Huang Ji Jing Shi Guan Wu Wai Pian Yan Yi (皇極經世觀物外篇衍義)

天數五，地數五，合而為十，數之全也。天以一而變四，地以一而變四，四者有體也，而其一者無體也，是謂有無之極也。天之體數四而用者三，不用者一也。地之體數四而用者三，不用者一也。是故無體之一以況自然也，不用之一以況道也，用之者三以況天地人也。

The numbers belonging to Heaven are five, and those belonging to Earth are also five. When combined, they make ten, which is the complete form of "number." Heaven begins from "one" and develops into four, and Earth also begins from "one" and develops into four. These four are tangible entities, while the "one" that gives rise to them is intangible and cannot be pointed to, thus it is called the extreme of "being" and "non-being." The "number of form" for Heaven is four, but only three are actually active, with one remaining unused. Similarly, the "number of form" for Earth is also four, with three being active and one remaining unused. Therefore, the intangible "one" is used to represent the natural state before Heaven and Earth were separated. The unused "one" is used to represent the "Dao" that generates all things without personally acting. The actual three that are in use are used to represent the three principles of Heaven, Earth, and Humanity.

體者八變，用者六變，是以八卦之象不易者四，反易者二，以六卦變而成八也。重卦之象不易者八，反易者二十八，以三十六變而成六十四也。故爻止於六，卦盡於八，策窮於三十六，而重卦極於六十四也。卦成於八，重於六十四，爻成於六，策窮於三十六而重於三百八十四也。

The system of the "body" undergoes eight transformations, while the system of the "use" undergoes six transformations. Therefore, among the eight trigrams, four remain unchanged when viewed upside down, namely Qian (Heaven), Kun (Earth), Kan (Water), and Li (Fire). Two pairs of trigrams become each other when reversed, namely Zhen (Thunder) and Gen (Mountain), Xun (Wind) and Dui (Lake). Altogether, these six trigrams generate the eight trigrams through transformation. The sixty-four hexagrams follow the same principle: eight remain unchanged when viewed upside down, and twenty-eight pairs become each other when reversed. Altogether, these thirty-six hexagrams generate the sixty-four hexagrams. Therefore, the number of lines (yao) does not exceed six, and the number of single trigrams does not exceed eight. The number of "counting units" (ce shu) for a single line does not exceed thirty-six, and the number of hexagrams does not exceed sixty-four. A single trigram is composed of three lines to form eight trigrams, and when combined, they form sixty-four trigrams. A hexagram consists of six lines, and the maximum number of "counting units" for a single line is thirty-six. Since each of the sixty-four hexagrams has six lines, the total number of lines is three hundred and eighty-four.

天有四時，一時四月，一月四十日。四四十六而各去其一，是以一時三月，一月三十日也。四時體數也，三月三十日用數也。體雖具四而其一常不用也，故用者止於三而極於九也。體數常偶，故有四有十二。用數常奇，故有三有九。

If calculated according to "body numbers," a year has four seasons, each season should have four months, and each month should have forty days. Four multiplied by four gives sixteen, but each layer must subtract one portion, so in reality each season has only three months, and each month has only thirty days. Four seasons, four months, and forty days belong to "body numbers," while three months and thirty days belong to "used numbers." Although body numbers are complete with four parts, one part is always left unused, so only three parts are actually used, leading to nine when multiplied to the extreme. Body numbers are always even, hence four and twelve; used numbers are always odd, hence three and nine.

大數不足而小數常盈者何也？以其大者不可見而小者可見也。故時止乎四，月止乎三，而日盈乎十也。是以人之肢體有四而指有十也。天見乎南而潛乎北，極於六而餘於七，是以人知其前，昧其後，而略其左右也。

Why larger units often seem insufficient while smaller ones frequently appear abundant? Because larger units are distant and hard to perceive, while smaller units are clear and countable. Thus, "time" only reaches four, "month" only reaches three, yet "day" fills up to ten. The human body follows this principle: there are only four limbs, yet ten fingers. Celestial bodies appear in the south and disappear in the north; the boundary between day and night reaches six parts but slightly exceeds, becoming seven parts. Therefore, people can only see clearly in front of them, cannot see behind, and can only roughly attend to the sides.

天體數四而用三，地體數四而用三，天克地地克天而克者在地，猶晝之餘分在地也，是以天三而地四，天有三辰，地有四行也。然地之火且見且隱，其餘分之謂耶？

Heaven's fundamental number is four but is used as three, while Earth's fundamental number is four and is also used as three. Heaven controls Earth, and Earth controls Heaven; they mutually control each other. The result of being controlled falls upon the Earth, just as the extra part of daylight is accounted for on the ground. Therefore, Heaven uses three and Earth uses four: Heaven has three luminous celestial bodies, the sun, moon, and stars, while Earth has four material elements, water, fire, soil, and stone. However, fire on Earth appears sometimes and disappears sometimes, unlike water, soil, and stone which are always present. Perhaps fire is that extra portion?

乾七子，兌六子，離五子，震四子，巽三子，坎二子，艮一子，坤至陰，故無子。乾七子，坤六子，兌五子，艮四子，離三子，坎二子，震一子，巽剛，故無子。

According to the order of the trigrams in the Earlier Heaven (Heavenly Origin) arrangement, each trigram produces a number of "sons" or descendants: Qian has seven sons, Dui has six, Li has five, Zhen has four, Xun has three, Kan has two, Gen has one; Kun, being the extreme of yin, has no sons. Another arrangement states: Qian has seven sons, Kun has six, Dui has five, Gen has four, Li has three, Kan has two, Zhen has one; Xun, being of a yang nature, has no sons. The first view is based on the principle that pure yin cannot generate independently, while the second view is based on the principle that pure yang cannot generate independently. Each interpretation takes a different perspective.

天有二正，地有二正，而共享二變以成八卦也。天有四正，地有四正，共享二十八變以成六十四卦也。是以小成之卦正者四，變者二，共六卦也。大成之卦正者八，變者二十八，共三十六卦也。乾坤坎離為三十六卦之祖，兌震巽艮為二十八卦之祖也。

Heaven has two unchanging trigrams, which are Qian and Li; Earth also has two unchanging trigrams, which are Kun and Kan. In addition, there are two pairs of trigrams that are reversed and combined, making up the Eight Trigrams. When forming compound hexagrams, Heaven has four trigrams, Earth has four trigrams, and there are twenty-eight pairs of reversed trigrams, making up the sixty-four hexagrams. Therefore, the Eight Trigrams, referred to as the 'small completion,' consist of four original trigrams and two reversed ones, totaling six. The sixty-four hexagrams, referred to as the 'great completion,' consist of eight original trigrams and twenty-eight reversed ones, totaling thirty-six. Qian, Kun, Kan, and Li are the ancestors of the thirty-six hexagrams, while Dui, Zhen, Xun, and Gen are the ancestors of the twenty-eight hexagrams.

乾坤七變，是以晝夜之極不過七分也。艮兌六變，是以月止於六，共為十二也。離坎五變，是以日止於五，共為十也。震巽四變，是以體止於四，共為八也。

Heavenly Trigrams (Qian and Kun) each have seven changes, so the extremes of day and night are limited to seven parts. At the summer solstice, day is seven parts and night is three parts; at the winter solstice, it is reversed. The trigrams Gen and Dui each have six changes, so the number of months is limited to six. When yin and yang combine, they form twelve months. The trigrams Li and Kan each have five changes, so the number of days is limited to five. When yin and yang combine, they form ten days, which are the ten Heavenly Stems. The trigrams Zhen and Xun each have four changes, so the number of forms is limited to four. When yin and yang combine, they form eight, which are the Eight Trigrams.

卦之正變共三十六，而爻又有二百一十六，則用數之策也。三十六去四則三十二也，又去四則二十八也，又去四則二十四也，故卦數三十二位，去四而言之也。天數二十八位，去八而言之也。地數二十四位，去十二而言之也。四者乾坤坎離也，八者並頤中孚大小過也，十二者兌震泰既濟也。

The original hexagram and the changing hexagram together total thirty-six. These thirty-six hexagrams have two hundred and sixteen lines, which is exactly the "number used" or "counting method" mentioned as the count of the hexagram Qian (Heaven) being two hundred and sixteen in the Great Treatise. Subtracting four from thirty-six gives twenty-eight, then subtracting another four gives twenty-four, and subtracting another four gives twenty. Therefore, the statement "the number of hexagrams is thirty-two" refers to subtracting four from thirty-six; "the number of Heaven is twenty-eight" refers to subtracting eight; and "the number of Earth is twenty-four" refers to subtracting twelve. The four subtracted refer to the four trigrams Qian, Kun, Kan, and Li. The eight subtracted include these four trigrams plus Yi (Repose), Zhongfú (Faithful Son), Daguò (Great Overcoming), and Xiaoguo (Small Overcoming). The twelve subtracted include these eight trigrams plus Dui (Lake), Zhen (Thunder), Tai (Great Passage), and Ji Ji (Completion).

日有八位而用止於七，去乾而言之也。月有八位而用止於六，去兌而言之也。星有八位而用止於五，去離而言之也。辰有八位而用止於四去震而言之也。日有八位而數止於七，去泰而言之也。月自兌起者，月不能及日之數也。故十二月常餘十二日也。

The sun is paired with the positions of the eight trigrams, but only seven are used, excluding the trigram Qian; the moon is paired with eight positions, but only six are used, excluding the trigram Dui; stars are paired with eight positions, but only five are used, excluding the trigram Li; the hour is paired with eight positions, but only four are used, excluding the trigram Zhen; the sun again is paired with eight positions, but the count only reaches seven, excluding the trigram Tai. The moon's position starts from Dui, which clearly indicates that the moon's movement is slower than the sun's. Therefore, after twelve lunar months, there are often twelve days left over, which is the reason for the need to intercalate a month in the calendar.

乾陽中陽，不可變，故一年只舉十二月也。震陰中陰，不可變，故一日之十二時不可見也。兌陽中陰，離陰中陽，皆可變，故日月之數可分也。是以陰數以十二起，陽數以三十起，而常存二六也。舉年見月，舉月見日，舉日見時，陽統陰也。是天四變含地四變，日之變含月與星辰之變也。是以一卦含四卦也。

Heavenly Stem Jia is yang within yang, pure and unchangeable, so it is only mentioned once a year with twelve months. Zhen is yin within yin, pure and unchangeable, so the twelve hours in a day are invisible. Dui is yang within yin, and Li is yin within yang, both of which can change, so the numbers of days and months can be divided. Therefore, the count of yin starts from twelve, and the count of yang starts from thirty, while the numbers two and six remain constant. Mentioning "year" shows "month," mentioning "month" shows "day," and mentioning "day" shows "hour," which reflects the principle of yang governing yin. In other words, the four changes of heaven include the four changes of earth, and the changes of day include those of the moon and stars, so one hexagram contains four hexagrams.

日一位，月一位，星一位，辰一位。日有四位，月有四位，星有四位，辰有四位，四四十有六位，盡此一變而日月之數窮矣。天有四變，地有四變，變有長也，有消也，十有六變而天地之數窮矣。日起於一，月起於二，星起於三，辰起於四，引而伸之，陽數常六，陰數常二，十有二變而大小之運窮矣。

The sun occupies one position, the moon one, the stars one, and the celestial stems one; beneath the sun there are four positions, beneath the moon four, beneath the stars four, and beneath the celestial stems four. Four multiplied by four gives sixteen positions. After completing this cycle of changes, the numbers of the sun and moon are exhausted. Heaven has four changes, and earth has four changes. Among these changes, there is growth and there is decline. After sixteen changes, the numbers of heaven and earth are exhausted. The sun begins with one, the moon with two, the stars with three, and the celestial stems with four. Following this pattern, the yang numbers always result in six, and the yin numbers always result in two. After twelve changes, the numbers of the great cycle and the small cycle are exhausted.

三百六十變為十二萬九千六百，十二萬九千六百變為一百六十七億九千六百一十六萬，一百六十七億九千六百一十六萬變為二萬八千二百一十一兆九百九十萬七千四百五十六億。以三百六十為時，以十二萬九千六百為日，以一百六十七億九千六百一十六萬為月，以二萬八千二百一十一兆九百九十一萬七千四百五十六億為年，則大小運之數立矣。

Multiply 360 by itself once to get 12,9600; multiply 12,9600 by itself once to get 1,679,616,0000; multiply 1,679,616,0000 by itself once to get 28,211,990,7456,0000. After this progressive scaling, take 360 as one "shi," 12,9600 as one "ri," 1,679,616,0000 as one "yue," and 28,211,990,7456,0000 as one "nian." The numbers for "da yun" and "xiao yun" are thus established.

二萬八千二百一十一兆九百九十一萬七千四百五十六億分而為十二，前六限為長，後六限為消，以當一年十二月之數，而進退三百六十日矣。一百六十七億九千六百一十六萬分而為三十，以當一月三十日之數，隨大運消長而進退六十日矣。十二萬九千六百分而為十二，以當一日十二時之數，而進退六日矣。三百六十以當一時之數，隨小運之進退以當晝夜之時也。

Divide the number of years, two million eight hundred and twenty-one thousand one hundred and eleven trillion nine hundred and ninety-one billion seven hundred and forty-five million six hundred, into twelve parts, the first six parts representing growth and the last six parts representing decline, corresponding to the twelve months of a year, with a total of three hundred and sixty days of movement. Divide the number of months, one hundred and sixty-seven billion nine thousand six hundred and sixteen million, into thirty parts, corresponding to the thirty days of a month, with a total of sixty days of movement according to the great cycle. Divide the number of days, twelve million nine thousand six hundred, into twelve parts, corresponding to the twelve hours of a day, with a total of six days of movement. Then take three hundred and sixty as the number for an hour, corresponding to the moments within day and night according to the small cycle.

十六變之數去其交數，取其用數，得二萬八千二百一十一兆九百九十一萬七千四百五十六億，分為十二限，前六限為長，後六限為消，每限得十三億九千九百六十八萬之一百六十七億九千六百一十六萬。每一百六十七億九千六百一十六萬年開一分，進六十日也。六限開六分，進三百六十日也。猶有餘分之一，故開七分，進三百六十六日也。其退亦若是矣。

The total number obtained from sixteen changes should subtract the overlapping numbers called 「交数」 and only take the effective numbers called 「用数」, resulting in 28,211,991,745,600. Divide this into twelve periods, the first six periods belong to growth and the last six to decline. Each period corresponds to 1,399,680,000,000,000. Every 167,961,600,000 years, one part is opened, advancing sixty days. After six periods, six parts are opened, advancing three hundred and sixty days. There is also a remaining part, so it is opened to seven parts in total, advancing three hundred and sixty-six days. The declining half is also calculated in the same way but in reverse.

十二萬九千六百，去其三者，交數也，取其七者，用數也。用數三而成於六，加餘分故有七也。七之得九萬七百二十年，半之得四萬五千三百六十年，以進六日也。日有晝夜，數有誂朒，以成十有二日也。每三千六百年進一日，凡四萬三千二百年進十有二日也。二千一百六十年以進餘分之六，合交數之二千一百六十年，共進十有二分以為閏也。故小運之變凡六十，而成三百六十有六日也。

This number, twelve thousand nine hundred and sixty, if we remove three tenths of it, results in the 'interleaving number' or 'cross number'; if we take seven tenths of it, that is the 'used number'. The used number is based on three and formed into six, then adding a little remainder, making it seven. Taking seven tenths gives nine thousand and seventy-two years, taking half of that gives four thousand five hundred and sixty years, which is used to advance six days. Days have two aspects, day and night, and numbers have two tendencies, surplus and deficiency. Together they form twelve days. Every three thousand six hundred years advances one day, so four thousand three hundred and twenty years advance twelve days. Another method uses two thousand one hundred and sixty years to advance the remainder of six, and adding the two thousand one hundred and sixty years occupied by the cross number, totaling twelve parts, which is used to accommodate the intercalary remainder. Therefore, the changes of the small cycle total sixty times, exactly forming three hundred and sixty-six days.

六者三天也，四者兩地也。天統乎體而托地以為體，地分乎用而承天以為用。天地相依，體用相附。

"Six" comes from "three" multiplied by one and added to itself, and "four" comes from "two" multiplied by one and added to itself. This is the "method of doubling" referred to in the study of the Earlier Heaven (primordial) principles. Heaven encompasses the "form," but it needs to be embodied on earth to manifest its shape; Earth takes charge of the "function," but it needs to receive the movement of Heaven to have function. Heaven and Earth rely on each other, and form and function depend on each other. Without one side, neither can stand alone.

乾為一，乾之五爻分而為大有，以當三百六十之數也。乾之四爻分而為小畜，以當十二萬九千六百之數也。乾之三爻分而為履，以當一百六十七億九千六百一十六萬之數也。乾之二爻分而為同人，以當二萬八千二百一十一兆九百九十萬七千四百五十六億之數也。乾之初爻分而為姤，以當七秭九千五百八十六萬六千一百十垓九千九百四十六萬四千八京八千四百三十九萬一千九百三十六兆之數也。是謂分數也。分大為小，皆自上而下，故以陽數當之。

In the Earlier Heaven sequence, the Trigram Qian (Heaven) is first. The fifth line of Qian changes to produce the hexagram Dali (Great Possession), corresponding to the number 360; the fourth line changes to produce Xiaoxu (Small Accumulation), corresponding to 129,600; the third line changes to produce Lu (Footwear), corresponding to 167,961,600; the second line changes to produce Tongren (Harmonious People), corresponding to 28,211,990,745,600; and the first line changes to produce Gu (Meeting), corresponding to 7,958,661,109,946,480,843,919,360. This is called 'fraction': dividing the large into the small, all derived from top to bottom, hence using the yang numbers to match it.

一生二為夬，當十二之數也。二生四為大壯，當四千三百二十之數也。四生八為泰，當五億五千九百八十七萬二千之數也。八生十六為臨，當九百四十四兆三千六百九十九萬六千九百一十五億二千之數也。十六生三十二為復，當二千六百五十二萬八千八百七十垓三千六百六十四萬八千八百京二千九百四十七萬九千七百三十一兆二千萬億之數也。三十二生六十四為坤，當無極之數也。是謂長數也，長小為大，皆自下而上，故以陰數當之。

From the perspective of the Earth (Kun), it is the method of doubling each time: one becomes two, forming Gua, corresponding to the number twelve; two becomes four, forming Da Zhuang, corresponding to the number four thousand three hundred twenty; four becomes eight, forming Tai, corresponding to the number five hundred fifty-nine million eight hundred seventy-two thousand; eight becomes sixteen, forming Lin, corresponding to the number nine hundred forty-four trillion three thousand six hundred ninety-nine million six hundred ninety-one thousand five hundred twenty; sixteen becomes thirty-two, forming Fu, corresponding to the number twenty-six million five hundred twenty-eight thousand eight hundred seventy myriads three thousand six hundred sixty-four million eight hundred eighty thousand two thousand nine hundred forty-seven million nine hundred seventy-three thousand one hundred twenty; thirty-two becomes sixty-four, forming Kun again, corresponding to an endless number of the Supreme Ultimate. This process is called the "long number": it grows the small into the large, proceeding from the lower to the upper, so it is paired with the yin numbers.

天統乎體，故八變而終於十六。地分乎用，故六變而終於十二。天起於一，而終於七秭九千五百八十六萬六千一百一十垓九千九百四十六萬四千八京八千四百三十九萬一千九百三十六兆。地起於十二，而終於二百四垓六千九百八十萬七千三百八十一京五千四百九十一萬八千四百九十九兆七百二十萬億也。

Heaven encompasses the "body," so it undergoes eight transformations and ends at sixteen; Earth governs the "function," so it undergoes six transformations and ends at twelve. The Heaven sequence starts from one and continues up to seven thousand nine hundred eighty-six million six hundred eleven thousand nine hundred forty-six thousand eight hundred forty-three million nine hundred thirty-six trillion. The Earth sequence starts from twelve and continues up to two hundred forty gai six thousand nine hundred eighty million seven hundred thirty-eight thousand one jing five thousand four hundred ninety-one million eight thousand four hundred ninety-nine trillion seven hundred twenty trillion.

有地然後有二，有二然後有晝夜。二三以變，錯綜而成，故易以二而生數，以十二而起，而一非數也，非數而數以之成也。天行不息，未嘗有晝夜，人居地上以為晝夜，故以地上之數為人之用也。

Heavenly Stems and Earthly Branches are the fundamental elements used in divination. The concept of "two" arises from the Earth, and with "two" comes the distinction between day and night. The interaction between "two" and "three" leads to the myriad phenomena, hence the Book of Changes begins counting from "two" and establishes positions based on twelve. The number "one" itself is not counted, yet all numbers depend on it for their existence. The heavens move ceaselessly without inherent day and night; humans on Earth observe the rising and setting of the sun and thus establish the names of day and night. Therefore, the calendar system uses numbers based on what is observed on Earth for practical human use.

天自臨以上，地自師以上，運數也。天自同人以下，地自遯以下，年數也。運數則在天者也，年數則在地者也。天自賁以上，地自艮以上，用數也。天自明夷以下，地自否以下，交數也。天自震以上，地自晉以上，有數也。天自益以下，地自豫以下，無數也。天之有數起乾而止震，餘入於無者，天辰不見也。地去一而起十二者，地火常潛也，故天以體為基而常隱其基，地以用為本而常藏其用也。

In the diagram of the primordial trigrams, the heavenly side starts from the trigram of Qian above the trigram of Lin, and the earthly side starts from the trigram of Shi above the trigram of Shi, which belongs to 'movement and number'. The heavenly side from Tongren downwards and the earthly side from Duan downwards belong to 'yearly number'. Movement and number are on the heavenly side, while yearly number is on the earthly side. The heavenly side from Ben upwards and the earthly side from Gen upwards belong to 'used number'; the heavenly side from Mingyi downwards and the earthly side from Pinyin downwards belong to 'intersecting number'. The heavenly side from Zhen upwards and the earthly side from Jin upwards belong to 'existing number'; the heavenly side from Yi downwards and the earthly side from Yu downwards belong to 'non-number'. The existing number of heaven starts from Qian and ends at Zhen, while the rest fall into the 'non' side, because the heavenly stars are dark and invisible. The numbers of the earth do not start from one but from twelve, because the fire in the earth is often hidden. Therefore, heaven takes 'body' as its foundation but often hides its foundation, while the earth takes 'use' as its fundamental aspect but often conceals its function.

