The combined numbers of the Earlier and Later Heaven Trigrams.

先後天八卦，既各有其本位本數，而體用相生，升降變化，由合而分，亦由分而合。是以《易》之《彖》、《象》凡涉言數者，亦各有體用之不同。先天八卦本數者，以河圖為體者也。後天八卦本數者，以洛書為體者也。先後天八卦合數者，兼先後天之象而納十干之數者也。此數相傳最古，虞氏《易》即用此數也。

The Earlier Heaven and Later Heaven Trigrams each have their own fundamental positions and numbers, and their principles and applications interact and transform with each other, rising and falling continuously. They merge and then separate, and also separate and then merge again. Therefore, in the Zhou Changes, the Commentary on the Judgment and the Image Commentary, wherever numbers are involved, they also differ in terms of principle and application. The fundamental numbers of the Earlier Heaven Trigrams are based on the Yellow River Chart, while the fundamental numbers of the Later Heaven Trigrams are based on the Luo Writing. As for the combined numbers of the Earlier and Later Heaven Trigrams, they integrate both the Earlier Heaven and Later Heaven Trigram forms, and are paired with the numbers of the ten Heavenly Stems. This system of numbers is said to be the most ancient. Yu Fan, a commentator of the Han dynasty, used this system in his annotations of the Zhou Changes. Therefore, when reading Han dynasty annotations of the Zhou Changes, whenever numbers are discussed, one must first determine which system the commentator is using, in order to avoid misinterpretation due to confusion.

古納甲圖：東方甲乙配乾坤，南方兌艮配丙丁，西方庚辛屬震巽，而坎戊離己中央，因壬癸為乾坤兼納也。此圖壬癸居北屬坎離，以坎離代乾坤。有作離一坎六.者，陰陽互根，亦自可通。並前兩圖合觀之，當知邵子數與《易》之分別矣。

The ancient Najia diagram assigns the heavenly stems and earthly branches as follows: in the east, Jia and Yi are paired with Qian and Kun; in the south, Bing and Ding are paired with Dui and Gen; in the west, Geng and Xin are paired with Zhen and Xun; while Wu is assigned to Kan and Ji is assigned to Li in the center. As for Ren and Gui, they are included by both Qian and Kun. This diagram places Ren and Gui in the north and assigns them to Kan and Li, using Kan and Li to replace Qian and Kun. There is also a version that assigns Li to one and Kan to six, taking the meaning that yin and yang depend on each other as roots, which is equally reasonable. When this diagram is combined with the previous two diagrams, it becomes clear how Shao Yong's system of numbers differs from the numerical system of the Zhou Changes.

天地範圍數，相傳即《連山》卦數。因其以艮為始終，所謂“範圍天地而不過，曲成萬物而不遺”者也。略舉例如左：

"The range of numbers covering heaven and earth" is said to be the hexagram numbers of the Xia Dynasty's "Lianshan" Yi. This system begins and ends with the Gen hexagram, which corresponds exactly to the meaning in the "Xici Zhuan" that "it encompasses all changes of heaven and earth without exceeding, and skillfully completes all things without omission." Below are a few examples, listed on the left side (the original book had a chart here, but the chart has been lost in the source).

右圖始艮一，終艮十，而又以艮七為用，象數體用皆艮，故有《連山》易數之名。雖未必即為《連山》，而其象則兼先後天，數則合河圖洛書。與納甲納音，融會而貫通之者也。天地萬物之數，莫能外於是矣。

The sequence of numbers in this diagram starts with "Gen" (Mountain) paired with one and ends with "Gen" paired with ten, with "Gen" paired with seven serving as the actual position used in practice. Thus, both the "body" (the essence of form and number) and the "function" (the application) of the symbolic and numerical system fall under "Gen." Because of this, this system is called the "Lianshan" system of divination. It may not be the original version of the "Lianshan" from the Xia dynasty, but it incorporates both the Earlier Heaven Trigrams and the Later Heaven Trigrams in terms of symbolic representation, and it conforms to both the Yellow River Chart and the Luo Writing in terms of numerical structure. Furthermore, it integrates both the "Najia" system (pairing the Eight Trigrams with the Heavenly Stems) and the "Nayin" system (pairing the sixty jiazi with the five tones and Five Phases) into a unified whole. There is no number related to the myriad things in the universe that can exist outside of this framework.

陽數極於九，陰數極於六。陽，天也。天之用皆見於地，故數至六而體全，得七而六數之用行也。太陽無七，太陰無十，而艮兼用一、七、十者，一始十終，七則具成終成始之用者也。

The number of Yang is limited to nine, while the number of Yin is limited to six. Yang belongs to Heaven, which itself has no form; its function must manifest on Earth to be visible. Therefore, the number reaches six, completing the "body" of Earth's aspect. Going further to seven, the "function" of six begins to operate — seven is the first step after six, marking the transition from the "body" to the "function." Among the Four Symbols, the number of "Sun" is nine rather than seven (seven belongs to Minor Yang), and the number of "Great Yin" is six rather than ten (ten lies beyond the Four Symbols). Only the Gate (Geng) hexagram uses the numbers one, seven, and thirteen: one is the starting point, ten is the endpoint, and seven is in the middle, possessing the function described in the "Commentary on the Hexagrams" as "the one that completes and begins all things." Therefore, this diagram begins with Geng one and ends with Geng ten, with Geng seven serving as the central point for practical application.

夫《易》開物成務，冒天下之道，如斯而已者，非他，即天一，地二，天三，地四，天五，地六，天七，地八，天九，地十之數也。八卦成列，天地之數，分陰分陽，與八卦並列，而五位配合，五行生布也，干支屬也。

The Great Treatise says that the Book of Changes can "open things and accomplish tasks, encompassing all the principles under heaven." This means developing all things and achieving success, covering all the principles of the world. What is meant by "nothing more than this" is the sequence of numbers listed in the Great Treatise: Heaven one, Earth two, Heaven three, Earth four, Heaven five, Earth six, Heaven seven, Earth eight, Heaven nine, Earth ten. Once the Eight Trigrams are arranged in order, these ten numbers distinguish yin and yang—odd numbers belong to Heaven and are yang, while even numbers belong to Earth and are yin—thus being paired with the Eight Trigrams. The ten numbers also pair up as one with six, two with seven, three with eight, four with nine, and five with ten, forming five groups of directions. From this, the Five Phases emerge and are arranged, and the assignments of the Heavenly Stems and Earthly Branches are determined accordingly.

