Da Yi Xiang Shu Gou Shen Tu (大易象數鉤深圖)

經名：大易象數鈞隱圖。元張理撰。底本未題撰人。三卷。底本出處：《正統道藏》洞真部靈圖類。參校版本：文淵閣四庫全書本經部易類（簡稱四庫本）。

This book is titled in the Daozang as "Da Yi Xiangshu Gouyin Tu," written by Zhang Li of the Yuan dynasty. The base text does not bear the author's name, and the entire work is divided into three volumes: upper, middle, and lower. The base text comes from the "Zhengtong Daozang" under the category of Lingtu (Spiritual Diagrams) in the Dongzhen Department. During the collation, another edition from the "Wenyuan Ge Siku Quanshu" under the category of Yi (Divination) in the Jing Department was consulted, and it is hereafter referred to as the "Siku Ben."

卷上：太極貫一之圖、易有太極圖、舊有此圖、太極函三自然奇耦之圖、德事相因皆本奇耦之圖、說卦八方之圖、乾知太始、坤作成物、大易象數鉤深圖目錄、天尊地卑、參天兩地圖、日月為易、河圖數圖、洛書數圖、河圖四象之圖、河圖始數益洛書成數圖、河圖八卦圖、乾元用九坤元用六圖、天地之數乾坤之策、河圖天地十五數圖、其用四十有九圖、乾坤六子圖、渾天六位圖、六位三極圖、伏羲先天圖、方圓相生圖、仰觀天文圖、俯察地理圖、伏羲八卦圖、八卦取象圖、文王八卦圖、八卦象數圖。

The first volume contains a total of thirty-two diagrams, arranged in the following order: The diagram of the Taiji encompassed in one, titled "The Diagram of Taiji Encompassed in One"; the diagram illustrating the sentence "The Book of Changes has the Taiji" from the Great Treatise, titled "The Diagram of 'The Book of Changes has the Taiji'"; an old diagram traditionally passed down from old editions; the diagram showing the Taiji containing three lines, naturally distinguishing odd and even, titled "The Diagram of Taiji Containing Three Lines, Naturally Distinguishing Odd and Even"; the diagram explaining the mutual dependence of virtue and affairs, both originating from odd and even, titled "The Diagram of Virtue and Affairs Being Mutually Dependent, Both Originating from Odd and Even"; the diagram illustrating the eight directions from the Sayings on the Hexagrams, titled "The Diagram of the Eight Directions from the Sayings on the Hexagrams"; the diagram explaining "The Heaven knows the beginning" (from the text); the diagram explaining "The Earth completes the things" (from the text) (here inserted is a line of the book's title in the printing block: "Catalogue of the Diagrams of the Great Changes: The Deep Insights of the Figures and Numbers"); the diagram explaining "Heaven is exalted and Earth is humble"; the diagram explaining "Participating in the heavens with two and five, leaning on the numbers," titled "The Diagram of Participating in the Heavens with Two and Five, Leaning on the Numbers"; the diagram explaining the formation of the character "Yi" from the combination of "Sun" and "Moon," titled "The Diagram of Sun and Moon Forming Yi"; the "He Tu Number Diagram"; the "Lu Shu Number Diagram"; the "He Tu Four Images Diagram"; the diagram explaining the combination of the generating numbers of He Tu with the completed numbers of Lu Shu, titled "The Diagram of the Starting Numbers of He Tu Enhanced by the Completed Numbers of Lu Shu"; the "He Tu Eight Trigrams Diagram"; the diagram explaining the use of all nines in the hexagram Qian and all sixes in the hexagram Kun; the diagram explaining the numbers of Heaven and Earth and the numbers of the trigrams Qian and Kun; the "He Tu Heaven and Earth Fifteen Numbers Diagram"; the diagram explaining the use of forty-nine in the Great Derivation; the diagram explaining the generation of the six subordinate trigrams from Qian and Kun; the "Holistic Heaven Six Positions Diagram"; the "Six Positions Three Poles Diagram"; the "Fu Xi Anterior Heaven Diagram"; the diagram explaining the mutual generation of the square and circular diagrams, titled "The Diagram of Square and Circle Mutually Generating"; the "Observing the Celestial Phenomena Diagram"; the "Observing the Terrestrial Phenomena Diagram"; the "Fu Xi Eight Trigrams Diagram"; the "Diagram of the Symbolic Meanings of the Eight Trigrams"; the "Wen Wang Eight Trigrams Diagram"; the "Diagram of the Symbolic Numbers of the Eight Trigrams."

