Ertiang (the extraordinary signs)

《荀九家易》，八卦逸象，共三十有一。雲出自河內女子獻《說卦》後，實皆由本經《彖》、《象》採取。其未見者，只坤之漿，巽之鸛二象，去留皆無關宏旨。惟荀爽《集解》，去古未遠，當有所本。而朱子亦仍陸氏《釋文》之舊，附各卦後。今列舉如左：

The "lost images" (逸象) of the eight trigrams in the "Xun Jiuya Yi" total thirty-one, which are not included in the "Shuo Gua Zhuan." It is said that these images appeared after a woman from Heinner presented the "Shuo Gua Zhuan," but in fact they were all collected from the "Commentary on the Judgment" and "Image Commentary" of the main text of the "Zhou Yi." Among these, only two images, "Kun as jiang" and "Xun as guan," lack support in the main text and commentaries, and whether they are retained or deleted does not affect the overall structure. However, Xun Shuang's "Jiexie" is not far from the ancient times and should have some basis; Zhu Xi also followed the old practice of Lu Deming's "Jingdian Xishu," attaching them after each trigram. The following is a list of them:

乾之象四：為龍，為直，為衣，為言。坤之象八：為牝，為迷，為方，為囊，為裳，為黃，為帛，為漿。震之象三：為玉，為鵠，為鼓(玉或作王。鵠，項氏云：“鵠鶴古通用，當作鶴。”)。巽之象二：為楊，為鸛。

The extraordinary images of Qian are four: dragon, straightness, clothing, and speech. The extraordinary images of Kun are eight: female, lost path, square, bag, lower garment, yellow, silk fabric, and drink. The extraordinary images of Zhen are three: jade, crane, and drum. Note: Some editions read 'king' instead of 'jade'; some say that 'crane' and 'goose' were interchangeable in ancient times, so it should be 'goose'. The extraordinary images of Xun are two: willow and stork.

坎之象八：為宮，為律，為可，為棟，為叢棘，為狐，為蒺藜，為桎梏。離之象一：為牝牛。艮之象三：為鼻，為虎，為狐。兌之象二：為常，為輔頰。

The extraordinary images of Kan include: palace, law, something that can be used, beam, thorny bushes (referring to the prison in the line "placed in thorny bushes" from the top line of Kan), fox, thorned weed, and shackles. The extraordinary image of Li is a female ox. The extraordinary images of Gen include: nose, tiger, and fox. The extraordinary images of Dui include: banner (or constant measure) and cheek.

孟氏逸象，傳自焦氏，亦自本經採取為多。間有互異者，以兩漢經師，各守師說，傳述不同。備錄如後，以資參證。

The esoteric interpretations of Meng Xi's school are passed down from Jiao Yanshou, and mostly drawn from the original text of The Zhou Changes. Occasionally, there are discrepancies with the Xun Jiujia, due to the fact that Han dynasty scholars each adhered to their own school's interpretations, leading to different transmissions. The following is a complete record for reference and verification.

乾為王，為先王，為明君，為人，為大人，為聖人，為賢人，為君子，為武人，為行人，為物，為易，為立，為直，為敬，為畏，為咸，為嚴，為堅剛，為道，為德，為盛德，為行，為性，為精，為言，為信，為善，為揚善，為積善，為良，為仁，為愛，為忿，為生，為祥，為慶，為天休，為嘉，為福，為介福，為祿，為先，為始，為知，為大，為盈，為茂，為肥，為好，為施，為利，為清，為治，為大謀，為高，為揚，為宗，為族，為高宗，為甲，為老，為舊，為古，為大明，為遠，為郊，為野，為門，為道門，為百，為歲，為頂，為朱，為衣，為圭，為蓍，為瓜，為龍。

The symbolic meaning of Qian. In terms of people: as a king, as a former king, as a wise ruler, as a person, as a great man, as a sage, as a virtuous person, as a gentleman, as a warrior, as a traveler. In terms of nature and character: as an object, as ease, as establishment, as straightness, as respect, as fear, as universality, as strictness, as firmness, as the Way, as virtue, as great virtue, as conduct, as nature, as essence. In terms of speech and morality: as speech, as trustworthiness, as goodness, as promoting goodness, as accumulating goodness, as good quality, as benevolence, as love, as anger. In terms of blessings and auspiciousness: as life, as auspiciousness, as celebration, as heavenly grace, as good fortune, as blessing, as great blessing, as official rank. In terms of time sequence and position: as first, as beginning, as knowledge, as great, as fullness, as flourishing, as fat, as good, as giving, as benefit, as clear, as governance, as great plan, as high, as promotion, as ancestor, as clan, as high ancestor (Wudi of the Yin dynasty), as Jia (the first heavenly stem), as old, as ancient, as great brightness, as far. In terms of land and objects: as the outskirts, as the wild, as a gate, as the gate path, as hundred, as year, as top, as red, as clothing, as jade bi, as chi grass, as melon, as dragon.

坤為臣，為順臣，為民，為萬民，為姓，為小人，為邑人，為鬼，為形，為身，為牝，為母，為躬，為我，為自，為至，為安，為康，為富，為財，為積，為聚，為萃，為重，為厚，為致，為用，為包，為寡，為徐，為營，為下，為容，為裕，為虛，為書，為邇，為近，為疆，為無疆，為思，為惡，為理，為體，為禮，為義，為事，為業，為大業，為庶政，為俗，為度，為類，為閉，為藏，為密，為默，為恥，為欲，為過，為丑，為積惡，為迷，為殺，為亂，為怨，為害，為遏惡，為終，為永終，為敝，為死，為喪，為冥，為晦，為夕，為莫夜，為暑，為乙，為年，為十年，為戶，為義門，為闔戶，為閉關，為盍，為土，為積土，為階，為田，為邑，為國，為邦，為大邦，為萬國，為異邦，為方，為鬼方，為裳，為級，為車，為輹，為器，為擊，為囊，為虎，為兕，為黃牛，為牝牛。

The symbolic meanings of the Trigram坤. In terms of people: as a minister, a compliant minister, as common people, as all the people, as the common folk, as a small person, as people of a town, as ghosts, as form, as body, as female, as mother, as self, as oneself. In terms of stability and accumulation: as ultimate, as safe, as well-being, as wealth, as property, as accumulation, as gathering, as convergence, as weight, as thickness, as attainment, as use, as encompassing, as few, as slow, as encircling, as lower, as capacity, as abundance, as emptiness, as writing, as near, as close, as boundary, as boundless, as thought. In terms of matters, principles, and moral education: as evil, as order, as body, as propriety, as righteousness, as affairs, as occupation, as great occupation, as various state affairs, as customs, as measure, as category. In terms of closure and concealment: as closure, as concealment, as secrecy, as silence, as shame, as desire, as excess, as ugliness, as accumulated evil, as confusion, as killing, as chaos, as resentment, as harm, as suppression of evil. In terms of conclusion, darkness, and obscurity: as end, as permanent end, as decay, as death, as loss, as darkness, as dusk, as evening, as night, as heat, as the heavenly stem 乙, as year, as ten years. In terms of gates, land, and territories: as gate, as righteous gate, as closing the gate, as closing the borders, as union, as soil, as accumulated soil, as step, as field, as town, as country, as state, as great state, as all states, as foreign state, as direction, as the distant land of the ghosts. In terms of objects and animals: as lower garment, as level, as carriage, as the part of the carriage axle, as vessel, as striking, as bag, as tiger, as rhinoceros, as yellow ox, as female ox.

