Earlier Heaven Trigrams Diagram

此伏羲方位之圖，易之本也。故乾一坤八、兌二艮七、離三坎六、震四巽五，各各相對，不惟其數合成九數，其畫亦各各相對合成九畫焉。夫九乃老陽之數，無所不包。自震至乾為順，自巽之坤為逆。數往順天而左行，皆已生之卦，故云「數往者順」；知來逆天而右行，皆未生之卦，故云「知來者逆」。

This is Fuxi's diagram of directions, the foundation of the Book of Changes. Therefore, Qian pairs with Kun, Dui pairs with Gen, Li pairs with Kan, and Zhen pairs with Xun; each pair of trigrams adds up to nine when their numbers are combined, and their lines also add up to nine. Nine is the number of old yang, encompassing all. From Zhen to Qian is in the order of heaven, and from Xun to Kun is in the reverse order. "Counting the past" follows the heavenly way to the left, counting already existing trigrams, so the Commentary on the Trigrams says, "Counting the past is in the order." "Knowing the future" goes against the heavenly way to the right, predicting trigrams that have not yet appeared, hence it is said, "Knowing the future is in the reverse order."

附圖一: 圖二 : 圖三: 圖四: 圖五 : 圖六： 圖七：

The original book is accompanied by seven illustrations, numbered one through seven; this edition only retains the titles of the illustrations, and the actual images have been lost.

後天為流行之用，出乎震，齊乎巽，相見乎離，致役乎坤，說言乎兌，戰乎乾，勞乎坎，成言乎艮，此文王方位之圖，易之用也。先天之離東坎西，象日月之出乎卯、入乎酉；後天之離南坎北，象天地之正子午。先天非後天，則無以成其變化；後天非先天，則無以自行。予按：先天，造化之初由心出跡之學；後天，生物之後因跡求心之學。心與道皆虛，不為物礙也；在先天之先不為無，在後天之後不為有，跡不能外也。朱子謂康節之學得於先天，看得道理透徹，自然前知耳。

The later heaven trigrams explain the function of things in the world. The "Say on the Trigrams" states that "all things emerge from Zhen (Thunder), align with Xun (Wind), meet at Li (Fire), are directed by Kun (Earth), expressed through Dui (Lake), struggle in Qian (Heaven), labor in Kan (Water), and completed in Gen (Mountain)." This is the King Wen's directional diagram, which represents the application of the Book of Changes. In the earlier heaven diagram, Li is in the east and Kan is in the west, symbolizing the rising of the sun and moon at the卯 (Mao) position and their setting at the酉 (You) position. In the later heaven diagram, Li is in the south and Kan is in the north, symbolizing the central axis of the universe, the子 (Zi) and午 (Wu) positions. Without the later heaven, the earlier heaven cannot complete its transformations; without the earlier heaven, the later heaven cannot function on its own. I believe that the earlier heaven is the study of the origin before creation, where form arises from the mind. The later heaven is the study of things after they have been created, where the mind is sought from form. Both the mind and the Dao are empty, not obstructed by external things. Before the earlier heaven, it is not "nothing," and after the later heaven, it is not "something." Form and traces always depend on it. Master Zhu said that Kangjie's learning relied on the earlier heaven, and with a thorough understanding of principles, he could foresee events.

經世衍易圖 太傳曰：易有太極，是生兩儀，兩儀生四象，四象生八卦，八卦定吉凶，吉凶生大業。予謂天地出於易，易非出於天地；聖人作易，而易不作於聖人也。易有太極者何也？當夫元氣渾淪，陰陽未判，是為太極〇

This is the "Classic of the World's Evolution through the Book of Changes." The "Great Treatise" says: "The Book of Changes contains the Taiji, from which the two principles (yin and yang) arise; the two principles generate the four images, the four images generate the eight trigrams, and the eight trigrams determine fortune and misfortune, which in turn give rise to great undertakings." I believe that heaven and earth arise from the Book of Changes, not the other way around; sages merely recorded the Book of Changes, but the Book of Changes itself was not created by sages. What does "the Book of Changes contains the Taiji" mean? When the primordial qi is undifferentiated and yin and yang have not yet been separated, this is the Taiji, represented by a hollow circle in the diagram.

及夫元氣既分動輒為陽 靜者為陰 動之上生一奇謂之陽 動之上生一偶謂之陰 靜之上生一奇謂之剛 靜之上生一偶謂之柔 合而言之陰陽剛柔四象也

When the vital energy splits into two parts, the active aspect is called Yang, and the passive aspect is called Yin. On top of 'movement', a single line is generated called Yang, and an even line is generated called Yin. On top of 'stillness', a single line is generated called Gāng, and an even line is generated called Róu. Together, Yin, Yang, Gāng, and Róu are known as the Four Symbols.

四象陽之上生一奇謂之太陽 生一偶謂之太陰 陰之上生一奇謂之少陽 生一偶謂之少陰 四象剛之上生一奇謂之少剛 生一偶謂之少柔 柔之上生一奇謂之太剛 生一偶謂之太柔

Among the four images, on top of 'Yang' arises a single line called Taiyang (Sun), and a double line called Taiyin (Moon). On top of 'Yin' arises a single line called Shaoyang (Less Yang), and a double line called Shaoyin (Less Yin). Also, on top of 'Gang' (strength) arises a single line called Shaogang (Less Gang), and a double line called Shaorou (Less Soft). On top of 'Rou' (softness) arises a single line called Taigang (Great Gang), and a double line called Tairou (Great Soft).

