Chapter Sixty-One: Observing Things

九者陽之極數，六者陰之極數。數極則反，故為卦之變也。震巽無策者，以當不用之數。天以剛為德，故柔者不見。地以柔為體，故剛者不生。是以震巽無策也。或先艮後兌離。乾用九，故其策九也，四之者以應四時，一時九十日也。坤用六，故其策亦六也。

Nine represents the extreme of the Yang number, and six represents the extreme of the Yin number. When numbers reach their extremes, they reverse, hence old Yang and old Yin serve as the basis for changing lines in a hexagram. The trigrams Zhen (Thunder) and Xun (Wind) are not assigned a count, as they are used as the unused portion. Heaven values firmness as its virtue, so the soft aspect does not appear; Earth values softness as its nature, so the firm aspect does not arise: thus Zhen and Xun have no count. There is also an arrangement where Gen (Mountain) comes first and Dui (Lake), Li (Fire) come later. Qian (Heaven) uses nine, so its count is based on nine, multiplied by four to correspond to the four seasons, with one season being ninety days. Kun (Earth) uses six, so its count is based on six.

奇數四，有一有二有三有四。策數四，有六有七有八有九。合而為八數，以應方數之八變也。歸奇合掛之數有六，謂五與四四也，九與八八也，五與四八也，九與四八也，五與八八也，九與四四也，以應圓數之變六也。

The remainder obtained from divining with yarrow stalks can be one, two, three, or four. The number of lines determined by the remainder also has four possibilities: six, seven, eight, and nine. When both sides are combined, there are eight numbers in total, corresponding to the eight transformations of the square number. As for combining the remainders and adding the single stalk that is set aside, the result has six possibilities: five and four four, nine and eight eight, five and four eight, nine and four eight, five and eight eight, nine and four four, corresponding to the six transformations of the round number.

奇數極於四，而五不用。策數極於九，而十不用。五則一也，十則二也。故去五十而用四十九也。奇不用五，策不用十，有無之極也，以況自然之數也。蓍數全，故陽策三十六與二十八，合之為六十四也。卦數去其四，故陰策二十四與三十二，合之為五十六也。九進之為三十六，皆陽數也，故為陽中之陽；七進之為二十八，先陽而後陰也，故為陽中之陰；六進之為二十四，皆陰數也，故為陰中之陰；八進之為三十二，先陰而後陽也，故為陰中之陽。

The count of the remainder stops at four, and five is not used; the count of the divination rods stops at nine, and ten is not used. This is because five returns to one, and ten returns to two. Therefore, the total number of divination rods is fifty, but only forty-nine is used in practice. The exclusion of five from the remainder and ten from the divination rods represents the two extremes of 'having' and 'not having,' symbolizing the natural generation of numbers. The divination rods are complete, so the number of yang rods, thirty-six, added to twenty-eight gives sixty-four. The number of yin rods, twenty-four, added to thirty-two gives fifty-six, as four yin rods have been removed. Nine, when counted in fours, gives thirty-six; both four and nine are yang numbers, so this is called yang within yang. Seven, when counted in fours, gives twenty-eight; four is yang and seven follows it as yin, so this is called yang within yin. Six, when counted in fours, gives twenty-four; both six and four are yin numbers, so this is called yin within yin. Eight, when counted in fours, gives thirty-two; it starts with yin and ends with yang, so this is called yin within yang.

蓍四進之則百，卦四進之則百二十。百則十也，百二十則十二也。歸奇合掛之數，得五與四四，則策數四九也；得九與八八，則策數四六也；得五與八八，得九與四八，則策數皆四七也；得九與四四，得五與四八，則策數皆四八也。為九者，一變以應乾也；為六者，一變以應坤也；為七者，二變以應兌與離也；為八者，二變以應艮與坎也。五與四四，去掛一之數，則四八三十二也；九與八八，去掛一之數，則四六二十四也；五與八八、九與四八，去掛一之數，則四五二十也；九與四四、五與四八，去掛一之數，則四四十六也。故去其三四五六之數，以成九八七六之策也。

The number of stalks used is twenty-five, and when counted by fours, it results in a total of one hundred. The number of lines in the hexagram is thirty, and when counted by fours, it results in one hundred twenty. When reduced, one hundred becomes ten, and one hundred twenty becomes twelve. The leftover numbers are combined with the initial one removed: those that result in five and four, or four, have a count of thirty-six; those that result in nine and eight, or eight, have a count of twenty-four; those that result in five and eight, or eight, or nine and four, or eight, have a count of twenty-eight; and those that result in nine and four, or four, or five and four, or eight, have a count of thirty-two. Those that result in nine can be matched with the trigram Qian with one change; those that result in six can be matched with the trigram Kun with one change; those that result in seven require two changes to match the trigrams Dui and Li; and those that result in eight require two changes to match the trigrams Gen and Kan. When five and four, or four, remove the initial one, the count becomes thirty-two; when nine and eight, or eight, remove the initial one, the count becomes twenty-four; when five and eight, or eight, or nine and four, or eight, remove the initial one, the count becomes twenty; and when nine and four, or four, or five and four, or eight, remove the initial one, the count becomes sixteen. Thus, it is precisely by removing the groups of three, four, five, and six that the counts of nine, eight, seven, and six are formed.

天一地二，天三地四，天五地六，天七地八，天九地十，參伍以變，錯綜其數也。如天地之相銜，晝夜之相交也。一者數之始，而非數也。故二二為四，三三為九，四四為十六，五五為二十五，六六為三十六，七七為四十九，八八為六十四，九九為八十一，而一不可變也。百則十也，十則一也，亦不可變也。是故數去其一而極於九，皆用其變者也。五五二十五，天數也；六六三十六，乾之策數也；七七四十九，大衍之用數也；八八六十四，卦數也；九九八十一，玄範之數也。

The Great Treatise says that Heaven is one and Earth is two, Heaven is three and Earth is four, Heaven is five and Earth is six, Heaven is seven and Earth is eight, Heaven is nine and Earth is ten. Odd and even numbers alternate, interacting three times and five times, changing and interweaving to form numbers, just as Heaven and Earth connect head to tail and day and night alternate. "One" is the beginning of numbers, but it is not counted as a number. Therefore, two multiplied by two is four, three multiplied by three is nine, four multiplied by four is sixteen, five multiplied by five is twenty-five, six multiplied by six is thirty-six, seven multiplied by seven is forty-nine, eight multiplied by eight is sixty-four, nine multiplied by nine is eighty-one, while one multiplied by one remains one, which cannot change. One hundred reduces to ten, ten reduces to one, which also cannot change. Therefore, counting should exclude "one" and take nine as the extreme, using only the part that can change. Five multiplied by five is twenty-five, which is the total of Heaven's numbers; six multiplied by six is thirty-six, which is the number of the yao of Qian; seven multiplied by seven is forty-nine, which is the number used in the Great Derivation; eight multiplied by eight is sixty-four, which is the number of the hexagrams; nine multiplied by nine is eighty-one, which is the number based on Yang Xiong's Tai Xuan and the Nine Categories of the Shang Shu Hong Fan.

大衍之數，其算法之源乎？是以算數之起，不過乎方圓曲直也。乘數，生數也；除數，消數也。算法雖多，不出乎此矣。《易》之大衍，何數也？聖人之倚數也。天數二十五，合之為五十；地數三十，合之為六十。故曰“五位相得，而各有合也”。五十者，蓍之數也；六十者，卦之數也。五者，蓍之小衍也。故五十為大衍也。八者，卦之小成，則六十四為大成也。

The great derivation number, roughly speaking, is the origin of all calculations. Therefore, the origin of arithmetic is no different from the forms of square, circle, curve, and straight line. Multiplication increases numbers, while division decreases them; although there are many names for calculation methods, they cannot escape these two categories. So what is the great derivation number in the Book of Changes? It is a number devised by the sages based on the numbers of heaven and earth. The numbers of heaven are one, three, five, seven, and nine, which total twenty-five; doubling this gives fifty. The numbers of earth are two, four, six, eight, and ten, which total thirty; doubling this gives sixty. Therefore, the Great Treatise says, "The five positions correspond to each other and each has its combination." Fifty is the number of the yarrow stalks, and sixty is the number of the hexagrams. Five is the "small derivation" of the yarrow stalks; extending this, fifty becomes the "great derivation." Eight is the "small completion" of the hexagrams; extending this, sixty-four becomes the "great completion."

五十分之則為十。若參天兩之，則為六。兩地又兩之，則為四。此天地分太極之數也。天之變六，六其六得三十六，為乾一爻之數也。積六爻之策，共得二百一十有六，為乾之策。六其四得二十四，為坤一爻之策。積六爻之數，共得一百四十有四，為坤之策。積二篇之策，乃萬有一千五百二十也。

Fifty is divided into five parts, each part being ten. If we take three according to 'Heavenly Principle' and double it, we get six; if we take two according to 'Dual Places' and double it, we get four. These are the numbers obtained from dividing the Taiji by Heaven and Earth. The changing number of Heaven is six; six sixes make thirty-six, which is the number of lines for the Qian trigram. The total number of lines for the six lines of Qian is two hundred and sixteen, which is the total number of lines for Qian. Six fours make twenty-four, which is the number of lines for the Kun trigram. The total number of lines for the six lines of Kun is one hundred and forty-four, which is the total number of lines for Kun. When the numbers of all the sixty-four hexagrams in the upper and lower parts of the Yi are added together, the total is eleven thousand five hundred and twenty, which corresponds to the number of all things.

