The Eight Trigrams divide into yin and yang.

八卦之上各生一奇一偶而為四畫者十六。邵子所謂“八分為十六”者是也。又謂兩儀之上各加八卦，又謂八卦之上各加兩儀。朱子曰：“此非某之說，乃康節之說；非康節之說，乃希夷之說；非希夷之說，乃孔子之說。但當日諸儒既失其傳，而方外之流陰相付受，以為丹灶之術。至今希夷、康節乃反之於易，而後其說始得復明於世。然與今《周易》次第行列多不同者，故聞者創見而不之信，只據見行《周易》緣文生義，穿鑿破碎，有不勝其杜撰者。此《啟蒙》之書所為作也。若能虛心遜志以求其通曉，玩之久熟，則天地變化之神，陰陽消長之妙，自將瞭然於心目之間，而有以識其奧矣。

Above the Eight Trigrams, each is supplemented by one odd and one even, resulting in sixteen hexagrams with four lines. This is what Shao Yong called "eight divided into sixteen." It can also be said that two yin-yang principles are added to each of the Eight Trigrams, or that two yin-yang principles are added to each of the Eight Trigrams. Zhu Xi said: this is not my own view, but Shao Kangjie's; not Shao Kangjie's, but Chen Tuan's (Master Xiyi); not Chen Tuan's, but originally Confucius's. It was only because the scholars of the Confucian tradition had lost this lineage that it was secretly passed down by people outside the orthodox, and used as a method for alchemy. Until Master Xiyi and Shao Kangjie returned it to the Book of Changes, this theory became clearly known again. However, it differs greatly from the current order of the hexagrams in the commonly used version of the Zhou Yi. Therefore, those who hear it at first may not believe it, and instead take the existing text of the Zhou Yi at face value, leading to fragmented and fabricated interpretations. I wrote the book "Yixue Mengting" precisely for this purpose. If one can be humble and patient, and put in the effort to understand thoroughly, and after careful consideration and familiarity, the subtle workings of heaven and earth, and the subtle changes of yin and yang, will become clear in one's mind, and one will be able to grasp its profound meaning.

以上自太極、河圖、洛書，皆可畫卦。邵子所謂“畫有易”是也。原卦序、卦畫，皆明卦理，非入用者耳。邵康節曰：乾南、坤北、離東、坎西、震東北、兌東南、巽西南、艮西北。自震至幹為順，自巽至坤為逆。後六十四卦方位仿此。

The above discussion shows that from the Taiji to the He Tu and Luo Shu, one can use them to draw the trigrams, which is what Shao Yong said, "There is the Book of Changes within the drawing." The original order of the trigrams and their drawing methods are meant to explain the principles of the trigrams, not for direct application. Now we will discuss the directions of the Eight Trigrams. Shao Yong said that the Earlier Heaven Trigrams have Qian in the south, Kun in the north, Li in the east, Kan in the west, Zhen in the northeast, Dui in the southeast, Xun in the southwest, and Gen in the northwest. Counting from Zhen to Qian is in a clockwise direction, while counting from Kun to Kun is in a counterclockwise direction. The circular diagram of the sixty-four trigrams is also arranged in this way.

《說卦》曰：“天地定位，山澤通氣，雷風相薄，水火不相射，八卦相錯。數往者順，知來者逆。是故易逆數也。雷以動之，風以散之，雨以潤之，日以烜之，艮以止之，兌以說之，乾以君之，坤以藏之。”

The Sayings on the Trigrams from the Zhou Changes says: Heaven and Earth established the positions of above and below, mountains and marshes communicate with each other, thunder and wind interact with each other, water and fire do not harm each other, and the Eight Trigrams thus interconnect. Counting in the past is forward reasoning, predicting the future is backward reasoning, so the Book of Changes works in reverse order. Thunder is used to move all things, wind is used to scatter all things, rain is used to nourish all things, sun is used to dry all things, mountain (Geng) is used to stop all things, marsh (Dui) is used to delight all things, Heaven (Qian) is used to govern all things, and Earth (Kun) is used to gather all things.

丘公云：“《易》曰：‘天地定位，山澤通氣，雷風相薄，水火不相射，八卦相錯，數往者順，知來者逆。’此先天八卦方位也。乾坤縱則六子橫，其數幹一、兌二、離三、震四、巽五、坎六、艮七、坤八。其方則乾南、坤北、離東、坎西、震東北、巽西南，艮西北、兌東南。自震至幹為順，自巽至坤為逆。

Qu Yuanhan said: The "Sayings on the Trigrams" from the "Zhou Yi" states, "Heaven and Earth are positioned, mountains and marshes communicate, thunder and wind interact, water and fire do not oppose each other, and the eight trigrams intersect." This describes the arrangement of the Earlier Heaven Trigrams. The trigrams Qian and Kun are arranged vertically above and below, while the remaining six trigrams are placed horizontally on both sides. Their numbers are Qian one, Dui two, Li three, Zhen four, Xun five, Kan six, Gen seven, and Kun eight. Their directions are Qian in the south, Kun in the north, Li in the east, Kan in the west, Zhen in the northeast, Xun in the southwest, Gen in the northwest, and Dui in the southeast. Counting from Zhen to Qian is in the direction of progression, while counting from Kun to Qian is in the direction of regression. Progression refers to the past, while regression refers to the future.

蓋震始交陰而陽生，巽始消陽而陰生。兌，陽之長者也；艮，陰之長。震、兌在天之陰，艮、巽在地之陽，故震、兌上陰而下陽，艮、巽上陽而下陰。幹、坤正上下之位，坎、離列左右之門，天地之所開闢，日月之所出入，春夏秋冬、晦朔弦望、晝夜寒暑，莫不由是而推，此先天之卦所以為理氣之體也。地法因之以推二十四位生殺之炁、二十四氣運化之機。明其消息陰陽，論其時日干支、孤虛旺相，以致於用，其理極矣。

Because Zhen is the trigram that begins to interact with yin and thus yang qi first arises, and Xun is the trigram that begins to diminish yang and thus yin qi first arises; Dui is a trigram that has yang growing within it, and Gen is a trigram that has yin growing within it. Zhen and Dui belong to the yin in the heavenly position, while Gen and Xun belong to the yang in the earthly position. Therefore, Zhen and Dui both have the top line as yin and the lower lines as yang, while Gen and Xun both have the top line as yang and the lower lines as yin. Qian and Kun occupy the upper and lower positions correctly, while Kan and Li stand on the left and right like two doors: the heavens and earth are thus opened, the sun and moon pass through, the changes of the four seasons, the waxing and waning of the moon's phases, and the alternation of day and night, cold and heat, none of these are not derived from here — this is why the earlier heaven trigrams can serve as the fundamental principle of 'li qi'. The methods of geomancy use this to investigate the life qi and killing qi on the twenty-four compass directions, and to explore the mechanisms of the twenty-four solar terms; understanding the growth and decline of yin and yang, discussing the distribution of the heavenly stems and earthly branches, as well as the 'gū', 'xū', 'wàng', and 'xiāng' positions, all the way down to practical application. The principles involved can be said to be fully explained.

