four, five, six, seven, eight, nine, and ten": these are the natural numbers of heaven and earth, from which change arises and by which ghosts and spirits operate. Confucius said: "What is the purpose of the Book of Changes? The Book of Changes opens up all things and accomplishes all affairs, encompassing the principles of the world, nothing more. Therefore, the sage uses it to harmonize the hearts of people throughout the world, to establish great achievements under heaven, and to resolve doubts throughout the world (the original text here is missing one character)." The term "open things" refers to specifically indicating good and bad fortune; "accomplish affairs" refers to achieving all worldly matters; and "encompass the principles of the world" means to include all the principles of the world comprehensively.

是故蓍之徳圓而神，卦之徳方以知：韓曰，圓者運而不窮，方者止而有分。光謂：蓍未形而不測，故曰神；卦已形而變通，故曰知。六爻之義，易以貢：發揮變化，以進於人。聖人以此洗心，退藏於密：洗心，滌諸邪惡，存養精明；藏密，返於無形。吉凶與民同患：豫以告之。神以知來，知以藏往：藏往謂不知其始，所以言往。其孰能與於此哉！

Therefore, the virtue of the yarrow stalks is round and profound, while the virtue of the hexagrams is square and wise. Han Kangbo said: the round is ever turning without end, while the square is still and has definite boundaries. Sima Guang said: the yarrow stalks have not yet taken form and are therefore unpredictable, hence called "spirit"; the hexagrams have already taken form and can be flexible and changeable, hence called "knowledge." "The meaning of the six lines depends on change": to bring out the changes and present them to people. "The sages use it to purify the mind and retreat into secrecy": "Purifying the mind" means removing all evil and cultivating purity and clarity; "retreating into secrecy" means returning to the formless. "It shares the joys and sorrows of the common people": to inform people of good and bad in advance. "Using the marvelous to foresee the future, using the wise to conceal the past": "Concealing the past" means not knowing its beginning, hence called "past." "Who could reach such a level?"

古之聰明睿知神武而不殺者夫：韓曰，服萬物而不以威刑。是以明於天之道，而察於民之故，是興神物以前民用：神物謂蓍，凡卜中然後用之，故曰以前民用。聖人以此齋戒，以神明其徳夫：韓曰，洗心曰齋，防患曰戒。光謂：徳盛則合於神明。

"This is probably referring to the ancient wise and intelligent person who is mighty yet does not resort to warfare," said Han Kangbo, meaning that he brings all things to submission without relying on force. "Therefore, he understands the principles of heaven and investigates the actual conditions of the people, and thus he uses the divining tortoise and yarrow stalks, these divine objects, to guide the people before they take action." The term "divine object" refers to the yarrow stalks; all affairs are first divined and found to be auspicious before they are carried out, hence the phrase "before the people use it." "The sage uses it to purify his body and mind, making his virtue profound and divine," said Han Kangbo, meaning that cleansing the mind is called "zhai," and guarding against calamities is called "jia." Sima Guang said: when virtue is great, it harmonizes with the divine.

是故闔戸謂之坤：坤主收斂。闢戸謂之乾：陽發生也。一闔一闢謂之變，往來不窮謂之通，見乃謂之象：防象可見而未有形。形乃謂之器：形質已定，各有常分。

Therefore, closing the door is called Kun: Kun governs gathering in and concealment. Opening the door is called Qian: that is the movement of yang energy. One closing and one opening is called transformation; continuous movement back and forth is called communication; manifestation is called image. The image is visible but does not yet have a definite form. When it has a form, it is called an object; when shape and substance are determined, each has its fixed nature.

制而用之謂之法：各守其分，不相為用，故聖人制而用之。利用出入，民咸用之謂之神：出外入內，無所不用，而百姓不知，故謂之神。右第十章。

"Creating and putting into use is called Fa": All things each hold their own position, originally not interacting with each other, so they rely on sages to create and put them into use. "Beneficial for people's daily activities and movements, the common people use it every day yet cannot explain it, this is called Shen": Whether going out or staying at home, it is used everywhere, yet the common people do not know its origin, hence it is called "Shen." This is the tenth chapter.