陽得陰而生，陰得陽而成，故蓍數四而九，卦數六而十也。猶干支之相錯，乾以六終，而支以五終也。卦有六十四，而用止六十者，何也？六十卦者，三百六十爻也。故甲子止於六十也。六甲，天道窮矣。是以策數應之，三十六與二十四合之則六十也，三十二與二十八合之亦六十也。乾四十八，坤十二，震二十，巽四十，離兌三十二，坎艮二十八，合之亦六十也。

Yang needs to connect with Yin to be generated, and Yin needs to connect with Yang to be formed. Therefore, the number of the divination sticks is paired with four and nine, and the number of hexagrams is paired with six and ten. This is like the mutual interaction between the Heavenly Stems and Earthly Branches: the ten Heavenly Stems cycle through six rounds to complete a cycle, and the twelve Earthly Branches cycle through five rounds to complete a cycle, both ending at sixty. There are sixty-four hexagrams in total, but in actual use only sixty are employed. Why is this so? Because sixty hexagrams correspond to three hundred and sixty lines, which matches the three hundred and sixty days in a year, and the cycle of Jiazi also lasts sixty. When the six Jia stems are completed, the heavenly cycle is completed. The numbers of the divination rods correspond to this as well: thirty-six plus twenty-four equals sixty, and thirty-two plus twenty-eight also equals sixty; forty-eight (Qian) plus twelve (Kun), twenty (Zhen) plus forty (Xun), thirty-two (Li and Dui) plus twenty-eight (Kan and Gen), all add up to sixty.

三四十二也，二六亦十二也。二其十二，二十四也。三八亦二十四也，四六亦二十四也。三其十二，三十六也。四九亦三十六也，六六亦三十六也。四其十二，四十八也。三其十六亦四十八也，六八亦四十八也。五其十二，六十也。三其二十亦六十也，六其十亦六十也。皆自然之相符也。（此蓋陰數分其陽數耳，是以相因也。如月初一分作十二也。二十四氣、七十二候之數，亦可因以明之。）

Three times four is twelve, and two times six is also twelve. The double of twelve is twenty-four, which is also three times eight or four times six. The triple of twelve is thirty-six, which is also four times nine or six times six. The quadruple of twelve is forty-eight, which is also three times sixteen or six times eight. The quintuple of twelve is sixty, which is also three times twenty or six times ten. Different methods lead to the same number, which is a natural harmony. (This is merely the yin numbers dividing the yang numbers, so they can be mutual factors. For example, dividing the first day of each month into twelve parts. The numbers of twenty-four solar terms and seventy-two climatic divisions in a year can also be explained in this way.)

四九三十六也，六六三十六也。陽六而又兼陰六之半，是以九也。故以二卦言之，陰陽各三也；以三爻言之，天地人各二也。陰陽之中，各有天地人。天地人之中，各有陰陽。故參天兩地而倚數也。

Four multiplied by nine is thirty-six, and six multiplied by six is also thirty-six. Yang itself occupies six, and it also takes half of the six of Yin, so altogether it makes nine. Therefore, in terms of the upper and lower hexagrams, Yin and Yang each occupy three lines. In terms of the three elements, Heaven, Earth, and Humanity each occupy two lines. Within Yin and Yang, each contains Heaven, Earth, and Humanity; within Heaven, Earth, and Humanity, each contains Yin and Yang. This is why it is said, "Three for Heaven, two for Earth, and the numbers are based on this." — taking three from Heaven and two from Earth, relying on them to establish all the numbers.

《易》有真數，三而已。參天者，三三而九。兩地者，倍三而六。參天兩地而倚數，非天地之正數也。倚者，擬也，擬天地正數而生也。《易》之數窮天地終始。或曰：“天地亦有終始乎？”曰：“既有消長，豈無終始？”天地雖大，是亦形器，乃二物也。

The true root number of the Yi is only three. The term "san tian" (three heavens) refers to three threes making nine, while "liang di" (two earths) refers to twice three making six. "San tian liang di er yi shu" (three heavens and two earths and thus the numbers are derived) does not refer to the actual numbers of heaven and earth, but rather to numbers that are imitated or compared to them—"yi" means to imitate or compare, and it is derived by analogy with the actual numbers of heaven and earth. The numbers of the Yi can exhaust the beginning and end of heaven and earth. Someone asks, "Does heaven and earth have a beginning and an end?" The answer is, "If there is waxing and waning, how could there not be beginning and end?" Although heaven and earth are vast, in the end they are merely two things, tangible objects.

《易》之生數，一十二萬九千六百，總為四千三百二十世。此消長之大數，衍三十年之辰數，即其數也。歲三百六十日，得四千三百二十辰。以三十乘之，得其數矣。凡甲子甲午為世首，此為經世之數，始於日甲月子星甲辰子。又云，此經世日甲之數，月子星甲辰子從之也。

The numbers of the Book of Changes are twelve thousand nine hundred and sixty, totaling four thousand three hundred and twenty generations, which is the total number of increase and decrease. Its origin is derived by calculating the number of cycles in thirty years: one year has three hundred and sixty days, each day contains twelve cycles, resulting in four thousand three hundred and twenty cycles; multiplying this by thirty years gives exactly twelve thousand nine hundred and sixty. Whenever the Jiazi or Jiawu cycles occur, they mark the beginning of a new generation. This is called the "Classic of the World" number, starting from the position where the day is Jia, the month is Zi, the star is Jia, and the hour is Zi. It is also said that this number in the Classic of the World has the day in the position of Jia, with the month Zi, the star Jia, and the hour Zi following in sequence.

十、百、千、萬、億為奇，天之數也。十二、百二十、千二百、萬二千、億二萬為偶，地之數也。十干天也，十二支地也，支干配天地之用也。乾者，乾之義，陽也；支者，枝之義，陰也。乾十而支十二，是陽數中有陰，陰數中有陽也。陽數一，衍之為十，十干之類是也；陰數二，衍之為十二，十二支、十二月之類是也。陽無十，故不足於後；陰無一，故不足於首。

Ten, hundred, thousand, ten thousand, and hundred million belong to the odd numbers, which are associated with Heaven; twelve, two hundred forty, one thousand two hundred, twelve thousand, and one hundred and two million belong to the even numbers, which are associated with Earth. The ten Heavenly Stems belong to Heaven, and the twelve Earthly Branches belong to Earth. When the Heavenly Stems and Earthly Branches are combined, it reflects the application of Heaven and Earth. "Stem" refers to the trunk of a tree, which is yang; "Branch" refers to branches, which is yin. The Heavenly Stems have ten, while the Earthly Branches have twelve, showing that yang contains yin and yin contains yang. The fundamental number of yang is one, which expands to ten, forming the ten Heavenly Stems; the fundamental number of yin is two, which expands to twelve, forming the twelve Earthly Branches and the twelve months. In the yang system, there is no "ten" as a complete unit, so it lacks one at the end; in the yin system, there is no "one," so it lacks one at the beginning.

陽數於三百六十上盈，陰數於三百六十上縮。體四而變六，兼神與氣也。氣變必有故，三百六十也。氣以六變，體以四分。天地之交十之三。

Taking a year of 360 days as the standard, the yang number has an excess in this count, while the yin number has a deficiency. The body itself is originally four, but when it changes, it becomes six. The two extra parts include both "shen" and "qi." The changes of qi must have a fixed standard, which is 360. Qi changes in groups of six, while the body is divided into four. The part where heaven and earth meet accounts for three-tenths.

凡事為之極，凡十之七，則可以正矣。蓋夏至之日，止於六十，兼之以晨昏分，可辨邑矣。庶幾乎十之七也。正音律數行至於七而止者，以夏至之日出於寅而入於戌，亥子丑三時，則日入於地，而目無所見。此三數不行者，所以比於三時也。故生物之數亦然。非數之不行也，有數而不見也。

When doing any task to the utmost, it is generally considered completed when reaching about seven-tenths. For example, on the summer solstice, the daylight lasts only for sixty minutes, but adding the faint light of morning and evening, it is enough to discern the outline of a city, which is nearly seven-tenths. When tuning musical scales, the count stops at seven, because on the summer solstice the sun rises at the hour of Yin and sets at the hour of Xu, and during the hours of Hai, Zi, and Chou, the sun is beneath the earth, and nothing can be seen with the eyes. The reason the count cannot proceed further is exactly corresponding to those three hours. The same principle applies to the numbers of living beings: it is not that the numbers cannot be counted further, but rather that although the numbers exist, people cannot see them.

天下之數出於理。違乎理，則入於術。世人以數而入術，故失於理也。

All numbers in the world arise from "li" (principle). Once one deviates from li, it degenerates into alchemy. People are only preoccupied with manipulating numbers and fall into the path of alchemy, thus losing sight of li—this is the boundary Shao Yong set for his theory of figures and numbers: numbers are used to perceive principle, not for fortune-telling or trickery.

太極既分，兩儀立矣。陽下交於陰，陰上交於陽，四象生矣。陽交於陰，陰交於陽，而生天之四象；剛交於柔，柔交於剛，而生地之四象。於是八卦成矣。八卦相錯，然後萬物生焉。是故一分為二，二分為四，四分為八，八分為十六，十六分為三十二，三十二分為六十四。故曰分陰分陽，迭用柔剛，易六位而成章也。

After the Taiji is divided into two, yin and yang are established. Yang comes down to combine with yin, and yin goes up to combine with yang, thus producing the four images. When yang combines with yin and yin combines with yang, the four images of heaven are generated: Taiyang (Great Sun), Taiyin (Great Yin), Shaoyang (Less Sun), and Shaoyin (Less Yin). When hardness combines with softness and softness combines with hardness, the four images of earth are generated: Taigang (Great Hardness), Tairou (Great Softness), Shaogang (Less Hardness), and Shaorou (Less Softness). At this point, the eight trigrams take shape. When the eight trigrams interact with each other, all things come into being. Therefore, one divides into two, two into four, four into eight, eight into sixteen, sixteen into thirty-two, and thirty-two into sixty-four. The "Say on the Trigrams" explains this: separating yin and separating yang, alternating the use of softness and hardness, the Book of Changes arranges six lines to form its chapters.