故太陽為乾，太陰為兌，少陽為離，少陰為震，少剛為巽，少柔為坎，太剛為艮，太柔為坤。此伏羲畫卦之自然形體次第，而孔子發明之，故曰：易有太極，是生兩儀，兩儀生四象，四象生八卦，八卦定吉凶。此言最為切要，古今說者雖多，惟康節、明道二先生之說得之。故康節所謂乾一、兌二、離三、震四、巽五、坎六、艮七、坤八，正謂此也。

Thus, the Sun is associated with the Trigram Qian, the Great Yin with Dui, the Lesser Yang with Li, the Lesser Yin with Zhen, the Lesser Strength with Xun, the Lesser Softness with Kan, the Great Strength with Gen, and the Great Softness with Kun. This is the natural sequence of forms that Fuxi created when he drew the trigrams. Confucius later explained and developed this, so the Great Treatise says, "The Book of Changes has the Taiji, from which the two principles arise; the two principles generate the four images; the four images produce the eight trigrams; the eight trigrams determine fortune and misfortune." These few words are most essential. Although many people have explained them throughout history, only two scholars, Kangjie (Shao Yong) and Mingdao (Cheng Hao), have truly grasped the essence. Kangjie's statement that Qian is one, Dui is two, Li is three, Zhen is four, Xun is five, Kan is six, Gen is seven, and Kun is eight, refers precisely to this order.

夫易之未作，易在太極之先；易之既作，一在太極之內。八卦畫而吉凶定，吉凶定而大業生。以言乎法象之大，則有易中之天地，乾坤是也；以言乎變通之大，則有易中之男女，震巽六子是也；以言乎著名之大，則有易中之日月，離坎是也；以言乎崇高之大，則有易中之富貴，日新月盛、富有大業是也；以言乎利用之大，則有易中之生人，神道設教、順動服民是也；以言乎深遠之大，則有易中之蓍龜，某爻吉、某爻凶是也。

Before the Book of Changes was written, the principles of the Book of Changes were already present before the Taiji; once the Book of Changes was completed, the concept of "one" was contained within the Taiji. When the eight trigrams were drawn, fortune and misfortune were determined; once fortune and misfortune were determined, great undertakings arose. In terms of the grandness of the model and image, the Book of Changes contains heaven and earth, represented by the trigrams Qian and Kun; in terms of the grandness of change and adaptability, the Book of Changes contains male and female, represented by the six trigrams Zhen, Xun, and the others; in terms of the grandness of clarity and manifestation, the Book of Changes contains sun and moon, represented by the trigrams Li and Kan; in terms of the grandness of elevation and dignity, the Book of Changes contains wealth and honor, meaning the daily renewal and flourishing of great achievements; in terms of the grandness of utility, the Book of Changes contains the way of nurturing the people, where sages established teachings through divine principles, acted in accordance with heaven, and won the people's allegiance; in terms of the grandness of depth and subtlety, the Book of Changes contains the divination tools of the tortoise shell, the yarrow stalks, and the methods of divination, which can determine whether a particular line is auspicious or inauspicious.

此皆言易中之大業。非聖人立卦作易，孰能備天下之物、致天下之用、成天下之器，若是其廣大悉備矣乎？天地之道，陰陽剛柔，有動靜之兩儀，必有一元之太極。康節明天地陰陽剛柔始於太極之動靜，與周子所傳太極相表裡。康節復窮其變交，推天之陰陽、地之剛柔各自相交而生八卦，有相交而天以乾兌離震四卦生西北十六位，而後陰陽之用盡焉；地以坤艮坎巽四卦升東南十六位，而後剛柔之用盡焉。

All these discussions pertain to the great principles of the Book of Changes. If it were not for the sages establishing trigrams and composing the Book of Changes, who else could comprehensively record all things under heaven, fully utilize all the functions of the world, and successfully create all the instruments, achieving such vastness and completeness? The way of heaven and earth involves yin and yang, firmness and flexibility, and movement and stillness, and thus there must be the primordial Taiji. Kangjie explained that the yin and yang, firmness and flexibility of heaven and earth originate from the movement and stillness of the Taiji, complementing the Taiji theory passed down by Zhou Dunyi. Kangjie further explored its interactions and transformations, deducing that the yin and yang of heaven and the firmness and flexibility of earth each interact to produce the Eight Trigrams: heaven uses the trigrams Qian, Dui, Li, and Zhen to generate the sixteen positions in the northwest, thereby exhausting the functions of yin and yang; earth uses the trigrams Kun, Gen, Kan, and Xun to generate the sixteen positions in the southeast, thereby exhausting the functions of firmness and flexibility.

雖然，天地自交而未至於相交以生物也。是故動靜者，天地分太極之初；四象者，天地稟太極之理；十六卦者，天地達太極之用，而用在於交也。太極為一，一生二為動靜，二生四為陰陽剛柔，四生八為八卦，八生十六為十六位。分天地，則天有十六位、地有十六位，為三十二矣，是皆加倍之數也。

But at this time, heaven and earth were only interacting within themselves, not yet interacting with each other to produce all things. Therefore, it is said: movement and stillness are the state of heaven and earth when they first separated from the Taiji; the four images are the principles that heaven and earth receive from the Taiji; the sixteen hexagrams are the applications of heaven and earth in realizing the Taiji, and this 'application' entirely lies in 'interaction'. Taiji is one; from one comes two, which are movement and stillness; from two comes four, which are yin and yang, hardness and softness; from four comes eight, which are the Eight Trigrams; from eight comes sixteen, which are the sixteen positions. When viewed separately, heaven has sixteen positions and earth has sixteen positions, making a total of thirty-two, all of which are numbers that double at each level.

一十六有二者天地各分其一用以為體是體也動之大者謂之太陽 動之小者謂之少陽 靜之大者謂之太陰 靜之小者謂之少陰 太陽為日太陰為月少陽為星少陰為辰日月星辰交而田之體盡矣靜之大者謂之太柔 靜之小者謂之少柔 動之大者謂之太剛 動之小者謂之少剛 太柔為水太剛為火少柔為土少剛為石水火土石變而地之體盡矣

The reason there are two sets of ten stems and branches is that heaven and earth each receive one set to serve as their "body." For heaven: the greatest movement is called the Sun, the lesser movement is called the Lesser Sun; the greatest stillness is called the Great Yin, the lesser stillness is called the Lesser Yin. The Sun corresponds to the sun, the Great Yin corresponds to the moon, the Lesser Sun corresponds to stars, and the Lesser Yin corresponds to the constellations. When the sun, moon, stars, and constellations intermingle, the body of heaven is complete (the original text's "田之体" is a miswriting of "天之体"). For earth: the greatest stillness is called the Great Softness, the lesser stillness is called the Lesser Softness; the greatest movement is called the Great Strength, the lesser movement is called the Lesser Strength. The Great Softness corresponds to water, the Great Strength corresponds to fire, the Lesser Softness corresponds to earth, and the Lesser Strength corresponds to stone. When water, fire, earth, and stone change, the body of earth is complete.

