The hexagram of Not Yet Completed (Lower trigram Kan (Water), Upper trigram Li (Fire))

坎下離上。未濟：亨，小狐汔濟，濡其尾，無攸利。處未濟而不果如此，何利之有？彖曰：未濟亨，柔得中也。凡得中皆有亨之道焉。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。濟難之道，惟克果斷乃罔後艱，非柔之所能也。象曰：火在水上，未濟。君子以慎辨物居方。蚤正以待之。

The hexagram of Not Yet Completed has the lower trigram Kan (Water) and the upper trigram Li (Fire). The hexagram statement says: It is smooth; a small fox is about to cross the river but gets its tail wet, and there is no benefit. Zhang Gen explains: To be in this situation of Not Yet Completed and yet not decisive, how can there be any benefit? The Commentary on the Judgment says: Not Yet Completed is smooth, because the yao (lines) of the soft (yin) are in the center. Zhang Gen says: All those that are in the center contain the principle of smoothness. The Commentary on the Judgment says: The small fox is about to cross the river, meaning it has not yet left the middle of the danger of Kan. Getting the tail wet and having no benefit, means it cannot complete the matter. Although all the yao are not in the right position, the interaction between the yang and yin is harmonious. Zhang Gen says: The way to cross danger is only by decisiveness, which prevents future troubles; this is not something the weak can achieve. The Image Commentary says: Fire on water is Not Yet Completed. The gentleman takes this as a model, carefully distinguishing things and arranging them in their proper places. Zhang Gen says: This is about preparing properly in advance, to await the future.

初六，濡其尾，吝。象曰：濡其尾，亦不知極也。此亦曳其輪而濡其尾者也。九二，曳其輪，貞吉。曳其輪而已，是以謂之中。象曰：九二貞吉，中以行正也。剛在險中故。六三，未濟，征凶，利涉大川。象曰：未濟征凶，位不當也。下卦皆在險，而二獨以中吉；初不量力，而三不當位，故其患如此也。

The line statement for the initial line says: the tail is wet, there is regret. The Small Image Commentary says: the tail is wet, which is also not knowing the limit. Zhang Gen explains: this is the situation of the initial line of Ji Ji where one drags the chariot wheel and gets the tail wet. The line statement for the second line says: dragging the chariot wheel, maintaining the right path brings good fortune. Zhang Gen says: it is only dragging the chariot wheel, so it is called 'centered'. The Image Commentary says: the second line maintains the right path and brings good fortune, because it follows the middle path. Zhang Gen says: because it is a strong line in a dangerous situation. The line statement for the third line says: not yet crossed over, going on an expedition is dangerous, it is suitable to cross the great river. The Image Commentary says: in the situation of not yet crossed over, going on an expedition is dangerous, because the line is not in the proper position. Zhang Gen says: the three lines of the lower trigram are all in danger, only the second line is good because it is centered; the initial line does not measure its strength, the third line is not in the proper position, so the calamity is like this.

九四，貞吉悔亡，震用伐方，三年有賞于大國。象曰：貞吉悔亡，志行也。已出險故。六五，貞吉無悔，君子之光，有孚吉。象曰：君子之光，其暉吉也。兼容並包，虛已委任之謂。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。處卦之外，孚於酒以全身可也，濡其首則已甚矣。未濟之終有既濟之象焉，飲酒可也，濡其首則過也。

The fourth line statement says: Upholding the correct path brings good fortune, and regret disappears; by exerting military strength to attack the Guifang, after three years one receives a reward from a great state (the character 'ghost' is missing below 'attack'). The Small Image Commentary says: Upholding the correct path brings good fortune and regret disappears, indicating that one's aspirations are carried out. Zhang Gen explains: Because it has already emerged from danger. The fifth line statement says: Upholding the correct path brings good fortune, without regret; this is the brilliance of the gentleman, and with sincerity comes good fortune. The Image Commentary says: The brilliance of the gentleman brings good fortune, as his radiance brings about good fortune. Zhang Gen says: This is about embracing all and being open, emptying oneself to receive others and entrusting them freely. The top ninth line statement says: Drinking with sincerity will not lead to error; but if one drinks to the point of wetting one's head, that sincerity is lost. The Image Commentary says: Drinking to the point of wetting one's head is also a lack of restraint. Zhang Gen says: It is situated outside the hexagram, and by indulging in wine to preserve itself, it is still acceptable; but when one drinks to the point of wetting one's head, it goes too far. The end of the hexagram of Not Yet Completed already contains the image of Completion, so a little wine is acceptable, but drinking to the point of wetting one's head is excessive.

繋辭解上。繋辭有三：有繋一卦之辭，所謂設卦觀象、繋辭焉而明吉凶是也；有繋一爻之辭，所謂繋辭焉以斷吉凶、是故謂之爻是也；有繋易之辭，所謂上下繋是也。葢聖人既本陰陽而寓吉凶之理於卦爻彖象矣，於是統而繋之，論其所以然，以示天下後世，使知其說而考之。始於修身，終於復命；始於參天地而成位，終於理天地而成能。以此處上，則帝王天子之徳也；以此處下，則元聖素王之道也。此先聖所以垂教之極致歟。

The Great Treatise explains that the term "xì cí" refers to three kinds. One is the words attached to a single hexagram, which is what the Great Treatise says: "setting up hexagrams to observe phenomena, and attaching words to clarify good and bad fortune." Another is the words attached to a single line, which is referred to as "attaching words to decide good and bad fortune, hence called a line." The third is the words attached to the entire Book of Changes, which are the Great Treatise itself, both upper and lower parts. Probably the sage used yin and yang to convey the principles of good and bad fortune through hexagrams, lines, taogua, and images. Then he summarized these ideas in this text to explain their reasons, making them clear to the world and future generations, so that people can understand this system and examine it carefully. It begins with self-cultivation and ends with returning to the mandate of heaven; it starts with participating in the workings of heaven and earth and achieving proper positions, and ends with governing heaven and earth and attaining all abilities. Applying this principle in a superior position is the virtue of a sovereign emperor; applying it in an inferior position is the way of those who have the virtue of a sage but lack the position. This is probably the ultimate teaching of the ancient sages for guiding and educating people.

天尊地卑，乾坤定矣。天尊地卑，則乾坤之體可見。卑髙以陳，貴賤位矣。上下既列，則貴賤之位可明。動靜有常，剛柔□矣。天動地靜，則剛柔之才可謂。方以類聚，物以群分，吉凶生矣。陰陽以辨則異同列，異同立則愛惡形；同者以類聚而相愛，異者以群分而相惡也；愛惡相攻，吉凶所以生也。在天成象，在地成形，變化見矣。陽輕清故升而為象，陰重濁故降而為成形；形象則山澤通氣、雷風相博、水火不相違，此萬物所以生而變化所以兆也。

The Great Treatise says: Heaven is above and exalted, Earth is below and humble, thus the positions of the Qian and Kun hexagrams are established. Zhang Gen explains: seeing Heaven's exaltation and Earth's humility, the forms of Qian and Kun become evident. The Great Treatise says: low and high are arranged in order, thus the distinctions of rank and status become clear. Zhang Gen says: once upper and lower are arranged, the positions of rank and status become clear. The Great Treatise says: movement and stillness each have their regularity, thus the distinctions of strength and softness are clearly separated (the character here is missing, it should be 'separated'). Zhang Gen says: Heaven moves and Earth is still, thus the nature of strength and softness is determined. The Great Treatise says: things gather according to their directions, species differentiate according to their groups, thus good fortune and misfortune arise. Zhang Gen says: once yin and yang are distinguished, similar and different things are arranged; once similarity and difference are established, love and hatred take shape; similar things gather together and love each other, different things separate into groups and hate each other; love and hatred clash with each other, thus good fortune and misfortune arise. The Great Treatise says: in the heavens it becomes the images of sun, moon, and stars; on the earth it becomes the forms of mountains, rivers, moving plants, thus change becomes apparent. Zhang Gen says: yang qi is light and clear, thus it rises to form heavenly images; yin qi is heavy and turbid, thus it descends to form earthly forms. With forms and images, thus mountains and marshes communicate their qi, thunder and wind interact with each other, water and fire do not hinder each other, this is the reason for the generation of all things and the emergence of change.

是故剛柔相摩，所以有八卦；八卦相蕩，所以有六十四卦。鼔之以雷霆，潤之以風雨，日月運行，一寒一暑，此所以有萬物。乾道成男，坤道成女，此萬物所以生生而窮，而人事於是乎始也。乾知大始，主通其數，父道也，君道也。坤作成物，主成其功，母道也，臣道也。乾以易知，坤以簡能，付之六子而已。

The Great Treatise says: Therefore, the strong and the yielding interact and move against each other. Zhang Gen explains: This is the origin of the Eight Trigrams. The Great Treatise says: The Eight Trigrams interact and move against each other. Zhang Gen says: This is the origin of the sixty-four Trigrams. The Great Treatise says: Use thunder and lightning to move them, and use wind and rain to nourish them; the sun and moon move, and the cold and heat alternate. Zhang Gen says: This is the origin of all things. The Great Treatise says: The Trigram Qian represents the way of the male, and the Trigram Kun represents the way of the female. Zhang Gen says: This is the reason for the continuous generation of all things without end, and the beginning of human affairs. The Great Treatise says: Qian governs the great beginning of all things. Zhang Gen says: It governs the principle of continuity, which is the way of the father and also the way of the ruler. The Great Treatise says: Kun is responsible for shaping all things. Zhang Gen says: It governs the accomplishment of the task, which is the way of the mother and also the way of the subject. The Great Treatise says: Qian governs with ease and wisdom, and Kun governs with simplicity and action. Zhang Gen says: The rest of the matters are left to the six other Trigrams: Zhen, Kan, Gen, Xun, Li, and Dui.