一始十終，順往逆來，六十四卦先後天往復循環，周而復始，而數有不周，獨闕西北。先天則艮闕，後天則乾無，而盈虛消長，於以無閥，皆出“乾知大始”。冒天下之道，以極天之數，定天下之象，通天下之志，定天下之業，斷天下之疑，興神物以前民用，盡在於斯矣。

These ten numbers start from one and go up to ten. Counting them in order or reversing the count, the sixty-four hexagrams cycle back and forth between the Earlier Heaven and Later Heaven arrangements, continuing endlessly. However, there is one place that remains incomplete: the Northwest is missing a position. According to the Earlier Heaven arrangement, the Northwest is Gen, which is not assigned a number; according to the Later Heaven arrangement, the Northwest is Qian, which also does not have a number. The reason the cycle of full and empty, increase and decrease in the universe can continue forever without being blocked is precisely because of this gap. The basis for this gap comes from the "Great Treatise" which says "Qian knows the beginning." Qian is only concerned with the beginning and does not fall into the realm of form and numbers. The "covering all the ways of the world" mentioned in the "Great Treatise" includes exhausting the numbers of Heaven, determining the images of the world, communicating the aspirations of people, achieving the affairs of the world, deciding the doubts of the world, and using divination tools like yarrow stalks to guide the daily lives of the people, all of which are included in this system of numbers.

坎子一，艮丑二寅三，震卯四，巽辰五巳六，離午七，坤未八申九，兌酉十，乾戌亥無數。子午南北至卯酉春秋分，寒暑往來，日月出入，先天咸無，後天乾無，皆以無出有。此《易》數之精義入神，《易》道之廣大悉備，皆在此八卦成列之時位象數。

The specific arrangement is as follows: Kan is placed at the center of the north and paired with Zi, receiving the number one; Gen spans the positions of Chou and Yin, with Chou receiving the number two and Yin receiving the number three; Zhen is placed at the center of the east and paired with Mao, receiving the number four; Xun spans the positions of Chen and Si, with Chen receiving the number five and Si receiving the number six; Li is placed at the center of the south and paired with Wu, receiving the number seven; Kun spans the positions of Wei and Shen, with Wei receiving the number eight and Shen receiving the number nine; Dui is placed at the center of the west and paired with You, receiving the number ten; Qian spans the positions of Xu and Hai, but is not assigned a number. Zi is at the center of the north, and Wu is at the center of the south, corresponding to the winter solstice and summer solstice; Mao is at the center of the east, and You is at the center of the west, corresponding to the spring equinox and autumn equinox. The coming and going of cold and heat, the rising and setting of the sun and moon all turn at these four points. The northwest position is not assigned a number in the Earlier Heaven arrangement (in the Earlier Heaven arrangement, the northwest belongs to Gen, which is already missing a number), and in the Later Heaven arrangement, Qian is not assigned a number. Both are generated from 'nothing' to create 'something'. The precision and subtlety of the numbers in the Book of Changes, and the comprehensiveness and vastness of the Way of the Book of Changes, all lie in the coordination of time, position, image, and number when the Eight Trigrams are arranged in sequence.

宋後言《易》，先別門戶，爭道統，宗宋者以老莊之說為異端，宗漢者以先天卦位為不經，而《易》遂無從言矣。程傳號為易學正宗，而程子《自序》，謂予所傳者辭也，冀學者由辭以得其意。然《彖》、《象》十翼之辭，無一辭一字，不由象數而來。舍象數而言辭，辭烏從得哉！此圖之數，前人所未言。清季青田端木鶴田氏始創為之圖，簡要精當，足與經傳相參證。與舊有諸圖會而通之，不但於數理之要領可得，而古今來占筮推步之本源，悉在於是矣。

After the Song dynasty, those who discussed the Book of Changes usually began by distinguishing schools of thought and competing for the transmission of the Way. Those who revered Song learning condemned the interpretations based on Laozi and Zhuangzi as heretical, while those who revered Han learning considered the Earlier Heaven hexagram arrangement to have no support in the classics. As a result, the Book of Changes became difficult to discuss. Cheng Yi's Yichuan Commentary on the Changes is claimed to be the orthodox interpretation of the Book of Changes, but in his own preface, Chengzi said that what he passed down was only the statements of the hexagram lines, hoping scholars would understand the meaning through the words. However, the texts of the Commentary on the Judgment, the Image Commentary, and the Ten Wings all come from the principles of images and numbers. If one ignores images and numbers and talks only about the statements, where would the basis of the statements come from? The numbers arranged in this diagram were never discussed by previous generations. It was not until the late Qing dynasty that a person from Qintian, Zhejiang, named Duanguohu (whose courtesy name was Hetian) first drew this diagram, which is clear and accurate enough to be verified with the classics. By integrating this diagram with the existing various diagrams of the Book of Changes, not only can the principles of numbers and reasoning be grasped, but also the origins of divination and astronomical calculations throughout history can be found within it.

既明方位象數，而氣可得言矣。氣不可見，顯之以象，定之以數，而驗之以候。五日為一候，故亦曰卦候。天地陰陽之消息，日月寒暑之往來，萬物生成，變化動靜，莫不先見乎氣。《彖》、《象》、《繫辭》，皆隱合氣候而未明言。

Once the directions and numerical principles have been explained, we can then discuss "qi." Qi is invisible and intangible, and can only be revealed through hexagrams, fixed by numbers, and verified by seasonal phenomena. The ancient calendar divided five days into one "hou," so this system of study is also called "hexagram and seasonal phenomena." In the universe, the waxing and waning of yin and yang, the movement of the sun and moon, the coming and going of cold and heat, and the generation, transformation, and activity of all things—all of these first manifest themselves through qi. The Commentary on the Judgment, the Image Commentary, and the Great Treatise actually contain the principles of climatic changes everywhere, though they do not explicitly state them.

言氣者莫著於京房，遂相傳京房卦氣，實非京氏所創也。周公之時訓與《月令·夏小正》，皆以象數為氣候之準，無不與圖書卦象契合。京氏特整齊而排比之，以六十卦直日用事，以風雨寒溫，定占候災變，或為京房之法耳。

The most famous explanation of the concept of "gu qi" (divinatory climate) comes from Jing Fang of the Western Han dynasty, leading to the tradition of "Jing Fang's Gu Qi." However, this system was not actually created by Jing Fang. It is said to have originated from the Duke of Zhou's "Shi Xun" (a text known as "The Lost Book of Zhou: Shi Xun Jie," which lists seventy-two seasonal signs), as well as from the "Li Ji: Yue Ling" and the "Da Dai Li Ji: Xia Xia Zheng." These texts used numerical patterns and symbolic correspondences to set standards for climate, and every part of them aligned with the Yellow River Chart, the Luo Writing, and the hexagram images. Jing Fang merely organized and arranged existing materials, arranging the sixty hexagrams to take turns governing each day, and then using actual weather conditions such as wind, rain, cold, and warmth to determine seasonal signs and omens of calamities. This method of divination might be the actual original contribution of Jing Fang.

