The Sixty-Four Hexagram Square and Circle Diagram

愚按：先天方圓二圖一一相應，故邵子曰：「變於內者應於外，變於外者應乎內；變於下者應乎上，變於上者應乎下。」蓋巽離兌以二十八陽應坎艮震之二十八陰。乾兌巽坎為上，則震離艮坤為下；乾兌離震為內，則巽坎艮坤為外。陽消陰長，每卦相效，未有變而不應者。

I believe theEarlier Heaven diagram's square and circular forms correspond one to one. Therefore, Shaozi said: changes within correspond to those outside, and changes outside correspond to those within; changes below correspond to those above, and changes above correspond to those below. The trigrams 《Xun》, 《Li》, and 《Dui》 correspond with twenty-eight yang lines to the trigrams 《Kan》, 《Gen》, and 《Zhen》 with twenty-eight yin lines. 《Qian》, 《Dui》, 《Xun》, and 《Kan》 are above, while 《Zhen》, 《Li》, 《Gen》, and 《Kun》 are below. 《Qian》, 《Dui》, 《Li》, and 《Zhen》 are inner, while 《Xun》, 《Kan》, 《Gen》, and 《Kun》 are outer. Yang diminishes and yin increases, and each trigram responds to the others, none of which change without a corresponding response from the opposite trigram.

變者從天，天左行，日應一度；應者法日，日右行，天應一度，皆左右相應也。日紀於星，乾離也；月會於辰，兌震也；水生於土，坤坎也；火潛於石，艮巽也，皆上下相應也。飛者棲木，離艮也；走者依草，震坤也；心肺相聯，乾巽也；肝膽相聯，兌坎也，皆內外相應也。所以易之六爻，初與四應，二與五應，三與上應，常相反對也。

The changing aspect follows Heaven: Heaven moves to the left, the sun responds to it by one degree; the responding aspect imitates the sun: the sun moves to the right, Heaven responds to it by one degree, this is called mutual left and right response. The sun uses the stars as its standard, that is, the trigrams Qian and Li; the moon meets the constellations, that is, the trigrams Dui and Zhen; water is born from earth, that is, the trigrams Kun and Kan; fire is hidden in stone, that is, the trigrams Gen and Xun, this is called mutual upper and lower response. Birds rest on trees, that is, the trigrams Li and Gen; beasts dwell in grass, that is, the trigrams Zhen and Kun; heart and lung are connected, that is, the trigrams Qian and Xun; liver and gallbladder are connected, that is, the trigrams Dui and Kan, this is called mutual internal and external response. Therefore, the six lines of the Book of Changes, the first and fourth lines correspond, the second and fifth lines correspond, the third and sixth lines correspond, always in pairs.

天地相合，牝牡相召：天陽地陰，天律地呂，天聲地倡。以乾兌離震居西北，倡地之五六七八一十六卦於東南，又交西南否、遯、訟、姤十六卦，是為寒暑晝夜，變飛走草木之性情形體。得動數十六卦，成二百五十六卦位，含四變，凡動物之成敗美惡，莫不由是。

Heaven and earth combine, yin and yang attract each other: Heaven is yang, earth is yin, Heaven initiates the sound, and earth responds in harmony. The trigrams Qian and Dui and Li and Zhen are located in the northwest, initiating the five, six, seven, and eight trigrams, totaling sixteen, in the southeast. They also interact with the sixteen trigrams of Po, Duan, Song, and Guo in the southwest. This forms the cold and heat, day and night, changing the nature, emotion, form, and body of all living things. The 'dynamic number' of sixteen trigrams forms 256 hexagram positions, containing four layers of change. All success or failure, beauty or ugliness of creatures are determined by this.

地音天和，以坤艮坎巽居東南，和天之一二三四一十六卦於西北，又交東北泰、臨、明夷、復十六卦，是為風雨露雷，變性情形體之飛走草木。得植數十六卦，成二百五十六卦位，含四變，凡植物之榮枯華實，莫不由是。

The earth first produces sound, and the heavens respond. The trigrams 《Kun》, 《Gen》, 《Kan》, and 《Xun》 are located in the southeast, responding to the first, second, third, and fourth trigrams of the heavens, which are in the northwest. They also intersect with the sixteen trigrams in the northeast, namely 《Tai》, 《Lin》, 《Mingyi》, and 《Fu》. This forms the elements of wind, rain, dew, and thunder, determining the nature, emotion, form, and body of plants and trees. It includes the 'plant numbers' of sixteen trigrams, forming 256 hexagram positions, containing four layers of change. All the flourishing and withering of plants, as well as their blooming and bearing fruit, are determined by this.

西南之卦自左而右，以觀動物。動物之命在首，附天以陽生乎下，在下之三十二卦其一皆向上者，命在上也，故人首在上而鳥獸皆橫生。東北之卦自上而下，以觀植物。植物之命在根，附地以陰生乎上，在上之三十二卦其一皆向下者，命在下也，故人腎在下而草木倒生。然後配以聲音之卦，則日月星辰之聲，天卦百五十二也；水火土石之音，地卦百五十二也。

The hexagrams in the Southwest are viewed from left to right to observe animals: the life of animals is in their heads, dependent on Heaven, with yang energy rising from below; among the lower thirty-two hexagrams, the 'one' is all facing upward, indicating life above, so humans have their heads upward, while birds and beasts grow horizontally. The hexagrams in the Northeast are viewed from top to bottom to observe plants: the life of plants is in their roots, dependent on Earth, with yin energy arising from above; among the upper thirty-two hexagrams, the 'one' is all facing downward, indicating life below, so the human kidney is below, while grass and trees grow in reverse. When combined with the hexagrams of sound, the 'sound' of sun, moon, stars belongs to the Heaven hexagrams, totaling one hundred and fifty-two; the 'sound' of water, fire, soil, and stone belongs to the Earth hexagrams, also totaling one hundred and fifty-two.