易則易知，簡則易從。易知則有親，故不言而人推高焉；易従則有功，故不言而人推厚焉。有親則可久，物莫離焉；有功則可大，物所歸焉。可久則賢人之徳，可大則賢人之業，所歸乎易知如此。易道有三：下焉者以之成已，中焉者以之成位，上焉者以之成能。成已者，六十四卦之義也；成位者，乾坤之徳也；成能者，大易之道也。引而伸之：成已者，君子事也；成位者，賢人事也；成能者，聖人事也。此言聖人法乾坤成位之事，故稱賢人焉。

The Great Treatise says: What is easy to understand is easily known, and what is simple is easily followed. What is easily known brings people close. Zhang Gen explains: Therefore, he does not need to speak, and people naturally recommend him as superior. The Great Treatise says: What is easily followed brings achievements. Zhang Gen says: Therefore, he does not need to speak, and people naturally commend him as generous. The Great Treatise says: What brings people close ensures longevity. Zhang Gen says: All things do not wish to leave him. The Great Treatise says: What brings achievements brings expansion. Zhang Gen says: All things turn toward him. The Great Treatise says: What ensures longevity is the virtue of the virtuous person, and what brings expansion is the career of the virtuous person. Zhang Gen says: All things turn toward the easy and simple person, like this. The principles of the Book of Changes have three levels: the lower level uses it to achieve oneself, the middle level uses it to achieve position, and the upper level uses it to achieve omnipotence. Achieving oneself is the meaning of the sixty-four hexagrams; achieving position is the virtue of the hexagrams Qian and Kun; achieving omnipotence is the great way of the entire Book of Changes. Extending this: achieving oneself is the matter of the gentleman, achieving position is the matter of the virtuous person, and achieving omnipotence is the matter of the sage. This passage discusses the matter of the sage emulating Qian and Kun to achieve position, so the text refers to 'the virtuous person'.

易簡而天下之理得矣。所謂大人舉禮樂則天地將為昭焉。天下之理得而成位乎其中矣。所謂致中和，天地位焉，萬物育焉。此章明聖人本陰陽作易以寓吉凶之理，而法其道以成位乎其中之事。易之大教其於此矣，故以為繋辭之首焉。

The Great Treatise says: If things are plain and simple, the principles of the world are fully understood. Zhang Gen explains: This is what the Book of Rites says, that the superior person establishes rites and music, and thus heaven and earth become clear. The Great Treatise says: When one understands the principles of the world, one fulfills one's position within heaven and earth. Zhang Gen says: This is what the Doctrine of the Mean refers to when it says, "Achieving the mean and harmony, heaven and earth are established in their positions, and all things flourish." Zhang Gen concludes: This chapter explains that the sage based the Book of Changes on yin and yang, embedding the principles of good fortune and misfortune within it, and following these principles to fulfill one's position within heaven and earth. The fundamental teaching of the Book of Changes lies here, which is why it is placed at the beginning of the Great Treatise.

夫易之為書，明吉凶而已。吉凶之理，其於六十四卦，而其原皆本於八卦，八卦又本於乾坤，故學易當自乾坤始。然乾坤無形，不可億度，觀諸天地乃可概見。葢乾，陽物也，統天者也；坤，陰物也，統地者也。觀天尊地畀，則乾坤上下之體定矣；畀髙以陳，則乾坤貴賤之位見矣；天動地靜，則乾坤剛柔之材審矣。

Zhang Gen said: The Book of Changes is nothing but explaining the principles of good fortune and misfortune. The principles of good fortune and misfortune are embodied in the sixty-four hexagrams, and their origin lies in the Eight Trigrams. The Eight Trigrams themselves come from Qian and Kun, so studying the Book of Changes should begin with Qian and Kun. However, Qian and Kun have no physical form, and cannot be guessed at in the abstract. Only by observing heaven and earth can we get a general idea. Approximately, Qian represents the yang element, governing heaven; Kun represents the yin element, governing earth. Seeing that heaven is exalted and earth is humble, the relative positions of Qian and Kun are established (the character "bì" under "dì" should be "bēi"); seeing that high and low are arranged in order, the positions of honor and humility of Qian and Kun are revealed; seeing that heaven moves and earth is still, the nature of firmness and softness of Qian and Kun is determined.

聖人設卦觀象，繋辭焉而明吉凶。惟因象設卦，故觀象繋辭。剛柔相推而生變化。此六十四卦所以殊用而吉凶各不同也。是故吉凶者，失得之象也；悔吝者，憂慮之象也；變化者，進退之象也；剛柔者，晝夜之象也。晝宜進，夜宜退；能憂則常得之，無虞則常失之矣。六爻之動，三極之道也。囚陰陽之理以寓人事，是天地之道而人法之也。

The Great Treatise says: The sage established the hexagram structure, observed the images of things, and attached words to explain fortune and misfortune. Zhang Gen explained: Because the hexagrams were established based on the images of things, it is necessary to observe the images and attach words. The Great Treatise says: The yielding and strong lines shift and generate change. Zhang Gen said: This is why the sixty-four hexagrams have different functions and different fortune and misfortune. The Great Treatise says: Therefore, fortune and misfortune are the images of gain and loss, regret and worry are the images of anxiety and thought, change is the image of advancement and retreat, and the yielding and strong lines are the images of day and night. Zhang Gen said: Daytime is for advancement, and nighttime is for retreat; those who maintain anxiety and caution often gain, while those without vigilance often lose. The Great Treatise says: The movement of the six lines reflects the principles of heaven, earth, and humanity. Zhang Gen said: Depending on the principles of yin and yang to relate to human affairs, this is the way of heaven and earth, which humans follow.

是故君子所居而安者，易之序也。大象也。所樂而玩者，爻之辭也。小象也。是故君子居則觀其象而玩其辭，考之於卦。動則觀其變而玩其占，決之於蓍。是以自天佑之，吉無不利。此聖人法六十四卦以修身應物之事，故曰君子而已。吉則行之，凶則道之，何不利之有？

The Great Treatise says: Therefore, the gentleman remains tranquil and at ease because the Book of Changes has established an order. Zhang Gen explains: This refers to the Great Images. The Great Treatise says: The gentleman delights in contemplating the line statements. Zhang Gen says: This refers to the Small Images. The Great Treatise says: Therefore, when the gentleman is at ease, he observes the hexagrams and contemplates the hexagram statements. Zhang Gen says: This is examining the hexagrams. The Great Treatise says: When taking action, he observes the changing lines and contemplates the divination statements. Zhang Gen says: This is using the yarrow stalks to make a decision. The Great Treatise says: Therefore, heaven supports him, and he is auspicious and beneficial in all things. Zhang Gen says: This passage discusses the sage emulating the sixty-four hexagrams to cultivate himself and respond to worldly affairs, so it is only referred to as 'gentleman'. If something is auspicious, he does it; if something is ominous, he avoids it. How could there be any disadvantage?

此章明聖人既設卦矣，然後觀其象而繋之辭以明吉凶，以教天下後世，使人法之可以無大過。是故有大象之辭，卦辭是也，泰之小往大來吉亨之類是已；有小象之辭，爻辭是也，拔茅彚征吉之類是已。二象之辭難不相同，皆因剛柔之變而已。剛柔相推而變化生，變化生則利害形，利害形則吉凶著；其在人則語黙進退之象，故聖人寓以得失悔吝之□焉。君子能居而安之、樂而玩之，因時應變，行其吉而違其凶，何不利之有？

Zhang Gen said: This chapter explains that after the sage has established the hexagrams, he observed the hexagram images and attached statements to clarify good and bad fortune, using them to teach the people of later generations, so that they can follow them and avoid great mistakes. Therefore, there are statements like the "Great Image" which are the hexagram statements, such as the statement of the Qian hexagram "small things go away, great things come, auspicious, smooth." There are also statements like the "Small Image" which are the line statements, such as the statement of the Qian hexagram "pulling the hemp grass, the auspicious signs follow." Although these two types of statements are different from each other, they are both based on the changes of yin and yang. The changes of yin and yang arise from their mutual interaction and movement; when changes occur, advantages and disadvantages take shape; when advantages and disadvantages take shape, good and bad fortune become evident. When applied to people, these represent the images of speaking or keeping silent, advancing or retreating. Therefore, the sage expressed judgments about gain and loss, regret and hardship within them. A gentleman can calmly accept these, take pleasure in contemplating them, adapt to the situation, follow the path of good fortune and avoid the path of misfortune; where then would there be any disadvantage?