黃粵洲曰：“上繫七爻，起中孚‘鳴鶴在陰’，十一爻起於咸‘憧憧往來’。”卦氣從中孚至井，八十九陽，九十一陰。咸至頤，八十九陰，九十一陽，與《繫傳》恰合。而孔子復於咸言“日月寒暑往來，陰陽屈伸”，是必三代已有此卦象氣候，孔子故於《繫傳》及之，否則安有如此之巧合乎？特著錄其圖。非僅為占卜之用也。

Huang Yuezhou says: The seven line statements cited in the Upper Transmission of the Great Treatise come from the first one in Zhongfou, Nine in the Second, which says "a crane calls in the shade"; the eleven line statements cited in the Lower Transmission start with the first one in Xian, Nine in the Fourth, which says "vague coming and going." According to the arrangement of the hexagram qi, from Zhongfou to Jing, there are eighty-nine yang lines and ninety-one yin lines; from Xian to Yi, there are eighty-nine yin lines and ninety-one yang lines. The two sections exactly reverse yin and yang, matching perfectly the order in which the Great Treatise cites these two hexagrams. Moreover, Confucius also mentions in the lower section of Xian "when the sun goes down, the moon comes up; when cold departs, heat comes" and talks about the mutual influence of yin and yang expanding and contracting. This shows that the study of hexagram patterns corresponding to climate was already present in the Xia, Shang, and Zhou dynasties. Confucius could therefore naturally include it in the Great Treatise; otherwise, how could such a coincidence occur? Therefore, this hexagram qi diagram is specially recorded—it is not merely for divination purposes.

京氏以六十卦當周天三百六十五度四分度之一，每卦值六日七分，故又名為六日七分術。坎離震兌為後天四正，別立為監司，分管二十四氣，不入六十卦之內。六十卦之中，更有復臨泰大壯夬乾姤觀否遁剝坤十二卦為闢卦，分領十二月，每月約五卦。始六日曰公卦，次闢卦，次侯卦，則值月中節氣交界。次大夫，次卿，以畢一月。周而復始。

Jing Fang used the sixty trigrams to correspond with the 365 and 1/4 degrees of the celestial cycle, with each trigram governing six days and seven parts (each day divided into eighty parts), so this method is also called the "Six Days and Seven Parts Method." Kan, Li, Zhen, and Dui are the four cardinal trigrams of the Later Heaven Trigrams, and they are drawn out separately to serve as "Supervisors," each responsible for a quarter of the twenty-four solar terms, and they are not included in the sixty trigrams. From the sixty trigrams, twelve trigrams—Fu, Lin, Tai, Da Zhuang, Guai, Qian, Gou, Guan, Po, Duan, Bo, and Kun—are selected as "Divine Trigrams" (also called Royal Trigrams), each governing one of the twelve months, with each month approximately corresponding to five trigrams. The order within a month is: the first six days are called "Common Trigrams," followed by the "Divine Trigrams," then the "Marquis Trigrams," which correspond to the transition points of the solar terms in the middle of the month; then the "Minister Trigrams," and finally the "Minister of State Trigrams." The month is thus fully arranged, and the cycle repeats.

卦氣起冬至，為中孚之二爻，至七日復卦，十二日復卦畢，第十三十四十五日則屯之內卦當之，約兩卦半當一氣，約十五爻當十五日也。小寒自屯四起，至謙與睽，亦兩卦半也。茲分舉其例如下：

The hexagram energy begins to count from the winter solstice. On the day of the winter solstice, it falls exactly on the second line of the hexagram Zhongfū (Middle Trust). Counting seven days, it enters the hexagram Fu (Return), and by the twelfth day, the hexagram Fu has finished. On the thirteenth, fourteenth, and fifteenth days, the three lines of the lower trigram of the hexagram Tun (Obstruction) take over. Thus, approximately every two and a half hexagrams correspond to a solar term, and about fifteen lines correspond to fifteen days. By the time of Xiaohan (Minor Cold), it starts from the fourth line of the hexagram Tun, passing through Qian (Humility) and Kui (Strife), again covering two and a half hexagrams. Below are examples illustrating this:

或謂京房卦氣出《易緯》，不足以望先天。然按之《繫辭》，既有中孚與咸之前徵，而驗之氣候，又與《時訓》、《夏小正》合，而邵子河洛先天諸數亦不能不採用其說。圖雖別用乾坤坎離，而河洛化工，仍取坎離震兌。蓋實始於《連山》曆法，四監周度。惟首起艮卦，然則京學之自來遠矣。

Some people say that Jing Fang's theory of the hexagram qi comes from the Han dynasty's "Yi Wei," which is not of the same level as the Earlier Heaven school. But when compared with the "Great Treatise," there are already two hexagrams, Zhongfou and Xian, as precedents. When verified against actual climate conditions, it also aligns with the "Shi Xun" and "Xia Xiaozheng." Even Shao Yong's derivation of the Yellow River Chart and Luo Writing and the numbers of the Earlier Heaven system could not avoid using this approach. Although Shao Yong's diagram uses the four hexagrams Qian, Kun, Kan, and Li as the four cardinal directions, when discussing the creative power of the Yellow River Chart and Luo Writing, he still refers to Kan, Li, Zhen, and Dui. This shows that this method actually originates from the Lianshan calendar system, which uses four hexagrams as "jian" (supervisors) to divide the entire celestial circle, except that Lianshan starts with Gen. Thus, the origin of Jing's school of thought is quite ancient.

闢卦主一年十二月，自冬至七日後起，陰陽往復，周而復始。朱子曰：“是當以一爻分三十分，陰陽進退日一分。如陰剝每日剝三十分之一，一月方剝得盡。陽長每日長三十分之一，亦一月方長得成。

The twelve trigrams of the twelve lunar months govern the twelve months of the year. Starting from the seventh day after the winter solstice, yin and yang alternate, continuing in a cycle. Zhu Xi said that each line should be further divided into thirty parts. Yin and yang advance or retreat by one part each day. For example, when yin removes yang, it removes one part of the line each day, taking a whole month to remove the entire line. Similarly, yang grows by one part each day, also taking a month to complete a full line.

故復之一陽，不是頓然便生，乃是自坤卦中積來。從小雪後一日生一分，竟大雪共三十日，生三十分，然後成冬至之一陽。姤之陰亦生於小滿，一日一分，積三十日，然後成夏至之一陰。觀此知陰陽絕續之際，果無一息之間斷也。”

Therefore, the yang line in the hexagram "Fu" does not suddenly appear only at the winter solstice, but rather accumulates bit by bit from the pure yin hexagram "Kun": starting after Minor Snow, one part is generated each day, passing through Major Snow, accumulating thirty parts over thirty days, and only at the winter solstice does it form a complete yang line. Similarly, the yin line in the hexagram "Gou" also begins to form after Minor Full, with one part generated each day, accumulating thirty parts over thirty days, and only at the summer solstice does it become a complete yin line. From this we can see that the moment of alternation between yin and yang is continuous without even a single breath's interruption. All of this is what Master Zhu said.

