The principles of imagery and numbers in both Buddhism and Taoism are fully contained in the Book of Changes.

《易》之為書也，廣大悉備。範圍天地，曲成萬物，故凡世界所有，無遠近，無今古，均不能出於《易》教之外。道教佛教，皆後起者也，而佛教創始於西域，更與中國之文化無關。乃聖人之作《易》，早定其數於三千年以前，而概括其教於卦象之中，並其科儀名類，亦皆一一列舉而豫定之。乃後來者冥然罔覺，順天地之理數，以自力進行。初未與《易》相謀，而事事物物胥一一準之，莫能相悖。始信孔子“天且不違況於人乎況於鬼神乎”之贊，為確有徵驗，而非以虛義為頌美之辭焉。

The book of Changes is vast and comprehensive, encompassing all aspects of the transformation of heaven and earth, and thoroughly revealing the nature of all things. Therefore, anything that exists in the world, regardless of its distance or time, falls within the scope of the teachings of the book of Changes. Taoism and Buddhism are later developments, and Buddhism originated in the West, having little to do with Chinese culture. However, the sages composed the book of Changes three thousand years ago, establishing the numbers of things beforehand, and including both religions within the hexagrams. Even their rituals, subjects, names, and classifications are all listed and predetermined without any omission. Later people were unaware of this, merely following the principles of heaven and earth and their own efforts, without consulting the book of Changes. Yet, everything they did coincided with the book of Changes, and could not be opposed. This is why they came to believe that Confucius' words in the "Commentary on the Literary Changes" of the Book of Changes, "Heaven does not violate, how then could people? How then could spirits and gods?" are indeed verified, and not just empty praise.

蓋天地之數，自天一地二至天九地十，八卦之入用準之。至乾而數為無，黃帝甲子，乾五支六，各分陰陽，以合八卦之用。至乾終戌亥，而數有孤虛（子一丑二至酉十盡於兌，至乾數無而於辰為虛。其對宮則為孤）。故乾坤陰陽皆極於己亥，己陽極陰始，亥陰極陽始。陰陽終始於己亥，而己亥實為天地陰陽之兩端（端者始也）。

The numbers of heaven and earth start from Tian Yi (Heaven One) and Di Er (Earth Two), continuing up to Tian Jiū (Heaven Ten) and Di Shí (Earth Ten), and the use of the Eight Trigrams follows these numbers. When reaching the position of Qian (Heaven), the number becomes "nothing." The Yellow Emperor created the Jiazi system, with five pairs of heavenly stems and six pairs of earthly branches, each divided into yin and yang to match the use of the Eight Trigrams. When reaching Qian, the sequence ends at Xu and Hai, and the numbers have "gū" (solitude) and "xū" (emptiness). Counting from Zi (one) to You (ten), the sequence ends at Dui (the last trigram). When reaching Qian, the number becomes nothing, but at Chen, it is "xū" (emptiness), and the corresponding trigram is "gū" (solitude). Therefore, the trigrams Qian and Kun (Heaven and Earth) both reach their extremes at Ji (six) and Hai (twelve). Ji is the end of yang and the beginning of yin, while Hai is the end of yin and the beginning of yang. Since yin and yang begin again at Ji and Hai, Ji and Hai are the two ends of heaven and earth ("end" meaning beginning).

聖人合陰陽之撰，通神明之德，先後皆履端伊始。己上先天乾兌卦，己履端始；亥下後天乾兌卦，亥履端始。是以聖人於己亥萬物終始，執其兩端，而用其中於民（天地子午正中，子一勿用。用子正在丑，用午正在未）。乃子丑中，天地協，使民協於中。南北乾坤坎離正中，堯舜通變宜民，垂衣裳而天下治。取諸乾坤，坎離水火，百姓日用而不知是也。