彖者，言乎象者也；爻者，言乎變者也。於象言象，則知爻者小象也；於爻言變，則知象者大象也。吉凶者，言乎其失得也；悔吝者，言乎其小疵也。吉凶悔吝生乎動，特有小大耳。無咎者，善補過也。本有過而能補，所以免咎。是故列貴賤者存乎位，齊小大者存乎卦。位不過六爻，卦不過陰陽，而吉凶所以不同者，惟其卦之義別耳；卦名定然後小大可見，爻彖可命。

The Great Treatise says: The彖 statement explains the overall image of the hexagram, while the line statement explains the changing aspects. Zhang Gen explains: Where the image is discussed, the term 'image' is used, indicating that the line statement belongs to the Small Image; where the line is discussed, the term 'change' is used, indicating that the彖 statement belongs to the Great Image. The Great Treatise says: 'Good fortune and misfortune' refer to gains and losses; 'regret and hardship' refer to minor faults. Zhang Gen says: Good fortune, misfortune, regret, and hardship all arise from movement, differing only in degree of severity. The Great Treatise says: 'Therefore, the arrangement of rank depends on the line position, and the distinction of size depends on the hexagram.' Zhang Gen says: The line positions are only six, and the hexagram consists of only yin and yang. Yet the differences in good fortune and misfortune arise because each hexagram has its own meaning. Once the hexagram name is fixed, its size becomes evident, and the line statements and彖 statements can then be named accordingly.

辨吉凶者存乎辭。此彖爻之不可窮也，非辭則情不可見。憂悔吝者存乎介。欲無悔吝者，當辨之於早也。震無咎者存乎悔。易之為教莫大於此，悔則動而轉禍為福矣。是故卦有小大，辭有險易。惟其取象如何耳，取象不同，言大則易，言小則險。辭也者，各指其所之。此無事之時所以當玩其辭，然後有事之時能惟變所適。此章全明繫辭之意，學者不可不委曲盡心焉，毋以一端而取也。

The Great Treatise says: The distinction between good fortune and misfortune lies in the words. Zhang Gen explains: This is where the彖statements and line statements are insufficient; without words, the actual situation cannot be seen. The Great Treatise says: The concern for regret and hardship lies in the subtle details. Zhang Gen says: If one wishes to avoid regret and hardship, one should discern matters early. The Great Treatise says: The ability to be shaken yet avoid error lies in repentance. Zhang Gen says: There is no greater teaching in the Book of Changes than this; if one can repent, one can transform misfortune into good fortune with a single movement. The Great Treatise says: Therefore, hexagrams have small and great ones, and statements have dangerous and easy ones. Zhang Gen says: This depends on what image is taken; if a different image is taken, the great ones are spoken of in an easy manner, and the small ones are spoken of in a dangerous manner. The Great Treatise says: What is meant by 'statements' is that they each indicate the direction of affairs. Zhang Gen says: This is why, when there is no affair, one should ponder the hexagram and line statements, so that when there is an affair, one can respond flexibly according to the changes. This chapter thoroughly explains the purpose of the 'Great Treatise'; students of the Book of Changes must not fail to carefully reflect on it, and must not stop at a single point.

易與天地準，故能彌綸天地之道。此聖人體易以成能之事，所謂因陰陽以統天地也。仰以觀於天文，日月是也。俯以察於地理，山川是也。是故知幽明之故。觀日月之象則天明可知，察山川之形則地幽可見。原始反終，故知死生之說。始於震終於艮，則始終之說可知；始於復而萬物生，終於剝而萬物死，則死生之說可知。精氣為物，游魂為變，是故知鬼神之情狀。生生死死，往來乎天地之間耳；精氣之聚而為生，散而為死，則以鬼神之情亦與人同而已。

The Great Treatise says: The Book of Changes is in harmony with heaven and earth, thus it can encompass and connect the principles of heaven and earth. Zhang Gen explains: This passage speaks of the sage who understands the principles of the Book of Changes and thus accomplishes all things, that is, governing heaven and earth by following yin and yang. The Great Treatise says: Looking up to observe the patterns of heaven. Zhang Gen says: This refers to the sun and moon. The Great Treatise says: Looking down to examine the patterns of earth. Zhang Gen says: This refers to mountains and rivers. The Great Treatise says: Therefore, one understands the nature of the hidden and the manifest. Zhang Gen says: Observing the patterns of the sun and moon, one can understand the manifest aspect of heaven; examining the forms of mountains and rivers, one can see the hidden aspect of earth. The Great Treatise says: Investigating the beginning and tracing back to the end, thus understanding the principles of life and death. Zhang Gen says: Starting from the Zhen trigram and ending with the Gen trigram, the principle of continuity is understood; starting from the Fu trigram and the birth of all things, ending with the Bo trigram and the death of all things, the principle of life and death is thus understood. The Great Treatise says: The vital energy gathers to form things, the wandering soul disperses to become change, thus understanding the nature of ghosts and spirits. Zhang Gen says: Life and death are merely moving back and forth within heaven and earth; when vital energy gathers, it becomes life; when it disperses, it becomes death. Thus, the nature of ghosts and spirits is no different from that of humans.

與天地相似，故不違。觀於易而知二者，則與天地相似矣，故莫之或違。知周乎萬物而道濟天下，故不過。與天相似，則知周乎萬物矣，故能以其道濟天下而莫之或過。旁行而不流。不過者經也，旁行者權也。樂天知命，故不憂。順天之數故。安土敦乎仁，故能愛。體地之徳故。範圍天地之化而不過。若然者，非特不違而已，又有以裁成其道。曲成萬物而不遺。非特不過而已，又有以輔相其宜。通乎晝夜之道而知。惟其能裁成輔相，故不違消息進退之理，此其所以無違過也。故神無方而易無體。變化不測，故曰無方；數所不及者，體而用之，故曰無體。

The Great Treatise says: The sage is similar to heaven and earth, so he does not contradict them. Zhang Gen explains: When one understands from the Book of Changes the matters of the hidden and the bright, of death and life, he becomes similar to heaven and earth, so there is nothing to contradict. The Great Treatise says: Wisdom pervades all things and the way he follows can help the world, so there is no excess or deficiency. Zhang Gen says: To be similar to heaven, wisdom pervades all things, so he can use his way to help the world without error. The Great Treatise says: He is flexible and adaptable without being unrestrained. Zhang Gen says: What does not err is the 'Classic', and what is flexible and adaptable is the 'Principle'. The Great Treatise says: He delights in the way of heaven, understands the mandate of heaven, so he is not worried. Zhang Gen says: Because he follows the fixed order of heaven. The Great Treatise says: He is content with his situation and sincere in benevolence, so he can love others. Zhang Gen says: Because he embodies the virtue of earth. The Great Treatise says: He nurtures all things under heaven and earth without error. Zhang Gen says: One who can do this does not merely avoid contradiction, but can further regulate and complete the way of heaven and earth. The Great Treatise says: He completes all things in a winding way, not missing any. Zhang Gen says: This is not only without error, but can further assist and harmonize with the proper way of all things. The Great Treatise says: He understands the principle of the alternation of day and night and knows it clearly. Zhang Gen says: Just because he can regulate and assist, he does not contradict the constant principles of decrease and increase, advance and retreat. This is why he neither contradicts nor has excess or deficiency. The Great Treatise says: Therefore, the spirit has no fixed place, and the Book of Changes has no fixed form. Zhang Gen says: Because it is changeable and unpredictable, it is said to be 'without fixed place'; it can also comprehend and apply what numbers cannot reach, so it is said to be 'without fixed form'.

一陰一陽之謂道。體而用之，寓於卦象者也，有所存焉，此易之所以為體而萬物之本也。繼之者善也。功用益顯，四徳是已。成之者性也。人皆具，惟是君子為能黙而該之。仁者見之謂之仁，知者見之謂之知，百姓日用而不知，故君子之道鮮矣。此易所以不得不興，而聖人所以不得不作也。顯諸仁，藏諸用。所以列於卦故曰顯，所以寓於此故曰藏。鼓萬物而不與聖人同憂。與民同患之道盡矣。盛徳大業至矣哉。內外兼進之謂。

The Great Treatise says: The alternation of yin and yang is called the Dao. Zhang Gen explains: By observing and applying it, it is embodied in the hexagrams; there is indeed something real within it, which is why the Book of Changes can serve as the fundamental principle and the origin of all things. The Great Treatise says: To follow it is to be good. Zhang Gen says: The function becomes more evident, and the four virtues of originality, prosperity, benefit, and constancy are thus manifested. The Great Treatise says: To realize it is to have nature. Zhang Gen says: Everyone possesses it, but only the gentleman can silently encompass it entirely. The Great Treatise says: The benevolent person sees it and calls it benevolence; the wise person sees it and calls it wisdom; common people use it daily without realizing it, so the way of the gentleman is rarely seen. Zhang Gen says: This is precisely why the Book of Changes had to arise and why the sages had to compose it. The Great Treatise says: To manifest benevolence and to conceal function. Zhang Gen says: It is arranged in the hexagrams, so it is called 'manifest'; it is contained within them, so it is called 'concealed'. The Great Treatise says: It stimulates all things without sharing the toil and worry of the sages. Zhang Gen says: The principle of sharing the hardships of the people is fully explained here. The Great Treatise says: Supreme virtue and great achievements, reaching the ultimate. Zhang Gen says: This refers to the simultaneous advancement of both internal and external aspects.