又按：六十四卦圓布者，乾盡午中，坤盡子中，離盡卯中，坎盡由中；陽生於子中，極於午中；陰生於午中，極於子中，其陽在南，其陰在北。方布者，乾始於西北，坤盡於東南，其陽在北，其陰在南。此陰陽對待之數。

Now looking at the sixty-four trigrams: in the circular arrangement, the trigram Qian ends at the center of Wu, and the trigram Kun ends at the center of Zi. The trigram Li ends at the center of Mao, and the trigram Kan ends at the center of You (the original text says "by center" but should be "center of You"). Yang is born at the center of Zi and reaches its peak at the center of Wu, while Yin is born at the center of Wu and reaches its peak at the center of Zi. Therefore, Yang is in the south and Yin is in the north. In the square arrangement, Qian begins at the northwest, and Kun ends at the southeast, so Yang is in the north and Yin is in the south. This is the numerical relationship of yin and yang being mutually complementary.

圓於外者為陽，方於內者為陰；圓者動而為天，方者靜而為地。圓圖乾在南、坤在北，方圖坤在南、乾在北；乾位陽畫多，坤位陰畫多，陰陽各以類而聚。圖以圓函方，見天包地外，地在天中矣。

Outside the circle represents yang, and inside the square represents yin; circular forms are dynamic and represent heaven, while square forms are static and represent earth. In the circular diagram, the Trigram Qian is located to the south and the Trigram Kun to the north; in the square diagram, the Trigram Kun is to the south and the Trigram Qian to the north. The position of Qian has more yang lines, while the position of Kun has more yin lines, with yin and yang gathering together according to their kinds. The whole diagram has the circle enclosing the square, showing that heaven encompasses earth externally, and earth is located within heaven.

方圖西北十六卦，天卦自相交；東南十六卦，地卦自相交。其斜行則乾、兌、離、震、巽、坎、艮、坤，自西北而東南，皆陰陽之純卦，所以不能生物也。西南十六卦，天去交地，天卦皆在上而生氣在首，故能生動物而頭向上；東北十六卦，地去交天，天卦皆在下，生氣在根，故能生植物而頭向下。其斜行則泰、損、既濟、益、恆、未濟、咸、否，自東北而西南，皆陰陽得偶之卦，所以生物也。

The sixteen hexagrams in the northwest are formed by the Heaven hexagram crossing with itself; the sixteen hexagrams in the southeast are formed by the Earth hexagram crossing with itself. The diagonal line of one row consists of 《Qian》, 《Dui》, 《Li》, 《Zhen》, 《Xun》, 《Kan》, 《Gen》, and 《Kun》, arranged from northwest to southeast. These are all pure hexagrams of yin and yang, so they cannot produce life. The sixteen hexagrams in the southwest are formed by Heaven crossing with Earth, with Heaven hexagrams above and life qi at the head, so they can produce animals with heads upward. The sixteen hexagrams in the northeast are formed by Earth crossing with Heaven, with Heaven hexagrams below and life qi at the root, so they can produce plants with heads downward. The diagonal line on this side consists of 《Tai》, 《Sun》, 《Ji Ji》, 《Yi》, 《Heng》, 《Wei Ji》, 《Xian》, and 《Pou》, arranged from northeast to southwest. These are all hexagrams of paired yin and yang, so they can produce life.

吾因是而知植物之命在於根，動物之命在於首也。又合二圖而觀之：方圖乾處圓圖亥位，謂之天門，是天氣下降也；坤處圓圖巳位，謂之地戶，是地氣上騰也。此兩十六卦，所謂陰陽互藏其宅也。

From this I understand that the life of plants lies in their roots, and the life of animals lies in their heads. When we combine the two diagrams, the hexagram Qian in the square diagram falls exactly on the亥 position in the circular diagram, called "Heaven's Gate," indicating the descent of heavenly energy. The hexagram Kun in the square diagram falls exactly on the巳 position in the circular diagram, called "Earth's Gate," indicating the ascent of earthly energy. These two groups of sixteen hexagrams are referred to as yin and yang mutually containing each other's dwelling places.

泰處圓圖寅位，謂之鬼方；否處圓圖申位，謂之人路。此兩十六卦，是天交地、地交天而生生不息，所以泰居寅而否居申，所謂陰陽各從其類也。夫圓圖主運行之事，運行者氣也，生物者質也；氣非質則無所附麗，質非氣則豈能生物哉？此見天有生物之氣，地有成物之形也。

The hexagram Tai falls in the position of Yin in the circular diagram, known as the "ghostly direction"; the hexagram Pǒ falls in the position of Shen in the circular diagram, known as the "human path." These two groups of sixteen hexagrams represent the continuous interaction between heaven and earth, and between earth and heaven, leading to perpetual generation and renewal. Therefore, Tai resides in Yin and Pǒ resides in Shen, which is referred to as yin and yang each following their own kind. The circular diagram primarily concerns movement: movement involves qi, while generation involves substance; if qi lacks substance, it has nowhere to rely upon, and if substance lacks qi, it cannot generate life. From this we can see that heaven possesses the qi for generating life, while earth possesses the form for completing things.