吳公云：“此伏羲先天八卦，蓋理氣之體也。天地定位，幹對坤也；山澤通氣，艮對兌也；雷風相搏，震對巽也；水火不相射，坎對離也。幹以純陽位居南，坤以純陰位居北，自乾坤交而男女生。離得坤之正性，故中虛，有日之象，日生於東，故正位乎東；坎得幹之正性，故中滿，有月之象，生於西，故正位乎西。

Wu Jingluan said: This is Fuxi's "Earlier Heaven Trigrams," which is the fundamental principle of "li qi." The saying "Heaven and Earth are positioned" refers to Qian and Kun facing each other; "Mountains and Marshes communicate qi" refers to Gen and Dui facing each other; "Thunder and Wind contend" refers to Zhen and Xun facing each other; "Water and Fire do not oppose" refers to Kan and Li facing each other. Qian, being purely yang, resides in the south; Kun, being purely yin, resides in the north. When Qian and Kun interact, the six sons and daughters are generated. Li obtained the proper nature of Kun, so its central line is empty, symbolizing the Sun; the Sun rises in the east, so Li's central position is in the east. Kan obtained the proper nature of Qian, so its central line is full, symbolizing the Moon; the Moon rises in the west, so Kan's central position is in the west. The four cardinal trigrams are thus established first.

四正既定，然後幹一變為巽，故巽居幹左；二變成艮，故艮居坎左；三變成坤。坤一變為震，故震居坤左；二變成兌，故兌居離左；三變成幹。此變化之序，自然之理也。其法自子中至午中為陽，午中至子中為陰。以六十四卦分佈為圓象，以推二十四氣之運用。

After the four cardinal directions have been properly established, the Trigram Qian changes first to Xun, so Xun is positioned to the left of Qian; then it changes again to Gen, so Gen is positioned to the left of Kan; after a third change it becomes Kun. Kun changes first to Zhen, so Zhen is positioned to the left of Kun; then it changes again to Dui, so Dui is positioned to the left of Li; after a third change it becomes Qian. This is the order of transformation, which follows the natural principle. Its application is: the half circle from the center of Zi to the center of Wu belongs to Yang; the half circle from the center of Wu to the center of Zi belongs to Yin; the sixty-four hexagrams are arranged in a circular diagram, used to determine the application of the twenty-four solar terms.

自冬至一陽生而復，周流至夏至初而為幹，故自子中至午中為天地長養萬物之氣，其數主生。故雷雨居春夏，盛茂生發繫焉。自夏至一陰生而始，流行至冬至初而為坤，故自午中至子中為天地歸藏之氣，其數主煞，故霜露居秋冬，結寔收藏繫焉。地法體之，以推四序、時日、支干、五行孤虛旺相之方，施之時事。羅經分配花甲，裝排八卦之繫，皆得理氣耳。”

From the winter solstice when the first yang energy begins to emerge, starting with the hexagram Fu, it flows smoothly until the summer solstice when the hexagram Qian is reached. Therefore, the half circle from the midpoint of the Zi hour to the midpoint of the Wu hour represents the vital energy of heaven and earth nurturing all things, which is associated with the principle of "birth." Thus, thunder and rain belong to spring and summer, and the flourishing and growth of grass and trees occur during this period. From the summer solstice, when the first yin energy begins to emerge, starting with the hexagram Guo, it flows smoothly until the winter solstice when the hexagram Kun is reached. Therefore, the half circle from the midpoint of the Wu hour to the midpoint of the Zi hour represents the vital energy of heaven and earth returning to concealment, which is associated with the principle of "destruction." Thus, frost and dew belong to autumn and winter, and the maturing and storing of fruits occur during this period. The method of geomancy observes this principle to investigate the four seasons, days and nights, the heavenly stems and earthly branches, and the directions where the five phases are "solitary," "vacant," "strong," and "prosperous." These are then applied to specific matters. The system of allocating the sixty Jiazi and arranging the eight trigrams on the Luojing compass is all meant to conform to the principles of qi and reason.

邵子曰：“此文王八卦，乃入用之位，後天之學也。”《說卦》曰：“帝出乎震，齊乎巽，相見乎離，致役乎坤，說音悅言乎兌，戰乎乾，勞乎坎，成言乎艮。”“神也者，妙萬物而為言者也。動萬物者莫疾乎雷，撓萬物者莫疾乎風，燥萬物者莫熯乎火，說萬物者莫說乎澤，潤萬物者莫潤乎水，終萬物始萬物者莫盛乎艮。故水火相逮，雷風不相悖，山澤通氣，然後能變化，既成萬物也。”

Shao Yong said: This set of the King Wen's Eight Trigrams is a system that can be directly applied to directions, belonging to the study of Later Heaven. The "Say of the Trigrams" in The Zhou Changes says: The Heavenly Emperor starts from the Zhen direction, proceeds to the Xun direction to harmonize, then to the Li direction to meet each other, then to the Kun direction to control all things, then to the Dui direction to make all things joyful (the character '说' is read as '悦'), then to the Qian direction to engage in conflict, then to the Kan direction to labor and fatigue, and finally to the Gen direction to complete. It also says: The term 'spirit' is used to describe the subtle process of nurturing all things. Nothing moves all things more swiftly than thunder, nothing shakes all things more swiftly than wind, nothing dries all things more intensely than fire, nothing pleases all things more appropriately than marsh, nothing moistens all things more abundantly than water, and nothing concludes and begins all things more completely than mountain. Therefore, water and fire pursue each other, thunder and wind do not contradict each other, mountain and marsh communicate with each other, and only then can transformation and movement take place, giving rise to all things.