卷中：四象合律圖、八卦納甲圖、剛柔相摩圖、八卦相蕩圖、六爻三極、五位相合、帝出震圖、曹卦之德、序上下經圖、三變大成圖、重易六爻圖、六十四卦天地數圖、十四卦萬物數圖、卦爻律呂圖、運會曆數圖、乾坤大父母圖、復妮小父母圖、八卦生六十四卦圖、八卦變六十四卦圖、陽卦順生陰卦逆生、復娠臨逛泰否六卦生六十四卦圖、六十四卦反對變圖。

The first half of the volume contains the following diagrams in order: the "Four Images and Twelve Tones" diagram explaining the combination of the Four Images with the Twelve Tones, the "Eight Trigrams and Ten Heavenly Stems" diagram explaining the assignment of the Heavenly Stems to the Eight Trigrams, a diagram illustrating "the interaction of firm and yielding," a diagram illustrating "the mutual transformation of the Eight Trigrams," a diagram explaining the division of the six lines into the three extremes of Heaven, Earth, and Humanity, a diagram explaining the pairing of the numbers of the five directions, the "Five Positions and Their Mutual Harmony" diagram, a diagram illustrating the "Imperial Departure from Zhen" from the "Commentary on the Trigrams," the "Deeds of the Divining Stalk and the Trigrams" diagram (mistakenly listed as "Deeds of the Cao Trigrams" in the catalog), a diagram arranging the order of the Upper and Lower Classics, the "Three Transformations Forming One Line" diagram, the "Repeating the Trigrams to Form Six Lines" diagram, the "Heaven and Earth Numbers of the Sixty-Four Trigrams" diagram, the "Numbers of All Things in the Sixty-Four Trigrams" diagram (missing the character "six" in the catalog), the "Trigram and Line and Twelve Tones" diagram, the "Cycle of Yuan, Hui, Yun, and Shi" diagram, a diagram taking the Trigrams Qian and Kun as the major parents, a diagram taking the Trigrams Fu and Guo as the minor parents (the catalog mistakenly writes "Ni" instead of "Guo"), a diagram explaining the generation of the sixty-four trigrams from the Eight Trigrams, a diagram explaining the transformation of the sixty-four trigrams from the Eight Trigrams, a diagram explaining the orderly generation of Yang trigrams and the reverse generation of Yin trigrams, a diagram explaining the generation of the sixty-four trigrams from the six trigrams Fu, Guo, Lin, Duan, Tai, and Poi (the catalog mistakenly writes "Shen" and "Gang" instead of "Guo" and "Duan"), and the "Opposition and Transformation of the Sixty-Four Trigrams" diagram.

乾坤易簡之圖、屯象之圖、蒙象養正圖、需須之圖、訟象之圖、師比御眾圖、大小畜吉凶圖、履虎尾之圖、否泰往來圖、同人之圖、大有守位圖、謙象之圖、豫象之圖、隨卦繫失圖、蠱象之圖、臨象之圖、觀國光之圖、噬嗑身口象圖、賁天文之圖、剝為陽氣種圖、復七日圖、元妄本中孚圖、頤靈龜圖。

