Chapter Sixty-One: Observing Things

太陽之體數十，太陰之體數十二；少陽之體數十，少陰之體數十二；少剛之體數十，少柔之體數十二；太剛之體數十，太柔之體數十二。進太陽、少陽、太剛、少剛之體數，退太陰、少陰、太柔、少柔之體數，是謂太陽、少陽、太剛、少剛之用數；進太陰、少陰、太柔、少柔之體數，退太陽、少陽、太剛、少剛之體數，是謂太陰、少陰、太柔、少柔之用數。

The "body number" of the Sun is ten, and the "body number" of the Moon is twelve; the "body number" of the Lesser Yang is ten, and the "body number" of the Lesser Yin is twelve; the "body number" of the Lesser Strength is ten, and the "body number" of the Lesser Softness is twelve; the "body number" of the Great Strength is ten, and the "body number" of the Great Softness is twelve. Here, the Sun, Moon, Lesser Yang, and Lesser Yin are the four celestial trigrams, corresponding to the Sun, Moon, Star, and Constellation. The Great Strength, Great Softness, Lesser Strength, and Lesser Softness are the four earthly trigrams, corresponding to Fire, Water, Stone, and Earth. All yang and strength trigrams take the number ten, which corresponds to the ten heavenly stems; all yin and softness trigrams take the number twelve, which corresponds to the twelve earthly branches. When the body numbers of the Sun, Lesser Yang, Great Strength, and Lesser Strength are added, and the body numbers of the Moon, Lesser Yin, Great Softness, and Lesser Softness are subtracted, the result is called the "operational number" of the Sun, Lesser Yang, Great Strength, and Lesser Strength. Conversely, when the body numbers of the Moon, Lesser Yin, Great Softness, and Lesser Softness are added, and the body numbers of the Sun, Lesser Yang, Great Strength, and Lesser Strength are subtracted, the result is called the "operational number" of the Moon, Lesser Yin, Great Softness, and Lesser Softness.

太陽、少陽、太剛、少剛之體數一百六十，太陰、少陰、太柔、少柔之體數一百九十二，太陽、少陽、太剛、少剛之用數一百一十二，太陰、少陰、太柔、少柔之用數一百五十二。以太陽、少陽、太剛、少剛之用數，唱太陰、少陰、太柔、少柔之用數，是謂日月星辰之變數；以太陰、少陰、太柔、少柔之用數，和太陽、少陽、太剛、少剛之用數，是謂水火土石之化數。日月星辰之變數一萬七千二十四，謂之動數；水火土石之化數一萬七千二十四，謂之植數。再唱和日月星辰水火土石之變化通數二萬八千九百八十一萬六千五百七十六，謂之動植通數。

The total numbers of the four yang and yang rigidity are 160, and the total numbers of the four yin and yin softness are 192. The numbers used for the four yang and yang rigidity are 112, and the numbers used for the four yin and yin softness are 152. The calculation is as follows: the four yang and yang rigidity each have a value of 10, adding up to 40, then multiplied by four to get 160; the four yin and yin softness each have a value of 12, adding up to 48, then multiplied by four to get 192; subtracting 48 from 160 leaves 112; subtracting 40 from 192 leaves 152. Using the numbers of the four yang and yang rigidity to 'sing' (initiate) the numbers of the four yin and yin softness, that is, multiplying 112 by 152, this is called the 'changing numbers' of the sun, moon, stars and planets; using the numbers of the four yin and yin softness to 'harmonize' (respond to) the numbers of the four yang and yang rigidity, it is still the product of these two numbers, called the 'transforming numbers' of water, fire, earth and stone. The changing numbers of the sun, moon, stars and planets are 17,224, called 'dynamic numbers', representing the total number of animals; the transforming numbers of water, fire, earth and stone are also 17,224, called 'static numbers', representing the total number of plants. Then multiplying the changing and transforming numbers of the sun, moon, stars and planets with those of water, fire, earth and stone, which is 17,224 multiplied by itself, resulting in 28,981,6576, called 'the common numbers of dynamic and static'.

日月星辰者，變乎暑寒晝夜者也。水火土石者，化乎雨風露雷者也。暑寒晝夜者，變乎性情形體者也；雨風露雷者，化乎走飛草木者也。暑變飛走草木之性，寒變飛走草木之情，晝變飛走草木之形，夜變飛走草木之體。雨化性情形體之走，風化性情形體之飛，露化性情形體之草，雷化性情形體之木。性情形體者，本乎天者也；飛走草木者，本乎地者也。本乎天者，分陰分陽之謂也；本乎地者，分柔分剛之謂也。夫分陰分陽分柔分剛者，天地萬物之謂也。備天地萬物者，人之謂也。

The sun, moon, stars, and constellations in the heavens generate below the heat, cold, day, and night: the sun produces heat, the moon produces cold, the stars produce day, and the constellations produce night. The water, fire, earth, and stone on the earth generate below rain, wind, dew, and thunder: water becomes rain, fire becomes wind, earth becomes dew, and stone becomes thunder. Heat, cold, day, and night further transform into the "nature, emotion, form, and body" of all things; rain, wind, dew, and thunder further generate the four categories of living beings: walking animals, flying birds, grass, and trees. Separately, heat produces the "nature" of flying birds, walking animals, and grass and trees, cold produces their "emotion," day produces their "form," and night produces their "body." Rain generates walking animals with nature, emotion, form, and body, wind generates flying birds, dew generates all kinds of grass, and thunder generates forests and trees. The system of nature, emotion, form, and body originates from heaven; the system of flying, walking, grass, and trees originates from earth. The system originating from heaven deals with the division of yin and yang; the system originating from earth deals with the division of softness and strength. The division of yin and yang, and the division of softness and strength, refer to the heavens and the earth and all things within them; and the one who can embody all the heavens and the earth within himself is the human being.

有日日之物者也，有日月之物者也，有日星之物者也，有日辰之物者也。有月日之物者也，有月月之物者也，有月星之物者也，有月辰之物者也。有星日之物者也，有星月之物者也，有星星之物者也，有星辰之物者也。有辰日之物者也，有辰月之物者也，有辰星之物者也，有辰辰之物者也。

Among all things, there are those that correspond to "day-day," "day-moon," "day-star," and "day-branch"; there are also those that correspond to "moon-day," "moon-moon," "moon-star," and "moon-branch"; further, there are those that correspond to "star-day," "star-moon," "star-star," and "star-branch"; and also those that correspond to "branch-day," "branch-moon," "branch-star," and "branch-branch." This method pairs the four celestial phenomena—day, moon, star, and branch—two by two, with the first character as the main and the second as the auxiliary, resulting in sixteen categories. These are used to encompass all categories of things in the world.