十分為百，百分為千，千分為萬，猶根之有乾，乾之有枝，枝之有葉。愈大則愈少，愈細則愈繁，合之斯為一，衍之斯為萬。是故乾以分之，坤以翕之，震以長之，巽以消之。長則分，分則消，消則翕也。乾坤定位也，震巽一交也，兌離坎艮再交也。故震陽少而陰尚多也，巽陰少而陽尚多也，兌離陽浸多也，坎艮陰浸多也，是以辰與火不見也。

Following this pattern, ten becomes a hundred, a hundred becomes a thousand, and a thousand becomes ten thousand, just like how tree roots produce trunks, trunks produce branches, and branches produce leaves. The larger the scale, the fewer the parts, and the more detailed the parts, the more numerous they are. When gathered together, they form one; when spread out, they become ten thousand. Therefore, Qian (Heaven) governs separation, Kun (Earth) governs gathering, Zhen (Thunder) governs growth, and Xun (Wind) governs reduction. When growth reaches its peak, it must separate; when separation reaches its peak, it must reduce; when reduction reaches its peak, it must gather. Qian and Kun determine the positions of upper and lower; Zhen and Xun are the initial interactions; Dui and Li are the secondary interactions. Therefore, Zhen represents the initial emergence of yang with yin still dominant, Xun represents the initial emergence of yin with yang still dominant, Dui and Li represent increasing yang, and Kan and Gen represent increasing yin. It is precisely because of this imbalance between yin and yang that the "Chen" (Dragon) in the heavenly four trigrams and the "Fire" in the earthly four elements are hidden.

一氣分而陰陽判。得陽之多者為天，得陰之多者為地。是故陰陽半而形質具焉，陰陽偏而性情分焉。形質又分，則多陽者為剛也，多陰者為柔也。性情又分，則多陽者陽之極也，多陰者陰之極也。兌離巽得陽之多者也，艮坎震得陰之多者也，是以為天地用也。乾陽極，坤陰極，是以不用也。

A single original qi splits into two parts, and yin and yang become clearly distinct. Those with more yang become heaven, and those with more yin become earth. When yin and yang each take up half, form and substance are established; when yin and yang are imbalanced, nature and emotion are differentiated. When form and substance are further divided, yang predominance leads to hardness, while yin predominance leads to softness. When nature and emotion are further divided, yang predominance reaches the extreme of yang, and yin predominance reaches the extreme of yin. Dui, Li, and Xun have more yang, while Gen, Kan, and Zhen have more yin, so these six trigrams are used for heaven and earth. Qian represents the extreme of yang, and Kun represents the extreme of yin. Being too pure and complete, they are not used.

乾坤之名位不可易也，坎離名可易而位不可易也，震巽位可易而名不可易也，兌艮名與位皆可易也。離肖乾，坎肖坤，中孚肖乾，頤肖離，小過肖坤，大過肖坎。是以乾、坤、離、坎、中孚、頤、大過、小過，皆不可易者也。離在天而當夜，故陽中有陰也；坎在地而當晝，故陰中有陽也。震始交陰而陽生，巽始消陽而陰生。兌陽長也，艮陰長也。震兌在天之陰也，巽艮在地之陽也。故震兌上陰而下陽，巽艮上陽而下陰。

The names and positions of the hexagrams Qian and Kun cannot be changed. The names of Kan and Li can be exchanged, but their positions cannot be changed. The positions of Zhen and Xun can be exchanged, but their names cannot be changed. The names and positions of Dui and Gen can both be exchanged. In terms of hexagram shapes, Li resembles Qian, Kan resembles Kun, Zhongfu resembles Qian, Yi resembles Li, Xiaoguo resembles Kun, and Daguo resembles Kan. When they are reversed, they remain the same as the original hexagram. Therefore, Qian, Kun, Li, Kan, Zhongfu, Yi, Daguo, and Xiaoguo are eight hexagrams that remain unchanged when reversed. Li belongs to heaven but is associated with the night position, showing that yang contains yin. Kan belongs to earth but is associated with the day position, showing that yin contains yang. Zhen is yang yang beginning to interact with yin and yang energy beginning to arise. Xun is yang yang beginning to be reduced and yin energy beginning to arise. Dui is yang increasing, and Gen is yin increasing. Zhen and Dui are yin on the heavenly side, while Xun and Gen are yang on the earthly side. Therefore, Zhen and Dui have the top line as yin and the lower lines as yang, while Xun and Gen have the top line as yang and the lower lines as yin.

天以始生言之，故陰上而陽下，交泰之義也；地以既成言之，故陽上而陰下，尊卑之位也。乾坤定上下之位，離坎列左右之門。天地之所闔闢，日月之所出入。是以春夏秋冬，晦朔弦望，晝夜長短，行度盈縮，莫不由乎此矣。

Heaven is spoken of in terms of the beginning of all things, so yin is above and yang is below, taking the meaning of the Tai hexagram, where heaven and earth interconnect; Earth is spoken of in terms of the completion of all things, so yang is above and yin is below, taking the meaning of each occupying its proper position according to rank and hierarchy. The positions of heaven and earth are established by Qian and Kun, while Li and Kan are arranged as left and right gates: here heaven and earth open and close, and the sun and moon rise and set. Therefore, the succession of the four seasons, the waxing and waning of the moon, the changes in the length of day and night, and the movement and variations of the sun and moon all originate from here.

乾四分取一以與坤，坤四分取一以奉乾，乾坤合而生六子，三男皆陽也，三女皆陰也。兌分一陽以與艮，坎分一陰以奉離，震巽以二相易，合而言之，陰陽各半。是以水火相生而相剋，然後既成萬物也。

Heaven gives a quarter of its yang to Earth, and Earth gives a quarter of its yin to Heaven. When Heaven and Earth combine, they produce six children: Zhen, Kan, and Gen, the three sons, are yang, while Xun, Li, and Dui, the three daughters, are yin. Dui gives a yang to Gen, Kan gives a yin to Li, and Zhen and Xun exchange their two lines. Altogether, yin and yang each make up half. Because of this, water and fire both generate and control each other, and all things are completed through this mutual generation and control.

乾坤縱而六子橫，《易》之本也。震兌橫而六卦縱，《易》之用也。起震終艮一節，明文王八卦也。天地定位一節，明伏羲八卦也。八卦相錯者，相交錯而成六十四卦也。數往者順，若順天而行，是左旋也，皆已生之卦也，故云數往也；知來者逆，若逆天而行，是右行也，皆未生之卦也，故云知來也。夫《易》之數由逆而成矣。此一節直解圖意，若逆知四時之謂也。

Heaven and Earth are arranged vertically, with the six sons placed horizontally, which represents the fundamental structure of the Book of Changes. The trigrams Zhen and Dui are placed horizontally, while the remaining six trigrams are arranged vertically, which illustrates the functional aspect of the Book of Changes. The passage in "Shuo Gua" that says "The Emperor emerges from Zhen... and the conclusion is expressed in Gen" refers to King Wen's trigrams. The passage that says "Heaven and Earth are positioned, mountains and marshes communicate through their energies" refers to Fuxi's trigrams. The term "eight trigrams interacting" means that the eight trigrams intermingle to form the sixty-four hexagrams. "Counting the past in a forward direction" follows the direction of Heaven, which is left rotation, and counts already formed hexagrams, hence called "counting the past." "Knowing the future in a reverse direction" goes against the direction of Heaven, which is right rotation, and predicts hexagrams that have not yet formed, hence called "knowing the future." The numerical system of the Book of Changes is established through reverse reasoning. This passage directly explains the purpose of the Earlier Heaven diagram, like foreseeing the four seasons in reverse.

陽在陰中，陽逆行；陰在陽中，陰逆行。陽在陽中，陰在陰中，則皆順行。此真至理，按圖可見之矣。順數之，乾一、兌二、離三、震四、巽五、坎六、艮七、坤八；逆數之，震一、離兌二、乾三、巽四、坎五、艮坤六也。

When yang is in the domain of yin, yang moves in reverse; when yin is in the domain of yang, yin also moves in reverse. When yang is in the domain of yang and yin is in the domain of yin, both move in the correct direction. This is the true fundamental principle, which becomes clear upon looking at the Earlier Heaven diagram. Counting forward, it is Qian one, Dui two, Li three, Zhen four, Xun five, Kan six, Gen seven, Kun eight. Counting backward, it is Zhen one, Li and Dui both two, Qian three, Xun four, Kan five, Gen and Kun both six.

四正者，乾坤坎離也。觀其象無反覆之變，所以為正也。卦之反對，皆六陽六陰也。在《易》則六陽六陰者，十有一對也。去四正者，八陽四陰、八陰四陽者，各六對也。十陽二陰、十陰二陽者，各三對也。

The term "four cardinal trigrams" refers to the trigrams Qian (Heaven), Kun (Earth), Kan (Water), and Li (Fire). When observing their images, they remain the same even when viewed upside down, showing no change, hence they are called "cardinal." Any two trigrams that are opposite to each other always combine to form six yang lines and six yin lines. In the Book of Changes, such pairs of six yang and six yin lines total eleven pairs. Excluding the four cardinal trigrams, there are six pairs of eight yang and four yin lines, and six pairs of eight yin and four yang lines; three pairs of ten yang and two yin lines, and three pairs of ten yin and two yang lines.

復至乾，凡百有十二陽；姤至坤，凡八十陽；姤至坤，凡百有十二陰；復至乾，凡八十陰。夫《易》根於乾坤，而生於姤復。蓋剛交柔而為復，柔交剛而為姤，自茲而無窮矣。無極之前，陰含陽也；有象之後，陽分陰也。陰為陽之母，陽為陰之父。故母孕長男而為復，父生長女而為姤。是以陽起於復，而陰起於姤也。

From the Fu hexagram to the Qian hexagram, there are 112 yang lines; from the Gou hexagram to the Kun hexagram, there are 80 yang lines; from the Gou hexagram to the Kun hexagram, there are 112 yin lines; and from the Fu hexagram to the Qian hexagram, there are 80 yin lines. The Book of Changes originates from Qian and Kun, but actually arises from Gou and Fu hexagrams: when yang withdraws to meet yin, it becomes Fu; when yin withdraws to meet yang, it becomes Gou. From here, change is endless. Before the "wuji" (formless state) becomes manifest, yin contains yang; once there is form, yang differentiates into yin. Yin is the mother of yang, and yang is the father of yin. Therefore, the mother gives birth to the eldest son, forming the Fu hexagram, and the father produces the eldest daughter, forming the Gou hexagram. Thus, yang energy begins with Fu, and yin energy begins with Gou.

