The Great Treatise says: The Book of Changes is vast and great.

分而為二以象兩，掛一以象三，揲之以四以象四時。

Take forty-nine stalks of yarrow and divide them randomly into two groups, symbolizing Heaven and Earth, the Two Principles. Then take one stalk from the group and set it aside, symbolizing Heaven, Earth, and Humanity, the Three Powers. Next, count the stalks in groups of four, symbolizing the four seasons of spring, summer, autumn, and winter.

義曰：夫大衍之數始本五十有五，然其所頼者四十有九。然四十九數未分之時則為一，以象太極天地未判之際；次分而為兩，以象陰陽分剖之理，於左手則為陽，於右手則為陰。

The original number of the Great Derivation is fifty-five, but actually used is forty-nine. These forty-nine lines are originally undivided and form a single whole, symbolizing the "Taiji" — the state before heaven and earth were differentiated. Then they are divided into two groups, symbolizing the principle of yin and yang being separated. The group held in the left hand represents yang, and the one in the right hand represents yin.

然陰陽既分而人事未備，又於左手之中掛其一於小指之間，以象三才，言天地人事萬品之類皆備於其間。又揲數之以象四時者，又以左右手握之，四數之，以象天之有春夏秋冬四時運轉、寒暑徃來不絶之義也。

Yin and yang have already been separated, but the dimension of human beings has not yet been placed, so another stalk is drawn from the left hand and placed between the index finger and the little finger to symbolize the 'Three Powers' (three elements), indicating that heaven, earth, human beings, and all categories of things are fully included within them. As for 'divining by four', the stalks in both hands are counted in groups of four, symbolizing the continuous movement of the four seasons of heaven, the unceasing alternation of cold and heat.

歸竒於扐以象閏，五歳再閏，故再扐而後掛。

The remaining remainder is placed between the fingers to symbolize the leap month. Since a leap month occurs twice every five years, the remainder is counted twice and then reset again.

義曰：言既揲數之，其有餘者則歸之於左手所掛一之處，以象其閏。然則天之有三百六十五度四分度之一，日行遲，一歳一周天；月行速，一月一周天。以全數言之，則日一年行三百六十度，餘有六度。

This refers to grouping numbers in sets of four, and then gathering the remainder to the place on the left hand where one had previously hung a counter, symbolizing the leap month. The full cycle of the heavens is 365 and 1/4 degrees: the sun moves slowly, completing one orbit around the sky in a year; the moon moves quickly, completing one orbit around the sky in a month. If calculated in whole numbers, the sun travels 360 degrees in a year, leaving an excess of six degrees.

是故聖人因此大衍天地生成之數，推測幽隠，以其揲蓍之數四數之，其有歸餘殘竒之數，則歸於所掛小指之間，以象其閏。既取歸餘殘竒之數以象其閏，然於二年之中為閏，又其數未備；於三年之中為一閏，又其數出剩，遂於五年□閏，則其數始足。

Therefore, the sage used the great derivation method of the numbers of heaven and earth to predict hidden matters. He counted the yarrow stalks in groups of four, and the remainder was placed between the index finger and the little finger, symbolizing an intercalary month. Since the remainder represented the intercalary month, two years would require one intercalary month, but the days were insufficient; three years would require one intercalary month, yet there was still some excess. Thus, by the fifth year, another intercalary month was added, and the days were then exactly made up.

故一歳之間所剰六度，又有六小月，是十二日也，三年之中凡三十六日，故閏一月；又剰六日，遂於五年之中積為二十四日，加此六日即為三十日，故五年□閏也。

Specifically, in a year there are six extra days, and each of the six small months is one day shorter, totaling twelve days. Over three years, this adds up to thirty-six days, so one leap month (thirty days) is inserted. After inserting the leap month, there are six days remaining. By the fifth year, another twenty-four days accumulate, adding to the previous six days to make exactly thirty days, so another leap month is inserted in the fifth year.