富有之謂大業。廣大悉備之謂。日新之謂盛徳。萬世無之謂。生生之謂易。變化無窮之謂。成象之謂乾。凡所以造始者皆乾之道。效法之謂坤。凡所以成終者皆坤之道。極數知來之謂占。通天下之性是也。通變之謂事。成天下之務事也。陰陽不測之謂神。凡不疾而速、不行而至、使民由之而不知者是也。聖人體此以治天下則天下治，帝王之能事畢矣。

The Great Treatise says: "What is everywhere present is called great achievement." Zhang Gen explains: "This means being vast and encompassing all things." The Great Treatise says: "Renewing every day is called great virtue." Zhang Gen says: "This means endless continuation for all generations." The Great Treatise says: "Continuous generation without end is called the Book of Changes." Zhang Gen says: "This means change has no limit." The Great Treatise says: "What creates forms is called Qian." Zhang Gen says: "Whatever begins something is under the way of Qian." The Great Treatise says: "What imitates established methods is called Kun." Zhang Gen says: "Whatever completes and concludes is under the way of Kun." The Great Treatise says: "To exhaust the divination numbers and foresee the future is called divination." Zhang Gen says: "This is the nature that connects all things under heaven." The Great Treatise says: "To understand change is called affairs." Zhang Gen says: "To accomplish the affairs of the world is called 'affairs'." The Great Treatise says: "What is beyond yin and yang is called spirit." Zhang Gen says: "Whatever is not hasty yet swift, does not move yet arrives, and leads the people without them knowing how, is spirit." The sage understands this principle to govern the world, and thus the world is well governed, and all the things a ruler can do are fully accomplished.

夫易廣矣大矣。以言乎逺則不御。極乎形氣之表。以言乎邇則靜而正。黙而該之。以言乎天地之間則備矣。所以有廣大之號。夫乾，其靜也専。無所待也。其動也直。無所屈也。是以大生焉。無所不覆。夫坤，其靜也翕。收斂之謂。其動也闢。敷施之謂。是以廣生焉。無所不載。

The Great Treatise says: The Book of Changes is truly vast and broad. In distant terms, it has no obstruction. Zhang Gen explains: It extends beyond the form and vital transformation. The Great Treatise says: In near terms, it is quiet and upright. Zhang Gen says: It silently encompasses everything. The Great Treatise says: In terms of the space between heaven and earth, it includes everything. Zhang Gen says: This is why it is called 'vast and broad'. The Great Treatise says: The Qian trigram, when still, is focused. Zhang Gen says: It has no waiting. The Great Treatise says: When it moves, it is upright and firm. Zhang Gen says: It has no bending. The Great Treatise says: Thus it produces 'greatness'. Zhang Gen says: It covers everything. The Great Treatise says: The Kun trigram, when still, is closed. Zhang Gen says: This means gathering in. The Great Treatise says: When it moves, it opens up. Zhang Gen says: This means spreading out and giving. The Great Treatise says: Thus it produces 'broadness'. Zhang Gen says: It carries everything.

廣大配天地，變通配四時，陰陽之義配日月，易簡之善配至徳。聖人之徳如此。能廣大則可以配天地，能變通則可以配四時，能顯晦則可以配日月，能易簡則可以配乾坤之至徳。廣大者，易之道也；變通者，易之用也；陰陽之義，易之行也；易簡之善，易之徳也。此皆成位之事。

The Great Treatise says: The Book of Changes is vast and broad, matching the heavens and earth; its ability to change and adapt matches the four seasons; its meaning of yin and yang matches the sun and moon; its simple and elegant virtue matches the highest virtue. Zhang Gen explains: This is how the sage's virtue is. Being vast and broad allows one to match heaven and earth; being able to change and adapt allows one to match the four seasons; being able to be clear or obscured allows one to match the sun and moon; being simple and elegant allows one to match the highest virtue of heaven and earth. The so-called vastness is the way of the Book of Changes; the so-called adaptability is its use; the so-called meaning of yin and yang is its operation; the so-called simplicity and elegance is its virtue. All of these belong to the matter of 'establishing position'.

子曰：易其至矣乎。不能以有加矣。夫易，聖人所以崇徳而廣業也。聖人體易而法天地之大，故徳崇而業廣，極髙明而道中庸之謂。知崇，北方之物也。禮卑，南方之物也。崇效天，卑法地。崇效天，故徳言崇；卑法地，故業言廣。天地設位，而易行乎其中矣。由而不知之耳。成性存存，道義之門。惟聖人謂能成其性而存之。惟能成性，故能存其所存；能存其所存，故道義之所自出也。道，天也，故徳以之崇；義，人也，故業以之廣。知夫天之所為，則知人之所為至矣，故聖人重禮治。此章言聖人立爻象之教不可違如此，學者當擬之而言、議之而動，則可以成變化之道，無施不可也。

The Great Treatise says: Confucius said, The Book of Changes is perhaps the ultimate. Zhang Gen explained: There is nothing more to add to it. The Great Treatise says: The Book of Changes is used by the sage to cultivate virtue and expand his undertakings. Zhang Gen said: The sage observes the principles of the Book of Changes and follows the vastness of heaven and earth, thus achieving lofty virtue and broad undertakings, which is what the Doctrine of the Mean refers to as 'attaining the highest excellence while following the middle way'. The Great Treatise says: Wisdom should be lofty. Zhang Gen said: Wisdom belongs to the north. The Great Treatise says: Ritual should be humble. Zhang Gen said: Ritual belongs to the south. The Great Treatise says: Lofty virtue follows heaven, and humility follows earth. Zhang Gen said: Lofty virtue follows heaven, so the term 'lofty' is used for virtue; humility follows earth, so the term 'broad' is used for undertakings. The Great Treatise says: Heaven and earth have set their positions, and the Book of Changes operates within them. Zhang Gen said: People merely follow it without realizing it. The Great Treatise says: To realize one's nature and always preserve it, this is the gate of righteousness. Zhang Gen said: Only the sage can talk about realizing his nature and preserving it. Only those who can realize their nature can preserve what should be preserved; those who can preserve what should be preserved become the source of the emergence of righteousness. 'Dao' belongs to heaven, so virtue relies on it to be lofty; 'yi' belongs to human beings, so undertakings rely on it to be broad. Understanding what heaven does, one can fully understand what humans should do, so the sage values governing the world with ritual. This chapter discusses how the sage's teaching of the yao images is so unchangeable; those who study the Book of Changes should first consider and then speak, first deliberate and then act, thus achieving the way of change, and thus be able to do anything smoothly.

聖人有以見天下之賾，而擬諸其形容。八卦是也。象其物宜。六十四卦是也。是故謂之象。聖人有以見天下之動，而觀其□通，以行其典禮，繋辭焉以斷其吉凶，是故謂之爻。象言其體，非極深不足以知之；爻言其用，非研幾不足以知之。典禮者，治人之具也。

The Great Treatise says: The sage is able to see the most hidden and intricate matters under heaven, and uses hexagrams to resemble their forms. Zhang Gen explains: This refers to the Eight Trigrams. The Great Treatise says: It symbolizes the appropriate conditions of various things. Zhang Gen says: This refers to the sixty-four hexagrams. The Great Treatise says: Therefore it is called 'Xiang' (image). The sage is able to see the changes of all things under heaven, observe the principles of their convergence and flow, and use them to establish rituals and regulations. He also ties on words to determine good and bad fortune, so it is called 'Yao' (line) (the character following 'its' is missing, and should be 'Hui'). Zhang Gen says: 'Xiang' refers to the essence, and one cannot understand it without probing the principles to their depths; 'Yao' refers to function, and one cannot understand it without thoroughly examining the subtle nuances. What is called ceremony and ritual is a tool for governing people.

言天下之至賾而不可惡也。故當擬之而後言。言天下之至動而不可亂也。故當議之而後動。擬之而後言。象有定體，故言擬。議之而後動。爻主通變，故言議。擬議以成其變化。神而明之謂。

The Great Treatise says: Discussing the most profound and complex matters of the world without causing aversion. Zhang Gen explains: Therefore, one should first consider and contemplate before speaking. The Great Treatise says: Discussing the most chaotic and changing affairs of the world without causing confusion. Zhang Gen says: Therefore, one should first deliberate and discuss before acting. The Great Treatise says: First consider and then speak. Zhang Gen says: Because things have fixed forms, the character 'ni' is used. The Great Treatise says: First deliberate and then act. Zhang Gen says: Because the yao (lines) are based on communication and change, the character 'yi' is used. The Great Treatise says: Relying on consideration and deliberation to achieve change. Zhang Gen says: This is called being mysterious yet clear.

鳴鶴在陰，其子和之；我有好爵，吾與爾靡之。道行於妻子，則無所往而不行矣。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？此所以貴乎擬議，五十而學易可以無大過如此。

The Great Treatise cites the line statement of Zhongfu hexagram nine two: A crane calls in the shade of a tree, its young crane responds; I have a good cup of wine, and I wish to share it with you. Zhang Gen explains: If a person's way can be practiced in his wife and children, then it can be practiced anywhere. The Great Treatise says: Confucius said, when a gentleman stays in his own house and speaks, his words are good, then even those a thousand miles away will respond, how much more so those nearby? When a gentleman stays in his own house and speaks, his words are not good, then even those a thousand miles away will turn away, how much more so those nearby? Words spoken from oneself are applied to the people; actions started from near will be seen far away. Words and deeds are the door hinges and crossbow mechanism of a gentleman; when the door hinge or crossbow mechanism is set in motion, honor and disgrace are determined by it. Words and deeds are what a gentleman uses to move heaven and earth, how can they not be cautious? Zhang Gen said: This is the reason for valuing 'imagination' (or 'conjecture'). Confucius said that at fifty one can study the Book of Changes without making great mistakes, the reason for this is here.