The sage harmonizes the system of yin and yang, comprehends the virtue of the divine, and begins both before and after with "starting at the beginning." Above the position of Ji is the Qian and Dui trigrams of the Earlier Heaven, so Ji is the beginning of starting at the beginning; below the position of Hai is the Qian and Dui trigrams of the Later Heaven, so Hai is also the beginning of starting at the beginning. Therefore, the sage takes both ends of the cycle of all things, Ji and Hai, and applies the concept of "center" to the people. (The天地 take Zi and Wu as the central positions; Zi is the "not to be used" position, but the use of Zi actually falls on Chou, and the use of Wu actually falls on Wei.) Thus, taking the middle between Zi and Chou, heaven and earth harmonize, and the people also harmonize with the center. The trigrams Qian, Kan, Li, and Kun are all located at the central positions. Yao and Shun understood their variations and made the people suitable, governing with ease and bringing great order to the world. The Great Treatise says this is taking the image of Qian and Kun. As for the use of Kan and Li, water and fire, these are daily uses of the people without their awareness.

故“人心惟危，道心惟微。惟精惟一，允執厥中”（子坎一，道心寅；艮三，人心子。一純丑，二精子，丑天地正中）。“中庸”乾二用中，皆天地大中之道，帝王立極，聖人立本，於己亥執其兩端，子丑用其中於民。斯堯舜之道，文周孔子所繼述，即《易》道用中之旨也。

Therefore, the "Book of Documents · Great Yu's Plan" says, "The human heart is perilous, the way heart is subtle; only by being meticulous and unified can one truly hold the middle." (The Son is Kan one, the way heart belongs to寅; the mountain is three, the human heart belongs to子. One is pure, paired with丑; two is meticulous, paired with子; 丑 is precisely the central point of heaven and earth.) "The Doctrine of the Mean" takes the use of the middle from the Nine in the Second line of the Qian hexagram, which represents the great middle way of heaven and earth. Emperors established their standard based on this, sages established their foundation based on this: holding both extremes on the Jihai positions, applying the middle at the 子丑 positions for the people. This is the way of Yao and Shun, also the way inherited and explained by King Wen, the Duke of Zhou, and Confucius. This is the essence of the "Yi" doctrine of "using the middle."

兩端各倚於一偏。東南偏辰巳，有陽無陰，主有生無死，道教是也（道教主長生不死）。西北偏戌亥，無陰無陽（乾數無），主無死無生，佛教是也。以其偏於一端也，對於用中而言，謂之異端。然天地既有其數，既開其端，即皆有其教。天地南北，子一陽，物出有，道教始。午一陰，物入無，佛教始。故子出而辰巳有者陽，於午一陰未生，入無之佛未見，其象有，有者皆道教。

Since they are both extremes, each tends to one side. The Southeast is biased toward Chen and Si, possessing yang but no yin, advocating life but not death, which is the doctrine of Taoism (Taoism takes immortality as its principle). The Northwest is biased toward Xu and Hai, possessing neither yin nor yang (the number of the乾 position is void), advocating neither death nor life, which is the doctrine of Buddhism. Because they each lean to one extreme, they are called heterodoxies in relation to the principle of the center. However, since heaven and earth have these numbers and have set these extremes, each has its own religion. Heaven and earth are divided into north and south: the Zi position has one yang, and all things emerge as "being," from which Taoism begins; the Wu position has one yin, and all things return to "non-being," from which Buddhism begins. Therefore, from the Zi position to Chen and Si, what is seen is all yang; at that time, the one yin of the Wu position has not yet emerged, and the Buddha, which returns to non-being, is not yet visible. Its image is "being," and all that belongs to "being" is Taoism.