然揲蓍之數歸餘殘竒，零止有一二三為殘竒。今註疏之說以謂四為殘竒，則非也。且四四數之是全數也，若以全數為殘竒，則無所據，但止有一二三為殘竒也。若無餘，則再扐而後掛之，然後見成閏積分之數也。

When counting the stalks of the yarrow divination, the remainder can only be one, two, or three. Modern commentaries that include four as a remainder are incorrect. Four is itself a complete set, so treating a complete set as a remainder has no basis. Therefore, the remainder can only be one, two, or three. If there is no remainder at the end, one should perform another count and then reset the count, so that the accumulated excess can be clearly shown.

然謂「再扐而後掛」者，蓋上言「歸竒於扐以象閏，五歲再閏，故再扐而掛之」是也。

The phrase "repeatedly handling the remainder before hanging it" refers to what was mentioned earlier: the leftover portion is held between the fingers to symbolize a leap month. Since a leap month occurs twice every five years, the remainder must be handled twice before it is hung again.

是故四營而成《易》。

Therefore, after going through four stages, one completes a single transformation.

義曰：「是故」者，連上文也。四營者，則謂四度經營而成變易也。四營者，則謂上「揲之以四以象四時，歸竒於扐以象閏，五歳再閏，故再扐而後掛」是也，凡此四度經營，然後成其變易之道。

Therefore, the two characters "是故" serve to connect with the previous text. The term "四营" refers to the process of completing one change through four operations. These four operations are exactly the ones mentioned earlier: dividing the yarrow stalks into two bundles, hanging one and representing the three heavens, counting four stalks at a time to symbolize the four seasons, and placing the remaining stalks between the fingers to represent the leap month (since there are two leap months in five years, the remaining stalks must be returned twice before hanging again). Only after completing these four procedures is one change of the yin-yang transformation completed.

十有八變而成卦。

After eighteen transformations, one hexagram is formed.

義曰：凡言一爻，凡三度揲之，則為一爻；一卦六爻，三六一十八，是十有八變而成一卦也。

Each time a line is obtained, it requires three instances of divining with the yarrow stalks to determine it; a hexagram consists of six lines, three multiplied by six equals eighteen, so it takes eighteen changes to form a hexagram.

八卦而小成。

The eight trigrams are drawn, and the foundation is thus complete.

義曰：言伏羲所畫八卦，乾、坤、艮、巽、震、離、坎、兌是也。八卦既立，寫其天地水火山澤風雷之象；水火山澤風雷之象既立，是以健、順、動、止、明、入、陷、說之性畢備，此八卦之小成者也。

This refers to the eight trigrams drawn by Fuxi, namely Qian, Kun, Gen, Xun, Zhen, Li, Kan, and Dui. Once the eight trigrams were established, they depicted the phenomena of heaven, earth, water, fire, mountain, marsh, wind, and thunder; once these phenomena were established, the eight qualities of vigorous strength (Qian), yielding flexibility (Kun), movement (Zhen), stillness (Gen), brightness (Li), penetration (Xun), danger (Kan), and harmony (Dui) were also fully embodied. This is the "minor completion" of the eight trigrams.

引而伸之，觸類而長之，天下之能事畢矣。

By extending and deriving the Eight Trigrams, when encountering similar things, they are expanded accordingly, thus encompassing all possible actions under heaven.

義曰：言文王因此八卦小成之後，遂引伸八卦為六十四卦，又因其事物萬品之類而増長之。若觸剛之事類，以次増長其剛；若觸柔之事類，以次増長其柔。是以天地之性、萬物之理、天下之情偽、萬物之本，至纎至悉，天下之能事無不畢載於其間。

This refers to King Wen building upon the initial formation of the Eight Trigrams, extending and combining them to form the sixty-four Hexagrams. He then continuously expanded them according to the categories of all things in the world. When encountering matters of a yang nature, he extended their yang aspects in order; when encountering matters of a yin nature, he extended their yin aspects in order. Thus, the nature of heaven and earth, the principles of all things, the true and false of the world, and the fundamental nature of all things, no matter how subtle or detailed, are all fully recorded within them. Everything that can be done under heaven is completely included.

顯道神徳行。

It reveals subtle principles and makes human virtue profound and mysterious.

