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

義曰：此又言人之愛惡相攻、逺近相取、盛衰相變、情偽相易、釁隙相乗而成寇盜之事，故孔子因言《易》中知寇盜之事乎，故發而問之曰「作《易》者其知盜乎」。

Here it also speaks of human love and hatred attacking each other, distance and nearness exchanging what they take and give, prosperity and decline transforming into each other, sincerity and falsehood alternating, and suspicion being exploited by others, thus leading to banditry. Therefore, Confucius uses this to say that the Zhou Changes already understand the principles behind the emergence of bandits, and he asks, "Did those who composed the Zhou Changes probably understand how bandits are brought about?"

《易》曰：「負且乗，致寇至。」

The Zhou Changes, the Hexagram Xie, Line Six in the Third says: A person who should be carrying things is now riding in a big cart, attracting robbers.

義曰：此《解》卦六三之辭也。夫解難之時，承蹇難之後，君子有才有位者則可以釋天下之難。六三之爻以陰柔之質居於陽位，以位言之則不中也，以身言之則不正也。夫以陰柔不中不正之小人而居君子之位，行其諂佞之行，荼毒良民，不可以久居其位，必為盜之所奪，人之所不與焉，故曰「負且乗，致寇至」。

This is the line statement of the sixth line in the third position of the hexagram "Jie" (Release). It occurs at the time of removing difficulties, following the hexagram "Jian" (Obstruction) which represents hardship. If a gentleman possesses both ability and position, he can relieve the people from their troubles. However, the sixth line in the third position is a yin line occupying a yang position. In terms of its position, it is not in the center; in terms of its nature, it is not proper. A person with a weak and unrighteous nature occupying a position of virtue engages in flattery and deceit, harming the good people. Such a person cannot maintain his position for long and will inevitably be removed by robbers, and will not gain the support of the people. Therefore it is said, "carrying a burden while riding a cart, leading to the arrival of bandits."

「負也者，小人之事也；乗也者，君子之器也。小人而乗君子之器，盜思奪之矣。」

Carrying burdens is a task for the petty person; riding in a carriage is an instrument used by the gentleman. Yet the petty person sits in the gentleman's carriage, prompting the bandit to harbor the desire for plunder.

義曰：負者，是負擔之小人；乗者，君子所乗之車也。夫人臣之位，佐君澤民，須賢者居之，則天下之人受其賜，而太平之功可致矣。夫君子之器必君子居之，若以負擔之小人而乗君子之器，不惟天下之所厭棄，抑亦為寇盜之所爭奪也。

"Fu" refers to commoners who carry burdens on their shoulders; "Cheng" refers to the carriage used by the virtuous. The position of a minister is to assist the sovereign and benefit the people, and it must be held by a virtuous person. Only then can the people throughout the land receive his grace, and the achievement of peace and prosperity can be realized. The utensils used by the virtuous must be used by the virtuous; if a commoner who carries burdens were to sit in the carriage of the virtuous, it would not only be despised by the people throughout the land, but would certainly invite contention from bandits.

「上慢下暴，盜思伐之矣。」

A person in a high position who is arrogant and oppressive towards those below will incite the thoughts of bandits to attack him.

義曰：夫小人居君子之位，驕慢在下之人，暴虐為政，不唯盜之所奪，抑亦為盜之侵伐矣。然則居人臣之位，處百官之上，必當任賢使能以居其位。今小人居君子之位，此蓋在上之人不能選賢任能，遂使小人乗時得勢而至於髙位，非小人之然也，蓋在上者選之不精也。

A petty person occupying the position of a superior will be arrogant and disrespectful to those below, and will govern with cruelty and brutality. In such a case, not only will he lose his position to bandits, but he will also invite their attacks. Therefore, those who hold positions among the officials must appoint capable and virtuous people to their posts. Now, petty persons have occupied the positions of the virtuous, which is actually due to the failure of those in power to select the virtuous and capable. It is not the petty persons who have the ability, but rather the failure of the superiors to choose carefully that has allowed them to seize power and rise to high positions.

「慢藏誨盜。」

"Negligent storage of property is like encouraging thieves."

義曰：夫爵祿之位、寳器之物，必當慎而藏之。苟不能自寶藏之，常守不謹，則是教誨竊盜之人以取之，是自己之招也，非盜賊之然也。

Titles and honors, as well as treasures and valuables, must be carefully stored and guarded. If they are not treated as precious things and properly kept, it is like inviting thieves to take them. This is self-inflicted and not the fault of the thieves.

「冶容誨滛。」

"Appearance and adornment that are overly alluring are equivalent to inciting lewdness."