In the latter half of the volume, the focus shifts to individual hexagrams, with diagrams presented in sequence: the diagram explaining the simplicity of the Heaven and Earth in the "Diagram of the Simplicity of Heaven and Earth," the symbolic diagram of the "Zun" hexagram, the diagram illustrating the principle of nurturing righteousness in the "Meng" hexagram, the diagram explaining the meaning of waiting in the "Xu" hexagram, the symbolic diagram of the "Song" hexagram, the diagram illustrating the governance of the "Shi" and "Bi" hexagrams, the diagram discussing the fortune and misfortune of the "Da Xu" and "Xiao Xu" hexagrams, the diagram of the "Lv" hexagram depicting "Walking on the Tiger's Tail," the diagram of the "Po" and "Tai" hexagrams showing their mutual transition, the diagram of the "Tong Ren" hexagram, the diagram of the "Da You" hexagram illustrating the maintenance of position, the symbolic diagram of the "Qian" hexagram, the symbolic diagram of the "Yu" hexagram, the diagram of the "Sui" hexagram depicting attachment and loss, the symbolic diagram of the "Gu" hexagram, the symbolic diagram of the "Lin" hexagram, the diagram of the "Guan" hexagram illustrating "Observing the Splendor of the State," the diagram of the "Shi He" hexagram symbolizing the mouth and teeth, the diagram of the "Ben" hexagram representing celestial phenomena, the diagram of the "Bo" hexagram showing the single yang line as the seed of yang energy, the diagram of the "Fu" hexagram illustrating "Recovery after Seven Days," the diagram of the "Wu Wang" hexagram emphasizing trust based on the "Zhong Fu" hexagram (the catalog entry "Yuan Wang" refers to "Wu Wang," with the character changed due to taboo in the Daozang edition), and the diagram of the "Yi" hexagram depicting "Abandoning Your Auspicious Turtle."

卷下：大過楝隆橈圖、習坎行險圖、離繼明圖、咸朋從圖、恆久之圖、逐象之圖、大壯羊藩圖、晉康侯之圖、明夷箕子圖、家人象圖、睽卦象圖、賽往來之圖、解出坎險圖、損益用中圖、央央之圖、娠遇之圖、萃聚之圖、升階之圖、困羨華葛萬株木圖、井鼎水火二用之圖、革卦爐精鼓鑄圖。

In the following section, the lower part of the text continues with the explanation of each hexagram, accompanied by diagrams. The previous entries in order are: the diagram of the hexagram "Da Guo" illustrating the image of a beam that may be raised or bent, the diagram of "Xi Kan" showing movement amidst danger, the diagram of "Li" illustrating the continuation of brightness and illumination in all directions, the diagram of "Xian" depicting "Friendship follows your thoughts," the diagram of "Heng" illustrating the principle of constancy, the diagram of "Dun" (with the note that the catalog entry "Zhu" is a mistake for "Dun"), the diagram of "Da Zhuang" showing a male sheep encountering a fence, the diagram of "Jin" illustrating "Kanghou used a gift of many horses," the diagram of "Ming Yi" depicting Ji Zi's internal hardship, the diagram of "Jia Ren," the diagram of "Kui," the diagram of "Jian" showing movement forward and backward (with the note that the catalog entry "Sai" is a mistake for "Jian"), the diagram of "Jie" illustrating escape from the peril of Kan, the diagram of "Sun" and "Gen" illustrating the principle of moderation, the diagram of "Gua" depicting the image of decisive action (with the note that the catalog entry "Yangyang" is a mistake for "Gua"), the diagram of "Gou" showing meeting, the diagram of "Cui" illustrating gathering, the diagram of "Sheng" depicting ascending steps, the diagram of "Kun" showing the images of thornbushes, grapevines, and stumps, the diagram of "Jing" and "Ding" illustrating the functions of water and fire, and the diagram of "Ge" depicting the process of smelting in a furnace.

震動心邊之圖、艮背象之圖、鴻漸南北圖、歸妹君娣之袂圖、豐日見斗之圖、旅次舍圖、巽林下圖、兌象之圖、渙躬之圖、節氣之圖、中孚小過卵翼生成圖、既濟未濟合律之圖、六十四卦卦氣圖、日月運行一寒一暑卦氣之圖、十三卦取象圖、三陳九卦之圖、參伍以變圖、十有八變圖、一陰一陽圖、先甲後甲圖、陰陽君民。