日日物者，飛飛也；日月物者，飛走也；日星物者，飛木也；日辰物者，飛草也。月日物者，走飛也；月月物者，走走也；月星物者，走木也；月辰物者，走草也。星日物者，木飛也；星月物者，木走也；星星物者，木木也；星辰物者，木草也。辰日物者，草飛也；辰月物者，草走也；辰星物者，草木也；辰辰物者，草草也。

These sixteen categories correspond to: "Day-Day" things are flying creatures among flying ones, "Day-Moon" things are running creatures among flying ones, "Day-Star" things are wooden creatures among flying ones, and "Day-Chronicle" things are grassy creatures among flying ones; "Moon-Day" things are flying creatures among running ones, "Moon-Moon" things are running creatures among running ones, "Moon-Star" things are wooden creatures among running ones, and "Moon-Chronicle" things are grassy creatures among running ones; "Star-Day" things are flying creatures among wooden ones, "Star-Moon" things are running creatures among wooden ones, "Star-Star" things are wooden creatures among wooden ones, and "Star-Chronicle" things are grassy creatures among wooden ones; "Chronicle-Day" things are flying creatures among grassy ones, "Chronicle-Moon" things are running creatures among grassy ones, "Chronicle-Star" things are wooden creatures among grassy ones, and "Chronicle-Chronicle" things are grassy creatures among grassy ones. The basis for this layer is that Day corresponds to flying creatures, Moon corresponds to running animals, Star corresponds to trees, and Chronicle corresponds to grasses. Therefore, after the four celestial symbols are paired, they fall to the earth and are specifically categorized as four types of living things: flying, running, grass, and wood.

有皇皇之民者也，有皇帝之民者也，有皇王之民者也，有皇伯之民者也。有帝皇之民者也，有帝帝之民者也，有帝王之民者也，有帝伯之民者也。有王皇之民者也，有王帝之民者也，有王王之民者也，有王伯之民者也。有伯皇之民者也，有伯帝之民者也，有伯王之民者也，有伯伯之民者也。

On the human side, they are also arranged in order: there are the people of "Huanghuang", the people of "Huangdi", the people of "Huangwang", and the people of "Huangbo"; there are the people of "Dihuang", the people of "Didi", the people of "Dingwang", and the people of "Dibao"; there are the people of "Wanghuang", the people of "Wangdi", the people of "Wangwang", and the people of "Wangbo"; there are the people of "Bohuang", the people of "Bodi", the people of "Bowing", and the people of "Bobo". This is pairing the four ranks of human officials—Huang, Di, Wang, and Bo—in pairs, just as the previous method paired the sun, moon, and stars to produce sixteen categories of things, thereby creating sixteen categories to fully classify all people under heaven.

皇皇民者，士士也；皇帝民者，士農也；皇王民者，士工也；皇伯民者，士商也。帝皇民者，農士也；帝帝民者，農農也；帝王民者，農工也；帝伯民者，農商也。王皇民者，工士也；王帝民者，工農也；王王民者，工工也；王伯民者，工商也。伯皇民者，商士也；伯帝民者，商農也；伯王民者，商工也；伯伯民者，商商也。

These sixteen categories correspond to the four classes of people: "Huanghuang" refers to the outstanding scholar, "Huangdi" refers to the farmer among scholars, "Huangwang" refers to the artisan among scholars, and "Huangbo" refers to the merchant among scholars; "Dihuang" refers to the scholar among farmers, "Didi" refers to the farmer among farmers, "Diwang" refers to the artisan among farmers, and "Dibo" refers to the merchant among farmers; "Wanghuang" refers to the scholar among artisans, "Wangdi" refers to the farmer among artisans, "Wangwang" refers to the artisan among artisans, and "Wangbo" refers to the merchant among artisans; "Bohuang" refers to the scholar among merchants, "Bodi" refers to the farmer among merchants, "Bowang" refers to the artisan among merchants, and "Bobo" refers to the merchant among merchants. This level of classification is: Huang corresponds to scholars, Di corresponds to farmers, Wang corresponds to artisans, and Bo corresponds to merchants—governance proceeds from high to low, and the people's occupations proceed from scholars to merchants in sequence.

飛飛物者，性性也；飛走物者，性情也；飛木物者，性形也；飛草物者，性體也。走飛物者，情性也；走走物者，情情也；走木物者，情形也；走草物者，情體也。木飛物者，形性也；木走物者，形情也；木木物者，形形也；木草物者，形體也。草飛物者，體性也；草走物者，體情也；草木物者，體形也；草草物者，體體也。

Going one layer deeper, the flying and walking correspond to the nature and emotion, while the wood and grass correspond to form and body. Thus, the things that fly within flying are the nature within nature; the things that walk within flying are the emotion within nature; the things that wood within flying are the form within nature; and the things that grass within flying are the body within nature. The things that fly within walking are the nature within emotion; the things that walk within walking are the emotion within emotion; the things that wood within walking are the form within emotion; and the things that grass within walking are the body within emotion. The things that fly within wood are the nature within form; the things that walk within wood are the emotion within form; the things that wood within wood are the form within form; and the things that grass within wood are the body within form. The things that fly within grass are the nature within body; the things that walk within grass are the emotion within body; the things that wood within grass are the form within body; and the things that grass within grass are the body within body.

士士民者，仁仁也；士農民者，仁禮也；士工民者，仁義也；士商民者，仁智也。農士民者，禮仁也；農農民者，禮禮也；農工民者，禮義也；農商民者，禮智也。工士民者，義仁也；工農民者，義禮也；工工民者，義義也；工商民者，義智也。商士民者，智仁也；商農民者，智禮也；商工民者，智義也；商商民者，智智也。

If we go one layer deeper among the four classes of people, each corresponds to one of the four virtues: the scholar corresponds to "benevolence," the farmer to "ritual," the artisan to "righteousness," and the merchant to "wisdom." Thus, a scholar among scholars is benevolence within benevolence; a farmer among scholars is benevolence within ritual; an artisan among scholars is benevolence within righteousness; and a merchant among scholars is benevolence within wisdom. A scholar among farmers is ritual within benevolence; a farmer among farmers is ritual within ritual; an artisan among farmers is ritual within righteousness; and a merchant among farmers is ritual within wisdom. A scholar among artisans is righteousness within benevolence; a farmer among artisans is righteousness within ritual; an artisan among artisans is righteousness within righteousness; and a merchant among artisans is righteousness within wisdom. A scholar among merchants is wisdom within benevolence; a farmer among merchants is wisdom within ritual; an artisan among merchants is wisdom within righteousness; and a merchant among merchants is wisdom within wisdom.

飛飛之物一之一，飛走之物一之十，飛木之物一之百，飛草之物一之千。走飛之物十之一，走走之物十之十，走木之物十之百，走草之物十之千。木飛之物百之一，木走之物百之十，木木之物百之百，木草之物百之千。草飛之物千之一，草走之物千之十，草木之物千之百，草草之物千之千。

These sixteen categories each have their own numerical values: flying corresponds to one, moving corresponds to ten, wood corresponds to hundred, and grass corresponds to thousand. The more agile and noble the category, the smaller its numerical value; the more abundant and humble the category, the larger its numerical value. Therefore, the flying within flying is one times one, the moving within flying is one times ten, the wood within flying is one times hundred, and the grass within flying is one times thousand; the flying within moving is ten times one, the moving within moving is ten times ten, the wood within moving is ten times hundred, and the grass within moving is ten times thousand; the flying within wood is hundred times one, the moving within wood is hundred times ten, the wood within wood is hundred times hundred, and the grass within wood is hundred times thousand; the flying within grass is thousand times one, the moving within grass is thousand times ten, the wood within grass is thousand times hundred, and the grass within grass is thousand times thousand.