震為帝，為主，為諸侯，為人，為士，為兄，為夫，為元夫，為趾，為出，為行，為徵，為作，為逐，為驚走，為警衛，為定，為百，為言，為講議，為問，為語，為告，為響，為聲，為音，為鳴，為夜，為交，為徵，為反，為後，為後世，為從，為守，為左，為生，為嘗，為緩，為寬仁，為樂，為笑，為喜笑，為笑言，為道，為陵，為祭，為鬯，為禾稼，為百穀，為草莽，為鼓，為筐，為馬，為糜鹿。

The symbolic meanings of the Trigram Zhen. In terms of people: it represents the Emperor, the ruler, the feudal lords, people, the scholar, the elder brother, the husband, and the first husband (the spouse of the first wife). In terms of actions: it represents the foot, going out, walking, marching, rising up, chasing, being startled and running, guarding, and settling. In terms of speech and sound: it represents a hundred, speech, discussion, asking, talking, informing, echo, sound, tone, and calling. In terms of time, position, and movement: it represents night, meeting, marching, returning, later, later generations, following, guarding, and the left. In terms of life, nourishment, and joy: it represents birth, tasting, being slow, being lenient and kind, joy, laughing, smiling joyfully, and laughing speech. In terms of worship, plants, and objects: it represents the way, a hill, worship, the sacred wine used in rituals, grain, all grains, grasses, a drum, a basket, a horse, and deer.

巽為命，為命令，為號令，為教令，為誥，為號，為號咷，為處女，為婦，為妻，為商旅，為隨，為入，為處，為入伏，為利，為齊，為同，為交，為進，為退，為舞，為谷，為長木，為苞，為楊，為果木，為茅，為白茅，為闌，為草木，為草莽，為杞，為葛藟，為薪，為庸，為休，為繩，為帛，為腰帶，為繑，為蛇，為魚，為鮒。

The symbolic meanings of Xun (Wind): In matters of commands: as destiny, as command, as decree, as instruction, as诰 (a type of imperial edict), as a call, as wailing. In matters of people: as a virgin, as a wife, as a spouse, as merchants. In matters of movement and stillness: as following, as entering, as dwelling, as hiding, as benefit, as harmony, as unity, as meeting, as advancing, as retreating, as dancing. In matters of plants and trees: as grain, as tall trees, as clusters of grass, as poplar, as fruit trees, as reed, as white reed, as fence, as plants, as grassy wilderness, as goji (a type of tree), as vine, as firewood, as wall, as shade. In matters of ropes, silk, insects, and fish: as rope, as silk, as waistband, as the belt for trousers, as snake, as fish, as small fish.

坎為聖，為雲，為玄云，為川，為大川，為河，為心，為志，為思，為慮，為憂，為謀，為惕，為疑，為艱，為蹇，為恤，為悔，為逖，為忘，為勞，為濡，為涕洟，為眚，為疾，為疾病，為疾癘，為疑疾，為災，為破，為罪，為悖，為欲，為淫，為寇盜，為暴，為毒，為瀆，為孚，為平，為法，為罰，為獄，為則，為經，為習，為入，為內，為聚，為脊，為要，為臀，為膏，為陰夜，為歲，為三歲，為尸，為酒，為叢木，為叢棘，為蒺藜，為棘匕，為穿木，為校，為弧，為弓彈，為木，為車，為馬。

The symbolic meanings of Kan. In the category of heaven and water: it represents a sage, clouds, dark clouds, rivers, great rivers, and rivers. In the category of mind, thoughts, and worries: it represents the heart, will, thought, consideration, worry, planning, vigilance, doubt, hardship, difficulty, concern, regret, distance, forgetting, labor, dampness, and tears and snot. In the category of calamity, disease, guilt, and blame: it represents disaster, illness, disease, epidemic, suspicious illness, calamity, ruin, guilt, disorder, desire, excess, bandits, violence, poison, and sacrilege. In the category of trust, law, and legal matters: it represents sincerity, fairness, law, punishment, court, standard, classic, repetition, entering, internal, and gathering. In the category of the human body and days and months: it represents the spine, waist, buttocks, fat, the private parts and night, years, three years, corpse, and wine. In the category of thick woods, instruments of punishment, chariots, and horses: it represents thick woods, thorny bushes, thorn weeds, a dagger made of thorny wood, a wooden stake, a yoke, a bow, a bowstring, wood, a chariot, and a horse.

離為女子，為婦，為孕，為惡人，為見，為飛，為爵，為日，為明，為先，為甲，為黃，為戎，為折首，為刀，為斧，為資斧，為矢，為飛矢，為黃矢，為網，為罟，為甕，為鳥，為飛鳥，為鶴，為隼，為鴻。

The symbolic meanings of the trigram Li (Fire). In the category of human beings: it represents a woman, a wife, pregnancy, and an evil person. In the category of visible brightness: it represents seeing, flying, a title (or a wine vessel), the sun, brightness, precedence, the first heavenly stem (Jia), and yellow. In the category of weapons: it represents military force, beheading enemies, a knife, an axe, a sharp axe, an arrow, a flying arrow, and a yellow arrow. In the category of nets and utensils: it represents a net, a fishing net, and a jar. In the category of flying birds: it represents a bird, a flying bird, a crane, a falcon, and a wild goose.

艮為弟，為小子，為君子，為賢人，為童，為童蒙，為僮僕，為官，為友，為閽，為時，為豐，為星，為沫，為霆，為果，為慎，為節，為待，為制，為執，為小，為多，為厚，為取，為舍，為求，為篤實，為道，為穴居，為石，為城，為宮室，為門闕，為廬，為牖，為居，為門庭，為宗廟，為社稷，為鼻，為肱，為背，為腓，為皮，為膚，為小木，為碩果，為豹，為狼，為小狐，為尾。

The symbolic meanings of Gen (Mountain). In human terms: as a younger brother, as a small person, as a gentleman, as a virtuous person, as a child, as a child learning, as a servant, as an official, as a friend, as a gatekeeper. In terms of weather and time: as time, as abundance, as stars, as faint starlight, as thunder. In terms of stopping, maintaining virtue, and conduct: as decisiveness, as caution, as restraint, as waiting, as control, as holding on, as smallness, as multitude, as thickness, as taking, as giving up, as seeking, as sincerity, as the Way. In terms of dwellings and structures: as cave-dwelling, as stone, as a city, as a palace, as gateways, as a hut, as a window, as dwelling, as gate and courtyard, as ancestral temple, as state and land. In terms of the human body: as the nose, as the upper arm, as the back, as the calf, as the skin, as the flesh. In terms of plants, trees, and animals: as small trees, as large fruits, as a leopard, as a wolf, as a small fox, as a tail.