丘公曰：“此文王八卦，乃入用之位，後天之位也。伏羲先天八卦，幹生於子，坎終於寅，坤生於午，離終於申，以明天之道也。至文王重卦，置幹於西北，退坤於西南，長子用事，而長女代母。坎離得位，而兌艮為偶，震巽為用也，以應地之方也。蓋兌、離、巽得陽之多者也，艮、坎、震得陰之多者也，是以為天地用也。

Qu Yuanhan said: This is the trigrams of King Wen, which are the practical directional arrangements, that is, the positions of Later Heaven. Fuxi's Earlier Heaven trigrams have Qian originating from Zi and Kan ending at Yin, while Kun originates from Wu and Li ends at Shen, used to explain the movement of Heaven. When King Wen reorganized the trigrams, he placed Qian in the Northwest and moved Kun to the Southwest, allowing Zhen to take charge as the eldest son and Xun to take the place of the mother, with Kan and Li each occupying their proper positions, Dui and Gen forming a pair, and Zhen and Xun taking on practical roles, corresponding to the directions of the earth. Since Dui, Li, and Xun are trigrams with more Yang, and Gen, Kan, and Zhen are trigrams with more Yin, they can be used by Heaven and Earth. Earlier Heaven focuses on the essence, while Later Heaven focuses on application, and this is exactly where the distinction lies.

幹極陽，坤極陰，是不用也。以方位言之，震、兌始交者也，故當朝夕之位。坎、離交之極者也，故當子午之宮。巽、艮不交而陰陽不雜也，故當中之偏也。幹、坤純陰純陽也，故為不用之位也。此後天方位所以始震而終艮也。羅經方位由是而立。其所以推測造化，察地理山川以別吉凶，蓋有至理存焉。此聖人明體致用之法也。”

Heavenly Stem Jia represents the extreme of yang, and Earthly Branch Zi represents the extreme of yin, hence they are placed as the unchanging trigrams. In terms of direction, Zhen and Dui are where yin and yang first begin to meet, so they are placed at the east and west positions where the sun rises and sets. Kan and Li are where the meeting of yin and yang reaches its peak, so they are placed at the Zi and Wu directions. Xun and Gen are where yin and yang do not interact and remain distinct, so they are placed at the four intermediate corners. Qian and Kun are purely yang and purely yin, hence they are fixed in their positions. This is why the Later Heaven direction starts with Zhen and ends with Gen. The compass directions are also established based on this. It is because of this that the compass can predict the workings of nature, examine geographical features and mountains and rivers to distinguish auspicious and inauspicious signs. There is indeed profound truth within this. This is precisely the method by which the sages understood the fundamental nature and applied it practically.

吳公云：“此文王後天八卦方位，蓋理氣之用也。‘帝出乎震’，震東方也，震為雷，雷奮發而物生，春為陽之始，故震居之。‘說言乎兌’，兌正西也，兌為澤，有儲聚之義，故為陰之始，故兌居之。震以一陽在下，兌以一陰在上，故曰始交。

Wu Jingluan said: This is the Later Heaven Trigrams arrangement of King Wen. It demonstrates the function of "li qi" (principle and energy). "The Emperor arises from Zhen," Zhen is located in the East; Zhen represents Thunder, which when it moves, it stimulates all things to grow. Spring is the beginning of yang energy, so Zhen is located in the East. "Speech is associated with Dui," Dui is located in Due West; Dui represents Lake, which has the meaning of storage and gathering. It is the beginning of yin energy, so Dui is located in the West. Zhen has one yang below, and Dui has one yin above, so they are said to be the trigrams at the beginning of the interaction between yin and yang. The East and West, one spreading out and one gathering in, form a complementary relationship.

‘齊乎巽’，巽東南也。巽為風，長育萬物，故居東南。‘成乎艮’，艮東北也。艮為山，山結止物。物作於春初，而止於冬末，萬物之所以成始成終者也，故艮居之。艮以一陽在上，巽以一陰在下，故云不交。

"Qí hū Xun," Xun is in the southeast; Xun represents wind, which can nurture and cultivate all things, so it resides in the southeast. "Chéng hū Gen," Gen is in the northeast; Gen represents mountain, which can condense and stop all things. All things begin to move in early spring and cease at the end of winter, and Gen is the place where all things can have a beginning and an end, so Gen resides in the northeast. Gen has one yang above, and Xun has one yin below, so they are hexagrams of yin and yang that do not interact with each other.

‘戰乎乾’，乾西北也。‘致役乎坤’，坤西南也。伏羲起乾坤於上下，取相交變化物之義。及其成功，男女用事，有父退居之義。陽以順動，故幹順退居西北。坤以逆行，故坤逆退處西南。言戰者，天地至此，肅殺之極。言役者，天地至此，肅殺之初。幹以純陽老亢，坤以純陰老極，無生成之意，故曰當不用之位。

"Fight in Qian," Qian is located in the Northwest; "Employ in Kun," Kun is located in the Southwest. Fuxi placed Qian and Kun at the top and bottom ends, representing the idea of Heaven and Earth interacting to generate all things. When achievements are completed, the six sons and daughters take over, implying the parents step back. Yang energy moves in a positive direction, so Qian follows and retreats to the Northwest; Yin energy moves in a negative direction, so Kun moves against the direction and retreats to the Southwest. It is said "fight" because at this point, the Heaven and Earth have reached the extreme of severity; it is said "employ" because at this point, the severity of Heaven and Earth has just begun. Qian is purely Yang and has reached the extreme of old age and excess, while Kun is purely Yin and has also reached the extreme of old age. Neither has the intention of generating all things, so they are said to be in a position of non-use.