孔子刪書斷自唐虞。唐虞日中天，南北用中，日未過中，其唐虞以上書是道教（黃帝為道家之祖，廣成空同皆道家言），非用中之道，故刪書刪之。而《易》之書所以明道，不明道教，是缺南北一偏，則《易》不備，不足以明道，故《易》象往來。自子一出有，其數逆來，起子西北來，而午東南，其卦為水天需，為火風鼎，其象為水火逆運，而以求有生無死。此其有陽無陰之一偏也，東南象也。

Confucius edited the Book of Documents, beginning from the time of the Yao and Yu Shun dynasties. The Yao and Yu Shun periods are like the sun at its zenith, with both north and south returning to the center, and the sun has not yet passed the meridian. The books prior to the Yao and Yu Shun belong to Daoism (the Yellow Emperor is the ancestor of Daoism, and figures like Guangchengzi and Kongtong are all Daoist teachings), which do not conform to the principle of the center, so Confucius deleted them when editing the Book of Documents. However, the Book of Changes is used to clarify the Dao. If Daoism is not explained, then the north and south are missing, and the Book of Changes would be incomplete and insufficient to clarify the Dao, hence the Book of Changes has both movement and return. Starting from the Zi position, one yang emerges and becomes existence, its number moves in reverse: coming from the northwest and going to the southeast, its hexagram is Water above Heaven, the Hexagram of Necessity, and Fire above Wind, the Hexagram of Tripod, its image is the reverse movement of water and fire, used to seek existence without death. This is one-sided with yang without yin, belonging to the image of the southeast.

是以西北來東南，其對卦言姤（西北乾對東南巽，為天風姤）言復（西南坤對東北艮，反震為地雷復），姤奼女而復嬰兒，需鼎服食以求長生之道者也。變則鼎折足需于泥而道敗，有生有死，有需“不速之客三人來”，道家所謂“三尸”“三彭”是也。故《易》四三為人爻，而游魂歸魂為鬼《易》（遊歸亦在四三兩爻。凡上五爻為天《易》，四三爻為人《易》，二初爻為地《易》，游魂歸魂為鬼《易》）。

Therefore, coming from the northwest to the southeast, in terms of the opposing trigrams, one is the hexagram "Gou" (the northwest trigram Qian opposing the southeast trigram Xun, forming the hexagram Tian Feng "Gou"), and the other is the hexagram "Fu" (the southwest trigram Kun opposing the northeast trigram Gen, reversed to Zhen, forming the hexagram Di Lei "Fu"). "Gou" is what the alchemists call "Chachan," and "Fu" is what they call "Infant." "Xu" and "Ding" represent the path of taking nourishment and cultivation to seek long life. Once things turn bad, it becomes "Ding" with "the tripod breaks its leg" and "Xu" with "waiting in the mud," indicating the decline of the Dao and the return to the cycle of life and death. The hexagram "Xu" also has "three unexpected guests come," which is what the Daoists refer to as "three corpses" and "three Peng." Therefore, the "Book of Changes" takes the third and fourth lines as the human lines, and the categories of "youhun" and "guihun" hexagrams as the ghostly hexagrams (both "youhun" and "guihun" are located on the third and fourth lines. All the top line and fifth line hexagrams are heavenly hexagrams, the third and fourth lines are human hexagrams, the second and first lines are earthly hexagrams, and the "youhun" and "guihun" hexagrams are ghostly hexagrams).

精氣為物，游魂為變，是故知鬼神之情狀。精氣為物者神，其道所謂神仙是也（艮寅人道，艮為山，故仙字從山從人。艮止其所，人極所自立也）。游魂為變者鬼，其道所謂尸彭是也。先天乾坤之位，而後天離坎居之。火上水下，其道未濟，魂升魄降（離魂坎魄），是死道也。故道以逆行。

The "Great Treatise" says, "Spiritual essence forms things, while wandering souls cause change; thus we know the nature of ghosts and spirits." The spiritual essence that gathers to form things is the divine, which in Taoism is called a celestial being. Since the position of "Geng Yin" (the second trigram of the Earthly Branches) represents the human realm, and "Geng" (Gen) represents mountain, the character for "celestial being" (xiān) includes "mountain" and "person." "Geng" signifies stopping at its place, which is precisely where human beings establish their own limits. The wandering soul that disperses to cause change is the ghost, which in Taoism is called "shi" (corpse) or "peng" (a mythical creature). In the Earlier Heaven arrangement, the trigrams for Heaven and Earth are positioned in certain directions, but in the Later Heaven arrangement, the trigrams for Fire and Water occupy those positions. Fire is above and Water is below, forming the hexagram "Not Yet Completed" (Wèi Jì). The soul ascends upward, while the body descends downward (Fire governs the soul, Water governs the body), which is the path toward death. Therefore, Taoist cultivation requires going against this path.