愚按：元會運世之數，一運當三百六十年，可以推歷代之治亂。子至卯，陰中陽，將治也；卯至午，陽中陽，極治也；午至酉，陽中陰，將亂也；酉至子，陰中陰，極亂也。先天圖自泰歷蠱而至否，自否歷隨而至泰，即南北之運數也。

I believe that the numbers of Yuan, Hui, Yun, and Shi, with each Yun corresponding to 360 years, can be used to calculate the rise and fall of dynasties: from Zi to Mao represents Yin within Yang, indicating the beginning of peace; from Mao to Wu represents Yang within Yang, indicating the peak of peace; from Wu to You represents Yang within Yin, indicating the onset of chaos; and from You to Zi represents Yin within Yin, indicating the peak of chaos. In the diagram of the Primordial Heaven, from Tai through Gu to Po, and then from Po through Sui back to Tai, this reflects the alternating cycles of north and south in the movement of the great numbers.

蓋泰與否相對，蠱與隨相對。故曰：自泰至否，其間有蠱；蠱之者誰？陰方用事，陽艮已止，陰邪巽入，否斯至矣。自否至泰，其間有隨；隨之者誰？陽震順動，兌陰隨之，民說無疆，泰無不宜。此否泰蠱隨，殆亦天門、地戶、人路、鬼方出入之交與？

The hexagram Tai contrasts with the hexagram Po, and Gu contrasts with Su. Therefore, moving from Tai to Po, one passes through Gu. Who causes the decay? It is the Yin energy that prevails, restraining the Yang with Gen, and the Yin evil secretly enters from Xun, thus bringing about Po. Moving from Po to Tai, one passes through Su. Who follows? It is the Yang energy that moves smoothly, with Zhen causing movement and Dui, the Yin, following along. The people rejoice without bounds, and thus Tai becomes universally appropriate. These hexagrams Po, Tai, Gu, and Su are probably precisely the gate of Heaven, the gate of Earth, the path of humanity, and the region of ghosts, where the meeting and separation of Heaven and Earth occur.

數往者順，自子至午，震離兌乾為治之象；知來者逆，自午至子，巽坎坤艮為亂之象。當背北面南觀之，即知順逆。唐至五代六甲子，半治半亂；宋乾德至今又六甲子，中經南人用事，南離隨氣過北而亂，康節蓋已推之。

"Numbers of the past are followed," from Zi to Wu, the trigrams Zhen, Li, Dui, and Qian follow in sequence, indicating a time of good governance; "Numbers of the future are reversed," from Wu to Zi, the trigrams Xun, Kan, Kun, and Gen follow in sequence, indicating a time of chaos. Facing south with the back to north, the order of sequence and reversal becomes clear. From the Tang Dynasty to the Five Dynasties, there were six Jiazi cycles, with half good and half bad; from the time of the Song Dynasty's Gande period to now, another six Jiazi cycles have passed, during which southern people held power, and the Li energy from the south moved north, leading to chaos. These insights were probably already calculated by Kangjie.

六甲子者，三百六十年也，即一日十二時之數。自堯甲辰期運，月巳、辰末、星癸，迄今月仍在午，辰方過酉，為年者三千六百六十，為世者僅一百二十二，何速哉！古今在天地閒，猶日暮耳。聖人通乎晝夜之道而知，能以一時觀萬時，一世觀萬世。予錄世運於十二會運之終，其有感也夫。

Six Jiazi cycles amount to three thousand six hundred years, exactly matching the number of twelve hours in a day. Starting from the Jia Chen year of Emperor Yao, when the period reaches the end of Si and Chen, the stars are at the position of Gui, and by today, the moon is still in Wu, having just passed You, totaling three thousand six hundred and sixty years, which is merely one hundred and twenty-two generations. How quickly time passes! From ancient times to the present, within the vast expanse of heaven and earth, it is no more than the span of a single day. The sage understands the principle of day and night and knows all things. He can observe ten thousand hours through one hour, and ten thousand generations through one generation. I have appended the cycle of world affairs at the end of the twelve great periods, out of deep reflection.

康節先生傳連山易於山林隱徳之士，以天一地二，天三地四，天五地六，天七地入，天九地十，分十等，曰：元會運世歲月日時分秒作皇極經世書，自元至時隸之卦而分杪行乎八卦之間，有卦有數，天地人物皆囿於其中，則卦數窮物之情，極物之變，雖鬼神之不測，與天地之無窮，亦難逃乎此數焉耳矣。

Master Kangjie received the transmission of the "Linked Mountains Changes" from a reclusive scholar of virtue in the mountains. He divided it according to the principles of "Heaven One, Earth Two, Heaven Three, Earth Four, Heaven Five, Earth Six, Heaven Seven, Earth Eight, Heaven Nine, Earth Ten," into ten levels, called "Yuan," "Hui," "Yun," "Shi," "Sui," "Yue," "Ri," "Shi," "Fen," and "Miao," and wrote them into the "Supreme Principles Governing the World." From "Yuan" to "Shi," all belong to the trigrams, while "Fen" and "Miao" operate between the Eight Trigrams. With trigrams and numbers, heaven, earth, people, and all things are included. The trigrams and numbers exhaust the forms of all things and fully comprehend their transformations. Even spirits, which are unpredictable, and heaven and earth, which are boundless, cannot escape this system of numbers.