是故易有太極，是生兩儀，兩儀生四象，四象生八卦，八卦定吉凶，吉凶生大業。易有太極：極者，中也，至也，一也；凡物之未分混而為一者皆為太極。兩儀：儀，匹也，分而為二，相為匹敵。四象：陰陽復分老少而為二，相為匹敵。大業：富有萬象。

Therefore, the Book of Changes speaks of the Taiji, from which the two principles emerge, from the two principles the four images arise, from the four images the eight trigrams come into being, and the eight trigrams determine fortune and misfortune, which in turn give rise to great undertakings. Sima Guang explained the phrase "the Book of Changes has the Taiji" by saying: the term "ji" implies the concept of center, ultimate, and unity; any state that has not yet differentiated and remains unified is called Taiji. As for the "two principles": "yi" means matching; dividing one into two, with each other forming a pair. As for the "four images": yin and yang each further divide into old and young, with each other forming a pair. As for "great undertakings": this refers to being rich in all phenomena.

太極者何？陰陽混一，化之本原也。兩儀者何？陰陽判也。四象者何？老少分也，七九八六，卦之端也。八卦既形，吉凶全也；萬物皆備，大業成也。極，中也；儀，匹也。

What is the Taiji? It is the unity of yin and yang, the fundamental principle of generation and transformation. What are the two principles (liang yi)? They are the differentiation of yin and yang. What are the four images (si xiang)? They are the division into old and young, represented by the numbers seven, nine, eight, and six, which are the beginnings of forming hexagrams. Once the eight trigrams are formed, the principles of good fortune and misfortune are complete; all things are included, and great achievements are realized. "Ji" means center, and "yi" means pair.

太極，天也；乾坤，日月也；四象，五宮也；八卦，十二辰也；六十四卦，列宿也；眾爻，三百六十有六度也。太極，地也；乾坤，山澤也；四象，四方也；八卦，九州島也；六十四卦，萬國也；眾爻，都邑也。

From the perspective of Heaven: The Taiji represents Heaven, Qian and Kun represent the sun and moon, the Four Symbols correspond to the five directions and the star palaces, the Eight Trigrams correspond to the twelve earthly branches, the sixty-four hexagrams correspond to the twenty-eight constellations and myriad stars, and the numerous lines (yao) correspond to the 366 degrees of the celestial circle. From the perspective of Earth: The Taiji represents Earth, Qian and Kun represent mountains and marshes, the Four Symbols correspond to the four directions, the Eight Trigrams correspond to the nine provinces, the sixty-four hexagrams correspond to the myriad states under heaven, and the numerous lines (yao) correspond to the various towns and cities.

太極，歲也；乾坤，寒暑也；四象，四時也；八卦，八節也；六十四卦，十二月也；眾爻，三百六旬有六日也。太極，王也；乾坤，方伯也；四象，四嶽也；八卦，州牧也；六十四卦，諸侯也；眾爻，卿大夫士也。

From the perspective of the seasons: the Taiji represents a year, Qian and Kun represent cold and heat, the Four Symbols represent the four seasons, the Eight Trigrams represent the eight solar terms, the sixty-four hexagrams represent the twelve months, and the numerous lines (yao) represent the 366 days of a year. From the perspective of human affairs: the Taiji represents the Son of Heaven, Qian and Kun represent the regional governors, the Four Symbols represent the four mountain officials, the Eight Trigrams represent the state governors, the sixty-four hexagrams represent the feudal lords, and the numerous lines (yao) represent the ministers, great officers, and commoners.

或問：太極有形無形？曰：合之則有，離之則無。何謂也？曰：請以宮喻。夫宮者，土木之為也，舉土木則無宮矣；土木者，堂墉棟宇也，舉堂墉棟宇則無土木矣。雖然，合而言之，則宮巍然在矣。

Someone asked: Is the Taiji (Supreme Ultimate) tangible or intangible? The answer was: When viewed as a whole, it is tangible; when viewed as separate parts, it is intangible. How should this be understood? The answer was: Please take a house as an example.the so-called house is made of earth and wood; but if you speak only of earth and wood, there is no house.the so-called earth and wood refers to hall, walls, beams, and eaves; but if you speak only of hall, walls, beams, and eaves, there is no earth and wood. Nevertheless, when these parts are combined, the house still stands firmly there.