一時止於三月，一月止於三十日，皆去其辰數也。是以八八之卦六十四而不變者八，可變者七。七八五十六，其義亦由此矣。陽爻晝數也，陰爻夜數也，天地相銜，陰陽相交，故晝夜相雜，剛柔相錯。春夏陽多也，故晝數多夜數少，秋冬陰多也，故晝數少夜數多。

At one time, only three months were calculated, and each month was considered to have thirty days, with the portion belonging to 'Chen' removed. Therefore, among the sixty-four hexagrams formed by the eight trigrams overlapping, there are eight that remain unchanged when reversed, while only seven types can change. Seven multiplied by eight gives fifty-six, and the reasoning comes from this. A yang line represents the number of days, while a yin line represents the number of nights. Heaven and Earth connect with each other, and yin and yang intermingle, so day and night are mixed together, and the qualities of yang and yin alternate. In spring and summer, yang energy is more prevalent, so the number of days is greater and the number of nights is less; in autumn and winter, yin energy is more prevalent, so the number of days is less and the number of nights is greater.

體數之策三百八十四，去乾坤坎離之策為用數三百六十。體數之用二百七十，去乾與坎離之策為用數之用二百五十二也。體數之用二百七十，其一百五十六為陽，一百十四為陰，去離之策，得一百五十二陽，一百一十二陰，為實用之數也。

The total number of counts in "ti shu" is 384. After subtracting the 24 counts of the four trigrams Qian, Kun, Kan, and Li, the remaining 360 counts are called "yong shu". Among the counts used in "ti shu", actually 270 are in use. After subtracting the counts of Qian and Kan and Li, the remaining 252 are called "yong shu of yong". Within the 270 counts used in "ti shu", 156 belong to yang and 114 belong to yin. After removing the counts of Li, we get 152 yang and 112 yin, which are the actual counts used.

蓋陽去離而用乾，陰去坤而用坎也。是以天之陽策一百十二，去其陰也。地之陰策一百十二，陽策四十，去其南北之陽也。極南大暑，極北大寒，物不能生，是以去之也。其四十為天之餘分耶？陽侵陰，晝侵夜，是以在地也。合之為一百五十二陽，一百十二陰也。陽去乾之策，陰去坎之策，得一百四十四陽，一百八陰，為用數之用也。

This is because on the yang side, the trigram Li (Fire) is excluded and only Qian (Heaven) is used, while on the yin side, the trigram Kun (Earth) is excluded and only Kan (Water) is used. Therefore, the yang count of Heaven is 112, which excludes the yin; the yin count of Earth is also 112, while the yang count is 40, which excludes the yang at the northern and southern extremes. The southern extreme is extremely hot, and the northern extreme is extremely cold, where all things cannot grow, so they are excluded. The remaining 40, perhaps, is the leftover yang of Heaven. When yang enters yin and day enters night, this portion falls to the earth. Combined, it remains 152 yang and 112 yin. If we further exclude the trigram Qian from the yang side and the trigram Kan from the yin side, we get 144 yang and 108 yin, which is called "the use of the numbers."

陽三十六，三之為一百八。陰三十六三之為一百八。三陽三陰，陰陽各半也。陽有餘分之一為三十六，合之為一百四十四陽，一百八陰也，故體數之用二百七十，而實用者二百六十四，用數之用二百五十二也。

The number of a yang line is thirty-six, and three times that makes one hundred and eight. A yin line also takes thirty-six, and three times that also makes one hundred and eight. Three yang lines and three yin lines are paired together, so yin and yang each take up half. There is an additional thirty-six for yang, which when combined makes one hundred and forty-four yang and one hundred and eight yin. Therefore, the total number of the body is two hundred and seventy, but the actual number used is two hundred and sixty-four. The number of the use is two hundred and fifty-two.

卦有六十四而用止乎三十六，爻有三百八十四而用止乎二百一十六也。六十四分而為二百五十六，是以一卦去其初上之爻亦二百五十六也，此生物之數也，故離坎為生物之主，以離四陽，坎四陰，故生物者必四也。陽一百一十二，陰一百一十二，去其離坎之爻則二百一十六也，陰陽之四十共為二百五十六也。是以八卦用六爻，乾坤主之也。六爻用四位，離坎主之也。故天之昏曉不生物而日中生物，地之南北不生物而中央生物也。

There are sixty-four hexagrams but only thirty-six are actually used. There are three hundred and eighty-four lines but only two hundred and sixteen are actually used. Each of the sixty-four hexagrams is divided into four parts, resulting in a total of two hundred and fifty-six. Each hexagram has six lines, but the first and sixth lines are excluded, leaving only the middle four lines. Thus, the sixty-four hexagrams also result in two hundred and fifty-six. This is called the 'number of generation'. Therefore, the trigrams Li (Fire) and Kan (Water) are the masters of generation. Li trigram has four yang lines when stacked, and Kan trigram has four yin lines when stacked, showing that the number of generation must be based on four. There are one hundred and twelve yang lines and one hundred and twelve yin lines. Removing the lines of the trigrams Li and Kan leaves two hundred and sixteen. Adding the remaining forty yin and forty yang lines respectively brings the total to two hundred and fifty-six. Therefore, the eight trigrams must use all six lines, with Qian (Heaven) and Kun (Earth) as the main ones. When using only the middle four lines, Li and Kan are the main ones. Hence, Heaven does not generate life during the early morning and evening but does so at noon, and Earth does not generate life at the north and south ends but does so at the center.

體數何為者也？生物者也。用數何為者也？運行者也，運行者天也，生物者地也。天以獨運，故以用數自相乘，而以用數之用為生物之時也。地偶而生，故以體數之用陽乘陰，為生物之數也。

"The body number" is used for nurturing all things. "The functional number" is used for continuous movement. The aspect of movement belongs to heaven, and the aspect of generating life belongs to earth. Heaven moves by itself, so the functional number is multiplied by itself, and the "function of the functional number" is used to determine the timing of generation. Earth needs to pair and mate to produce offspring, so the yang number from the function of the body number is multiplied by the yin number to determine the quantity of living things.

天數三，故六六而又六之，是以乾之策二百一十有六。地數兩，故十二而十二之，是以坤之策百四十有四也。乾用九，故三其八為二十四，而九之亦二百一十六，兩其八為十六，而九之亦百四十有四。坤用六，故三其十二為三十六，而六之亦二百一十六，兩其十二為二十四，而六之亦百四十有四也。坤以十二之三，十六之四，六之一與半為乾之餘分，則乾得二百五十二，坤得一百八也。陽四卦，十二爻八陽四陰。以三十六乘其陽，以二十四乘其陰，則三百八十四也。

Heaven's number is three, so six multiplied by six and three gives thirty-six, which multiplied by six results in two hundred and sixteen for the trigram Qian. Earth's number is two, so twelve multiplied by twelve gives one hundred and forty-four for the trigram Kun. For Qian using all nines, three eights make twenty-four, which multiplied by nine gives two hundred and sixteen; two eights make sixteen, which multiplied by nine gives one hundred and forty-four. For Kun using all sixes, three twelves make thirty-six, which multiplied by six gives two hundred and sixteen; two twelves make twenty-four, which multiplied by six gives one hundred and forty-four. Then, Kun gives up three from twelve, four from sixteen, and half from six to supplement Qian's share, so Qian gets two hundred and fifty-two and Kun gets one hundred and eight. The four trigrams of yang have twelve lines, with eight yang lines and four yin lines. Multiplying thirty-six by the yang lines and twenty-four by the yin lines together gives exactly three hundred and eighty-four.

體有三百八十四而用止於三百六十何也？以乾坤坎離之不用也。乾坤坎離之不用所以成三百六十之用也。故萬物變易而四者不變也，夫惟不變，是以能變也。用止於三百六十而有三百六十六何也？數之贏也。數之贏則何用也？乾之全用也。乾坤不用則離坎用半也。乾全用者何也？陽主贏也。乾坤不用者何也？獨陽不生，專陰不成也。離坎用半何也？離東坎西，當陰陽之半，為春秋晝夜之門也。或用乾或用離坎何也？主陽而言之，故用乾也。主贏分而言之，則陽侵陰晝侵夜，故用離坎也。陽主贏，故乾全用也。陰主虛，故坤全不用也。陽侵陰陰侵陽，故坎離用半也。是以天之南全見而北全不見，東西各半見也。離坎陰陽之限也，故離當寅，坎當申，而數常踰之者，蓋陰陽之溢也。然用數不過乎寅，交數不過乎申。

The fundamental numbers amount to 384, but the numbers actually used only reach 360. Why is this so? Because the four trigrams Qian, Kun, Kan, and Li are not used in practice. It is precisely because these four trigrams are not used that the numbers used amount to 360. Therefore, although all things change ceaselessly, these four remain constant. Only by being constant can other changes be established. The numbers used amount to 360, yet there is also 366. What is the extra number? It is the surplus of numbers. What is the use of the surplus? It is the full use of Qian. Since Qian and Kun are not used, Kan and Li are only used half. Why is Qian considered to be fully used? Because yang is associated with surplus. Why are Qian and Kun not used? Because isolated yang cannot produce, and pure yin cannot form. Why is Kan and Li only used half? Because Li is located in the east and Kan in the west, exactly at the midpoint of yin and yang, the gate of spring equinox and autumn equinox, and the boundary of day and night. Why sometimes Qian is said to be used and sometimes Kan and Li? When considering yang alone, Qian is used; when considering the surplus part, yang intrudes into yin, day into night, so Kan and Li are used. Yang is associated with surplus, so Qian is fully used; yin is associated with depletion, so Kun is fully not used; yang intrudes into yin and yin also intrudes into yang, so Kan and Li are each used half. Therefore, the southern part of heaven is entirely visible, the northern part entirely invisible, while the eastern and western parts are each visible half. Kan and Li are the boundaries of yin and yang, so Li is at the position of寅 and Kan at the position of申. However, actual numbers often cross these boundaries, which is due to the overflow of yin and yang. Nevertheless, the numbers used never exceed the position of寅, and the numbers of transition never exceed the position of申.

乾四十八，而四分之一分為陰所克。坤四十八，而四分之一分為所克之陽也。故乾得三十六而坤得十二也。陽主進，是以進之為三百六十日。陰主消，是以十二月消十二日也。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，坎艮五，坤六也。

The number of measures for Qian is forty-eight, with a quarter of it being overcome by yin; the number of measures for Kun is also forty-eight, with a quarter of it being the part that is overcome by yang. Therefore, Qian actually has thirty-six, and Kun actually has twelve. Yang represents advancement, so it progresses to form three hundred and sixty days; yin represents retreat, so twelve days are subtracted over the course of twelve months. Counting the Earlier Heaven trigrams in order, they are Qian one, Dui two, Li three, Zhen four, Xun five, Kan six, Gen seven, Kun eight; counting them in reverse order, Zhen is one, Li and Dui are both two, Qian is three, Xun is four, Kan and Gen are both five, and Kun is six.

乾四十八，兌三十，離二十四，震十。坤十二，艮二十，坎三十六，巽四十。乾三十六，坤十二，離兌巽二十八，坎艮震二十。圓數有一，方數有二，奇偶之義也。六即一也，十二即二也。

Each trigram is associated with a certain number of策 (counting units): Qian (Heaven) has 48, Dui (Lake) has 30, Li (Fire) has 24, Zhen (Thunder) has 10; Kun (Earth) has 12, Gen (Mountain) has 20, Kan (Water) has 36, Xun (Wind) has 40. If we consider only the yang numbers, Qian has 36, Kun has 12, Li, Dui, and Xun each have 28, while Kan, Gen, and Zhen each have 20. The circular numbers take one as their fundamental basis, while the square numbers take two as their fundamental basis; this is the distinction between odd and even. Six is merely derived from one, and twelve is merely derived from two.

天圓而地方，圓者數之起一而積六，方者數之起一而積八，變之則起四而積十二也。六者常以六變，八者常以八變，而十二者亦以八變，自然之道也。八者天地之體也，六者天之用也，十二者地之用也。天變方為圓而常存其一，地分一為四而常執其方。天變其體而不變其用也，地變其用而不變其體也。六者並其一而為七，十二者並其四而為十六也。陽主進，故天並其一而為七。陰主退，故地去其四而止於十二也，是陽常存一而陰常晦一也，故天地之體止於八，而天之用極於七，地之用止於十二也。圓者裁方以為用，故一變四，四去其一則三也。三變九，九去其三則六也。

Heaven is round and Earth is square. The number of the round comes from one and accumulates to six, while the number of the square comes from one and accumulates to eight. When changing and transforming, they start from four and accumulate to twelve. Those belonging to six change in cycles of six, those belonging to eight change in cycles of eight, and those belonging to twelve change along with eight. This is the natural principle. Eight is the form shared by Heaven and Earth, six is the function of Heaven, and twelve is the function of Earth. Heaven transforms its form into roundness but retains the 'one'; Earth divides one into four but always keeps its squareness. Heaven changes its form but does not change its function, while Earth changes its function but does not change its form. Adding the retained one to six makes seven, and adding the divided four to twelve makes sixteen. Yang is active and advances, so Heaven includes the one to make seven; Yin is passive and retreats, so Earth subtracts the four and stops at twelve. This is why Yang always retains a part and Yin always hides a part. Therefore, the form of Heaven and Earth stops at eight, the function of Heaven reaches seven, and the function of Earth stops at twelve. The round path must transform the square to achieve its function, so one becomes four, and four minus the one becomes three; three becomes nine, and nine minus the three becomes six.

方者展圓以為體，故一變三，並之四也，四變十二，並之十六也。故用數成於三而極於六，體數成於四而極於十六也。是以圓者徑一而圍三，起一而積六。方者分一而為四，分四而為十六，皆自然之道也。

The square's path must spread out in a circle to form its body, so one becomes three, and including itself, it totals four; four becomes twelve, and including itself, it totals sixteen. Therefore, the number used to establish the three reaches its extreme at six, and the number of the body established at four reaches its extreme at sixteen. Thus, the diameter of a circle is one while its circumference is three, starting from one, it accumulates to six; the square divides one into four, then divides four into sixteen: all of this follows naturally.

一役二以生三，三去其一則二也。三生九，九去其一則八也，去其三則六也。故一役三，三復役二也。三役九，九復役八與六也。是以二生四，八生十六，六生十二也。三並一則為四，九並三則為十二也，十二又並四則為十六。故四以一為本，三為用。十二以三為本，九為用。十六以四為本，十二為用。圓者六變，六六而進之，故六十變而三百六十矣。方者八變，故八八而成六十四矣。陽主進，是以進之為六十也。

One drives two and produces three; three minus one returns to two. Three produces nine; nine minus one is eight, and nine minus three is six. Therefore, one drives three, and three in turn drives two; three drives nine, and nine in turn drives eight and six. Thus, two produces four, eight produces sixteen, and six produces twelve. Three plus one is four, nine plus three is twelve, and twelve plus four is sixteen. Therefore, four is based on one and uses three, twelve is based on three and uses nine, and sixteen is based on four and uses twelve. The circle has six transformations, and six multiplied by six gives thirty-six; the square has eight transformations, and eight multiplied by eight gives sixty-four. Yang represents advancement, so advancement leads to sixty.

蓍數不以六而以七，何也？並其餘分也。去其餘分則六，故策數三十六也。是以五十者，六十四卦閏歲之策也。其用四十有九者，六十卦一歲之策也，歸奇掛一猶一歲之閏也。卦直去四者何也？天變而地效之，是以蓍去一則卦去四也。

Why does the use of numbers in divination with yarrow stalks take seven instead of six? It is because the remaining fraction is also included. If the remaining fraction is excluded, it would be six, so the number of stalks used for one line is thirty-six. Therefore, the number fifty in the Great Derivation is used to match the sixty-four hexagrams and the leap year in the calendar. Among these, the actual number used is forty-nine, which corresponds to the sixty hexagrams of a regular year. When counting the remaining stalks and setting aside one stalk during the divination process, it is analogous to inserting a leap month in a year. As for why the number is reduced by four directly when casting the hexagrams, it is because heaven changes first and earth follows, so reducing one stalk in the yarrow stalks corresponds to reducing four hexagrams.

圓者徑一圍三，重之則六。方者徑一圍四，重之則八也。裁方而為圓，天所以運行。分大而為小，地所以生化。故天用六變，地用四變也。

The diameter of a circle is one, and its circumference is three; doubling this gives six. The diameter of a square is one, and its circumference is four; doubling this gives eight. Carving a square into a circle represents how heaven can continuously move and function. Dividing a large number into smaller numbers represents how earth can give birth and nurture. Therefore, heaven uses six as its principle, and earth uses four as its principle.

一八為九，裁為七。八裁為六，十六裁為十二，二十四裁為十八，三十二裁為二十四，四十裁為三十，四十八裁為三十六，五十六裁為四十二，六十四裁為四十八也。一分為四，八分為三十二，十六分為六十四，以致九十六分為三百八十四也。

One and eight together make nine; if one part is cut off, it becomes seven. Following the ratio of subtracting one from four parts, we proceed: eight becomes six, sixteen becomes twelve, twenty-four becomes eighteen, thirty-two becomes twenty-four, forty becomes thirty, forty-eight becomes thirty-six, fifty-six becomes forty-two, and sixty-four becomes forty-eight. If we instead use the method of dividing, one becomes four, eight becomes thirty-two, sixteen becomes sixty-four, and so on up to ninety-six becoming three hundred eighty-four. This matches exactly the number of hexagrams (sixty-four) and lines (three hundred eighty-four) in the Yijing.

一生六，六生十二，十二生十八，十八生二十四，二十四生三十，三十生三十六，引而伸之，六十變而生三百六十矣，此運行之數也。四生十二，十二生二十，二十生二十八，二十八生三十六，此生物之數也。故乾之陽中策三十六，兌離巽之陽策二十八，震坎艮之陽策二十，坤之陽策十二也。

The sequence for the circle is: one generates six, six generates twelve, twelve generates eighteen, eighteen generates twenty-four, twenty-four generates thirty, and thirty generates thirty-six; continuing in this way, sixty changes generate three hundred and sixty, which is called "the number of movement." The sequence for the square is: four generates twelve, twelve generates twenty, twenty generates twenty-eight, and twenty-eight generates thirty-six; this is called "the number of generation." Therefore, the yang number of Qian is thirty-six, the yang numbers of Dui, Li, and Xun are twenty-eight, the yang numbers of Zhen, Kan, and Gen are twenty, and the yang number of Kun is twelve.

圓者一變則生六，去一則五也。二變則生十二，去二則十也。三變則生十八，去三則十五也。四變則二十四，去四則二十也，五變則三十，去五則二十五也。六變則三十六，去六則三十也。是以存之則六六，去之則五五也。五則四而存一也，四則三而存一也，三則二而存一也，二則一而存一也，故一生二，去一則一也。二生三，去一則二也。三生四，去一則三也。四生五，去一則四也。是故二以一為本，三以二為本，四以三為本，五以四為本，六以五為本。

The circle's path begins with one, which transforms into six; subtracting one leaves five. Two transforms into twelve; subtracting two leaves ten. Three transforms into eighteen; subtracting three leaves fifteen. Four transforms into twenty-four; subtracting four leaves twenty. Five transforms into thirty; subtracting five leaves twenty-five. Six transforms into thirty-six; subtracting six leaves thirty. Therefore, keeping the full number results in six sixes, while subtracting layer by layer results in five fives. Five is formed by four plus one, four is formed by three plus one, three is formed by two plus one, and two is formed by one plus one. Thus, one gives rise to two, and removing that one leaves one. Two gives rise to three, and removing that one leaves two. Three gives rise to four, and removing that one leaves three. Four gives rise to five, and removing that one leaves four. Therefore, two is based on one, three is based on two, four is based on three, five is based on four, and six is based on five, with each layer arising successively from the previous.

方者一變而為四，四生八，並四而為十二。八生十二，並八而為二十。十二生十六，並十二而為二十八。十六生二十，並十六而為三十六也。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。五十者蓍數也，六十者卦數也。五者蓍之小衍，故五十為大衍也。八者卦之小成，則六十四為大成也。

The way of the square begins with one, which transforms into four; from four come eight, and combining the original four gives twelve; from eight come twelve, and combining the original eight gives twenty; from twelve come sixteen, and combining the original twelve gives twenty-eight; from sixteen come twenty, and combining the original sixteen gives thirty-six. What is the "Great Derivation" (大衍) mentioned in the Book of Changes? It refers to numbers, which are the numbers relied upon by the sage to establish the system. The heavenly numbers are one, three, five, seven, and nine, which add up to twenty-five; doubling this gives fifty. The earthly numbers are two, four, six, eight, and ten, which add up to thirty; doubling this gives sixty. Therefore, the Great Treatise says, "The five positions are in harmony and each has its corresponding element." Fifty is the number of the divination sticks, and sixty is the number of the hexagram lines. Five is the small derivation of the divination numbers, so fifty is called the Great Derivation; eight is the small completion of the hexagram numbers, so sixty-four is called the Great Completion.