‘相見乎離’，離正南也，夏至陽極陰生，故離居之。‘勞乎坎’，坎正北也，冬至陰極陽生，故坎居之。坎陽居中，故為交之極。此先天之卦也，乃至文王重卦而後用以有行也。地法體之，以道造化所以生殺之故，辨方正位，趨吉避凶，良有以也。”

"Meeting at Li" refers to Li being located in the direction of Due South; at the Summer Solstice, Yang reaches its peak and the first Yin begins to emerge, hence Li resides in the South. "Toiling at Kan" refers to Kan being located in the direction of Due North; at the Winter Solstice, Yin reaches its peak and the first Yang begins to emerge, hence Kan resides in the North. Kan has a Yang line in the center, so it is said to represent the meeting of Yin and Yang at their extremes. All these hexagrams originally come from the Earlier Heaven arrangement. Only after King Wen reorganized the hexagrams did they become truly applicable and put into practice. The method of geography examines these principles to explain the reasons for generation and destruction in nature. It is used to determine directions and correct seating positions, to seek good fortune and avoid misfortune, and indeed has a solid basis.

按：天干出於河圖。天一生壬水，地六生癸水；天三生甲木，地八生乙木；天七生丙火，地二生丁火；天九生庚金，地四生辛金；天五生戊土，地十生己土。地支出於洛書。子、午、卯、酉得天陽之數，居四正。寅、申、巳、亥、辰、戌、丑、未得地陰之數，而居四隅。陽數奇，故各主其一；陰數偶，故各主其二。辰、戌、丑、未土無定位，寄居四隅。

Note: The ten heavenly stems originate from the Yellow River Chart. The heavenly number one generates the water stem Ren, and the earthly number six generates the water stem Gui; the heavenly number three generates the wood stem Jia, and the earthly number eight generates the wood stem Yi; the heavenly number seven generates the fire stem Bing, and the earthly number two generates the fire stem Ding; the heavenly number nine generates the metal stem Geng, and the earthly number four generates the metal stem Xin; the heavenly number five generates the earth stem Wu, and the earthly number ten generates the earth stem Ji. The twelve earthly branches originate from the Luo Writing. The branches Zi, Wu, Mao, and You are associated with the yang numbers, so they occupy the four cardinal directions of east, south, west, and north. The branches Yin, Shen, Si, Hai, and the groups Chen, Xu, Chou, and Wei are associated with the yin numbers, so they reside in the four corners. Yang numbers are odd, so each of the four cardinal directions is governed by a single earthly branch. Yin numbers are even, so each of the four corners is governed by two earthly branches. The branches Chen, Xu, Chou, and Wei belong to earth, and since earth has no fixed direction, it resides in the four corners.

陳希夷曰：“天干始於甲，終於癸，河圖生成之數也。地支起於子，終於亥，洛書奇偶之數也。陽自復始，六變而幹陽備；陰自姤始，六變而坤陰成。合二六之數為十二辰。夫甲、丙、戊、庚、壬，陽干也，子、寅、辰、午、申、戌，陽支也；乙、丁、己、辛、癸，陰干也，丑、卯、巳、未、酉、亥，陰支也。法以陽干配陽支，陰干配陰支。猶木之有幹有枝。

Chen Tuan said: The ten heavenly stems start from Jia and end at Gui, following the principle of the generating numbers and completed numbers from the Yellow River Chart; the twelve earthly branches start from Zi and end at Hai, following the principle of the odd and even numbers from the Luo Writing. Yang energy begins with the Fu hexagram and undergoes six transformations to complete the pure yang of the Qian hexagram; yin energy begins with the Gu hexagram and undergoes six transformations to complete the pure yin of the Kun hexagram. The combination of the two Six Harmonies forms the twelve earthly branches. The yang stems are Jia, Bing, Wu, Geng, and Ren; the yang branches are Zi, Yin, Chen, Wu, Shen, and Xu. The yin stems are Yi, Ding, Ji, Xin, and Gui; the yin branches are Chou, Mao, Si, Wei, You, and Hai. The pairing method is to match yang stems with yang branches and yin stems with yin branches, just as a tree has a main trunk and branches. The pairing of stems and branches never allows for the mixing of yin and yang.

以六甲配五子，自甲子為首，次第推排，而盡於癸亥。仍以干支本數計其成數，總其成數干支若干，然後以五數除之，其餘數以先天河圖象數冠之，周其有聲者，納之以五行之音，是為六甲納音。

Using six Jia stems (Jiazi, Jiaxu, Jiashen, Jiawu, Jiachen, Jiayin) to match five Zi branches (Jiazi, Bingzi, Wuzi, Gengzi, Renzi), starting from Jiazi and proceeding in order, continuing until Guihai. Then, calculate the numbers corresponding to each stem and branch according to their inherent values, summing the numbers for each group of stem and branch. Divide the total by five; the remainder is named according to the imagery and numbers of the Earlier Heaven Yellow River Chart. If the sequence results in a sound, it is paired with the sound of the Five Phases. This is called 'Nayin of the Six Jia'.

聖人推以入用，以分金六十位定佈於二十四，以正五行為各宮之主，以六甲大五行為緯，察其分金之胎、養、衰、死之氣，定其孤、虛、旺、相之卦，內有戊己為龜甲空亡，甲乙為補接之空，以是消息陰陽，立葬乘氣，定命審音，今之大五行也。

The sages developed this system for practical use, distributing the sixty "dividing gold" positions among the twenty-four compass mountains. They used the "correct five phases" as the governing element of each palace, and the six jia "great five phases" (i.e., nayin five phases) as the meridians and latitudes. They examined the qi of each dividing gold position in terms of its state of conception, nurturing, decline, and death, determining which category of hexagram it belonged to: "solitary," "vacant," "prosperous," or "auspicious." Among these, the positions of Wu and Ji were considered "tortoise shell void," while those of Jia and Yi were considered "connecting void." Using this system to balance yin and yang, to take advantage of life qi at the time of burial, to determine a person's destiny and examine their nayin, is what is today called the "great five phases."