列子曰：“一氣不頓進。”又曰：“天道密移，疇覺之哉！”聖人作《易》，仰觀俯察，知天地陰陽之運行消息甚微，人無從覺，故以懸象著明之日月，分畫八卦，象陰象陽，以《易》道示人，天道斯昭昭矣。更以六十四卦，合周天之度，自疏而密，由略而詳。由一年十二月，分日分時分刻，以逮秒忽之微，均可顯之以象，推之以數，豈但為吉凶占卜之用哉！

The "Liezi" says: "One breath does not advance all at once." A single breath does not reach its full extent in one step. It also says: "The way of heaven moves secretly, who can perceive it?" The way of heaven quietly shifts in the background, who can notice it? The sages composed the "Yi Jing" by observing the heavens above and examining the geography below. They understood that the movement and change of yin and yang in heaven and earth are extremely subtle, so subtle that people cannot feel them. Therefore, they took the words from the "Great Treatise" that "the most manifest of all celestial phenomena is the sun and moon," and used the sun and moon as a standard to divide the Eight Trigrams. They used a yang line to represent yang and a yin line to represent yin, thus presenting the way of the "Yi Jing" to people, making the way of heaven clearly visible. Further, they used the sixty-four hexagrams to match the degrees of the celestial cycle. Starting from the broad to the detailed, from the general to the specific: from the twelve months of a year, down to days, hours, moments, and even to the extremely fine units of seconds and instances, all can be displayed through images and calculated through numbers. How could this be merely for divining fortune and misfortune?

聖功王道基於是，百姓日用宥於是。彼自絕於天而言人者固背道，舍人以言天者，豈知道哉！孔子之《易》，明天地人三極之通，而齊之於木道(見於風雷益《彖傳》“木道乃行”。古今言《易》者均未注意，而道家亦由之而不知致。《易》道大用始終不明，可慨也夫！)。坎離秉天地之中，震兌劑陰陽之和，以成位育之功。釋道二教，闡咸恆之義，裁成輔相，協乎泰否，所以皆範圍於《易》數之內，而莫能外乎！進象數而言氣精微之蘊，更非潛心玩索，不能會其通也。

The achievements of sages and the governance of emperors are all based on this principle, and the daily lives of common people are also included within its scope. Those who ignore heaven and talk only about human affairs clearly deviate from the Way; conversely, those who ignore human affairs and talk only about heaven do not truly understand the Way. Confucius' transmission of the Book of Changes explains that heaven, earth, and humanity are interconnected, and unifies them under the concept of "wooden way" (this is stated in the Commentary on the Judgment of the Hexagram 41, "Yi" (Benefit), "the wooden way is now in motion"). Throughout history, those who have interpreted the Book of Changes have not paid attention to the fact that Daoism constantly uses this principle without understanding its underlying reasons. The greatest function of the Way of the Book of Changes has never been clearly explained, which is truly regrettable. The hexagrams Kan and Li embody the central positions of heaven and earth, while Zhen and Dui regulate the harmonious balance of yin and yang. Together, they achieve the effect described in the Zhongyong (Doctrine of the Mean), "heaven and earth are in their proper places, and all things flourish." The teachings of Buddhism and Daoism actually expound the meanings of the hexagrams Xian and Heng. Their practices of "completing the way of heaven and earth and assisting in their suitability" do not go beyond the scope of the hexagrams Tai and Pian. Therefore, both religions are encompassed within the numerical system of the Book of Changes and cannot escape from it. As for further exploring the subtle implications of "qi" based on the imagery and numbers, one must first calm the mind and repeatedly contemplate it to fully grasp and integrate it.

按：一卦值六日，共三百六十日，而歲度周，尚餘五日四分日之一。每日以八十分計，五日四分日之一，共得四百二十分，每卦應得七分，故合計六日七分，一卦始畢。五日為一候，三候成一氣，約一氣盡十六爻，為兩卦又四爻。是每月五卦，又盈兩爻也。故卦氣起中孚之二爻。節氣有長短，卦爻亦有盈縮。此揚子雲《太玄》所以分七百二十九贊，以兩贊當一日，以當一歲三百六十四日半，而更以立踦贏二贊，以為坤縮也。

According to this, one hexagram corresponds to six days, and sixty hexagrams total three hundred and sixty days, which completes the measure of one year, with an additional five and one fourth days. If each day is divided into eighty parts, then five and one fourth days amount to four hundred and twenty parts. Dividing these among the sixty hexagrams, each hexagram receives seven parts. Thus, altogether it amounts to six days and seven parts, which makes one hexagram fully accounted for. Five days make a "候" (period), and three periods form a solar term. A solar term roughly uses up sixteen lines, which is two hexagrams and four lines. Therefore, in addition to the five hexagrams per month, there are two more lines, so the starting point of the hexagram energy does not fall on the first line of the Zhongfou hexagram but on its second line. Since solar terms vary in length, the distribution of hexagram lines also varies in expansion and contraction. This is precisely why Yang Xiong (styled Zi Yun) divided his work "Tai Xuan" into seven hundred and twenty nine "zan" (praise): two zan correspond to one day, which exactly matches the three hundred and sixty four and a half days of a year. Additionally, he established two more zan, "qi" and "ying", to account for the remaining days, corresponding to the "contraction" of the Earth element.

卦氣起《中孚·九二》“鳴鶴在陰”。鶴陽鳥也，居漢陰地，陽生於陰之義也。終於頤，“頤者養也”，歸養中宮，至中孚復出。斯造化之機軸。孔子贊《易》，以人事言天道，故贊《中孚·九二》曰“天下應之”，曰“天下之樞機”，可謂天人合一。冬烘先生以附會兩字抹煞之，吾無言矣。

The starting point of the hexagram qi is set at the line "The cry of the crane in the shade" from the hexagram Zhongfu, line nine two. The crane is a yang bird, yet it perches by the water in a shady place, which corresponds to the meaning of the winter solstice when the first yang emerges from the extreme yin. The end of the hexagram qi is at the hexagram Yi. The "Sequence of Hexagrams" says "Yi means nourishment," indicating that the qi returns to the central palace for nurturing, and once it is fully nourished, it re-emerges from Zhongfu. This is the axis of the cycle of creation and transformation. Confucius explained the Yi in terms of human affairs to explain the heavenly way. In the "Great Treatise," when explaining Zhongfu, line nine two, he said "It responds from a thousand miles away," and also said that words and deeds are "the pivot of the gentleman." This can be considered an explanation of the unity of heaven and humanity. Those迂腐 old gentlemen merely dismiss it with the two words "forced interpretation," and I have nothing more to say.

日行與天度每不相及，因有歲差。東晉虞喜云：“五十年退一度。”何承天云：“百年退一度。”隋劉約云：“七十五年退一度。”唐僧一行又以八十三年退一度，許衡郭敬皆謂六十六年有餘退一度，較前說為近。

The sun's annual movement differs slightly from the full circle, thus causing the phenomenon known as "precession of the equinoxes." Yu Xi of the Eastern Jin dynasty said that the sun would regress by one degree every fifty years. He Chengtian of the Southern Song dynasty claimed it would regress by one degree every hundred years. Liu Zhuo of the Sui dynasty (originally written as "Liu Yue") stated it would regress by one degree every seventy-five years. The Buddhist monk Yixing of the Tang dynasty proposed that it would take eighty-three years for the sun to regress by one degree. Xu Heng and Guo Shoujing of the Yuan dynasty (originally written as "Guo Jing") both believed that the sun would regress by one degree in about sixty-six years, which is closer to actual measurements than the previous views.