降炎上之火，升潤下之水，龍飛在天（震為龍，震下一陽由坎而出，龍飛在天，即取坎填離之說。丹家所謂龍從火裡出者是也。震位東方，亦青龍之位，其德為仁。仁屬陽，主升，乾九五爻其候也），虎履其尾（兌為虎，兌上一陰為陰之始，而位於正西白虎之位，其德為義。義屬陰，陰主降，降則變兌見為巽伏。故道家曰伏虎，又曰虎向水中生也），皆於三四兩爻反復其道。

To bring down the fire that naturally ascends and to raise up the water that naturally descends is called "Dragon Soaring in Heaven." (The trigram Zhen represents the Dragon; the yin line below Zhen comes from Kan. "Dragon Soaring in Heaven" corresponds to the Daoist practice of "taking Kan to fill Li," which is also referred to as "the Dragon emerging from fire." The position of Zhen is in the East, which is the position of the Azure Dragon; its virtue is benevolence. Benevolence is yang and is associated with rising, which corresponds to the ninth line of the fifth position in the Qian hexagram.) This is also called "Tiger Treading Its Tail." (The trigram Dui represents the Tiger; the yang line above Dui is the beginning of yin. Its position is in the West, the position of the White Tiger; its virtue is righteousness. Righteousness is yin and is associated with descending. When it descends, Dui transforms into Xun, which is hidden. Therefore, Daoists speak of "subduing the Tiger" and also say "the Tiger is born from water.") All of these involve the repetition of the principles in the third and fourth lines.

九四六三，陰陽反覆，是為雷澤歸妹，故歸妹天地大義人終始，為六十四卦之大歸魂卦也。先天乾，後天離，火天大有；先天坤，後天坎，地水師。大有眾也，師眾也。三人為眾，皆需之不速之客三人，故魂魄具而三尸即伏於中，是必損之三人損一，而後致一得天地之道。是《易》於道教明著其象，而魏伯陽之《參同契》，借《易》卦以明丹學，與《易》義無涉者，猶不與焉。儒者禁言異端，於他書則是，於《易》則非。《易》備萬物萬象，此道教東南一偏象，不可不知者也。

Nine in the Fourth and Six in the Third exchange their yin and yang, resulting in the trigram of Thunder over Marsh, known as "Return of the Maiden." Therefore, "Return of the Maiden" represents "the great principle of heaven and earth" and "the beginning and end of human beings," making it the largest returning soul hexagram among the sixty-four hexagrams. In the Earlier Heaven arrangement, the position of Heaven is occupied by Fire in the Later Heaven arrangement, forming the hexagram of Fire in Heaven, "Great Possession"; and the position of Earth in the Earlier Heaven is occupied by Water in the Later Heaven, forming the hexagram of Water on Earth, "The Army." "Great Possession" represents the multitude, and "The Army" also represents the multitude. Three people make a multitude, which corresponds to the three people mentioned in the hexagram "Need" with the line "Three unexpected guests come." Therefore, when the soul and spirit are complete, the three corpses are hidden within, and it is necessary to follow the principle of "One person is lost among three travelers" from the hexagram "Loss," reducing one person to achieve the unity of one, thus attaining the principle of heaven and earth. This is the image of the Book of Changes clearly displayed in Taoism. As for Wei Boyang's "Three Coinciding Treatise," which uses hexagrams to discuss alchemy but has nothing to do with the meaning of the Book of Changes, it should not be included. Scholars who prohibit discussion of heterodox views are correct when applied to other books, but incorrect when applied to the Book of Changes. The Book of Changes encompasses all things and phenomena. This southeastern aspect of Taoism is something that should not be unknown.