自太極之判，以陰陽剛柔為天地之用，乃體之用也；自陰陽剛柔分太少，生為八卦，為天地之體，乃用之體也。今日月星辰交而天之體盡，水火土石交而地之體盡，則主生言之；而天以日月星辰交為十六卦也，地以水火土石交為十六卦也，則十六卦又各為生物之體，則主位言之也。

From the perspective of the division of the Taiji, taking yin and yang and firmness and softness as the functions of heaven and earth, this is "function within the body"; from yin and yang and firmness and softness further divided into major and minor to produce the Eight Trigrams, serving as the forms of heaven and earth, this is "body within the function." Now, speaking of the intersection of sun, moon, and stars exhausting the body of heaven, and the intersection of water, fire, soil, and stone exhausting the body of earth, this is from the perspective of "originating." Heaven produces sixteen trigrams through the intersection of sun, moon, and stars, and earth produces sixteen trigrams through the intersection of water, fire, soil, and stone. These sixteen trigrams then become the fundamental forms of living beings, this is from the perspective of "position."

太者得氣之多，少者得氣之少也。日月星辰麗乎天，而乾為日者太陽也，兌為月者太陰也，離為星者少陽也，震為辰者少陰也。日月星辰交，而日有四位：乾、夬、大有、大壯；月有四位：履、兌、暌、歸妹；星有四位：同人、革、離、豐；辰有四位：無妄、隨、噬嗑、震，而為十六矣。非天之體盡於此乎？

The term "Tai" refers to receiving more energy, while "Shao" refers to receiving less. The sun, moon, and stars are attached to heaven: The trigram Qian represents the sun, belonging to Taiyang; the trigram Dui represents the moon, belonging to Taiyin; the trigram Li represents the stars, belonging to Shaoyang; and the trigram Zhen represents the morning star, belonging to Shaoyin. After the sun, moon, and stars intersect, the sun has four positions—Qian, Gua, Da You, and Da Zhuang; the moon has four positions—Lu, Dui, Kui, and Gui Mei; the stars have four positions—Tong Ren, Ge, Li, and Feng; and the morning star has four positions—Wu Wang, Sui, Shi He, and Zhen. Together, they form sixteen hexagrams. Is not the essence of heaven exhausted here?

水火土石麗乎地，而坤為水者太柔也，艮為火者太剛也，坎為土者少柔也，巽為石者少剛也。水火土石交，而水有四位：坤、剝、比、觀；火有四位：謙、艮、蹇、漸；土有四位：師、蒙、坎、渙；石有四位：升、蠱、井、巽，而為十六矣。非地之體盡於此乎？

Water, fire, earth and stone are attached to the earth: The hexagram "Kun" represents water, belonging to the category of excessive softness; the hexagram "Gen" represents fire, belonging to the category of excessive firmness; the hexagram "Kan" represents earth, belonging to the category of slight softness; the hexagram "Xun" represents stone, belonging to the category of slight firmness. After the intermingling of water, fire, earth and stone, water has four hexagrams — "Kun," "Bo," "Bi," and "Guan"; fire has four hexagrams — "Qian," "Gen," "Jian," and "Jian"; earth has four hexagrams — "Shi," "Meng," "Kan," and "Huan"; stone has four hexagrams — "Sheng," "Gu," "Jing," and "Xun," making a total of sixteen hexagrams. Has the nature of the earth not been fully exhausted?

洪範以水火木金土為造化之用，此以五行有石土無金木者：木為土之子，有土無木，母孕子胎也；石者金之胞，有石而無金，子藏母胞也。

The *Hongfan* uses water, fire, wood, metal, and earth as the Five Phases for generating and transforming; yet here, the Five Phases include stone and earth but not metal or wood. The reason is that wood is the son born from earth, so even though earth is present, wood is not listed, just as a mother carries a fetus in her womb. Stone is the amniotic membrane of metal, so even though stone is present, metal is not listed, just as a son is hidden within the mother's womb.

天地四象圖 日月星辰麗乎天，而乾兌離震生；水火土石麗乎地，而坤艮坎巽生。日午中而氣熱，故為暑；月子中而氣冷，故為寒。月十干之星為陽而主晝，十二支辰為陰而主夜，皆天之氣也。水降而為雨，地氣上騰也；火熾而生風，地氣旁達也；地氣夜升而為露，星殞有聲而主雷，皆地之氣也。

This is the diagram of the Four Images of Heaven and Earth. The sun, moon, and stars are attached to heaven, originating from the trigrams Qian, Dui, Li, and Zhen. Water, fire, soil, and stone are attached to earth, originating from the trigrams Kun, Gen, Kan, and Xun. When the sun reaches the position of Wu, which is the center, the heat is strongest, so it governs the summer season. When the moon reaches the position of Zi, which is the center, the cold is strongest, so it governs the winter season. The ten heavenly stems are associated with stars that are yang and govern the day, while the twelve earthly branches are associated with the hours that are yin and govern the night. These are all the heavenly qi. When water descends, it becomes rain, which is the earth qi rising up. When fire is intense, it produces wind, which is the earth qi spreading out in all directions. The earth qi rises at night and condenses into dew. When stars fall and make a sound, it indicates thunder. These are all the earth qi.