兌為妹，為妙，為妻，為朋，為友，為講習，為刑人，為小，為少，為密，為通，為見，為右，為下，為少知，為契。右舉象至四百四十餘，然猶未能盡也。別本坎下有竊象，巽下有繫象，兌下有窺象，殆逸之中又有逸歟！

The extraordinary images of Dui: as sister, as a beautiful young woman, as wife, as friend, as companion, as study, as executioner (someone who has been punished), as small, as young, as secret, as communication, as appearance, as right, as lower, as little knowledge, as contract (or mark). The above examples amount to over four hundred and forty items, yet they are still not exhaustive. Other versions also mention additional images: under Kan, there is "stealing"; under Xun, there is "tying"; under Dui, there is "peeking." It seems there are even more extraordinary images beyond these.

《易》注如《瞿塘來氏集註》等，均有補象，要皆由《彖》、《象》十翼之辭，擬議以意增補。然來氏乾之為郊為野等補象均已列《孟氏逸象》之中，而又補之。殆來氏僻居巫峽，得書不易，《孟氏逸象》，或未之見耳。

Commentaries on The Zhou Changes, such as Lai Zhide's "Jutang Lai Shi Yijing Jizhu," all have their own "supplementary images." Generally, these are interpretations and additions based on the words of the Ten Wings, such as the Commentary on the Judgment and the Image Commentary. However, the images of Qian as a suburb and as a wilderness that Lai added were already included in the "Mengshi Yixiang." He added them again anyway. Probably because Lai lived in the area around Wuxia, where books were hard to find, and he may never have seen the "Mengshi Yixiang."

實則《說卦》廣象，簡而能賅，提綱挈領，各卦《彖》、《爻》之象，無不可會通演繹，而各得其變化。及根本之所在，必字字而擬之補之，則泥象以言《易》，而《易》反不可見矣。各家補象，爰不復贅錄。

In fact, the images presented in the "Shuo Gua Zhuan" are concise yet comprehensive, capturing the essence and leading the way. The images found in each hexagram's "Tuan Ci" and "Xiao Ci" can all be understood and derived from them, each able to seek its own transformation and find its fundamental nature. If one insists on comparing each character literally or adding supplementary explanations, then one would become confined by the images and lose sight of the "Yi." Therefore, the additional images provided by various schools are not copied here one by one.

參象者，乃八卦陰陽交變，未能以一卦之本象或變象盡之，因參合兩卦之象而會通之，其例已見於《廣象》。順德鄭氏《易譜》，觸類引伸，並證以前史占驗之詞，列為參象，亦足為初學之隅反也。

The term "参象" refers to the situation where, during the interaction and change of yin and yang in the Eight Trigrams, the meaning of a single trigram's original or transformed image is insufficient. Therefore, the images of the two trigrams before and after the change are combined to derive meaning. This method has already been illustrated in the previous section on "Broad Images." A person from Shunde, Guangdong, named Zheng compiled a section on "参象" in his work "Yi Pu," extending related concepts and verifying them with divinatory statements from historical records. This approach is sufficient to help beginners make connections and apply principles to similar situations.

離之艮，為火焚山，山敗之象。於人為言，敗言為讒，故又為讒言之象。乾之兌，天降為澤，為天子降心逆公之象。震之離，火反燒木，有女嫁反害其母之象。巽見艮，為山之材，而之乾有照以天光之象。坤之乾，又見艮，有廷實旅百，奉之以玉帛之象。蓋艮為廷實旅百，乾為玉而坤為帛也。坤之震，曰安而能殺，為公侯之象。

Li changes to Gen: Li fire is below and Gen mountain is above, which is the image of fire burning the mountain and the mountain being destroyed. In terms of human affairs, Li also represents speech, and broken speech is slander, so this is also the image of slander. Qian changes to Dui: Heaven descends to become a marsh, which is the image of the Son of Heaven humbling himself to welcome the feudal lords. Zhen changes to Li: Zhen represents wood and Li represents fire, wood naturally produces fire, but now fire burns the wood, just like a daughter getting married and harming her mother. Xun meets Gen: Gen represents mountain and Xun represents wood, which is wood on the mountain; when it changes to Qian, Qian represents heaven, forming the image described in the "Zuo Zhuan" case of Chen Jingzhong's divination, "there is timber on the mountain and it is illuminated by the light of heaven." Kun changes to Qian and meets Gen: This is the image described in the "Zuo Zhuan" as "a hundred items are presented in the courtyard, and they are offered with jade and silk," because Gen represents the hundred items displayed in the courtyard, Qian represents jade and Kun represents silk. Kun changes to Zhen: The divination conclusion in the "Zuo Zhuan" case of Bi Wan's career choice says "secure yet capable of killing," Kun is still and Zhen represents肃杀, which is exactly the image of a marquis or duke.

坤之坎，坤貞也，坎和也。和以率貞，有信之象。震之坤，震為足，坤靜而不動，有足居之之象。震車也，坤馬也，又為車從馬之象。震為長兄，坤為母，又有兄長之，母覆之之象。又為眾，眾又歸之之象。乾之坤，君降為臣也，為不終為君之象。乾天子也，變坤三爻皆出於乾，又為三出於天子之象。坎之巽，為夫從風，風隕妻之象。蓋風為隕落物也。

Heavenly Stem: Jia, Yi, Bing, Ding, Wu, Ji, Geng, Xin, Ren, Gui Earthly Branch: Zi, Chou, Yin, Mao, Chen, Si, Wu, Wei, Shen, You, Xu, Hai Trigrams: Qian (Heaven), Dui (Lake), Li (Fire), Zhen (Thunder), Xun (Wind), Kan (Water), Gen (Mountain), Kun (Earth) Kun changes into Kan: Kun represents firmness and stability, while Kan represents harmony and smoothness. Using harmony to lead firmness indicates the image of sincerity. Zhen changes into Kun: Zhen represents the foot, and Kun is still and unmoving, which is the image of "the foot resting" mentioned in the "Zuo Zhuan" example of Bi Wan's divination; Zhen represents a chariot and Kun represents a horse, which is the image of "the chariot following the horse"; Zhen represents the elder brother and Kun represents the mother, which is the image of "the elder brother supporting and the mother covering"; Kun also represents the people, so there is also the image of "the people returning to it." Qian changes into Kun: the king descends to become a minister, indicating the image of not being able to remain a king forever. Qian is the Son of Heaven, and after changing into Kun, all three lines come from Qian, forming the image of three times originating from the Son of Heaven. Kan changes into Xun: Kan represents the husband and Xun represents wind, indicating the image of the husband moving with the wind and the wind blowing the wife down — because wind is the thing that causes objects to fall.