士士之民一之一，士農之民一之十，士工之民一之百，士商之民一之千。農士之民十之一，農農之民十之十，農工之民十之百，農商之民十之千。工士之民百之一，工農之民百之十，工工之民百之百，工商之民百之千。商士之民千之一，商農之民千之十，商工之民千之百，商商之民千之千。

The numbers corresponding to the four classes of people are also determined in the same way: the scholar is paired with one, the farmer with ten, the artisan with a hundred, and the merchant with a thousand. Thus, among the scholars, the scholar is one of one, the farmer is one of ten, the artisan is one of a hundred, and the merchant is one of a thousand; among the farmers, the scholar is ten of one, the farmer is ten of ten, the artisan is ten of a hundred, and the merchant is ten of a thousand; among the artisans, the scholar is a hundred of one, the farmer is a hundred of ten, the artisan is a hundred of a hundred, and the merchant is a hundred of a thousand; among the merchants, the scholar is a thousand of one, the farmer is a thousand of ten, the artisan is a thousand of a hundred, and the merchant is a thousand of a thousand.

一一之飛當兆物，一十之飛當億物，一百之飛當萬物，一千之飛當千物。十一之走當億物，十十之走當萬物，十百之走當千物，十千之走當百物。百一之木當萬物，百十之木當千物，百百之木當百物，百千之木當十物。千一之草當千物，千十之草當百物，千百之草當十物，千千之草當一物。

The value of each position is fixed, and the quantity of various things corresponds accordingly, in inverse proportion. The larger the position, the smaller the quantity it can represent. Starting from zhaoguan (myriad of myriad), yiyi (myriad), wan (ten thousand), qian (thousand), bai (hundred), shi (ten), and finally one, there are seven levels. A bird corresponding to one of zhaoguan can equal a quantity of zhaoguan, a bird corresponding to ten of zhaoguan can equal a quantity of yiyi, a bird corresponding to one hundred of zhaoguan can equal a quantity of wan, and a bird corresponding to one thousand of zhaoguan can equal a quantity of qian. A beast corresponding to one of ten can equal a quantity of yiyi, a beast corresponding to ten of ten can equal a quantity of wan, a beast corresponding to one hundred of ten can equal a quantity of qian, and a beast corresponding to one thousand of ten can equal a quantity of bai. A tree corresponding to one of bai can equal a quantity of wan, a tree corresponding to ten of bai can equal a quantity of qian, a tree corresponding to one hundred of bai can equal a quantity of bai, and a tree corresponding to one thousand of bai can equal a quantity of shi. A plant corresponding to one of qian can equal a quantity of qian, a plant corresponding to ten of qian can equal a quantity of bai, a plant corresponding to one hundred of qian can equal a quantity of shi, and a plant corresponding to one thousand of qian can equal only one item.

一一之士當兆民，一十之士當億民，一百之士當萬民，一千之士當千民。十一之農當億民，十十之農當萬民，十百之農當千民，十千之農當百民。百一之工當萬民，百十之工當千民，百百之工當百民，百千之工當十民。千一之商當千民，千十之商當百民，千百之商當十民，千千之商當一民。

A single soldier is equivalent to a million people; ten soldiers are equivalent to ten million people; a hundred soldiers are equivalent to a hundred thousand people; a thousand soldiers are equivalent to a thousand people. A single farmer is equivalent to a hundred million people; ten farmers are equivalent to a million people; a hundred farmers are equivalent to a thousand people; a thousand farmers are equivalent to a hundred people. A single worker is equivalent to a hundred thousand people; ten workers are equivalent to a thousand people; a hundred workers are equivalent to a hundred people; a thousand workers are equivalent to ten people. A single merchant is equivalent to a thousand people; ten merchants are equivalent to a hundred people; a hundred merchants are equivalent to ten people; a thousand merchants are equivalent to one person.

為一一之物能當兆物者，非巨物而何？為一一之民能當兆民者，非巨民而何？為千千之物能分一物者，非細物而何？為千千之民能分一民者，非細民而何？固知物有大小，民有賢愚。移昊天生兆物之德而生兆民，則豈不謂至神者乎？移昊天養兆物之功而養兆民，則豈不謂至聖者乎？吾而今而後，知踐形為大。非大聖大神之人，豈有不負於天地者乎？

A single thing that can match the value of a myriad of things is not the greatest thing, what else could it be? A single person who can match the value of a myriad of people is not the greatest person, what else could it be? A thing that is part of a thousand things but only gets a fraction of one thing's worth is not the smallest thing, what else could it be? A person who is part of a thousand people but only gets a fraction of one person's worth is not the smallest person, what else could it be? Therefore, things have differences in size, and people have distinctions in wisdom and foolishness. Who could transfer the benevolence of the vast heavens that nurtures myriad things to nurture myriad people? Such a person could be called "the Supreme God." Who could transfer the function of the vast heavens that sustains myriad things to sustain myriad people? Such a person could be called "the Supreme Sage." From now on, I have come to understand what Mencius said in "The Complete Heart" chapter: "To fulfill the form given by heaven completely" — to fully realize the inherent nature contained within the body given by heaven — is the greatest matter in the world. Without being a great sage or a supreme god, who would not辜负 the heavens and the earth?

夫所以謂之觀物者，非以目觀之也。非觀之以目，而觀之以心也。非觀之以心，而觀之以理也。天下之物莫不有理焉，莫不有性焉，莫不有命焉。所以謂之理者，窮之而後可知也；所以謂之性者，盡之而後可知也；所以謂之命者，至之而後可知也。此三知者，天下之真知也，雖聖人無以過之也。而過之者，非所以謂之聖人也。

What is meant by "observing things" (观物) is not using the eyes to see; it is not using the eyes, but using the mind to see; and it is not merely using the mind, but using "principle" (理) to see. All things in the world contain "principle," contain "nature," and contain "destiny." To know "principle," one must investigate it thoroughly; to know "nature," one must fully express it; to know "destiny," one must reach it directly. This is exactly what the "Sayings of the Trigrams" (说卦) says: "Investigate principle thoroughly, exhaust nature completely, and thus reach destiny." This knowledge of the three—principle, nature, and destiny—is the true knowledge in the world. Even sages cannot surpass it. If anyone claims to have surpassed it, then he is not worthy to be called a sage.

夫鑑之所以能為明者，謂其能不隱萬物之形也。雖然鑑之能不隱萬物之形，未若水之能一萬物之形也。雖然水之能一萬物之形，又未若聖人之能一萬物之情也。聖人之所以能一萬物之情者，謂其聖人之能反觀也。所以謂之反觀者，不以我觀物也。不以我觀物者，以物觀物之謂也。既能以物觀物，又安有我於其間哉？是知我亦人也，人亦我也，我與人皆物也。

A mirror is called clear because it can reflect the forms of all things without concealment. However, although a mirror can reflect the forms of all things without concealment, it is still inferior to water, which can reflect the forms of all things as one, blending them into a unified whole. Although water can blend the forms of all things into one, it is still inferior to a sage, who can blend the feelings of all things into one. The reason a sage can blend the feelings of all things is because he can "reverse observation." Reverse observation means not viewing things from the perspective of "I." Not viewing things from the perspective of "I" means viewing things from the perspective of the things themselves. If one can view things from the perspective of the things themselves, then where is the "I" in between? From this we can understand: I am a person, a person is me, and I and others are all things.