義曰：上既言天地之數，天下之能事畢載於《易》，故可以顯明其萬物之理、萬事之情，原其所由，不知所以然而然，又可以神其徳行，莫見其跡也。

The previous text has already explained the numbers of heaven and earth, and all things under heaven are fully recorded in The Zhou Changes. Therefore, it can reveal the principles of all things and the circumstances of all affairs, tracing their causes. Although people cannot explain why things are so, they naturally are so. It can also make human virtue become mysterious and unpredictable, making its traces invisible.

是故可與酬酢，可與佑神矣。

Therefore it can respond to humans and assist the functions of the deities.

義曰：酬酢者，謂報答之辭也。言《易》之道既言天地幽賾之事，又顯明萬事之理，又以蓍數明其吉凶之事，知其未來，明其已徃，使人占兆之，知其吉凶之驗，使人從善而去惡，從吉而背凶，若響之應聲而應對之也。

"Chouce" refers to the words of guests and hosts responding to each other. This means the Way of the Zhou Changes (I Ching) explains the profound and hidden matters of the universe, reveals the principles of all things, and uses the numbers of the yarrow stalks to indicate auspicious and inauspicious outcomes: foreseeing the future, clearly understanding the past, allowing people to see the verification of auspicious and inauspicious through divination, thus abandoning evil and following goodness, seeking auspiciousness and avoiding misfortune. Its response to people is like an echo responding to a sound, immediate and accurate.

可與佑神者，言《易》道既言吉凶之事，使人占之，從吉而懼凶，是可以佑明神之徳而行事者也。

What is meant by "being able to assist the divine," is that the principles of the Zhou Changes (I Ching) have already explained matters of good and bad fortune, enabling people to inquire through divination, thereby moving towards auspiciousness and being cautious of misfortune. This is equivalent to assisting the divine in cultivating virtue, providing a basis for human action.

易有聖人之道四焉。

The Zhou Changes contains four methods left by the sages for future generations. The phrase "the way of the sage has four aspects" refers to using the Book of Changes to express ideas, to guide actions, to create objects, and to divinate and seek answers to doubts.

義曰：此已下至「易有聖人之道四焉，此之謂也」為一章。言大易之道探賾索隠以成其道，故所用之道有四焉。

Hu Yuan explains: From this sentence onwards, up to the phrase "Zi Yu: The Book of Changes contains four ways of the sage," this constitutes one chapter. This chapter discusses that the principles of the Zhou Changes can penetrate to the most profound and intricate aspects, and can uncover the most subtle and hidden truths. Through this effort, it has established its own system of rules. Because of this, there are four paths derived from this system that are available for people to use.

以言者尚其辭。

Anyone who uses the Zhou Changes to make statements or express opinions places the greatest importance on the Hexagram Statements and Line Statements.

義曰：言則謂大易之中所述之言辭也。言聖人探賾索隠作為大易，聖人之情顯見於言辭之間，故君子之人慾觀大易之意，必觀聖人諸卦爻所繋屬之文辭，見聖人之情意也。

Hu Yuan explains: Here, the term "yan" refers to the textual statements recorded in the Zhou Yi. The sages explored the profound and sought out the subtle, thus composing the Zhou Yi. The meanings they wished to convey to future generations are clearly revealed in these textual statements. Therefore, those who wish to understand the essence of the Zhou Yi must carefully read the hexagram statements and line statements attached to the sixty-four hexagrams and the 384 lines. From these words, one can discern the true intentions of the sages.

以動者尚其變。

Anyone who uses the Zhou Changes to decide their actions and conduct places the greatest importance on the changes of the hexagram lines.