義曰：冶者，天冶也。夫強暴之男不能侵人之正女，今女子不能內守閨門之行，反自妖冶其容，妝麗其色，使外人之窺覩而生不軌滛欲之心，是敎誨滛者使侵於己也。此蓋非外物之然，蓋己身之不正所招也。

"Yě" refers to an alluring and extravagant appearance. A strong and fierce man, by nature, cannot infringe upon a virtuous woman who remains steadfast in her moral conduct. Now, if a woman fails to uphold the proper virtue within her home, and instead adorns her appearance with excessive beauty and embellishment, making her looks alluring and her demeanor enticing, she invites improper and lustful thoughts from outsiders. This is akin to inciting wicked people to commit offenses against herself. This is not caused by external factors, but rather results from her own lack of moral integrity.

至如小人在位，不能慎守其身，貪殘荼毒，恃其崇髙，耽其驕慢，以至為寇之所奪，亦由已之所招也，故復引《易》「負且乗」雲。

Similarly, small people occupying high positions cannot be cautious in preserving themselves, being greedy and cruel, oppressing the people. Relying on their lofty status, they indulge in arrogance and pride, leading eventually to the loss of everything at the hands of bandits. This is a result they bring upon themselves. Therefore, Confucius once again cites the phrase from the Zhou Changes, 'bearing a burden and riding a cart,' to conclude the point.

《易》曰：「負且乗，致寇至。」盜之招也。

The Zhou Changes say: "A person who should be carrying things is now riding in a big cart, thereby attracting robbers." This is precisely how one brings robbers upon oneself.

義曰：言小人乗君子之位，必為盜之所奪者，蓋由己身不正而然也。然則上文首尾皆稱「《易》曰負且乗」者，蓋欲人慎重其事，故再言之。

This refers to a petty person occupying the position of a superior person, who will inevitably be deprived by a robber, because his own conduct is not upright. As for this passage, both the beginning and the end cite "The Book of Changes says: 'to bear and to ride,' " because it is intended to remind people to be especially cautious about this matter, so it is deliberately repeated.

〇義曰：按此一章有脫落之處，亦有倒錯之文。何以知之？按下文云「子曰：知變化之道，其知神之所為乎」，下文又不言變化之道；又一章言「天一地二，天三地四，天五地六，天七地八，天九地十」，下文又不言天地之事；「大衍之數五十有五」而經文止言四十有九。以此推之，則此文倒錯而脫漏矣。

Hu Yuan remarked: examining this passage, there are both missing parts and reversed order of words. How do we know this? The text below says, "Confucius said: those who understand the principle of change should also understand the workings of the divine," but it does not proceed to explain the principle of change. Another place mentions "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," but it does not continue to discuss the numbers of Heaven and Earth. Moreover, the great derivation number should be fifty-five, yet the text only mentions forty-nine. From this we can infer that the text must have some reversed order and missing parts.

今當先言「子曰：知變化之道者，其知神之所為乎」，次言「天一地二，天三地四，天五地六，天七地八，天九地十」，又次言「天數五，地數五，五位相得而各有合。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。乾之策二百一十有六，坤之策百四十有四，凡三百有六十，當期之日。二篇之策萬有一千五百二十，當萬物之數也」。

In my opinion, the correct order should be: first, saying "Confucius said: Those who understand the principle of change also roughly understand the workings of the divine." Then, saying "Heavenly numbers one, earthly numbers two; heavenly numbers three, earthly numbers four; heavenly numbers five, earthly numbers six; heavenly numbers seven, earthly numbers eight; heavenly numbers nine, earthly numbers ten." Next, saying "Heavenly numbers have five, earthly numbers have five. The five positions are paired two by two, each having its counterpart. The total of heavenly numbers is twenty-five, the total of earthly numbers is thirty. The combined numbers of heaven and earth total fifty-five, which is what brings about change and the mysterious workings of ghosts and spirits. The sixty lines of the Qian hexagram amount to two hundred and sixteen divination sticks, and the sixty lines of the Kun hexagram amount to one hundred and forty-four divination sticks. Together they total three hundred and sixty, exactly matching the number of days in a year. The combined number of divination sticks from the upper and lower parts totals eleven thousand five hundred and twenty, exactly matching the number of all things."