震之坎，在春木旺龍德之時，為廢水之氣。來見乘加，昇陽未布，隆陰仍積，坎為刑獄，為刑獄壅濫之象。乾之離，為中天出日，有光顯之象，離之艮，為日落西山之象。艮之離，為山下起日，乃方升之象。艮之坎，為山嶽變海之象。坎之艮，為深谷為陵之象。

Zhen transforms into Kan: Zhen represents spring wood which is at its peak and the dragon's virtue is flourishing, while Kan water is already in a state of decline. Yet it rises upon this, causing the ascending yang energy to not yet spread out, and the heavy yin energy still to accumulate. Kan governs punishment and litigation, so this indicates a situation where punishment and litigation are blocked and overflowing. Qian transforms into Li: this represents the sun rising to the zenith, shining brightly. Li transforms into Gen: this represents the sun setting in the west. Gen transforms into Li: this represents the sun rising from beneath the mountain, just beginning to rise in the east. Gen transforms into Kan: this represents mountains turning into the sea. Kan transforms into Gen: this represents deep valleys turning into hills.

坎月也，變震為雷生明，變兌為上弦之月，變乾為十五夜月，變巽為十八晚初虧月，變艮為下弦月，變坤為晦。離日也，變震為初出日，變乾為中天之日，變巽為方斜之日，變艮為落山之日，坤知入地矣。離之坤，曰太陽入地，有退休之象，有傷夷之象。巽見乾之兌，有花木被馬毀折之象。

The trigram Kan represents the moon: when Kan transforms into Zhen, it symbolizes the beginning of the moon's illumination, corresponding to the trigram Zhen with the stem assignment of the moon's initial rise; when it transforms into Dui, it represents the waxing moon; when it transforms into Qian, it represents the full moon on the fifteenth day; when it transforms into Xun, it represents the moon beginning to wane on the eighteenth night; when it transforms into Gen, it represents the waning moon; and when it transforms into Kun, it represents the last day of the moon, the new moon. This sequence illustrates the order of the stem assignments of the moon paired with the eight trigrams. The trigram Li represents the sun: when Li transforms into Zhen, it symbolizes the rising sun at dawn; when it transforms into Qian, it represents the sun at noon; when it transforms into Xun, it represents the sun beginning to set in the west; when it transforms into Gen, it represents the sun setting on the mountain; and when it transforms into Kun, it indicates the sun has entered the earth. The transformation of Li into Kun is called the sun entering the earth, symbolizing both retreat and rest, as well as injury and damage. When Xun meets Qian and transforms into Dui: Xun represents flowers and trees, Qian represents a horse, and Dui represents destruction, symbolizing the image of flowers and trees being trampled and destroyed by a horse.

離之坎，坎來乘物，為月來掩日之象。郭景純曰：“變坎加離，厥象不燭，必有欺蔽之象。”坎之離，為月往日來。離甲冑，用兵戈之象也。而之坎知遇險於前，又不成出兵之象。坤之乾，為自地昇天之象。艮之坤，有舍高就卑，去畸嶇從平坦之象。坎之巽，風還吹水，有波濤之象。坎之兌，水竭耳聾，臣壅主聽之象。

The trigram Li transforms into Kan: Kan comes over Li, symbolizing the moon covering the sun. Guo Pu said, "When Kan transforms and comes over Li, the image is one of darkness and lack of illumination, indicating certain deceit and obstruction." When Kan transforms into Li: this signifies the moon departing and the sun returning. Li represents armor, indicating the use of weapons; but once it transforms into Kan, it shows there is danger ahead, thus becoming an unfavorable sign for military action. When Kun transforms into Qian: this represents rising from the earth to the heavens. When Gen transforms into Kun: this signifies abandoning high places and moving towards low ones, leaving rugged terrain for smooth ground. When Kan transforms into Xun: the wind turns back to blow over the water, symbolizing waves. When Kan transforms into Dui: Kan represents the ear, Dui represents a marsh, and the water has dried up, symbolizing dryness and deafness, indicating that ministers are blocking the ruler's hearing.

坤之坎，有平地開通之象。兌之艮，兌口舌講和，而艮又止之，有欲和不成和之象。乾之離，為圓器在爐灶之側。坎之乾，為雲從龍。巽之艮，為風從虎。震之離，離為矢，而火還燒震木，有張弧反射之象。

The transformation of the hexagram Kūn into Kan signifies Kūn representing flat land and Kan representing a ditch, indicating the image of a passage being opened on flat land. The transformation of Dui into Gen signifies Dui governing speech and negotiation, but Gen stops it, indicating the image of wanting to reconcile but failing to do so. The transformation of Qian into Li signifies Qian representing roundness and Li representing fire, indicating the image of a round vessel placed beside a stove. The transformation of Kan into Qian signifies Kan representing clouds and Qian representing a dragon, indicating the image of "clouds following the dragon." The transformation of Xun into Gen signifies Xun representing wind and Gen representing a tiger, indicating the image of "wind following the tiger." The transformation of Zhen into Li signifies Li representing arrows, while the fire of Li burns the wood represented by Zhen, indicating the image of drawing a bow and arrow only to shoot oneself.

離之乾，在乾宮為同復於父，為歸宗。震木之艮，有木入山之象。坎之震，兌之震，為水澤中木，如逢坎離同位，乃其木是湯藥煎煮之象。坎之艮，為官司刑獄而止不復升矣。艮之巽，為居其所而風自播而今自行。

When the hexagram Li changes to Qian: If within the Qian trigram, Li is the daughter born from Qian, and now it changes back to Qian, this signifies returning to the father's side and reverting to ancestral roots. When Zhen wood changes to Gen: This represents transporting wood into the mountains. When Kan water changes to Zhen, or when Dui marsh changes to Zhen: Water and marsh give rise to wood, and if Kan and Li are also in the same position, this indicates wood being boiled by water and fire, like decocting medicine. When Kan changes to Gen: Kan represents litigation, and Gen represents stopping, indicating that legal matters have reached an end and will not be pursued further. When Gen changes to Xun: Gen represents a place of residence, and Xun represents wind, indicating that a person remains in their original place while the wind spreads naturally, and matters spread on their own.

陰陽化合，播為五行。《禮運》曰：“布五行於四時，和而後月生也。”五行非質也，實天地陰陽之氣。氣有盛衰，而時位乘之，而生克變化之跡著也。氣不可見，仍見之於八卦之象。

Yin and yang interact and transform, spreading out to become the Five Phases. The Book of Rites, The Mandate of the Duke of Zhou says: "Distribute the Five Phases through the four seasons, and harmony allows the moon to be born." The Five Phases are not specific substances; they are actually the qi of heaven and earth, yin and yang. Qi has periods of abundance and decline, and with the influence of time and position in between, the traces of generation and overcoming, transformation and change become evident. Qi itself is invisible, so it still relies on the trigrams of the Eight Trigrams to be perceived.