補義甲、己、子、午九，乙、庚、丑、未八，丙、辛、寅、申七，丁、壬、卯、酉六，戊、癸、辰、戌五，巳亥是四數。符其支干，總成其數，卻以五數除之，不滿五者作納音。如零一納音屬火，零二屬土，零三屬水，零四屬金，零五屬水。惟火、水、土、木無聲，故其數異。

The method for determining the Nayin sound element involves the following: Jia and Ji with Zi and Wu are counted as nine, Yi and Geng with Chou and Wei are counted as eight, Bing and Xin with Yin and Shen are counted as seven, Ding and Ren with Mao and You are counted as six, Wu and Gui with Chen and Xu are counted as five, and Si and Hai are counted as four. Take the group of heavenly stem and earthly branch to be calculated, apply these numbers, sum them up, and divide by five. The remainder determines the Nayin element: a remainder of one belongs to fire, two to earth, three to water, four to metal, and five to water. This is because fire, water, earth, and wood are inherently silent, so their corresponding numbers differ from the usual pattern.

此納甲取象太陰之義。法先天八卦方位而推之者也。《易》曰：“天垂象，見吉凶，聖人象之。日往則月來，月往則日來，日月相推而明生焉。”又曰：“天地盈虛，與時消息。”夫天象之可見者，莫如日月，故日月麗天而運行，寒暑陰陽循環不已。

The concept of "Najia" is derived from the imagery of the waxing and waning of the moon, and is deduced according to the arrangement of the Earlier Heaven Trigrams. The Great Treatise of the Zhou Changes states: "Heaven reveals celestial phenomena, indicating auspicious and inauspicious signs; sages take them as a model. When the sun has passed, the moon comes; when the moon has passed, the sun comes; the sun and moon alternate, thus producing brightness." The Commentary on the Judgment of the Book of Abundance also says: "The fullness and emptiness of heaven and earth change with the seasons." Among visible celestial phenomena, none are more evident than the sun and moon, so the sun and moon are attached to heaven and move in their courses, while the cold and heat, yin and yang, cycle ceaselessly.

而盈虛消息之理，於是而見，造化變通之機，由是而推。日為陽之象，陽中含陰，離二陽在外，而一陰居中，故離為日之正體。月為陰之象，陰中含陽。坎二陰在外而一陽居中，故坎為月之正體。蓋日無遲速，而月有盈虛，卦有變化，而時有配納。

The principle of waxing and waning, and the increase and decrease of things, can be seen from this. The mechanism of transformation and change in the universe can also be understood from this. The sun represents the image of yang, with yang containing yin: the Li hexagram has two yang lines on the outside and one yin line in the middle, so Li is the true form of the sun. The moon represents the image of yin, with yin containing yang: the Kan hexagram has two yin lines on the outside and one yang line in the middle, so Kan is the true form of the moon. The sun's movement has no distinction of speed or slowness, but the moon has cycles of fullness, deficiency, waxing, and waning. Hexagrams change, and thus the seasons correspondingly take on their assigned stems. The method of Najia (stem assignment) is precisely based on the changing phases of the moon.

月本無光，麗日而明。以不明之體言之，則純陰而象坤，晦朔之時也。越三日而哉生明，始資日之明而有光，因謂之朏，陽之初生也。昏見於庚，震一○之象也，故震納庚。越五日而資日之半明，因謂之上弦，陽之將半也。昏見於丁兌，二○之象也，故兌納丁。

The moon itself does not emit light; it shines by reflecting the light of the sun. In its unilluminated state, it is purely yin and resembles the Earth (Kun), which corresponds to the new moon (when the moon is not visible) and the dark moon (when the moon is completely dark). After three days, it begins to show some light, borrowing the sun's light to become visible, called "Fei," which signifies the beginning of yang. In the evening, it appears in the direction of Geng, corresponding to the trigram Zhen, which represents thunder and has one yang line at the bottom (depicted as a hollow circle), hence Zhen is associated with Geng. After five more days, it receives half the sun's light, called "Shangxian," which indicates yang is about to reach half. In the evening, it appears in the direction of Ding, corresponding to the trigram Dui, which represents lake and has two yang lines (two hollow circles), hence Dui is associated with Ding.

越十五日，與日對，資日之全明而大圓，因謂之望，言三陽具備也。昏見於甲，幹三○之象也，故幹納甲。又三日而哉生魄，與日之望偏而陰始生，因謂之魄，言陰復生也。晨見於辛，巽一●之象也，故巽納辛。又五日而生晦，半資日之明，因謂之下弦，言陰生至半也。晨見於丙，艮二●之象也，故艮納丙。

On the fifteenth day, the moon and the sun are directly opposite, borrowing the full light of the sun and thus becoming fully bright, called "wan" (full moon), indicating that all three lines are yang and have been completed. In the evening, it appears at the position of Jia, which is the image of the Qian hexagram with three yang lines (three empty circles), so Qian hexagram is assigned the stem Jia. Three days later, the "po" (moon's dark part) begins to appear, which is already leaning to one side and the initial emergence of yin energy, called "po," indicating the beginning of yin. In the morning, it appears at the position of Xin, which is the image of the Xun hexagram with one yin line at the bottom (one filled circle), so Xun hexagram is assigned the stem Xin. Five days later, it gradually becomes obscured, borrowing only half of the sun's light, called "xia xian" (lower crescent), indicating that yin has grown to half. In the morning, it appears at the position of Bing, which is the image of the Gen hexagram with two yin lines (two filled circles), so Gen hexagram is assigned the stem Bing.

又六日而與日交會，日之明全不相資，復晦而不明，因謂之晦。晝沒於乙，坤三●之象也，故坤納乙。此一月之消息盈虛也。地法因之，以推八卦之變，分納各幹於八卦之位，用以統十二支之方，配以五行之位，本乎坎也。

Six days later, the moon and sun meet, and the moon is completely unable to borrow the sun's light, becoming dark again, which is called 'hui' (darkness). During the day, the moon disappears in the Yi position, which corresponds to the image of the K'un trigram with three yin lines (three solid circles). Therefore, K'un trigram includes Yi. This describes the waxing and waning of the moon within a month. The methods of geomancy rely on this to explore the changes of the eight trigrams. Each heavenly stem is assigned to a direction of the eight trigrams, used to govern the twelve earthly branches. Then, the five phases are combined. The fundamental principle lies in Kan (water), which represents the moon's true nature.