太極者，一也，物之合也，數之元也。引而伸之，觸類而長之，則算不能勝也，書不能盡也，口不能宣也，心不能窮也。掊而聚之，歸諸一；析而散之，萬有一千五百二十，未始有極也。

The concept of the Taiji, or Supreme Ultimate, is referred to as "one," representing the essence and totality of all things, the fundamental origin of numbers. When extended and inferred, it is infinite in calculation, endless in writing, and boundless in speech and thought. When gathered and condensed, it is reduced to a single "one"; when analyzed and dispersed, it becomes as numerous as 11,520, and there is no end to it.

陰陽相違，非太極則不成；剛柔相戾，非中正則不行。故天下之徳誠眾矣，而萃於剛柔；天下之道誠多矣，而□於中正。剛柔者，徳之府；中正者，道之津。是故有剛而無中正則暴以亡，有柔而無中正則邪以消。嗚呼！中正之於人也，其厚矣哉！

Yin and Yang are opposite to each other; without the Taiji, they cannot be realized. Strength and softness are opposing; without the Middle and Righteousness, they cannot be carried forward. Therefore, the virtues of the world are indeed numerous, yet they all converge in strength and softness; the paths of the world are indeed diverse, yet they all return to the Middle and Righteousness. Strength and softness are the repositories of virtue, and the Middle and Righteousness is the passage of the great way. Therefore, if there is only strength without the Middle and Righteousness, it will lead to cruelty and destruction; if there is only softness without the Middle and Righteousness, it will lead to wickedness and extinction. Alas! The Middle and Righteousness is of great benefit to mankind.

剛者抑之，柔者掖之，不慮而成，不思而得，不卜而中，不筮而吉。“天下同歸而殊塗，一致而百慮”，非中正而何？書曰“沈潛剛克，髙明柔克”，以中正也。孔子曰“中庸之為徳也，其至矣乎”，又曰“詩三百，一言以蔽之，曰思無邪”。易之卦六十有四，其爻三百八十有四，得之則吉，失之則凶者，其惟中正乎！

To restrain the strong and support the weak; thus, there is no need for careful planning and success comes naturally, no need for anxious thinking and understanding comes naturally, no need for divination and correctness is naturally achieved, no need for seeking omens and auspiciousness naturally follows. The Great Treatise says, "All things in the world take different paths yet arrive at the same destination, and all considerations converge to one point," that common destination and convergence, is not precisely "zhongzheng" (uprightness and correctness)? The Book of Documents, Hongfan, says, "For those who are deep, yielding, and weak, use strength to govern; for those who are lofty, arrogant, and strong, use gentleness to govern," which speaks of the way of zhongzheng. Confucius says, "The virtue of zhongyong (the mean) is perhaps the ultimate," and also says, "The Book of Poetry has three hundred poems; to summarize them in one phrase, it is 'thinking without deviation.'" The Zhou Changes contain sixty-four hexagrams and three hundred and eighty-four lines; what is gained brings good fortune, what is lost brings misfortune, and perhaps only "zhongzheng" is such a thing.

剛，夏也；柔，冬也；中，春也；正，秋也。何謂才？曰：聰明強勇。何謂行？曰：孝友忠信。何謂徳？曰：中和正直。何謂道？曰：逺大高深。行以濟才，徳以濟行，道以濟徳。是故才而不以行則凶，行而不以徳則偏，徳而不以道則隘，四者兼足，謂之聖人。

Heavenly Stems are paired with summer, Earthly Branches with winter, the middle with spring, and correctness with autumn. What is called "cai" (talent)? It is said: intelligent, strong, and brave. What is called "xing" (virtue)? It is said: filial, friendly, loyal, and trustworthy. What is called "de" (virtue)? It is said: harmonious and upright. What is called "dao" (way)? It is said: far-reaching and profound. Using "xing" to complete "cai," using "de" to complete "xing," and using "dao" to complete "de." Therefore, having talent without the restraint of virtue is dangerous, having virtue without the elevation of virtue is narrow-minded, and having virtue without the penetration of the great way is confined. When these four are all sufficient, one is called a sage.