次言「大衍之數五十有五，其用四十有九。分而為二以象兩，掛一以象三，揲之以四以象四時，歸竒於扐以象閏，五歳再閏，故再扐而後掛。是故四營而成《易》，十有八變而成卦，八卦而小成，引而伸之，觸類而長之，天下之能事畢矣。顯道神徳行，是故可與酬酢，可與佑神矣」。

Then it says, "The number of the Great Transformation is fifty-five, but actually forty-nine are used. They are divided into two groups to symbolize the two principles of heaven and earth, and one is drawn out and hung to symbolize the three elements. Each group of four is counted to symbolize the four seasons, and the remaining numbers are held between the fingers to symbolize the leap month. There are two leap months in five years, so the remaining numbers are counted twice before hanging. Thus, four procedures complete one transformation, eighteen transformations complete one hexagram, and when the eight trigrams are drawn, it is considered a small completion. Then it is extended and developed, growing according to its kind, so that all things and principles under heaven are included. It reveals principles and demonstrates virtue, so it can be used to respond to people and assist the divine."

〇子曰：「知變化之道者，其知神之所為乎？」

Confucius said: Those who understand the way of change probably also understand the workings of "shen." Here, "shen" does not refer to ghosts or spirits, but rather to the natural, unpredictable power of yin and yang transformation.

義曰：此言大《易》之道知變化之理，知神所為也。夫天地生成之道，變化萬品，春生夏長，秋殺冬藏，自然而然，莫知其變化神用之理，故大《易》之道知其變化之理，其知神之所為乎。

This explains that the way of the Zhou Changes (I Ching) can comprehend the principles of change, thus understanding the workings of the "spiritual." The laws of transformation through heaven and earth produce myriad forms: spring brings birth, summer brings growth, autumn brings decline, and winter brings storage. All things occur naturally, and no one can fully explain the reasons behind the changes and the mysterious workings. Therefore, those who understand the principles of change in the Zhou Changes also comprehend the workings of the "spiritual."

天一地二，天三地四，天五地六，天七地八，天九地十。

The first is heaven's number, the second is earth's number; the third is heaven's number, the fourth is earth's number; the fifth is heaven's number, the sixth is earth's number; the seventh is heaven's number, the eighth is earth's number; the ninth is heaven's number, the tenth is earth's number. Odd numbers belong to heaven, even numbers belong to earth. The ten numbers are divided into two columns exactly.

義曰：此言天地生成之數也。夫天以一生水，生數一；地以二生火，生數二；天以三生木，生數三；地以四生金，生數四；天以五生土，生數五。此是天地之生數也。如是則陰無匹，陽無耦，故地以六成水，故成數六；天以七成火，故成數七；地以八成木，成數八；天以九成金，成數九；地以十成土，成數十。陰陽有匹而物乃成，故謂之成數也。

This passage discusses the numbers associated with the generation of elements in the cosmos. Heaven produces water with the number one, so the generative number of water is one; Earth produces fire with the number two, so the generative number of fire is two; Heaven produces wood with the number three, so the generative number of wood is three; Earth produces metal with the number four, so the generative number of metal is four; Heaven produces earth with the number five, so the generative number of earth is five. These five numbers are called the 'generative numbers' of Heaven and Earth. However, only generative numbers exist, and neither yin nor yang has a corresponding pair. Therefore, Earth completes water with the number six, making the completed number of water six; Heaven completes fire with the number seven, making the completed number of fire seven; Earth completes wood with the number eight, making the completed number of wood eight; Heaven completes metal with the number nine, making the completed number of metal nine; Earth completes earth with the number ten, making the completed number of earth ten. Yin and yang now have corresponding pairs, and thus things are truly formed. These five numbers are called the 'completed numbers'.

然數之所起，本起於陰陽。陰陽徃來見於日道：十一月冬至日南極，陽來而陰徃，冬水位也，以一陽生為水數；五月夏至日北極，陰進而陽退，夏火位也，當以一陰生為火數，陰不名竒，數必以耦，故以二陰生為火數也。

As for the origin of these numbers, they come from yin and yang. The movement of yin and yang is reflected in the path of the sun's movement: in the eleventh month, at the winter solstice, the sun reaches its southernmost point, and yang energy begins to return while yin energy retreats. Winter corresponds to the element of water in the Five Phases, and at this time, the first yang energy emerges, so the number for water is one. In the fifth month, at the summer solstice, the sun reaches its northernmost point, and yin energy begins to enter while yang energy retreats. Summer corresponds to the element of fire in the Five Phases, and the number for fire should be based on the emergence of the first yin energy; however, yin is not named with an odd number, so an even number is used instead. Therefore, the number for fire is two.