一元十等數（乾當太極，以一元為一年）一元之數。 十二會（坤當元氣，以一會為一年）三百六十運（天以一運為一年）。 四千三百二十世（地以世為一年）一十二萬九千六百年。 一百五十五萬五千二百月，四千六百六十五萬六千日。 五億五千九百八十七萬二千時。 兌卦一百六十七億九千六百一十六萬分 二千一十五億五千三百九十二萬杪 一會三十運，三百六十世，一會之數。 一萬八百年 十二萬九千六百月，三千三百八十八萬八千日，四千六百六十五萬六千時。 履卦一十二億九千九百六十八萬分。 一百六十七億九千六百一十六萬秒。 一運十二世，三百六十年，一運之數 四千三百二十月，一十二萬千六百日，一百五十五

The number of one yuan is divided into ten levels: the "Heaven" (Qian) corresponds to the Taiji, treating one yuan as one year. The number of one yuan is as follows: one yuan contains twelve sessions, with each session treated as one year, corresponding to the "Earth" (Kun), which represents the original qi. The number of three thousand six hundred revolutions, with each revolution treated as one year, the number of four thousand three hundred twenty generations, with each generation treated as one year, the number of twelve million nine thousand six hundred years, one hundred fifty-five thousand five hundred twenty months, four million six hundred sixty-five thousand six hundred days, fifty million five thousand nine hundred eighty-seven thousand two hundred hours; paired with the "Lake" (Dui) trigram, it is one hundred sixty-seven million nine thousand six hundred sixteen ten-thousandths, two thousand one hundred fifteen million five thousand three hundred ninety-two seconds. One session contains thirty revolutions and three thousand six hundred generations, with each generation treated as one year, the number of one session is as follows: one ten thousand eight hundred years, twelve million nine thousand six hundred months, thirty-three million eight hundred eighty-eight thousand eight hundred days, four million six hundred sixty-five thousand six hundred hours; paired with the "Footwear" (Lv) trigram, it is twelve million nine thousand nine hundred sixty-eight ten-thousandths, one hundred sixty-seven million nine thousand six hundred sixteen thousand seconds. One revolution contains twelve generations and three hundred sixty years, with each generation treated as one year, the number of one revolution is as follows: four thousand three hundred twenty months, twelve million nine thousand six hundred days (the original text is missing the character "jiu"), one hundred fifty-five thousand and more hours—the original text ends here.

一會 三十運， 三百六十世，一會之數。 一萬八百年 十二萬九千六百月， 三千三百八十八萬八千日， 四千六百六十五萬六千時。 履卦（集成無“履卦”二字）一十二億九千九百六十八萬分。 一百六十七億九千六百一十六萬秒。 一運 十二世， 三百六十年，（一運之數） 四千三百二十月， 一十二萬九千六百日， 一百五十五萬五千二百時。 四千六百六十五萬六千分。 五億五千九百八十七萬二千秒。

Here is a repetition of the above categories. A period of thirty cycles, three thousand six hundred generations, this is the number of a great cycle; one million eight hundred years, twelve million nine thousand six hundred months, three hundred thirty-eight million eight thousand days, four million six hundred sixty-five thousand six hundred hours; corresponding to the hexagram of "Walking" (the "Kanji Tu Shu Cheng Ji" edition does not have the term "Walking Hexagram"), which is twelve hundred million nine hundred sixty-eight thousand parts, one hundred sixty-seven million nine thousand six hundred sixteen seconds. A cycle: twelve generations, three hundred and sixty years, this is the number of a cycle; four thousand three hundred twenty months, twelve million nine thousand six hundred days, one hundred and fifty-five thousand five hundred and twenty hours, four million six hundred sixty-five thousand six hundred parts, five hundred million five hundred ninety-eight thousand seven hundred twenty seconds.

一世 三十年 三百六十月 一萬八百日 一十二萬九千六百時 三百八十八萬八千分。 四千六百六十五萬六千秒。 一年 十二月 三百六十日 四千三百二十時 一十二萬九千六百分 一百五十五萬五千二百秒

The number of years: thirty years, three thousand six hundred months, eleven thousand eight hundred days, one hundred twenty-nine thousand six hundred hours, three million eight hundred eighty-eight thousand parts, and forty-six million six hundred fifty-six seconds. The number of one year: twelve months, three thousand six hundred days, forty-three thousand two hundred hours, one hundred twenty-nine thousand six hundred parts, and one million five hundred fifty-five thousand two hundred seconds. Here, the terms "parts" and "seconds" refer to the time units established in the "Huang Ji Jing Shi," which are different from the modern "minutes" and "seconds."

一月 三十日 三百六十時 一萬八百分 一十二萬九千六百秒 一日 十二時 三百六十分 四千三百二十秒 一時 三十分 三百六十秒 一分 十二秒 一秒

The number of days in one month: thirty days, three hundred and sixty hours, ten thousand and eight hundred moments, twelve thousand nine hundred and sixty seconds. The number of days in one day: twelve hours, three hundred and sixty moments, four thousand three hundred and twenty seconds. The number of moments in one hour: thirty moments, three hundred and sixty seconds. One moment contains twelve seconds. The last unit is one second.