蓍德圓，以況天之數，故七七四十九也，五十者存一而言之也。卦德方，以況地之數，故八八六十四也，六十者去四而言之也。蓍者用數也，卦者體數也。用以體為基，故存一也。體以用為本，故去四也。圓者本一，方者本四，故蓍存一而卦去四也。蓍之用數七，並其餘分，亦存一之義也。掛其一，亦去一之義也。

The nature of the yarrow stalks is round, used to represent the number of Heaven, so they are counted as forty-nine, which is seven times seven. It is said to be fifty because the one unused stalk is also included. The nature of the hexagrams is square, used to represent the number of Earth, so they are counted as sixty-four, which is eight times eight. It is said to be sixty because the four unused hexagrams are subtracted. The yarrow stalks belong to the category of 'used numbers,' while the hexagrams belong to the category of 'essential numbers.' The used must be based on the essential, so one stalk is retained. The essential must be based on the used, so four hexagrams are subtracted. The round is based on one, and the square is based on four, hence the yarrow stalks retain one and the hexagrams remove four. The used number of the yarrow stalks is seven, and the remaining fraction is included, which is exactly the meaning of 'retaining one.' When divining with the yarrow stalks, one stalk is first suspended, which is exactly the meaning of 'removing one.'

蓍之用數，掛一以像三，其餘四十八則一卦之策也。四其十二為四十八也，十二去三而用九，四三十二所去之策也。四九三十六所用之策也。以當乾之三十六陽爻也。十二去五而用七，四五二十所去之策也，四七二十八所用之策也，以當兌離之二十八陽爻也。十二去六而用六，四六二十四所去之策也，四六二十四所用之策也，以當坤之二十四陰爻也。十二去四而用八，四四十六所去之策也，四八三十二所用之策也，以當坎艮之二十四爻，並上卦之八陰為三十二爻也。是故七九為陽，六八為陰也。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。

The divination method using the yarrow stalks begins by hanging one stalk to symbolize the Three Powers. The remaining forty-eight stalks are used for a single hexagram. Four times twelve equals forty-eight. From twelve, subtract three and use nine; four times three equals twelve, which is the number of stalks subtracted, and four times nine equals thirty-six, which is the number of stalks used, corresponding to the thirty-six yang lines of the Qian hexagram. From twelve, subtract five and use seven; four times five equals twenty, which is the number of stalks subtracted, and four times seven equals twenty-eight, which is the number of stalks used, corresponding to the twenty-eight yang lines of the Dui and Li hexagrams. From twelve, subtract six and use six; four times six equals twenty-four, which is the number of stalks subtracted, and four times six equals twenty-four, which is the number of stalks used, corresponding to the twenty-four yin lines of the Kun hexagram. From twelve, subtract four and use eight; four times four equals sixteen, which is the number of stalks subtracted, and four times eight equals thirty-two, which is the number of stalks used, corresponding to the twenty-four lines of the Kan and Gen hexagrams, plus the eight yin lines of the upper trigram, totaling thirty-two lines. Therefore, seven and nine belong to yang, while six and eight belong to yin. Nine is the extreme number of yang, and six is the extreme number of yin. When numbers reach their extremes, they must reverse, so nine and six become the changing lines of the hexagram. The Zhen and Xun hexagrams are not included in the count of stalks, serving as the unused portion. Heaven's virtue is firm and strong, so its flexible aspect does not appear; Earth's nature is gentle and yielding, so its strong aspect does not emerge, hence Zhen and Xun do not have a count of stalks.

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。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，為五與四四也，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，以應圓數之六變也。乾並餘分七為七政？

Heavenly Stem Qian uses all nines, so its measure is based on nine, multiplied by four to correspond to the four seasons, each season being ninety days. Earthly Stem Kun uses all sixes, so its measure is based on six. The remaining odd numbers from divination with yarrow stalks can be one, two, three, or four; the numbers used to form lines can be six, seven, eight, or nine. Combined, these make eight numbers, corresponding to the eight transformations of the directions. When the remaining measures are combined with the hanging measures, there are six possible results: five paired with two fours, nine paired with two eights, five paired with four and eight, nine paired with four and eight, five paired with two eights, and nine paired with two fours, corresponding to the six transformations of the circle. Qian includes the remaining fraction to make seven, which is probably what is meant by the 'seven governing principles'.

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。卦有六十四而用止於六十者何也？六十卦者，三百六十爻也。故甲子止於六十也，六甲而天道窮矣。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。

The number of odd numbers used in divination reaches four, and five is not included; the number of lines in a trigram reaches nine, and ten is not included. Five is actually one, and ten is actually two, so the great derivation uses fifty but actually only employs forty-nine. Odd numbers do not use five, and the lines do not use ten. This is the extreme of "having" and "not having," used to illustrate the natural and spontaneous numbers. There are sixty-four hexagrams, but in practice only sixty are used. Why is this so? Because sixty hexagrams contain three thousand six hundred lines, so one cycle of Jiazi reaches sixty, and after six cycles, the heavenly path completes one full cycle. The numbers of the lines correspond exactly to this: thirty-six plus twenty-four equals sixty, and thirty-two plus twenty-eight also equals sixty.

乾四十八，坤十二，震二十，巽四十，離兌三十二，坎艮二十八，合之為六十。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，先陰後陽也。故為陰中之陽。

The trigram Qian has 48, Kun has 12, Zhen has 20, Xun has 40, Li and Dui combined have 32, and Kan and Gen combined have 28. When paired two by two, they all add up exactly to 60. The number of stalks used in divination is not reduced, so the yang stalks, which are 36, added to 28 give 64. The number of hexagrams is reduced by four, so the yin stalks, which are 24, added to 32 give 56. The number nine is derived by adding four to four, resulting in 36, which is entirely yang, so it is called 'yang within yang'. The number seven is derived by adding four to four, resulting in 28, which starts with yang and then turns to yin, so it is called 'yang within yin'. The number six is derived by adding four to four, resulting in 24, which is entirely yin, so it is called 'yin within yin'. The number eight is derived by adding four to four, resulting in 32, which starts with yin and then turns to yang, so it 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。歸奇合卦之數得五與四四，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 heavenly stems is twenty-five, and using four to advance it results in one hundred. The number of trigrams is thirty, and using four to advance it results in one hundred twenty. One hundred reduces to ten, and one hundred twenty reduces to twelve. Combining the remaining sticks with those used in the casting: if five and two fours are obtained, the number of lines is four multiplied by nine; if nine and two eights are obtained, the number of lines is four multiplied by six; if five and two eights, or nine and four or eight, the number of lines is four multiplied by seven; if nine and two fours, or five and four or eight, the number of lines is four multiplied by eight. If nine is obtained, it is one change, corresponding to Heaven; if six is obtained, it is one change, corresponding to Earth; if seven is obtained, it is two changes, corresponding to Lake and Fire; if eight is obtained, it is two changes, corresponding to Mountain and Water. If five and two fours are obtained, removing the stick used in the casting results in four multiplied by three, which is twelve; if nine and two eights are obtained, removing the stick used in the casting results in four multiplied by six, which is twenty-four; if five and two eights, or nine and four or eight, removing the stick used in the casting results in four multiplied by five, which is twenty; if nine and two fours, or five and four or eight, removing the stick used in the casting results in four multiplied by four, which is sixteen. It is precisely by subtracting three, four, five, and six that the numbers 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。

Heavenly One, Earthly Two, Heavenly Three, Earthly Four, Heavenly Five, Earthly Six, Heavenly Seven, Earthly Eight, Heavenly Nine, Earthly Ten, intermingle and change in a complex manner, combining and interacting with each other, just as Heaven and Earth connect with each other and day and night intermingle. "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. Only one multiplied by one remains one, and cannot change. One hundred reduces to ten, ten reduces to one, and also cannot change. Therefore, numbers must exclude one and reach up to nine, taking only the parts that can change. Five multiplied by five is twenty-five, which is the heavenly number. Six multiplied by six is thirty-six, which is the number of the trigram Qian. Seven multiplied by seven is forty-nine, which is the number used in the Great Changes. 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 used in Yang Xiong's Tai Xuan and Hong Fan's nine categories.

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。陰無一，陽無十。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。

The fundamental numbers of the Great Derivation are the origin of arithmetic. Therefore, all calculations begin with the forms of square, circle, curve, and straight line. Multiplication belongs to the number of growth, while division belongs to the number of reduction; although there are many names for calculation methods, they all fall within this scope. The yin side does not have the number one, and the yang side does not have the number ten; yang needs to meet yin in order to generate, and yin needs to meet yang in order to form. Therefore, the number of the yarrow stalks is based on four and completes at nine, while the number of the hexagrams is based on six and completes at ten. This is similar to the interweaving of the heavenly stems and earthly branches, where the heavenly stems cycle six times and the earthly branches cycle five times, both concluding together at 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。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。以六爻言之，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。

Three times four is twelve, two times six is also twelve; two twelves make twenty-four, three times eight is also twenty-four, four times six is also twenty-four; three twelves make thirty-six, four times nine is also thirty-six, six times six is also thirty-six; four twelves make forty-eight, three times sixteen is also forty-eight, six times eight is also forty-eight; five twelves make sixty, three times twenty is also sixty, six times ten is also sixty: all these naturally correspond with each other. Four times nine is thirty-six, six times six is also thirty-six: yang originally has only six, but it also takes half of yin's six, thus forming nine. In terms of the upper and lower trigrams, yin and yang each occupy three lines; in terms of a single trigram with six lines, heaven, earth, and humanity each occupy two lines. Yin and yang each contain heaven, earth, and humanity, and heaven, earth, and humanity each contain yin and yang. Therefore, it is said, "Three lines for heaven, two lines for earth, and the numbers rely on this principle."

陽數一，衍之而十，十干之類是也。陰數二，衍之為十二，十二支十二月之類是也。一變而二，二變而四，三變而八卦成矣。四變而十有六，五變而三十有二，六變而六十四卦備矣。易有真數三而已矣，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。

The number for Yang is one, which expands to ten, giving rise to the ten Heavenly Stems; the number for Yin is two, which expands to twelve, giving rise to the twelve Earthly Branches and the twelve months. One transforms into two, two transforms into four, and three transformations lead to the eight Trigrams. Four transforms into sixteen, five transforms into thirty-two, and six transformations result in the sixty-four Hexagrams. This is the method of successive doubling in the study of the Earlier Heaven (Earlier Heaven) system. The true fundamental numbers of the Book of Changes are only three: "参天" (partaking in Heaven) refers to three multiplied by three to make nine; "两地" (partaking in Earth) refers to three doubled to make six. "参天两地而倚数" (partaking in Heaven and Earth to derive numbers) does not refer to the original numbers of Heaven and Earth; "倚" (relying on) means comparison, referring to numbers derived by analogy with the original numbers of Heaven and Earth.

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。一十百千萬億，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。

The numbers generated by the Book of Changes amount to twelve thousand nine hundred and sixty, which totals four thousand three hundred and twenty generations, representing the great number of increase and decrease. By extending the numbers of the thirty-year cycle, one arrives precisely at this number. A year consists of three hundred and sixty days, totaling four thousand three hundred and twenty hours. Multiplying this by thirty yields the number. All generations begin with the years of Jiazi and Jiawu, which is called the "number governing the world." The beginning is marked by the day being Jia, the month being Zi, the star being Jia, and the hour being Zi. It is also said that this is the number of "Jia day" within the governing of the world, with the month Zi, star Jia, and hour Zi all following in sequence. The sequence of one, ten, hundred, thousand, ten thousand, and hundred million belongs to the odd numbers, which are the numbers of heaven; while the sequence of twelve, two hundred and twenty, one thousand two hundred, twenty thousand, and two million belongs to the even numbers, which are the numbers of earth.

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。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。陽數於三百六十上盈，陰數於三百六十上縮。

The number fifty, when divided evenly, becomes ten. If we take the number three from "参天" and double it, we get six; if we take the number two from "两地" and double it, we get four: these are the numbers derived from the division of the Taiji by Heaven and Earth. In the diagram of the Earlier Heaven (Earlier Heaven) circle, from the Fu hexagram to the Qian hexagram there are 112 yang lines; from the Guu hexagram to the Kun hexagram there are 80 yang lines. From the Guu hexagram to the Kun hexagram there are 112 yin lines; from the Fu hexagram to the Qian hexagram there are 80 yin lines. The number of yang lines exceeds 360, while the number of yin lines is less than 360.

人為萬物之靈，寄類於走走陰也。故百二十。有一日之物，有一月之物，有一時之物，有一歲之物，有十歲之物，至於百千萬皆有之，天地亦物也,亦有數焉。

Human beings are the most spiritually endowed among all things. If classified according to categories, they can only be placed under the category of 'movement' (走), which belongs to the yin category. Therefore, the fixed number of human life is one hundred and twenty. All things have their own durations: some live only one day, some one month, some one hour, some one year, some ten years, and some even hundreds, thousands, or even ten thousand years. The heavens and the earth themselves are also things, so they too have their fixed numbers.

卦之反對皆六陽六陰也，在易則六陽六陰者，十有二對也。去四正則八陽四陰，八陰四陽者，各六對也。十陽二陰，十陰二陽者，各三對也。

When a hexagram and its opposite are viewed together, the total number of yin and yang lines must be six yin and six yang. Among the sixty-four hexagrams in the Book of Changes, there are twelve pairs that are complementary in this way. Excluding the four primary hexagrams, Qian, Kun, Kan, and Li, there are six pairs in each of the groups: eight yang and four yin, and eight yin and four yang; and three pairs in each of the groups: ten yang and two yin, and ten yin and two yang.

圓者星也，曆紀之數其肇於此乎？方者土也，畫州並土之法其仿於此乎？蓋圓者，河圖之數。方者，洛書之文。故羲文因之而造易，禹箕敘之而作範也。

The round shape represents the stars in the sky, and the numbers used in calendars and years of record probably originated from this. The square shape represents the earth's soil, and the methods for dividing regions and measuring land probably imitated this. Generally, the round is associated with the numerical patterns of the River Chart (He Tu), and the square is associated with the textual patterns of the Lo Shu. Therefore, Fuxi and King Wen derived the Book of Changes (Yi Jing) from them, and Yu the Great and Ji Zi recorded the Classic of Documents (Hong Fan) based on them.

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，故易六位而成章也。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。

After the Taiji is divided, the two principles (Yin and Yang) are established. Yang enters into Yin below, and Yin enters into Yang above, thus producing the four images. When Yang interacts with Yin and Yin interacts with Yang, the heavenly four images are generated. When hardness interacts with softness and softness interacts with hardness, the earthly four images are generated, and thus the eight trigrams are formed. When the eight trigrams intermingle with each other, then all things come into being. Therefore, one divides into two, two into four, four into eight, eight into sixteen, sixteen into thirty-two, thirty-two into sixty-four. Therefore, the "Sayings on the Trigrams" says: after dividing Yin, divide Yang again, alternating between soft and hard, so the Book of Changes has six positions and forms the text. Further down, ten becomes a hundred, a hundred becomes a thousand, a thousand becomes ten thousand, like roots producing trunks, trunks producing branches, branches producing leaves: the bigger the less, the smaller the more numerous; when gathered together they are one, but when spread out they become myriad. Therefore, Qian governs division, Kun governs gathering, Zhen governs growth, Xun governs decline; when growth reaches its limit it divides, when division reaches its limit it declines, and when decline reaches its limit it gathers.

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。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。

Qian and Kun each occupy their respective positions. Zhen and Xun are formed from the initial interaction of yin and yang. Dui, Li, Kan, and Gen are formed from the subsequent interaction. Therefore, Zhen has relatively less yang and still more yin, while Xun has relatively less yin and still more yang. Dui and Li have gradually increasing yang, while Kan and Gen have gradually increasing yin. This is why the celestial element of heaven and the terrestrial element of fire are hidden. When the unified qi is divided, yin and yang become distinct. Where there is more yang, it becomes heaven; where there is more yin, it becomes earth. In places where yin and yang are balanced, form and substance are present. In places where yin or yang prevails, nature and emotion become distinct. When form and substance are further divided, those with more yang become strong, and those with more yin become soft. When nature and emotion are further divided, those with more yang reach the extreme of yang, and those with more yin reach the extreme of yin.

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。乾四分取一以與坤，坤四分取一以奉干，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。

Dui, Li, and Xun have more yang, while Gen, Kan, and Zhen have more yin, so they are used by heaven and earth. Qian has yang to the extreme, and Kun has yin to the extreme; being too pure and full, they are not used. Qian takes one part from its four parts and gives it to Kun, and Kun also takes one part from its four parts and returns it to Qian. The union of Qian and Kun produces the six sons: the three yang trigrams are male, and the three yin trigrams are female. Dui gives one yang to Gen, Kan gives one yin to Li, and Zhen and Xun exchange two lines with each other. In total, yin and yang each receive half, so water and fire both generate and control each other, and thus all things are finally formed.

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，是以乾坤坎離中孚頤大小過皆不可易者也。

The names and positions of the trigrams Qian and Kun cannot be changed. The names of Kan and Li can be exchanged but their positions cannot be altered. 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. The trigram Li resembles Qian in shape, Kan resembles Kun, Zhongfu resembles Qian, Yi resembles Li, Xiaoguo resembles Kun, and Daguo resembles Kan. Therefore, the eight trigrams Qian, Kun, Kan, Li, Zhongfu, Yi, Daguo, and Xiaoguo remain the same even when reversed.

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。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。

The Trigram Li is located in the sky but governs the night, so it is yang containing yin; the Trigram Kan is located on the ground but governs the day, so it is yin containing yang. The Trigram Zhen is yang initially entering yin and thus yang begins to arise, while the Trigram Xun is yang beginning to retreat and thus yin begins to arise. The Trigram Dui is yang growing, and the Trigram Gen is yin growing. The Trigrams Zhen and Dui belong to the yang within heaven, while the Trigrams Xun and Gen belong to the yang within earth. 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. Heaven refers to the initial emergence of all things, so yin is above and yang is below, representing the harmonious union of heaven and earth. Earth refers to the completion of all things, so yang is above and yin is below, representing the established order of hierarchy.

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。由下而上謂之升，自上而下謂之降。升者生也，降者消也，故陽生於下，陰生於上，是以萬物皆反生。陰生陽，陽生陰，陰復生陽，陽復生陰，是以循環而無窮也。

Heavenly Stem and Earthly Branches establish the positions of above and below, while the Trigrams Qian (Heaven) and Kun (Earth) determine the left and right gates. Heaven and Earth open and close here, and the sun and moon rise and set through this. Therefore, the succession of the four seasons, the waxing and waning of the moon, the length of day and night, and the movement of the sun and moon with their increasing and decreasing paths—all these come from here. Moving upward from below is called "ascending," and moving downward from above is called "descending." Ascending represents growth, and descending represents decline. Yang arises from below, and Yin arises from above, so all things are born in reverse. Yin gives rise to Yang, and Yang gives rise to Yin. Yin again gives rise to Yang, and Yang again gives rise to Yin, thus forming a continuous cycle without end.

陰陽生而分二儀，二儀交而生四象，四象交而生八卦，八卦交而生萬物，故二儀生天地之類，四象定天地之體。四象生日月之類，八卦定日月之體。八卦生萬物之類，重卦定萬物之體。類者生之序也，體者象之交也。推類者必本乎生，觀體者必由乎象。生則未來而逆推，像則既成而順觀。是故日月一類也，同出而異處也，異處而同象也。推此以往，物焉逃哉。

Yin and yang first divide into two principles, which intersect to produce the four images, which intersect to produce the Eight Trigrams, which intersect to produce all things. Therefore, the two principles give rise to heaven and earth, while the four images determine the forms of heaven and earth; the four images give rise to sun and moon, while the Eight Trigrams determine the forms of sun and moon; the Eight Trigrams give rise to all things, while the combined trigrams determine the forms of all things. "Class" refers to the order of generation, while "form" refers to the combination of images. To investigate categories must begin with the order of generation, while to observe forms must begin with the images. Discussing generation involves tracing back from what has not yet come to be; discussing form involves observing what has already taken shape. Therefore, sun and moon belong to the same category, arising from the same source but occupying different positions; although their positions differ, their forms are the same. By following this method of deduction, can anything in the world escape this principle?

天變時而地應物，時則陰變而陽應，物則陽變而陰應，故時可逆知，物必順成，是以陽盈而陰隨，陰逆而陽順。語其體則天分而為地，地分而為萬物，而道不可分也。其終則萬物歸地，地歸天，天歸道，是以君子貴道也。

The changes in the heavens relate to the seasons, and the responses in the earth relate to all things. In terms of the seasons, it is the yin that changes first and the yang follows in response; in terms of all things, it is the yang that changes first and the yin follows in response. Therefore, the seasons can be calculated in reverse to predict them in advance, but all things must develop in order to be completed. Thus, when yang is full, yin follows accordingly, and although yin may act in reverse, yang continues in its proper course. In terms of the structure of forms, heaven differentiates the earth, the earth differentiates all things, but only the "Dao" cannot be divided. At the end, all things return to the earth, the earth returns to heaven, and heaven returns to the Dao. Therefore, the gentleman values the Dao most.

有變則必有應也，故變於內者應於外，變於外者應於內，變於下者應於上，變於上者應於下也。天變而日應之，故變者從天，而應者法日也。是以日紀乎星，月會於辰，水生於土，火潛於石，飛者棲木，走者依草，心肺之相聯，肝膽之相屬無他,變應之道也。本乎天者親上，本乎地者親下，故變之與應，常反對也。

Whenever there is a change, there must be a response: if the inner part changes, the outer part responds; if the outer part changes, the inner part responds; if the lower part changes, the upper part responds; if the upper part changes, the lower part responds. Heaven changes first, and the sun follows in response, so the changing side submits to Heaven, and the responding side follows the sun. Therefore, the sun governs the stars as a standard, the moon and the stars meet and harmonize, water arises from the earth, fire is hidden in stones; flying creatures rest on trees, moving creatures dwell among grasses; the heart connects with the lungs, the liver relates to the gallbladder. There is no other reason for this; it is all based on the principle of change and response. The source in Heaven is closely connected to the upper part, and the source in Earth is closely connected to the lower part. Therefore, the changing side and the responding side are always in opposite positions.