諸卦不交於乾坤者，則生於否泰。否泰，乾坤之交也。乾坤起自奇偶，生自太極。自泰至否，其間則有蠱矣；自否至泰，其間則有隨矣。一變而二，二變而四，三變而八卦成矣。四變而有十六，五變而三十有二，六變而六十四卦備矣。

All hexagrams that do not directly arise from the interaction of Qian and Kun are generated from the hexagrams of Bǐ and Tà; Bǐ and Tà themselves are the products of the interaction between Qian and Kun. Qian and Kun originate from the two lines of odd and even, emerging from the Taiji. Transitioning from the Tà hexagram to the Bǐ hexagram involves the Gu hexagram; transitioning from the Bǐ hexagram back to the Tà hexagram involves the Sui hexagram. As for the sequence of generating hexagrams: one change produces two, two changes produce four, three changes form the eight trigrams, four changes produce sixteen, five changes produce thirty-two, and six changes complete the sixty-four hexagrams.

至哉！文王之作《易》也，其得天地之用乎？故乾坤交而為泰，坎離交而為既濟也。乾生於子，坤生於午，坎終於寅，離終於申，以應天之時也。置乾於西北，退坤於西南，長子用事，而長女代母。坎離得位，兌艮為偶，以應地之方也，王者之法其盡於是矣。

What an amazing achievement! King Wen composed the Book of Changes, probably mastering the "use" of heaven and earth. Thus, Heaven and Earth interact to form Tai, and Water and Fire interact to form Ji Ji. The energy of Heaven originates at the Zi position, and the energy of Earth originates at the Wu position. Water concludes at the寅 position, and Fire concludes at the申 position; this corresponds to the sequence of heaven's time. Placing Heaven in the Northwest and Earth in the Southwest, with Zhen (Thunder) as the eldest son taking charge and Xun (Wind) as the eldest daughter acting as the mother, Water and Fire each occupying their proper positions, Dui (Lake) and Gen (Mountain) forming a pair—this corresponds to the directions of the earth. The principles for a ruler to govern the world are all contained within this.

《易》者，一陰一陽之謂也。震兌始交者也，故當朝夕之位。離坎交之極也，故當子午位。巽艮雖不交，而陰陽猶雜也，故當用中之偏位。乾坤純陰陽也，故當不用之位。坤純三女於西南，乾純三男於東北。道生天，天生地。及其功成而身退，故子繼父禪，是以乾退一位也。

The Book of Changes refers to the alternation of yin and yang. The trigrams Zhen and Dui represent the initial meeting of yin and yang, so they are placed at the positions of morning and evening. The trigrams Li and Kan represent the extreme meeting of yin and yang, so they are placed at the Zi position and the Wu position. The trigrams Xun and Gen, although not directly meeting, still contain a mixture of yin and yang, so they are placed in positions that are slightly biased within the dynamic positions. The trigrams Qian and Kun represent pure yang and pure yin, so they are placed in positions of existence without use. Thus, Kun gathers three daughters in the Southwest, and Qian gathers three sons in the Northeast. The Dao gives birth to heaven, and heaven gives birth to earth; when achievements are completed, the self withdraws, like a son succeeding his father's abdication, so Qian steps back one position from its original place.

《易》之首於乾坤，中於坎離，終於水火之交不交，皆至理也。自乾坤至坎離，以天道也；自咸恆至既濟未濟，以人事也。乾坤交而為泰，變而為雜卦也。上經起於三，下經起於四，皆交泰之義也。

The Book of Changes begins with the trigrams Qian (Heaven) and Kun (Earth), and in the middle it includes Kan (Water) and Li (Fire). It concludes with Ji Ji (Water and Fire in mutual interaction) and Wei Ji (Water and Fire not interacting), all expressing extremely subtle principles. From Qian and Kun to Kan and Li, this section discusses the principles of Heaven; from Xian (Harmony) and Heng (Permanence) to Ji Ji and Wei Ji, this section discusses human affairs. When Qian and Kun interact, they form the Tai trigram. Further changes lead to the complex trigrams listed in the Zage (Miscellaneous Trigrams). The Upper Canon contains thirty trigrams, beginning with the number three; the Lower Canon contains thirty-four trigrams, beginning with the number four: three represents the number of Heaven, and four represents the number of Earth. The combination of Heaven's three and Earth's four signifies the harmonious interaction between Heaven and Earth.

乾坤坎離為上篇之用，兌艮震巽為下篇之用也。頤、中孚、大過、小過為二篇之正也。乾坤天地之本，坎離天地之用。是以《易》始於乾坤，中於坎離，終於既濟未濟。而泰否為上經之中，咸恆為下經之首，皆言乎其用也。故《易》者，用也。乾用九，坤用六，大衍用四十九，而潛龍勿用也。大哉用乎！吾於此見聖人之心也。

The four trigrams used in the upper section are Qian, Kun, Kan, and Li; the four trigrams used in the lower section are Dui, Gen, Zhen, and Xun; while Yi, Zhongfú, Daguò, and Xiaoguò are the main trigrams that connect both sections. Qian and Kun represent the fundamental nature of heaven and earth, while Kan and Li represent their functions. Therefore, the Book of Changes begins with Qian and Kun, places Kan and Li in the center, and concludes with Ji Ji and Wei Ji. Tai and Po are in the middle of the upper section, while Yan and Heng are at the beginning of the lower section, all discussing the concept of "use" (yong). Thus, the Book of Changes is fundamentally about "use." Qian speaks of "Yong Ji," Kun speaks of "Yong Liu," the Great Derivation involves fifty numbers but uses forty-nine, and Qian's initial line, Chou Ji, also speaks of "Qian Long Wu Yong." The concept of "use" is of great importance! From here, I see the mind of the sage.

夫卦各有性有體，然皆不離乾坤之門，如萬物受性於天，而各為其性也。在人則為人之性，在禽獸則為禽獸之性，在草木則為草木之性。不知乾，無以知性命之理。在人則乾道成男，坤道成女；在物則乾道成陽，坤道成陰。

Each trigram has its nature and its essence, yet none can be separated from the gate of Qian and Kun; just as all things receive their fundamental nature from Heaven, yet each becomes its own nature: when it falls upon a person, it becomes the nature of a person; when it falls upon birds and beasts, it becomes the nature of birds and beasts; when it falls upon grass and trees, it becomes the nature of grass and trees. Without understanding Qian, one cannot understand the principles of nature and destiny. When applied to human beings, the principle of Qian gives rise to masculinity, and the principle of Kun gives rise to femininity; when applied to all things, the principle of Qian gives rise to yang, and the principle of Kun gives rise to yin.

君子於《易》，玩象、玩數、玩辭、玩意。象起於形，數起於質，名起於言，意起於用。有意必有言，有言必有象，有象必有數。數立則象生，象生則言彰，言彰則意顯。象數則筌蹄也，言意則魚兔也。得魚兔而忘筌蹄則可也，舍筌蹄而求魚兔則未見其得也。

A gentleman studying the Book of Changes should repeatedly reflect on four things: the meaning of the hexagrams, the numbers associated with them, the statements of the lines, and the implied meanings beyond the statements. The meaning of the images comes from their forms, the numbers come from their materials, the names come from words, and the meaning comes from their functions. Meaning must rely on words, words must rely on images, and images must rely on numbers. Once the numbers are established, the images arise; once the images arise, the words become clear; once the words become clear, the meaning is revealed. The relationship between images and numbers is like the fish trap and rabbit foot mentioned in the Zhuangzi. The relationship between words and meaning is like the fish and rabbit that the trap and foot are used to catch. If one catches the fish and rabbit and then forgets the trap and foot, that is acceptable; but if one forgets the trap and foot and tries to seek the fish and rabbit in vain, no one has ever succeeded in doing so.

《易》有意象，立意皆所以明象。統下三者有言象，不擬物而直言以明事；有象象，擬一物以明意；有數象，七日、八月、三年、十年之類是也。《易》有內象，理致是也；有外象，指定一物而不變者是也。自然而然，不得而更者，內象內數也，他皆外象外數也。乾為天之類，本象也；為金之類，別象也。

The Yi contains "yi xiang" (meaning images). Whenever there is an intention, it is to clarify the image, and it encompasses three categories: first, "yan xiang" (verbal image), which does not compare with specific things but directly explains an event through words; second, "xiang xiang" (image image), which explains the meaning by comparing it with something else; third, "shu xiang" (numerical image), such as "seven days," "eight months," "three years," and "ten years" in the line statements of the hexagrams. The Yi also has "nei xiang" (inner image), which refers to the direction of meaning and principle; and "wai xiang" (outer image), which refers to a fixed reference to a specific thing without change. Whatever is natural and unchangeable belongs to inner image and inner number; the rest are outer image and outer number. For example, the Qian hexagram takes the image of heaven as its original image; taking the image of metal is its alternative image.

乾，奇也，陽也，健也。故天下之健，莫如天。坤，偶也，陰也，順也。故天下之順，莫如地，所以順天也。震，起也，一陽起也。起，動也。故天下之動，莫如雷。坎，陷也，一陽陷於二陰。陷，下也。故天下之下，莫如水。艮，止也，一陽於是而止也。故天下之止，莫如山。巽，入也，一陰入二陽之下。故天下之入，莫如風。離，麗也，一陰離於二陽，其卦錯然成文而華麗也。故天下之麗，莫如火。故又為附麗之麗。兌，說也，一陰出於外而說於物。故天下之說，莫如澤。

Qian is the odd trigram, belonging to yang, with the virtue of being strong and vigorous. Therefore, nothing in the world is more strong and vigorous than heaven. Kun is the even trigram, belonging to yin, with the virtue of being gentle and compliant. Therefore, nothing in the world is more gentle and compliant than earth, which is used to follow and support heaven. Zhen is "movement," with a yang line at the bottom rising up; movement is action, so nothing in the world is more active than thunder. Kan is "sinking," with a yang line sinking between two yin lines; sinking is downward movement, so nothing in the world moves downward as much as water. Gen is "stopping," with a yang line rising to the top and then stopping; therefore, nothing in the world stops as much as a mountain. Xun is "entering," with a yin line penetrating beneath two yang lines; therefore, nothing in the world enters as much as wind. Li is "adornment," with a yin line attached between two yang lines, forming a pattern through the interweaving of the trigrams, appearing splendid and ornate; therefore, nothing in the world is more splendid than fire; from "adornment" it also derives the meaning of attachment and reliance. Dui is "joy," with a yin line exposed, causing all things to be joyful; therefore, nothing in the world brings more joy than a marsh.