日月星辰自相交，而天之變盡於十六卦；水火土石自相交，而地之變盡於十六卦。是天地之氣凝結而生物，有物斯有質，有質則有數。故乾在天成象為月，在地成形為火，火與日本一體，故陽燧取於日而得火；兌在天成象為月，在地成形為水，水與月本一體，故方諸取於月而得水；離在天成象為星，在地成形為石，石與星本一體，故傳言星殞為石。

The sun, moon, and stars interrelate with each other, and the changes of heaven are fully expressed in the sixteen trigrams. Water, fire, earth, and stone also interrelate with each other, and the changes of earth are fully expressed in the sixteen trigrams. This is how the vital energies of heaven and earth condense to produce all things: when there is an object, there is form; when there is form, there is number. Therefore, the trigram 「Qian」 (Heaven) takes the form of the sun in heaven and the form of fire on earth—fire and the sun are essentially the same, so using a concave bronze mirror called 「Yang Sui」 to face the sun can produce fire (the original text mistakenly says 「formed as the moon」, it should be 「formed as the sun」). The trigram 「Dui」 (Lake) takes the form of the moon in heaven and the form of water on earth—water and the moon are essentially the same, so using a vessel called 「Fang Zhu」 to face the moon can produce water. The trigram 「Li」 (Fire) takes the form of stars in heaven and the form of stone on earth—stone and stars are essentially the same, so ancient texts say that falling stars become stones.

震在天成象為辰，在地成形為土，辰與土本一體。故自日月星之外，高而蒼蒼者皆辰也；自水火石之外，廣而茫茫者皆土也。蓋日月星辰猶人之有耳目口鼻，水火土石猶人之血氣骨肉也。是故數者，盡天下之物則也；得乎數，則物之則、事之理無不在焉。不明乎數，不明乎善矣；不誠乎數，不誠乎身矣。

The trigram Zhen represents thunder in heaven and earth. In heaven, it forms the image of Chen; in earth, it takes the form of soil. Chen and soil are essentially one, so apart from the sun, moon, and stars, the vast expanse above is Chen; apart from water, fire, stone, the boundless terrain below is soil. The sun, moon, stars, and constellations are like a person's ears, eyes, mouth, and nose; water, fire, soil, and stone are like a person's blood, qi, bones, and flesh. Therefore, "numbers" can exhaust the principles of all things under heaven and earth. When one masters numbers, the principles of things and the truths of affairs are all contained within them. Without understanding numbers, one cannot comprehend "goodness"; without being sincere and without falsehood in numbers, one cannot achieve "sincerity" in oneself.

易之與極，其旨若相似而致用實不同。易之與極，八卦名同而位殊，爻同而旨異。位之殊，先天後天之圖可識矣；旨之異，卦同而象不同也。故易之乾為天、為君，而極則為日、為暑；易之兌為澤、為金，而極則為寒、為月；易之離為火、為日，而極則為星、為晝；易之震為雷、為木，而極則為辰、為夜；易之巽為風、為木，而極則為石、為雷；易之坎為水、為月，而極則為土、為露；易之艮為山、為土，而極則為火；易之坤為地、為土，而極則為水、為雨矣。

The principles of the Book of Changes (Yi) and the Huangji Jingshi seem similar at first glance, but their actual applications differ. Both schools use the same names for the eight trigrams, but their positions differ. The lines of the trigrams are the same, but the meanings they convey are different. The difference in position can be identified by comparing the diagram of the primordial (Qian Tian) and the diagram of the later heaven (Hou Tian). The difference in meaning lies in the fact that although the trigrams are the same, the images they represent differ. Therefore, in the Yi, the trigram Qian represents Heaven and the sovereign; in the Huangji Jingshi, it represents the sun and summer. In the Yi, the trigram Dui represents a marsh and metal; in the Huangji Jingshi, it represents cold and the moon. In the Yi, the trigram Li represents fire and the sun; in the Huangji Jingshi, it represents stars and daylight. In the Yi, the trigram Zhen represents thunder and wood; in the Huangji Jingshi, it represents the hour of the dragon and night. In the Yi, the trigram Xun represents wind and wood; in the Huangji Jingshi, it represents stone and thunder. In the Yi, the trigram Kan represents water and the moon; in the Huangji Jingshi, it represents earth and dew. In the Yi, the trigram Gen represents a mountain and earth; in the Huangji Jingshi, it represents fire. In the Yi, the trigram Kun represents earth and earth; in the Huangji Jingshi, it represents water and rain.

易以占為神，極以算為智。占者聽圓變之蓍，以求將見之象；算者布一定之卦，以銜無窮之數。占則取象於天，神之研幾也；算則斷在於人，智之極深也。神以知來，而未嘗不藏往；知以藏往，而未嘗不知來也。左為天，右為地。日月星辰麗乎天，而離震乾兌居之；水火土石麗乎地，而坤艮坎巽居之。體數有四，布算之法皆源於此。 附圖8：

The Book of Changes uses divination to represent "the divine," while the Huangji treats calculation as "wisdom." The person performing divination relies on the flexible and changing yarrow stalks to seek out the emerging images; the person performing calculation arranges fixed hexagrams to connect endless numbers. Divination draws images from heaven, belonging to the subtle and profound exploration of the divine; calculation is based on human judgment, belonging to the deep exploration of wisdom. The divine can know the future, yet it does not exclude the past; wisdom can contain the past, yet it does not exclude knowing the future. On the diagram, the left side represents heaven and the right side represents earth: the sun, moon, and stars are attached to heaven, occupied by the hexagrams Li, Zhen, Qian, and Dui; water, fire, soil, and stone are attached to earth, occupied by the hexagrams Kun, Gen, Kan, and Xun. There are four types of numerical principles, and the method of calculation originates from here. The original text includes an illustration of eight diagrams below.