陽交於陰，而生蹄角之類也。剛交於柔，而生根荄之類也。陰交於陽，而生羽翼之類也。柔交於剛，而生支干之類也。天交於地，地交於天，故有羽而走者，足而騰者，草中有木，木中有草也。各以類而推之，則生物之類不過是矣。走者便於下，飛者利於上，從其類也。陸中之物水中必具者，猶影像也，陸多走，水多飛者，交也。是故巨於陸者必細於水，巨於水者必細於陸也。

Heavenly Yang meets earthly Yin, producing creatures with hooves and horns; Heavenly Yang meets earthly Yin, producing plants with roots and stems; earthly Yin meets heavenly Yang, producing creatures with feathers and wings; earthly Yin meets heavenly Yang, producing branches and trunks. Heaven meets earth, and earth meets heaven, so there are creatures with feathers that can only walk, and creatures with feet that can leap; there are trees growing in grass, and grass growing among trees. Each category follows its own pattern. Creatures that walk are suited for movement on the ground, while creatures that fly are suited for ascending. Each follows its own kind. On land, there are certain creatures, and in water there are corresponding ones, like a shadow reflecting its shape. On land there are many walking animals, but in water there are many flying creatures, due to the interaction of heaven and earth. Therefore, creatures that are large on land are small in water, and creatures that are large in water are small on land.

虎豹之毛猶草也，鷹鸇之羽猶木也。木者星之子，是以果實像之。葉陰也，華實陽也。枝葉軟而根幹堅也。人之骨巨而體繁，木之乾巨而枝葉繁，應天地之數也。

The fur of tigers and leopards has patterns resembling grass; the feathers of eagles and hawks have shapes like the branches of trees. Trees are the offspring of stars, so the shape of their fruits is modeled after stars. Leaves belong to the yin, while flowers and fruits belong to the yang; branches and leaves are soft, while roots and trunks are firm. Human bones are coarse and the body has many limbs; the main trunk of a tree is coarse and has many branches, which corresponds to the fixed principle in the universe that 'the greater something is, the fewer its parts; the smaller something is, the more numerous its parts.'

動者體橫，植者體縱，人宜橫而反縱也。飛者有翅，走者有趾，人之兩手翅也,兩足趾也。飛者食木，走者食草，人皆兼之而又食飛走也。故最貴於萬物也。

A moving body is horizontal, a long body is vertical; humans should be like beasts moving horizontally, yet they stand upright. Creatures that fly have wings, those that walk have toes; human hands are like wings, and feet are like toes. Creatures that fly eat the fruits of trees, those that walk eat grass; humans eat both, and also consume what flies and walks, thus being the most exalted among all things.

體必交而後生，故陽與剛交而生心肺，陽與柔交而生肝膽，柔與陰交而生腎與膀胱，剛與陰交而生脾胃，心生目，膽生耳，脾生鼻，腎生口，肺生骨，肝生肉，胃生髓，膀胱生血，故乾為心，兌為脾，離為膽，震為腎，坤為血，艮為肉，坎為髓，巽為骨，泰為目，中孚為鼻，既濟為耳，頤為口，大過為肺，未濟為胃，小過為肝，否為膀胱。

The form must necessarily combine to produce something, so yang and strength combine to produce the heart and lungs, yang and flexibility combine to produce the liver and gallbladder, flexibility and yin combine to produce the kidneys and bladder, and strength and yin combine to produce the spleen and stomach. From the internal organs come the five senses and their physical forms: the heart produces the eyes, the gallbladder produces the ears, the spleen produces the nose, the kidneys produce the mouth, the lungs produce bones, the liver produces flesh, the stomach produces marrow, and the bladder produces blood. In terms of trigrams, Qian corresponds to the heart, Dui to the spleen, Li to the gallbladder, Zhen to the kidneys, Kun to blood, Gen to flesh, Kan to marrow, Xun to bones, Tai to the eyes, Zhongfú to the nose, Ji Ji to the ears, Yi to the mouth, Da Guo to the lungs, Wei Ji to the stomach, Xiao Guo to the liver, and Pǐ to the bladder.

天地有八象，人有十六象，何也？合天地而生人，合父母而生子，故有十六象也。心居肺，膽居肝，何也？言性者必歸之天，言體者必歸之地。地中有天，石中有火，是以心膽象之也。心膽之倒垂何也？草木者，地之體也。人與草木皆反生，是以倒垂也。

Heaven and Earth have only eight images, but humans have sixteen images. This is because humans are formed by combining Heaven and Earth, and by combining father and mother. When these two are multiplied together, humans have sixteen images. Why is the heart hidden in the lung and the gallbladder attached to the liver? When discussing "nature," it must be traced back to Heaven; when discussing "body," it must be traced back to Earth. The Earth contains Heaven, and stone contains fire. The heart and gallbladder are taken as symbols of this inclusion. Why are the heart and gallbladder hanging upside down? Grass and trees are the forms of Earth, and humans and grass trees are both born upside down, so the heart and gallbladder are also upside down.

口目橫而鼻耳縱，何也？體必交也。故動者宜縱而反橫，植者宜橫而反縱，皆交也。天有四時，地有四方，人有四支，是以指節可以觀天，掌文可以察地，天地之理具指掌矣，可不貴之哉！

The mouth and eyes are horizontal, while the nose and ears are vertical, which is why they are structured this way. This is because the body must have parts that intersect with each other. Therefore, things that should be long and vertical end up being horizontal, and things that should be horizontal end up being long, all due to the intersecting nature. Heaven has the four seasons, Earth has the four directions, and humans have four limbs. Thus, by observing the joints of the fingers, one can understand the changes of heaven's seasons, and by examining the patterns on the palms, one can comprehend the features of the Earth. The principles of heaven and earth are all contained within a person's hands, so how can we not hold them in high regard?

神統於心，氣統於腎，形統於首，形氣交而神主乎其中，三才之道也。人之四肢各有脈也，一脈三部，一部三候，以應天數也。心藏神，腎藏精，脾藏魂，膽藏魄。胃受物而化之，傳氣於肺，傳血於肝，而傳水穀於脬腸矣。

The spirit is governed by the heart, qi is governed by the kidney, and form is governed by the head. When form and qi meet, the spirit is in charge of them, which is the principle of the three categories of heaven, earth, and humanity. Each limb of a person has its own pulse, and one pulse is divided into three parts: cun, guan, and chi. Each part has three pulses: floating, middle, and deep, corresponding to the numbers of heaven. The heart holds the spirit, the kidney holds the essence, the spleen holds the soul, and the gallbladder holds the魄. The stomach receives food and digests it, sends qi to the lungs, sends blood to the liver, and then sends the residue of food and drink to the bladder and intestines.

天圓而地方，天南高而北下。是以望之如倚蓋，然地東南下，西北高。是以東南多水，西北多山也。天覆地，地載天，天地相函。故天上有地，地上有天。

Heaven is round and Earth is square. Heaven is high to the south and low to the north, so it appears like a tilted canopy. Earth is low in the southeast and high in the northwest, so there is more water in the southeast and more mountains in the northwest. Heaven covers Earth, and Earth supports Heaven. Heaven and Earth include each other, so there is Earth in Heaven and Heaven in Earth.

天渾。渾於上而不可測也。故觀斗數以占天也。斗之所建，天之所行也。魁建子，杓建寅，星以寅為晝也。斗有七星，是以晝不過乎七分也。天行所以為晝夜，日行所以為寒暑，夏淺冬深，天地之交也。左旋右行，天日之交也。

The heavens are a complete whole, high and vast above, beyond measurement, so we can only observe the degrees of the Big Dipper to predict celestial phenomena. The direction pointed by the handle of the Big Dipper is where the sky has reached. When the handle of the Dipper points to the Zi position and the spoon points to the Yin position, the star calendar begins the day with Yin and counts it as day. The Big Dipper has seven stars, so the portion of the day does not exceed seven parts. The movement of the heavens causes day and night, and the movement of the sun causes cold and heat; summer is when the sun moves shallowly, and winter is when the sun moves deeply, which is the manifestation of the interaction between heaven and earth; the heavens rotate to the left while the sun moves to the right, which is the manifestation of the interaction between heaven and the sun.

日朝在東，夕在西，隨天之行也。夏在北，冬在南，隨天之交也。天一周而超一星，應日之行也。春酉正，夏午正，秋卯正，冬子正，應日之交也。

The sun rises in the east and sets in the west, following the movement of the celestial bodies; in summer it tends to the north, and in winter to the south, following the meeting of heaven and earth. When the heavens complete a full cycle, they pass through an additional star position, which corresponds to the sun's movement. In spring, the sun is at the酉 position, in summer at the午 position, in autumn at the卯 position, and in winter at the子 position, which corresponds to the sun's meeting points.

日以遲為進，月以疾為退，日月一會而加半日減半日，是以為閏餘也。日一大運而進六日，月一大運而退六日，是以為閏差也。日行陽度則盈，行陰度則縮，賓主之道也。月去日則明生而遲，近日則魄生而疾，君臣之義也。

The sun is considered to be advancing when it moves slowly, and the moon is considered to be retreating when it moves quickly. Each time the sun and moon meet, the sun gains half a day and the moon loses half a day, which forms the concept of 'leap remainder'. The sun advances six days in one great cycle, while the moon retreats six days in one great cycle, which forms the concept of 'leap difference'. When the sun moves through yang degrees, it becomes full; when it moves through yin degrees, it becomes diminished, which reflects the principle of guest and host interacting. When the moon is far from the sun, it produces brightness and moves slowly; when it is close to the sun, it produces darkness and moves quickly, which reflects the principle of ruler and minister following each other.

陽消則生陰，故日下而月西出也。陰盛則敵陽，故月望而東出也。天為父，日為子，故天左旋，日右行。日為夫，月為婦，故日東出，月西生也。日月之相食，數之交也。日望月則月食，月掩日則日食，猶水火之相剋也。是以君子用智，小人用力。

When yang wanes, yin arises, so when the sun sets in the west, the moon appears in the west. When yin becomes full, it is strong enough to resist yang, so on the full moon day, the moon rises in the east. Heaven is the father, the sun is the son, so heaven rotates to the left while the sun moves to the right. The sun is the husband, the moon is the wife, so the sun rises in the east while the moon shines in the west. The mutual eclipses of the sun and moon result from their paths crossing: when the sun and moon are exactly opposite, the moon is eclipsed; when the moon covers the sun, the sun is eclipsed, just as water and fire mutually control each other. Therefore, the virtuous person acts with wisdom, while the petty person acts with force.

日隨天而轉，月隨日而行，星隨月而見，故星法月，月法日，日法天。天半明半晦，日半贏半縮，月半盈半虧，星半動半靜，陰陽之義也。天晝夜常見，日見於晝，月見於夜而半不見，星半見於夜，貴賤之等也。月晝可見也，故為陽中之陰，星夜可見也，故為陰中之陽。

The sun follows the heavens in its movement, the moon follows the sun, and the stars follow the moon in their appearance. Therefore, stars take their pattern from the moon, the moon from the sun, and the sun from the heavens. The heavens are half bright and half dark, the sun is half full and half diminished, the moon is half full and half waning, and the stars are half active and half still. All these are manifestations of the principle of yin and yang being balanced. The heavens are visible day and night, the sun is only visible during the day, the moon is visible at night but not always, and the stars are only visible half the time at night. This reflects the hierarchy of respect and status. The moon can be seen during the day, so it is yin within yang; the stars are only visible at night, so they are yang within yin.

天奇而地耦，是以占天文者，觀星而已，察地理者，觀山水而已，觀星而天體見矣，觀山水而地體見矣。天體容物，地體負物，是故體幾於到也。極南大暑，極北大寒，故南融而北結，萬物之死地也。夏則日隨斗而北，冬則日隨斗而南，故天地交而寒暑和，寒暑和而物乃生焉。

Heaven's numbers are odd, and Earth's numbers are even. Therefore, those who study celestial phenomena only need to observe the stars; those who examine geographical features only need to look at mountains and rivers. Observing the stars reveals the form of Heaven, and observing mountains and rivers reveals the form of Earth. The form of Heaven can contain all things, and the form of Earth can support all things. Therefore, considering only their forms, they are almost close to the Dao. The southernmost point is extremely hot, and the northernmost point is extremely cold. The south melts, and the north solidifies; these are all the death places of all things. In summer, the sun follows the Big Dipper to the north, and in winter, the sun follows the Big Dipper to the south. Thus, Heaven and Earth meet, and the cold and heat balance, allowing all things to grow.

天以剛為德，故柔者不見，地以柔為體，故剛者不生，是以震，天之陰也。巽，地之陽也。有陽而陰效之，故至陰者辰也，至陽者日也，皆在乎天，而地則水火而已，是以地上皆有質之物。陰伏陽而形質生，陽伏陰而性情生，是以陽生陰，陰生陽，陽克陰，陰克陽。陽之不可伏者，不見於地。陰之不可克者，不見於天。伏陽之少者，其體必柔，是以畏陽而為陽所用。伏陽之多者，其體必剛，是以御陽而為陰所用，故水火動而隨陽，土石靜而隨陰也。

Heaven is characterized by strength and uprightness, so its soft aspect is not visible. Earth is characterized by softness and compliance, so its strong aspect does not manifest on the earth. Therefore, Zhen (Thunder) is the yin within Heaven, and Xun (Wind) is the yang within Earth. Always the yang comes first, and yin follows by imitating it. Thus, the extreme of yin is Chen (Earth Dragon), and the extreme of yang is the sun, both existing in Heaven. As for Earth, there are only water and fire, so the surface of the earth is filled with tangible things. Yin conceals yang, and form and substance are generated; yang conceals yin, and nature and emotion are generated. Therefore, yang generates yin, and yin generates yang; yang overcomes yin, and yin also overcomes yang. That yang which cannot be concealed does not appear on the earth; that yin which cannot be overcome does not appear in Heaven. The yang that is concealed is less, so its body is soft and it fears yang and is used by yang; the yang that is concealed is more, so its body is strong and it can resist yang and is used by yin. Therefore, water and fire are active and follow yang, while earth and stone are still and follow yin.

陽生陰，故水先成。陰生陽，故火後成。陰陽相生也，體性相須也。是以陽去則陰竭，陰盡則陽滅。金火相守則流，火木相得則然，從其類也。水遇寒則結，遇火則竭，從其所勝也。

Yang produces Yin, so water first takes form; Yin produces Yang, so fire later takes form. Yin and Yang generate each other mutually, and body and nature depend on each other. Therefore, if Yang departs from Yin, Yin becomes exhausted; if Yin reaches its limit, Yang is extinguished. Metal and fire remain together, causing metal to melt; fire and wood meet, causing wood to burn, each following its own kind. Water meets cold air and freezes, meets fire and dries up, all yielding to the one that overcomes it.

陽得陰而為雨，陰得陽而為風，剛得柔而為雲，柔得剛而為雷，無陰則不能為雨，無陽則不能為雷。雨柔也，而屬陰，陰不能獨立，故待陽而後興。雷剛也，而屬體，體不能自用，必待陽而後發也。

When Yang meets Yin, rain is formed; when Yin meets Yang, wind is formed; when strength meets flexibility, clouds are formed; when flexibility meets strength, thunder is formed. Without Yin, rain cannot fall; without Yang, thunder cannot occur. Rain is flexible and belongs to Yin; Yin cannot exist alone, so it waits for Yang to arise. Thunder is strong and belongs to the body; the body cannot act on its own, so it waits for Yang to initiate its movement.

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，震兌為耦，以應地之方也，王者之法其盡於是矣！

King Wen's creation of the Book of Changes is truly remarkable, surely because he deeply understood the principles of the heavens and earth. The Qian and Kun trigrams intersect to form the Tai卦, while the Kan and Li trigrams intersect to form the Ji Ji卦. The Qian trigram originates from the Zi position, and the Kun trigram originates from the Wu position. The Kan trigram concludes at the寅 position, and the Li trigram concludes at the申 position, used to correspond with the heavenly sequence of time. Additionally, the Qian trigram is placed in the Northwest, while the Kun trigram is positioned in the Southwest. The eldest son Zhen trigram takes charge, and the eldest daughter Xun trigram takes the place of the mother, with Kan and Li each occupying their proper positions. The Zhen and Dui trigrams form pairs, used to correspond with the earthly directions. This is where the principles of governance for a ruler managing the world are fully embodied.

乾坤天地之本，坎離天地之用，是以易始於乾坤，中於坎離，終於既未濟。而否泰為上經之中，咸恆當下經之首，皆言乎其用也。坤統三女於西南，乾統三男於東北，上經起於三，下經終於四，皆交泰之義也。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！吾於此見聖人之心矣。

Heaven and Earth are the fundamental principles, 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. The Yu Tai (Obstruction and Prosperity) are in the middle of the Upper Canon, and Xian and Heng are at the beginning of the Lower Canon. All these discuss the concept of "use" (yong). Kun governs the three female trigrams located in the Southwest, while Qian governs the three male trigrams located in the Northeast. The Upper Canon starts with "three" and the Lower Canon ends with "four," both containing the meaning of Heaven and Earth interacting harmoniously. Therefore, the Book of Changes discusses "use": Qian uses nine, Kun uses six, the Great Derivation uses forty-nine, and the initial line, Chou Ji, specifically mentions the hidden dragon that should not be used. The significance of "use" is profound! From here, I see the intention of the sages.

乾坤交而為泰，變而為雜卦也。乾坤坎離為上篇之用，兌艮震巽為下篇之用也。頤中孚大小過為二篇之正也。易者，一陰一陽之謂也。震兌始交者也，故當朝夕之位。離坎交之極者也，故當子午之位。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。

Heaven and Earth combine to form the卦 of Tai, and further changes lead to the various hexagrams listed in the Zage. The hexagrams Qian, Kun, Kan, and Li belong to the upper section, while Dui, Gen, Zhen, and Xun belong to the lower section. Yi, Zhongfú, Daguò, and Xiaoguò are the correct hexagrams shared by both upper and lower sections. The Book of Changes refers to the principle of one yin and one yang. Zhen and Dui are hexagrams representing the initial meeting of yin and yang, hence they occupy the eastern and western positions. Li and Kan are hexagrams representing the extreme meeting of yin and yang, hence they occupy the southern and northern positions. Xun and Gen, although not directly meeting, still contain a mixture of yin and yang, hence they occupy positions that are usable but slightly off-center. Qian and Kun are pure yang and pure yin, hence they occupy positions that are present but not used.

乾坤縱而六子橫，易之本也。震兌橫而六卦縱,易之用也。天之陽在南而陰在北，地之陰在南而陽在北，人之陽在上而陰在下，既交則陽下而陰上。辰數十二，日月交會謂之辰。辰,天之體也，天之體，無物之氣也。

The trigrams Qian (Heaven) and Kun (Earth) are arranged vertically, with the six other trigrams placed horizontally, which represents the fundamental nature of the Book of Changes. The trigrams Zhen (Thunder) and Dui (Lake) are placed horizontally, with the remaining six trigrams arranged vertically, which represents the functional aspects of the Book of Changes. The yang of Heaven is located to the south, while the yin is located to the north; the yin of Earth is located to the south, while the yang is located to the north; in humans, the yang is above and the yin is below. When they combine, the yang descends to the lower position and the yin ascends to the upper position. The number of Chen is twelve, and the place where the sun and moon meet is called Chen. Chen represents the form of Heaven, and the form of Heaven originally consists of a mass of invisible qi.

天之陽在南，故日處之。地之剛在北，故山處之，所以地高西北，天高東南也，天之神棲乎日，人之神發乎目，人之神寤則棲心，寐則棲腎，所以象天，此晝夜之道也。雲行雨施，電發雷震，亦各從其類也。吹噴吁呵呼，風雨雲霧雷，言相類也。萬物各有太極兩儀四象八卦之次，亦有古今之象。雲有水火土石之異，他類亦然。

Heaven's yang is in the south, so the sun resides there; earth's strength is in the north, so mountains and hills are there. Therefore, the terrain is high in the northwest and low in the southeast, while the sky's trend is high in the southeast and low in the northwest. The divine spirit of heaven dwells on the sun, and the divine spirit of man manifests in the eyes; when the human spirit is awake, it resides in the heart, and when asleep, it resides in the kidney. This is taking the form of heaven, which is the reason for day and night. Clouds drift, rain falls, lightning flashes, and thunder rumbles, each following its own category. The five kinds of breaths—blow, spray, sigh, exhalation, and shout—are similar to wind, rain, clouds, mist, and thunder. All things have their own levels of the Taiji, two principles, four images, and eight trigrams, and also have their own ancient and modern forms. Clouds are classified as belonging to water, fire, earth, or stone, and other things are also like this.