同人先號咷而後笑。子曰：君子之道，或出或處，或黙或語；二人同心，其利斷金；同心之言，其臭如蘭。此又明言行不必同也，惟其當而已矣。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。此又明慎則寡過之義，故曰以約失之者鮮矣。

The Great Treatise cites the fifth line of the Hexagram of Mutual Harmony, saying: To harmonize with others, first grieve and weep bitterly, then laugh and rejoice. Confucius said: A gentleman's way of dealing with the world involves sometimes taking office and sometimes retreating, sometimes remaining silent and sometimes speaking out; when two people are of the same mind, their sharpness is sufficient to cut through metal; words spoken in harmony have the fragrance of orchids. Zhang Gen explained: This further illustrates that speech and action need not be forced to be the same, as long as they are appropriate. The Great Treatise cites the first line of the Hexagram of Great Excess, saying: Using white reed grass as a mat, there will be no mistake. Confucius said: Placing it directly on the ground would already be sufficient, so why use reed grass as a mat? Where would there be any mistake? This is the height of caution. Reed grass itself is very thin, yet its use can be very significant; if this caution is carried through, nothing will be lost. Zhang Gen said: This further illustrates the principle that caution leads to fewer mistakes, so Confucius said, 'Those who are restrained are rarely at fault.'

勞謙君子，有終吉。謙之利如此，可不務乎？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。此又明寡過之義，不特以慎為美，又以謙為貴。亢龍有悔。亢之害如此，可不戒乎？子曰：貴而無位，髙而無民，賢人在下位而無輔，是以動而有悔也。此不謙之咎。

The Great Treatise cites the line statement of the卦 of Humility, line nine three: A diligent and humble gentleman can achieve a good ending and is auspicious. Zhang Gen explains: The benefits of humility are so great, how could one not strive to do it? The Great Treatise says: Confucius said, exerting effort without boasting, having merit without claiming virtue, this is the extreme of sincerity and thickness; it refers to those who take their own merit but are willing to be below others. Virtue should be grand, propriety should be respectful; so called humility is to be extremely respectful in order to maintain one's position. Zhang Gen says: This also illustrates the principle of avoiding mistakes, not only valuing caution but also valuing humility. The Great Treatise cites the line statement of the卦 of Heaven, line upper nine: A dragon that has risen to the extreme will have regret. Zhang Gen says: The harm of being overly exalted is so great, how could one not be cautious? The Great Treatise says: Confucius said, having a high position but no actual duties, being in a high place but without the people, the virtuous are in lower positions and there is no one to assist, thus any action will bring regret. Zhang Gen says: This is the mistake caused by not being humble.

不出戶庭，無咎。藉用白茅，慎以往也；不出戶庭，慎以居也。子曰：亂之所生也，則言語以為階。君不密則失臣，臣不密則失身，幾事不密則害成，是以君子慎密而不出也。此又明寡過之義，不獨以謙為貴，又當以不密為戒。

The Great Treatise cites the Line Statement of the first line of the节卦 (Gathered Joy) saying: "Not leaving one's courtyard gate will not lead to fault." Zhang Gen explains: "Using white reed grass as a mat refers to being cautious in action; not leaving the courtyard refers to being cautious in residence." The Great Treatise says: Confucius said, "Disasters often arise from careless speech." A ruler's careless speech will lose his ministers; a minister's careless speech will lead to his death; secret matters disclosed carelessly will cause harm. Therefore, a gentleman guards secrecy and does not speak carelessly. Zhang Gen says: This further illustrates the principle of avoiding mistakes. It is not only valuable to be humble, but also one should regard "careless speech" as a warning.

子曰：作易者其知盜乎？易曰：負且乘，致冦至。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；上慢下暴，盜思伐之矣。慢藏誨盜，冶容誨淫。易曰：負且乘，致冦至。盜之招也。此又明寡過之義，當以任重為終，故曰仁以為己任，不亦重乎？知此則可以保天下國家矣。

The Great Treatise says: Confucius said, the person who composed the Book of Changes must have understood the psychology of thieves. The hexagram Jie (Dismissing) in the Book of Changes says, "Carrying goods while sitting on a carriage, leading to the arrival of bandits." Carrying goods is the work of a petty person, while riding in a carriage is the tool of a gentleman; a petty person sitting on a gentleman's carriage invites bandits to rob him. Being arrogant towards superiors and cruel towards inferiors invites bandits to attack him. Neglecting the guarding of property is like teaching people to steal; appearing seductive is like inviting people to commit lust. The Book of Changes says, "Carrying and riding, leading to the arrival of bandits," which is precisely how one invites bandits. Zhang Gen explained that this also illustrates the principle of avoiding wrongdoing, and should be summarized as "shouldering great responsibilities," so Zengzi said, "To take benevolence as one's responsibility, is it not a heavy task?" Understanding this principle allows one to preserve the world and the state.

聖人雖立象以盡意，而意有不可以言盡，故繋辭焉以盡其言；而言又有不可以窮，故卦爻之辭亦舉其大略耳，觸□而長之，然後易之道明。故聖人舉是數爻而廣喻之以為教，使學者知其□而期於自得也。如鳴鶴在陰其子和之，象以為中心願焉，而繋辭乃推言行之動天地；同人先號咷而後笑，象以為中直爾，而繋辭乃有出處語黙、斷金如蘭之義。故所貴乎觸□而長之者如此，學易者不可不知也。

Zhang Gen said: The sage, although setting up hexagrams to exhaust his mind, still finds that there are parts of his mind that cannot be fully expressed in words, so he adds statements to complete the expression. But words also have their limits, so the statements of the hexagrams and lines can only give a general idea. One must rely on the ability to infer from similar cases and expand upon them in order to understand the principles of the Book of Changes. (The three missing characters here are all supposed to be "类".) Therefore, the sage cites these line statements as examples to illustrate the principles, so that those who study the Book of Changes can learn to infer from one instance to many, and hope that they can understand it by themselves. For example, the line statement of Zhongfu Nine Two, "A crane calls in the shade, its young respond in harmony," the Xiao Xiang only says that this expresses an inner wish, but the Xi Ci Zhuan extends it to the idea that words and deeds are sufficient to move heaven and earth. Similarly, the line statement of Tong Ren Nine Five, "First crying and then laughing," the Xiao Xiang only says that this expresses being in the center and having a straightforward heart, but the Xi Ci Zhuan extends it to the meaning of being in the right place and keeping silent at the right time, two people with the same mind can cut through metal, and their fragrance is like orchids. This shows the value of inference and extension, which students of the Book of Changes should not be ignorant of.

子夏問巧笑倩兮、美目盻兮、素以為絢兮，而子曰繪事後素，固已出於詩人之意外矣；子夏又云禮後乎，又出於仲尼之意外，故曰起予者商也，始可與言詩已矣。葢六經俱然，不獨詩也，而易象尤重，此聖人所以至於韋編三絶而不知老之將至也。

Zhang Gen said: Zixia asked about the meaning of "A smile so charming, eyes so bright, white as the jade, yet adorned with colors," and Confucius answered "Painting after white," which already went beyond the original intention of the poet. Zixia then said, "Then rites come later," which went beyond Confucius's original meaning, so Confucius said, "It was Bo Shang who inspired me, now I can discuss the Book of Poetry with you." Perhaps the Six Classics are all like this, not only the Book of Poetry, but the Book of Changes especially emphasizes this point; this is why Confucius read the Book of Changes so much that he broke the leather thongs of the bamboo slips three times, yet was unaware of his own aging.

大衍之數五十，其用四十有九。案：朱子語類云，自大衍之數五十至再扐而後掛，便接乾之策二百一十有六，至可與佑神矣，為一節，是論大衍之數；自天一至地十，卻連天數五至而行鬼神也，為一節，是論河圖五十五之數。今其文間斷差錯，不相連接，舛誤甚明，是朱子之時節次已錯。今此本天一至十二十字移在第十章首，而天數五至而行鬼神也四十四字移在再扐而後掛之下，即朱子所見舛誤之本也。

The Great Treatise says: The number of the Great Derivation is fifty, but actually forty-nine are used. (Comment by the editors of the Siku Quanshu: Zhu Xi's "Yuliu" states that from "The number of the Great Derivation is fifty" to "After twice separating and hanging," the text should directly continue with "The measure of the Qian trigram is two hundred and sixteen" up to "It can assist the gods." This section discusses the number of the Great Derivation. From "Heaven one" to "Earth ten," and then continuing with "The heavenly number is five" to "and thus the movement of ghosts and spirits is achieved," this is another section discussing the number of the Yellow River Chart, which is fifty-five. Now this passage is fragmented and disordered, with parts not connecting properly, and the errors are very obvious. It is evident that the order of the chapters was already wrong during Zhu Xi's time. This current edition has moved the twenty characters from "Heaven one" to "Earth ten" to the beginning of the tenth chapter, and has also moved the forty-four characters from "The heavenly number is five" to "and thus the movement of ghosts and spirits is achieved" below "After twice separating and hanging," which is exactly the same as the disordered version Zhu Xi saw.)

聖人既為卦爻以示教，而卦可以藏往而不可以知來，爻有變動，學者莫知所適，故作為大衍之法，質諸神明以求之，使天下後世有考焉。四時十二月二十四氣與閏，是為一歲，天地之功成而萬物之理備矣，所以成變化而行鬼神數具此矣，而蓍之數適合焉，是謂神物，故取而用之。

Zhang Gen said: The sages have already created hexagrams and lines to demonstrate and teach people. However, hexagrams can only record past events and cannot foresee the future, and lines are ever-changing. Therefore, those who study the Book of Changes have no clear direction. Hence, they created the method of large derivation with yarrow stalks, seeking answers from the divine, so that future generations may have a standard. The four seasons, twelve months, twenty-four solar terms, and the leap month together make up a year. The functions of heaven and earth are thus completed, and the principles of all things are fully explained. Therefore, the number that can produce change and movement, and govern ghosts and spirits, is all contained here. The number of yarrow stalks coincides exactly with it, which is called "a divine object," so it is used.