義曰：動則謂諸卦諸爻也，變，動也。言聖人仰觀俯察作為大易，設為六十四卦，其爻有得位者，有失位者，有變有動，有正有不正，有中有不中，有應有不應者，是諸卦之爻有變動者也。既有變動，則吉凶悔吝生乎動矣。有動而悖於理者則凶，有動而合於道者則吉。是故君子之人凡欲知其吉凶悔吝存亡之幾，必先觀其諸卦諸爻之變動，然後可以知吉凶之事、悔吝之虞、變通之理，然後趨其善而背其惡，向其吉而避其凶，所以致身於無過也。

Hu Yuan explains: Here, the term "movement" refers to the lines of each hexagram; "change" means transformation. The sage observed celestial phenomena and examined terrestrial features, and based on these observations, composed the Zhou Changes, arranging them into sixty-four hexagrams. Each line within a hexagram may be in an appropriate position or not, may change or remain static, may be upright and just or not, may be centered or not, and may have corresponding or non-corresponding relationships with the upper and lower parts. This means that the lines of each hexagram are all in a state of movement. Since there is movement, the four outcomes of good fortune, misfortune, regret, and hardship all arise from it: if action goes against reason, the result is misfortune; if action follows the right path, the result is good fortune. Therefore, a person of virtue who wishes to foresee the signs of good fortune, misfortune, regret, and hardship, as well as success or failure, must first clearly understand the changes of each line in each hexagram. Only then can one discern which matters will bring good fortune and which will bring misfortune, where regret and shame may lie, and how to adapt and change. Once understood, one should turn toward goodness and away from evil, pursue good fortune and avoid misfortune, thus ensuring that one's conduct in life is free from error.

以制器者尚其象。

Anyone who uses the Zhou Changes to create objects places the greatest importance on the imagery represented by the hexagrams.

義曰：象則謂大易之中聖人所設六十四卦之法象也。至如伏羲作結繩而為網罟，蓋取諸離；神農作耒耜取諸益；宮室取大壯；弧矢取諸睽。如此之類，皆是尚其法象也。故君子欲觀制器之用，必觀聖人設卦制器之法象也。

Hu Yuan explained: Here, the term "xiang" refers to the set of sixty-four hexagrams established by the sages in the Zhou Changes, which serve as models to follow. For example, Fuxi tied ropes into a net to catch fish and hunt, drawing upon the meaning of the Li hexagram, which symbolizes attachment and the net. Shen Nong made farming tools like the plow, drawing upon the meaning of the Yi hexagram, which signifies benefiting the people. Building houses was based on the Da Zhuang hexagram, which represents strength and stability. Making bows and arrows was based on the Kui hexagram, which signifies control through separation. Such examples show that all these inventions were based on the hexagrams. Therefore, those with aspirations should understand the principles of making objects by studying the sages' establishment of hexagrams and their symbolic representations, and following the principles of creating objects based on these symbols.

以卜筮者尚其占。

Anyone who uses divination with a turtle shell or yarrow stalks to inquire about matters most values the result obtained from the divination.

義曰：筮則謂蓍策龜兆之占筮也。夫凡人之生，必有疑貳之事、得失之理，不得以前知，是故聖人作為大易，設為六十四卦，有變通之理，有吉凶之驗。以其凡人不能無疑、不能無吉凶，然吉凶之道雖聖人有所不知。聖人既有所不知，必謀之於鬼神，以明得失吉凶之事。然鬼神之道至幽至隠，不可以形覩，不可以象窺，然莫知其所與人有異。然聖人必謀之者，是故假其至誠，取其蓍龜之數，審之於天地之數，明諸卦諸爻變動之理，以明過去未來之事，則必以卜筮占策，然後可以前知矣。

Hu Yuan explains: Here, the term "shì" refers to the method of divination using the stems of the artemisia plant for calculation and the cracks on turtle shells for interpretation. People living in the world inevitably encounter matters they cannot decide upon and principles they cannot clearly discern, unable to know the outcome in advance. Therefore, the sage composed the Zhou Changes, setting up the sixty-four hexagrams, which contain both the principles of change and the evidence of good and bad fortune. Since ordinary people cannot be without doubts and cannot avoid encountering good or bad fortune, and even the principles of good and bad fortune are not always clear to the sages, the sages, when they have uncertainties, must consult the spirits and gods in order to understand the gains and losses and the good and bad fortune. However, the way of spirits and gods is extremely subtle and hidden, invisible in form and indiscernible in appearance, so people cannot know what difference it makes to them. The sages still consult them by relying on their sincere heart, using the numbers shown by the artemisia stems and the turtle shells, verifying them with the numbers of heaven and earth, clarifying the principles of change in each hexagram and line, thus seeing the past events that have already occurred and the future events that have not yet arrived. In this way, divination and calculation are indispensable, relying on them to foresee the outcome in advance.