二至相去東西之度凡一百八十，南北之度凡六十。冬至之月，所行如夏至之日。夏至之月，所行如冬至之日。四正者，乾坤坎離也。觀其象無反覆之變，所以為正也。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。此真至之理，按圖可見之矣。草類之細入於坤。五行之木，萬物之類也。五行之金，出乎石也。故水火土石不及金木，金木生其間也。

The distance between the winter solstice and the summer solstice is 180 degrees in the east-west direction and 60 degrees in the north-south direction. In the month of the winter solstice, the moon's path is like that of the sun at the summer solstice; in the month of the summer solstice, the moon's path is like that of the sun at the winter solstice. The term "four cardinal directions" refers to Qian, Kun, Kan, and Li. When observing their trigrams, they remain unchanged even when reversed, hence they are called cardinal. When yang is in yin, yang moves in reverse; when yin is in yang, yin moves in reverse. When yang is in yang and yin is in yin, both move in the normal direction. This is a very clear principle, which can be understood by referring to the diagram of the primordial structure. The smallest grasses are classified under Kun. Among the Five Phases, wood belongs to the category of all things; metal comes from stone. Therefore, water, fire, earth, and stone do not necessarily relate to metal and wood, which are merely derived from these four.

得天氣者動，得地氣者靜。陽之類圓，成形則方。陰之類方，成形則圓。木之枝幹，土石之所成也，所以不易。葉花，水火之所成，故變而易也。

Those that receive the heavenly energy are active, while those that receive the earthly energy are tranquil. Those of yang nature tend toward roundness, but once they take form, they become square. Those of yin nature tend toward squareness, but once they take form, they become round. The branches and trunks of trees are formed from the consolidation of earth and stone energies, hence they are firm and unchanging. The leaves and flowers are formed from the consolidation of water and fire energies, hence they change constantly with the seasons.

東赤，南白，西黃，北黑，此正色也。驗之於曉午暮夜之時，可見之矣。冬至之子中，陰之極。春分之卯中，陽之中。夏至之午中，陽之極。秋分之酉中，陰之中。凡三百六十，中分之則一百八十，此二至二分相去之數也。

The east is red, the south is white, the west is yellow, and the north is black; these are the true colors of the four directions. By observing at dawn, noon, dusk, and midnight, one can see this clearly. On the winter solstice, the sun is at the center of the zodiac sign zi, which is the extreme of yin; on the spring equinox, it is at the center of the zodiac sign mao, which is the midpoint of yang; on the summer solstice, it is at the center of the zodiac sign wu, which is the extreme of yang; and on the autumn equinox, it is at the center of the zodiac sign you, which is the midpoint of yin. The entire celestial circle is 360 degrees. If it is split in half, it becomes 180 degrees, which is the measure of the distance between the two solstices and two equinoxes.

陽中有陰，陰中有陽，天之道也。陽中之陽，日也，暑之道也。陽中之陰，月也，以其陽之類，故能見於晝。陰中之陽，星也，所以見於夜。陰中之陰，辰也，天壤也。辰之於天猶天地之體也，地有五行，天有五緯，地止有水火，天復有日月者，月為真水，日為真火，陰陽真精，是生五行，所以天地之數各五，陽數獨盈於七也。是故五藏之外又有心包，絡命門而七者，真心離火，命門坎水，五藏生焉，精神之主，性命之根也。

Heaven contains Yin and Yin contains Yang, which is the principle of Heaven. Yang within Yang is the sun, governing the heat of summer; Yang within Yin is the moon, which still belongs to the category of Yang, so it can be seen during the day. Yin within Yin is the stars, which appear only at night. Yin within Yin is also called Chen, which is the empty space in the heavens. Chen to Heaven is like the body to the universe. On earth there are the five elements of water, fire, earth, wood, and metal; in the heavens there are the five bright stars. The earth has only water and fire, but the heavens have the sun and moon as well: the moon is true water, the sun is true fire. This true essence of Yin and Yang gives rise to the five elements. Therefore, both Heaven and Earth have five numbers, but the number of Yang is greater, making it seven. Therefore, in addition to the five internal organs of the human body, there are the heart wrapper and the life gate, making a total of seven. The true heart belongs to the fire element, and the life gate belongs to the water element. The five internal organs arise from these, and they are the masters of spirit and the roots of life and death.

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。魚者水之族也，蟲者風之族也。目口凸而耳鼻竅，竅者受聲嗅氣，物或不能閉之，凸者視色別味，物則能閉之也，四者雖象於一，而各備其四矣。水者火之地，火者水之氣。黑者白之地,寒者暑之地。

"The term 'Gan' (Heavenly Stem) refers to the trunk of a tree, which is yang; 'Zhi' (Earthly Branch) refers to the branch of a tree, which is yin. There are ten Heavenly Stems and twelve Earthly Branches, showing that yang contains yin and yin contains yang. Fish belong to the category of water, and insects belong to the category of wind. The eye and mouth are protruding, while the ear and nose are hollow openings: the hollow openings are used to receive sound and smell, and external things may block them; the protruding parts are used to see colors and taste, and external things can close them. These four, though each representing one thing, each contain four functions. Water is the dwelling place of fire, and fire is the vapor of water; black is the dwelling place of white, and cold is the dwelling place of heat."

草伏之獸毛如草之莖，林棲之鳥羽如林之葉，類使之然也。石之花，鹽消之類也。水之物無異乎陸之物，各有寒熱之性，大較則陸為陽中之陰，而水為陰中之陽。日月星辰共為天，水火土石共為地，耳目鼻口共為首，髓血骨肉共為身，此乃五之數也。

Wild animals hiding in grass have fur resembling the stems of grass; birds resting in the forest have feathers like the leaves of the forest: all these are examples of things resembling their kind. Flowers growing on stones are actually substances like salt and nitrate. The creatures in water and those on land are not fundamentally different, each having their own cold or hot nature; generally speaking, land belongs to the yin within yang, and water belongs to the yang within yin. The sun, moon, stars, and constellations together form the heavens; water, fire, earth, and stone together form the earth; the ear, eye, nose, and mouth together form the head; marrow, blood, bones, and flesh together form the body: all these are included within the number 'five'.

火生於無，水生於有。辰至日為生，日至辰為用，蓋順為生而逆為用也。易有三百八十四爻，真天文也。

Fire is generated from "nothingness," while water is generated from "somethingness." Moving from Chen to the day represents the order of generation, while moving from the day to Chen represents the order of application; generally speaking, counting in the forward direction signifies generation, and counting in the reverse direction signifies application. The Book of Changes contains 384 lines, which is truly the writing of heaven.

鷹鵰之類食生，而雞之類不專食生。虎豹之類食生，而貓犬之類食生又食穀，以類推之，從可知矣。馬牛皆陰類，細分之則馬為陽而牛為陰。飛之類喜風而敏於飛上，走之類喜土而利於走下。禽蟲之卵，果穀之類也，穀之類多子，蟲之類亦然。蠶之類，今歲蛾而子，來歲則子而蠶。蕪菁之類，今歲根而苗，來歲則苗而子，此皆一歲之物也。

Eagles and kites eat only live creatures, while chickens do not exclusively eat live creatures. Tigers and leopards eat only live creatures, while cats and dogs eat both live creatures and grains. By following this method of classification, the rest can be understood similarly. Horses and cattle belong to the yin category; when further divided, horses belong to the yang category while cattle belong to the yin category. Those that can fly prefer wind and are good at flying upwards; those that can walk prefer earth and are good at moving downwards. The eggs produced by birds and insects correspond to the fruits and grains of plants; grains produce many seeds, and insects also produce many offspring. For example, silkworms: this year they are moths that lay eggs, and next year the eggs become silkworms; turnips: this year they grow shoots from their roots, and next year the shoots produce seeds. These are all examples of creatures that complete a cycle within one year.

天之氣運北而南則治，南而北則亂，亂久則復北而南矣，天道人事皆然，推之歷代，可見消長之理也。在水者不瞑，在風者瞑。走之類上睫接下，飛之類下睫接上，類使之然也。在水而鱗，飛之類也，龜獺之類，走之類也。

The movement of heavenly energy from north to south brings peace to the world; when it moves from south to north, the world becomes chaotic. When chaos lasts long, it will turn back to moving from north to south. The way of heaven and the affairs of people are like this. By examining the rise and fall of dynasties throughout history, the principle of increase and decrease becomes clear. Creatures living in water close their eyes when they sleep, while those living in wind close their eyes when they sleep; those that walk have their upper eyelashes connected to their lower eyelashes, while those that fly have their lower eyelashes connected to their upper eyelashes. All these are characteristics of the creatures. Creatures living in water but having scales actually belong to the category of flying creatures; creatures like turtles and otters, which live in water but walk, actually belong to the category of walking creatures.

夫四象，若錯綜而用之，日月天之陰陽，水火地之陰陽，星辰天之剛柔，土石地之剛柔。飛之走，雞鳧之類是也，走之飛，龍馬之屬是也。陽主舒長，陰主慘急，日入盈度，陰從於陽。日入縮度，陽從於陰。

The four symbolic figures, when combined and used together, indicate: the sun and moon represent the yin and yang of heaven, while water and fire represent the yin and yang of earth. The stars and constellations represent the firm and flexible aspects of heaven, while soil and stone represent the firm and flexible aspects of earth. Those that belong to the category of flying but are close to walking are like chickens and wild ducks; those that belong to the category of walking but are close to flying are like dragons and horses. Yang governs expansion and growth, while yin governs contraction and urgency. When the sun enters the full phase, yin follows yang; when the sun enters the contracted phase, yang follows yin.

神者人之主，將寐在脾，熟寐在腎，將寤在肝，正寤在心。天地之大寤在夏，人之神則存於心。水之族以陰為主，陽次之，陸之類以陽為主，陰次之，故水類出水則死，風類入水則死。然有出入之類，龜蟹鵝鳧之類是也。

The spirit is the master of a person: when about to fall asleep, the spirit resides in the spleen; when fully asleep, it resides in the kidney; when about to wake up, it resides in the liver; and when fully awake, it resides in the heart. The greatest clarity of heaven and earth is in summer, and the spirit of a person usually resides in the heart. Water creatures mainly belong to yin, with yang as secondary, while land creatures mainly belong to yang, with yin as secondary; thus, water creatures die when they leave water, and wind creatures die when they enter water. However, there are also creatures that can move between water and land, such as turtles, crabs, geese, and ducks.

天地之交十之三。天火無體之火也，地火有體之火也。火無體，因物以為體。金石之火烈於草木之火者，因物而然也。氣形盛則魂魄盛，氣形衰則魂魄亦從而衰矣。魂隨氣而變，魄隨形而止，故形在則魄存,形化則魄散。

Heaven and Earth intersect in a ratio of three parts out of ten. The fire in Heaven is fire without form, while the fire on Earth is fire with form; fire originally has no form, and it takes shape through external objects. The fire produced by striking metal and stone is more intense than the fire produced by burning wood and grass, precisely because the external objects differ. When the qi and form are vigorous, the hun and po are also vigorous; when the qi and form decline, the hun and po also decline. The hun moves with the qi, while the po rests with the form; thus, when the form remains, the po stays, and when the form dissipates, the po vanishes.

星為日餘，辰為月餘。星之至微如沙塵者，隕而為堆阜。藏者天行也，府者地行也，天地並行則配為八卦。八卦相錯者，相交錯而成六十四卦也。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。

Stars are the residual energy of the sun, and the constellations are the residual energy of the moon; the finest particles of stars, like sand, falling down accumulate into hills. The five internal organs correspond to the movements of heaven, and the six external organs correspond to the movements of earth; when heaven and earth proceed in harmony without contradiction, the internal and external organs correspond to the eight trigrams. The phrase "the eight trigrams intermingle" means that the eight trigrams intertwine to form the sixty-four hexagrams. The root of the Book of Changes lies in the trigrams Qian and Kun, and its development arises from Gu and Fu: when yang enters yin, the hexagram Fu is formed, and when yin enters yang, the hexagram Gu is formed; from here, the derivation is endless.

龍能大能小，然亦有制之者，受制於陰陽之氣，得時則能變化，變變則不能也。一歲之閏六陰六陽，三年三十六日，故三年一閏。五年六十日，故五歲再閏。先天圖中，環中也。月體本黑，受日之光而白。水在人之身為血，土在人之身為肉。

Dragons can grow large or small, but there are things that can control them; they are always subject to the regulation of yin and yang energies. When the proper season comes, they can change; when the season is inappropriate, they cannot. The surplus of a year consists of six yin and six yang days, totaling twelve days. Over three years, this accumulates to thirty-six days, so a leap month is added every three years. Over five years, this accumulates to sixty days, so another leap month is added within five years. The key point of the diagram of the Supreme Origin lies in the central point, which is called the "circle in the center." The moon itself is originally black, but it appears white when illuminated by sunlight. Water in the human body becomes blood, and earth in the human body becomes flesh.

膽與腎同陰，心與脾同陽，心主目，脾主鼻。陽中陽日也，陽中陰月也，陰中陽星也，陰中陰辰也。柔中柔水也，柔中剛火也，剛中柔土也，剛中剛石也。鼻之氣目見之，口之言耳聞之，以類應也。

The liver and kidney belong to yin, while the heart and spleen belong to yang; the heart governs the eyes, and the spleen governs the nose. Yang within yang is the sun, yang within yin is the moon, yin within yin is the star, and yin within yin is the hour. Softness within softness is water, softness within firmness is fire, firmness within softness is earth, and firmness within firmness is stone. The breath exhaled from the nose is visible to the eyes, and the words spoken from the mouth are heard by the ears, because they are of the same kind and correspond to each other.

倚蓋之說，崑崙四垂而為海，推之理則不然，夫地直方而靜，豈得如圓動之天乎？動物自首生，植物自根生，自首生命在首，自根生命在根。海潮者，地之喘息也，所以應月者，從其類也。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？

There is a view called "Yi Gai" which holds that Kunlun Mountain hangs down on all four sides to form the sea; but according to rational consideration, this is not the case. The earth is originally square and still, how could it be like the rotating heaven? Animals begin to grow from their heads, while plants begin to grow from their roots; those that grow from the head have their life tied to the head, and those that grow from the root have their life tied to the root. Sea tides are the breathing of the earth, and they correspond with the moon because they belong to the same category. The Zhen trigram is symbolized as a dragon, with one yang line moving beneath two yin lines, exactly matching the shape of the Zhen trigram; beneath the deep abyss there are things that move, are they not dragons?

風類水類，大小相反。天之陽在東南，日月居之。地之陰在西北，火石居之。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，明交錯而成六十四也。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，是右旋也，皆未生之卦也，故云知來也。夫易之數，由逆而成矣。

Wind and Water are of two kinds, and their sizes are exactly opposite. The Yang of Heaven is in the Southeast, so the sun and moon reside there; the Yin of Earth is in the Northwest, so fire and stone reside there. The passage in "Shuo Gua" that says "The Emperor comes forth from Zhen... and is completed in Gen" refers to the King Wen's eight trigrams. The passage that says "Heaven and Earth are positioned" refers to the Fuxi's eight trigrams. When it says "the eight trigrams are intermingled," it refers to the eight trigrams being interwoven to form the sixty-four trigrams. "Counting the past is in accordance with the way" means following Heaven's movement, which is left rotation, referring to already formed trigrams, hence "counting the past." "Knowing the future is in opposition to the way" means opposing Heaven's movement, which is right rotation, referring to trigrams that have not yet been formed, hence "knowing the future." The numbers of the Book of Changes are established through reverse reasoning.

堯典三百六旬有六日，夫日之餘盈也六，則月之餘盈也亦六，若去日月之餘十二，則有三百五十四，乃日行之數，以十二除之，則得二十九日。

The Shangshu · Yaodian says that a year consists of 366 days. The excess on the sun's side is six days, so the excess on the moon's side is also six days. If the excesses from both the sun and the moon, totaling twelve days, are subtracted, then 354 days remain, which is the number of days the sun travels through. Dividing this by twelve gives twenty-nine days per month.

素問肺主皮毛，心脈，脾肉，肝筋，腎骨，上而下，外而內也。心血腎骨交法也，交即用也。乾為天之類，本象也。為金之類,別象也。天地並行則藏府配，四藏天也，四府地也。

The *Su Wen* says that the lung governs the skin and hair, the heart governs the blood vessels, the spleen governs the muscles, the liver governs the tendons, and the kidney governs the bones; this is an order from top to bottom, from outside to inside. The heart is paired with blood and the kidney with bone, using a method of mutual pairing, where "intersection" means "use." The乾 trigram taking the image of heaven is its original image, while taking the image of metal is its secondary image. Heaven and earth operate in parallel without contradiction, and the zang organs are paired with the fu organs: the four zang organs belong to heaven, and the four fu organs belong to earth.

乾奇也，陽也，健也，故天下之健莫如天。坤耦也，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，又如附麗之麗。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 a nature 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 a nature of being gentle and compliant. Therefore, nothing in the world is more gentle and compliant than earth, which follows and supports heaven. Zhen is "movement," with one yang rising from below. Movement means action, so nothing in the world is more active than thunder. Kan is "sinking," with one yang sinking between two yins. Sinking means going downward, so nothing in the world is more downward-moving than water. Gen is "stopping," with one yang stopping here. Therefore, nothing in the world is more capable of stopping than a mountain. Xun is "entering," with one yin entering beneath two yangs. Therefore, nothing in the world is more capable of penetrating than wind. Li is "adhering," with one yin adhering between two yangs. The trigram lines interweave and form patterns, appearing beautiful and splendid. Therefore, nothing in the world is more splendid than fire. The character "丽" also implies the meaning of attachment. Dui is "joy," with one yin revealing itself externally, causing all things to be joyful. Therefore, nothing in the world is more capable of bringing 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。人寓形於走類者何也，走類者，地之長子也。自泰至否，其間則有蠱矣。自否至泰，其間則有隨矣.

Fire is dark inside and bright outside, so the Yang line of the Li hexagram is outside, and the function of fire is to radiate outward. Water is dark outside and bright inside, so the Yang line of the Kan hexagram is inside, and the function of water is to conceal inwardly. Why do people寄托 their bodies in the category of quadrupeds? Because quadrupeds are the eldest son born from the earth. From the Tai hexagram to the Pi hexagram, one must pass through the Gu hexagram; from the Pi hexagram back to the Tai hexagram, one must pass through the Sui hexagram.

天有五辰，日月星辰與天為五。地有五行，金木水火與土為五。有溫泉而無寒火，陰能從陽而陽不能從陰也。有雷則有電，有電則有風，雨生於水，露生於土，雷生於石，電生於火，雷與風同為陽之極，故有電必有風。木之堅非雷不能震，草之柔非露不能潤。

Heaven has five stars: sun, moon, stars, and the celestial sphere, together with heaven itself, making five. Earth has five elements: metal, wood, water, fire, and soil. In the world there are hot springs but no cold fire, showing that yin can obey yang, but yang cannot obey yin. When there is thunder, there must be lightning; when there is lightning, there must be wind. Rain comes from water, dew comes from soil, thunder comes from stone, and lightning comes from fire. Thunder and wind are both products of yang reaching its extreme, so lightning must be accompanied by wind. Wood is hard, so it cannot be moved unless by thunder; grass is soft, so it cannot be moistened unless by dew.

陽尊而神，尊故役物，神故藏用，是以道生天地萬物而不自見也，天地萬物亦取法乎道矣。陽者道之用，陰者道之體，陽用陰，陰用陽，以陽為用則尊陰，以陰為用則尊陽也。

Yang is both noble and mysterious: because it is noble, it can control all things; because it is mysterious, it conceals its function and does not reveal itself. Just as the "Dao" generates heaven and earth and all things without revealing itself, heaven and earth and all things take their pattern from the Dao. Yang is the function of the Dao, and Yin is the essence of the Dao; Yang uses Yin, and Yin also uses Yang. When Yang is used, Yin is revered; when Yin is used, Yang is revered.

陰幾於道，故以況道也。六變而成三十六矣，八變而成六十四矣，十二變而成三百八十四矣，六六而變之，八八六十四變而成三百八十四矣，八八而變之，七七四十九變而成三百八十四矣。

Yin is close to the Dao, so it is used to compare with the Dao. Six changes make thirty-six, eight changes make sixty-four, and twelve changes make three hundred eighty-four. If we use six and six to calculate, eight times eight makes sixty-four changes resulting in three hundred eighty-four; if we use eight and eight to calculate, seven times seven makes forty-nine changes resulting in three hundred eighty-four: the paths differ but the outcome is the same.

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。性非體不成，體非性不生，陽以陰為體，陰以陽為體，動者性也，靜者體也。在天則陽動而陰靜，在地則陽靜而陰動。性得體而靜，體隨性而動，是以陽舒而陰急也。

Before the ultimate principle was divided, yin contained yang; after forms had already taken shape, yang divided yin. Yin is the mother of yang, and yang is the father of yin. Therefore, the mother nurtured the eldest son to form the Fu hexagram, and the father gave birth to the eldest daughter to form the Guo hexagram. Thus, yang begins with the Fu hexagram and yin begins with the Guo hexagram. Nature without form cannot exist, and form without nature cannot manifest; yang uses yin as its form, and yin also uses yang as its form. The active aspect is nature, and the static aspect is form. In the heavens, yang is active and yin is static; in the earth, yang is static and yin is active. When nature is united with form, it becomes stable; when form follows nature, it becomes active. Therefore, yang is slow and yin is quick.

陽不能獨立，必得陰而後立，故陽以陰為基。陰不能自見，必待陽而後見，故陰以陽為唱。陽知其始而享其成，陰效其法而終其勞。

Yang cannot stand alone; it must rely on Yin to be stable, so Yang regards Yin as its foundation. Yin cannot manifest by itself; it waits for Yang before it can appear, so Yin regards Yang as its leader. Yang knows the beginning and enjoys the results, while Yin follows Yang's pattern and bears the final labor.