火內暗而外明，故離陽在外，火之用，用外也。水外暗而內明，故坎陽在內，水之用，用內也。震為龍，一陽動於二陰之下，震也。重淵之下有動物者，豈非龍乎？兌，說也，其他說皆有所害，惟朋友講習無說於此，故言其極者也。以尊降卑曰臨，以上觀下曰觀。

The inner part of fire is dark, while the outer part is bright, so the hexagram "Li" (Fire) places the yang lines at the top and bottom and the yin line in the middle: the two yang lines outside symbolize the spreading light of fire, while the single yin line in the middle represents the inner darkness of the fire's core. The function of fire is to illuminate and burn outwardly, so it is said to be "using the outside." Water is the opposite: the surface of water is dark and not transparent, yet its inner part is clear and bright, so the hexagram "Kan" (Water) places the yang line in the middle and the yin lines at the top and bottom: the single yang line in the middle symbolizes the clarity within water, while the two yin lines outside represent the darkness of the water's surface. The function of water is to moisten and contain inwardly, so it is said to be "using the inside." Thus, Shao Yong's method of establishing hexagrams is to first understand the nature of an object and then determine how its hexagram should be arranged. The hexagram "Zhen" (Thunder) is taken as the image of a dragon: a single yang line beginning to move beneath two yin lines, which is the shape of the hexagram Zhen; in the deepest part of a vast abyss, there is still a living creature capable of movement, which is not precisely a dragon? The hexagram "Dui" (Lake) signifies joy. Other forms of joy often come with some harm, but the joy from friends discussing learning has no harm at all, so the "Great Image Commentary" of the hexagram Dui says "the superior person uses friendship to study and discuss," referring precisely to this kind of pure joy. When the superior party humbles itself to be below the inferior party, it is called "Lin" (Approaching); when one is in a superior position and looks down upon the inferior, it is called "Guan" (Observing). The names of the hexagrams Lin and Guan are derived from the relationship between the upper and lower trigrams.

復次剝，明治生於亂乎？姤次夬，明亂生於治乎？時哉！時哉！未有剝而不復，未有夬而不姤者。防乎其防，邦家其長，子孫其昌。是以聖人貴未然之防。是謂《易》之大綱。寂然不動，反本復靜，坤之時也。感而遂通天下之故。陽動於中，間不容髮，復之義也。

In the sequence of hexagrams in The Zhou Changes, the hexagram of "Recovery" immediately follows the hexagram of "Decrease," which clearly shows that peace arises from chaos. Similarly, the hexagram of "Meeting" follows the hexagram of "Final Decision," which clearly shows that chaos arises from peace. The key lies entirely in the concept of "time," entirely in the concept of "time!" There has never been a decrease that reaches its end without a recovery, nor has there ever been a complete dominance of yang without a renewed encounter with yin. If a state can establish defenses layer by layer before calamities take shape, the state will endure long and its descendants will flourish. Therefore, sages place the greatest emphasis on preventing things before they occur, which is the main principle of the entire Zhou Changes. The hexagram of "Earth" has all six lines as pure yin, remaining still and quiet, with all things returning to their origin and reverting to stillness, which represents the period governed by "Earth." The "Commentary on the Hexagrams" mentions "when there is a response, one can understand all the workings of the world," which refers to the hexagram of "Recovery"—a single yang line beginning to stir among the many yin lines, with no space even for a hair to be inserted between stillness and movement. This is the meaning of "Recovery."

不見動而動，妄也，動於否之時是也。見動而動，則為無妄。然所以有災者，陽微而無應也。有應而動，則為益矣。大過，本末弱也。必有大德大位，然後可救常分。有可過者，有不可過者。有大德大位，可過者也，伊周其人也，不可懼也；有大德無大位，不可過也。孔孟其人也，不可悶也。其位不勝德邪？大哉位乎！待才（一雲時）用之宅也。

There is no sign of action yet one acts forcefully, which is called "wandering without purpose." In the hexagram of "Non-Action," when heaven and earth are not in communication and the upper and lower parts are blocked, acting recklessly is exactly this kind of situation. Acting only when there is a clear sign of action is called "No Wandering." However, the hexagram of "No Wandering" still mentions "calamity without wandering," because the yang lines are weak and do not receive support from corresponding lines. If there is support and then action takes place, it becomes the hexagram of "Increase," resulting in gain. In the hexagram of "Great Excess," the first and sixth lines are all yin lines, so the "Commentary on the Judgment" says it "has weak beginning and end," meaning the root and the tip are not firm. In such a situation, one must have great virtue and hold a high position to rescue this extraordinary difficulty. Some people can act boldly beyond ordinary people, while others cannot. Those who have both great virtue and high position belong to the category that can act boldly, like Yi Yin and the Duke of Zhou, who do not need to fear. Those who have great virtue but no high position cannot act forcefully, like Confucius and Mencius, who do not need to be distressed. Is it that their positions are not suitable for their virtue? The role of position is indeed significant; it is the house waiting for talent (or timing) to reside and display its abilities.

作《易》者，其如知乎？聖人知天地萬物之理，而一以貫之。夫《易》者，聖人長君子消小人之具也。及其長也，闢之於未然；及其消也，闔之於未然。一消一長，一闔一闢，渾渾然無跡。非天下之至神，其孰能與於此？神者，《易》之主也，所以無方；《易》者，神之用也，所以無體。神無方而《易》無體，滯於一方，則不能變化，非神也；有定體則不能變通，非《易》也。《易》雖有體，體者象也，假象以見體，而本無體也。

The sages who composed the Zhou Yi were probably those who truly understood the principles of heaven and earth. They comprehended the principles of all things in the universe and used a fundamental principle to connect them. The Zhou Yi is a tool used by the sages to cultivate the virtuous and eliminate the petty. To cultivate the virtuous, one should open the door before the matter occurs; to eliminate the petty, one should close the door before the matter occurs. One elimination and one growth, one closing and one opening, all unified without leaving any trace. If it is not the most profound and mysterious existence, who could participate in such a realm? "Shen" is the master of the Zhou Yi, so it does not reside in a fixed place; the Zhou Yi is the manifestation of "Shen," so it does not take a fixed form. The Great Treatise says, "Shen has no fixed place and the Zhou Yi has no fixed form." Once it is fixed in a particular direction, it cannot change freely, and thus it is not "Shen"; once it has a fixed form, it cannot be flexible, and thus it is not the Zhou Yi. Although the Zhou Yi also speaks of "body," its body is only the "image" of the hexagrams and lines, using the image to show the body, and in itself, it has no physical form.

《易》無體也，曰既有典常，則是有體也，恐遂以為有體，故曰不可為典要。既有典常，常也。不可為典要，變也。生而成，成而生，《易》之道也。元亨利貞，變易不常，天道之變也；吉凶悔吝，變易不定，人道之應也。天變而人效之，故元亨利貞，《易》之變也；人行而天應之，故吉凶悔吝，《易》之應也。以元亨為變，則利貞為應；以吉凶為應，則悔吝為變。元則吉，吉則利，應之亨則凶，凶則應之以貞；悔則吉，吝則凶。是以變中有應，應中有變也。變中之應，天道也。故元為變，則亨應之；利為變，則應之以貞。應中之變，人事也。故變則凶，應則吉；變則吝，應則悔也。悔者吉之先，而吝者凶之本，是以君子從天不從人。

The Zhou Changes originally had no fixed form. The Great Treatise says, "It has established principles," which at first glance seems to suggest it has a fixed form. Shao Yong was worried that people might mistakenly think it has a physical entity, so the Great Treatise immediately follows with, "It cannot be taken as a fixed standard." "It has established principles" refers to its constant aspect, while "It cannot be taken as a fixed standard" refers to its changing aspect. It arises and moves toward completion, and once completed, it renews itself. This is the way of the Zhou Changes. The four virtues, "Yuan, Heng, Li, Zhen," are constantly changing and belong to the aspect of "change" in the heavenly way; the four outcomes, "Ji, Xiong, Hui, Lin," are uncertain and belong to the aspect of "response" in the human way. Heaven changes first, and humans follow it, so Yuan, Heng, Li, Zhen are the "change" of the Zhou Changes; humans act first, and Heaven responds to them, so Ji, Xiong, Hui, Lin are the "response" of the Zhou Changes. If "Yuan and Heng" are considered as change, then "Li and Zhen" are response; if "Ji and Xiong" are considered as response, then "Hui and Lin" are change. Gaining Yuan brings Ji, Ji leads to profit, and the corresponding Heng may hide Xiong, while Xiong requires Zhen to respond. Hui can turn into Ji, and Lin tends toward Xiong. Therefore, change contains response, and response also contains change. The response within change belongs to the heavenly way, so taking Yuan as change, Heng responds to it; taking Li as change, Zhen responds to it. The change within response belongs to human affairs, so when humans act recklessly, they invite Xiong, but when they follow the way, they gain Ji; reckless change leads to Lin, while following the way leads to Hui. Hui is a precursor to Ji, and Lin is the root of Xiong. Therefore, the gentleman prefers to follow the heavenly way rather than be swayed by human tricks.