自冬至以及夏至當為陽來，正月為春，木位也，三陽已生，故為木數；夏至以及冬至當為陰進，八月為秋，秋金位也，四陰已生，故四為金數；三月，春之季，季土位也，五陽以生，故五為土數。此其生數之由也，故五行始於水而終於土者，此也。

From the winter solstice to the summer solstice, the yang energy gradually increases: the first month belongs to spring, which in the Five Phases is wood, and at this time three yang energies have already emerged, so three is the number of wood. From the summer solstice to the winter solstice, the yin energy gradually increases: the eighth month belongs to autumn, which in the Five Phases is metal, and at this time four yin energies have already emerged, so four is the number of metal. The third month is the last month of spring, and the last month of each season belongs to earth. At this time five yang energies have already emerged, so five is the number of earth. This is the origin of the five generating numbers, and it is also why the Five Phases begin with water and end with earth.

然則天是純陽，故為竒而稱九；地是純陰，故為偶而稱十。是竒偶之數以分陰陽之象，故陽數竒者，一三五七九是也；陰數偶者，二四六八十是也。故天地竒偶之大數，總而言之五十有五，陽數竒故其數二十有五，陰數偶故其數三十。

Heaven is entirely yang, so it uses odd numbers, with nine being the largest odd number; Earth is entirely yin, so it uses even numbers, with ten being the largest even number. These two categories of numbers, odd and even, are used to distinguish between the two types of phenomena, yin and yang: the odd numbers belonging to yang are one, three, five, seven, and nine; the even numbers belonging to yin are two, four, six, eight, and ten. Therefore, the total of these odd and even numbers combined is fifty-five: the total of the yang numbers is twenty-five, and the total of the yin numbers is thirty.

是以天一加天三是四，四又加其天五是九，九又加其天七是十六，十六又加其天九是二十五數也。地數自二者，自二加其地四是六，六又加其地六是十二，十二又加其地八是二十，二十又加其地十是地數三十也。

The specific calculation is as follows: The heavenly numbers start from one, one plus three equals four, four plus five equals nine, nine plus seven equals sixteen, sixteen plus nine equals twenty-five, which is the total of the heavenly numbers. The earthly numbers start from two, two plus four equals six, six plus six equals twelve, twelve plus eight equals twenty, twenty plus ten equals thirty, which is the total of the earthly numbers.

是以天地之數五十有五，以成變化之道，以盡生成之數，所以成天下之務。故天之數合而成二十有五，地之數合而三十。自天一至五是天之五數，自地二至十是地之五數也，故言天數五，地數五。

Therefore, the total number of the heavenly and earthly numbers is fifty-five, which is used to accomplish the way of change and to exhaust the numbers of all things in transformation, thus managing all affairs under heaven. The total of the heavenly numbers is twenty-five, and the total of the earthly numbers is thirty. Looking at the column of heavenly numbers: heaven one, heaven three, heaven five, heaven seven, heaven nine, there are five numbers of heaven; looking at the column of earthly numbers: earth two, earth four, earth six, earth eight, earth ten, there are also five numbers of earth. Therefore, the classic says, "Heaven has five numbers, earth has five numbers."

天數五，地數五，五位相得而各有合。

Heavenly numbers have five, earthly numbers have five. The five positions pair with each other in pairs, each having its corresponding match.

義曰：自天一合於地之六為水，自地二合於天之七為火，自天三合於地之八為木，自地四合於天之九為金，自天五合於地之十為土，是五位相得而各有合者也。

Heavenly One and Earthly Six combine to form water; Earthly Two and Heavenly Seven combine to form fire; Heavenly Three and Earthly Eight combine to form wood; Earthly Four and Heavenly Nine combine to form metal; Heavenly Five and Earthly Ten combine to form earth. This is the meaning of the five positions pairing with each other, each having its corresponding match.

天數二十有五。

The total of the heavenly stems is twenty-five.

義曰：言天之數竒，自一三五七九合為二十五也。

This refers to the heavenly stems, which are all odd numbers. Adding one, three, five, seven, and nine together gives a total of twenty-five.

地數三十。

The total of the Earthly Numbers is thirty.

義曰：言地數偶，自二四六八十合而為三十也。

This refers to the fact that the Earthly Branches are all even numbers. Adding two, four, six, eight, and ten together gives a total of thirty.

凡天地之數五十有五，此所以成變化而行鬼神也。

The numbers of Heaven and Earth combine to make fifty-five, which is precisely what enables the transformation and operation of all things, achieving the subtle and mysterious workings of ghosts and spirits.