聖人作《易》，既極數定象，復發其凡於蠱巽之《彖》、《爻》。先後甲庚，各舉其端，而全《易》卦爻之陰陽五行無不可以此類推。而卦氣占候、九宮三式之術數雖繁，亦無能越此範圍。列象如右。卦數另詳下篇。

The sage composed the Zhou Changes, having exhausted the numbers and established the images. He also indicated the principles in the Tuang Cite of the Gu hexagram and the line statement of the Xun hexagram's Nine in the Fifth: the Gu hexagram says "three days before the Jia day, three days after the Jia day," and the Xun hexagram's Nine in the Fifth says "three days before the Geng day, three days after the Geng day," each providing a single clue. From this, all the yin and yang and the five phases in the entire Zhou Changes can be inferred. As for the methods of divination such as the hexagram qi and the nine palaces, Taiyi, Leigong, and Liunin, although their names are numerous, they all fall within this scope. Now I list the images of the five phases on the right. As for the hexagram numbers, they will be discussed in detail in the next section.

水火木金土，分陰分陽，有柔剛，各有配偶，共為十象，舊稱八卦。土金木皆有二，惟水火各一，實未知震兌各具水火之用也。震兌為陰陽出入之門，日月往來之路，不啻五行生化之原，故後天與坎離皆居中位。坎離居先天乾坤之位，震兌即居先天坎離之位。參觀《內經》，則陰陽升降，五行生化之作用，更顯著矣。

Water, fire, wood, metal, and earth are each divided into yin and yang, and each has soft and hard aspects. They are paired two by two, resulting in a total of ten phenomena. In ancient times, they were only referred to by the eight trigrams. Within the eight trigrams, earth, metal, and wood each occupy two trigrams (Kun and Gen for earth, Qian and Dui for metal, Zhen and Xun for wood), but water and fire each occupy only one trigram (Kan for water, Li for fire). This is because people did not realize that Zhen and Dui also possess the functions of water and fire. Zhen and Dui are the gateways for yin and yang to enter and exit, the pathways for the sun and moon to pass through. They are truly the fundamental sources of the generation and transformation of the five phases. Therefore, in the later heaven trigram arrangement, they occupy the central positions of the four cardinal directions, just like Kan and Li. In the earlier heaven diagram, Kan and Li occupy the positions of Qian and Kun, while Zhen and Dui occupy the positions of Kan and Li. Further examination of the Huangdi Neijing reveals that the functions of yin and yang rising and falling, and the generation and transformation of the five phases, become even more evident.

意象影象者，日本易學之名詞也。經學諸書，自唐開元時傳入日本者為多。故日人講《易》，多宗李鼎祚《集解》，其占筮亦用唐人之揲法。卦象取用，有所謂意象者，如以震為船，翼為剪，離為鏡，艮為亭，類取形似，無甚深意義。但象本無方，意動成象，故得意既可忘象，亦能成象。

"The concepts of 'intentional image' and 'imagery' are terms used in Japanese Yi studies. Most classical Chinese texts were transmitted to Japan during the Kaiyuan period of the Tang dynasty, so Japanese scholars generally follow Li Dingzuo's Collected Explanations of the Zhou Changes when discussing the I Ching. They also use the Tang dynasty method of divination with yarrow stalks. When they employ hexagram images, they refer to 'intentional images,' such as viewing Zhen as a boat, Xun as scissors, Li as a mirror, and Gen as a pavilion, all based on resemblance in shape, without deeper meaning. However, hexagrams themselves do not have fixed forms; images can be formed by mere thought. Therefore, since one can 'attain the meaning and forget the image,' one can also create images through intention."

《易》冒天下之道，以八卦相錯，陰陽反覆，能曲成萬物而不遺者，正以象之變化無盡，而肆應不窮。盈天地間唯萬物，生生不已，《易》亦生生不已。萬物之孳乳，日積月累，其數量為巧曆所不能計，而《易》之八卦，足以盡之。非神而明之，其孰能與於斯？

The Zhou Changes (I Ching) can encompass the principles of the world because of the intermingling of the Eight Trigrams and the constant transformation of yin and yang, thus achieving a subtle formation of all things without omission. Because the changes of the hexagrams are inexhaustible, their application to all affairs is also inexhaustible. What fills the universe is myriad things, which continuously generate and multiply. The I Ching also continuously generates and transforms. Myriad things constantly reproduce and proliferate, accumulating day by day, their numbers so vast that even the most skilled in calculations cannot count them. Yet the eight trigrams of the I Ching are sufficient to include them all. Without the ability to grasp the subtle and profound, who could enter into such a realm?

海通而後，西學東漸，名物之繁，百倍於昔。而鼎新革故，索之於《易》，無不各有其數，各有其象。如廣象以乾為金為玉，金玉或非伏羲畫卦時所有物。而三代以後，既有其物，而即以伏羲所畫乾卦之象當之。以三代之時，物質之最精最堅莫金玉若也。而今則金剛石之精粹堅剛，更出金玉之上，自可由金玉而更廣之以乾為金剛石。乾之因物付物，仍莫不確合而確肖也。

Since the opening of the sea ban, Western learning has spread eastward, bringing with it a multitude of names and objects far exceeding the number of those from before. However, when these new things are sought for in the Zhou Yi, each has its own number and its own image. For example, the "Shuo Gu" section of the Zhou Yi uses the trigram Qian to represent metal and jade. Metal and jade were not necessarily things that existed when Fuxi drew the trigrams. Yet after the Xia, Shang, and Zhou dynasties, since such objects did exist, the image of the Qian trigram was used to represent them. During the Xia, Shang, and Zhou periods, there was nothing more refined and hard than metal and jade. Now, diamond is even purer and harder than metal and jade, so it is natural to extend the image of Qian from metal and jade to diamond. The Qian trigram, by assigning images according to the things, remains perfectly appropriate and accurate.

廣象以坎為輿，坤為大輿，震為大塗，合坎通坤載震行而定其象，以當時載物之具，莫利於輿，莫過於大輿。而通行之路，莫便捷於大塗故也。今則交通之廣，運輸之捷，器用日新，幾非一名一物所能限。然則占事知來，制器尚象，非由廣象更推而廣之，安能盡其用哉！

The broad symbolic meanings take the Trigram Kan as representing a vehicle, the Trigram Kun as representing a large cart, and the Trigram Zhen as representing a broad road. This is because these trigrams combine the meanings of Kan's fluidity, Kun's capacity to carry, and Zhen's movement. In ancient times, there was no transportation tool more convenient than a vehicle, no vehicle more capable of carrying heavy loads than a large cart, and no road more convenient for travel than a broad road. Today, however, transportation is far more extensive, transport is much faster, and tools and objects are constantly evolving in new and unprecedented ways, almost beyond the capacity of any single term or object to define. Therefore, if we are to "predict future events through divination" and "create tools based on symbolic forms," we cannot fully exhaust their applications unless we extend our understanding of these broad symbolic meanings further outward.

以卦言之，小過飛鳥遺之音，固未知今日之有飛機也，而象已確肖之。既未濟之曳其輪，未必知今日之有汽機也，而象已不啻曲繪之。古未嘗有化學之分劑也，而今日化學各原質之分化輕重，其量劑數無不與八卦之數合。

In terms of the hexagrams: The statement of the hexagram "Small Crossing" mentions "the sound left by a flying bird." Although ancient people did not know about airplanes today, this image is already very similar to an airplane. The hexagrams "Already Crossing" and "Not Yet Crossing" mention "dragging the wheel," which may not have referred to steam engines, yet the image is already almost exactly described. In ancient times, there were no chemical elements or their ratios, yet the weights and proportions of elements when they are separated in modern chemistry all correspond exactly with the numbers of the eight trigrams.