元者，春也，仁也。春者時之始，仁者德之長。時則未盛，而德足以長人，故言德而不言時。亨者，夏也，禮也。夏者時之盛，禮者德之文。盛則必衰，而文不足救之，故言時而不言德，故曰“大哉，乾元！而上九有悔也”。利者，秋也，義也。秋者時之成，義者德之方，萬物方成而獲利，義者不通於利，故言時而不言德也。貞者，冬也，智也。冬者時之末，智者德之衰。正則吉，不正則凶。故言德而不言時也。故曰利貞者，性情也。元亨利貞之德，各包吉凶悔吝之事。雖行乎德，若違於時，亦或凶矣。

"Yuan" corresponds to spring among the four seasons and to benevolence among the five constants. Spring is the beginning of the yearly sequence, and benevolence is the virtue most capable of fostering growth. At this time, the season is not yet vigorous, yet benevolence is sufficient to nurture others. Therefore, when discussing "Yuan," the focus is on virtue rather than on the season. "Heng" corresponds to summer and to propriety. Summer is the most flourishing stage of the seasonal cycle, and propriety is the external adornment of virtue. After reaching its peak, decline is inevitable, and mere adornment cannot prevent this decline. Therefore, when discussing "Heng," the focus is on the season rather than on virtue—hence the Commentary on the Judgment of the Qian hexagram praises "Great is the Qian Yuan," while the top line of the Qian hexagram warns of "An exalted dragon brings regret." "Li" corresponds to autumn and to righteousness. Autumn is the stage of the seasonal cycle when fruits are harvested, and righteousness is the standard of upright virtue. When all things have just matured and gained benefit, those who act with righteousness do not regard private gain as the norm. Therefore, when discussing "Li," the focus is again on the season rather than on virtue. "Zhen" corresponds to winter and to wisdom. Winter is the end of the seasonal cycle, and wisdom is the virtue closest to exhaustion. Upholding correctness brings good fortune, while failing to do so brings misfortune. Therefore, when discussing "Zhen," the focus again returns to virtue rather than to the season. Thus, the Wenyan of the Qian hexagram states, "Li zhen refers to nature and disposition." The four virtues of Yuan, Heng, Li, and Zhen each encompass the four categories of human affairs: good fortune, misfortune, regret, and hardship. Even if a person acts according to virtue, if they go against the timing, they may still invite misfortune.

初與上同，然上之亢，不及初之進也；二與五同，然二之陰中，不及五之陽中也；三與四同，然三處下卦之上，不若四之近君也。六虛者，六位也，虛以待變動之事也。《易》有三百八十四爻，真天文也。圖雖無文（先天圖也），吾終日言而未嘗離乎是。蓋天地萬物之理盡在其中矣。先天圖者，環中也。

A hexagram consists of six lines. The first line and the top line are both at the two ends of the hexagram, but the top line is in a position of extreme fullness and excess, which is not as promising as the first line, which is in the beginning stage and has potential for progress. The second line and the fifth line are both in the middle positions of the upper and lower trigrams, but the second line is a yin position, which is not as esteemed as the fifth line, a yang position. The third line and the fourth line are both at the boundary between the upper and lower trigrams, but the third line is only at the top of the lower trigram, which is not as close to the fifth line, the position of the ruler, as the fourth line is. The "six voids" mentioned in the Great Treatise refer to the six lines of a hexagram. They are called "voids" because these six positions are empty and waiting for the movement of events to fill them. The Zhou Changes contain sixty-four hexagrams and 384 lines, which is truly a celestial map. Although the Earlier Heaven diagram has no characters on it, I have been discussing it constantly without ever leaving it, because the principles of heaven and earth and all things are contained within it. The Earlier Heaven diagram, in the end, is about the circular center.

先天學，心法也。故圖皆自中起，萬化萬事生乎心也。先天學主乎誠，至誠可以通神明，不誠則不可以得道。先天之學，心也；後天之學，跡也。堯之前，先天也；堯之後，後天也。後天乃效法耳。《易》始於三皇，《書》始於五帝，《詩》始於三王，《春秋》始於五霸。所謂皇帝王霸者，非獨謂三皇五帝三王五霸而已，但用無為則皇也，用恩信則帝也，用公正則王也，用智力則霸也。

The study of the Earlier Heaven is a practice of cultivating the mind. Therefore, all diagrams of the Earlier Heaven begin from the center of the circle, symbolizing that all things, with their myriad changes and complexities, originate from the mind. The Earlier Heaven emphasizes "sincerity" as its core principle: when sincerity reaches its utmost, it can connect with the divine; without sincerity, one cannot attain the Way. The Earlier Heaven focuses on the mind, while the Later Heaven focuses on the traces left by the mind. Before the reign of Emperor Yao, it belonged to the Earlier Heaven; after Emperor Yao, it belonged to the Later Heaven. The Later Heaven is merely following the pattern of the Earlier Heaven. In terms of classic texts, the Zhou Yi began in the time of the Three Sovereigns, Fuxi, Shen Nong, and the Yellow Emperor. The Shang Shu began in the time of the Five Emperors. The Shi Jing began in the time of Xia Yu, Shang Tang, and the Western Zhou's King Wen, King Wu, and King Cheng. The Chun Qiu began in the time of the Five Hegemons. The terms "Sovereign," "Emperor," "King," and "Hegemon" do not refer solely to the specific individuals of the Three Sovereigns, Five Emperors, Three Kings, and Five Hegemons. Rather, those who governed the world through "non-action" are called Sovereigns, those who ruled through benevolence, virtue, and righteousness are called Emperors, those who ruled through fairness and integrity are called Kings, and those who ruled through wisdom and military strength are called Hegemons.

法始乎伏羲，成乎堯，革於三王，極於五霸，絕於秦。萬世治亂之跡，無以逃此矣。秦穆公伐鄭敗，而有悔過自誓之言。此非止霸者之事，幾於王道，能悔則無過矣。此聖人所以錄於書末也。平王名雖王，實不及一小國之諸侯。齊晉雖侯，而實僭王。此《春秋》之名實也。子貢欲去告朔之餼羊。羊，名也；禮，實也。名存而實亡，猶愈於名實俱亡。苟存其名，安知後世無王者作？是以有所待也。

The system of governing the world was first established by Fuxi, perfected by the Tang Yao, and then altered by the Xia, Shang, and Zhou dynasties' kings. It was pushed to its extreme by the Five Hegemons of the Spring and Autumn period, and finally ended with the Qin dynasty. The pattern of disorder and order throughout the ages cannot escape this line. When Duke Mu of Qin failed to capture Zheng at the Xiang Valley, he returned home and composed the "Qin Shi," expressing much regret and self-reproach. This was not merely the conduct of a hegemon, but almost that of a king. Being able to repent is equivalent to having no fault, which is why the sage included the "Qin Shi" as the last chapter of the "Book of Documents." The Son of Heaven, King Ping of Zhou, in name was the ruler of all under heaven, but in reality was no better than a small feudal lord. Meanwhile, the states of Qi and Jin, though nominally dukes, actually exercised the authority of the Son of Heaven. This is what the "Spring and Autumn Annals" aimed to clarify, the distinction between "name" and "reality." Zigan wanted to remove the sacrificial ram used in the monthly ritual of the new moon, but Confucius forbade it. The ram was the "name," while the ritual was the "reality." If the name remains while the reality is lost, it is better than both name and reality being lost. As long as the name remains, how can we be sure that a true king will not appear in later generations? Preserving the name is to leave a hope for the future.

秦穆公有功於周，能遷善改過，為霸者之最；晉文侯世世勤王，遷平王於洛，次之；齊桓公九合諸侯，不以兵車，又次之；楚莊強大，又次之；宋襄公雖霸而力微，會諸侯而為楚所執，不足論也。治《春秋》者，不先定四國之功過，則事無統理，不得聖人之心矣。《春秋》之間有功者，未見大於四國者。有過者，亦未見大於四國者也。故四國者，功之首，罪之魁也。五霸者，功之首，罪之魁也。

Qin Mu Gong had meritorious service to the Zhou royal house and was capable of reforming his ways for the good. Among the hegemonic rulers, he should be ranked first. Jin Wen Hou was diligent in serving the king's affairs across generations, and he escorted King Ping of Zhou to the eastern capital of Luoyi, ranking second. Qi Huan Gong convened the feudal lords in several alliances without resorting to military force, ranking third. Chu Zhuang Wang had a powerful state, ranking fourth. Song Xiang Gong, although he was called a hegemon, had weak power. He was captured by Chu during a conference of the feudal lords. He is not worth mentioning. Those who study the Spring and Autumn Annals should first clearly determine the merits and faults of the four states of Qin, Jin, Qi, and Chu. Otherwise, the historical events will lack a coherent order, and one will not be able to grasp the mind of the sage. During the entire period of the Spring and Autumn Annals, there were no greater merits than these four states, nor were there greater faults. Therefore, these four states were both the first in merit and the first in wrongdoing. The Five Hegemons were also like this; their merits were first, and their faults were also first.

《春秋》者，孔子之刑書也，功過不相掩。聖人先褒其功，後貶其罪。故罪人有功者，亦必錄之，不可不恕也。某人受《春秋》於尹師魯，師魯受於穆伯長。某人後復攻伯長，曰：“《春秋》無褒，皆是貶也。”田述古曰：“孫復亦云，《春秋》有貶而無褒。”曰《春秋》禮法廢，君臣亂，其間有能為小善者，安得不進之也。況五霸實有功於天下，且五霸固不及於王，不猶愈於左衽乎？安得不與之也？治《春秋》者，不辨名實，不定五霸之功過，則未可言治《春秋》。先定五霸之功過而治《春秋》，則大意立。若事事求之，則無緒也。《春秋》為君弱臣強而作，故謂之名分之書。

The Spring and Autumn Annals is a book of judgment composed by Confucius, in which merit and demerit are not obscured from each other. The sage first commends someone's merit and then criticizes his faults. Therefore, even if a person has committed a crime, if he has done some good deeds, they must be recorded as well, and some leniency must be shown. A person learned the Spring and Autumn Annals from Yin Zhu (style name Shilu), who in turn had learned it from Mu Xiu (style name Boyang). Later, this person criticized Mu Xiu, saying, "The Spring and Autumn Annals has no commendation, it is entirely about censure." Tian Shugǔ added, "Sun Fu also said that the Spring and Autumn Annals has censure but no commendation." Shao Yong replied, "In the time of the Spring and Autumn Annals, the rites and laws were neglected, and the order between sovereign and minister was confused. In such a time, if someone still did a little good deed, how could we not commend him? Moreover, the Five Hegemons indeed did some good to the world. Although the Five Hegemons were not as good as the Way of the King, they were still much better than the Central Plains becoming a barbarian culture of unclothed hair and left sleeves. How could we not give them some recognition? Those who study the Spring and Autumn Annals must first distinguish between name and reality and judge the merits and faults of the Five Hegemons. Only then can they be said to understand the Spring and Autumn Annals. First determine the merits and faults of the Five Hegemons, and then read the whole book. If you read it piece by piece, you will not be able to get the main idea. The Spring and Autumn Annals was written to address the situation of declining royal authority and strong ministerial power, so it is called a book about 'names and positions.'"