此所以能用天下之目為己之目，其目無所不觀矣；用天下之耳為己之耳，其耳無所不聽矣；用天下之口為己之口，其口無所不言矣；用天下之心為己之心，其心無所不謀矣。夫天下之觀，其於見也不亦廣乎？天下之聽，其於聞也不亦遠乎？天下之言，其於論也不亦高乎？天下之謀，其於樂也不亦大乎？夫其見至廣，其聞至遠，其論至高，其樂至大，能為至廣至遠至高至大之事，而中無一為焉，豈不謂至神至聖者乎？非惟吾謂之至神至聖，而天下亦謂之至神至聖。非惟一時之天下謂之至神至聖，而千萬世之天下亦謂之至神至聖者乎？過此以往，未之或知也已。

Only in this way could the sage use the eyes of all under heaven as his own eyes, so nothing would be beyond his sight; use the ears of all under heaven as his own ears, so nothing would be beyond his hearing; use the mouths of all under heaven as his own mouth, so nothing would be beyond his speech; use the hearts of all under heaven as his own heart, so nothing would be beyond his planning. Using the eyes of all under heaven, is his vision not extremely broad? Using the ears of all under heaven, is his hearing not extremely far-reaching? Using the mouths of all under heaven, is his speech not extremely refined? Using the hearts of all under heaven, is his planning not extremely grand? His vision is extremely broad, his hearing extremely far-reaching, his speech extremely refined, his planning extremely grand. He can accomplish the most extensive, the most distant, the highest, and the greatest things, yet his heart contains nothing that he deliberately does. Is this not what may be called "the most divine and sacred"? Not only do I call him the most divine and sacred, but all under heaven also call him the most divine and sacred; not only does the present world call him the most divine and sacred, but even the world of a thousand generations hence will also call him the most divine and sacred. As for the realm beyond this, it is beyond my knowledge.

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 Great Treatise of the Book of Changes uses the numbers one, three, five, seven, and nine as the heavenly numbers, totaling five; and the numbers two, four, six, eight, and ten as the earthly numbers, also totaling five. Together, they form the complete number ten. The heavens generate the four trigrams from the number one, and the earth also generates the four trigrams from the number one. The four generated are tangible, while the original one, which is the source, is intangible. This is called the dual extremes of "being" and "non-being." The heavenly number is four in form but only three are actually used, leaving one unused; the earthly number is also four in form but only three are actually used, leaving one unused. Therefore, the intangible one is used to represent "nature," and the unused one is used to represent "the Way." The three actually used represent the three elements of heaven, earth, and humanity.

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。

In terms of the numerical structure, Heaven has four seasons, each season consisting of four months, and each month consisting of forty days. Four multiplied by four gives sixteen, but each layer must subtract one portion. Therefore, in reality, each season has only three months, and each month has only thirty days. The four seasons are called "body numbers," while three months and thirty days are called "used numbers." Although the body number includes four parts, one part is always present but not used, so the used number only reaches three. Even when taken to the extreme, it does not exceed three times three, which is nine. 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。是以人之支體有四，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。

Large numbers are always insufficient, while small numbers often have a surplus. Why is this so? Because large things are invisible, while small things are visible. Therefore, the measure of time reaches four, the measure of the month reaches three, yet the day fills up to ten. The human body is the same: the limbs are only four, but the fingers are ten. The heavenly phenomena appear in the south and conceal themselves in the north; the visible limit in the south is six, and adding the surplus part makes seven. Humans are the same: they know what is in front of them, but are completely ignorant of what is behind them, and can only roughly attend to what is on the left and right.

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，猶晝之餘分在夜也。是以天三而地四，天有三辰，地有四行也。然地之大，且見且隱，其餘分之謂耶？

Heaven's fundamental number is four but its active use is three, while Earth's fundamental number is four but its active use is three. Heaven overcomes Earth and Earth overcomes Heaven; they mutually overcome each other, but the result of being overcome falls upon Earth, just as the extra part of daylight is accounted for in the night. Therefore, Heaven takes three and Earth takes four: among the four celestial phenomena of sun, moon, stars, and constellations, the constellations are invisible, so only the sun, moon, and stars are visible, making three. Among the four earthly elements of water, fire, soil, and stone, all four are present, hence they are called the four elements. However, Earth is so vast, yet it sometimes appears and sometimes disappears, which is probably what is meant by 'remainder' or 'excess'.

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 number of the subject moves through eight transformations, while the number of the object moves through six transformations. Therefore, among the eight trigrams, those that remain unchanged when viewed upside down are four (Qian, Kun, Kan, and Li). Those that transform into another trigram when viewed upside down form two pairs (Zhen and Gen, Xun and Dui). These four unchanged trigrams and two pairs of transformed trigrams make up six units of change, from which the eight trigrams are formed. In the case of the sixty-four hexagrams, there are eight trigrams that remain unchanged, and twenty-eight pairs that transform into another trigram. These eight unchanged trigrams and twenty-eight pairs of transformed trigrams make up thirty-six units of change, from which the sixty-four hexagrams are formed. Therefore, the lines end at six, the trigrams end at eight, the number of divination rods (cè shù) is exhausted at thirty-six, and the hexagrams reach their maximum at sixty-four. The trigrams are formed by eight, and when combined they become sixty-four; the lines are formed by six, and when combined they become three hundred eighty-four lines.

天有二正，地有二正，而共用二變以成八卦也。天有四正，地有四正，而共用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、離、坎為三十六卦之祖也，兌、震、巽、艮為二十八卦之祖也。

Heaven has two "correct" trigrams (Qian and Li), Earth has two correct trigrams (Kun and Kan). In addition, they share two sets of reversed and transformed trigrams, making up the eight trigrams in total. When applied to the sixty-four hexagrams, Heaven has four correct trigrams, Earth has four correct trigrams, and they share twenty-eight sets of reversed and transformed trigrams, making up the sixty-four hexagrams in total. In the smaller formation of the eight trigrams, there are four trigrams that remain correct without transformation, and two pairs of trigrams that are reversed and transformed, making a total of six trigrams. In the larger formation of the sixty-four hexagrams, there are eight trigrams that remain correct without transformation, and twenty-eight pairs of trigrams that are reversed and transformed, making a total of thirty-six trigrams. Qian, Kun, Li, and Kan are the ancestors of those thirty-six trigrams, while Dui, Zhen, Xun, and Gen are the ancestors of those twenty-eight pairs of transformed trigrams.

卦之正變共三十六，而爻有二百一十六，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、離、坎也；八者，並頤、中孚、大小過也；十二者，並兌、震、泰、既濟也。

The original hexagram and the resulting hexagram together total thirty-six. Each hexagram has six lines, so thirty-six multiplied by six gives two hundred and sixteen lines, which is exactly the number of lines in the hexagram of Qian (Heaven), known as the "use number" or "count of lines." Thirty-six minus four gives thirty-two, then minus four gives twenty-eight, and then minus four gives twenty-four. Therefore, the number of hexagrams is thirty-two, which is derived by removing four from thirty-six; the number of heavenly stems is twenty-eight, derived by removing eight from thirty-six; and the number of earthly branches is twenty-four, derived by removing twelve from thirty-six. The four removed are Qian, Kun, Li, and Kan. The eight removed are these four plus Yi (Repose), Zhongfú (Middle Trust), Da Guo (Great Overcoming), and Xiao Guo (Small Overcoming). The twelve removed are these eight plus Dui (Lake), Zhen (Thunder), Tai (Great Peace), and Ji Ji (Completion), including their opposing hexagrams.