義曰：此已下聖人因其揲蓍以考天地幽賾之事，明其天地萬物之理，故以蓍草之數占之，以明陰陽之用也。言天地之數自二十五至三十，總而合之則有五十五數，以成陰陽竒耦之數，成其變化之道、萬品之數，而行乎鬼神之幽賾者也。

From here on, it says that sages used the method of counting yarrow stalks to investigate the profound and obscure matters of the universe, and to elucidate the principles of heaven and earth and all things. Therefore, they used the numbers of yarrow stalks for divination, thereby revealing the workings of yin and yang. The numbers of heaven and earth are twenty-five for heaven and thirty for earth, totaling fifty-five. With these numbers, they formed the odd and even numbers of yin and yang, established the way of change and the numbers of myriad things, and thus operated within the mysterious and indescribable realm of ghosts and spirits.

乾之策二百一十有六。

The total number of yarrow stalks used in the six lines of the Qian hexagram is two hundred and sixteen.

義曰：夫乾坤二卦，陰陽之象。陽爻竒，故一爻有三十六策；陰爻偶，故一爻有二十四策。自乾坤而下凡三百八十四爻，陰陽之數相半，故陽爻一百九十二，陰爻亦一百九十二，總而言之有三百八十四爻。故乾為老陽，一爻有三十六策，二爻是七十二策，三爻是一百單八策，四爻是一百四十四策，五爻是一百八十策，六爻是二百一十有六策也。

The trigrams Qian (Heaven) and Kun (Earth) represent yin and yang. A yang line is odd, and one line contains thirty-six stalks of yarrow; a yin line is even, and one line contains twenty-four stalks of yarrow. From the trigrams Qian and Kun downwards, the sixty-four trigrams contain a total of three hundred eighty-four lines, with yin and yang each accounting for half. Therefore, there are one hundred ninety-two yang lines and one hundred ninety-two yin lines, making a total of three hundred eighty-four lines. The trigram Qian has six lines, all old yang: one line contains thirty-six stalks, two lines contain seventy-two stalks, three lines contain one hundred eight stalks, four lines contain one hundred forty-four stalks, five lines contain one hundred eighty stalks, and six lines contain two hundred sixteen stalks.

坤之策百四十有四。

The total number of stalks in the six lines of the Kun hexagram is 144.

義曰：夫坤爻偶，故一爻有二十四策，二爻有四十八策，三爻有七十二策，四爻有九十六策，五爻有一百二十策，六爻有一百四十四策。是乾坤之十二爻竒偶之策總而言之有三百六十，是故聖人因其乾坤竒偶之數，成為一歳凡三百六十日也。

The Kun hexagram has all six lines as yin lines, which are even, so each line contains twenty-four strategies. Two lines contain forty-eight strategies, three lines contain seventy-two strategies, four lines contain ninety-six strategies, five lines contain one hundred and twenty strategies, and all six lines together contain one hundred and forty-four strategies. Thus, adding the odd and even strategies of the twenty-four lines in the Qian and Kun hexagrams, the total is exactly three hundred and sixty. Therefore, the sages based the number of days in a year on the odd and even numbers of the Qian and Kun hexagrams.

凡三百有六十，當期之日。

The combined number of stalks used in the Qian and Kun hexagrams is 360, exactly equivalent to the number of days in a year.

義曰：夫乾坤之策凡三百有六十，聖人因之以成為一歳，一歳之內凡三百有六十日。然天之有三百六十五度四分度之一，故月行速，一月一周天；日行遲，一歳一周天。若以全數言之，則一歳三百六十日餘其六度。

The combined number of stalks used in the divination with the Qian and Kun trigrams is 360. The sages used this to determine the length of a year, which consists of 360 days. However, the actual celestial cycle is 365 and one fourth days. The moon moves quickly, completing one orbit around the sky in a month; the sun moves slowly, taking a whole year to complete one orbit. If we take whole numbers, there are six extra degrees beyond the 360 days of a year.

又一歳有六小月，三年之中餘三十六日，故為一閏。一閏之中又餘六日，又於五年之中積其二十四日，合前六日成三十日，又為一閏，是五歳再閏也。此言「期之日」，為一歳之期也。

In addition, within a year there are six small months, each lacking one day, so over three years, thirty-six days accumulate. Therefore, a leap month is set. After setting the leap month, there are still six days remaining; by the fifth year, another twenty-four days accumulate, combining with the previous six days to make thirty days, so another leap month is set—this is why a leap month is set twice in five years. The term 'period day' mentioned in the text refers to the full cycle of a year.

二篇之策，萬有一千五百二十，當萬物之數也。

The total number of stalks used in the divination of the upper and lower parts of the Zhou Changes is eleven thousand five hundred and twenty, which exactly corresponds to the number of all things.