一秒在瞬息，細之又細，分而歸律呂聲音以取數，所以窮盡天地間萬變萬化萬事萬物也。

A moment is so short that it can be said to be extremely brief; if divided further, it would be measured by the pitch and tone of musical scales. Through such successive divisions and deductions, one can fully comprehend the myriad changes and transformations of all things in heaven and earth.

以太極觀天地，則天地亦一物也。蓋天地雖大，不過形氣之凝結耳。経者對緯之名，以元為經，則始終此元而已矣。

Viewing from the perspective of the Taiji, heaven and earth are no more than a single entity; although vast, heaven and earth are ultimately formed by shape and energy. "Jing" is a term established in relation to "wei"; taking "Yuan" as the Jing, then from beginning to end it is merely this one Yuan.

以會為緯，則有十二變焉，凡此十有二變，在一元則有十有二會，在一運則為十有二世，有一歲則為十有二月，有一日則為十有二時，在一分則為十有二秒，十有二變之數，無往而不在焉，則變者其緯也。不變者其經也。於緯之中，有以執其經於變之中，有以守其常也。共三百六十運，分二十四氣，每一氣之首蔵四爻準閏，運世年為大運，皆起泰損大畜，節月日時為小運，皆起升蒙蠱井，毎運一卦中四爻直事。

Taking "Hui" as the vertical line, there are twelve transformations. These twelve transformations manifest as twelve Hui in a great cycle, twelve generations in a great movement, twelve months in a year, twelve hours in a day, and twelve seconds in a minute; the number of twelve transformations is everywhere. What changes is the vertical line, while what remains constant is the horizontal line; within the vertical line, one must grasp the horizontal line, and within the transformation, one must hold fast to the constant. A great cycle consists of three hundred and sixty movements, divided into twenty-four solar terms, with four lines hidden at the beginning of each solar term to serve as the excess days. Movements, generations, and years belong to the "great movement," and all start with the hexagrams of "Tai," "Sun," "Da Xu," and "Jie"; months, days, and hours belong to the "small movement," and all start with the hexagrams of "Sheng," "Meng," "Gu," and "Jing." Each movement uses one hexagram, with four lines taking turns to govern affairs.

日甲月子一星三十辰，三百六十年，一萬八百， 復此一會，但有天耳未有地也，地未有何況人乎。然是理是策已具於無形之中矣。逆而推之，可以推之其必有三十運，三百六十世，一萬八十年，而當笫一會之數也。節始冬至，閏爻泰卦至戊寅，笫十五運節交小寒，閏爻大有卦。

The sun is represented by Jia, the moon by Zi, the star by one, and the celestial stem by thirty. Together they total three thousand six hundred years and one hundred and eight thousand. This corresponds to the hexagram of Fu (Return). At that time, there was only heaven, and no earth; if earth did not yet exist, how could there be human beings? However, this principle and this system of calculation were already present in an invisible form. If we trace back, we can determine that there must have been thirty cycles, three thousand six hundred generations, and one hundred and eight thousand years, exactly matching the number of the first cycle. The solar terms begin with the winter solstice, and the leap line corresponds to the hexagram Tai (Peace). When it reaches Wuyin, the fifteenth cycle, the solar term transitions to Xiaohan (Minor Cold), and the leap line corresponds to the hexagram Dàyǒu (Great Possession).

月丑二星六十辰七百二十年，二萬一千六百，臨 臨此一會但有地耳未有人也。且未有而況物乎然是理是數已具，於無形之中矣，逆而推之，可以知其六十運七百二十世二萬一千六百年，而當笫二會之數也。節交大寒，閏爻渙卦至戊申笫四十五運，節交立春，閏爻晉卦。

The month is Chou, the star is Er, the stem and branch are sixty, seven hundred and twenty years, twenty-one thousand six hundred years. This period corresponds to the hexagram of "Approaching" (Lin): at that time there was only earth, and there were no people; people had not yet appeared, let alone all things. However, this principle and these numbers were already present in an invisible form. By working backwards, we can know that it consists of sixty cycles, seven hundred and twenty ages, and twenty-one thousand six hundred years, exactly matching the numbers of the second period. When the solar term reaches the Great Cold, the leap yao is the hexagram of "Dispersing" (Huan); when it reaches the forty-fifth cycle, the solar term is the Beginning of Spring, and the leap yao is the hexagram of "Progress" (Jin).

月寅三星九十辰一千八十年，三萬二千四百泰 當此一會之半，既已有人亦復有物，人物既具，則必有主之者矣。斯時也，豈非三皇之時乎？然易有其象，未有其辭，既不傳事，亦難考，是故逆而推之，運世可知也，節交雨水，閏爻屯卦，至戊寅笫七十六運，節交驚蟄，閏爻震卦。

The moon is in the position of寅, the star is in the position of San, the celestial stem and earthly branch are at ninety, and the duration is one thousand and eight hundred years, thirty-two thousand four hundred, matching the Hexagram of Tai. At the midpoint of this period, humans had already appeared, and all things were already complete; since both humans and objects were present, there must have been someone to govern them. At this time, was it not precisely the era of the Three Sovereigns? However, at that time, the Book of Changes had only the hexagram images but no hexagram statements, and the events had not been passed down, making it difficult to verify. Therefore, we can only trace back, and the cycles and eras can still be inferred. When the solar term reaches Rain Water, the leap yao corresponds to the Hexagram of Zun. When reaching Wuyin and the seventy-sixth cycle, the solar term reaches Start of Thunder, and the leap yao corresponds to the Hexagram of Zhen.