陽能知而陰不能知，陽能見而陰不能見也。能知能見者為有，故陽性有而陰性無也。陽有所不遍而陰無所不遍也，陽有去而陰常居也，無不遍而常居者為實，故陽體虛而陰體實也。天地之本，其起於中乎！是以乾坤屢變而不離乎中。人居天地之中，心居人之中，日中則盛，月中則盈，故君子貴中也。本一氣也，生則為陽，消則為陰，故二者一而已矣。四者二而已矣，六者三而已矣，八者四而已矣。是以言天不言地，言君不言臣，言父不言子，言夫不言婦也。然天得地而萬物生，君得臣而萬化行，父得子，夫得婦而家道成。故有一則有二，有二則有四，有三則有六，有四則有八。

Heavenly energy can be known and seen, while earthly energy cannot. Those that can be known and seen are called "having existence," so the nature of heavenly energy is "having existence" and the nature of earthly energy is "non-existence." Heavenly energy has areas it cannot cover, while earthly energy is everywhere present; heavenly energy has times when it departs, while earthly energy remains constantly. Being everywhere present and constantly remaining is called "real," so the body of heavenly energy is empty and the body of earthly energy is real. The fundamental principle of heaven and earth probably originates from "center." Therefore, the trigrams Qian and Kun constantly change but never depart from the center. A person is located in the center of heaven and earth, and the heart is located in the center of the body. The sun reaches its peak at noon, and the moon is fullest at the midpoint of the month, so the gentleman values the concept of "center" most. Originally, it was just a single qi; when it grows it is called yang, and when it declines it is called yin, so the two are actually one. Four is merely two twos, six is merely two threes, and eight is merely two fours. Therefore, once heaven is mentioned, there is no need to mention earth again; once the ruler is mentioned, there is no need to mention the subject again; once the father is mentioned, there is no need to mention the son again; once the husband is mentioned, there is no need to mention the wife again. However, heaven cannot produce myriad things without earth, and the ruler cannot achieve myriad transformations without the subject, and the father cannot establish family order without the son, and the husband cannot maintain the household without the wife. Therefore, there is one, then two; there is two, then four; there is three, then six; there is four, then eight.

有意必有言，有言必有象，有象必有數，數立則像生，像生則言著彰，言著彰則意顯，像數則筌蹄也，言意則魚兔也，得魚兔而忘筌蹄可也，舍筌蹄而求魚兔，則未見其得也。

Whenever there is a thought, there must be words; whenever there are words, there must be an image; whenever there is an image, there must be a number. When the number is fixed, the image arises; when the image arises, the words become clear; when the words become clear, the thought becomes evident. The image and number are merely the bamboo traps used to catch fish and the nets used to catch rabbits. The words and thoughts are the fish and rabbits themselves. It is acceptable to obtain the fish and rabbits and forget the traps. But if one abandons the traps and tries to seek the fish and rabbits in vain, then no one has ever succeeded in obtaining them.

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。

Heaven changes first and people follow it, so yuan, heng, li, and zhen are the "change" in the Book of Changes. People act first and Heaven responds to them, so ji, xiong, hui, and lin are the "response" in the Book of Changes. If we take yuan and heng as change, then li and zhen are response; if we take ji and xiong as response, then hui and lin are change. Yuan leads to ji, and ji is responded to by li; heng contains xiong, and xiong is responded to by zhen. Hui eventually leads to ji, and lin eventually leads to xiong. Therefore, change contains response, and response contains change. The response within change belongs to the way of Heaven, so when yuan is change, heng responds to it; when li is change, zhen responds to it. The change within response belongs to human affairs, so change leads to xiong, and response leads to ji; change leads to lin, and response leads to hui. Hui is the prelude to ji, and lin is the root of xiong. Therefore, the gentleman follows Heaven and not human beings.

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，故言時不言德也。貞者，冬也，智也，冬者時之末，智者德之衰，貞則吉，不貞則凶，故言德而不言時也。故曰。利貞者，性情也。

"Yuan" corresponds to spring and benevolence. Spring is the beginning of the four seasons, and benevolence is the leader of all virtues; at this time the season has not yet reached its peak, yet virtue is sufficient to sustain people, so it is spoken of in terms of virtue rather than season. "Heng" corresponds to summer and ritual. Summer is the peak of the four seasons, and ritual is the adornment of virtue; when something reaches its peak it must inevitably decline, and adornment cannot save it, so it is spoken of in terms of season rather than virtue. Therefore, the "Wenyan" both praises "Great is Qian Yuan" and mentions the upper ninth line having regret. "Li" corresponds to autumn and righteousness. Autumn is the maturity of the four seasons, and righteousness is the uprightness of virtue; when all things have just matured and there is harvest, righteousness does not align with benefit, so it is spoken of in terms of season rather than virtue. "Zhen" corresponds to winter and wisdom. Winter is the end of the four seasons, and wisdom is the decline of virtue; to hold to correctness brings good fortune, while failing to do so brings misfortune, so it is spoken of in terms of virtue rather than season. Therefore, the "Wenyan" says "Li Zhen refers to nature and disposition."

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。象起於形，數起於質，名起於言，意起於用。天下之數出乎理，違乎理則入於術，世人以數而入術，故失於理也。

The Dao gives rise to Heaven, and Heaven gives rise to Earth; when achievements are completed, it steps back into a secondary position, just as a son inherits and the father transfers power. Therefore, in the later Heaven's position, Qian (Heaven) steps back one position. Forms give rise to images, qualities give rise to numbers, words give rise to names, and usage gives rise to meaning. All numbers in the world originate from 'principle' (li); once principle is violated, it falls into 'technique' (shu). People treat numbers merely as techniques, thus losing them in terms of principle.

天可以理盡而不可以形盡，渾天之術以形盡天，可乎？精義入神以致用也，不精義則不能入神，不能入神則不能致用。為治之道必通其變，不可以膠柱，猶春之時不可行冬之令也。

Heaven can be fully understood through principles, but not through form; the method of the浑天 school, which tries to understand Heaven through physical forms, is it feasible? Only after thoroughly studying the meaning and principles can one reach the profound and subtle realm, and then can one talk about practical application: without thoroughly studying the principles, one cannot reach the profound, and without reaching the profound, one cannot apply it practically. The principles of governing the world must be flexible and adaptable, and one cannot be rigid like fixing the tuning pegs of a zither. Just as one cannot apply the policies of winter in spring.

自然而然，不得而更者，內象內數也，他皆外象外數也。天道之變，王道之權也。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。其在人則為人之性，在禽獸則為禽獸之性，在草木則為草木之性。

All that is natural and unchangeable belongs to the internal phenomena and internal numbers; everything else is external phenomena and external numbers. The changes of heaven's way serve as the basis for the king's need to exercise flexible governance. Each trigram has its own nature and its own essence, yet none can be separated from the gate of the way of heaven and earth; just as all things receive their inherent nature from heaven and thus become a particular nature: human beings have the nature of humans, animals have the nature of animals, and plants have the nature of plants.

天以氣為主，體為次。地以體為主，氣為次，在天在地者亦如之。氣則養性，性則乘氣，故氣存則性存，性動則氣動也。堯之前，先天也。堯之後，後天也。後天乃效法耳。

Heaven takes priority in terms of qi and then in terms of form, while Earth takes priority in terms of form and then in terms of qi; all things in Heaven and Earth are similarly distinguished in this way. Qi nourishes nature, and nature controls qi. Therefore, if qi exists, nature exists, and if nature moves, qi moves. Before Yao it was considered "before Heaven," and after Yao it was considered "after Heaven"; after Heaven is merely imitating before Heaven.

天之象數則可得而推，如其神用則不可得而測也。自然而然者，天也，唯聖人能索之。效法者，人也，若時行時止，雖人也，亦天也。生者性，天也。成者形，地也。日入地中，交精之象。

The phenomena and numbers of Heaven can be calculated, but its mysterious functions are beyond measurement. Naturally inherent and originally so, belonging to Heaven, can only be explored by the sage; those who follow laws and regulations and act accordingly belong to humanity. However, if one acts when appropriate and stops when appropriate, even though it comes from human action, it is actually in harmony with Heaven. The nature that brings forth all things belongs to Heaven; the form that shapes all things belongs to Earth. When the sun sinks into the earth, it represents the image of Heaven and Earth meeting and their vital energies intermingling.

體四而變六，兼神與氣也。氣變必六，故三百六十也。凡事為之極，幾十之七則可止矣。蓋夏至之日止於六十，兼之以晨昏，分可辨色矣。庶幾乎十之七也。圖雖無文，吾終日言未嘗離乎是，蓋天地萬物之理盡在其中矣。

The fundamental principle is four, while transformation involves six, incorporating both spirit and qi; the changes of qi must be six, hence forming a total of three hundred and sixty. Whenever doing something, once it reaches about seven-tenths completion, one should stop. On the day of Summer Solstice, sunlight stops at sixty units, and adding the morning and evening periods, the sky is still distinguishable, which is about seven-tenths. Although the diagram of the Primordial Heaven has no characters, I have never left it, because the principles of heaven and earth and all things are included in this diagram.

氣一而已，主之者乾也，神亦一而已，乘氣而變化，出入於有無死生之間，無方而不測者也。不知乾，無以知性命之理。時然後言，乃應變而言，言不在我也。仁配天地謂之人，唯仁者真可以謂之人矣。生而成，成而生，易之道也。

Qi is a single entity, and it is governed by Qian. The spirit is also a single entity, which rides upon Qi and changes, entering and exiting between existence and non-existence, life and death, without a fixed place and thus unpredictable. Without understanding Qian, one cannot comprehend the principles of life and death. Speaking at the right time is to speak in accordance with change, and the words are not under my control. Only those who can match "ren" with heaven and earth can be called human, and only the virtuous truly deserve to be called a person. Being born and then becoming, becoming and then being again, this is the principle of the Book of Changes.

氣者，神之宅也。體者，氣之宅也。天六地四，天以氣為質，而以神為神，地以質為質，而以氣為神，唯人兼乎萬物而為萬物之靈，如禽獸之聲，以其類而各能其一，無所不能者，人也。推之他事，亦莫不然，唯人得天地日月交之用，他類則不能也。人之生真可謂之貴矣！天地與其貴而不自貴，是悖天地之理，不祥莫大焉。

Qi is the dwelling place of the divine, and the body is the dwelling place of qi. The number for Heaven is six, and the number for Earth is four. Heaven uses qi as its substance and the divine as its spirit; Earth uses substance as its substance and qi as its spirit. Only humans possess all things and thus become the spiritual essence of all things. For example, the calls of birds and beasts can only produce one kind of sound according to their kind; nothing is capable of doing everything, except humans. This is also true in other matters: only humans can receive the function of the union of Heaven and Earth and the sun and moon. Other creatures cannot. To live in the world, humans can truly be considered noble! Since Heaven and Earth have given this nobility to humans, if humans do not value themselves, they are violating the principles of Heaven and Earth, and there is nothing more ominous than this.

燈之明暗之境，日月之象也。月者，日之影也。情者，性之影也。心性而膽情，性神而情鬼。心為太極，又曰道為太極。形可分，神不可分。陰事大半，蓋陽一而陰二也。

Light and darkness have a boundary, which is the image of the sun and moon. The moon is the shadow of the sun, and affection is the shadow of nature. The mind belongs to nature, and the胆 belongs to affection. Nature is close to the divine, while affection is close to the ghostly. The mind is the Taiji, and also the Dao is the Taiji. The physical form can be divided, but the spirit cannot. In the world, things belonging to yin make up most, because yang has only one, while yin has two.

冬至之後為呼，夏至之後為吸，此天地一歲之呼吸也。以物喜物，以物悲物，此發而中節者也。不我物則能物物。任我則情，情則蔽，蔽則昏矣。因物則性，性則神，神則明矣。潛天潛地，不行而至，不為陰陽所攝者，神也。

After the winter solstice, heaven and earth exhale; after the summer solstice, they inhale. This is the inhalation and exhalation of heaven and earth in a year. To be happy because something is worth being happy about, and to be sad because something is worth being sad about, this is what the Doctrine of the Mean calls "expressing feelings in moderation." Only by not claiming things as one's own can one truly master all things. To act according to one's own private desires is emotion; with emotion comes obstruction, and with obstruction comes darkness. To follow the nature of things is the true nature; to see this nature is to connect with the divine, and to connect with the divine is to have clarity. Those who can sink into heaven and earth, who do not need to move yet can reach everywhere, who are not bound by yin and yang, are the divine.

天之孽，十之一猶可違。人之孽，十之九不可逭。先天之學，心也。後天之學，跡也。出入有無死生者，道也。神無所在，無所不在，至人與他心通者，以其本於一也。道與一，神之強名也。以神為神者，至言也。

Heavenly calamities sent down from above, ten parts of them can have one part escaped; calamities caused by human actions, nine parts out of ten cannot be escaped. "The study of the先天" deals with the mind, while "the study of the后天" deals with traces. Those who can move between existence and non-existence, life and death, are following the Dao. The divine does not have a fixed place, yet is present everywhere. The sage can communicate with others' minds because originally they are the same. "Dao" and "One" are both artificial names given to the divine; to say directly "the divine is divine" is the most appropriate expression.

身地也，本靜，所以能動者，血氣使之然也。生生長類，天地成功。別生分類，聖人成能。以物觀物，性也。以我觀物，情也。性公而明，情偏而暗。陽主闢而出，陰主翕而入。

The body belongs to the earth and is originally still; it is the blood and qi that make it move. The continuous generation of all things and the proliferation of their kinds is the achievement of heaven and earth; the classification and distinction of all things is the skill of the sages. Viewing things from the perspective of things themselves is nature; viewing things from the perspective of oneself is emotion. Nature is impartial and clear, while emotion is biased and obscure. Yang is dominant in opening up and extending outward, while Yin is dominant in gathering in and moving inward.

日在於水則生，離則死，交與不交之謂也。陰對陽為二，然陽來則生，陽去則死，天地萬物生死主於陽，則歸之於一也。神無方而性有質。發於性則見於情，發於情則見於色，以類而應也。

The sun lives in water and dies when it leaves the water, which illustrates the distinction between connection and disconnection. Yin and Yang form a pair through their opposition, yet Yang brings life when it comes and causes death when it departs. Since the life and death of all things in heaven and earth are governed by Yang, ultimately it is all one. The spirit has no fixed place, but nature has a tangible quality. From nature comes emotion, and from emotion comes expression in color, which is the principle of mutual correspondence among similar things.

以天地生萬物，則以萬物為萬物。以道生天地，則天地亦萬物也。人之貴，兼乎萬物，自重而得其貴，所以能用萬類。凡人之善惡，形於言，發於行，人始得而知之。但萌諸心，發於慮，鬼神已得而知之矣。此君子所以慎獨也。氣變而形化。

From the perspective of the generation of all things from heaven and earth, all things are merely all things; but from the perspective of the Dao generating heaven and earth, heaven and earth are no more than one of the myriad things. The value of human beings lies in their possession of the principles of all things. Only when a person values himself truly can he possess this value and thus be able to control all creatures. Human goodness and evil are expressed through words and actions, and only then do others know about them. But as soon as a thought arises in the mind, even before it is expressed, the spirits already know. This is why the gentleman is careful in his solitude. When the vital energy changes, the form also changes.

人之類，備乎萬物之性。人之神則天地之神，人之自欺，所以欺天地，可不戒哉？人之畏鬼亦猶鬼之畏人，人積善而陽多，鬼亦畏之矣，積惡而陰多，鬼不畏之矣。大人者，與鬼神合其吉凶，夫何畏之有？

Human beings possess the nature of all things. The spirit of a person is the same as the spirit of heaven and earth. If a person deceives himself, he is actually deceiving heaven and earth; how can he not be cautious? People fear ghosts, but in reality, ghosts also fear people: if a person accumulates good deeds, his yang energy is abundant, and ghosts fear him; if he accumulates evil deeds, his yin energy is abundant, and ghosts do not fear him. As for great men, they can harmonize with the auspicious and inauspicious of ghosts and spirits; what then is there to fear?

至理之學非至誠則不至，物理之學或有所不通，不可以強通，強通則有我，有我則失理而下入於數矣。心一而不分，則能應萬物，此君子所以虛心而不動也。聖人利物而無我。明則有日月，幽則有鬼神。夫聖人六經，渾然無跡，如天道焉。春秋錄實事，而善惡形於其中矣。

The study of the highest principles cannot reach its perfection without reaching the state of utmost sincerity. As for the study of physical phenomena, there are sometimes things that cannot be fully understood, and one should not force understanding. Forcing understanding introduces the self, and when the self is present, reason is lost, and one falls into the realm of numerology and divination. When the mind is focused and not scattered, it can deal with all things, which is why the gentleman must be humble and not act recklessly. The sage benefits all things without preserving a private self. In the bright places, the sun and moon shine; in the dark places, ghosts and spirits observe. The six classics composed by the sage are unified and seamless, like the way of heaven. The Book of Spring and Autumn simply records events truthfully, and good and evil naturally appear within them.

中庸之法，自中者天也，自外者人也。韻法闢翕者律天，清濁者呂地，先閉後開者，春也。純開者，夏也。先開後閉者，秋也。冬則閉而無聲。東為春聲，陽為夏聲，此見作韻者亦有所至也。銜凡冬聲也。

The principles of the Doctrine of the Mean: the natural harmony from within belongs to the heavenly, while the artificial pursuit from outside belongs to humanity. The principles of tonal patterns: the distinction between open and closed syllables belongs to the 'Lu' (laws), corresponding to heaven; the distinction between clear and dull sounds belongs to the 'Lv' (regulations), corresponding to earth. Sounds that first close then open are spring tones, entirely open sounds are summer tones, sounds that first open then close are autumn tones, and winter tones are closed and silent. The 'Dong' rhyme is spring tone, the 'Yang' rhyme is summer tone, thus it can be seen that those who established the rhyme categories had their own understanding; the 'Xian' and 'Fan' rhymes are winter tones.

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。不見動而動，妄也。動乎否之時，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。精氣為物，形也。游魂為變，神也。又曰。精氣為物，體也。游魂為變，用也。君子之學以潤身為本，其治人應物，皆餘事也。

In a state of stillness and returning to the original nature, returning to quietness, that is the time of the Earth Trigram (Kun); when there is a response, it connects throughout the world, so the Yang force in the middle initiates quickly, without a moment's delay, which is the meaning of "Fu." If there is no sign of movement yet it moves, that is "Wang," which is moving recklessly during a time of blockage. If there is a sign of movement and then it moves, that is "Wu Wang"; however, the hexagram Wu Wang still brings calamity, because the Yang is still weak and there is no corresponding force above. If there is a response and then movement occurs, it becomes the hexagram Yi. "Jing Qi Wei Wu" refers to form, while "You Hun Wei Bian" refers to spirit; it also says, "Jing Qi Wei Wu" refers to body, while "You Hun Wei Bian" refers to function. The gentleman studies with the cultivation of himself as the foundation, and matters of governing people and dealing with things are secondary.

剸割者，才力也。明辨者，智識也。寬洪者，德器也，三者不可闕一。無德者責人，怨人，易滿，滿則止也。能循天理動者，造化在我也。學不際天人，不足謂之學。人必有德器，然後喜怒皆不妄為，卿相為匹夫，以至學問高天下，亦若無有也。

Those who can decisively judge are endowed with ability; those who can clearly discern are endowed with wisdom; those who are broad-minded and generous are endowed with virtue: these three are indispensable. A person without virtue tends to blame and resent others, and is easily self-satisfied. Once self-satisfied, he stops advancing. Those who act in accordance with the principles of heaven hold their destiny in their own hands. If one's study does not integrate heaven and humanity, it cannot be called true learning. A person must first possess virtue, then his joy and anger will not be reckless. At that point, whether he holds a high official position or is merely an ordinary person, even if his learning surpasses all others, he will regard it as if it were nothing.

得天理者不獨潤身，亦能潤心，不獨潤心，至於性命亦潤。曆不能無差，今之學曆者但知曆法，不知曆理，能布算者落下閎也，能推步者甘公石公也。落下閎但知曆法，揚雄知曆法又知曆理。顏子不遷怒不貳過，皆情也，非性也。不至於性命不足謂之好學。揚雄作玄，可謂見天地之心者也。

Those who understand heavenly principles not only nourish their bodies but also nourish their hearts; not only their hearts but also their lives are fully nourished. Calendars cannot be entirely accurate; nowadays, those with academic qualifications only understand calendar calculations but do not understand the principles behind them. Those skilled in calculation are Lü Haogong, and those skilled in astronomical prediction are Gan Gong and Shi Gong; Lü Haogong only understood calendar calculations, but Yang Xiong understood both calendar calculations and their principles. Yanzi practiced not transferring anger and not repeating mistakes, which is still within the realm of emotion rather than nature; without reaching the level of integrating knowledge with life and death, one is not qualified to be called a true scholar. Yang Xiong composed the "Tai Xuan," which can be said to be the work of someone who saw the heart of heaven and earth.

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。莊周雄辯，數千年一人而已。如庖丁解牛曰踟躕四顧，孔子觀呂梁之水曰蹈水之道無私，皆至理之言也。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，一闢一闔，渾渾然無跡，非天下之至神，其孰能與於此？

The Book of Changes has no fixed form. Some people say: The Great Treatise mentions "there are established principles," which implies it has a form. This is to prevent people from taking it as having a fixed form, so it also says "it cannot be taken as a standard." "There are established principles" refers to constancy, while "it cannot be taken as a standard" refers to change. Zhuangzi's eloquence is unparalleled for thousands of years. For example, in the chapter "On Cultivating Life," he writes about the butcher Ding dissecting an ox, describing his confident and self-satisfied demeanor and his ability to look around freely; in the chapter "On Attaining Life," he describes Confucius watching the swift current of Lüliang, saying the way of swimming is to have no self-interest. These are all expressions of ultimate truths. The Book of Changes is a tool used by sages to cultivate the virtuous and suppress the petty. When the virtuous should flourish, they are already given a path before the matter takes shape; when the petty should be eliminated, the door is already closed before the matter takes shape. One elimination and one flourishing, one opening and one closing, all in a seamless whole without any trace. Unless one is the most profound and mysterious person, who could participate in such things?