天地南北子一陽物出有，為恆有象（先天西南巽，東北震，為雷風恆象）。午一陰物入無，為咸無象（先天東南兌，西北艮，為澤山咸象）。咸無佛教也。午一陰生，午而戌亥，萬物歸無，為後天西北乾象。咸無反恆有，《春秋·莊七年》“夏四月夜，恆星不見”，為周莊王甲午，即佛誕生之日矣。佛誕生，天地咸象感，而恆星不見，而《易》已早徵其兆於先後天卦矣。

Heaven and earth are divided into north and south. The position of Zi (the rat) is where one yang begins to arise, and all things emerge into existence, which represents the image of "having" in the Hexagram 18 (Heng). In the Earlier Heaven arrangement, the southwest is Xun (wind) and the northeast is Zhen (thunder), together forming the Hexagram Heng (Thunder over Wind). The position of Wu (the horse) is where one yin begins to arise, and all things return to non-existence, which represents the image of "non-being" in the Hexagram 2 (Xian). In the Earlier Heaven arrangement, the southeast is Dui (lake) and the northwest is Gen (mountain), together forming the Hexagram Xian (Lake over Mountain). The "non-being" governed by Xian corresponds to Buddhism. When one yin arises at Wu, from Wu to Xu and Hai, all things return to non-existence, which is exactly the image of the northwest in the Later Heaven, represented by Qian (heaven). The "non-being" of Xian and the "having" of Heng are opposites. The Spring and Autumn Annals records that in the seventh year of Duke Zhuang of Zhou, during the summer fourth month, the night was so dark that the fixed stars were not visible. That year was Jiawu, the year of the birth of the Buddha. At the time of the Buddha's birth, heaven and earth responded to the image of Xian, hence the fixed stars were not visible. The Yi Jing had already revealed this sign in the Earlier Heaven and Later Heaven hexagrams.

故八卦於咸無順往，自東南午，而西北子，其卦為風火家人，為天水訟。家人由內出外，訟違行不親，其象為火水順滅，而以歸無死無生。此其無陰無陽之一偏也。西北乾剛乾金，故佛金剛不壞。佛說經金剛獨顯，為咸感應象。西北戌入夜明火，而佛始燃燈，西北天地以濟不通，而佛度彼岸（《易》利涉大川，皆由坎之乾東北往西南卦）。

Therefore, the Eight Trigrams in the hexagram "Xian" (咸) move in a forward direction on the "wu" (无) line: from the Southeast position of Wu to the Northwest position of Zi, resulting in the hexagram Wind Fire "Jiaoren" (家人) and Heaven Water "Song" (讼). "Jiaoren" represents movement from within to outside, while "Song" indicates conflicting actions that do not harmonize. The image is of fire and water successively extinguishing, returning to a state of neither death nor life. This is one aspect of the absence of yin and yang. The Northwest belongs to Qian (乾), which is strong and represents metal, so Buddhism refers to "Jingang bu huai" (金刚不坏), meaning "diamond-like indestructibility." The Sutra of Diamond (金刚经) is most prominent among the sutras spoken by the Buddha, precisely reflecting the image ofsympathetic response (induction) in the hexagram Xian. The position of Xu (戌) in the Northwest lights up at night, hence the Buddhist concept of the lamp of illumination. The Northwest is where heaven and earth are separated and do not communicate, so Buddhism speaks of crossing to the other shore. In the Book of Changes, whenever it says "li shexia chuan" (利涉大川), it refers to moving from Kan to Qian, from the Northeast to the Southwest.