是以君子將有為也，將有行也，問焉而以言，其受命也如響。

Therefore, when a person of virtue is about to take action, they first consult the Zhou Changes, expressing their doubts to it. It responds to the inquiry and provides guidance, like an echo responding to a sound, answering immediately without hesitation.

義曰：言君子之人既能觀此四者之事，凡有所施為，凡有所行徃，必先問焉而以言，考其蓍龜之靈、占筮之策、通變之理、吉凶之道，然後其受命也如響之應聲，無有逺近幽深。

Hu Yuan explained: A person of virtue, having understood the four things mentioned above, namely the words, changes, images, and omens, will certainly first consult the Book of Changes when about to do something or travel. He will examine the responses from the divination with yarrow stalks and tortoise shells, the numbers obtained through divination, the principles of change and the indications of good or bad fortune. Then the response given will be as clear and direct as an echo to a call, able to answer any question whether it is near or far, subtle or profound.

遂知來物。

Thus one can foresee what is about to happen.

義曰：言此大易之道告示於人，無有遐逺邇近幽深宻之間，皆前知其吉凶禍福之驗，天地陰陽之理，將來之事、已徃之失，皆前知矣。

Hu Yuan explained: The way of the Zhou Changes teaches people, regardless of whether the matter in question is distant or near, hidden or profound, it can reveal in advance the signs of good fortune, misfortune, blessings, and calamities. The principles of yin and yang changes in heaven and earth, matters yet to come, and past transgressions can all be known beforehand through it.

非天下之至精，其孰能與於此。

If it were not the most subtle principles of the world, what else could reach such a level?

義曰：言大易之道，若非至極精妙、通達天下，其孰能與於此哉。

Hu Yuan explained: The way of the Zhou Changes is not profound and subtle to the extreme, and not universally comprehensible, then what else could reach such a level?

參伍以變，錯綜其數。

Using numbers like three and five to interactively deduce changes, interweaving and combining them for calculation.

義曰：參則謂三也，伍則謂伍也。言天一之數有三有五，至如天之一下交於地之六生水，地之十上交於天之五生土，是天地之數三五通變，上下錯雜綜統，以成萬物之數。

Hu Yuan explains: "San" means three, and "Wu" means five. This refers to the fact that both the heavenly and earthly numbers contain three and five: for example, the heavenly number six comes down to combine with the earthly number six to produce water, and the earthly number ten goes up to combine with the heavenly number five to produce earth. Thus, the numbers of heaven and earth rely on the mutual interaction and transformation between three and five, their intermingling above and below, and their comprehensive integration, to generate the numbers of all things.

通其變，遂成天地之文。

By integrating these changes, the intricate interweaving patterns of the universe are formed.

義曰：言天地陰陽之道、通變之理、化裁之跡，老陰老陽之數交而相雜，以成天地之文，若剛柔晝夜之道、寒暑徃來之功、青赤交雜之類。二百一十有六以定乾之老陽之象，一百四十四策以定坤之老陰之象，如此之類，他皆可知也。

Hu Yuan explained: The operation and transformation of yin and yang, the principles of shaping and nurturing, all arise from the interaction and intermingling of the two fundamental numbers, old yin and old yang, which weave the patterns of the world. This is similar to phenomena such as the contrast between hardness and softness, the alternation of day and night, the succession of cold and heat, and the intermingling of blue and red. Specifically, in terms of numbers: The Qian hexagram has all six lines as old yang, with each line representing thirty-six strategies, totaling two hundred and sixteen strategies, which establishes the image of old yang for Qian. The Kun hexagram has all six lines as old yin, with each line representing twenty-four strategies, totaling one hundred and forty-four strategies, which establishes the image of old yin for Kun. By analogy, the principles of the other hexagrams can be understood in the same way.

極其數，遂定天下之象。

By pushing these numbers to their ultimate conclusion, the forms of all things under heaven are thereby determined.