愚嘗考之：陽一為奇，陰二為偶，是以一元之數起於乾，故乾為起數之端，猶一歲包年月日時而為之也。乾之後有兌，兌為月，其數二，衍之為十二，猶一歲有十二月也；兌之後有離，離為日，其數三，衍之為三百六十，猶一歲有三百六十日也；離之後有震，震為時，其數四，衍之為四千三百二十，猶一歲有四千三百二十時也。

I once studied: Yang is odd, beginning with one, and Yin is even, beginning with two. Therefore, the number "one" originates from the Trigram Qian (Heaven), and Qian is the beginning of counting, just as a year includes years, months, days, and hours. After Qian comes Dui (Lake), which represents the month, with the number two; extending this, it becomes twelve, just as a year has twelve months. After Dui comes Li (Fire), which represents the day, with the number three; extending this, it becomes three hundred and sixty, just as a year has three hundred and sixty days. After Li comes Zhen (Thunder), which represents the hour, with the number four; extending this, it becomes four thousand three hundred and twenty, just as a year has four thousand three hundred and twenty hours.

此一二三四為天地生物之始數，陽之所以先乎陰也。震之後繼以巽五，陰元之氣莫先於此，是以巽元之年數衍之為十二萬九千六百年，為起數之端。坎六繼之，是為巽元之月數，衍之為一百五十五萬五千二百月；艮七又繼之，是為巽元之日數，衍之為四千六百六十五萬六十日；若夫巽元之時數，則居坤之八焉，又衍之為五萬五千九百八十七萬二千時。此五六七八又為天地成物之終數，陰之所以承乎陽也。

These numbers one, two, three, and four are the initial numbers of heaven and earth generating all things, clearly indicating that yang comes before yin. After the Trigram Zhen (Thunder), comes the Trigram Xun (Wind), which is in the fifth position. The yin origin's energy begins here, so the number of years for the Xun origin is calculated as 129,600 years, serving as the starting point. The Trigram Kan (Water) is in the sixth position, representing the monthly count of the Xun origin, calculated as 1,555,200 months; the Trigram Gen (Mountain) is in the seventh position, representing the daily count of the Xun origin, calculated as 46,656,000 days (the original text is missing one 'thousand'). As for the hourly count of the Xun origin, it falls in the eighth position, the Trigram Kun (Earth), calculated as 559,872,000 hours. These numbers five, six, seven, and eight are the concluding numbers of heaven and earth forming all things, clearly indicating that yin follows yang.

由是重而衍之，以至於八，則乾之世數四千三百二十，衍之為五萬五千九百八十七萬二千；兌之世數五萬一千八百四十，衍之為六十七萬一千八百四十六萬四千。循而推之，皆可概見。

From this, we can further derive the numbers for the eighth layer. The number of generations for the Trigram Qian (Heaven) is 43,200, which can be derived as 559,872,000. The number of generations for the Trigram Dui (Lake) is 51,840, which can be derived as 6,718,464,000. Following this sequential calculation, the numbers for the remaining trigrams can also be approximately determined.

大抵乾兌離震之數，包巽坎坤艮在其中。子至巳上六辰皆屬乾，謂之先天；自午至亥下六辰皆屬坤，謂之後天。後天皆效先天而為之，故曰「成象謂之乾，效法謂之坤」，可舉隅而知。 附圖9：

In general, the numbers of the trigrams 乾, 兑, 离, and 震 already include 巽, 坎, 坤, and 艮. From Zi to Si, the first six earthly branches belong to 乾, called Xian Tian (Earlier Heaven); from Wu to Hai, the latter six earthly branches belong to 坤, called Hou Tian (Later Heaven). The Later Heaven follows the pattern of the Earlier Heaven, so the Great Treatise says, "Forming an image is called 乾, following and emulating is called 坤." Knowing one corner allows one to infer the rest. The original text includes a diagram nine.

伏羲六十四卦圓圖（此乃先天之所覆也） 愚謂圓圖者，天地之陰陽也。在天為日月星辰、寒暑晝夜，謂之流行之易，言其天地四時流行而不息也。其卦皆從中起：自坤生者始於復，自乾生者始於姤，皆在天地之中。中者，心也，萬事萬化生於心。是康節之學本於先天之易，尚象而不尚辭，蓋欲示不言之教，如伏羲六十四卦初無言語文字也。

The Circular Diagram of Fuxi's Sixty-Four Hexagrams (this refers to the scope covered by the diagram of the Heaven and Earth). I believe the circular diagram discusses the yin and yang of heaven and earth: in heaven it is the sun, moon, stars, cold and heat, day and night, called "the changing of the easy," which refers to the continuous movement and transformation of heaven and earth through the four seasons. Its hexagrams all begin from the center: those derived from the Hexagram of Earth start from the Hexagram of Reversion, and those derived from the Hexagram of Heaven start from the Hexagram of Meeting, both originating from the center of heaven and earth; "center" is the heart, and all things and transformations originate from the heart. This shows that Kangjie's learning is based on the ancient Book of Changes, emphasizing hexagram images rather than hexagram statements, aiming to carry out education without words, just like the Sixty-Four Hexagrams originally drawn by Fuxi contained no characters at all.

圖左三十二陽卦，春以發生，夏以長養，自復至乾得一百一十二陽爻、八十陰爻，是陽數多陰數少，即春夏之晝長而熱也。圖右三十二陰卦，秋以收斂，冬以包藏，自姤至坤得一百一十二陰爻、八十陽爻，是陰數多陽數少，即秋冬之晝短而寒也。

The left half of the diagram consists of thirty-two yang trigrams, representing the growth and flourishing of spring and summer. From the trigram "复" to "乾," there are 112 yang lines and 80 yin lines, with more yang and fewer yin lines, corresponding to the longer days and warmer weather of spring and summer. The right half of the diagram consists of thirty-two yin trigrams, representing the gathering and concealment of autumn and winter. From the trigram "姤" to "坤," there are 112 yin lines and 80 yang lines, with more yin and fewer yang lines, corresponding to the shorter days and colder weather of autumn and winter.