分而為二以象兩。陰陽。掛一以象三。沖氣。揲之以四以象四時。歸竒於扐以象閏，五歲再閏，故再扐而後掛。言再扐而後掛，則未扐不掛可知；言掛而後言揲，則掛亦揲可知。凡分揲無常數，惟意所欲，質諸鬼神之義也。葢分而為二，先揲其左，後揲其右，皆扐其餘數，謹其竒耦，然後掛而又四揲之，觀其餘以定陰陽焉。三者皆竒為老陽，皆耦為老陰，一竒為少陽，一耦為少陰。凡三揲而成六爻。是四營而成易，十有八變而成卦，每卦每爻必具三才之義也。故曰萬物負陰而抱陽，沖氣以為和，此不易之理也，後世以三金易之，葢得其遺法。

The Great Treatise says: divide the yarrow stalks into two bundles to symbolize the two principles of heaven and earth. Zhang Gen explains: this is yin and yang. The Great Treatise says: draw out one stalk and hang it to symbolize the three elements. Zhang Gen says: this one stalk symbolizes the harmonious qi. The Great Treatise says: count four by four to symbolize the four seasons; the remaining stalks are clasped between the fingers to symbolize the leap month; in five years there are two leap months, so two clasps are made and then hung. Zhang Gen says: since it says 'clasp twice and then hang,' it shows that before clasping, nothing is hung; since it first mentions hanging and then counting, it shows that after hanging, counting is done. All division and counting have no fixed numbers, depending entirely on the present moment, which is precisely the way of consulting spirits. Probably, first divide into two bundles, first count the left, then the right, clasping the remainders, carefully distinguishing odd and even, then hang them and count four by four, determining yin and yang by the remaining number. If all three are odd, it is old yang; if all are even, it is old yin; if one is odd, it is young yang; if one is even, it is young yin. In total, three counts form one line, eighteen counts form six lines. This is what the Great Treatise says: four steps complete one count, eighteen counts complete one hexagram, and each hexagram and each line must necessarily contain the meaning of the three elements. Therefore, the Tao Te Ching says 'all things carry yin and embrace yang, and the harmonious qi is formed between them,' which is an unchanging principle; later generations substituted three copper coins for the yarrow stalks, probably still following this ancient method.

天數五，地數五，五位相得而各有合。五行之所以生成也。天數二十有五，地數三十，凡天地之數五十有五，此所以成變化而行鬼神也。故乾坤之策取焉。乾之策二百一十有六。參天之數。坤之策百四十有四。兩地之數。凡三百有六十，當期之日。乾坤之策，乾坤一爻共六十□，此一候之數也，故三百六十日而七十二候具焉。二篇之策萬有一千五百二十，當萬物之數也。大衍之數所以五十也。

The Great Treatise says: Heaven has five numbers, Earth has five numbers, and the five positions are paired two by two, each having their union. Zhang Gen explains: This is the principle of the generation of the Five Phases. The Great Treatise says: The total of Heaven's numbers is twenty-five, and the total of Earth's numbers is thirty, making a total of fifty-five for Heaven and Earth together. This is why it can accomplish transformation and movement of ghosts and spirits. Zhang Gen says: Therefore, the number of lines in the hexagrams of Qian and Kun are derived from here. The Great Treatise says: The number of lines for Qian is two hundred and sixteen. Zhang Gen says: That is the number of 'ascending to Heaven'. The Great Treatise says: The number of lines for Kun is one hundred and forty-four. Zhang Gen says: That is the number of 'two Earths'. The Great Treatise says: Together they total three hundred and sixty, which corresponds to the number of days in a year. Zhang Gen says: The number of lines for Qian and Kun, with each of them having one line combined, is sixty (the character here is missing), which corresponds to the number of a seasonal period; thus, in three hundred and sixty days there are seventy-two seasonal periods. The Great Treatise says: The total number of lines in the upper and lower parts of the Book of Changes is eleven thousand five hundred and twenty, which corresponds to the number of all things. Zhang Gen says: This is why the number of the Great Derivation is fixed at fifty.

是故四營而成易。陰陽體也。十有八變而成卦。陰陽之氣全。八卦而小成，四時具矣。引而伸之，觸類而長之，萬物之義備矣，天下之能事畢矣。體常盡交，無所不過之謂。顯道。所謂顯諸仁。神徳行。所謂藏諸用。是故可與酬酢，可與佑神矣。所謂鼓萬物而不與聖人同憂。

The Great Treatise says: Therefore, four procedures complete one transformation. Zhang Gen explains: This is the form of yin and yang. The Great Treatise says: Eighteen transformations complete one hexagram. Zhang Gen says: At this point, the qi of yin and yang is complete. The Great Treatise says: The Eight Trigrams are small achievements. Zhang Gen says: At this point, the four seasons are complete. The Great Treatise says: By extending it, and applying it to similar cases, the principles of all things are complete, and all things that can be done under heaven are done. Zhang Gen says: This refers to investigating the constant way and exhausting the mutual interactions, so as to be universally penetrating. The Great Treatise says: It manifests the Dao. Zhang Gen says: This is what was previously mentioned, "Manifesting it through benevolence." The Great Treatise says: It makes virtue profound and mysterious. Zhang Gen says: This is what was previously mentioned, "Hiding it in its use." The Great Treatise says: Therefore, it can be used to respond and interact, and can be relied upon to assist the divine. Zhang Gen says: This is what was previously mentioned, "It stimulates all things without sharing the worries of the sages."

大衍之數，一歲之數也；天地之數，五行之數也。五行運於天地之間，五歲而小成，故五日為一候，三候而為氣，二氣而為月，三氣而為節，二節而為時。四時八節，十二月二十四氣，凡七十二候，三百六十日而歲功成，乾坤之策具於此矣。故欲求乾坤之策以合大衍之數，當自五位始。所謂五位者，有相得之位，有相合之位；其相得也分而為十日，其相合也分而為十二辰。

Zhang Gen said: The great derivation number is the number of a year, and the number of heaven and earth is the number of the Five Phases. The Five Phases move within heaven and earth, completing a small cycle in five years. Therefore, five days make a wait, three waits make an energy, two energies make a month, three energies make a node, and two nodes make a time. With four seasons, eight nodes, twelve months, and twenty-four solar terms, there are in total seventy-two waits and three hundred and sixty days, completing the function of a year. The numbers of Qian and Kun are all included here. Therefore, if one wishes to seek the numbers of Qian and Kun to match the great derivation number, one should start from the "five positions." The five positions have positions that are mutually paired and positions that are mutually combined. The mutually paired ones are divided into the ten heavenly stems, and the mutually combined ones are divided into the twelve earthly branches.

故天一與地二相得而為甲乙，天三與地四相得而為丙丁，天五與地六相得而為戊己，天七與地八相得而為庚辛，天九與地十相得而為壬癸，此屬乎天者也。其相合也，天一生水於亥子而地六成之，地二生火於巳午而天七成之，天三生木於寅卯而地人成之，地四生金於申酉而天九成之，天五生土於辰戌丑未而地十成之，此屬乎地者也。

Zhang Gen said: Therefore, the Heaven One and Earth Two combine to form Jia and Yi, Heaven Three and Earth Four combine to form Bing and Ding, Heaven Five and Earth Six combine to form Wu and Ji, Heaven Seven and Earth Eight combine to form Geng and Xin, Heaven Nine and Earth Ten combine to form Ren and Gui. These belong to the Heaven side. As for the mutual combinations: Heaven One generates water at the positions of Hai and Zi, and Earth Six completes it; Earth Two generates fire at the positions of Si and Wu, and Heaven Seven completes it; Heaven Three generates wood at the positions of Yin and Mao, and Earth Eight completes it; Earth Four generates metal at the positions of Shen and You, and Heaven Nine completes it; Heaven Five generates earth at the positions of Chen, Xu, Chou, and Wei, and Earth Ten completes it; these belong to the Earth side.

天道常動，故十曰運乎上；地道常靜，故十二辰定乎下。天地相合而後萬物生於甲子而終於癸亥，凡六十日而一周，是謂之策。此五日所以為一候，而五歲所以為小成，故曰天六地五，數之常也。水木土屬乎天地之間，天合其生成之數，凡六六六三十六，故乾之策二百一十有六；火金屬乎地，是謂兩地，合其生成之數，凡四四六二十四，故坤之□一百四十有四；合乾坤之□三百有六十，是謂一歲，而萬物所以終始可見矣，變化之所以成、鬼神之所以行可知矣。

Zhang Gen said: The heavenly way is always in motion, so the ten heavenly stems move above; the earthly way is always still, so the twelve earthly branches are fixed below. When heaven and earth combine, all things begin to grow from Jiazi and end at Guihai, making a total of sixty days for one cycle, which is called "cè." This is why five days make one waiting period and five years make a small completion, so the "Guoyu" says "heaven has six, earth has five" is the regular number. Water, wood, and earth are between heaven and earth. Heaven combines their generating numbers, which are six plus six plus six, totaling thirty-six, so the number of cè for Qian is two hundred and sixteen; fire and metal belong to earth, which is called "two earths." Combining their generating numbers, they are four plus four plus six, totaling twenty-four, so the number of cè for Kun is one hundred and forty-four (the two missing characters are both "cè"). The total number of cè for Qian and Kun is three hundred and sixty, which is one year. Thus, all things have a beginning and an end, and the transformation that generates and the movement of ghosts and spirits are understood.