洪悟齋理曰：“支干納卦法者，坎離得乾坤之中爻，中名土之位，故納戊巳。戊己者，天干之中。戊陽土也，納於坎，己陰土也，納於離，從其類也。幹之六位，三甲三壬。坤之六位，三乙三癸納之。此四干係於乾坤之內外。乾坤，諸卦之父母，奇偶變化，萬物終始皆在焉，故始甲乙，終壬癸，以包六卦。

Hong Wu Zhai (named Li) said: The method of incorporating heavenly stems into trigrams is as follows: The trigrams Kan and Li receive the middle yao of Qian and Kun, with the center being the position of earth, so the heavenly stems Wu and Ji are incorporated. Wu and Ji are the middle two heavenly stems among the ten: Wu is the yang earth, incorporated into Kan; Ji is the yin earth, incorporated into Li, each belonging to its own category. The six yao positions of Qian incorporate three Jia and three Ren; the six yao positions of Kun incorporate three Yi and three Gui; these four heavenly stems belong to the inner and outer trigrams of Qian and Kun. Qian and Kun are the parents of all other trigrams. The changes of odd and even, the beginning and end of all things, are contained within them. Therefore, starting from Jia and Yi, ending with Ren and Gui, the remaining six trigrams are included in between.

所納之幹，括始終也。地理論二十四卦無戊己者，除居中央五，天地之元根。離外陽，故陽外壬配之；坎外陰，故坤外癸配之。其地支之寅、戌、巳、丑、亥、未、卯、辰各從其類納合焉。

The heavenly stems included here fully encompass both the beginning and the end. In geographical divination, the twenty-four directions are used without including Wu and Ji, because the central number five is excluded—this is the fundamental origin of heaven and earth. The outer trigram of Li belongs to yang, so the outer line of Qian, which is Ren, is used to match it; the outer trigram of Kan belongs to yin, so the outer line of Kun, which is Gui, is used to match it. As for the earthly branches Yin, Xu, Si, Chou, Hai, Wei, Mao, and Chen, they are each included in the trigrams that correspond to their own type.

坎正北為水，申子辰三合水局也，故隸於坎；離正南為火，寅午戌三合火局也，故隸於離；震正東為木，亥卯未三合木局也，故隸於震；兌正西為金，巳酉丑三合金局也，故隸於兌。離、坎、震、兌四正也，故納乾而配支。幹、坤、艮、巽四隅也，故納乾而已。此支各統於卦之義矣。”

The trigram Kan is located in the north and belongs to water. The three branches Shen, Zi, and Chen form a triple harmony of water, so these three branches are associated with Kan. The trigram Li is located in the south and belongs to fire. The three branches Yin, Wu, and Xu form a triple harmony of fire, so these three branches are associated with Li. The trigram Zhen is located in the east and belongs to wood. The three branches Hai, Mao, and Wei form a triple harmony of wood, so these three branches are associated with Zhen. The trigram Dui is located in the west and belongs to metal. The three branches Si, You, and Chou form a triple harmony of metal, so these three branches are associated with Dui. The trigrams Li, Kan, Zhen, and Dui are the four cardinal trigrams, so they both incorporate heavenly stems and are paired with earthly branches. The trigrams Qian, Kun, Gen, and Xun are the four corner trigrams, so they only incorporate heavenly stems and are not paired with earthly branches. This is the reason why each earthly branch is associated with a particular trigram.

此以後天八卦輔以支干而定其方位之次也。按《青囊經》曰：“聖人因八卦以推天時，用地支以配天干，制為土圭，別理地宜，以立人極。”陳希夷釋之曰：“八卦為象數之始，天干所以附八卦，而地支所以佐天干也。故至人因卦以推時，用支以配幹，而定其方位之次，制為土圭之器，以消息天地孤虛之氣，蓋自上古伏羲命大撓氏始立八卦之方，而先未有支干也。

This is a method of determining the order of the twenty-four directions using the Later Heaven Trigrams and supplementing them with the Heavenly Stems and Earthly Branches. According to the Qingnang Jing, "sages used the Eight Trigrams to investigate the heavenly seasons, paired the Earthly Branches with the Heavenly Stems, and made the soil gnomon to distinguish the suitability of soil in different regions, thus establishing the standards for human conduct." Chen Tuan explained that the Eight Trigrams are the starting point of symbols and numbers, the Heavenly Stems are established based on the Eight Trigrams, and the Earthly Branches further support the Heavenly Stems. Therefore, the enlightened ones use the trigrams to determine the seasons, pair the branches with the stems, and thus arrange the order of directions. They also made the soil gnomon to regulate the "gū" and "xū" energies in the universe. In other words, the trigrams determine the seasonal changes, while the stems and branches determine the directions on the ground. Only when these two are combined can the order of the compass be arranged. Tracing back, in ancient times, Fu Xi assigned the Eight Trigrams to specific directions, and at that time there were no Heavenly Stems or Earthly Branches.

至堯命羲和考中星，始用十二辰位。周公作指南車，有其形而無方。至玄女授赤松子，始用卦氣支干分配而成二十四位，以為神器。法以天數二十有五，扐一以為體，而二十四氣備。地數三十，去六以為用，而二十四氣全。

At the time of Emperor Yao, Xi Shi and He Shi were commissioned to observe the celestial stars and established the twelve earthly branches. The use of the twelve branches began then. The Duke of Zhou invented the south-pointing chariot, which had only the form of pointing but not yet the division of directions. It was only after the Mysterious Lady of the Ninth Heaven taught Chisuizi that the twenty-four positions were created by matching the trigrams with the heavenly stems and earthly branches, making them a sacred tool for geomancy. The method of determining these numbers is as follows: the total number of heavenly numbers is twenty-five, from which one number is removed to leave the original essence, and the remaining twenty-four correspond exactly to the twenty-four solar terms. The total number of earthly numbers is thirty, from which six are subtracted for practical use, and the remaining twenty-four also correspond exactly to the twenty-four solar terms. This is how the twenty-four positions on the compass came to be.