左右三十二而為六十四卦，又以春夏秋冬分之，各四其六十四，而為一千五百三十六卦之氣，以運行於天。四象立體，六甲循環，以見皇帝王霸之跡治；三百六旬有六日轉旋，乾坤主之，屬乎天地之造化。衍之為元會運世，散之為歲月日時。事有體用而分皇帝王霸，業有心跡而分易書詩禮春秋，理無往而不在其

The trigrams are divided into two groups of thirty-two, making a total of sixty-four trigrams. These are then divided into four parts according to the four seasons, and the sixty-four trigrams are multiplied four times, resulting in a total of fifteen hundred and thirty-six trigrams, which circulate in the heavens. The four fundamental elements establish their essence, and the sixty Jiazi cycles continuously, thus revealing the governance of emperors, kings, and rulers. The rotation of the year, consisting of three hundred and sixty-six days, is governed by the trigrams Qian and Kun, representing the creation and transformation of heaven and earth. Extending this principle leads to the concepts of Yuan, Hui, Yun, and Shi, which spread out to include years, months, days, and hours. Events have both essence and function, hence distinguishing between emperors, kings, and rulers. Achievements have both intention and manifestation, hence distinguishing the classics of the I Ching, Shang Shu, Shi Jing, Li Ji, and Chun Qiu. This principle is present in all things.

伏羲六十四卦方圖 愚謂方圖者，地道之剛柔也。在地為水火土石、風雨露雷，謂之對待之易，言其承天時行以生物也。其卦皆從中起，自中而起則震巽之一陰一陽，故陰至巽而伏，亦至巽而止；陽至震而休，亦自震而生。陰陽二氣交乎震巽，實坎離交乎黃庭之象也。

The "Fuxi Sixty-Four Trigrams Square Diagram." I believe the square diagram discusses the principle of hardness and softness in the earth. On the earth, it includes water, fire, soil, stone, wind, rain, dew, and thunder, which is called "the mutual opposition of the Book of Changes." It refers to how it follows the heavenly timing and operates to nurture all things. All the trigrams originate from the center; starting from the center, they fall upon the trigrams Zhen and Xun, which represent one yin and one yang. Yin reaches Xun and becomes hidden, and also reaches Xun and comes to rest; yang reaches Zhen and rests, and also originates from Zhen. The interaction of yin and yang energies meets at Zhen and Xun, which is actually the meeting of Kan and Li energies at the "Central Palace" (the central part of the body as described by Daoist alchemists).

內一截三十二陽卦，西北角乾，東北角泰；外一截三十二陰卦，西南角坤，東南角否，亦共六十而為六十四卦。又以元會運世分之，各四其六十四，以為二百五十六位之卦體，以生物於地。四四立體，四九為用，以見律呂音聲、陽唱陰和、動植飛走、出生入死，坎離主之，屬乎地之造化。故邵子有詩云：「天地定位，否泰交類；山澤通氣，咸損見義；雷風相薄，恆益起意；水火相射，既濟未濟。四象相交成十六事，八卦相蕩為六十四。」此正言方圖之意也。 附圖10：

Inside the first layer are thirty-two yang trigrams, with the trigram 《Qian》 (Heaven) at the northwest corner and the trigram 《Tai》 (Peace) at the northeast corner; outside the first layer are thirty-two yin trigrams, with the trigram 《Kun》 (Earth) at the southwest corner and the trigram 《Po》 (Disaster) at the southeast corner. Together, they form the sixty-four trigrams. Then, according to the divisions of yuan, hui, yun, and shi, they are each divided into four, and the sixty-four trigrams are multiplied four times, forming a structure of two hundred and fifty-six trigrams, used to represent living beings on earth. Four multiplied by four in three dimensions, and four multiplied by nine in application, thus revealing that the tones of the musical scale, the harmonious interaction of yang and yin, and the birth and death of animals and plants, birds and beasts, are all governed by Kan (Water) and Li (Fire), which belong to the creative power of the earth. Therefore, Shaozi wrote a poem saying: Heaven and Earth are positioned, 《Po》 and 《Tai》 are interrelated; Mountains and Marshes communicate, 《Xian》 and 《Sun》 show meaning; Thunder and Wind interact, 《Heng》 and 《Yi》 express intention; Water and Fire oppose each other, 《Ji Ji》 and 《Wei Ji》 are formed. The four elements interacting form sixteen matters, and the eight trigrams interacting form sixty-four. This is exactly explaining the meaning of the square diagram. The original book includes ten accompanying diagrams.

朱子曰：先天圖自左方《震》初，為冬至，《離》、《兌》中，為春分，至《乾》之末，而交夏至，右方自《巽》初為夏至，《坎》、《艮》中，為秋分，至《坤》之末，而交冬至。圖之順逆左右，先儒說之詳也。

Master Zhu said: The diagram of the Heavenly Stem begins with the trigram Zhen (Thunder) on the left, corresponding to the winter solstice; it reaches the middle between Li (Fire) and Dui (Lake), corresponding to the spring equinox; and reaches the end of Qian (Heaven), corresponding to the summer solstice. On the right side, starting with Xun (Wind), it corresponds to the summer solstice; it reaches the middle between Kan (Water) and Gen (Mountain), corresponding to the autumn equinox; and reaches the end of Kun (Earth), corresponding to the winter solstice. The principle of the diagram's order and reverse order has already been explained in detail by previous scholars.

夫《乾》一、《兌》二、《離》三、《震》四，已生之卦也。其序自南而北。若卦氣運行，則自北而南，一陽生於《震》始。故邵子以冬至之半為《復》。十一月中也。

The trigrams 乾 (Qian), 兑 (Dui), and 离 (Li) are already formed trigrams, and their order is arranged from south to north. However, when considering the movement of the trigram energies, it flows from north to south, with one yang beginning to arise from the trigram 震 (Zhen). Therefore, Shao Yong designated the period of the winter solstice, specifically the middle of the Zi month, as the trigram 复 (Fu), which corresponds to the middle of the eleventh month.