The next set includes: a diagram explaining the hexagram Zhen (Thunder) which moves in the heart and is manifested in external forms (the directory entry "bian" is a mistake for "ji" meaning "trace"), a diagram explaining the hexagram Gen (Mountain) "Gen qi bei" (keeping still on the back), a diagram explaining the hexagram Jian (Gradual Progress) with the image of wild geese flying south and north, a diagram explaining the hexagram Gui Mei (Return of the Maiden) with the image of the ruler and the maiden's sleeves overlapping, a diagram explaining the hexagram Feng (Brightness) "ri zhong jian dou" (the star Dou visible at noon), a diagram explaining the hexagram Lu (Traveler) with the image of lodging during a journey, a diagram explaining the hexagram Xun (Wind) "Xun zai chuang xia" (wind beneath the bed) (the directory entry "lin" is a mistake for "chuang" meaning "bed"), a diagram of the hexagram Dui (Joy) with its symbolic imagery, a diagram explaining the hexagram Huan (Dispersal) "Huan qi gong" (dispersing oneself), a diagram explaining the hexagram Jie (Moderation) with its alignment to the twenty-four solar terms, a diagram explaining the hexagrams Zhong Fu (Sincerity) and Xiao Guo (Minor Excess) with the image of bird eggs hatching and generating life, a diagram explaining the hexagrams Ji Ji (Completion) and Wei Ji (Non-Completion) with their alignment to the five tones, the diagram of the sixty-four hexagram qi (energy) chart, a diagram explaining the movement of the sun and moon, the alternation of cold and heat, and their correspondence with the hexagram qi, a diagram explaining the thirteen hexagrams mentioned in the Great Treatise with their symbolic imagery and the creation of tools, a diagram explaining the three times the Great Treatise discusses the nine hexagrams, a diagram explaining the concept of "san wu yi bian" (three and five transformations), a diagram explaining the process of eighteen transformations forming one hexagram, a diagram explaining the statement "yi yin yi yang zhi wei dao" (the interplay of yin and yang is called the Dao), a diagram explaining the hexagram Gu (Restlessness) "xian jia san ri, hou jia san ri" (three days before and after the first day of the month), and the diagram of "Yin Yang Jun Min" (Yin and Yang, Ruler and Subject).

陰陽奇耦、二儀得十變化、十日五行相生、大衍之數圖、搽曹之法圖、河圖百六數、八卦司化圖、類聚群分圖、通乎晝夜圖、陽中陰、陰中陽、序卦圖、雜卦圖、太玄準易卦名圖、太玄準易卦氣圖、皇極經世全數圖、邵氏皇極經世圖、溫公潛虛擬玄圖、潛虛性圖、說卦配方圖、古今易學傳授圖。

The final set includes: "Yin and Yang Odd and Even" explaining that odd trigrams represent yang and even trigrams represent yin; a diagram illustrating how the two principles generate ten and thus produce change; a diagram showing the relationship between the ten heavenly stems and the Five Phases; a diagram explaining the number of the Great Derivation; a diagram illustrating the method of divining by counting the yarrow stalks, with the catalog entry "cha cao" being a mistake for "che zhi"; a diagram of the River Chart with the extreme number 106; a diagram showing each trigram governing a particular type of transformation; a diagram illustrating the principle of "classifying things by their nature and grouping objects by their kind"; a diagram explaining the concept of "understanding the principle of day and night"; a diagram of "Yang containing Yin"; a diagram of "Yin containing Yang"; a diagram illustrating the sequence of the "Sequence of Trigrams"; a diagram showing the reversal in the "Miscellaneous Trigrams"; a diagram comparing the names of the trigrams in the Book of Changes with those in Yang Xiong's Tai Xuan; a diagram comparing the trigram energies with those in the Tai Xuan; a diagram of all the numbers in Shao Yong's Huang Ji Jing Shi; the "Shao氏 Huang Ji Jing Shi Diagram"; a diagram of Sima Guang's Qian Xu imitating the Tai Xuan; a diagram from Qian Xu discussing the nature; a diagram assigning the "Say of Trigrams" to directions; and a diagram recording the transmission of the study of the Book of Changes through generations.