乾七子，兌六子，離五子，震四子，巽三子，坎二子，艮一子，坤全陰，故無子。乾七子，坤六子，兌五子，艮四子，離三子，坎二子，震一子，巽陰剛，故無子。乾坤七變，是以晝夜之極不過七分也；兌艮六變，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。

According to the Earlier Heaven Trigrams in the order of Qian, Dui, Li, Zhen, Xun, Kan, Gen, and Kun, Qian can generate seven "Zi," Dui six, Li five, Zhen four, Xun three, Kan two, Gen one, and Kun, being purely yin and in the last position, generates none. If the trigrams are counted in pairs as Qian and Kun, Dui and Gen, Li and Kan, Zhen and Xun, then Qian generates seven "Zi," Kun six, Dui five, Gen four, Li three, Kan two, Zhen one, and Xun, being yin in the position below two yang, generates none. The pair Qian and Kun reaches seven, so the extremes of day and night are only seven parts; the pair Dui and Gen reaches six, so the moon only reaches six, and together they form twelve months; the pair Li and Kan reaches five, so the sun only reaches five, and together they form ten days (ten heavenly stems); the pair Zhen and Xun reaches four, so the body only reaches four, and together they form eight (eight trigrams).

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 Japanese use eight positions but actually employ only seven, omitting the position of Qian; the moon originally uses eight positions but employs only six, omitting the position of Dui; stars originally use eight positions but employ only five, omitting the position of Li; the hour (辰) originally uses eight positions but employs only four, omitting the position of Zhen; the day originally uses eight positions but the paired number only reaches seven, omitting the hexagram Tai. As for the moon starting from Dui, it is because the moon's movement is slower than the sun's, so twelve lunar months are often shorter than the number of days in a solar year, requiring an additional twelve days to make up the difference.

乾陽中陽，不可變，故一年止舉十二月也；震陰中陰，不可變，故一日十二時，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。

Heavenly Stem Qian represents Yang within Yang, pure and unmingled, with no possibility of further change, hence the twelve months of a year can be directly counted. Zhen represents Yin within Yin, also without further change, so the twelve hours of a day can only be calculated but not seen in form. Dui contains Yin within Yang, and Li contains Yang within Yin; both can undergo further change, hence the distinction between days and months. Therefore, the Yin numbers start from twelve (twelve Chens, twelve months), while the Yang numbers start from thirty (thirty days in a month). Within both, the basic numbers 'two' and 'six' are always preserved.

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。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。

When you mention the year, you see the month; when you mention the month, you see the day; when you mention the day, you see the hour. This is because the yang principle governs the yin. Therefore, the four transformations of heaven include the four transformations of earth, and the changes of the sun include the changes of the moon and the stars. Thus, one hexagram contains four hexagrams. The sun occupies one position, the moon one, the stars one, and the stars (or the celestial stems and earthly branches) one. The sun has four positions, the moon four, the stars four, and the stars four. Four multiplied by four makes sixteen positions. When these sixteen positions are completed in a cycle, the numbers of the sun and moon are exhausted.

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。衍而伸之，陽數常六，陰數常二。十有二變，而大小之運窮矣。

Heaven has four changes, Earth has four changes, and within each change there is a growing aspect and a declining aspect; four multiplied by four makes sixteen changes, and thus the numbers of Heaven and Earth are exhausted. The sun starts counting from one, the moon from two, the stars from three, and the constellations from four; when these are extended and developed, the numbers belonging to the Yang are always six, and those belonging to the Yin are always two. By following this pattern through twelve changes, the great cycles and small cycles are also 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，以二萬八千二百一十一兆九百九十萬七千四百五十六億為年，則大小運之數立矣。

Three hundred and sixty multiplied by itself becomes twelve million nine thousand six hundred; twelve million nine thousand six hundred multiplied by itself becomes one hundred sixty-seven billion nine thousand six hundred and sixteen thousand; one hundred sixty-seven billion nine thousand six hundred and sixteen thousand multiplied by itself becomes two thousand eight hundred and eleven trillion nine hundred ninety million seven thousand four hundred and fifty-six billion. Each layer is the previous layer multiplied by itself once, increasing step by step. (The "zhaog" used by Shao Yong refers to "billion billion," that is, ten thousand trillion.) Then take three hundred and sixty as "time," twelve million nine thousand six hundred as "day," one hundred sixty-seven billion nine thousand six hundred and sixteen thousand as "month," and two thousand eight hundred and eleven trillion nine hundred ninety million seven thousand four hundred and fifty-six billion as "year," and thus the numbers for great cycles and small cycles are established.

二萬八千二百一十一兆九百九十萬七千四百五十六億，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，隨大運之消長，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 million nine hundred and ninety million seven thousand four hundred and fifty-six, into twelve parts, with the first six parts representing growth and the last six parts representing decline, corresponding to the twelve months of a year, with a cycle of three hundred and sixty days. Divide the number of months, one hundred and sixty-seven million nine thousand six hundred and sixteen thousand, into thirty parts, corresponding to the thirty days of a month, with a cycle of sixty days following the changes of 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 cycle of six days. Three hundred and sixty is used to correspond to the number of moments in an hour, following the changes of the small cycle, exactly matching the moments of day and night.

十六變之數，去其交數，取其用數，得二萬八千二百一十一兆九百九十萬七千四百五十六億，分為十二，前六限為長，後六限為消，每限得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衍開一分，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，進三百六十日也。其退亦若是矣。

The total number obtained from sixteen changes, after subtracting the "intersecting number" that is not used, leaves the actual number used, which is two billion eight hundred and twenty-one million one hundred and ten thousand nine hundred and ninety million seven hundred and forty-five thousand six hundred and sixty. This number is divided into twelve parts, with the first six parts representing growth and the last six parts representing decline. Each part equals one hundred and sixty-seven billion nine hundred and sixty-one million six hundred and sixteen. Each one hundred and sixty-seven billion nine hundred and sixty-one million six hundred and sixteen is considered as one fraction, and each fraction corresponds to sixty days. Six fractions correspond to three hundred and sixty days. There is also a remaining fraction, so it is extended to seven fractions, still counting as three hundred and sixty days. The calculation for the declining side is done in the same way.

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，數有朓肭，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。餘二千一百六十年，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，凡六十而成三百六十六日也。

This number, twelve thousand nine hundred and sixty, has ten parts. Three parts are removed as the 'intersecting number', and seven parts are used as the 'utilized number'. The utilized number originally comes from three, is sufficient for six, and then adds an extra part, making it seven. Taking seven tenths of it gives nine thousand and seventy-two years. Halving it gives four thousand five hundred and sixty years, which is used to advance six days. Since days are divided into day and night, and the moon's movement has 'tiao' and 'nu' (the moon appears earlier than expected at the end of the month is called 'nu', and appears later than expected at the beginning of the month is called 'tiao'), combining both sides forms twelve days. Calculating by advancing one day every three thousand six hundred years, four thousand three hundred and twenty years exactly advance twelve days. The remaining two thousand one hundred and sixty years advance six parts. Adding this to the two thousand one hundred and sixty years from the intersecting number, it totals twelve parts, which is used for intercalation. Therefore, the changes in the small cycle, when completed sixty, form a year of three hundred and sixty-six days.

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，而終於二百四秭六千九百八十萬七千三百八十一垓五千四百九十一萬八千四百九十九兆七百二十萬億也。

Heaven uses "body" as its governing principle, so it proceeds through eight transformations and ends at sixteen; Earth uses "function" as its distribution, so it proceeds through six transformations and ends at twelve. Heaven starts counting from one and continues until it reaches seven zhi, nine hundred and fifty-eight thousand six hundred and eleven gai, nine thousand nine hundred and forty-six million four thousand eight jing, eight thousand four hundred and thirty-nine million one hundred and thirty-six zhao. Earth starts counting from twelve and continues until it reaches two hundred and four zhi, six million nine hundred and eighty thousand seven hundred and thirty-eight gai, five thousand four hundred and ninety-one million eight thousand four hundred and ninety-nine zhao, seven hundred and twenty trillion. These two large numbers represent the ultimate limits of Heaven's and Earth's numbers respectively.