義曰：言聖人窮極天下之數、陰陽之策、萬事之理、纎介之微，然後可以定天下之法象也。

Hu Yuan explained: The sages investigated all numbers in the world, the numbers of yin and yang in the divination sticks, and the principles of all things, pushing their inquiry to the finest and most subtle level, thus being able to determine various exemplary forms worthy of emulation throughout the world.

非天下之至變，其孰能與於此。

If it were not the principle that exhausts all transformations, what else could reach this level?

義曰：言大易之道極窮天地之數，以成天下之法象。若非天下至變至通之道，其曷能與於此哉。

Hu Yuan explained: The way of the Zhou Changes investigates the numbers of heaven and earth to their utmost, thereby creating images available for the world to follow. If it were not for the principle most adept at change and most capable of comprehending things, how could such a feat be achieved?

易無思也，無為也，寂然不動，感而遂通天下之故。

The Zhou Changes themselves have no thoughts or deliberate actions, remaining quietly still and unmoving; once touched by human sincerity, they immediately connect and reveal the origins and developments of all things throughout the world.

義曰：言大易之道能極盡天下之數，極盡天下之事，然而易之道不假思慮，任用自然；不須經營，任用自動。寂然不見其跡，黙然不見其形。若聖人以至誠之心感而行之，則通變之理、萬事之宜自然而達矣。

Hu Yuan explained: The way of the Zhou Changes can thoroughly investigate all numbers and affairs in the world, yet it itself does not employ any deliberation; everything is left to nature. It does not need deliberate planning or arrangement; everything is left to spontaneous action. It is quiet to the point of being invisible, and silent to the point of having no trace. As long as the sage uses a heart of utmost sincerity to connect with it and follows its guidance in action, then the principles of change and the proper measures for handling all matters will naturally become clear.

非天下之至神，其孰能與於此。

If it were not the most profound and mysterious principle in the world, what else could reach such a level?

義曰：夫非忘象者則無以制象，非遺數者無以極數。至精者無筮策而不可亂，至變者體一而無不周，至神者寂然而無不應，斯蓋功用之母、象數所由立也。言大易之道若非道極妙、變化如神、極深研幾、探賾索隱，其孰與於此哉。

Hu Yuan explains: One who cannot forget the form cannot control the form; one who cannot set aside numbers cannot exhaust numbers. The subtlest aspect does not become confused even without using the divining sticks; the most changeable aspect is unified in essence yet present everywhere. The most mysterious aspect is still and quiet yet responsive everywhere. These three aspects are the root of all functions and the foundation of the hexagrams and numbers. The way of the Zhou Changes is not profound, not changeable, not exploring the hidden depths, nor searching out the subtle details, who could surpass it?

夫易，聖人之所以極深而研幾也。

The Zhou Changes is the means used by the sages to explore profound principles and investigate subtle beginnings.

義曰：此以下又明聖人作易之道，極窮幽隱，識照幾先，而作其易者也。深者，則謂未有其理、未見其形而聖人極深其用者也；幾則謂有其理未形，則謂之幾也。言聖人作易，以極其有理未形之幾也。

Hu Yuan explains: From here on, it further explains the intention of the sage in composing the Book of Changes. He thoroughly investigates the hidden aspects, seeing clearly before the matter becomes evident. Thus he composed the Book of Changes. The term 'deep' refers to when the principle has not yet taken form and the outward signs have not yet appeared, yet the sage has already thoroughly examined its function to its extreme. The term 'ji' refers to when the principle already exists but has not yet formed, and this emerging, yet not fully revealed, beginning is called 'ji'. This means that the sage composed the Book of Changes precisely to exhaust those beginnings which have some principle but have not yet taken form.

唯深也，故能通天下之志。

Exactly because the Book of Changes can explore the profound and hidden, it is able to connect the hearts and aspirations of people throughout the world.