子曰：知變化之道者，其如神之所為乎。易有聖人之道四焉。濟世之具。以言者尚其辭。謂繋辭。以動者尚其變。謂爻。以制器者尚其象。謂卦。以卜筮者尚其吉。謂大衍。是以君子將有為也，將有行也，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。此卜筮所以當之。

The Great Treatise says: Confucius said, those who understand the principle of change also understand the workings of the divine. The Book of Changes contains four principles of the sage's way. Zhang Gen explained: this refers to tools for benefiting the world. The Great Treatise says: those who use it for speech value its words. Zhang Gen said: this refers to the Great Treatise. The Great Treatise says: those who use it for action value its change. Zhang Gen said: this refers to the lines. The Great Treatise says: those who use it for making objects value its symbolic images. Zhang Gen said: this refers to the hexagrams. The Great Treatise says: those who use it for divination value its prophecies of good or ill. Zhang Gen said: this refers to the method of divining with yarrow stalks. The Great Treatise says: therefore, when a gentleman is about to act or take action, he consults it, and it responds with words. Its response is as quick as an echo, whether far or near, deep or hidden, it can foresee future events. If it is not the most subtle thing in the world, who could achieve this? Zhang Gen said: this passage corresponds exactly to the section on divination.

參伍以變。謂九六。錯綜其數。謂六爻。通其變，遂成天地之文。謂八卦。極其數，遂定天下之象。謂六十四卦。非天下之至變，其孰能與於此。此制器所以當之。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。此言動者所以當之。

The Great Treatise says: They change and interact in groups of three and five. Zhang Gen explains: This refers to the old yang number nine and the old yin number six. The Great Treatise says: Interweave and combine their numbers. Zhang Gen says: This refers to the six lines. The Great Treatise says: Connect and comprehend their changes, thus forming the brilliance of heaven and earth. Zhang Gen says: This refers to the Eight Trigrams. The Great Treatise says: Exhaust the numbers, thus establishing the forms of all things under heaven. Zhang Gen says: This refers to the sixty-four hexagrams. The Great Treatise says: If it is not the most changeable thing in the world, who could achieve this? Zhang Gen says: This passage corresponds to the "making of tools" section. The Great Treatise says: The Book of Changes has no thoughts, no actions, is still and motionless, but once it receives a response, it comprehends all affairs under heaven. If it is not the most marvelous thing in the world, who could achieve this? Zhang Gen says: This passage corresponds to the "speech" and "action" sections.

夫易，聖人之所以極深而研幾也。唯深也，故能通天下之至。此之謂至變。唯幾也，故能成天下之務。唯神也，故不疾而速，不行而至一。此之謂至神。子曰：易有聖人之道四焉者，此之謂也。此章明易之謂教有聖人之道四焉，據上諸事，是亦聖人所以應世之跡而已。以言者尚其辭，以動者尚其變，至神之事也；以制器者尚其象，至變之事也；以卜筮者尚其占，知精之事也。唯深也故能通天下之志，遂知來物；唯幾也故能成天下之務，遂成天下之文，定天下之象；唯神也故不疾而速，不行而至，遂通天下之故。

The Great Treatise says: The Book of Changes is used by the sage to explore profound mysteries and examine subtle details. Because it is profound, it can connect the hearts of people throughout the world. Zhang Gen explains: This is called "ultimate change." The Great Treatise also says: Because it understands subtle details, it can accomplish all affairs under heaven. Because it is marvelous, it does not rush yet moves swiftly, does not walk yet reaches its destination. Zhang Gen says: This is called "ultimate marvel." The Great Treatise says: Confucius spoke of "The Book of Changes contains four ways of the sage." This refers to these. Zhang Gen says: This chapter clarifies that the Book of Changes, as a means of education, contains four ways of the sage. According to the above statements, they are merely traces left by the sage in dealing with the world. Speaking with emphasis on words belongs to "ultimate marvel"; acting with emphasis on change belongs to "ultimate change"; making objects with emphasis on images belongs to "ultimate precision." Because it is profound, it can connect the hearts of people throughout the world and foresee future events; because it understands subtle details, it can accomplish all affairs under heaven, achieve the brilliance of the world, and establish the forms of the world; because it is marvelous, it does not rush yet moves swiftly, does not walk yet reaches its destination, and connects all events throughout the world.

天一，地二，天三，地四，天五，地六，天七，地八，天九，地十。案：漢書律曆志引天一至地十二十字，與天數五至而行鬼神也四十四字相連，則班固時此簡猶未錯也。朱子本義雲此簡本在第十章之首，則已舛誤矣，此本亦仍錯簡之舊。此重言卦蓍之妙用。

The Great Treatise says: Heaven is one, Earth is two, Heaven is three, Earth is four, Heaven is five, Earth is six, Heaven is seven, Earth is eight, Heaven is nine, Earth is ten. (Comment by the editors of the Siku Quanshu: When cited in the "Book of Han · Laws and Calendars," these twenty characters from "Heaven one" to "Earth ten" were connected with the forty-four characters from "Heavenly numbers five" to "and thus the actions of ghosts and spirits are carried out." This shows that at the time of Ban Gu, this bamboo slip had not yet become disordered. Zhu Xi's "Original Meaning of the Zhou Changes" says that this bamboo slip originally began the tenth chapter, which already indicated disorder; this version still follows the old disorder.) Zhang Gen says: This passage is again explaining the miraculous function of the hexagrams and the yarrow stalks.

子曰：夫易何為者也？夫易開物成務。陽以開之，陰以成之。冒天下之道，如斯而已者也。不離五行之數。是故聖人以通天下之志，以定天下之業，以斷天下之疑。萬物莫能逃數故也。謂明卦爻之辭所以辨吉凶者也。

The Great Treatise says: Confucius explained that the Book of Changes is used for opening up all things and accomplishing affairs. Zhang Gen explained that it uses Yang to open them up and Yin to accomplish them. The Great Treatise says: it encompasses all the principles under heaven, and that is all. Zhang Gen said: all of this depends on the numbers of the Five Phases. The Great Treatise says: thus the sage uses it to unify the aspirations of people throughout the world, to establish the affairs of the world, and to decide the doubts of the world. Zhang Gen said: because all things cannot escape this number. This refers to understanding how the words of the hexagrams and lines are used to distinguish between good fortune and misfortune.

是故蓍之徳圓而神。蓍之知來故曰圓，通變故曰神。卦之徳方以知。卦有定體故曰方，預言禍福故曰知。六爻之義易以貢。觀其動爻以斷吉凶。聖人以此洗心，退藏於宻，吉凶與民同患。既有以藏往，又有以洗心退藏，待其來則應之。神以知來，知以藏往，其孰能興於此哉。古之聰明睿知神武而不殺者夫。有以研萬物之理然後有以藏往，有以窮萬物之數然後有以知來，可以通天下之志、定天下之業、□天下之疑，使天下萬世服從聽順而不知所以然，是以謂之神武而不殺者也。

The Great Treatise says: The virtue of the yarrow stalks is round and profound. Zhang Gen explains: The yarrow stalks can foresee the future, hence they are called "round"; they can comprehend changes, hence they are called "profound." The Great Treatise says: The virtue of the hexagrams is square and wise. Zhang Gen says: The hexagrams have fixed forms, hence they are called "square"; they can predict calamity and fortune, hence they are called "wise." The Great Treatise says: The significance of the six lines lies in their ability to contribute to the determination of good and evil according to change. Zhang Gen says: This is by observing the changing lines to determine good and evil. The Great Treatise says: The sages use these to purify their minds and retreat into secrecy; good fortune, ill fortune, calamity, and blessing are shared with the people. Zhang Gen says: He can preserve the past and purify his mind and retreat into secrecy, and when matters arise, he can respond appropriately. The Great Treatise says: To foresee the future with profound insight, and to preserve the past with wisdom, who can reach this level? It must be the ancients who were wise and intelligent, possessed divine martial virtue, yet did not resort to warfare. Zhang Gen says: One must study the principles of all things to be able to preserve the past; one must exhaust the numbers of all things to be able to foresee the future; thus one can unify the hearts of the people, establish great undertakings, resolve the doubts of the world, and make the people of all generations obey without knowing why, hence he is called "divine martial yet not killing."

是以明於天之道而察於民之故，是興神物以前民用。明於天之道，故有以興神物；察於民之故，故有以前民用。聖人以此齊戒，以神明其徳夫。齊戒者，將與民同患故也；神明其徳，顯仁藏用之謂也。蓍卦既設，則天下之故無不知，雖千萬世之後吉凶無不著，非神而何？

The Great Treatise says: Therefore, once he understands the principles of Heaven, and investigates the actual conditions of the people, he then uses divination tools such as yarrow stalks and tortoise shells to guide the people before they act. Zhang Gen explains: Understanding the principles of Heaven enables the emergence of divine objects; investigating the actual conditions of the people allows him to act ahead of the people's needs. The Great Treatise says: The sage uses these to perform purification rites, making his virtue profound and clear. Zhang Gen says: What is meant by purification rites is that he is about to share in the people's hardships; what is meant by making virtue profound and clear is what was previously mentioned, "manifesting virtue in benevolence and concealing its use." Once the divination tools and hexagrams are established, all worldly affairs become clear; even the fortune or misfortune of a thousand years later becomes evident. Is this not profound?