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，以當二萬八千一百一十一兆九百九十萬七千四百五十六億之數也；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。（如一分為十二，十二分為三百六十也。）

The hexagram Qian consists of six pure yang lines, represented as 'one'. The fifth line of Qian, when divided from yang into yin, forms the hexagram Dàyǒu, used to represent the number 360. The fourth line, when further divided, forms the hexagram Xiaoxù, used to represent the number 12,9600. The third line, when divided again, forms the hexagram Lǚ, used to represent the number 167,96160000. The second line, when divided again, forms the hexagram Tongren, used to represent the number 28,111,990,745,600,000,000 (the original text here reads '111 zhi', differing from the previous '211 zhi', likely due to a transmission error). The first line, when divided again, forms the hexagram Gòu, used to represent the number 7 zhi 9,586,610,110,994,648,439,193,600,000,000,000. This method is called 'fractioning': dividing a large number into smaller ones, with each line being divided from top to bottom in sequence. Thus, the yang number is matched accordingly. (For example, one is divided into twelve, and twelve is further divided into 360.)

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，當五萬五千九百八十七萬二千之數也；八生十六為臨，當九百四十三千六百九十九萬六千九百一十五億二千萬之數也；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。

In reverse, starting from the坤 (Earth) trigram and growing upwards: one gives rise to two, forming the Guai hexagram, corresponding to the number twelve; two gives rise to four, forming the Da Zhuang hexagram, corresponding to the number four million three hundred twenty; four gives rise to eight, forming the Tai hexagram, corresponding to the number fifty-five thousand nine hundred eighty-seven thousand two hundred; eight gives rise to sixteen, forming the Lin hexagram, corresponding to the number nine hundred forty-three thousand six hundred ninety-nine thousand six hundred ninety-one million five thousand two hundred million; sixteen gives rise to thirty-two, forming the Fu hexagram, corresponding to the number twenty-six million five hundred twenty-eight thousand eight hundred seventy myriad three thousand six hundred sixty-four thousand eight hundred eighty-eight hundred million two thousand nine hundred forty-seven million nine hundred seventy-three thousand one hundred twenty million; thirty-two gives rise to sixty-four, forming the Kun hexagram, which corresponds to the number 'wuji' (no extreme), too vast to measure. This process is called 'chang shu' (growth number): transforming small into large, with each line growing from the bottom up, so the yin number is used to match it.

天自臨以上，地自師以上，運數也。天自同人以下，地自遁以下，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。

On this diagram of numbers, the heavenly side from the Qian hexagram upwards and the earthly side from the Shī hexagram upwards belong to "yùn shù" (movement numbers); the heavenly side from the Tóngrén hexagram downwards and the earthly side from the Dùn hexagram downwards belong to "nián shù" (year numbers). "Yùn shù" is governed by heaven, while "nián shù" is governed by earth. The heavenly side from the Bēn hexagram upwards and the earthly side from the Gèn hexagram upwards belong to "yòng shù" (used numbers), which are actually in use; the heavenly side from the Míngyí hexagram downwards and the earthly side from the Pǐ hexagram downwards belong to "jiāo shù" (intersecting numbers), which are not used at the boundary. The heavenly side from the Zhèn hexagram upwards and the earthly side from the Jìn hexagram upwards belong to "yǒu shù" (existing numbers), which can still be measured; the heavenly side from the Yì hexagram downwards and the earthly side from the Yù hexagram downwards belong to "wú shù" (non-numerical numbers), which can no longer be calculated.

天之有數，起乾而止震，餘入於無者，天辰不見也。地去一而起十二者也，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。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。

The numbers that can be measured on the heavenly side start from the Qian trigram and end with the Zhen trigram, while the rest fall into the category of "nothingness." This corresponds to the fact that the "Chen" element in the four heavenly trigrams is invisible. On the earthly side, the count starts from twelve after removing "one," which corresponds to the fact that the "Fire" element in the four earthly trigrams often remains hidden. Therefore, heaven takes form as its foundation but always keeps the foundation hidden; earth takes function as its foundation but always keeps the function concealed. A year has only three months, and a month has only thirty days, because the number corresponding to "Chen" has been subtracted. Thus, in the sixty-four hexagrams formed by the eight trigrams overlapping eight times, there are eight that remain unchanged when reversed, while the remaining seven groups are changeable. Seven multiplied by eight gives fifty-six, and the reasoning comes from this as well.

有地然後有二，有二然後有晝夜。二三以變，錯綜而成，故《易》以二為生數，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。

First there was the earth, then the number two came into being; with the emergence of two, there was a distinction between day and night. Two and three interact and intermingle with each other, thus generating all numbers. Therefore, the Book of Changes uses two as the originating number, starting the count from twelve, while one itself is not considered a number. Though it is not a number, all numbers depend on it for their origin. The celestial bodies move without ceasing, originally having no distinction between day and night; it was only when humans lived on the earth that day and night became differentiated. Therefore, the Book of Changes takes the numbers used on the earth as the numbers used by humans.

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。

Yang lines represent the number of daylight, and Yin lines represent the number of darkness. Heaven and Earth connect head to tail, and Yin and Yang intermingle with each other, so day and night are interwoven, and hardness and softness are intertwined. In the seasons of spring and summer, Yang energy is abundant, so the number of Yang lines is greater and the number of Yin lines is smaller; in the seasons of autumn and winter, Yin energy is abundant, so the number of Yang lines is smaller and the number of Yin lines is greater. The number of Yang and Yin lines in a hexagram corresponds to the length of day and night in a year.

體數之策，三百八十四。去乾坤離坎之策，為用數三百六十。體數之用，二百七十。去乾與離坎之策，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。蓋陽去離而用乾，陰去坤而用坎也。

The total number of策 (counting units) is 384, which is the sum of six lines for each of the sixty-four hexagrams. After subtracting the 24策 of the four trigrams Qian, Kun, Li, and Kan, the remaining 360 is called the "useful number." Among the total body number, actually used is 270; after subtracting the策 numbers of Qian and Li and Kan, the remaining 252 is called the "useful number of the useful." Among these 270, 156 belong to Yang and 114 to Yin. After removing the策 number of Li, there are 152 Yang and 112 Yin, which is the truly practical number. The reason is that on the Yang side, Li is discarded and Qian is used, and on the Yin side, Kun is discarded and Kan is used.

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。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。

Therefore, the yang count of Heaven is 112, which is the number after subtracting the yin. The yin count of Earth is also 112. There is another forty yang counts, which are left after removing the yang at the north and south poles: the extreme south is scorching hot and the extreme north is bitterly cold, and neither can support life, so they are subtracted. These forty counts are roughly the excess of Heaven. Yang encroaches on yin, and day encroaches on night; this excess falls to Earth. Combined, there are 152 yang and 112 yin. Then, subtract the count of Qian (Heaven) from the yang and the count of Kan (Water) from the yin, resulting in 144 yang and 108 yin, which is called "the use of the numbers." A yang line corresponds to 36 counts, three times that is 108; a yin line also corresponds to 36 counts, three times that is 108: three yang and three yin, so yang and yin are exactly half each. There is another excess of yang, which is 36, making the total 144 yang and 108 yin. Therefore, the total of the numbers is 270, but the actual usable number is 264, and the use of the numbers is 252.