鄭氏《易譜》引環中子說曰：“周天三百六十五度四分度之一，是正數也。”邵子《皇極》曰：“三百六十五度二十五分七十五秒(邵子以一度作百分，京氏以一日作八十分，故其數異。)。”其二十五分即四分度之一矣，又另多七十五秒，是天過正數外七十五秒也。而歲周止得二百六十五日二十四分二十五秒，是日不及正數二十五秒也。假以天所多七十五秒，補日所少二十五秒，作百秒為一分，則天恰合正數，日亦恰足正數矣。

The Zheng family's "Yi Pu" cites the words of Huanzhongzi, saying that the entire circle of the sky is 365 and 1/4 degrees, which is a standard number, also called the "correct number." Shao Yong in his "Huang Ji Jing Shi" gives a more detailed account: 365 degrees, 25 minutes, and 75 seconds. (Shao Yong divides one degree into 100 parts, while Jing Fang divides one day into 80 parts, so their numbers appear different.) In Shao's calculation, the 25 minutes correspond to a quarter of a degree; in addition, there are 75 seconds more, indicating that the actual movement of the sky exceeds the standard number by 75 seconds. However, the actual cycle of a year is only 365 days, 24 minutes, and 25 seconds (the original text says "265 days," which is likely a mistake for "365 days"). This is 25 seconds less than the standard number. In other words, the sky moves a little more, while the day moves a little less, and the two do not align. If the 75 seconds that the sky moves extra are used to make up for the 25 seconds that the day is short, and then 100 seconds are combined to form one minute for overall calculation, then the sky exactly matches the standard number, and the day also exactly makes up for the standard number—thus the sky and the day each return to their correct positions, and the calculation of the precession of the equinoxes has a common basis.

今乃日止二十四分，比天二十五分為欠一分又二十五秒，比天七十五秒為欠五十秒，故天行餘一分五十秒也。然則日之於大，每年退一分五十秒，十年退十五分也。六十年則退九十分，再加六年，又退九分，是六十六年，其退九十九分，是一度尚欠一分。以每年一分五十秒計之，則一分當八個月，便是六十六年零八個月，即退天一度也。曆法今密於古，當詳求之，以定卦值星度之位。庶數自密合，無毫釐釐之差。於萬事萬物之動靜吉凶，胥可以是準之矣。

Nowadays, the sun has only twenty-four parts, which is one part less than the sky's twenty-five parts. Additionally, considering the difference in seconds, the sun is short by fifty seconds compared to the sky's excess of seventy-five seconds. Therefore, the sky moves one part and fifty seconds more than the sun each year. Continuing this calculation: the sun lags behind the sky by one part and fifty seconds each year. After ten years, it lags by fifteen parts; after sixty years, it lags by ninety parts. Adding six more years, it lags by nine parts, totaling sixty-six years of lagging by ninety-nine parts. This is one part short of a full degree, with each degree being one hundred parts. Calculating the remaining one part at a rate of one part and fifty seconds per year, this remaining part corresponds to about eight months. Therefore, accurately speaking, it takes sixty-six years and eight months for the sun to lag behind the sky by one degree, which exactly matches the previous statement by Xu Hong and Guo Shoujing that "after more than sixty-six years, the sun lags by one degree." Today's calendar is more precise than ancient ones, so we should carefully calculate this to determine the star degrees corresponding to each trigram. In this way, the numbers will naturally align precisely, without any deviation, and the movements, stillness, auspiciousness, and misfortune of all things can be accurately determined.

萬氏彈峰曰：“乾附於坤，坤歸於乾。坤之游魂乾仍歸乾，坤仍歸坤，坤仍歸坤，謂之歸魂。”六子互變，震巽二長，乃四孟月之主。五爻變後退歸四位，震附於巽，巽附於震為游魂。震仍歸震，巽仍歸巽為歸魂。

In the Ming dynasty, Wan Tingyan (pen name: Tanfeng) said: When the trigram Qian changes to its wandering soul form, it attaches to Kun; when the trigram Kun changes to its returning soul form, it returns to Qian. In the wandering soul form of the trigram Kun, Qian still belongs to Qian and Kun still belongs to Kun, which is called "returning soul" (the original text has a repeated character error). The six sons trigrams also change in this way: Zhen and Xun are the elder son and elder daughter, governing the four first months, that is, the first, fourth, seventh, and tenth months. After a trigram changes from the first line up to the fifth line to become the fifth generation trigram, it no longer continues to change upwards, but returns to the fourth line to change into a wandering soul form. Thus, the wandering soul of the Zhen trigram attaches to Xun, and the wandering soul of the Xun trigram attaches to Zhen. Then, when it changes further down to the returning soul form, Zhen still belongs to Zhen and Xun still belongs to Xun.

坎離二中，乃四仲月之主。五爻變後，退歸四位。離附於坎，坎附於離，為游魂。離仍歸離，坎仍歸坎，為歸魂。坎離之游魂在乾坤，乾坤之游魂在坎離。此四正互換之卦。艮兌二少，乃四季月之主。五爻變後，退歸四位。艮附於兌，兌附於艮，為游魂。艮仍歸艮，兌仍歸兌，為歸魂。艮兌之游魂在震巽，震巽之游魂在艮兌。此四隅互換之卦也。此正《說卦》“神也者”一章，去乾坤而言六子之義，乾坤主一歲之運，一卦管一月。六子為四時之主，一卦管十日。月有值月之卦，日月值日之卦，亦理數自然也。

The trigrams Kan and Li represent the middle son and middle daughter, governing the four middle months, which are the second, fifth, eighth, and eleventh months. When the fifth line changes, it returns to the fourth line and becomes a wandering soul. Thus, the wandering soul of the Li trigram attaches to Kan, and the wandering soul of the Kan trigram attaches to Li. When returning to its original state, Li still belongs to Li, and Kan still belongs to Kan. The wandering souls of the Kan and Li trigrams fall upon the Qian and Kun trigrams, and the wandering souls of the Qian and Kun trigrams fall upon the Kan and Li trigrams. This is the mutual exchange between the four cardinal trigrams. The trigrams Gen and Dui represent the young son and young daughter, governing the four seasonal months, which are the third, sixth, ninth, and twelfth months. Similarly, when the fifth line changes, it returns to the fourth line and becomes a wandering soul. The wandering soul of the Gen trigram attaches to Dui, and the wandering soul of the Dui trigram attaches to Gen. When returning to its original state, Gen still belongs to Gen, and Dui still belongs to Dui. The wandering souls of the Gen and Dui trigrams fall upon the Zhen and Xun trigrams, and the wandering souls of the Zhen and Xun trigrams fall upon the Gen and Dui trigrams. This is precisely the intention of the passage in the "Sayings on the Trigrams" that says, "The divine is the one who subtly governs all things and is spoken of in terms of it," which omits Qian and Kun and focuses solely on the six sons. Qian and Kun govern the great destiny of a year, with one trigram governing a month; the six sons govern the four seasons, with one trigram governing ten days. Thus, there are trigrams that govern the month and trigrams that govern the day. This is naturally the way of the reasoning of numbers. The character "month" in the phrase "day and month values" is likely a mistake for the character "have."