是故闔戶謂之坤，闢戶謂之乾。言萬物所以出入也。一闔一闢謂之變，往來不窮謂之通。此論卦之徳，言萬物所以始終也。見乃謂之象，形乃謂之器，制而用之謂之法，利用出入，民咸用之謂之神。此論蓍之徳。陰陽各二，老少各二。是故易有太極。所謂太初。是生兩儀。一竒一耦。兩儀生四象。此乾坤所以三畫而後成卦。四象生八卦。八方之義。所以設八卦定吉凶，愛惡自此始；吉凶生大業，人道自此成。

The Great Treatise says: Therefore, closing the door is called Kun, and opening the door is called Qian. Zhang Gen explains: This is talking about the principle of the entry and exit of all things. The Great Treatise says: One closing and one opening is called change, and the coming and going without end is called communication. Zhang Gen says: This passage discusses the virtue of the hexagrams, explaining the principle that all things have a beginning and an end. The Great Treatise says: Manifesting is called xiang, becoming a form is called qi, making it and using it is called fa, entering and exiting and being used by the people is called shen. Zhang Gen says: This passage discusses the virtue of the yarrow stalks. Yin and yang each have two kinds, old and young each have two kinds. The Great Treatise says: Therefore, the Book of Changes has the Taiji. Zhang Gen says: This is also called Taichu. The Great Treatise says: The Taiji produces the two principles. Zhang Gen says: This is one odd and one even. The Great Treatise says: The two principles produce the four images. Zhang Gen says: This is why Qian and Kun are drawn with three lines to form the hexagrams. The Great Treatise says: The four images produce the eight trigrams. Zhang Gen says: This refers to the meaning of the eight directions. The Great Treatise says: The eight trigrams are used to determine good fortune and misfortune. Zhang Gen says: Likes and dislikes begin from here. The Great Treatise says: Good fortune and misfortune produce great undertakings. Zhang Gen says: Human conduct is realized from here.

是故法象莫大乎天地，變通莫大乎四時。是以聖人效之而立卦。縣象著明莫大乎日月。是以聖人象之而立象。崇髙莫大乎富貴，備物致用，立成器以為天下利，莫大乎聖人。通而變之，使民不倦，必得崇髙備物之事。探賾棠鉤深致逺，以定天下之吉凶，成天下之亹亹者，莫大乎著。

The Great Treatise says: There is no image more worthy of being followed than heaven and earth, and no change more thorough and penetrating than the four seasons. Zhang Gen explains: Therefore, the sage modeled himself after them and established the hexagrams. The Great Treatise says: Nothing is higher and more luminous than the sun and moon suspended in the heavens. Zhang Gen says: Therefore, the sage took their images and established the symbolic representations. The Great Treatise says: Nothing is higher than wealth and honor; nothing surpasses the sage in preparing objects, exhausting their functions, and making tools to benefit the world. Zhang Gen says: To achieve the transformation and make the people tireless, there must be high status and complete tools. The Great Treatise says: To explore the profound, seek out the hidden, draw from the distant, and determine the fortune and accomplish the ceaseless endeavors of the world, nothing surpasses the yarrow stalks (this sentence has a missing character in the manuscript; the common version reads 'explore the profound, seek out the hidden, draw from the distant'; 'zhe' should be 'zhi').

是故天生神物，聖人則之。所以有繋辭。天地變化，聖人效之。所以有效。天垂象，見吉凶，聖人象之。所以有象。河出圖，洛出書，聖人則之。所以有卦。易有四象，所以示也。竒耦之畫一也，八卦二也，六十四卦三也，三百八十四爻四也。繋辭焉，所以告也。觀陰陽之形象而繋卦爻之辭以明吉凶，使天下後世或動或靜可以免於大過，非以告而何？定之以吉凶，所以斷也。定之以吉凶，吉凶生大業之位，所以斷也，以斷天下之疑之謂。

The Great Treatise says: Therefore, Heaven produces divination tools such as the yarrow stalks and tortoise shells, and the sage takes them as models. Zhang Gen explains: Therefore, there is the Great Treatise. The Great Treatise says: The transformation of Heaven and Earth, the sage imitates it. Zhang Gen says: Therefore, there is the method of imitation. The Great Treatise says: Heaven reveals signs and images, showing good fortune and misfortune, and the sage takes them as models. Zhang Gen says: Therefore, there is the concept of 'image'. The Great Treatise says: The Yellow River produces a diagram, the Luo River produces a book, and the sage takes them as models. Zhang Gen says: Therefore, there is the hexagram. The Great Treatise says: The Book of Changes has four images, used to make clear. Zhang Gen says: The odd and even lines are the first level, the eight trigrams are the second level, the sixty-four hexagrams are the third level, and the three hundred and eighty-four lines are the fourth level. The Great Treatise says: Attaching words to the text is used to inform. Zhang Gen says: Observing the images of yin and yang and attaching words to the hexagram lines to explain good fortune and misfortune, so that people in all generations, whether in action or stillness, can avoid great mistakes, is this not 'informing'? The Great Treatise says: Using good fortune and misfortune to judge, is used for decision-making. Zhang Gen says: Using good fortune and misfortune to judge, good fortune and misfortune also determine the status of great undertakings, so it is used for decision-making, meaning deciding the difficulties of the world.

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。信思乎順，又以尚賢也，是以自天佑之，吉無不利也。此章通言立卦之因。

The Great Treatise cites the line statement of the upper ninth line of the Great Possession hexagram, saying: "Being protected by heaven, it is auspicious and beneficial in all matters." Confucius explains: "The term '佑' refers to assistance. What heaven assists is the person who follows the way of heaven. What the people assist is the person who is trustworthy. Being trustworthy and thinking of following the way of heaven, and also valuing the virtuous, thus heaven protects him, it is auspicious and beneficial in all matters." Zhang Gen says: This chapter throughout discusses the reason for establishing the hexagrams.

子曰：書不盡言，言不盡意，然則聖人之意其不可見乎？子曰：聖人立象以盡意，設卦以盡情偽，繋辭焉以盡其言，變而通之以盡利，鼔之舞之以盡神。變而通之者，若黃帝堯舜設法立制之謂；鼓之舞之者，若黃帝堯舜使民由之而不知之謂。作易之□至於是而極矣，非聖人孰能與此，故終之曰神而明之存乎其人，黙而成之不言而信，茍不能然，欲舉而措之天下之民不可得也。

The Great Treatise says: Confucius said, words cannot fully express the meaning in one's mind, so how can the mind of the sage be unseen? Confucius then said: The sage established hexagrams to exhaust the mind, set up the structure of the hexagrams to exhaust the truth and falsehood of things, attached words to fully express the meaning, used change and communication to exhaust its benefits, and used encouragement and movement to exhaust its subtleties. Zhang Gen explained: What is meant by 'changing and communicating' is like the Yellow Emperor, Yao, and Shun establishing laws and systems; what is meant by 'encouraging and moving' is like the Yellow Emperor, Yao, and Shun guiding the people without them knowing why. The purpose of composing the Book of Changes reaches its peak here; who else but a sage could participate? Therefore it concludes with 'the divine and clear is in the person, silently achieving it and being trusted without speaking.' If one cannot do this, wanting to spread it to the people under heaven is impossible.

乾坤其易之縕邪。乾坤成列而易立乎其中矣，乾坤毀則無以見易，易不可見則乾坤或□乎息矣。是故形而上者謂之道，形而下者謂之器，化而裁之謂之變，推而行之謂之通，舉而錯之天下之民謂之事業。

The Great Treatise says: The trigrams Qian and Kun are roughly where the Book of Changes is concealed. When Qian and Kun are arranged into form, the Book of Changes is established within them; if Qian and Kun are destroyed, the Book of Changes would be invisible; if the Book of Changes is invisible, then Qian and Kun would be nearly at a standstill (the character following 'or' is missing and should be 'ji'). Therefore, what is above form is called Dao, and what is below form is called Qi. To transform and regulate it is called change, to spread it out is called communication, and to take it up and apply it to the people under heaven is called undertaking a cause.

是故夫象，聖人有以見天下之賾，而擬諸其形容，象其物宜，是故謂之象。聖人有以見天下之動，而觀其□通，以行其典禮，繋辭焉以斷其吉凶，是故謂之爻。極天下之賾者存乎卦，鼔天下之動者存乎辭，化而裁之存乎變，推而行之存乎通，神而明之存乎其人，黙而成之不言而信存乎徳行。此章統明立象之意。

The Great Treatise says: So when it speaks of "images," it is because the sage saw the most profound and intricate matters in the world and used the hexagrams to resemble their forms, symbolizing the appropriate conditions of various things, hence called images. The sage observed the changes of all things in the world and examined the principles of their convergence and flow (the character here is missing, it should be "converge"), based on which he established rituals and institutions, and attached words to determine auspiciousness and misfortune, hence called lines. The hexagram exhausts all the profound and intricate things in the world; the words stimulate the movement of all things; transformation nurtures and regulates; extension and implementation are achieved through communication; the mysterious and clear is understood by people; and the silent accomplishment, convincing without words, is achieved through virtue. Zhang Gen said: This chapter generally explains the purpose of establishing the hexagrams.