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 uses four lines, resulting in two hundred and fifty-six; alternatively, if the first and top lines are removed from each hexagram, leaving four lines, the total is again two hundred and fifty-six—this is called the 'number of generation'. Therefore, the trigrams Li (Fire) and Kan (Water) are the main trigrams of generation, because Li has four yang lines in its upper and lower parts, and Kan has four yin lines in its upper and lower parts. This shows that the principle of generation is based on the number four. With one hundred and twelve yang lines and one hundred and twelve yin lines, removing the lines of Li and Kan leaves two hundred and sixteen; the remaining forty lines on each side of yin and yang together make two hundred and fifty-six. Therefore, the eight trigrams each use six lines, with Qian (Heaven) and Kun (Earth) as the main ones; among the six lines, only four are used, with Li and Kan as the main ones. This principle applies in reality as follows: Heaven does not generate life at dusk or dawn, but only at noon; Earth does not generate life at the poles, but only in the temperate zones.

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 function of the body numbers is for generating life. The function of the numbers is for operation. The heavens are in charge of operation, and the earth is in charge of generating life. The heavens operate alone, without a mate, so they use the numbers to multiply by themselves, and use the "function of the numbers" as the timing for generating life. The earth must have pairs to produce offspring, so it uses the yang aspect of the body numbers to multiply with the yin, and uses this as the number for generating life.

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。

Heavenly numbers are taken as three, so after multiplying six by six and then by six again, the result is 216, which is the number of divination lines for Qian as mentioned in the Great Treatise. Earthly numbers are taken as two, so multiplying twelve by twelve gives 144, which is the number of divination lines for Kun. Qian uses nine, so three times eight is twenty-four, and multiplying that by nine again gives 216; two times eight is sixteen, and multiplying that by nine again gives 144. Kun uses six, so three times twelve is thirty-six, and multiplying that by six again gives 216; two times twelve is twenty-four, and multiplying that by six again gives 144. If the three parts of twelve, four parts of sixteen, and half a part of six from the side of Kun are considered as the excess parts of Qian, then Qian would have 252 and Kun would have 108.

體有三百八十四，而用止於三百六十，何也？以乾、坤、離、坎之不用也。乾、坤、離、坎之不用，何也？乾、坤、離、坎之不用，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。

The total number of elements is 384, but only 360 are actually used. This is because the four trigrams Qian (Heaven), Kun (Earth), Li (Fire), and Kan (Water) are retained but not used. Why are these four trigrams not used? Because their non-use allows the remaining 360 to function. Thus, although all things change constantly, these four remain constant. It is precisely because they are constant that they enable change in other things. The number of uses is only 360, yet a year actually has 366 days. Why is there this surplus? It is due to the excess in the count. How is this surplus handled? It is entirely taken up by Qian. Since Qian and Kun are not used, the roles of Li and Kan are each taken up by half. Why is the surplus entirely taken by Qian? Because yang governs the surplus. Why are Qian and Kun not used? Because isolated yang cannot produce, and pure yin cannot form. Why do Li and Kan each take up half? Because Li is in the east and Kan is in the west, at the boundary of yin and yang, serving as the gateway for the beginning of spring and autumn and the transition between day and night.

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，故離坎用半也。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，而數常逾之者，蓋陰陽之溢也。然用數不過乎寅，交數不過乎申也。（或離當卯，坎當酉。）

Sometimes the trigram Qian is used, and sometimes Li and Kan are used. This is because when referring to the yang aspect, Qian is chosen; but when considering the surplus part, yang intrudes into yin, day into night, so Li and Kan are used. Yang represents fullness, so Qian is fully used; yin represents emptiness, so Kun is not used at all. Since yang intrudes into yin and yin also intrudes into yang, Li and Kan are each used half. This corresponds to the heavens: the southern sky is fully visible, the northern sky is fully invisible, and the east and west each show half. Li and Kan represent the boundary between yin and yang, so Li is at the寅 position and Kan is at the申 position. However, actual numbers often cross this boundary, which is due to yin and yang overflowing. But numbers cannot exceed寅, and the crossing of numbers cannot exceed申. (Some say Li is at the卯 position and Kan is at the酉 position.)

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。乾四十八而四分之一為陰所克；坤四十八而四分之一為所克之陽也。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。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。

The numbers associated with each of the eight trigrams are: Qian (Heaven) 48, Dui (Lake) 30, Li (Fire) 24, Zhen (Thunder) 10, Kun (Earth) 12, Gen (Mountain) 20, Kan (Water) 36, and Xun (Wind) 40. If we consider only the yang lines, Qian has 36, Kun has 12, Li, Dui, and Xun each have 28, while Kan, Gen, and Zhen each have 20. Originally, Qian had 48, but a quarter of it was subtracted by yin; Kun originally had 48, but a quarter of it was added from yang. Therefore, Qian actually has 36 and Kun actually has 12. Yang represents advancement, so it accumulates to 360 days; yin represents reduction, so twelve lunar months are twelve days shorter than a year. The four trigrams associated with yang have twelve lines, eight of which are yang lines and four are yin lines. Multiply 36 by the number of yang lines and 24 by the number of yin lines, 288 plus 96 equals exactly 384.

圓者，星也，曆紀之數，其肇於此乎？方者，土也，畫州井地之法，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。圓數有一，方數有二，奇偶之義也。六即一也，十二即二也。

The circular side relates to the stars and the numbers used in calendars and year records, which probably originated from this. The square side relates to the land, the method of dividing the country into nine provinces and managing the well-field system, which probably followed this model. In the end, the circular represents the numbers of the Yellow River Chart, and the square represents the writings of the Luo Writing. Therefore, Fuxi and King Wen used it to create the Book of Changes, and Great Yu and Ji Zi used it to compose the Classic of Documents. The fundamental number of the circular is one, and the fundamental number of the square is two, which is the distinction between odd and even. Six is merely six times one, still belonging to one, and twelve is merely six times two, still belonging to two.

圓者徑一圍三，重之則六。方者徑一圍四，重之則八也。天圓而地方。圓者之數起一而積六，方者之數起一而積八。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，故天並其七而為七；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。

The circumference of a circle with a diameter of one is three, and doubling it gives six. The circumference of a square with a diameter of one is four, and doubling it gives eight. Heaven is round, and Earth is square. Therefore, the number of the circle starts from one and accumulates to six, while the number of the square starts from one and accumulates to eight. If we go one step further, starting from four, it accumulates to twelve. Six always changes according to six, eight always changes according to eight, and twelve changes according to eight. This is all in accordance with the natural order. Eight is the "body" shared by both Heaven and Earth; six is the "function" of Heaven; twelve is the "function" of Earth. Heaven transforms the square into a circle but always retains the "one"; Earth divides one into four but always keeps the square. Heaven changes its body but not its function; Earth changes its function but not its body. Adding one to six gives seven, and adding four to twelve gives sixteen. Yang is about advancement, so Heaven includes that one to become seven; Yin is about retreat, so Earth removes the four and stops at twelve. This shows that Yang always preserves the "one," while Yin always hides the "one." Therefore, the body of Heaven and Earth stops at eight, while the function of Heaven reaches seven and the function of Earth stops at twelve.