義曰：二篇者，言乾坤上下之二篇也。夫伏羲畫八卦已後，文王重為六十四，以其《易》道廣大，卦義淵深，乾坤能始生萬物，故以乾坤為上經之首，以坎離而終之，故為上篇之終；自咸恆明人事之大，故為下篇之首，以既濟未濟而終之，故為下篇之終。

"The two chapters" refer to the Upper and Lower Sections, both beginning with the trigrams Qian and Kun. After Fuxi drew the Eight Trigrams, King Wen overlapped them to form the sixty-four hexagrams. Because the principles of the Zhou Changes are vast and the meanings of the hexagrams are profound, and since Qian and Kun can give birth to all things, Qian and Kun are used as the beginning of the Upper Section, while Kan and Li are used as its ending. The Lower Section begins with the hexagrams Xian and Heng, because the relationship between husband and wife is the fundamental aspect of human affairs, and ends with the hexagrams Ji Ji and Wei Ji.

凡此上下二篇有三百八十四爻，陰陽之數各半，故乾之爻一百九十二，坤之爻亦一百九十二。凡陽爻三十六策，十爻是三百六十策，一百爻是三千六百策，二百爻是七千二百策，卻於二百爻中退八爻，三八二十四，除卻二百四十策，又六八四十八，又除四十八策，是乾之爻一百九十二爻，都總策數是六千九百一十二策。

The upper and lower parts together contain 384 lines. Yin and Yang each account for half, so there are 192 Yang lines and 192 Yin lines. Each Yang line is worth 36 strategies. Ten lines amount to 360 strategies, 100 lines amount to 3,600 strategies, and 200 lines amount to 7,200 strategies. However, there are actually only 192 Yang lines, so we need to subtract 8 lines from 200. First, subtract 24 strategies for 8 lines, then subtract another 48 strategies for another 8 lines. Thus, the total number of strategies for 192 Yang lines is 6,912.

陰爻亦一百九十二爻，毎一爻策數是二十四策，十爻是二百四十策，一百爻是二千四百策，二百爻是四千八百，卻於二百爻內除了八爻，二八一十六，是一百六十策，又四八三十二，又除三十二策，內有一百九十二爻，都總策數是四千六百八策也。

The Yin lines also total 192, with each line corresponding to 24 counts: ten lines make 240 counts, one hundred lines make 2,400 counts, and two hundred lines make 4,800 counts. Similarly, subtract eight lines from two hundred lines—eight times twenty is one hundred sixty, first subtract one hundred sixty counts, then four times eight is thirty-two, subtract another thirty-two counts. Thus, the total counts for 192 Yin lines amount to 4,608.

以乾之六千九百一十二策，合坤之四千六百八策，都合為一萬一千五百二十策，以象萬物之數矣。然則陰陽奇耦之數，其中有萬、有千、有百、有十，故可以極天下之務，成天下之事，夫萬物之數無所不備矣。

The number of 6,912 strategies from the Yang lines and 4,608 strategies from the Yin lines, when added together, total 11,520 strategies, symbolizing the numbers of all things. It is evident that within the numbers of Yin and Yang, the units of ten thousand, thousand, hundred, and ten are all present, thus enabling the completion of all affairs under heaven and encompassing all things.

然此皆是老陰老陽之數也，而乾坤之間亦有少陰少陽之數也。故少陽之數七，四七二十八，是少陽之數也；少陰之數八，故四八三十二，是少陰之數也。

However, the above calculations are for the old yin and old yang numbers. Between the Heaven and Earth trigrams, there are also the numbers for the young yin and young yang. The number for young yang is seven; four multiplied by seven gives twenty-eight, so one line of young yang has twenty-eight counts. The number for young yin is eight; four multiplied by eight gives thirty-two, so one line of young yin has thirty-two counts.

自二十八至十爻二百八十，一百爻是二千八百，二百爻是五千六百策，又於二百爻內除八爻，二八一十六，一百六十，又八八六十四，是六十四策，除了二百二十四策，內有五千三百七十六。

Using the calculation of twenty-eight strokes for each young yang line: ten lines amount to two hundred and eighty strokes, one hundred lines amount to two thousand eight hundred strokes, and two hundred lines amount to five thousand six hundred strokes; then subtract eight lines from two hundred lines—twenty-eight times eight is one hundred and sixty strokes, eight times eight is sixty-four strokes, totaling two hundred and twenty-four strokes subtracted. The remaining one hundred and ninety-two young yang lines have a total of five thousand three hundred and seventy-six strokes.