陰陽不相讓，五行不兼容，正也；陰陽醇而五行不雜，中也。陽盛則陰□，陰盛則陽□；火進則木退，土興則水衰。陰陽之治無少無多，五行之守無偏無頗，尸之者其太極乎！故太極之徳，一而已。

Yin and Yang do not yield to each other, and the Five Phases do not mix with each other; this is called "Zheng." Yin and Yang are pure, and the Five Phases do not interfere with each other; this is called "Zhong." When Yang energy is strong, Yin energy weakens; when Yin energy is strong, Yang energy weakens. When fire energy rises, wood energy retreats; when earth energy emerges, water energy diminishes. The regulation of Yin and Yang is neither deficient nor excessive, and the Five Phases maintain their proper roles without deviation or tilt; the principle governing all of this is probably the Taiji. Therefore, the virtue of Taiji, in the end, is simply "one."

是故法象莫大乎天地，變通莫大乎四時，縣象著明莫大乎日月，崇髙莫大乎富貴，備物致用、立成器以為天下利莫大乎聖人，探賾索隠、鉤深致逺，以定天下之吉凶、成天下之亹亹者，莫大乎蓍龜。富貴：富有四海，貴為天子。備物致用：蕃肓萬物，以為人用。立成器以為天下利：謂法度也。亹亹，勉勉也，使人去凶就吉。

Therefore, there is no greater model to follow than heaven and earth, no greater transformation and penetration than the four seasons, no more lofty and luminous presence in the sky than the sun and moon, no greater exalted and illustrious status than wealth and honor, and no greater completeness of objects, fullness of utility, and creation of tools for the benefit of the world than the sage. Investigating the profound, searching for the subtle, drawing out the deep and summoning the great, thus determining the fortune and misfortune of the world and encouraging people to strive diligently, there is nothing greater than the yarrow stalks and turtle shells. Sima Guang explains 'wealth and honor' as possessing the whole world and being the Son of Heaven. He explains 'completeness of objects and achieving their use' as multiplying all things for human use. He explains 'establishing instruments to benefit the world' as referring to laws and regulations. 'Wěiwěi' means diligence, referring to guiding people to avoid misfortune and seek good fortune.

是故天生神物，聖人則之；天地變化，聖人效之；天垂象，見吉凶，聖人象之；河出圖，洛出書，聖人則之。易有四象，所以示也；繫辭焉，所以告也；定之以吉凶，所以□也。易曰“自天佑之，吉無不利”。子曰：佑者，助也。天之所助者，順也；人之所助者，信也。履信思乎順，又以尚賢也，是以自天佑之，吉無不利也。右第十一章。

Therefore, heaven produces divine objects such as the yarrow stalks and tortoise shells, and the sage takes them as models; when heaven and earth undergo changes, the sage imitates them; when heaven manifests signs and reveals auspicious or inauspicious omens, the sage takes them as symbols; when the Yellow River produces the dragon pattern and the Luo River produces the turtle script, the sage takes them as models. The Book of Changes contains four types of hexagrams, used to make clear; attaching words to them, used to inform; determining auspiciousness and inauspiciousness, used to make decisions (the original text here is missing one character). The Great Possession hexagram, line nine, says: When heavenly protection descends, it is auspicious and there is no disadvantage. Confucius says: "You" means assistance. What heaven assists is the person who follows the way of heaven; what the people assist is the person who upholds trustworthiness. Practicing trustworthiness and constantly following the way of heaven, and also honoring the virtuous, thus heavenly protection descends, it is auspicious and there is no disadvantage." This is the eleventh chapter.

子曰：書不盡言：言有不可書者。言不盡意：然則聖人之意，其不可見乎？意有不可言者。子曰：聖人立象以盡意：象能盡言外之意。設卦以盡情偽：盡萬物之情偽。繫辭焉以盡其言：盡群言之要。變而通之以盡利：若“冥豫成，有渝，無咎”。鼓之舞之以盡神。

Confucius said: "Written words cannot fully express speech," because some things cannot be written. "Speech cannot fully express the mind," so how can the mind of the sage be known? Because some minds cannot be spoken. "Confucius said: the sage established hexagrams to exhaust the mind," meaning hexagrams can express meanings beyond speech. "Setting up the hexagram structure to exhaust the truth and falsehood of things," meaning the true and false of all things are revealed. "Attaching words to exhaust what is to be said," meaning the essential points of many words are summarized. "Changing it to exhaust the benefit of things," for example, the sixth line at the top of the Yu hexagram says, "In the state of confusion and indulgence, if there is a change, there will be no error." "Stimulating and reviving it to exhaust the marvelous."