京氏卦氣，出於納甲。八宮世應，皆與卦氣一貫。用八宮納甲之法，而莫名其義，得萬氏著明之。始知其天然之序，不假人為。特錄其圖如下，與下《卦用》章八宮參看。

Jing Fang's theory of hexagram qi is rooted in the concept of Najia. The positions of the world and the responding elements in the eight trigrams are all connected with the hexagram qi. People only use the oral formula of Najia for the eight trigrams without understanding the underlying principles. It was not until Wan Tingyan explained it clearly that people realized this order is naturally generated and not artificially arranged. Therefore, his diagram is specially included here for comparison with the section on the eight trigrams in the next chapter titled "Hexagram Usage."

八卦名位象數氣候既明，而用可得言矣。大用大效，小用小效，大小雖殊，其理則一。《彖》、《象》十翼，皆以明用。而無一辭一字，不根於象數。自象數失傳，專尚夫辭。乃望文生義，以今概古，論愛惡不出六爻之外，言變化限於兩象之中。而《彖》、《象》十翼之大義，不明於世也久矣。

The names, directions, symbolic images, numbers, and climatic associations of the Eight Trigrams have already been explained. Now we can discuss their "application." When applied on a grand scale, it produces great results; when applied on a small scale, it produces small results. Although the scale of application differs, the underlying principle remains the same. The Commentary on the Judgment, the Image Commentary, and the Ten Wings were all written to explain this "application," and every word and sentence is rooted in the symbolic images and numbers. Since the symbolic images and numbers have been lost, scholars have focused only on the textual expressions, leading them to misunderstand the original meanings by applying modern ideas to ancient texts. Discussions of love and hatred remain confined within the scope of the six lines, and explanations of change are restricted within the two trigrams above and below. As a result, the true meaning of the Commentary on the Judgment, the Image Commentary, and the Ten Wings has remained obscure for a long time.

朱子《本義》，遂以《易》為聖人教人卜筮之書，以占卜為《大易》之本義。後之學者，既宗程朱，又蔑視數學小道而不屑言，是欲渡而去其楫，卒致占卜之用亦無可徵驗，反不若壬、遁、火珠之術為足憑。《易》道之大，乃盡失其用。舉世徒震其名，視為神秘杳渺而莫敢問津。嗚呼！是誰之過哉！

Zhu Xi wrote The Original Meaning of the Zhou Changes, and he frankly regarded the Book of Changes as a book that sages used to teach people how to divinate. He regarded divination as the original meaning of the Great Change. Later scholars, respecting both Cheng Yi and Zhu Xi, looked down upon the methods of figures and numbers as an inferior path, and did not even mention them. This is like trying to cross a river but first throwing away the oars, resulting in not being able to verify even the function of divination. Instead, methods such as the Six Nines, Dun Jia, and The Forest of Fire Pearls proved more reliable. The Way of the Book of Changes is so vast, yet it has completely lost its function. The whole world is only frightened by its reputation, regarding it as mysterious and distant, and dare not inquire further. Alas, who is to blame for this?

行遠自邇，登高自卑，乾簡坤易，古聖已詔我矣。近取諸身，簡之至也。遠取諸物，易之至也。故又曰：《易》簡而天下之理得矣。天下之理得，而用無不彰。其為用焉，孰大於是？京氏八宮世應飛伏之說，經學家素鄙為術數，而不入於經傳。而其為用簡易，深合於乾坤之變化。

To travel a long distance, one must start from a short step; to climb a high mountain, one must begin from a low place. The Creative (Qian) takes "simplicity" as its virtue, and the Earthly (Kun) takes "ease" as its virtue. Ancient sages have already told us this principle. "Taking from the body nearby" is simplicity to its extreme; "taking from objects afar" is ease to its extreme. Therefore, the Great Treatise says: "Ease and simplicity enable the principles of the world to be understood." Once the principles of the world are grasped, their applications naturally become evident. When it comes to "application," is there anything greater than this? Jing Fang's theory of the eight palaces, the World and Response Lines, and the flying and hidden lines has long been looked down upon by scholars as numerology and not allowed into the classics. However, in practice, it is simple and easy to apply, deeply in harmony with the principles of the Creative and Earthly.

朱子知其用，以囿於世故，不敢昌言，僅取八宮世應歌訣，列《本義》之前，亦與隱名注《參同契》。同一苦心也。程子《易傳》，雖自稱尚辭，亦不能廢陰陽世應之例。術家專取八宮身世遊歸飛伏之用，而又不明乾坤簡易之理，逐末忘本，與經生之有體無用，同一蔽也。

Zhu Xi actually understood its usefulness, but due to the constraints of conventional beliefs, he dared not openly declare it, and only listed the verses on the eight palaces and their corresponding lines at the beginning of the "Original Meaning of the Zhou Changes"; this was the same careful intention as when he concealed his real name to comment on the "Compendium of the Three Traditions of the Zhou Changes." Although Cheng Yi's "Commentary on the Changes by Yichuan" claimed to focus on literary expression, it ultimately could not abandon the framework of yin and yang and the lines of world and response. Conversely, the numerological scholars specialized in using the positions of the body, the world, the wandering soul, the returning soul, and the flying and hidden lines from the eight palaces, yet they did not understand the fundamental principle of simplicity and ease in the trigrams of heaven and earth, focusing on the superficial while forgetting the essential. This is actually the same kind of confusion as that of the scholars of the classics, who have the form but no practical use.

頻年講習，博考周諮，始知三《易》之卦爻象數，同源共貫。京氏之學，實遠符《連山》之曆數，近合《周易》之變通。稽諸經傳，證例正多，爰取為立用之準。有精於術數者，更深求之。以推衍《彖》、《象》十翼之辭，其相得有合者，必不止如吾之所知。知無盡而無窮，占卜云乎哉！

I have studied for many years, extensively examined, and sought advice from many sources, only then realizing that the hexagrams, lines, images, and numbers in the three books of divination, the Lianshan, Guicang, and Zhouyi, all originate from the same source and are interconnected. Jingfang's teachings, when viewed from a distant perspective, align with the calendrical calculations of the Lianshan, and when viewed from a near perspective, they conform to the principle of change in the Zhouyi. By comparing them with the classic texts, there are many verified examples, so I take them as the standard for practical application. In the future, if someone skilled in numerology delves deeper, using them to deduce the words of the Commentary on the Judgment, the Image Commentary, and the Ten Wings, there will certainly be more points of agreement than what I now know. Thus, the truths to be known are boundless, far beyond the limits of the two words "divination."

《易》之大用，孔子《繫傳》，言之詳矣。特後儒類以文字釋之，致孔子之徵言精義，皆忽略讀過，而莫名其蘊蓄宏深之妙。果能以孔子之言，一一以八卦之象數證之，則一字一義，無不各有體用之所在，亦無不各與象數相發明，而“為用不窮”一語決非以空言了之者也。

The great application of the Book of Changes is explained in detail by Confucius in the Great Treatise. However, later Confucian scholars have generally interpreted it through textual analysis and word meanings, leading to Confucius' subtle words being read superficially, and no one being able to grasp the profound and subtle meanings contained within. If we could truly use the images and numbers of the Eight Trigrams to verify every sentence of Confucius, then each word and meaning would have both form and function, and each would be mutually illuminating with the images and numbers. The statement in the Great Treatise that "its application is inexhaustible" would not be a mere superficial phrase.