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，大德大位，可過者也，伊周其人也，不可懼也。有大德無大位，不可過者也，孔孟其人也，不可悶也，其位不勝德耶？大哉位乎！待時用之宅也。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。

The hexagram Da Guo has a diagram where the first and last lines are weak, while the middle is overly strong. It must be saved by someone with great virtue and high position. In terms of common distinctions, there are those who can act in extraordinary ways and those who cannot. Those with great virtue and high position can act, as was the case with Yi Yin and the Duke of Zhou, who did not need to fear. Those with great virtue but no high position cannot act, as was the case with Confucius and Mencius, who did not need to be depressed. Is it that position is insufficient to bear their virtue? Position is indeed of great importance, for it is merely a room waiting for the right moment to be used. The hexagram Fu comes right after Bo, aiming to explain that a time of order arises from a time of chaos. The hexagram Guo comes right after Guai, aiming to explain that a time of chaos arises from a time of order. Timing, timing! There has never been a case where Bo reaches its end without Fu following, nor has there ever been a case where Guai reaches its end without Guo following. If one can set defenses early at the right places, the state will endure long and the descendants will flourish. Therefore, sages most value prevention before things arise, which is called the main idea of the Book of Changes.

先天學，心法也。故圖皆自中起，萬化萬事生乎心也。所行之路不可不寬，寬則少礙。知易者不必引用講解，始為知易。孟子著書，未嘗及易，其間易道存焉，但人見之者鮮耳。人能用易，是為知易，如孟子可謂善用易者也。

"The study of the Heavenly Origin" is a system of inner principles, so all diagrams related to the Heavenly Origin start from the center. Since countless changes and myriad affairs originate from the mind, one's path in life should not be narrow, for a broader path leads to fewer obstacles. To truly understand the Book of Changes, one does not necessarily need to quote classical texts. Mencius never mentioned the Book of Changes in his writings, yet the principles of the Book of Changes are present in his works, though few can perceive them. Only those who can apply the Book of Changes in their lives can be said to truly understand it. Mencius can be considered someone who skillfully applies the principles of the Book of Changes.

所謂皇帝王伯者，非獨三皇五帝三王五伯而已，但用無為則皇也，用恩信則帝也，用公正則王也，用知力則伯也。鬼神無形而有用，其情狀可得而知也，於用則可見之矣。若人之耳目鼻口手足，草木之枝葉花實顏色，皆鬼神之所為也。福善禍淫，主之者誰耶？聰明正直，有之者誰耶？不疾而速，不行而至，任之者誰耶？皆鬼神之情狀也。

The terms "Huang," "Di," "Wang," and "Bo" do not refer exclusively to the Three Huang, Five Di, Three Wang, and Five Bo: anyone who governs the world by non-action is called a Huang, anyone who governs by benevolence, virtue, and righteousness is called a Di, anyone who governs by fairness and integrity is called a Wang, and anyone who governs by wisdom and strength is called a Bo. Ghosts and spirits have no physical form but do have functions; their nature can be known through their actions. For example, the ears, eyes, nose, mouth, hands, and feet of humans, and the branches, leaves, flowers, fruits, and colors of plants, are all the works of ghosts and spirits. Who brings blessings to the virtuous and calamities to the wicked? Who is wise and upright? Who is not hasty yet swift, not moving yet arrives? These are the manifestations of ghosts and spirits.

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。有像象，擬一物以明意。有數象，七日八月三年十年之類是也。易之數窮天地始終，或曰，天地亦有始終乎？曰。既有消長，豈無終始？天地雖大，是亦形器，乃二物也。易有內象，理致是也。有外象，指定一物而不變者是也。

The Book of Changes has "intentional images" (yi xiang). Any intention is established to clarify the hexagram image, which encompasses three types. There is "verbal image" (yan xiang), which does not compare to specific objects but directly explains principles through words. There is "resemblant image" (xiang xiang), which clarifies the intention by comparing it to a particular object. There is "numerical image" (shu xiang), such as "seven days," "eight months," "three years," and "ten years" found in the line statements of the hexagrams. The numbers in the Book of Changes can exhaust the beginning and end of heaven and earth. Someone asks: Do heaven and earth have a beginning and an end? The answer is: If there is growth and decline, how could there not be a beginning and an end? Although heaven and earth are vast, they are still tangible objects, merely two things. The Book of Changes has "inner image," which is the direction of meaning and principle; and "outer image," which refers to a fixed object.

在人則乾道成男，坤道成女，在物則乾道成陽，坤道成陰。神無方則易無體，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。事無大小，皆有道在其間，能安分則謂之道，不能安分謂之非道。

In human beings, the principle of Heaven (Qian) gives rise to males, and the principle of Earth (Kun) gives rise to females; in things, the principle of Heaven gives rise to yang, and the principle of Earth gives rise to yin. Spirits have no fixed location, so the Book of Changes (Yi) has no fixed form. Once fixed in a particular place, it cannot change, and thus it is not a spirit; once it has a fixed form, it cannot be flexible, and thus it is not the Book of Changes. The Book of Changes seems to have a form, but what is called form is actually just an image; using the image to show the form, the form itself does not exist. Whether the matter is big or small, there is a principle within it: being content with one's proper position is called the principle, and not being content with one's proper position is called not following the principle.

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。六虛者，六位也，虛以待變動之事也。六爻六卦，有形則有體，有性則有情。天主用，地主體，聖人主用，百姓主體，故日用而不知。

The numerical sequence of the correct pitch stops at seven because on the day of Summer Solstice, the sun rises at the hour of Yin and sets at the hour of Xu, and by the hours of Hai, Zi, and Chou, the sun has already gone underground, making it impossible for the eyes to see anything. These three hours are thus not further counted, which corresponds to these three hours. Similarly, the numerical sequence of living beings also stops not because the numbers cannot continue, but because the numbers exist yet are not visible. The term "six voids" refers to the six yao positions; they are called "void" because they remain empty, waiting for changes to fill them. The six yao correspond to the six hexagrams, which have form and substance, as well as nature and emotion. The heavenly ruler governs "use," the earthly ruler governs "form"; the sage governs "use," while the common people govern "form," so the common people use things every day without realizing it.

法始乎伏羲，成於堯，革於三王，極於五伯，絕於秦。萬事治亂之跡無以逃此矣。神者，易之主也，所以無方。易者，神之用也，所以無體。循理則為常，理之外則為異矣。

The laws and regulations for governing the world began with Fuxi, were established by Yao, and underwent changes during the Xia, Shang, and Zhou dynasties. By the time of the Five Hegemons of the Spring and Autumn period, they had reached an extreme, and by the Qin dynasty, they had completely ceased. The patterns of order and disorder in all worldly affairs cannot escape this trend. The divine is the master of the Book of Changes, so it has no fixed place; the Book of Changes is the function of the divine, so it has no fixed form. Following the conventional is called "constant," while going beyond the conventional is called "strange."

火以性為主，體次之。水以體為主，性次之。陽性而陰情，性神而情鬼。易之首於乾坤，中於坎離，終於水火之交不交，皆至理也。

Fire is primarily characterized by its nature and secondarily by its form, while water is primarily characterized by its form and secondarily by its nature. Yang is associated with nature, and Yin is associated with emotion. Nature is close to the divine, while emotion is close to the demonic. The Book of Changes begins with Qian and Kun, places Kan and Li in the center, and concludes with Ji Ji and Wei Ji, which represent the meeting and not meeting of water and fire. All of these contain extremely subtle principles.

太極一也，不動生二，二則神也，神生數，數生象，像生器。太極不動，性也，發則神，神則數，數則像，像則器，器之變，復歸於神也。

The Taiji is one, and it remains unmoving, giving rise to two, which is the divine. The divine gives rise to numbers, numbers give rise to images, images give rise to objects. The unmoving aspect of Taiji is the nature; once it moves, it becomes the divine, and with the divine comes numbers, with numbers comes images, with images comes objects. Once objects change, they return again to the divine.

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，奇偶生自太極。天使我有，是之謂命。命之在我之謂性，性之在物之謂理。朔易以陽氣自北方而生，至北方而盡，謂變易循環也。

All hexagrams that do not directly interact with Qian and Kun arise from the hexagrams of Bao and Tai; and Bao and Tai are precisely the results of Qian and Kun interacting. Qian and Kun originate from the odd and even lines, and odd and even lines come from the Taiji. Heaven gives me this body and this life, which is called "ming"; when "ming" falls upon me, it is called "xing"; when "xing" falls upon things, it is called "li". The "Shuoshan" in the "Shangshu·Yaodian" refers to the yang energy rising from the north and ending in the north, which signifies the meaning of change and cycle.

春陽得權，故多旱。秋陰得權，故多雨。元有二，有生天地之始者，太極也。有萬物之中各有始者，生之本也。天地之心者，生萬物之本也。天地之情者，情狀也，與鬼神之情狀同也。

In spring, yang energy is dominant, so there is often drought; in autumn, yin energy is dominant, so there is often rain. The term "yuan" has two meanings: one is the ultimate beginning from which heaven and earth originate, which is the Taiji; the other is the beginning inherent in each thing, which is its fundamental nature.the so-called "heaven and earth's heart" refers to the fundamental source that nurtures all things;所谓 "heaven and earth's sentiment" refers to its manifested appearance, which is similar to the nature of ghosts and spirits.

莊子與惠子游於濠梁之上。莊子曰。條魚出游從容，是魚樂也。此盡己之性能盡物之性也。非魚則然，天下之物則然。若莊子者，可謂善通物矣。老子知易之體者也。無思無為者，神妙致一之地也。聖人以此洗心，退藏於密。太極，道之極也。太玄，道之元也。太素，色之本也。太一，數之始也。太初，事之初也。其成功則一也。

The "Zhuangzi · Autumn Waters" records that Zhuangzi and Hui Shi were strolling on a bridge over the Hao River. Zhuangzi said: "The white minnows swim leisurely and freely, this is the joy of the fish." This is precisely being able to fully express one's own nature, thus also being able to fully express the nature of all things. Not only do fish act like this, but all things in the world do so as well. Someone like Zhuangzi can be said to be good at understanding the feelings of things. Laozi was someone who understood the "body" of the "Book of Changes." "No thinking, no action" is the state of profound mystery returning to unity; the sage uses this to purify the mind and retreat into the quiet and hidden. "Taiji" is the ultimate of the Dao, "Taixuan" is the origin of the Dao, "Taisu" is the fundamental of form and color, "Taiyi" is the beginning of numbers, and "Taichu" is the beginning of events. Although the names are different, they all accomplish the same thing.

太羹可和，玄酒可漓，則是造化亦可和可漓也。易地而處則無我也。誠者主性之具，無端無方者也。至哉留侯，善藏其用。素問密語之類，於術之理可謂至矣。

The original essence of food without seasoning can still be harmonized, and plain water can also be diluted with something light. This shows that nature itself can be harmonized and diluted. By placing oneself in another's position, the attachment to "self" can be eliminated. "Sincerity" is the means to uphold one's true nature, it has no beginning or end, no fixed direction or place. Zhang Liang, the Master of the Left, was truly remarkable, as he was most skilled at concealing his own role. The cryptic passages in the "Su Wen" can be considered to have reached the ultimate in explaining medical principles.

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。或問顯諸仁藏諸用，曰，若日月之照臨，四時之成歲，是顯仁也。其度數之然而不知其所以然，是藏用也。君子於易玩象，玩數，玩辭，玩意。

Suppose Gu Snu killed someone, Shun would regard abandoning the world as discarding a pair of broken shoes, secretly taking his father along and fleeing, settling by the seaside, living the rest of his life happily and forgetting about the world. This shows that even though a sage may possess the whole world, he cannot exchange it for the natural affection in his nature. Someone asks how to explain "manifesting virtue and concealing its function." The answer is: the shining of the sun and moon, the cycle of the four seasons, is "manifesting virtue"; the measure and order within them, though known, are not understood by people, which is "concealing function." A gentleman studying the Book of Changes should contemplate its images, its numbers, its words, and its meanings.

兌說也，其它皆有所害，惟朋友講習無，說於此，故言其極者也。中庸非天降地出，揆物之理，度人之情，行其所安，是為得矣。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。

Dui represents joy. Other forms of joy may lead to harm, but joy among friends in discussion and mutual improvement is without harm. The Book of Changes cites this to indicate the ultimate expression of joy. The principles discussed in the Zhongyong are not something that drop from the sky or sprout from the earth; they can be understood by examining the principles of things and observing human nature, and by acting in accordance with one's inner peace. The four virtues of Yuan, Heng, Li, and Zhen each encompass the four categories of good fortune, misfortune, regret, and loss. Even when following these virtues, if they are not in harmony with the right timing, misfortune may still occur.

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，然唯湯武則可，非湯武則是篡也。陰者陽之影，鬼者人之影也。

King Tang of Shang exiled King Jie of Xia, and King Wu of Zhou attacked King Zhou of Shang, but people did not regard these as acts of regicide. The reasoning is similar to what Mencius said: "It is considered proper for men and women not to touch each other," which is "ritual," but if a sister-in-law falls into water, one should reach out to save her, which is "flexibility." Therefore, Confucius both honored Boyi and Shuqi and acknowledged King Tang and King Wu: Boyi and Shuqi upheld benevolence, while King Tang and King Wu acted with righteousness. However, such actions could only be performed by King Tang and King Wu; if someone else had done it, it would be considered usurpation. Yin is the shadow of Yang, and ghosts are the shadows of humans.

秦穆公有功於周，能遷善改過，為伯者之最。晉文侯世世勤王，遷平王於洛，次之。齊威公九合諸侯，不以兵車，又次之。楚莊強大，又次之。宋襄公雖伯而力微，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，有過者亦未見大於四國也，故四者功之首，罪之魁也。人言春秋非性命書，非也。至於書郊牛之口傷，改卜牛，牛死乃不郊，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，豈容人特立私意哉？又曰春秋聖人之筆，削為天下之至公，不知聖人之所以為公也。如因牛傷則知魯之潛郊，因初獻六羽則知舊潛八佾，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。

King Qin Mu Gong rendered great service to the Zhou royal house, was able to correct his mistakes and improve himself, and among the hegemonic rulers he was the best. The Jin Wenhou dynasty was diligent in serving the king generation after generation, and moved the King Ping of Zhou to Luoyi, which was the next level. Duke Huan of Qi convened the feudal lords nine times without using military force, which was the next level again. Duke Zhuang of Chu had great power, and was the next level after that. Duke Xiang of Song, although he was called a hegemon, had weak power, and was captured by Chu when he tried to convene the feudal lords, so he is not worth mentioning. Those who study the Spring and Autumn Annals should first determine the merits and faults of these four states, otherwise the matter will lack order and one will not understand the mind of the sage. In the Spring and Autumn period, there were no greater merits than these four states, nor were there greater faults. Therefore, these four families were both the first in merit and the leading in fault. Some people say that the Spring and Autumn Annals is not a book about the principles of life and death, but this is wrong. Take for example the record of a cow injured in its mouth at the temple sacrifice, then a new cow was chosen, but it died, so the temple sacrifice was not held, yet the three distant sacrifices were still performed. This is exactly a criticism of Lu's actions. Where is the sage's private heart? It is precisely because he had no self. Is this not a statement arising from the principles of life and death? Others say that the Spring and Autumn Annals only judges things according to their own nature, and there is no room for private opinions. Yet others say that the Spring and Autumn Annals is the most impartial book in the world, made by the sage's every stroke and deletion. But they do not understand on what basis the sage could be impartial. For example, from the incident of the injured cow, one can know that Lu had overstepped in its temple sacrifice; from the record of 'initial offering of six feathers,' one can know that Lu had previously used eight rows of dancers, which was an overstep; from the record of 'newly building the chicken gate,' one can know that there was no chicken gate before. These were not deliberately arranged by the sage. Therefore, the Spring and Autumn Annals is a book that fully expresses the principles of life and death.

易之為書，將以順性命之理者，循自然也。孔子絕四從心，一以貫之，至命者也。顏子心齋屢空，好學者也。子貢多積以為學，億度以求道，不能刳心滅見，委身於理，不受命者也。春秋循自然之理而不立私意，故為盡性之書也。

The Book of Changes is about following the principles of nature and destiny. Confucius could eliminate the four faults of desire, certainty, rigidity, and self-importance, and act from the heart without contradiction, thus being a person who understands the heavenly mandate. Yan Hui could practice inner stillness and forget self, remaining joyful even in poverty, thus being a diligent learner. Zigong relied on accumulation and calculation to seek knowledge and the Way, but could not eliminate his own cleverness and preconceptions, and entrust himself entirely to principle, thus not being someone who had received the heavenly mandate. The Spring and Autumn Annals follow the principles of nature without personal bias, thus also being a book that fully expresses human nature.

初與上同，然上亢，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。人之貴，兼乎萬物，自重而得其貴，所以能用萬類。至理之學非至誠則不至。素問陰符，七國時書也。

The first line and the top line belong to the same category, but the top line has reached the extreme of excess, so it is not as good as the first line which is still advancing. The second line and the fifth line belong to the same category, but the second line is in the middle of a yin position, so it is not as good as the fifth line which is in the middle of a yang position. The third line and the fourth line belong to the same category, but the third line is at the top of the lower trigram, so it is not as good as the fourth line which is closer to the position of the ruler. Human beings are precious because they possess the principles of all things; only by valuing themselves can they truly possess this preciousness and thus control all creatures. The study of the highest principles cannot reach its ultimate truth without reaching the state of sincerity. The "Su Wen" and the "Yin Fu Jing" are both works from the time of the Warring States period.

顯諸仁，藏諸用，孔子善藏其用乎？莊荀之徒失之辯。伯夷義不食周粟，至餓且死，只得為仁而已。三人行必有師焉，至於友一鄉之賢，天下之賢，以天下為未足，又至於尚論古人，無以加焉。義重則內重，利重則外重。

"Displaying it among people and concealing it in use," Confucius was probably the one most skilled at concealing his own role. The school of Zhuangzi and Xunzi had the flaw of being fond of argumentation. Boyi upheld righteousness and refused to eat food from the Zhou dynasty, even starving to death, yet he only achieved the character of "ren" (benevolence). "When three people walk together, there must be someone who can be my teacher," from this, one can extend to associate with the virtuous people in one's hometown, then with the virtuous people throughout the world; still not satisfied, one goes further to comment on ancient sages. At this point, there is no further to go. Those who value righteousness place importance within; those who value profit place importance outside.

能醫人能醫之疾，不得謂之良醫，醫人之所不能醫者，天下之良醫也。能處人所不能處之事，則能為人所不能為之事也。人患乎自滿，滿則止也。故禹不自滿，假所以為賢，雖學亦當常若不足，不可臨深以為高也。人茍用心，必有所得，獨有多寡之異，智識之有淺深也。

A doctor who can cure diseases that others can also cure is not a truly good doctor; a doctor who can cure diseases that others cannot is considered the best in the world. Similarly, someone who can handle matters that others cannot handle can accomplish what others cannot. The most dangerous flaw in people is self-satisfaction, for once one becomes self-satisfied, they stop progressing. Therefore, Yu the Great never became self-satisfied or arrogant, which is why he became a great and virtuous person. Even if one is already studying, one should always feel that there is still much to learn, and not think oneself superior just because one stands on the edge of a deep valley. As long as a person is willing to put in effort, they will surely gain something, though the amount gained varies according to the depth of their knowledge.

理窮而後知性，性盡而後知命，命知而後知至。凡處失在得之先，則得亦不喜。若處得在失之先，則失難處矣,必至於隕穫。人必內重，內重則外輕，茍內輕，必外重，好利好名無所不至。天下言讀書者不少，能讀書者少，若得天理真樂，何書不可讀，何堅不可破，何理不可精？

The principles are thoroughly investigated to understand nature, and nature is fully expressed to understand destiny. Only when destiny is understood can one reach the ultimate. Those who first consider loss before gain will not be overly joyful when they actually gain. Those who first consider gain before loss will find it hard to cope when they lose, inevitably leading to despair and loss of purpose. One must value the inner self; if the inner self is valued, the outer world will naturally be light. If the inner self is neglected, the outer world will inevitably be pursued, leading to a focus on fame and profit, and anything can be done. There are many who call themselves scholars, but few truly understand reading. If one truly experiences the genuine joy of heavenly principles, then any book can be read, any difficulty can be overcome, and any principle can be mastered.

天時地理人事，三者知之不易。資性得之天也，學問得之人也。資性，由內出者也。學問，由外入者也。自誠明，性也，自明誠學也。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。

Heavenly timing, geographical conditions, and human affairs are three things that are not easy to truly understand. Talent is obtained from Heaven, while learning comes from human effort: talent arises from within, while learning is poured in from outside. The Doctrine of the Mean says "self-true clarity" which belongs to nature, and "self-clear clarity" which belongs to study. Boyi and Liuxiahu each possessed one aspect of the sage: Boyi possessed the sage's "purity," while Liuxiahu possessed the sage's "harmony." Confucius, however, was pure when appropriate and harmonious when appropriate, acting when necessary and resting when necessary; thus he possessed the sage's "timing."

太玄九日當兩卦，餘一卦當四日半。用兵之道，必待人民富，倉廩實，府庫充，兵強名正，天時順，地利得，然後可舉。老子五千言，大抵皆明物理。

The Taixuan text matches nine heavens with two trigrams, leaving one trigram to correspond with four and a half heavens. The principles of warfare require waiting until the people are well-off, granaries are full, treasuries are abundant, military strength is strong, the cause is just, the heavens are favorable, and the land is advantageous before one can take up arms. The Dao De Jing of Laozi, in its five thousand words, mainly explains natural phenomena.