是故但以象言，或猶疑為附會之適相巧合。若更證之以數度，參之以陰陽剛柔之氣運，而形質狀態，性情功用，無不一一彰明顯著。此意象之為用，非經生家鑽研故紙，取經傳之一名一物，自稱補象之足並論也。我國雖無意象之名，而京焦管郭之占象，見於本傳及《易林》、《洞林》諸書者，其以意廣古人之象者，固不勝指數。故特著之，為初學擴其心胸之一助焉。

Therefore, if we consider only the images, some people might doubt that it is merely a forced connection that happens to coincide. But if we further verify with numbers and measurements, and refer to the yin and yang and the qualities of hardness and softness to explore, then the forms, states, natures, and functions of things will all become clear and distinct. This is the function of "intentional image" (意象), which is far beyond the capability of those scholars who merely study old texts, who pick out a name or an object from the classics and claim it as "complementing the image" (补象). Although our country does not have the term "intentional image," the divination methods based on images used by Jing Fang, Jiao Yanshou, Guan Lu, and Guo Pu are recorded in their biographies and in works such as the "Forest of Changes" (焦氏易林) and "Deep Forest" (洞林). There are countless examples in these works where they expanded on the images of ancient times through their own thoughts. Therefore, we specially highlight this school of thought to help beginners broaden their minds.

影象之說，當本於吾國相傳之卦影。卦影之術，始於晉唐，而盛於南宋。嚴君平亦即其儔，今已失傳。而日本之所謂影象，類似吾國之伏象。惟不限以震伏巽，艮伏兌，大概與意象略同。說詳東京易學討論會丁巳年發行之易學雜誌，亦足供學者之參考也。

As for the concept of 「image」, it should be based on our traditional 「guaying」. The technique of guaying originated during the Jin and Tang dynasties, and became popular in the Southern Song dynasty; Yu Zun (styled Junping) of the Western Han dynasty also belonged to this school. However, this method has now been lost. The Japanese concept of 「image」 is similar to our 「fuxiang」, except that it does not limit itself to fixed pairings such as Zhen concealing Xun or Gen concealing Dui. Generally speaking, it is quite similar to the concept of imagery. For detailed explanations, refer to the 「Yixue Zazhi」 (Journal of Yi Studies) published by the Tokyo Yi Studies Discussion Society in the Dingsi year (1917), which may be of interest to scholars.

“天一，地二。天三，地四。天五，地六。天七，地八。天九，地十。”又曰“天數二十有五，地數三十。天地之數，五十有五。”河圖洛書之數，即此五十有五之數所分佈而進退者也。聖人則圖畫卦，是故卦之數即圖書之數，亦即天地之數也。“大衍之數五十，其用四十有九”者，所以衍《易》，即以衍此五十有五之數者也。

The Great Treatise says: "Heaven is one, Earth is two; Heaven is three, Earth is four; Heaven is five, Earth is six; Heaven is seven, Earth is eight; Heaven is nine, Earth is ten." It also says: "The number of Heaven is twenty-five, the number of Earth is thirty; the total number of Heaven and Earth is fifty-five." The odd numbers one, three, five, seven, and nine belong to Heaven, and when added together they total twenty-five; the even numbers two, four, six, eight, and ten belong to Earth, and when added together they total thirty. When these two are combined, the total is fifty-five. The numbers of the Yellow River Chart and the Luo Writing are the result of the distribution and alternation of these fifty-five numbers. The sages took inspiration from the Yellow River Chart and the Luo Writing to draw the trigrams, so the numbers of the trigrams are the same as the numbers of the charts and writings, which are the numbers of Heaven and Earth. As for "the number of great derivation is fifty, but only forty-nine is used," this is used for the derivation of the Zhou Changes, but the subject of derivation still does not go beyond these fifty-five numbers. Thus, "the numbers of Heaven and Earth" and "the number of great derivation" are originally two different things, and it is necessary to distinguish them clearly first.

自宋儒竄易經文，以“天一地二”一節，移置“大衍之數五十”以前，兩數遂相混合，併為一談。異論紛若，左支右吾，卒無是處。漢學家雖力糾其繆，而於兩節之數理，亦未能分析清楚，與卦象《彖傳》相證明。乃沿繆襲誤，以迄於今。

Since the Song dynasty Confucian scholars altered the text, moving the section "Heaven is one, Earth is two" before "The Great Derivation consists of fifty," the numbers of Heaven and Earth and the numbers of the Great Derivation became mixed together and were regarded as one thing. Thus, various conflicting interpretations arose, and no single explanation could be fully consistent. Although Qing dynasty Han scholars made great efforts to correct this error, they were still unable to clearly analyze the numerical reasoning of these two sections. Moreover, they did not use the hexagram images and the Commentary on the Judgment to cross-verify each other, leading to the perpetuation of errors up to the present day.

程朱而後，言《易》者皆崇理論，言象者已不多，言數者尤少。偶有一鱗半爪，又皆似是而非。同人講習，幾於無可取資。爰就所知，略貢芻蕘。所憾數學既淺，又荒廢日久，自知膚淺已甚。姑引其端，以待專家之續竟其緒也。

After Cheng Yi and Zhu Xi, those who interpreted the Book of Changes mostly emphasized principles and meanings, while those who discussed images became rare, and those who dealt with numbers even fewer. Occasionally, there were some fragments, but they were ambiguous and not clear. When people gathered to study together, there was almost nothing to draw upon. Therefore, based on my own understanding, I briefly offer my shallow opinions. Regrettably, my knowledge of mathematics is shallow, and I have neglected it for a long time. I am fully aware that my views are very superficial, and I merely intend to start the discussion, hoping that experts will continue this line of thought.

乾一，兌二，離三，震四，巽五，坎六，艮七，坤八之數，邵子《皇極經世》之數，所謂先天數也。相傳康節從李挺之氏學《易》三年，未能窺其奧，請益於李，叩其要旨。李乃授以一二三四五六七八之八字，康節言下大悟，恍然於乾兌離震巽坎艮坤之天然位次，與數適合。

This sequence of numbers,乾 one, 兑 two, 离 three, 震 four, 巽 five, 坎 six, 艮 seven, 坤 eight, is the numerical system used in Shao Yong's "Huang Ji Jing Shi," which is commonly referred to as the "Earlier Heaven Numbers." It is said that Shao Yong (posthumously known as Kangjie) studied the Book of Changes with Li Zhicai (given name Tingzhi) for three years but still did not grasp its profound meaning. He then asked Li Zhicai for the essential principles. Li Zhicai simply taught him the words one, two, three, four, five, six, seven, and eight. At that moment, Shao Yong suddenly understood that the natural order of 乾, 兑, 离, 震, 巽, 坎, 艮, and 坤 perfectly corresponds to the numbers one through eight.