八卦之用，皆本於乾坤，後天坎離代乾坤之用，而六十四卦之用，莫不由乾坤而生。孔子曰：“剛柔相摩，八卦相蕩。鼓之以雷霆，潤之以風雨。日月運行，一寒一暑。乾道成男，坤道成女。”天地萬物之用，備於是矣(雷霆震與艮風雨巽與兌皆相反之卦也，日月坎離與乾坤皆相對之卦也。詳玩其象，八卦之用可悟矣。)。

The use of the Eight Trigrams originates from Qian and Kun. In the Later Heaven arrangement, the trigrams Kan and Li take over the functions of Qian and Kun, yet the use of the sixty-four hexagrams all comes from Qian and Kun. Confucius said in the Great Treatise: the strong line and the flexible line rub against each other, the Eight Trigrams move and interact with each other, thunder is used to stir them, wind and rain are used to nourish them, the sun and moon alternate in their movement, thus producing the alternation of cold and heat. The way of Qian gives rise to male, and the way of Kun gives rise to female. The functions of heaven and earth and all things are fully contained in these words. Thunder refers to the trigram Zhen, which is opposite to Gen; wind and rain refer to the trigram Xun, which is opposite to Dui; sun and moon refer to Kan and Li, which are opposite to Qian and Kun respectively. These sentences actually go through the Eight Trigrams by means of the relationships of 'opposition' and 'reciprocity'. If one carefully examines these trigrams, one can understand their functions.

而又承之以“乾知大始，坤作成物”。《易》之大用，孰逾於是？故乾用九，坤用六。六十四卦，皆乾坤之用，皆九六之用。乾無方體用不可見，故乾九之用，用於坤六。《傳》曰：“顯諸仁，藏諸用。”乾顯而坤藏，惟藏而用乃顯焉。乾坤象也，九六數也。象數不明，用何由顯？為圖如左，餘卦類推。

Then Confucius added another sentence: "The Creative is aware of the great beginning, and the Receptive forms the completed things." Is there any greater use in the Book of Changes than these two sentences? Therefore, the Creative has "All Nines" and the Receptive has "All Sixes." All sixty-four hexagrams are the use of the Creative and the Receptive, and also the use of the numbers nine and six. The Creative has no position and no form, and its use is invisible. Therefore, the use of nine in the Creative must be manifested through the six of the Receptive in order to become visible. The Great Treatise says: "Manifest it in benevolence, conceal it in use." The Creative is the one that manifests, and the Receptive is the one that conceals. Only by first concealing can use be revealed. The Creative and the Receptive are the images, and nine and six are the numbers; if the relationship between images and numbers is not understood, how can use be revealed? Here is the diagram on the left, and the rest of the hexagrams can be inferred in the same way.

端木鶴田曰：“乾坤天地一二，始子復一，丑臨二。而臨二坎爻，其初復一震爻。天地一二子丑數造始(坎震屯)，一主日，二主月。子復一交午七數，為復‘七日吉’。丑臨二交未八數，為臨‘八月凶’。故七八正當子丑一二正位。《易》，七八數之正也，九六數之變也。七吉以七而九進為用，午進而七數之正。進而用九數之變，乾用九是也。八凶以八而六退為用，未退而八數之正，退而用六數之變，坤用六是也。六坎數，九震數，皆天地一二造始數。乾坤卦用七八正爻用九六變，此其數是也。”

Endumu Guo Hu says: Qian and Kun represent Heaven and Earth, paired with the initial numbers one and two. In the twelve trigrams of the Great Break, the month of Zi (rat) corresponds to the hexagram Fu, paired with one; the month of Chou (ox) corresponds to the hexagram Lin, paired with two. The number two paired with Lin is exactly the number of lines in Kan, while the number one paired with Fu is exactly the number of lines in Zhen. When Kan and Zhen are stacked together, they form the hexagram Tun. The numbers one and two of Heaven and Earth are thus established in the positions of Zi and Chou, initiating all things. One governs the day, two governs the month. The hexagram Fu, paired with one in the Zi position, intersects with the number seven in the opposite position Wu, so the statement of the Fu hexagram says, "After seven days it returns," which is considered auspicious. The hexagram Lin, paired with two in the Chou position, intersects with the number eight in the opposite position Wei, so the statement of the Lin hexagram says, "By the eighth month there is misfortune." This shows that seven and eight are exactly in their original positions of Zi and Chou, one and two. In the Book of Changes, seven and eight are the normal numbers, while nine and six are the abnormal numbers. Seven is auspicious because it progresses from seven to nine, using nine as its number: the position of Wu advances, first reaching seven, the normal number, then further using nine, the abnormal number. The "use of nine" in Qian is exactly this. Eight is inauspicious because it retreats from eight to six, using six as its number: the position of Wei retreats, first reaching eight, the normal number, then further using six, the abnormal number. The "use of six" in Kun is exactly this. Six is the number of Kan, and nine is the number of Zhen, both belonging to the numbers of Heaven and Earth that initiate all things. The hexagrams Qian and Kun use the normal numbers seven and eight in their line positions, but when they are used, they employ the abnormal numbers nine and six, which is exactly this system of numbers.

晁氏公武曰：“餘有志學《易》，本好王氏，妄謂弼之外，自有名象者。果得京氏傳，而文字顛倒舛訛，不可訓知。迨其服習甚久，漸有所窺，今二十有四年矣。乃能以其象數辨正文字，而私識之曰：是書兆乾坤之二象以成八卦，凡八變而六十有四，於其往來升降之際，以觀消息盈虛於天地之元，而酬酢乎萬物之來者，炳然在日也。

In the Song dynasty, Zhao Gongwu said: I resolved to study the Book of Changes, and originally favored the school of Wang Bi. However, I secretly suspected that there should be another school of study concerning the names and images of the hexagrams. Later, I indeed obtained the Jing's Tradition of the Changes, but the text was disordered and confused, making it difficult to read. Only after repeated study over a long period did I gradually begin to understand its principles. By now, twenty-four years have passed. Now I can use its figures and numbers to correct the text, and I have privately recorded my insights: this book begins with the two trigrams Qian (Heaven) and Kun (Earth), generating the eight trigrams, and through eight successive transformations, forms the sixty-four hexagrams. In observing the movement and changes of the lines within the hexagrams, one can perceive the waxing and waning, fullness and emptiness of the fundamental principles of Heaven and Earth, and thus respond to the coming of all things, with clarity as clear as the sun at noon.