五行生成，二氣對待，北一南二，東三西四，中五沖氣，奠居中處。明河圖五行生成之氣，推洛書九宮推移之跡。制以水北火南，木東金西，土中生成，化育有定序矣。天以一生水，坎者水之位也，故子正北。癸得地六之陰，水之柔也，故癸次於子。水不止則流蕩而忘反，必土以止之，則能生物。丑者土之柔也，故丑次於癸。

The Five Phases have both generating and forming aspects, with yin and yang energies opposing each other in pairs: North is one, South is two, East is three, West is four, and Central Five is the harmonious energy that resides in the middle. This is to clarify the generating energies of the Five Phases as depicted in the Yellow River Chart, and to trace the movement of the Nine Palaces in the Luo Writing. Thus, water is located in the North, fire in the South, wood in the East, metal in the West, and earth in the center, establishing a definite order for generation and nurturing. Heaven begins with water, and坎 (Kan) is the original position of water, so Zi (the first branch) is located in the North. Gui (the tenth heavenly stem) receives the yin aspect of the earthly number six, representing the soft aspect of water, so Gui comes after Zi. If water is not restrained, it would flow endlessly without returning, but it must be stopped by earth to nurture all things; Chou (the second earthly branch) represents the soft aspect of earth, so it comes after Gui.

艮為山，土之剛也，故艮次子、丑而居東北，所以代震之施化也。土合而化氣，將以生木。寅為稚木，故寅次於艮。甲得天三之陽，木之剛也，故甲次於寅。震者木之旺也，故卯居正東。乙得地八之陰，木之柔也，故乙次於卯。木非土無以盛，辰者土之正氣，故辰次於乙木者，陽之穉也。

Gen represents mountain, which is the firm aspect of earth. Therefore, Gen comes after Zi and Chou and is located in the northeast, taking the place of Zhen to carry out the function of nurturing and transforming. Earth凝聚 and transforms into qi, about to give birth to wood; Yin is the young wood, so Yin comes after Gen. Jia receives the yang of the heavenly number three, representing the firm aspect of wood, so Jia comes after Yin. Zhen is the most vigorous part of wood, so Mao is located due east. Yi receives the yin of the earthly number eight, representing the gentle aspect of wood, so Yi comes after Mao. Wood cannot flourish without earth; Chen is the pure essence of earth, so Chen comes after Yi—wood at this time is still young yang.

木非旺不能生火，故巽為旺木而次於辰。旺極必齊生，所生火也。巳為火之初氣，故巳次於巽。丙得天七之火，陽之剛也，故丙次於巳。離者火之位也，故午居正南。丁得地二之陰，火之柔也，故丁次於午。火旺必有止，將以生土也，故未次於丁。坤者地之體，土之正氣也，故坤次於未。

Wood cannot generate fire unless it reaches its peak, so Xun is the flourishing wood and is placed after Chen. When the flourishing reaches its peak, it gives rise to fire; Si is the initial stage of fire, so Si is placed after Xun. Bing receives the heavenly number seven, representing the strong yang aspect of fire, so Bing is placed after Si. Li is the center of fire, so Wu is located due south. Ding receives the earthly number two, representing the gentle yin aspect of fire, so Ding is placed after Wu. After fire is strong, it must come to rest and give rise to earth, so Wei is placed after Ding. Kun is the essence of the great earth, representing the pure yang of earth, so Kun is placed after Wei.

土旺必生金，申者金之初氣也，故申次於坤。庚得天九之陽，金之剛也，故庚次於申。兌者金之位也，故酉居正西。辛得地四之陰，金之柔也，故辛次於酉。金非土無以成，戊者土之正氣也，故戊次於辛。金者陰之稚也，金不盛不能化，故幹為旺金而次於戊。旺極而化成，所以生水也。亥為水之初氣，故亥次於幹。壬得天乙之陽，水之剛也，故壬次於亥。於是二十四位有定方矣。

After the earth is strong, metal is generated. Shen is the initial energy of metal, so it comes after Kun. Geng receives the yang energy of nine, representing the strong aspect of metal, so it comes after Shen. Dui is the original position of metal, so You is located due west. Xin receives the yin energy of four, representing the gentle aspect of metal, so it comes after You. Metal cannot be formed without earth. Xu is the pure energy of earth, so it comes after Xin. Metal is young and yin, and cannot change without being strong, so Qian, representing strong metal, comes after Xu. When metal reaches its peak it transforms into water. Hai is the initial energy of water, so it comes after Qian. Ren receives the yang energy of the heavenly one, representing the strong aspect of water, so it comes after Hai. At this point, the twenty-four directions of the compass have fixed positions.

戊己得大地之中，天五地十之氣，故中處以為金母。金伏天干之戊土，而制於地支之午火，藏於地支之子水，本居子之中也，故土圭之器，其休以木，其用以金，而化成於水火。子水丙火寄跡於土中，其子午之正中既定，則天地之正氣從可知矣。神哉！

The heavenly stem Wu and Ji represent the central earth and the combined energies of heaven and earth, so they are located in the center and serve as the mother of metal. Metal is hidden within the earth of Wu and is controlled by the fire of the午 branch, and it is stored in the water of the子 branch. Metal is originally located at the center of the子 branch. Therefore, the instrument called the soil gnomon, its handle is made of wood, its needle is made of metal, and its function lies between water and fire to transform them. The water in the子 branch and the fire in the丙 branch both reside within the earth; once the center of the子 and午 branches is determined, the correct energies of heaven and earth can be understood. Truly marvelous!

江右山人徐善繼述 同著。先天卦配洛書，值陽數者為浄陽，值陰數者為浄陰。其支干各統於卦。此浄陰浄陽之定位也，法以先天卦乾南坤北、離東坎西四正之卦，配洛書戴九履一，左三右七之陽數，而為浄陽；先天艮、震、巽、兌四隅之卦，配洛書二四為肩，六八為足之陰數，而為浄陰。其支干亦各統於卦。為陰陽，然不曰陰陽，而必曰凈陰凈陽者，欲其不相駁雜也。地法因之。故陽龍必須陽向，陽水來去則吉，而雜陰則凶；陰龍必須陰向，陰水來去則吉，而雜陽則凶，本乎此也。