少陰之數三百二十。爻三百二十，一百爻三千二百，二百爻六千四百，卻於二百爻內除了八爻，三八二十四，二百四十，又二八一十六，一十六策，內有六千一百四十四。

For the lesser yin lines: each line has 32 counts, ten lines total 320 counts, one hundred lines total 3,200 counts, two hundred lines total 6,400 counts; similarly, subtract eight lines from two hundred lines—three times eight is twenty-four, two times eight is sixteen, totaling 256 counts subtracted. The remaining 192 lesser yin lines have a total of 6,144 counts.

共計少陰少陽之數一萬一千五百二十，當萬物之數，是少陰少陽與老陰老陽其數皆一也。此不言少陰少陽，止言老陰老陽者，蓋《易》以變為占，言其變則神其用，舉其大則明其小。

The number of six thousand one hundred and forty-four for the minor yin and five thousand three hundred and seventy-six for the minor yang together total eleven thousand five hundred and twenty, which is exactly equivalent to the number of all things. This shows that the total number of the minor yin and minor yang is completely the same as that of the old yin and old yang. The classic text does not mention minor yin and minor yang but only refers to old yin and old yang because the Zhou Changes use changing lines to make predictions: it is only by referring to the changing lines that their subtle and profound function becomes evident; by mentioning the greater one, the smaller one is naturally understood.

蓋老陰老陽、少陰少陽，其數皆一，亦有萬一千五百二十，當萬物之數，故但言老陰老陽，而少陰少陽從可知矣。然必曰老陽、老陰、少陽、少陰者，蓋陽以老為尊，陰以少為貴。

Old Yin and old Yang, along with young Yin and young Yang, all total the same number, 11,520, which is equivalent to the number of all things. Therefore, the classic text only discusses old Yin and old Yang, and young Yin and young Yang can be inferred accordingly. As for why there are distinctions between old Yang, old Yin, young Yang, and young Yin, it is because among Yang, the old is esteemed, and among Yin, the young is valued.

大衍之數五十，其用四十有九。

The large-scale divination of the numbers of heaven and earth relies on fifty yarrow stalks, but actually only forty-nine are used.

義曰：按此大衍之數當有五十有五，何以明之？按上文言「天一地二，天三地四，天五地六，天七地八，天九地十」，是天數二十有五，地數三十，總而五十有五也。今經文但言五十者，蓋簡編脫漏矣。

Hu Yuan says: Here the number of great derivation should be fifty-five. Why is that so? The previous text mentions "Heaven one, Earth two, Heaven three, Earth four, Heaven five, Earth six, Heaven seven, Earth eight, Heaven nine, Earth ten." The total of Heaven numbers is twenty-five, and the total of Earth numbers is thirty, making a total of fifty-five. Now the text only says fifty, which should be due to a missing character in the bamboo slips.

然則天地生成之道始於太極，是故聖人因其天地生成之道自然之理，積其成數，總而五十有五，以明天地之大法。今註疏之說但言其用五十，殊不知天地生成之數，上言「天一地二，天三地四，天五地六，天七地八，天九地十」之數，上文既言五十有五之數，豈得止言五十哉？此註疏之非也。

The way of Heaven and Earth generating things begins with the "Taiji," which is the original unity before Heaven and Earth were separated. Therefore, the sage followed the natural way of Heaven and Earth's generation, accumulating various numbers to total fifty-five, thereby revealing the fundamental principles of Heaven and Earth. Current interpretations only mention fifty, but they fail to understand the numbers of Heaven and Earth's generation: since the above has already listed "Heaven one, Earth two" up to "Heaven nine, Earth ten," it has already shown the total to be fifty-five. How can they only say fifty? This is an error in the annotations.

歴代以來言之者甚眾：京房則五十者，謂十日、十二辰、二十八宿也，凡五十，其一不用者，天之生氣將欲以虛來實，故用四十九焉；馬季長云，《易》有太極，是北辰也，太極生兩儀，兩儀生日月，日月生四時，四時生五行，五行生十二月，十二月生二十四氣，北辰居位不動，其餘四十九轉運而用也。

Many scholars throughout history have explained this sentence. Jing Fang believed that the number fifty refers to the ten heavenly stems, twelve earthly branches, and twenty-eight constellations, which together total fifty. Among them, one is left unused because the heavenly life qi relies on a vacant position to attract the actual existence, so only forty-nine are used. Ma Rong (style name Jichang) said that the Zhou Changes contain the concept of "Taiji" (Supreme Ultimate), which is the North Star; Taiji gives rise to the two principles (yin and yang), which give rise to the sun and moon, which give rise to the four seasons, which give rise to the five phases, which give rise to the twelve months, which give rise to the twenty-four solar terms; the North Star remains stationary in its position, while the other forty-nine are in motion and used in rotation.