義曰：夫人之深，未有其理，未有其形，而又天下之心億兆其心，而聖人以己之深可以通天下之志，何也？蓋天下之心雖億兆之心，而聖人以己之心可以見天下之心，以己之志可以見天下之志。何則？夫人情莫不欲飽暖而惡其飢寒，人情莫不欲壽考而惡其短折，人情莫不欲富貴而惡其貧賤，人情莫不欲安平而惡其勞苦。是故聖人以己之心推天下之心，億兆之眾深情厚貎皆可以見矣。雖億兆之心至多而難見，而聖人但以一己之心、一身之勞逸，雖未見其理、未顯其形，則天下之心自然而見矣。

Hu Yuan explained: What is meant by "deep and subtle" is that the principles have not yet taken form, and the manifestations have not yet appeared. Moreover, the thoughts of people throughout the world are countless, so how could a sage, relying solely on his own deep insight, be able to understand the minds of all people? The principle lies in this: although the thoughts of the world are countless, the sage can use his own mind to illuminate the minds of all people, and his own aspirations to illuminate the aspirations of all people. Why is that? Because human nature is such that no one does not desire to be well-fed and clothed and to avoid hunger and cold, no one does not desire longevity and avoid early death, no one does not desire wealth and honor and avoid poverty and low status, no one does not desire peace and stability and avoid hardship and toil. Therefore, the sage can use his own mind to infer the minds of all people, and thus the true feelings and the superficial appearances of the hearts of millions can be discerned. Although the hearts of people are numerous and hard to fully understand, the sage only needs to rely on his own heart and his own experiences of toil and ease to feel them out. Even if the principles have not yet taken form and the manifestations have not yet appeared, the hearts of all people will naturally be illuminated.

唯幾也，故能成天下之務。

Because the Book of Changes can investigate the initial signs, it is able to accomplish all worldly affairs.

義曰：幾者，是有理未形之謂也。夫君子之人慾極天下之務，必先博學之，審問之，慎思之，明辨之，篤行之。既能如是，則雖天下之務、萬事之微盡可見矣，所謂知至知終者是也。

Hu Yuan explained: The term "ji" refers to the principle that already exists but has not yet taken form. A person of virtue who wishes to accomplish all worldly affairs perfectly must first achieve broad learning, thorough inquiry, careful thinking, clear discernment, and practical implementation, which are the five aspects mentioned in the "Zhongyong" chapter of the "Liji." When one reaches this level, all worldly affairs and the subtle details of things become clear, which is what the "Qian" hexagram's "Wenyan" says, knowing the beginning and the end.

唯神也，故不疾而速，不行而至。

Because the Book of Changes is profound and unpredictable, it does not require urgency and yet acts swiftly, does not require movement and yet reaches its destination.

義曰：夫大易之道極深研幾，無思無為，寂然不動，能通天下之志，能定天下之務，是其功如神，不疾而速，不行而至者也。

Hu Yuan explained: The way of the Zhou Changes investigates the profound depths thoroughly and explores the initial signs, while remaining free from thought and action, still and unmoving. Yet it can connect with the aspirations of people throughout the world and accomplish the affairs of the world. This effect is like that of a divine being, acting swiftly without being urged and arriving without moving.

子曰：易有聖人之道四焉者，此之謂也。

Confucius said: The Zhou Changes contain the four paths of the sage, which are the above mentioned contents.

義曰：此又言大易能通微妙，以言者尚其辭，以動者尚其變，以制器者尚其象，以卜筮者尚其占，故天下之能事畢矣。然則首尾俱言聖人之道四者，蓋為此一章之中所陳者三事：一曰非天下之至精，二曰非天下之至變，三曰非天下之至神。皆是廣言大易之道，然三事之中亦不出於聖人之道四，故首尾總而結之也。

Hu Yuan explained: Here again it is said that The Zhou Changes can comprehend the subtle and profound: those who speak emphasize its words, those who act emphasize its changes, those who make objects emphasize its hexagrams, and those who divinate emphasize its judgments. All things under heaven are thus fully covered. This chapter begins and ends with the phrase "the way of the sage has four aspects," because the passage mentions three things: first, "it is not the most refined of the world," second, "it is not the most changeable of the world," and third, "it is not the most divine of the world." These three sentences discuss The Zhou Changes from a broad perspective, and all three matters fall within the four aspects mentioned earlier, so the chapter begins and ends with the same sentence to summarize.