Xu Shanji and Xu Shanshu, brothers from Jiangxi, jointly authored this text. The Earlier Heaven Trigrams are combined with the numbers of the Luo Square. Those values that are yang are considered "pure yang," and those that are yin are considered "pure yin." Each branch and stem is also assigned to the trigram it belongs to. This is the method of determining "pure yang" and "pure yin." The four main trigrams of the Earlier Heaven Trigrams—Qian (Heaven) in the south, Kun (Earth) in the north, Li (Fire) in the east, and Kan (Water) in the west—are paired with the yang numbers of the Luo Square, "nine on top, one beneath, three on the left, seven on the right," and are designated as "pure yang." The four corner trigrams of the Earlier Heaven Trigrams—Gen (Mountain), Zhen (Thunder), Xun (Wind), and Dui (Lake)—are paired with the yin numbers of the Luo Square, "two and four on the shoulders, six and eight on the feet," and are designated as "pure yin." Each branch and stem is also assigned to the trigram it belongs to. Originally, it is simply yin and yang, but instead of directly saying yin and yang, they use "pure yin" and "pure yang" to indicate that they should be pure and not mixed. This method is used in geomancy. Therefore, a yang dragon must be paired with a yang direction, and yang water coming and going is auspicious; if yin is mixed in, it becomes inauspicious. A yin dragon must be paired with a yin direction, and yin water coming and going is auspicious; if yang is mixed in, it becomes inauspicious—the basis for this is here.

按：羅經方位，以十二位為陽，以十二位為陰。幹、甲、乙、坎、癸、申、辰、離、壬、寅、戌陽位，艮、丙、巽、辛、兌、丁、巳、丑、震、庚、亥、未陰位。葢法先天方位，而配以洛書象數而推明者也。

The twenty-four directions of the compass are divided into twelve yang positions and twelve yin positions. The yang positions are Qian, Jia, Yi, Kan, Gui, Shen, Chen, Li, Ren, Yin, Xu (the original text lists only eleven, but according to the principle of pure yang, there should also be Kun, though the original text is missing this entry, and it is recorded as is); the yin positions are Gen, Bing, Xun, Xin, Dui, Ding, Si, Chou, Zhen, Geng, You, Wei. This system is derived from the positions of the Earlier Heaven Trigrams, combined with the numerical and symbolic calculations of the Luo Writing, making it clear and explicit.

先天卦位幹、坤、坎、離居四正之位，陽位也；洛書象數一、九、三、七居四陽之位，奇數也。故幹、坎、坤、離以居陽位而為陽，甲、乙、壬、癸以配陽卦而為陽，寅、戌以陽支而配離從火，申、辰以陽支而配坎從水，故十二位為陽也。

In the Earlier Heaven arrangement of trigrams, Qian, Kun, Kan, and Li occupy the four cardinal positions, which are yang positions; in the Luo Book's numerical arrangement, the numbers one, nine, three, and seven are located in the four yang directions, which are odd numbers. Therefore, the four trigrams Qian, Kan, Kun, and Li are considered yang because they are located in yang positions; the four heavenly stems Jia, Yi, Ren, and Gui are considered yang because they are paired with yang trigrams; the branches Yin and Xu are originally yang branches and are considered yang because they triple harmonize with Li (Fire); the branches Shen and Chen are originally yang branches and are considered yang because they triple harmonize with Kan (Water). Together, the four trigrams, four heavenly stems, and four branches make up exactly twelve yang positions.

先天卦位震、巽、兌、艮居四隅之位，陰位也。洛書象數以二、四、六、八居四陰之位，隅數也。故震、巽、兌、艮居陰位而為陰，酉、丁、庚、辛以配陰卦而為陰。亥、未以陰支而配震從木，巳、丑以陰支而配兌從金，故十二位陰也。

In the Earlier Heaven arrangement of trigrams, the trigrams Zhen, Xun, Dui, and Gen are located in the four corners, which are considered yin positions. In the Luo Writing numerical system, the numbers two, four, six, and eight are located in the four yin directions, which are corner numbers. Therefore, the four trigrams Zhen, Xun, Dui, and Gen are considered yin because they occupy yin positions; the four heavenly stems You, Ding, Geng, and Xin are considered yin because they are paired with yin trigrams; the two earthly branches Hai and Wei, which are inherently yin, are also considered yin because they triple harmonize with Zhen and thus belong to wood; the two earthly branches Si and Chou, which are inherently yin, are also considered yin because they triple harmonize with Dui and thus belong to metal. Combined, the four trigrams, four heavenly stems, and four earthly branches make up exactly the twelve yin positions.

是陰陽各有十二路，而地理家從陰位者，陰為天地之始，萬物之母。陰有生生之意，而陽無焉，故貴陰而賤陽。凡行龍行水，將從並朝，各得其位而不雜，則陰陽和，造化備矣。以其位陰陽言之，則純陽純陰，似若無生意者。

Thus, yin and yang each have twelve paths. Geomancers tend to focus on the yin positions because yin is the beginning of heaven and earth and the mother of all things; yin contains the meaning of continuous generation, while yang does not, so yin is esteemed and yang is regarded as inferior. Whenever a dragon line, a water course, and the accompanying hills and supporting features are each in their proper positions without mixing, then yin and yang are in harmony, and the workings of nature are complete. If we consider only the yin and yang of directions, pure yang and pure yin seem to lack vitality.

以卦氣干支之陰陽言之，則陽中有陰焉，陰中有陽焉。何則？幹、坎以陽卦從陽，宜也，而坤、離為陰；甲、壬以陽干從陽，宜也，而乙、癸為陰；巽、兌以陰卦從陰，宜也，而艮、震為陽；丁、辛以陰干從陰，宜也，而丙、庚為陽。於是陰陽和而奇偶備，此堪興家所以本先天理氣，而用後天方位也。

But if we consider the yin and yang of the trigrams and the heavenly stems and earthly branches, we can see that there is yin within yang and yang within yin. Why is this so? The trigrams Qian and Kan are yang trigrams that follow yang, which is natural; yet the trigrams Kun and Li are considered yin. The heavenly stems Jia and Ren are yang stems that follow yang, which is natural; yet the stems Yi and Gui are considered yin. The trigrams Xun and Dui are yin trigrams that follow yin, which is natural; yet the trigrams Gen and Zhen are considered yang. The heavenly stems Ding and Xin are yin stems that follow yin, which is natural; yet the stems Bing and Geng are considered yang. In this way, yin and yang are in harmony, and odd and even are complete. This is precisely why geomancers base their qi and qi-qi (energy and its movement) on the principles of the Earlier Heaven, while using the Later Heaven for directions. Yin and yang interpenetrate; one cannot merely look at the surface.