月卯四星一百二十辰，一千四百四十年，四萬三千二百，大壯 大壯此當笫四會，計一百二十運，一千四百四十世，四萬三千二百年，節交春分，閏爻損卦至戊申笫一百零五運，節交清明，閏爻夬卦。

The month is represented by Mao, the star by Si, the day stem by 120, the number of years by 1,440, and the number of centuries by 43,200. The Great Strength hexagram corresponds to the fourth cycle, encompassing 120 periods, 1,440 generations, and 43,200 years. When the solar term reaches Spring Equinox, the leap trigram is the Loss hexagram; when reaching the period of Wushen and the 105th period, the solar term reaches Clear and Bright, and the leap trigram is the Victory hexagram.

月辰五星一百五十辰，一千八百年，五萬四千，夬卦 夬此當第五會，計一百五十運，一千八百世，五萬四千年，節交穀雨，閏爻坎卦，至戊寅第一百三十五運，節交立夏，閏爻蠱卦。

The moon is called Chen, the stars are called Wu, Chen is 150, 1,800 years, and Wu is 54,000. The卦夬 is in the fifth cycle, totaling 150 cycles, 1,800 generations, and 54,000 years. When the solar term reaches Gu Yu, the leap line is the卦 Kan; when reaching Wuyin, the 135th cycle, the solar term is Li Xia, and the leap line is the卦 Gu.

月巳六星一百八十辰，二千一百六十年，六萬四千八百，乾 乾此當笫六會，計一百八十運二千一百六十世，六萬四千八百年，節交小滿，閏爻比卦比卦至戊申笫一百六十五運，節交芒種，閏爻頤卦，當壬戍笫一百七十九運。 黃帝即位，此運二千一百四十五，在戊申世甲子年也。少昊氏即位，在此運二千一百四十八辛亥世甲辰年。 帝堯即位在此運二千一百五十六，已未世甲辰年。 帝舜即位此運二千二百二十八，辛酉世丙辰年。

The moon is in the position of Si, the stars are six, the celestial stems and earthly branches total 180, and the duration is 2,160 years, 64,800 years. The Qian hexagram corresponds to the sixth cycle, which includes 180 cycles, 2,160 generations, and 64,800 years. When the solar term reaches Xiaoman, the leap trigram is the Bi hexagram; when it reaches Mangzhong, the leap trigram is the Yi hexagram; and again when it reaches Renxu, the 179th cycle. The Yellow Emperor ascended the throne in the 2,145th generation of this cycle, which is the Jiazi year of the Wushen generation; the Xiaohao ascended the throne in the 2,148th generation of this cycle, which is the Jiachen year of the Xinhai generation; the Emperor Yao ascended the throne in the 2,156th generation of this cycle, which is the Jiachen year of the Jiwei generation; and the Emperor Shun ascended the throne in the 2,228th generation of this cycle, which is the Bingchen year of the Xinyou generation.

月午七星二百一十辰，二千五百二十年，七萬五千六百，姤 此第七會計二百一十運，二乾五百二十世，七萬五千六百年，節交夏至，閏爻大畜卦，當甲於第一百八十一運，二乾一百六十一世，甲子年即夏禹王八年也。

The moon is at Wu, the star is at Qi, the celestial stem is at two hundred and ten, and the year is two thousand five hundred and twenty. This is the seventh cycle, paired with the hexagram Gou, totaling two hundred and ten ages, two thousand five hundred and twenty generations, and seven thousand five hundred and sixty years. At the solstice of summer, the leap line is the hexagram Daxu. In the year Jiazi, the 181st age, the 2161st generation, which is the year of Jiazi, it coincides with the eighth year of King Yu of Xia.

乙丑第一百八十二通二千一百七十三世，甲子年夏孔甲三十三年也。 丙寅第一百八十三運二千一百八十五世。甲子年商王般辛十年也。 丁卯第一萬八十四運，二千一百九十七世，甲子年商紂十八年至己卯周武王初年。 戊辰第一百八十五運，二千二百單九世，甲子年周幽王五年也。 已巳第一百八十六運，二乾二百二十一世，甲子年周威烈王九年至二千二百二十八世乙未年，漢高袓元年也。

Yichou, the 182nd cycle, the 2173rd generation, its Jiazi year is the 33rd year of Kong Jia of the Xia dynasty. Bingyin, the 183rd cycle, the 2185th generation, its Jiazi year is the 10th year of King Pan Geng (originally written as 'Pan Xin') of the Shang dynasty. Dingmao, the 184th cycle (originally mistakenly written as 'the 18,400th cycle'), the 2197th generation, its Jiazi year is the 18th year of King Zhou of Shang; to Jimao year it is the first year of King Wu of Zhou. Wuchen, the 185th cycle, the 2209th generation, its Jiazi year is the 5th year of King You of Zhou. Jisi, the 186th cycle, the 2221st generation, its Jiazi year is the 9th year of King Wei Lie of Zhou; to the 2228th generation's Yiwei year, it is the first year of Emperor Gaozu of Han.