天地數有無，以輔相左右民。左為輔，天地數甲三庚九，三九為二十七輔，是乾震無妄卦，乃天地有之數，而知無者妄也。右為相，天地數辛四乙八，四八為三十二相，是巽坤觀卦，乃天地無之數，而知觀者空也。故佛說以三十二相觀，不可以三十二相觀。

The numbers of Heaven and Earth have both "existence" and "non-existence," used to assist and guide the people. On the left is "auxiliary": the numbers of Heaven and Earth, Jia is three and Geng is nine; three and nine combine to make twenty-seven, which represents the "auxiliary" aspect. The trigram is Qian below and Zhen above, the hexagram of "Without Delusion," which represents the number of Heaven and Earth as "existence." Thus, what is called "non-existence" is delusion. On the right is "reflection": the numbers of Heaven and Earth, Xin is four and Yi is eight; four and eight combine to make thirty-two, which represents the "reflection" aspect. The trigram is Kun below and Xun above, the hexagram of "Observation," which represents the number of Heaven and Earth as "non-existence." Thus, what is observed is emptiness. Therefore, Buddhism says on one hand to observe with thirty-two aspects, and on the other hand, not to observe with thirty-two aspects.

是以戌西北巽入無，辛四西北物往來入無。有乙八辛四，坤巽入，升不來，而四於東南巽不果。西北乾木果，故佛說四果，謂入而實無所入。往來而實無往來，不來而實無不來，有法而實無有法，為四果，皆西北四戌入無數。四西北右相合一（合子一），即是一合相，而無見有，即非一合相，皆西北數西北相也。

Therefore,戌 is located in the northwest. The trigram Xun governs entry and return to nothingness. The number Xin, which is four, resides in the northwest. All things come and go, ultimately returning to nothingness. With Yi eight and Xin four, the trigrams Kūn and Xun govern entry, ascending without returning. The number four in the southeast trigram Xun is called 'not completed,' while in the northwest trigram Qian it is called 'wood fruit.' Therefore, Buddhism speaks of 'four fruits': entering yet there is nowhere to enter, coming and going yet there is no coming or going, not arriving yet there is no not arriving, having a method yet there is no method. These four aspects are the four fruits, all resulting from the number four and the戌 entering nothingness in the northwest. The number four in the northwest is the right 'aspect,' combining with the number one (i.e., the position of Zi), forming 'one combined aspect.' From nothingness, one perceives existence, hence it is also said 'it is not one combined aspect.' All these are the numbers and aspects of the northwest.

西北戌亥數無為空，而乾為門，故佛教曰空門。先天西北艮，艮為山，故佛門曰山門，佛祖曰開山。先後天乾艮合為遁，故又曰遁入空門。全《易》陰陽爻數，各一百零八，故佛之紀數，皆一百零八。西北陰，陰數窮於六，故佛至六祖而止（陰數窮於九，故道家丹以九轉）。西北咸，神無方而《易》無體，不疾而速，不行而至。咸感至神，故佛道感應至神。《易》備萬物萬象，此佛教於西北一偏象，不可不知者也。以上據端木鶴田氏之說而推衍之，其義尚多未盡，然亦可見其大概矣。

The numbers of the western and northwestern directions,戌 and 亥, are considered empty and void, and since the乾 represents a gate, Buddhism refers to it as the "empty gate." In the Earlier Heaven arrangement, the western north is associated with 艮, which represents a mountain, so the Buddhist gate is called the "mountain gate," and the Buddha is called the "mountain opener." In the Earlier Heaven, the乾 combines with the Later Heaven's 艮 to form the Hexagram of Retreat, so it is also said that one "retreats into the empty gate." The entire Book of Changes has 108 yin and yang lines, so Buddhist counting uses 108. The western north belongs to yin, and the extreme of yin numbers is six, so the Chan school of Buddhism stops at the sixth patriarch. The extreme of yang numbers is nine, so Taoist alchemy talks about nine transformations. The western north is associated with the Hexagram of Attraction, which says "the spirit has no fixed form and the Book of Changes has no fixed body." It does not hurry but naturally becomes fast, does not move but naturally arrives; the Hexagram of Attraction is aboutsympathetic response and reaches a miraculous level, so both Buddhism and Taoism talk about the miraculous nature ofsympathetic response. The Book of Changes encompasses all things and phenomena, and this western north aspect in Buddhism is something that should not be unknown. The above is based on the explanation of the scholar Du Mu Hetian, with further deductions. There are many meanings not fully explained, but one can get a general idea.