十二月丑初小寒，其卦為《頤》、《屯》、《益》，月半大寒，則《震》、《噬嗑》、《隨》。正月寅初立春，其卦為《無妄》，為《明夷》，月半雨水，則《賁》、《既濟》、《家人》，二月卯初驚蟄，其卦為《豐》、《離》、《革》，月半春分，則《同人》、《臨》，

In the first part of the twelfth month (Chou month), when the Minor Cold begins, the corresponding hexagrams are The颐 (Yi), The屯 (Zun), and The益 (Yi); when the Major Cold begins in the middle of the month, the corresponding hexagrams are The震 (Zhen), The噬嗑 (Shi He), and The随 (Sui). In the first part of the first month (Yin month), when the Beginning of Spring begins, the corresponding hexagrams are The无妄 (Wu Wang), The明夷 (Ming Yi); when the Rain Water begins in the middle of the month, the corresponding hexagrams are The贲 (Ben), The既济 (Ji Ji), and The家人 (Jia Ren). In the first part of the second month (Mao month), when the Awakening of Insects begins, the corresponding hexagrams are The丰 (Feng), The离 (Li), and The革 (Ge); when the Vernal Equinox begins in the middle of the month, the corresponding hexagrams are The同人 (Tong Ren) and The临 (Lin).

三月辰初清明，其卦為《損》、《節》、《孚》，（此處應為《中孚》卦，省略一“中”字）月半穀雨，則《歸妹》、《暌》、《兌》，四月巳初立夏，其卦為《履》、《泰》，月半小滿，則《大畜》、《需》、《小畜》，五月午初芒種，其卦為《大壯》、《大有》、《夬》，至《乾》之末交夏至焉。

In the beginning of the third month (the month of the Dragon, Chen), when it meets Qingming, the corresponding hexagrams are "Loss" "Moderation" and "Faith" (which should be "Middle Faith," with the character "中" omitted in the original text). When it meets Guyu in the middle of the month, the corresponding hexagrams are "Return of the Young Wife" "Strife" and "Joy." In the beginning of the fourth month (the month of the Snake, Si), when it meets Lixia, the corresponding hexagrams are "Following" and "Great Crossing." When it meets Xiaoman in the middle of the month, the corresponding hexagrams are "Great Accumulation" "Necessity" and "Small Accumulation." In the beginning of the fifth month (the month of the Horse, Wu), when it meets Mangzhong, the corresponding hexagrams are "Great Strength" "Great Possession" and "Parting." At the end of the hexagram "Qian" comes Jiashan.

《巽》五、《坎》六、《艮》七、《坤》八，未生之卦也。其圖自西而北，若卦氣之行，自一陰生於《巽》始，故夏至午之半為《姤》，五月中也，

The trigrams 《Xun》, 《Kan》, 《Gen》, and 《Kun》 are all unformed trigrams, arranged from west to north on the diagram. In terms of the movement of the trigrams' energies, the initial yin begins with 《Xun》, so the half of the summer solstice, specifically the middle of the month of Wu, is designated as the trigram 《Gou》, which corresponds to the middle solar term of the fifth lunar month.

六月未初小暑，其卦為《大過》、《鼎》、《恆》，月半大暑，則《巽》、《井》、《蠱》，七月申初立秋，其卦為《升》、《訟》，月半處暑，則《困》、《未濟》、《解》，八月酉初白露，其卦為《渙》、《坎》、《蒙》，月半秋分，則《師》、《遯》，九月戌初寒露，其卦為《咸》、《旅》、《小過》，月半霜降，則《漸》、《蹇》、《艮》，十月亥初立冬，其卦為《謙》、《否》，月半小雪，則《萃》、《晉》、《豫》，十一月子初大雪，其卦為《觀》、《比》、《剝》、，至坤之末交冬至焉，即子之半也。

In June (the month of Wei), at the beginning when the Minor Heat begins, the corresponding hexagrams are Great Excess, Cauldron, and Constancy; when the Major Heat begins in the middle of the month, the corresponding hexagrams are Wind, Well, and Pestilence. In July (the month of Shen), at the beginning when the Beginning of Autumn begins, the corresponding hexagrams are Ascending and Strife; when the Beginning of Autumn begins in the middle of the month, the corresponding hexagrams are Obstruction, Non-Completion, and Release. In August (the month of You), at the beginning when the White Dew begins, the corresponding hexagrams are Dispersing, Water, and Innocence; when the Autumn Equinox begins in the middle of the month, the corresponding hexagrams are Army and Retreat. In September (the month of Xu), at the beginning when the Cold Dew begins, the corresponding hexagrams are Attraction, Travel, and Small Excess; when the Frost Descent begins in the middle of the month, the corresponding hexagrams are Gradual Progress, Obstruction, and Mountain. In October (the month of Hai), at the beginning when the Beginning of Winter begins, the corresponding hexagrams are Humility and Non-Preponderance; when the Minor Snow begins in the middle of the month, the corresponding hexagrams are Convergence, Progress, and Joy. In November (the month of Zi), at the beginning when the Heavy Snow begins, the corresponding hexagrams are Observation and Comparison and Decrease; when the hexagram of Earth comes to its end, the Winter Solstice occurs, which is the middle of the month of Zi.

此三十二卦屬陰，以當秋冬，子至巳，《乾》、《兌》、《離》、《震》，六陽月，其節有四，冬至、立春、春分、立夏也。午至亥，《巽》、《坎》、《艮》、《坤》，六陰月，其節有四，夏至、立秋、秋分、立冬也。一年八節二之，計一十六卦，外有十六卦，三之計四十八卦，並之則六十四卦，以當一期之氣候，所以定時成歲，行鬼神成變化也。

These thirty-two trigrams are yin in nature and correspond to the seasons of autumn and winter. From Zi to Si, there are six yang months governed by the trigrams Qian, Dui, Li, and Zhen, with four major solar terms: Winter Solstice, Start of Spring, Spring Equinox, and Start of Summer. From Wu to Hai, there are six yin months governed by the trigrams Xun, Kan, Gen, and Kun, with four major solar terms: Summer Solstice, Start of Autumn, Autumn Equinox, and Start of Winter. There are eight solar terms in a year, each paired with two trigrams, totaling sixteen trigrams. In addition, there are another sixteen trigrams, each paired with three parts, totaling forty-eight trigrams. When these two groups are combined, they make up the sixty-four trigrams, corresponding to the climate of a whole year. By using this method, one can determine the seasons, accomplish the achievements of the year, carry out the use of spirits, and bring about the changes of all things.