庚午第一百八十七運，二乾二百三十三世，甲子年漢宣帝五鳯元年也。 辛末第一百八十入運，二乾二百四十五世，甲子年西晉惠帝未興元年至二千二百五十五世內戊寅年唐高祖武德元年。 壬申年笫一百八十九運二千二百五十七世甲子唐高宗麟德元年至二千二百六十六世丙申年，宋太袓元年也。 癸西笫一百九十運二千二百六十九世甲子年，宋仁宗天聖二年，至二千二百七十七世甲子年，元至元元年丁未，入此大有卦九二爻。 甲戌第一百九十一運，二千二百八十一世，乃明朝洪武十七年，甲子入此運，戊寅第一百九十五運，節交小暑閏爻履卦。

Gengwu, the 187th cycle, the 2233rd generation, its Jiazi year is the first year of Han Xuan Di's Wufeng era. Xinwei, the 188th cycle, the 2245th generation, its Jiazi year is the first year of Western Jin Hui Di's Yongxing era (the original text says 'Weixing'); by the 2255th generation's Wuyin year, it is the first year of Tang Gaozu's Wude era. Renshen, the 189th cycle, the 2257th generation, its Jiazi year is the first year of Tang Gaozong's Lindi era; by the 2266th generation's Bingshen year, it is the founding year of Song Taizu's reign. Guiyou, the 190th cycle, the 2269th generation, its Jiazi year is the second year of Song Renzong's Tiansheng era; by the 2277th generation's Jiazi year, it is the first year of the Yuan Dynasty's Ziyuan era, and the Dingwei year enters the line nine two of the Dàyǒu hexagram. Jiaxu, the 191st cycle, the 2281st generation, it is exactly the 17th year of Ming Hongwu's reign, the Jiazi year entering this cycle. By Wuyin, the 195th cycle, the solar term meets Xiaoshushu, and the leap line is the Lǚ hexagram.

月未八，星二百四十，辰三千八百八十，年八萬六千四百。遯 遯此當第八會，計二百四十運，二千八百八十世，八萬六千四百年，節交大暑，閏爻隨卦至戊申第二百二十五運，節交立秋，閏爻漸卦。

The month is in the sign of Wei, the star is the eighth, the day is two thousand eight hundred and eighty (the original text says 'three thousand eight hundred and eighty,' which is inconsistent with the following text), and the year is eighty-six thousand four hundred. The hexagram Duan (Avoiding) corresponds to the eighth cycle, totaling two hundred forty changes, two thousand eight hundred and eighty generations, and eighty-six thousand four hundred years. When the solar term reaches the beginning of the heat (Dazhu), the leap trigram is the hexagram Sui (Following); when reaching Wushen and the 225th change, the solar term reaches the beginning of autumn (LiQiu), and the leap trigram is the hexagram Jie (Gradual Progress).

月申九，星二百七十，辰三千二百四十，年九萬七千二百。否 否此當第九會，計二百七十運，三千二百四十世，九萬七千二百年。節交處暑，閏爻剝卦，至戊寅第笫二百五十五運，節交白露，閏爻升卦。

The month is Shen, the star is Jiū, the day pillar is Sanqian'erbaoshi, and the year is Jiǔwànqīqiānèrshí. The Gua "Pu" (Obstruction) is in the ninth cycle, totaling two hundred seventy cycles, three thousand two hundred forty generations, and nine thousand seven hundred twenty years. When the solar term reaches the beginning of the White Dew, the leap line is the Gua "Sheng" (Increase).

月酉十，星三百，辰三千六百，年十八萬八千。觀。 觀此當第十會，計三百運，三千六百世，一十萬八千年，節交秋分，閏爻升卦，至戊申第二百八十五運，節交寒露，閏爻鼎卦。

The month is You, the star is ten, the day is three thousand six hundred, and the year is ten thousand eight hundred. The Guan hexagram corresponds to the tenth cycle, which includes three hundred periods, three thousand six hundred generations, and ten thousand eight hundred years. When the solar term reaches Autumn Equinox, the leap line is the Sheng hexagram; when reaching the Wushen, the second hundred and eighty-fifth period, and the solar term reaches Cold Dew, the leap line is the Ding hexagram.

月戍十一，星三百三十，辰三千九百六十，年一十一萬八千八百，《剝》。 此第十一會計三百三十運，三千九百六十世，一十一萬八千八百年，節交霜降，閏爻《否》卦戊寅，第三百一十五運，節交立冬閏爻《益》卦，當此一會之半，從有入無謂之閉物，則其視於開物，相去遠矣。然則如是而已乎，祝氏曰：窮則變，變則通，—元之後，安知不復有一元以繼之。

The month is戌, the star is eleven, the celestial stem and earthly branch combination is Wuyin, the year is eleven ten thousand eight hundred and eighty, and it corresponds to the hexagram of "Breaking Up." This is the eleventh cycle, comprising three hundred and thirty changes, three thousand nine hundred and sixty generations, and eleven ten thousand eight hundred and eighty years. At the time of the frost descent solar term, the leap line is the hexagram of "Non-communication"; when reaching Wuyin and the three hundred and fifteenth change, at the time of the beginning of winter solar term, the leap line is the hexagram of "Increase." In the middle of this cycle, all things return from existence to non-existence, called "closing things." Compared to the initial "opening things," they are already very different. Is this the end? Zhu said: when something reaches its extreme, it will change; when it changes, it will become unblocked. After one cycle, who knows if another cycle will not follow?