今有人登兩臺，兩臺皆等則不見其高，一臺高，然後知其卑下者也。一國一家一身皆同，能處一身則能處一家，能處一家則能處一國，能處一國則能處天下。心為身本，家為國本，國為天下本。心能運身，茍心所不欲，身能行乎？人之精神貴藏而用之，茍衒於外，則鮮有不敗者。如利刃，物來則剸之，若恃刃之利而求割乎物，則刃與物俱傷矣。

If a person stands on two platforms of equal height, there is no way to tell which is higher; only when one is higher can the other be seen as lower. The principles of a country, a family, and an individual are the same: one can only manage well one's own body before being able to manage a family, and only after managing a family can one manage a country; only after managing a country can one manage the world. The mind is the root of the body, the family is the root of the country, and the country is the root of the world. The mind controls the body; if the mind does not will it, can the body still move? Human spirit is valuable when it is kept and used internally; if it is constantly shown off outwardly, few are those who do not fail. It is like a sharp blade: it cuts only when something comes close to it; if one relies on the blade's sharpness to actively cut things, then both the blade and the object will be damaged.

言發於真誠，則心不勞而逸，人久而信之。作偽任數，一時或可以欺人，持久必敗。人貴有德，小人有才者有之矣，故才不可恃，德不可無。天地日月，悠久而已。故人當存乎遠，不可見其邇。君子處畎畝，則行畎畝之事。居廟堂，則行廟堂之事，故無入不自得。

Speech that comes from sincerity does not weary the heart and brings ease; over time, people naturally believe him. But if one acts deceitfully and uses tricks, he may deceive people for a while, but eventually he will surely fail. A person's value lies in virtue; among small people there are also those with talent, so talent should not be relied upon, and virtue must not be lacking. Heaven and earth, the sun and moon, are merely enduring for a long time; therefore, people should look far ahead and not only focus on the present. A gentleman, when he is among the fields, should do the work of the fields; when he is in the court, should do the work of the court: thus he can find contentment wherever he is.

智數或能施於一朝，蓋有時而窮，惟至誠與天地同久。天地無則至誠可息，茍天地不能無，則至誠亦不息也。室中造車，天下可行，軌轍合故也，茍順義理，合人情，日月所照皆可行也。斂天下之善則廣矣，自用則小。

Wisdom and scheming may show results quickly, but they eventually reach their limits; only sincerity can endure as long as heaven and earth. If heaven and earth can return to nothingness, sincerity can also cease; but if heaven and earth cannot return to nothingness, then sincerity will never cease. Making a cart inside a room, though made in a confined space, can still travel throughout the world because the wheel tracks match the size. Similarly, if something follows righteousness and conforms to human feelings, it can be effective wherever the sun and moon shine. Collecting the good deeds of the world brings a broad mind; relying only on one's own opinion limits one's vision.

漢儒以反經合道為權，得一端者也。權，所以平物之輕重，聖人行權，酌其輕重而行之，合其宜而已，故執中無權者，猶為偏也。王通言春秋王道之權，非王通莫能及此。故權在一身，則有一身之權，在一鄉，則有一鄉之權，以至於天下，則有天下之權，用雖不同，其權一也。

In the Han dynasty, Confucian scholars regarded "violating the constant principles but conforming to the Dao" as "quán" (权), but they only grasped one end of it. Actually, "quán" originally refers to the weight of a balance used to measure the weight of objects; when a sage acts with "quán," he merely weighs things carefully and acts accordingly so that everything is in harmony. Therefore, those who only adhere strictly to the middle way without knowing how to use "quán" are still biased. Wang Tong said that the "Spring and Autumn Annals" is the "quán" of the Way of the King; no one else had ever reached this understanding. Thus, "quán" in one's own body is the "quán" of that body, in one's village it is the "quán" of that village, and when extended to the whole world, it is the "quán" of the world. Although the scope of application differs, the concept of "quán" remains the same.

夫弓固有強弱，然一弓二人張之，則有力者以為弓弱，無力者以為弓強，故有力者不以己之力有餘而以為弓弱，無力者不以己之力不足而以為弓強，何不思之甚也？一弓非有強弱也，二人之力強弱不同也。今有食一杯在前，二人大餒而見之，若相遜，則均得食也。相奪則爭，非徒爭之而已，或不得其食矣。此二者皆人之情也，知之者鮮，知此則天下之事皆如是也。

A bow may be strong or weak, but when two people pull the same bow, the one with greater strength will say the bow is soft, while the one with less strength will say the bow is hard. The stronger person refuses to admit that his strength is excessive, insisting instead that the bow is soft; the weaker person refuses to admit that his strength is insufficient, insisting instead that the bow is hard. How little do they consider the matter! In reality, a single bow has no inherent strength or weakness; it is the differing strengths of the two people pulling it that create this perception. Similarly, if two extremely hungry people see a bowl of rice at the same time, if they are polite and take turns, both can eat; but if they fight over it, they will quarrel, and worse, neither may get to eat. These two situations are common human behaviors, yet few understand them. If one understands this, then one can see that all things in the world are like this.

先天學主乎誠，至誠可以通神明，不誠則不可以得道。良藥不可以離手，善言不可以離口。事必量力，量力故能久。學以人事為大，今之經典，古之人事也。春秋三傳之外，陸淳啖助可以兼治。季札之才近伯夷，叔向子產晏子之才相等，管仲用智數，晚識物理，大抵才力過人也。

The study of the "先天" school emphasizes sincerity: ultimate sincerity can connect with the divine, but without sincerity, one cannot attain the Way. Good medicine cannot be separated from the hands, and good words cannot be separated from the mouth. Doing things must be based on one's capacity, for only by measuring one's capacity can one sustain effort. In studying学问, human affairs are of primary importance; the classics of today are precisely the human affairs of ancient times. In studying the Spring and Autumn Annals, in addition to the three commentaries, the works of Lu Chun and Dan Zhu from the Tang dynasty can also be studied together. Ji Zha's talent is close to Bo Yi's; Shu Xiang, Zi Chang, and Yan Zi have comparable talents; Guan Zhong used intelligence and strategy, but only in his later years did he understand the principles of nature, and he was generally a person of extraordinary talent.

五霸者，功之首，罪之魁也，春秋者，孔子之刑書也，功過不相掩，聖人先褒其功，後貶其罪，故罪人有功亦必錄之，不可不恕也。新作兩觀，新者，貶之也，誅其舊無也，初獻六羽，初者，褒之也，以其舊潛八佾也。

The Five Hegemons were both the first in merit and the foremost in wrongdoing; The Spring and Autumn Annals is a legal text by Confucius. Merit and wrongdoing cannot cancel each other out. The sage first praised the merit and then criticized the wrongdoing. Therefore, even if someone had wrongdoing, if they had merit, it would still be recorded, and one must not entirely lack compassion. "Newly building two pavilions" uses the word "new" to criticize him, implying that there was no such thing before; "First offering six feathers" uses the word "first" to praise him, because previously he had used eight rows of dancers, which was an overstep.

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，不猶愈於潛竊乎？安得不與之也！治春秋者，不辯名實，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，則無緒矣。

A person learned the Spring and Autumn Annals from Yin Shilu, who in turn learned it from Mu Bochang; later this person criticized Mu Bochang, saying that the Spring and Autumn Annals contained no commendation, only censure. Tian Shugǔ said: Sun Fu also said that the Spring and Autumn Annals contained censure but no commendation. The teacher said: During the time of the Spring and Autumn Annals, the rites and laws were neglected, and the relationship between ruler and subject was disordered. If there was someone who did a small good deed, how could it not be praised? Moreover, the Five Hegemons actually contributed to the world. Although the Five Hegemons were not as great as the sovereigns, they were still better than those who secretly overstepped their authority. How could their merits not be acknowledged? Those who study the Spring and Autumn Annals must first distinguish between names and realities, and determine the merits and faults of the Five Hegemons. Only then can they be said to study the Spring and Autumn Annals properly. First determine the merits and faults of the Five Hegemons, and then study the Spring and Autumn Annals; the main idea will be clear. If you go into details, you will only get confused.

凡人為學，失於自主張太過。平王名雖王，實不及一國之諸侯，齊晉雖侯而實潛王，皆春秋之名實也。子貢欲去告朔之餼羊，羊名也，理實也，名存而實亡，猶愈於名實俱亡。茍存其名，安知後世無王者作？是以有所待也。春秋為君弱臣強而作，故謂之名分之書。

When people study, they often make mistakes by being too independent in their own judgment. King Ping of Zhou was nominally the Son of Heaven, but in reality he was not even as powerful as a feudal lord of a state; Qi and Jin were nominally only dukes, but in fact they carried out the duties of a king. These are examples of the problem of name versus reality in the Spring and Autumn Annals. Zigan wanted to remove the live sheep used in the ritual of the New Moon sacrifice; the sheep was the "name," but the meaning of the ritual was the "reality." If the name remains but the reality is lost, it is still better than losing both name and reality. Therefore, we should leave the name for now, for who knows if a true king may arise in the future? Thus, we must leave a bit of hope. The Spring and Autumn Annals were written because the king was weak and the ministers were strong, so it is called a book that discusses the proper distinctions of rank and position.

聖人之難在不失仁義忠信而成事業，何如則可，在於絕四。有馬者借人乘之，舍己從人也。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。

The difficulty for the sage lies in maintaining benevolence, righteousness, loyalty, and trustworthiness while still achieving great accomplishments. How can this be done? It is by completely abandoning the four attitudes of attachment to one's own views, insistence on one's own way, stubbornness, and self-centeredness. A person who owns a horse and is willing to let someone else ride it is giving up his own possession to comply with another's need. Someone asks, "What does 'difficulty in finding talent' mean?" The answer is: only when faced with major affairs can one truly see how hard it is to find capable people. Another question: why specifically mention talent? The answer is: talent is the good quality given by heaven, and learning is used to complete and perfect this quality. Another question: there were also ancient people who achieved great accomplishments without relying on learning, so why must we emphasize learning? The answer is: Zhou Bo and Huo Guang were able to accomplish great things precisely because they lacked learning, so their achievements were not complete. A person without learning cannot understand things clearly, and without understanding things clearly, he becomes stubborn and unenlightened.

人有出人之才必有剛克，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。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。聖人則動不踰矩，何義之畏乎？

A person who possesses talent beyond the ordinary must necessarily have a strong and resolute nature. When this strength is used in a just and proper way, it is sufficient to establish great achievements and bear hardships. But if it is misapplied elsewhere, it may turn into something evil. Therefore, Confucius commented on Shen Chang, saying, "He cannot be considered strong," because he had desires and appetites, which inevitably make him lack true strength. The gentleman understands righteousness, which is the quality of the virtuous; the petty person only understands profit. Only the sage can forget both righteousness and profit. The gentleman respects righteousness, so he refrains from certain actions; the petty person is fearless in everything. As for the sage, his every movement conforms to propriety, so there is no need for him to fear righteousness.

為學養心患在不由直道，去利慾，由直道，任至誠，則無所不通。天地之道直而已，當以直求之，若用智數，由徑以求之，是屈天地而循人慾也，不亦難乎？事無鉅細，皆有天人之理，修身人也，遇不遇天也，得失不動心所以順天也，行險僥倖是逆天也。求之者人也，得之與否天也，得失不動心所以順天也，強取必得是逆天理也，逆天理者患禍必至。

Doing scholarly work and cultivating the mind is hindered by not following the straight path. By removing selfish desires and following the straight path with sincerity, there is nothing that cannot be understood. The way of heaven and earth is simply the character of "straightness," so one should seek it through straightness. If one uses cunning and scheming, taking shortcuts to achieve goals, that is bending heaven and earth to accommodate human desires, which is not easy at all. Whether big or small, every matter contains both heavenly and human principles: cultivating oneself is the human aspect, while meeting or not meeting is the heavenly aspect. Remaining unmoved by gains and losses is in harmony with heaven; taking risks forby chance (侥幸 means侥幸, which is a term for侥幸, meaning to take chances or to rely on luck) is against heaven. Seeking is a human endeavor, while whether one can obtain is a matter of heaven. Remaining unmoved by gains and losses is in harmony with heaven; insisting on forcefully obtaining is against heavenly principles, and those who violate heavenly principles will surely face calamity.

魯之兩觀，郊天大禘，皆非禮也。諸侯茍有四時之禘，以為常祭可也，至於五年大禘，不可為也。仲弓可使南面，可使從政也。誰能出不由戶？戶，道也。未有不由道而能濟者也。不由戶者，鎖穴隙之類是也。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。

The two pavilions in Lu state, as well as the sacrificial rites for heaven at the outskirts and the great禘 ritual, are all against propriety. If a feudal lord performs the禘 ritual four times a year, it can be considered a regular sacrifice; but the great禘 held once every five years should not be done. Confucius said that Zhonggong was capable of facing south and sitting, meaning he was qualified for government service. "Who can go out without passing through a gate?" The gate represents the Way; there has never been a successful endeavor without following the Way. To bypass the gate is like tunneling through a wall, which is improper. "To hear much and choose the good to follow" means even though one hears much, one must choose the good and follow it. The "识" in "to see much and distinguish" means to discern, meaning even though one sees much, one must be able to distinguish.

落下閎改顓帝曆為太初曆，子云準太初而作太玄，凡八十一卦，九分共二卦，凡一五隔一四，細分之則四分半當一卦，氣起於中心，故首中卦。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。一陰一陽之謂道，道無聲無形不可得而見者也，故假道路之道而為名。人之有行必由於道。一陰一陽，天地之道也，物由是而生，由是而成也。

Hualang revised the Zhuan Xu calendar into the Tai Chui calendar, and Yang Xiong followed the Tai Chui calendar to compose the Tai Xuan, consisting of eighty-one sections. These are divided into nine parts, corresponding to two trigrams, with five days followed by four days; further细分, four and a half days correspond to one trigram. The qi originates from the center, so the term 'center' is placed first. The elements Yuan, Heng, Li, and Zhen represent change without adherence to the constant, which is the way of heaven; the elements Ji, Xiong, Hui, and Lin represent change without fixedness, which is the response of human affairs. 'One yin and one yang is called the Dao,' the Dao has no sound or form, so it is named after the word 'Dao' meaning path, as people must follow a path to travel. One yin and one yang represent the way of heaven and earth, and all things are generated and formed through it.

顯諸仁者，天地生萬物之功，則人可得而見也。所以造萬物，則人不可得而見，是藏諸用也。十干天也，十二支地也，支干配天地之用也。易始於三皇，書始於二帝，詩始於三王，春秋始於五霸。自乾坤至坎離，以天道也。自咸恆至既濟未濟，以人事也。人謀人也，鬼謀天也，天人同謀而皆可，則事成而吉也。

"Manifesting virtue" refers to the visible effects of heaven and earth nurturing all things, which people can observe. However, the process by which heaven and earth create all things is not visible, which is called "concealing its function." The ten heavenly stems belong to heaven, and the twelve earthly branches belong to earth; when they are combined, it represents the expression of heaven and earth's functions. The Book of Changes began with the Three Sovereigns, the Book of Documents began with the emperors Yao and Shun, the Book of Poetry began with the kings of Xia, Shang, and Zhou, and the Spring and Autumn Annals began with the Five Hegemons. From Qian to Kan and Li, it discusses the heavenly way; from Xian to Ji Ji and Wei Ji, it discusses human affairs. Human planning belongs to the human side, while divine planning belongs to the heavenly side; when heaven and humanity plan together and both say it is feasible, the matter will succeed and bring good fortune.

變從時而便天下之事，不失禮之大經。變從時而順天下之理，不失義之大權者，君子之道也。五星之說自甘公石公始也。人智強則物智弱。莊子著盜跖篇，所以明至惡，雖聖賢亦莫能化，蓋上智與下愚不移故也。魯國之儒一人者，謂孔子也。

Adapting to the times while making things convenient for the world without losing the great principle of ritual; adapting to the times while making the principles of the world harmonious without losing the great authority of righteousness: this is the way of the gentleman. The theory of the five elements—metal, wood, water, fire, and earth—began with Gan Gong and Shi Gong. When human skill becomes strong, the skill of things becomes weak. Zhuangzi wrote the chapter "Thief Che" to illustrate that even the virtuous cannot reform the extremely wicked, because the superior wise and the inferior foolish are unchangeable. The phrase "there is only one Confucian in Lu" refers to Confucius himself.

天下之事始過於重猶卒於輕，始過於厚猶卒於薄，況始以輕始以薄者乎？故鮮失之重，多失之輕。鮮失之厚，多失之薄。是以君子不患過乎重，常患過乎輕，不患過乎厚常患過乎薄也。莊子齊物未免較量，較量則爭，爭則不平，不平則不和。無思無為者，神妙致一之地也，聖人以此洗心，退藏於密。當仁不讓於師者，進仁之道也。

All things in the world, if begun with excessive weight, will eventually become light; if begun with excessive thickness, will eventually become thin; and how much more so if they are begun with lightness and thinness? Therefore, people rarely fail by being too heavy, but mostly by being too light; rarely fail by being too thick, but mostly by being too thin. Therefore, the gentleman does not worry about being too heavy, but worries about being too light; does not worry about being too generous, but worries about being too stingy. Zhuangzi's "Harmonizing Things" ultimately cannot avoid comparison; once there is comparison, there is contention; once there is contention, there is injustice; once there is injustice, there is discord. "No thought, no action" is the profound and unified state, which the sage uses to purify the mind and retreat into the quiet and hidden place. "Acting with righteousness without yielding to the teacher" is the path leading to benevolence.

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，能悔則無失也。此聖人所以錄於書末也。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。文中子曰。易樂者必多哀，輕施者必好奪，或曰，天下皆爭利棄義，吾獨若之何？子曰。舍其所爭，取其所棄，不亦君子乎？若此之類，理義之言也，心跡之判久矣，若此之類，造化之言也。

Qin Mu Gong failed in his campaign against Zheng, yet left behind words of regret and self-vow, which is not merely the conduct of a hegemon, but approaches the way of the king. To repent and correct oneself means there is no great fault, which is why the sage included the "Qin Shi" at the end of the "Shang Shu." Liu Xuan asked what "wu wei" means. The answer said: when one speaks at the right time, people do not tire of his words; when one laughs at the right time, people do not tire of his laughter; when one takes what is appropriate to righteousness, people do not tire of his taking: this is called "wu wei." Weng Tong said: those who are too easily happy will surely suffer much sorrow; those who give freely will surely love to take by force. Someone asked: since everyone in the world is competing for profit and abandoning righteousness, what should I do? Weng Tong said: abandon what everyone is competing for, and take up what everyone has abandoned; is that not the way of the gentleman? Such words are about reason and righteousness. The mind and its manifestations have been separated for a long time; when one speaks to this level, it is speaking about the workings of nature.

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。金需百鍊然後精，人亦如此。佛氏棄君臣父子夫婦之道，豈自然之理哉？

Zhuangzi's writing is bold and unrestrained, as seen in the story of the water crossing at Lüliang, where he expresses himself to the utmost. The chapter "Daozhi" discusses matters beyond help, where such people are beyond even the sages' ability to deal with. The chapter "Yufu" speaks of things that cannot be forced, where even the sages cannot impose their will. These statements precisely convey the principle of active and non-active action: acting in accordance with the way is non-active, while forcing action is active. Gold becomes pure only after being refined a hundred times; human beings are the same. The Buddha rejects the ways of sovereign and subject, father and son, husband and wife. Is this in accordance with the way of nature?

志於道者，統而言之，志者，潛心之謂也，德者，得於己，有形故有據，德主於仁，故曰依。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，素位而行之義也。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。

"The statement 'to have a mind set on the Dao' is a general summary: 'To have a mind set on' means to immerse one's heart deeply in it; 'to rely on virtue' refers to having actual attainment within oneself, something tangible and visible, hence 'to rely on virtue.' Virtue is centered on benevolence, so it follows by saying 'to rely on benevolence.' Zhuangzi says: even if a cook does not cook, the chief priest will not cross over the wine vessels and ritual implements to take his place. This precisely reflects the meaning of a gentleman 'not thinking beyond his position,' content with his proper place and acting accordingly. When Jin State's Hu Shegu killed Yang Chufu, the Spring and Autumn Annals recorded it as 'Jin killed its大夫 Yang Chufu,' because the words were leaked from above; if the ruler is careless with secrecy, he will lose his ministers, hence it is recorded as the state killing him.

人得中和之氣則剛柔均，陽多則偏剛,陰多則偏柔。作易者其知盜乎？聖人知天下萬物之理而一以貫之。以尊臨卑曰臨，以上觀下曰觀。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，心必先期，固不化我，有己也。記問之學未足以為事業。學在不止，故王通云，沒身而已。

Human beings receive the harmonious vital energy, so the qualities of firmness and softness are balanced. If yang energy is excessive, it tends toward firmness; if yin energy is excessive, it tends toward softness. The statement "The author of the Book of Changes probably understood the principle of theft" suggests that the sage comprehends the principles of all things in the universe and can apply them consistently. To hold a high position while governing the lowly is called "governing by presence." To observe from above and look down upon below is called "observation." The four principles of "no arbitrary assumption, no absolute certainty, no stubbornness, no self-centeredness" are combined as one, but when separated, they are two; when combined again, they are two, but when separated again, they are four. They originate from "having an intention" and culminate in "having a self." Once there is an intention, there is certainty, and certainty arises from intention. Once there is stubbornness, there is self-centeredness, and self-centeredness arises from stubbornness. Having an intention means the mind is already expecting something. Stubbornness means having one's own private interests. Merely relying on memorization and hearing is insufficient for achieving great deeds. Learning is valuable only when it never stops, so Wang Tong said: never stop until death.