而陰陽交錯，順逆往來，無不妙合。極深研幾，遂得貫澈天人，成《皇極經世》一書。程子嘆為內聖外王之學，朱子《木義》，又取其大小方圓各圖，弁諸經首。其後言《易》者，即以先天數為易數。於卦爻《彖》、《象》之言數者，如“七日”“八月”“十年”“九陵”之類，悉以先天數當之，歧誤乃不可究詰。

Moreover, the interplay of yin and yang, moving forward and backward, coming and going, is all perfectly matched with this system of numbers. From this, he deeply studied the subtle aspects and finally understood the principles of heaven and human affairs, composing the book "Huang Ji Jing Shi." Cheng Yi praised it as the study of inner sagehood and outer kingship. Zhu Xi's "The Original Meaning of the Zhou Changes" also adopted his diagrams of large and small circles and square and circle, placing them before the text. Since then, those who explained the "Zhou Changes" have directly regarded the Earlier Heaven numbers as the numbers of the "Zhou Changes." Whenever the Book of Changes and its line statements, as well as the Commentary on the Judgment and Image Commentary, mention numbers, such as the "seven days to return" in the hexagram "Fu," the "eight months with calamity" in "Lin," the "ten years to name" in "Zun," and the "ascend to the high hill" in "Tong Ren," they all apply the Earlier Heaven numbers, leading to many erroneous interpretations that are beyond reckoning.

夫邵子先天數，非不合也。特邵子別有妙悟，以一二三四五六七八為主，如算學之數根。乾兌離震巽坎艮坤，只為其數之符號耳，故用乾兌離震巽坎艮坤可也，用日月星辰水火土石亦無不可也。

In fact, the Earlier Heaven numbers of Zhao Shi are not inconsistent. Zhao Shi had his own profound insight: he took the numbers one, two, three, four, five, six, seven, and eight as the main elements, just like the fundamental numbers in arithmetic; the trigrams Qian, Dui, Li, Zhen, Xun, Kan, Gen, and Kun are merely symbols of these numbers. Therefore, using Qian, Dui, Li, Zhen, Xun, Kan, Gen, and Kun to represent them is acceptable, and using his own terms from his writings, such as "sun, moon, stars, water, fire, earth, and stone," to represent them is equally valid.

因邵子未嘗以此注《易》，但借卦爻以演其數，而所得之數理，變化分合，仍能與《易》相符。所謂殊途同歸，法異而實不異也。若以言《易》，則自當以乾兌離震巽坎艮坤為主。先後體用，各有其數。與邵子之數同出天一地二之十數，並圖如左：

Zhang Zhengzhi never used this set of numbers to comment on the Yi Jing, but instead used the trigrams and lines to deduce his numbers. The numerical principles he derived still conform to the Yi Jing in terms of change and combination. This is called "different paths leading to the same destination"—different methods but the same essence. However, if these numbers are to be used in explaining the Yi Jing, they should naturally take the eight trigrams—Qian, Dui, Li, Zhen, Xun, Kan, Gen, and Kun—as their main focus. The Earlier Heaven and Later Heaven, as well as the essence and function, each have their own numbers. They all originate from the same set of ten numbers known as "Tian Yi Di Er." The following diagrams are now listed on the left.

乾一對坤八，合九。兌二對艮七，合九。離三對坎六，合九。震四對巽五，合九。四九合三十六。乾陽三畫，坤陰六畫，合九。兌四畫，艮五畫，合九。離四畫，坎五畫，合九。震五畫，巽四畫，合九。四九亦合三十六。

First, look at the numbers: Qian (Heaven) has one and Kun (Earth) has eight, adding to nine; Dui (Lake) has two and Gen (Mountain) has seven, adding to nine; Li (Fire) has three and Kan (Water) has six, adding to nine; Zhen (Thunder) has four and Xun (Wind) has five, adding to nine. Four nines together make thirty-six. Now look at the lines: Qian has three yang lines, making three strokes; Kun has three yin lines, each line broken into two, making six strokes. Adding these two trigrams gives nine; Dui has four strokes and Gen has five, adding to nine; Li has four strokes and Kan has five, adding to nine; Zhen has five strokes and Xun has four, adding to nine. Four nines together also make thirty-six. Thus, whether calculated by numbers or by strokes, the total is exactly the same.

八卦相蕩成六十四，除乾坤坎離頤中孚大小過八卦反覆不變，餘五十六皆一卦反覆成二卦，實只二十八卦。合乾坤等不變之八卦，亦共合三十六卦。三十六者，六之自乘也。故邵子曰“三十六宮都是春”，乃用六藏九，為邵子之獨有心得，別具用法。

The eight trigrams interact and transform into the sixty-four hexagrams. Except for the eight trigrams—Qian, Kun, Kan, Li, Yi, Zhongfú, Daguò, and Xiaoguò—which remain unchanged when reversed, the remaining fifty-six hexagrams each form another hexagram when reversed. Thus, in actuality, there are only twenty-eight hexagram forms. Adding the eight unchanging trigrams, the total becomes thirty-six hexagrams. Thirty-six is the square of six. Therefore, in his poem, Shao Yong wrote, "Thirty-six palaces are all spring." This is Shao's unique insight, using six while concealing nine, and it has its own special method.

故依此數方位，與五行干支納甲皆不相合。納甲之象與乾一兌二之數無關，漢學家力闢先天卦位，而於乾一兌二之數，無能辯駁。偶有言者，亦隔靴搔癢，無當於理。茲另圖先天八卦之合洛書河圖數如下：

This is precisely why the arrangement based on this set of numbers does not align with the Five Phases, the Heavenly Stems and Earthly Branches, or the Najia system. The images derived from the Najia system are inherently unrelated to the sequence of the trigrams as乾 one, 兑 two. Qing dynasty Han scholars strongly criticized the Earlier Heaven trigram positions, but they could not refute this sequence of numbers. Occasionally, someone would mention it, but their comments were like scratching an itch through a boot, missing the point entirely. Now, another diagram is drawn to illustrate how the Earlier Heaven trigrams correspond with the numbers of the Luo Writing and the Yellow River Chart, as follows:

聖人則圖畫卦，卦數即圖書之數。圖書之一六，皆從下起，陽從一始，陰以六終，皆歸藏於北方，未有從上起者。邵子先天數，獨悟“易逆數也”一語，故反用圖書而逆由乾位起一，藏九不用，為兩數之對待。如洛書之藏十，其妙用在卦順則數逆，卦逆則數順，故仍不悖於陽順陰逆之天則。錯綜變化，而無不相通。

The sage derived the trigrams by following the patterns of the Yellow River Chart and the Luo Writing. Therefore, the numbers of the trigrams correspond to those of the charts. In the charts, the number one and six are both counted from the bottom: yang begins with one and yin ends with six, and both are concealed in the north, never counted from the top. However, Zhao Zǐ's Earlier Heaven numbers uniquely understood the sentence "The Book of Changes reverses the numbers" from the "Explanations of the Trigrams." Therefore, he reversed the numbers of the charts, starting with one from the Qian position, concealing nine, making one and nine correspond as two opposing numbers, just as the Luo Writing conceals ten. Its subtle use lies in the fact that when the trigram sequence proceeds normally, the numbers reverse, and when the trigram sequence reverses, the numbers proceed normally. Thus, it still does not contradict the natural principle of "yang follows the order and yin reverses." Through the transformations of reversal and combination, there is no lack of mutual connection.