月亥十二，星三百六十，辰四千三百二十，年一十二萬九千六百。《坤》。 此第十二會，計三百六十運，四千三百二十世，一十二萬九千六百年。節交小雪圖閏爻戊申，第三百四十五運，運交大雪閏爻，比卦當此為混沌之世，浩浩無窮，生生不息，天運循環，無往不復，經子會，又復開天矣。康節先生所以書日甲月子星甲辰子者，以日甲後有乙日、丙日，丁之元元也。

The month is亥, the star is twelve, the earthly branch is four thousand three hundred twenty, the year is twelve thousand nine hundred sixty, and it corresponds to the 《Kun》 trigram. This is the twelfth cycle, totaling three hundred sixty changes, four thousand three hundred twenty ages, and twelve thousand nine hundred sixty years. The solar term meets Xiaoxue (here the original text has an error or omission); by Wushen, the third hundred and forty-fifth change, it meets Daxue, and the leap trigram is 《Bi》. At this time, it is the age of chaos, boundless and vast, yet still continuously generating and transforming; the heavenly cycle continues, with movement followed by return, and once the Zi cycle is passed, the heavens once again begin anew. Master Kangjie wrote "day Jia, month Zi, star Jia, branch Zi" because after a Jia day there are still Yi, Bing, Ding days, and beyond one Yuan there are still other Yuan.

每三百六十年配也二十四氣，毎一氣一年，各準四爻，共二百五十六卦，—千五百三十六爻，而卦變一周，周而復始也，歷代不復贅演，自午會第十一運甲子世戊申年夬卦九五爻直事，乃洪武元午也。至甲子年乃洪武十七年也。

Every 360 years corresponds to the 24 solar terms, with each term governing a year, each paired with four lines, resulting in a total of 256 hexagrams and 1,536 lines; after one cycle of hexagram changes, the process repeats. The detailed calculations through the ages are not recounted here. Starting from the eleventh cycle of the午 (Wu) period and the Jiazi era's Wushen year, the line nine in the fifth position of the Guai hexagram takes charge, which coincides with the first year of the Ming dynasty's Hongwu era; by the Jiazi year, it reaches the seventeenth year of Hongwu.

月為小運卦，起《升》、《蒙》、《蠱》、《井》，每一分二氣，當氣之日，未當氣時辰之前，是前節氣之卦，既交氣時辰之後，交氣時辰多少，用蔵閏四爻，次日子時，方用正節氣之四爻，此經世書蔵閏之法也。

The hexagram for the month belonging to the "minor cycle" starts with the hexagrams of Ascending, Ignorance, Restlessness, and Well. Each hexagram governs two solar terms. On the day of the intersection of terms, for the time before the intersection, the hexagram of the previous solar term is still used. After the intersection time, according to the amount of time passed since the intersection, the "hidden leap" is first applied to the fourth line. Only on the next day at the hour of Zi (midnight) does the fourth line of the current solar term officially come into use. This is the method of "hidden leap" described in the "Classic of the World."

逐月用卦，以節氣而藏，惟以晦朔弦望之虛也，月大則七日三時為春，七日三時為夏，七日三時為秋，七日三時為春冬，此經世書之用卦，所以備氣盈虛之妙用，而元會運世各有縮，為一元、一會、一運、一世、一年、一月、一日、一時及微而一秒，亦可準元元會運世與歲月日時，此分秒所以行乎其間，斂大為小，衍小為大，大以用小，小以用大，所以自天地而至豪釐之事物，皆不能逃乎卦數也。

The use of hexagrams for each month is based on the solar terms to adjust for the leap month. This is because between the new moon, full moon, upper waxing moon, and lower waning moon, there is naturally a cycle of fullness and emptiness. When a month is a large month, it is divided into seven days three times as spring, seven days three times as summer, seven days three times as autumn, and seven days three times as winter. The "Classic of the World" uses hexagrams in this way to encompass both the fullness of the seasons and the emptiness of the new moon. The concepts of yuan, hui, yun, and shi each have their own cycles of expansion and contraction. Whether it is a yuan, a hui, a yun, a shi, a year, a month, a day, an hour, or even as fine as a second, they can all be compared with yuan, hui, yun, shi and the years, months, days, and hours to deduce. "Fen" and "miao" move within this framework: transforming large into small and small into large; using the large to manage the small and the small to manage the large. Therefore, from the heavens and earth down to the smallest details, nothing can escape the hexagram numbers.

經世書蔵閏，各有妙旨，蔵閏所以為運行顯閏，所以為休咎，如顯閏則一日二十四，分為閏，一月二十四時為閏，（五刻當一時）一年二十四日為閏，（六十刻當一日）一世二十四月為閏，—運二十四年為閏，一會二十四世為閏，閏主天地內之兵革疫歷饑荒，然亦分下為—十六，以分野推之。

The "Jingshi Book" explains that the hidden leap years have their own profound meanings: hidden leap years are used to promote the movement of time, while visible leap years are used to determine fortune and misfortune.the so-called visible leap years means that in a day, twenty-four parts are added as a leap; in a month, twenty-four hours are added as a leap (five parts equal one hour); in a year, twenty-four days are added as a leap (sixty parts equal one day); in a lifetime, twenty-four months are added as a leap; in a cycle, twenty-four years are added as a leap; in an era, twenty-four lifetimes are added as a leap. The leap years oversee calamities such as warfare, plague, and famine between heaven and earth; however, they are further divided into sixteen parts, and these are used to determine the fate according to the earthly regions.