大抵辨三《易》，運五行，正四時，謹二十四氣，志七十二候，而位五星，降二十八宿，其進退以幾，為一卦之主者謂之世。奇耦相與，據一以起二而為主之相者謂之應。世之所位而陰陽之肆者，謂之飛。陰陽肇乎所配，而終不脫乎本，以應顯佐神明者謂之伏。起乎世而周乎內外，參乎本數以紀月者謂之建。終之始之，極乎數而不可窮以紀日者，謂之積。會於中而以四為用，一卦備四卦者，謂之互。

In general, this book distinguishes the three Yis, namely the Lianshan, Guicang, and Zhouyi, and operates according to the Five Phases, regulates the four seasons, carefully observes the twenty-four solar terms, records the seventy-two phases, and arranges the positions of the five planets and the twenty-eight constellations. Among these, the one that becomes the main element of a hexagram according to the subtle movement and change of the lines within the hexagram is called 'Shi'; the one that pairs odd and even numbers, starts from one to generate two, and supports the Shiyao is called 'Ying'; the position where the Shiyao resides, with yin and yang clearly revealed, is called 'Fei'; the yin and yang that arise according to the paired hexagram, ultimately not departing from their original palace, and secretly assisting the divine is called 'Fu'; the one that starts from the Shiyao, covers both the inner and outer hexagrams, and records the months by referring to the numbers of the original palace is called 'Jian'; the one that has a beginning and an end, exhausts its number yet never runs out, and is used to record days is called 'Ji'; and the one that gathers in the middle four lines, uses the fourth line as the main element, and includes four hexagrams within a single hexagram is called 'Hu'.

乾建於甲子於下，坤建於甲午於上。八卦之上，乃生一世之初，分五世之位。其五世之上，乃為游魂之世。五世之初，乃為歸魂之世。而歸魂之初，乃生後卦之初。其建剛日剛節氣，柔日則中氣，其數虛則二十有八，盈則三十有六。其可言者如此。”晁氏之說，可謂挈《京易》之綱領矣。茲分列八宮暨飛伏諸例如下，若應與配位五行六神諸說，詳下《爻位》、《爻數》各章。

The Trigram Qian begins from the lower Jiazi, and the Trigram Kun begins from the upper Jiawu. On top of the eight pure trigrams, the first generation trigram emerges, and then the positions of the five generations trigrams are sequentially divided. Above the fifth generation is the wandering soul generation, and at the beginning of the fifth generation is the returning soul generation. At the beginning of the returning soul generation, the beginning of the next trigram emerges. When starting the calculation, if it is a strong day, it is paired with the solar term; if it is a weak day, it is paired with the intercalary solar term. Its numbers, when deficient, are twenty-eight, and when full, are thirty-six. These are roughly the points that can be explained. The above is what Chao Gongwu said. Chao's discussion can be said to have captured the essence of the Jingshi Yi. Below are the various rules for the eight palaces and the flying and hidden trigrams. As for the concepts of the response line, positioning, the five phases, and the six spirits, they are detailed in the chapters on "Yao Position" and "Yao Number" below.

八純卦各以五行所屬為主，乾金坎水艮土震木巽木離火坤土兌金，所謂進退以幾而為一卦之主者謂之世也。本宮不變，初爻變為一世，至五爻變為五世，上爻六世，即本宮，謂之宗廟不變。初至七世仍以三爻變為游魂，八世下三爻，全復本宮，為歸魂。故二世為地《易》，三四世為人《易》，五六世為天《易》，游魂歸魂為鬼《易》。

The eight pure hexagrams each have their own Five Phases as their main element: Qian belongs to Metal, Kan to Water, Gen to Earth, Zhen to Wood, Xun to Wood, Li to Fire, Kun to Earth, and Dui to Metal. This is what Chao said about "the world" (shi), which refers to the line that becomes the main element of a hexagram according to the subtle movement of advancing and retreating. When the original hexagram remains unchanged, the world is located at the top line. If the first line changes, it becomes the first world hexagram, and so on, changing up to the fifth line to form the fifth world hexagram. If the top line changes, it becomes the sixth world, which returns to the original hexagram, so the top line is called "ancestral temple" (zongmiao) and is fixed as unchanging. Counting from the first line to the seventh change, the third line (i.e., the fourth position) is taken as the changing line to form the "ghost hexagram" (gu yi). When reaching the eighth change, the three lines of the lower trigram return to their original state in the original hexagram, forming the "returning soul hexagram" (gui hun). Therefore, the second world hexagram is called "earthly change" (di yi), the third and fourth world hexagrams are called "human change" (ren yi), the fifth and sixth world hexagrams are called "heavenly change" (tian yi), and the ghost hexagrams are called "ghost change" (gu yi).

乾坎艮震巽離坤兌之序，決非京氏所創。《繫傳》曰：“乾知大始，坤作成物。”雖乾坤對舉，而詳玩後天八卦方位，及六十四卦之次序，所謂“仰以觀於天文，俯以察於地理。天道下濟，地道上行”者，皆足以見八宮之用，即分陰分陽之大義也。

The order of the eight trigrams,乾, 坎, 艮, 震, 巽, 离, 坤, 兑, is certainly not the invention of Jing Fang. The Great Treatise says: "乾 knows the great beginning, 坤 forms things." Although both 乾 and 坤 are mentioned here, when we carefully consider the positions of the Later Heaven Trigrams and the order of the sixty-four hexagrams, it is clear that the reasoning behind the arrangement of the eight trigrams is in line with what the Great Treatise says: "Looking up to observe the heavenly phenomena, looking down to examine the geographical features," as well as "the heavenly way descends and shines brightly, the earthly way is low but ascends." These statements sufficiently reveal the purpose behind the order of the eight trigrams, which is precisely the meaning of "dividing yin and yang."

八卦東震西兌，東西平衡，若地平線。故巽離坤三陰卦，實處於地之上，所謂地道卑而上行也。而乾坎艮三陽卦，皆處於地之下，所謂天道下濟也。上下以震兌為始終，故雷澤歸妹曰“天地大義人終始”者此也。震之始，始於乾，“乾知大始”也。兌之終，終於坤，坤“代終”也。三《易》之卦，爻象皆同，不同者其序耳。八宮之序，或謂出於《連山》，非無所見也。

Among the eight trigrams, Zhen is located in the east and Dui in the west, facing each other east and west to achieve balance, just like a horizon line. Therefore, the three yin trigrams Xun, Li, and Kun are actually situated above this line, which corresponds to the saying "the way of the earth is low but ascends upward." The three yang trigrams Qian, Kan, and Gen are all located below this line, which corresponds to "the way of heaven descends to nourish." The upper and lower parts are connected by Zhen and Dui as their starting and ending points. Thus, the Commentary on the Judgment of the hexagram Guimei (Thunder over Marsh) states "the great principle of heaven and earth" and "the beginning and end of human beings," referring precisely to this. The "beginning" represented by Zhen originates from Qian, meaning "Qian knows the great beginning"; the "end" represented by Dui culminates in Kun, meaning that Kun can "replace the end." The hexagrams of the three collections of the Book of Changes have the same lines and images, differing only in their order. Some people say that the order of the eight palaces comes from Lianshan, and this statement is not without basis.