若論先天八卦之本數，則自當取則河圖，陰逆陽順，以合於一六二七三八四九之匹偶。而陰陽相對，皆得五數。如雷風一四合五也，水火二三合五也，山澤七八合十五，天地九六合十五，皆五也。仍以五為中樞。而一六為地雷復，九四為天風姤，二七為水澤節，三八為火山旅。所謂布五行於四時，無不合也。

If we are to discuss the numbers of the Earlier Heaven Trigrams themselves, then we should naturally refer to the Yellow River Chart: yin moves in reverse and yang moves in the usual direction, in order to correspond with the four pairs of numbers: one and six, two and seven, three and eight, four and nine. Yin and yang are paired oppositely, and the results are all multiples of five: thunder and wind are one plus four to make five, water and fire are two plus three to make five, mountain and marsh are seven plus eight to make fifteen, heaven and earth are nine plus six to make fifteen, all of which are reduced to five, still taking five as the central number. Now looking at the trigrams formed by these pairs: one and six form the hexagram of earth and thunder, Fu; nine and four form the hexagram of heaven and wind, Gou; two and seven form the hexagram of water and marsh, Jie; three and eight form the hexagram of fire and mountain, Lv. The statement in the "Book of Rites: The Ritual Propriety" that "the five elements are distributed through the four seasons" is fully consistent with all of this.

和而後月生，此納甲所以用先天之象，而取後天之數也。此理千餘年來，未有發明。由於不知陽順陰逆之數，以邵氏之數，強解京、焦之《易》，紛紜糾結，遂莫可究詰矣。陽數順由一始，為一三七九。陰數逆由四起，為四二八六。宋以後，皆以二四六八為陰數之用，此其根本之錯誤也。

The Li Yun continues saying, "Harmony comes first, then the moon is born," which precisely explains why the method of Najia uses the Earlier Heaven hexagrams but employs the Later Heaven numbers. This principle has not been revealed for over a thousand years. Because people do not understand the principle of yang numbers progressing in a positive direction starting from one, in sequence one, three, seven, nine, and yin numbers regressing starting from four, in sequence four, two, eight, six, they have forcedly applied Shao Yong's numbers to interpret Jing Fang and Jiao Yanshou's Yi, leading to confusion and making it impossible to trace the origin. In fact, the yang numbers proceed in order from one, three, seven, nine, while the yin numbers regress from four, two, eight, six. Since the Song dynasty, people have generally used two, four, six, eight as yin numbers, which is a fundamental error.

陽順陰逆圖數，餘於庚申之秋，始由“乾乘六龍”一語悟得“乘六”之法，繪圖以明之。始知極數定象，通變成文，參伍錯綜，皆在陽順陰逆。而千餘年來，似是而非之註釋，均可一掃而空矣。圖說另詳《易數偶得》。

Concerning the diagram and numbers of yang moving in order and yin moving in reverse, I only understood the method of "riding six" from the phrase "when the time comes to ride six dragons" in the Commentary on the Judgment of the Qian hexagram, and drew a diagram to explain it during the autumn of the Gengshen year (1920). It was then that I fully realized the essence of the Great Treatise's statements: "by reaching the extreme of numbers, one determines the images of the world," "by comprehending the changes, one forms the writings of heaven and earth," and "by combining three and two, one transforms and interweaves the numbers." The key lies entirely in the four characters "yang moving in order and yin moving in reverse." With this understanding, all the ambiguous interpretations over a thousand years can be completely discarded. The diagram and explanation are detailed in my work "Accidental Insights on the Numbers of the Book of Changes."

坎一坤二震三巽四離九艮八兌七乾六。乾坎相連，一與六合。坤兌相連，二與七合。震艮相連，三與八合。巽離相連，四與九合。水火金木之數，各有配合，獨闕五十兩數。

The Later Heaven Trigrams are paired with the numbers of the Luo Writing as follows: Kan one, Kun two, Zhen three, Xun four, Li nine, Gen eight, Dui seven, and Qian six. Qian is connected to Kan, with one and six combining, representing the number of water; Kun is connected to Dui, with two and seven combining, representing the number of fire; Zhen is connected to Gen, with three and eight combining, representing the number of wood; Xun is connected to Li, with four and nine combining, representing the number of metal. The numbers for the four elements of water, fire, metal, and wood are each paired, but the numbers five and ten are missing.

非闕也，坎一離九合十，中央戊己，而坤艮二八，亦合十為丑未，皆五與十土數所分寄，方位與洛書合，而數亦兼符納甲。其說已詳《卦位》章先天納甲圖，茲不贅述。更以數之順序，並列與洛書參照，則第一章二八易位，二五構精，兩圖之妙更可見矣。

In fact, it is not a matter of deficiency. When the number one from Kan and the number nine from Li are added together, they total ten, which corresponds to the central position of Wu and Ji (the earth elements). Similarly, when the number two from Kun and the number eight from Gen are added, they also total ten, which corresponds to the earth positions of Chou and Wei. The numbers five and ten, which represent the earth numbers, are thus located in these positions. Their directions correspond with the Luo Writing, and their numbers also align with the Najia stem assignment. This principle was explained in the chapter on "Hexagram Positions" in the Earlier Heaven Najia diagram, so we will not repeat it here. If these numbers are then arranged in order and compared with the Luo Writing, the subtle meanings discussed in the first chapter regarding the mutual exchange of Kun and Gen, and the interaction between two and five to form a vital essence, will become even more evident.

坎離乾巽震兌坤艮皆相對，與卦位合。惟坤二與艮八之位互易，五運中樞，而十暗寓於八方。所謂通變化而行鬼神者，即在此坤艮易位之妙用。故曰“神樞鬼藏”，向來道家珍為神秘。非入其門奧者，不肯輕洩。實則邵子天根月窟，子正在丑，午正在未數言，已不啻明明揭示，特後人不自悟耳。

The trigrams Kan and Li, Qian and Xun, Zhen and Dui, and Kun and Gen are all paired opposites, perfectly matching the positions of the hexagrams. However, the positions of Kun two and Gen eight are exchanged. As a result, the number five becomes the central axis of rotation, while the number ten is implicitly contained within the eight directions. The "Great Treatise" says, "It communicates transformation and moves spirits and ghosts," and the profound application lies in the exchange of positions between Kun and Gen. Therefore, practitioners call it "the divine axis and the hidden spirits," a secret highly valued by Daoists, not easily revealed to those who have not reached the inner understanding. In fact, Shao Yong's statements about "the heavenly root and the lunar cave," and "the proper position of Zi is in Chou, and the proper position of Wu is in Wei," clearly reveal this principle, but later generations have failed to comprehend it themselves.