荀爽則曰，卦各有六爻，六八四十八，加乾坤二用，凡有五十，乾初九「潛龍勿用」，故用四十九也；鄭康成則曰，天地之數五十有五之數，五十有五者，其六以象六畫之數，故減之，用四十九；王弼則曰，演天地之數，所頼者五十，其一不用者，以其虛無非所用也；子夏則曰，其一不用者，太極也，無可名之，謂之太極。

Xun Shuang said: Each of the eight trigrams has six lines, making 48 in total. Adding the 'Use of Nine' in the Qian trigram and the 'Use of Six' in the Kun trigram, there are fifty in total. However, the Qian trigram's initial line says 'The dragon remains hidden and is not used,' so in reality only forty-nine are used. Zheng Xuan (styled Kangcheng) said: The number of heaven and earth is fifty-five, from which six are left out to symbolize the six lines of a trigram, thus subtracting six, leaving forty-nine. Wang Bi said: The calculation of heaven and earth's numbers is based on fifty, and one line is left out because it represents nothingness, which is not used. The Zixia Commentary on the Changes says: The line that is not used is the 'Taiji,' because it cannot be named, so it is called Taiji.

此皆殊無所據，獨鄭康成、姚信、董過三人皆言天地之數五十有五，然而又不知四十九之用。今註疏之說但言聖人推測天地之數止用五十，非數而數以之通，不用而用以之成，又言虛一以象虛無之氣，此皆近於荘老空空之說，以惑後世。

These statements all lack solid evidence. Only three scholars, Zheng Xuan, Yao Xin, and Dong Yu, all argued that the number of heaven and earth is fifty-five, but they failed to explain why the actual number used is forty-nine. The current interpretations only say that the sages inferred the number of heaven and earth and took fifty, and they talk about "it is not a number, yet it enables numbers to function; it is not used, yet it enables functions to be completed," and they also mention setting aside one rod to symbolize the void qi. All these are close to the empty talk of the Zhuangzi and Laozi, which will only confuse later generations.

今止取五十有五之數，以其上文既言天數二十五、地數三十，是天地生成之數自然之理，萬有一千五百二十陰陽竒耦之數，天下人事之理、萬事之情、萬品之物，無不總此生成自然之數。

Now I take the number fifty-five. Since the text above has already explained that the number of heaven is twenty-five and the number of earth is thirty, this reflects the natural process of generation and transformation of heaven and earth. The number eleven thousand five hundred twenty, which represents the yin and yang odd and even numbers, encompasses the principles of all human affairs, the conditions of all things, and the categories of all creatures. Nothing is left out of this system of naturally generated numbers.

然而其所頼者四十有九，何則？夫天數二十五，地數三十，是老陰老陽之數也。以數言之，陰數多於陽數，而陰者是臣之象也，陽者是君之象也。今地數三十，陰之盛於陽，臣之盛於君，子盛於父，卑盛於尊，此至逆之象也。

So why is the number forty-nine actually used? The number of heavenly principles is twenty-five, and the number of earthly principles is thirty. These are the numbers representing old yin and old yang. In terms of numbers alone, the yin numbers are greater than the yang numbers; and yin symbolizes ministers, while yang symbolizes the sovereign. Now, the earthly principles are thirty, and yin surpasses yang, which is like ministers surpassing the sovereign, sons surpassing fathers, and the lowly surpassing the superior. This is an extremely rebellious image.

是故聖人因其天地生成之數自然之理，酌其老陰老陽之數，以其陰不可過於陽，臣不可盛於君，故於地數三十之中去其六策，又合於坤之一策二十四，遂以地數以卑為尊，故去其六數，止以二十四合於天數二十五，共為四十九數，取其陰下於陽、臣下於君、子下於父、卑下於尊，此是至順之道也，故其用四十有九，然後可以神其用矣。

Therefore, the sage based the natural principles of the generation and transformation of heaven and earth, weighing the numbers of old yin and old yang: since yin cannot exceed yang, and a minister cannot surpass a king, he subtracted six from the earth number thirty to make it exactly twenty-four, matching the single line of the Kun hexagram. Thus, the earth number is esteemed by being humble and submissive. After subtracting the six, twenty-four was combined with the heavenly number twenty-five, totaling forty-nine. This reflects the meaning of yin residing below yang, a minister below a king, a son below a father, and the humble below the exalted, embodying the most harmonious principle. Therefore, only when actually using forty-nine stalks can the function of the divination become profound and marvelous.