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。方者引圓以為體，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。

A circle is formed by cutting and shaping a square, so one becomes four; four removes one part, leaving three. Three becomes nine, and nine removes three parts, leaving six. A square is formed by drawing a circle and taking its form, so one becomes three, and including itself makes four; four becomes twelve, and including itself makes sixteen. Therefore, numbers used for the circle reach their peak at six, while numbers used for the form reach their peak at sixteen. Hence, the diameter of a circle is one, and its circumference is three, starting from one, it accumulates to six. A square divides one into four, and four divides again into sixteen—these are all natural principles.

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。（更思之。）

The number six changes once to produce six, subtract one part to leave five; changes twice to produce twelve, subtract two parts to leave ten; changes three times to produce eighteen, subtract three parts to leave fifteen; changes four times to produce twenty-four, subtract four parts to leave twenty; changes five times to produce thirty, subtract five parts to leave twenty-five; changes six times to produce thirty-six, subtract six parts to leave thirty. Therefore, calculating by keeping the original is six times six equals thirty-six, while calculating after subtraction is five times five equals twenty-five. Similarly, five is four plus one, four is three plus one, three is two plus one, two is one plus one. Thus, one produces two, subtracting that one part still leaves one; two produces three, subtracting one part leaves two; three produces four, subtracting one part leaves three; four produces five, subtracting one part 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. (This requires further reflection.)

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。一生三，並而為四也；十二生二十，並而為三十二也；二十八生三十六，並而為六十四也。（更思之。）

The number of the square changes once to become four; four generates eight, and combining the original four gives twelve; eight generates twelve, and combining the original eight gives twenty; twelve generates sixteen, and combining the original twelve gives twenty-eight; sixteen generates twenty, and combining the original sixteen gives thirty-six. Now looking at the total: one generates three, and combining the two numbers gives four; twelve generates twenty, and combining the two numbers gives thirty-two; twenty-eight generates thirty-six, and combining the two numbers gives exactly sixty-four hexagrams. (This part requires further reflection.)

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十二，十二又並四則為十六。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。（更思之。）

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 turns back to drive two; three drives nine, and nine turns back to drive eight and six. Thus, two produces four, eight produces sixteen, and six produces twelve. Three plus one is four; nine plus three is twelve; twelve plus four is sixteen. Hence, four is based on one and uses three; twelve is based on three and uses nine; sixteen is based on four and uses twelve. (This requires further reflection.)

裁方而為圓，天之所以運行；分大而為小，地之所以生化。故天用六變，地用四變也。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，以至九十六分為三百八十四也。

Cutting and shaping square into circle, this is the reason heaven can move ceaselessly; dividing the large into the small, this is the reason earth can give birth and nurture all things. Therefore, heaven moves through six transformations, and earth through four. Cutting is done according to the ratio of removing one part out of four: one plus eight equals nine, removing one fourth leaves seven; eight is cut to six, sixteen to twelve, twenty-four to eighteen, thirty-two to twenty-four, forty to thirty, forty-eight to thirty-six, fifty-six to forty-two, and sixty-four to forty-eight. Division is done according to fourfold multiples: one divided into four, eight into thirty-two, sixteen into sixty-four, continuing up to ninety-six divided into three hundred eighty-four—exactly the number of lines in the sixty-four hexagrams, three hundred eighty-four lines.

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。

One generates six, six generates twelve, twelve generates eighteen, eighteen generates twenty-four, twenty-four generates thirty, and thirty generates thirty-six; following this pattern of adding six each time, when it reaches sixty changes, it produces three hundred and sixty, which is called "the number of movement." Another pattern is four generates twelve, twelve generates twenty, twenty generates twenty-eight, and twenty-eight generates thirty-six, with each step adding eight, which is called "the number of generation." Therefore, following this pattern to assign the yang numbers to the Eight Trigrams: Qian is thirty-six, Dui and Li and Xun are each twenty-eight, Zhen and Kan and Gen are each twenty, and Kun is twelve.

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。六變而成三十六矣，八變而成六十四矣，十二變而成三百六十四矣。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。

A circular path involves six changes progressing step by step, resulting in sixty changes and thus three hundred and sixty; a square path involves eight changes, so eight multiplied by eight equals sixty-four. Yang represents forward movement, so it progresses to sixty. Further calculation: six changes result in thirty-six, eight changes result in sixty-four, and twelve changes result in three hundred and sixty-four (the original text is like this, but it is suspected that it should be three hundred and sixty). If six by six is considered one section of change, then sixty-four changes result in three hundred and eighty-four; if eight by eight is considered one section of change, then forty-nine changes also result in three hundred and eighty-four. Both paths, when taken to their extremes, lead to the three hundred and eighty-four lines of the sixty-four hexagrams.

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 heavenly numbers, so they take seventy-seven, which is forty-nine; saying the great derivation number is fifty refers to including the one that is not used. The nature of the hexagrams is square, used to represent the earthly numbers, so they take eight eights, which is sixty-four; saying sixty refers to excluding the four trigrams of heaven, earth, fire, and water. The yarrow stalks belong to the number of use, while the hexagrams belong to the number of form: use must be based on form, so one is left unused; form must be based on use, so four are removed. A circle is based on one, a square is based on four, hence the yarrow stalks leave one and the hexagrams remove four. The number of use for the yarrow stalks takes seven, and the remaining is included, which also means 'keeping one'; when casting the hexagram, one stalk is first set aside, which also means 'removing one'.

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。其用四十有九，六十四卦一歲之策也。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 is the number seven used instead of six in the divination process? Because the remaining portion is included. If the remainder is excluded, it would be six, so the number of lines in a hexagram is calculated as six multiplied by six, resulting in thirty-six. This is why the number fifty is used to match the number of hexagrams with the leap year's cycle; actually using forty-nine corresponds to the regular year's cycle. When divining with yarrow stalks, the leftover stalks are gathered and one is set aside first, just as a leap month is added in a year. Why does the hexagram directly remove four? Because heaven changes first and earth follows: when the yarrow stalks remove one, the hexagram accordingly removes four.

蓍之用數，掛一以象三。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，以當艮坎之二十四爻，並上卦之八陰，為三十二爻也。是故七九為陽，六八為陰也。

The number of stalks used in divination is forty-nine. First, one stalk is set aside to represent the three components of heaven, earth, and humanity. The remaining forty-eight stalks correspond to the number of lines in a hexagram, which is calculated as four multiplied by twelve, resulting in forty-eight. From twelve, subtract three and use nine: four multiplied by three equals twelve, which is the number of lines removed; four multiplied by nine equals thirty-six, which is the number of lines used, matching the thirty-six yang lines of the Qian hexagram. From twelve, subtract five and use seven: four multiplied by five equals twenty, which is the number of lines removed; four multiplied by seven equals twenty-eight, which is the number of lines used, matching the twenty-eight yang lines of the Dui and Li hexagrams. From twelve, subtract six and use six: four multiplied by six equals twenty-four, which is the number of lines removed; four multiplied by six equals twenty-four, which is the number of lines used, matching the twenty-four yin lines of the Kun hexagram. From twelve, subtract four and use eight: four multiplied by four equals sixteen, which is the number of lines removed; four multiplied by eight equals thirty-two, which is the number of lines used, matching the twenty-four lines of the Gen and Kan hexagrams plus the eight yin lines of the hexagram, totaling thirty-two lines. Therefore, seven and nine belong to yang, while six and eight belong to yin.