人言《春秋》非性命之書，非也。至於書“郊牛之口傷，改卜牛。牛死乃不效，猶三望”，此因魯事而貶之也。聖人何容心哉？無我故也，豈非由性命而發言也？又云，《春秋》皆因事而褒貶，豈聖人特立私意哉？人知《春秋》聖人之筆削，為天下之至公，不知聖人之所以為公也。如因牛傷，則知魯之僭郊；因初獻六羽，則知舊僭八佾；因新作雉門，則知舊無雉門。皆非聖人有意於其間，故曰《春秋》盡性之書也。魯之兩觀郊天大禘，皆非禮也。諸侯苟有四時之禘，以為常祭可也，至於五年大禘，不可為也。

Some people say that the Spring and Autumn Annals is not a book discussing the principles of human nature and destiny. This is incorrect. Take for example the record in the Spring and Autumn Annals about the sacrifice for the state's ancestral worship: the ox used for the sacrifice had an injury on its mouth, so they consulted the oracle and replaced it with another ox. The new ox died, so the sacrifice was not held, yet the three lesser sacrifices were still performed. This record uses a specific event from Lu state to criticize its actions. Did the sage have any private intentions in this? No, because he acted without self-interest. Is this not exactly what comes from the source of human nature and destiny? Others say that the Spring and Autumn Annals merely discusses matters as they are, and how could the sage have his own private views? People only know that the sage's writing and editing are the most impartial in the world, but they do not know why the sage could be so impartial. For example, because the record mentions the injured ox, we know that Lu state had overstepped its authority by performing the heavenly sacrifice. Because it mentions 'six feathers' in the first offering, we know that Lu state had previously used the eight-row dance reserved for the Son of Heaven. Because it mentions 'the new construction of the Zhi Gate,' we know that Lu state originally did not have a Zhi Gate. These were not things the sage had in mind to expose. Therefore, the Spring and Autumn Annals is a book that fully reveals human nature. The construction of the two pavilions before the palace gate, the sacrifice of the heavenly rites, and the great ancestral sacrifice held every five years in Lu state all violated the rites. If a feudal lord only performed the four seasonal ancestral sacrifices, it was acceptable as a regular ritual. However, the great ancestral sacrifice held every five years was absolutely wrong.

始作兩觀，始者，貶之也，誅其舊無也。初獻六羽，初者，褒之也，以其舊僭八佾也。晉狐射姑殺陽處父，《春秋》書“晉殺其大夫陽處父”，上漏言也。君不密則失臣，故書“國殺”。夫聖人之經，渾然無跡，如天道焉。故《春秋》錄實事，而善惡形於其中矣。《春秋》三傳之外，陸淳啖助可以兼治。

The Spring and Autumn Annals records "the beginning of two gate towers," using the word "beginning" to criticize, indicating that Lu State had never had such an overstepping gate towers before, which were reserved for the Son of Heaven. It records "the first offering of six feathers," using the word "first" to praise, because Lu State had always used the Son of Heaven's standard of eight dancing performers, and now reducing it to six feathers conforms to the proper ritual for a feudal state. When Fu Gu of Jin State sent people to kill Yang Chu Fu, the Spring and Autumn Annals records it as "Jin killed its minister Yang Chu Fu," because the Jin king had leaked the secret. The Zhou Changes, Great Treatise says, "If the ruler is not cautious, he loses his ministers," so the historian did not record the murderer's name, but wrote that the whole state killed him. The sages' classic texts are unified and subtle, like the operation of the heavenly way; thus, the Spring and Autumn Annals simply records events, and goodness and evil naturally emerge from the records. In studying the Spring and Autumn Annals, in addition to the Left Zhuan, Gongyang Zhuan, and Gu Liang Zhuan, the interpretations of Lu Chu and Dan Zhu from the Tang dynasty can also be considered together.

管仲用智數，晚識物理，大抵才力過人也。叔向、子產、晏子之才相等埒，季札之才近伯夷。伯夷義不食周粟，至餓且死，止得為仁而已。伯夷、柳下惠得聖人之一端，伯夷得聖人之清，柳下惠得聖人之和。孔子時清時和，時行時止，故得聖人之時。顯諸仁，藏諸用，孟子善藏其用乎？

Guan Zhong relied on intelligence and strategy, and only in his later years did he understand the principles of things, generally surpassing ordinary people in ability and strength. The three men Shu Xiang of Jin, Zi Chang of Zheng, and Yan Ying of Qi had about the same ability; the ability of Ji Zha of Wu was close to that of Bo Yi. Bo Yi adhered to righteousness and refused to eat food from the Zhou dynasty, dying of starvation on Shouyang Mountain, achieving only the character of "ren" (benevolence). Bo Yi and Liu Xiaohui each attained one aspect of the sage's virtue: Bo Yi possessed the sage's "qing" (purity), while Liu Xiaohui possessed the sage's "he" (harmony). Confucius, however, was clear when he should be clear and harmonious when he should be harmonious, taking office when appropriate and retreating when appropriate, so he possessed the sage's "shi" (timeliness). The "Great Treatise" says that heaven and earth "manifest in ren (benevolence) and conceal in their use." Mencius was probably the kind of person who was good at concealing his own function.

聖人之難，在不失仁義忠信而成事業，何如？則可在於絕四：毋意、毋必、毋固、毋我。合而言之則一，分而言之則二。合而言之則二，分而言之則四。始於有意，成於有我。有意然後有必，必生於意。有固然後有我，我生於固。意有心必有待固不化我，有己也。

The difficulty for the sage lies in maintaining benevolence, righteousness, loyalty, and trustworthiness while still achieving success in his endeavors. How can this be done? The answer is found in the "Four Things to Avoid" mentioned in the "Analects of Confucius · Zihan": not to speculate without basis, not to expect absolutely, not to be stubborn, and not to be self-opinionated. When viewed together, these four form one matter; when viewed separately, they are two. When viewed again together, they form two; when viewed again separately, they become four. The beginning lies in "intention," and the completion lies in "self." First there is speculation, then there is absolute expectation, for "expectation" arises from "intention." First there is stubbornness, then there is self, for "self" arises from "stubbornness."the so-called "intention" refers to a thought fixed in the mind;the so-called "expectation" refers to a sense of anticipation in the mind;the so-called "stubbornness" refers to being rigid and unwilling to change;the so-called "self" refers to always setting up a separate self.

劉絢問無為，對曰：“時然後言，人不厭其言；樂然後笑，人不厭其笑；義然後取，人不厭其取。”此所謂無為也。時然後言，乃應變而言，言不在我也。知之為知之，不知為不知，聖人之性也。苟不知而強知之，非情而何？失性而情則眾人矣。

A student named Liu Xuan asked what "wu wei" means. Shao Yong answered by quoting Confucius' praise of Gong叔 Wenzi from the "Analects of Confucius": "When it is time to speak, then speak, and others will not be annoyed by his words; when one is truly happy, then laugh, and others will not be annoyed by his laughter; when it is appropriate to take, then take, and others will not be annoyed by his taking." This is what is called "wu wei." To speak only when it is time to speak is to act in accordance with the changes of circumstances, and the initiative does not lie in oneself. "To say what one knows and to say one does not know when one does not know" is the nature of the sage. If one does not know but pretends to know, what else could it be but the action of "qing"? To abandon one's nature and fall into the realm of "qing" is the same as ordinary people.

志於道者，統而言之，志者，潛心之謂也。德者，得於己，有形故可據。德主於仁，故曰依。君子喻於義，賢人也。小人喻於利而已。義利兼忘者，唯聖人能之。君子畏義而有所不為，小人直不畏耳。聖人則動不逾矩，何義之畏乎？

The Analects of Confucius, in the chapter Shu Er, says, "Set your heart on the Dao, base yourself on virtue, and rely on benevolence." What is meant by "setting one's heart on the Dao" is a general statement; "setting one's heart" means to immerse one's mind deeply. "Virtue" refers to something that has already been attained within oneself; since it has taken form, it can be relied upon. Virtue is centered on benevolence, so "relying on" benevolence is appropriate. Those who understand from the perspective of righteousness are gentlemen, which is the level of the virtuous; common people only understand from the perspective of profit. As for those who completely forget both righteousness and profit, only sages can do that. Gentlemen refrain from certain actions out of reverence for righteousness; common people simply do not know what reverence is. Sages, however, act naturally without ever exceeding the boundaries of propriety, so why would they need to revere righteousness?