《乾》、《坤》、《坎》、《離》分配四時，主二十四氣，《坤》盡子中，交《離》初爻冬至，上爻驚蟄，《離》盡卯中，交乾初爻春分，上爻芒種，《乾》盡午中，交《坎》初爻夏至，上爻白露，坎盡酉中，交《坤》初爻秋分，上爻大雪。

The four trigrams Qian, Kun, Kan, and Li are assigned to the four seasons and oversee the twenty-four solar terms. The trigram Kun ends in the middle of the Zi month, followed by the first line of the trigram Li corresponding to the winter solstice and the top line corresponding to the start of惊蛰 (Jingzhe). The trigram Li ends in the middle of the Mao month, followed by the first line of the trigram Qian corresponding to the spring equinox and the top line corresponding to Mangzhong. The trigram Qian ends in the middle of the Wu month, followed by the first line of the trigram Kan corresponding to the summer solstice and the top line corresponding to BaiLu. The trigram Kan ends in the middle of the You month, followed by the first line of the trigram Kun corresponding to the autumn equinox and the top line corresponding to Daxue.

春、夏、秋、冬各有六十四卦氣，皆從中起，子、午、卯、酉為四仲，二分二至當之，寅、申、巳、亥為四孟，四立當之，經世曆以冬至為天地之元，元之元也。故去四正卦，而用三百六十卦氣圖，以春分為人物之元，亦元之元也。故用六十四卦而四之，而二百五十六位卦氣圖。

The four seasons each have the energy of sixty-four hexagrams, all starting from the center. The months of Zi, Wu, Mao, and You are the four middle months, corresponding to the two solstices (Spring Equinox and Autumn Equinox) and the two solstices (Winter Solstice and Summer Solstice). The months of Yin, Shen, Si, and Hai are the four beginning months, corresponding to the four beginnings of the seasons (Start of Spring, Start of Summer, Start of Autumn, Start of Winter). The calendar in the "Jingshi" text takes the Winter Solstice as the beginning of heaven and earth, which is the "primary center within the primary," so it uses only the hexagram energy diagram of 360 hexagrams, excluding the four cardinal trigrams Kan, Li, Zhen, and Dui. It also takes the Spring Equinox as the beginning of human beings, which is also the "primary center within the primary," so it multiplies the sixty-four hexagrams by four, resulting in a hexagram energy diagram of 256 positions.

以冬至子中為世之元，春分卯中為元之元，夏至午中為會之元，秋分酉中為運之元，各六十四卦，各以氣運而更疊值事。開物於寅中，而起於驚蟄者，二月初氣也。閉物於戌中，而終於立冬者，十月初氣也。

Taking the winter solstice (the middle of the Zi month) as the beginning of the "world," the spring equinox (the middle of the Mao month) as the beginning of the "origin," the summer solstice (the middle of the Wu month) as the beginning of the "convergence," and the autumn equinox (the middle of the You month) as the beginning of the "movement," each is paired with the sixty-four hexagrams, and each takes turns in turn according to the seasonal changes to oversee affairs. The creation of all things begins in the Yin month, but actually starts at the Awakening of Insects, which is the first solar term of the second month; the concealment of all things occurs in the Xu month, but actually ends at the Beginning of Winter, which is the first solar term of the tenth month.

何也？曰：寅中戌中雖主月會而言，其用實由乎節氣，地之生物以氣為機，天之氣先至，而後地之物應之，氣之來常先半月，氣以舒而常盈，用以疾而常縮，故關朗子云：當期之數，過者謂之氣盈，不及者謂之朔虛，朔者盈虛之不齊，積微之久，中氣中有居於月晦者，必閏以置之，乃復於初經，本於先天，故中朔同起卦氣，因先天卦氣取中氣，以主月元會運世，皆從中起，所謂舉正於中也。

Why? Because although寅 and戌 are considered in terms of the month and the constellation, the actual factor at work is the solar term. Living things on earth respond to the qi: the heavenly qi arrives first, and then the earthly things respond accordingly. The arrival of qi usually occurs half a month earlier. Since the qi is gradual, there is often surplus; when it is used quickly, there is often deficiency. Therefore, Guan Langzi said: the number of days in a year should be complete, the excess is called "qi surplus," and the deficiency is called "new moon deficiency." Since the surplus and deficiency of the new moon are not consistent, over time, the middle qi will fall on the last day of the month. Therefore, a leap month must be inserted to return to the original regular pattern. This method originates from theEarlier Heaven (primordial heaven), so the middle qi and the new moon day start the hexagram qi together. According to the primordial hexagram qi, the middle qi is used to govern the month. The terms yuan, hui, yun, and shi all begin with "zhong" (middle), which is called "establishing the correct through the middle."

卦圖曰：大運法當從經世，數起於星甲、辰子，小運法當依卦氣圖，起甲仲巳孟日，天統乎體，氣之體生於四仲，故大運甲子當冬至，而二十四氣之中，皆得子午卯酉之四中也，氣之用行於四立，故小運甲寅當立春，而二十四氣之首，皆得寅、申、巳、亥，而生乎孟矣。

The hexagram diagram states that the calculation of the great destiny should follow the numbers from the "Classic of the World," starting from "Star Jia" and "Chen Zi." The calculation of the small destiny should follow the hexagram qi diagram, starting from the day of Jia, which belongs to the middle, and the day of Si, which belongs to the first. Heaven governs the "body," and the body of qi originates from the four middles, so the great destiny of Jiazi corresponds to the winter solstice, and the middle qi among the twenty-four solar terms all fall on the positions of Zi, Wu, Mao, and You, which are the four middles. The use of qi flows through the four beginnings, so the small destiny of Jiayin corresponds to the beginning of spring, and the first solar term among the twenty-four solar terms all fall on the positions of Yin, Shen, Si, and Hai, which are the four firsts.