誰能出不由戶？戶，道也。未有不由道而能濟者也。不由戶者，開穴隙之類是也。多聞，擇其善者而從之。雖多聞，必擇善而從之；多見而識之，識別也。雖多見，必有以別之。三人行，必有師焉。至於友一鄉之賢、天下之賢，以天下為未足。又至於上論古人，無以加焉。當仁不讓於師者，進人之道也。有馬者，借人乘之，舍己以從人也。

The Analects of Confucius, in the chapter Yong Ye, says, "Who can go out without passing through a door?" Here, the term "door" symbolizes the Dao. There has never been a case where one can achieve success without following the Dao. Those who do not go through the door are like those who dig through walls or take shortcuts. Confucius says, "Listen to much, and choose the good to follow." Although listening to much is good, one must select the good and follow it. He also says, "See much and recognize it," where "recognize" means to discern. Although seeing much is good, one must be able to discern. "When three people are walking, one of them must be a teacher," from which one can extend to associate with the virtuous people in one's town, then in the whole world. If even the whole world is not enough, one can go back to the ancients and associate with them, which is the highest level of learning. "When one is responsible for righteousness, one should not be hesitant to take the lead," which is a way to encourage people to strive forward. "Those who have horses should let others ride them," which refers to abandoning one's own preconceptions and listening to others.

或問：“才難，何謂也？”曰：“臨大事然後見才之難也。”曰：“何獨言才？”曰：“才者，天之良質也，學者所以成其才也。”曰：“古人有不由學問而能立功業者，何必曰學？”曰：“周勃、霍光能成大事，唯其無學，故未盡善也。”人而無學，則不能燭理。不能燭理，則固執而不通。

Someone asked: "Confucius said 'talent is hard to find,' what did he mean?" Shao Yong answered: "It is only when facing major affairs that one can see how difficult it is to find talent." Again asked: "Why does he emphasize talent especially?" He answered: "Talent is the excellent quality given by Heaven, and learning is used to bring out this quality." Again asked: "There were also ancient people who achieved great deeds without relying on learning, so why must one speak of learning?" He answered: "Zhou Bo pacified the House of Li, and Huo Guang replaced the King of Changyi, both accomplished great things, but because they lacked learning, their deeds were not perfect." If a person lacks learning, he cannot understand principles clearly; if he cannot understand principles clearly, he will be stubborn and unable to see things comprehensively.

人有出人之才，必以剛克中。剛則足以立事業，處患難。若用於他，反為邪惡。故孔子以申棖為焉得剛。既有欲心，必無剛也。仲弓可使南面，可使從政也。顏子不遷怒，不貳過。遷怒貳過，皆情也，非性也。不至於性命，不足以謂之好學。

A person who possesses extraordinary talent must necessarily use his strength to restrain himself and adhere to the middle way. Strength is essential for establishing achievements and for standing firm in adversity; if this strength is directed elsewhere, it may turn into evil. Therefore, in the "Analects of Confucius," someone cited Sheng Cheng as an example of a strong person, but Confucius said, "Sheng Cheng has desires; how can he be strong?" Since Sheng Cheng has desires in his heart, he cannot be considered strong. As for Zhonggong, Confucius said he "can govern the southern region," meaning he is capable of governing affairs. Yan Hui achieved "not transferring anger to others and not repeating the same mistake," for transferring anger and repeating the same mistake are both activities of "qing" (emotions), not "xing" (nature). If learning does not reach the level of understanding the principles of human nature and destiny, it cannot be called "good learning."

顏子不貳過，孔子曰“有不善未嘗不知，知之未嘗復行”是也，是一而不再也。韓愈以為將發於心而使能絕去，是過與顏子也。過與是為私意，焉能至於道哉？或曰：“與善不亦愈於與惡乎？”曰：“聖人則不如是，私心過與善惡同矣。”

Yan Hui "does not repeat the same mistake," which refers to Confucius' words from the Great Treatise of the Zhou Changes, "when there is an unvirtuous act, one has never failed to know it; when one knows it, one has never repeated it." Han Yu, however, interpreted this as Yan Hui being able to cut off the thought as soon as it began to arise in his mind. This interpretation elevates Yan Hui beyond reasonable bounds. To elevate someone beyond measure introduces the private intentions of the commentator, which cannot reach the Way. Someone else said, "It is better to over-praise a person's virtue than to over-criticize his faults." Shao Yong replied, "The sages do not do this. As soon as there is a private motive, over-praising and over-criticizing are equally flawed."

知《易》者不必引用講解，是為知《易》。孟子之言未嘗及《易》，其間《易》道存焉，俾人見之者鮮耳。人能用《易》，是為知《易》。如孟子，可謂善用《易》者也。瞽瞍殺人，舜視棄天下猶棄敝屣也，竊負而逃，遵海濱而處終身，欣然樂而忘天下，聖人雖天下之大，不能易天性之愛。湯放桀，武王伐紂，而不以為弒者，若孟子言“男女授受不親，禮也；嫂溺則援之以手，權也”。故孔子既尊夷齊，亦與湯武。夷齊仁也。湯武義也。唯湯武則可，非湯武則是篡也。

A true understanding of the I Ching does not require one to cite classical texts immediately; this is what it means to truly understand the I Ching. Mencius never mentioned the I Ching in his writings, yet the principles of the I Ching are hidden within his words, but few are able to perceive them. A person can only be said to understand the I Ching when they can apply its principles to real situations. Mencius can be considered someone who skillfully applies the I Ching. In the chapter "The Mind in Full" of the Mencius, he imagines a scenario where if Shun's father, Gu Suo, had killed someone, Shun would regard the world as nothing more than a pair of broken straw shoes, secretly carrying his father away and living by the seaside for the rest of his life, happy and content, forgetting about the world. This shows that in the hearts of the sages, although the world is vast, it cannot replace the natural affection a person has for their father. When Tang displaced the Xia ruler Jie and King Wu of Zhou overthrew the Shang ruler Zhou, people did not regard these actions as regicide. The reasoning is similar to what Mencius said: "Men and women do not exchange things with each other, this is propriety; but if the sister-in-law is drowning, one should help her with one's hand, this is a matter of emergency." There are exceptions to the established norms. Therefore, Confucius both revered Boyi and Shuqi, who refused to eat the grain of the Zhou dynasty, and approved of the actions of Tang and Wu. Boyi and Shuqi upheld righteousness, while Tang and Wu acted with justice. Only people like Tang and Wu could do such things; if others did, it would be considered a usurpation.

《中庸》非天降地出，揆物之理，度人之情，行其所安，是為得矣。《中庸》之法，自中者，天也；自外者，人也。《老子》五千言，大抵皆明物理。老子知《易》之體者也。《莊子》曰：“庖人雖不治庖，尸祝不越樽俎而代之。”此君子思不出其位，素位而行之意也。

The principles explained in the Zhongyong are not some mysterious things that drop from heaven or sprout from the earth; they are simply understanding the principles of things and observing the feelings of people's hearts, doing what makes one's heart at ease. The practice of Zhongyong has two aspects: those that arise from the upright nature within oneself belong to heaven; those that come from external norms and constraints belong to human beings. The Dao De Jing consists of about five thousand words, mostly explaining the principles of things. Laozi understood the "body" of the Zhouyi. The Zhuangzi's "Free and Untrammeled Excursion" says: "Even if a cook does not cook, the chief priest will not cross the ritual vessels to take his place in cooking." This exactly matches the meaning of the Zhouyi's Gen hexagram, which says "a gentleman's thoughts do not go beyond his position," and the Zhongyong's statement, "act according to one's position."

《莊子·齊物》未免乎較量。較量則爭，爭則不平，不平則不和。莊子與惠子游於濠梁之上，莊子曰：“鰷魚出游從容，是魚樂也。”此盡己之性，能盡物之性也。非魚則然，天下之物皆然。若莊子者，可謂善通物矣。莊子雄辯，數千年一人而已。如庖丁解牛，曰“躊躇四顧”。孔子觀呂梁之水，曰“蹈水之道無私”，皆至理之言也。

The "Zhiwu Lun" section of the "Zhuangzi" ultimately cannot avoid comparison and calculation. Once there is comparison, there is contention; once there is contention, there is injustice; once there is injustice, harmony cannot be achieved. Zhuangzi and Hui Shi were strolling on a bridge over the Hao River, and Zhuangzi said, "The small fish swim leisurely and freely, this is the joy of the fish." This is exactly what the "Zhongyong" says: first to fulfill one's own nature, then one can fulfill the nature of all things. Not only the fish are like this; all things in the world are like this. A person like Zhuangzi can be said to be good at communicating with all things. Zhuangzi's eloquence has been unparalleled for thousands of years. For example, in "Yangsheng Zhu," the story of Bo Ding dissecting an ox is told, saying that after he finished, he lifted his knife and stood up, looking around with a proud and thoughtful expression; in "Dashi," the story of Confucius watching a waterfall at Lüliang is told, saying that the skill of a good swimmer lies in following the nature of the water without personal bias: these are all examples of explaining principles to their very core.

莊子氣豪，若呂梁之事，言之至者也。《盜跖》，言事之無可奈何者，雖聖人亦莫如之何。《漁父》，言事之不可強者，雖聖人亦不可強。此言有為無為之理，順理則無為，強則有為也。莊子著《盜跖篇》，所以明至惡，雖至聖亦莫能化。蓋上智與下愚不移故也。魯國之儒一人者，謂孔子也。莊荀之徒失之辯。佛氏棄君臣父子夫婦之道，豈自然之理哉？智哉！留侯善藏其用。

Zhuangzi has a bold and grand style, as seen in the passage about the man who walks on the waters of Lüliang, which is where he expresses his ideas to the fullest. The essay "Daozhi" discusses situations where there is nothing one can do about a matter, even the sages cannot change it. The essay "Yufu" talks about situations where one cannot force things, even the sages cannot impose their will. These two essays clearly distinguish between "having action" and "non-action": following the natural course of things is non-action, while forcing things is having action. Zhuangzi wrote "Daozhi" to explain that even the worst people cannot be transformed by the highest sages, because Confucius said, "Only the highly intelligent and the completely foolish cannot be changed." In "Zhuangzi," it says that the true Confucian in Lu state was only one person, referring to Confucius himself. Zhuangzi and Xunzi and others have the problem of being too argumentative. Buddhism gives up the moral duties between ruler and subject, father and son, and husband and wife, is this in accordance with the natural way? Liang Zhangliang truly has wisdom, for he is most skilled at concealing his talents.