右《太極圖》，周敦實茂叔傳二程先生。茂叔曰：無極而太極。太極動而生陽，動極而靜，靜極復動，一動一靜，互為其根，分陰分陽，兩儀立焉。陽變陰合而生水、火、木、金、土。五氣順布，四時行焉。五行一陰陽也。陰陽一太極也。太極本無極也。五行之生也，各一其性。無極之真，二五之精，妙合而凝。乾道成男，坤道成女，二氣交感，化生萬物。萬物生生，而變化無窮焉。

The diagram on the right is the Taiji Diagram passed down by Zhou Dunyi (also known as Zhou Dunshi, whose courtesy name was Maoshu) to Cheng Hao and Cheng Yi. Maoshu said: the "wuji" (formless and imageless) is the ultimate principle, which is also called "taiji." When taiji moves, it produces yang; when movement reaches its extreme, it turns into stillness; when stillness reaches its extreme, it once again begins to move. Movement and stillness are each the foundation of the other, thus differentiating into yin and yang, and the two principles of heaven and earth are established. Yang qi moves and changes, while yin qi condenses and combines, thus producing water, fire, wood, metal, and earth. These five elements spread in order, and the four seasons of spring, summer, autumn, and winter come into being. In the end, the five elements are merely yin and yang, and yin and yang are ultimately taiji, which itself is originally wuji. When each of the five elements is generated, it possesses its own nature. The true essence of wuji, combined with the two qi of yin and yang and the essence of the five elements, mysteriously converges and condenses: the path of Qian gives rise to male, the path of Kun gives rise to female, and the two qi interact and harmonize, giving birth to all things. All things continuously generate and transform from generation to generation, and change has no end.

太極未有象數，惟一氣耳。一氣既分，輕清者上為天，重濁者下為地，太極生兩儀也。兩儀既分，則金、木、水、火四方之位列，兩儀生四象也。水數六，居坎而生乾；金數九，居兌而生坤；火數七，居離而生巽；木數八，居震而生艮，四象生八卦也。

In the Taiji stage, there was no form or number, only a single mass of primordial qi. When this mass divided, the light and clear part rose to become Heaven, and the heavy and turbid part sank to become Earth. This is called "Taiji gives birth to the Two Principles." Once the Two Principles were separated, metal, wood, water, and fire each occupied the directions of east, south, west, and north respectively. This is called "the Two Principles give birth to the Four Symbols." Water has the number six and is located in the Kan position, giving rise to Qian; metal has the number nine and is located in the Dui position, giving rise to Kun; fire has the number seven and is located in the Li position, giving rise to Xun; wood has the number eight and is located in the Zhen position, giving rise to Gen. This is called "the Four Symbols give birth to the Eight Trigrams."

乾三畫而為天者，以一含三也。坤六畫而為地者，耦三而為六也。天一地二之本數，天奇地耦之本畫，不待較而可知，然妙理在乎一含三、二含六耳。乾一含三，故索為三男，而皆奇；坤二含六，故索為三女，而皆耦。此天地生成之理，豈不妙哉？

Heaven is represented by three lines because "one" contains "three"; Earth is represented by six lines because "three" doubled becomes "six." The fundamental numbers for Heaven and Earth are one and two respectively, and the fundamental lines for Heaven are odd while those for Earth are even, which is clear without comparison. The truly profound principle lies in "one contains three" and "two contains six." Heaven, by containing three, combines with Earth to produce the three male trigrams, Zhen, Kan, and Gen, whose main lines are all odd; Earth, by containing six, combines with Heaven to produce the three female trigrams, Xun, Li, and Dui, whose main lines are all even. This is the principle by which Heaven and Earth generate all things. Is it not marvelous?

震為雷，雷出於地下，故一陽在下。坎為水，水畜於地中，故一陽在中。艮為山，山形於地上，故一陽在上。然陽動陰靜，以動為基者，故動震是也。以靜為基者，故止艮是也。動者在中，非內非外，故或流或止，或動或靜焉。此坎所以為水。

The Trigram Zhen represents Thunder, which originates from beneath the earth, so the single Yang line in Zhen is placed at the bottom. The Trigram Kan represents Water, which accumulates in the earth, so the single Yang line in Kan is placed in the middle. The Trigram Gen represents Mountain, which stands upright on the earth, so the single Yang line in Gen is placed at the top. However, Yang is active and Yin is passive: those based on movement are the "movement" of Zhen; those based on stillness are the "stillness" of Gen. As for the Yang line in the middle, it is neither inside nor outside, so it sometimes flows and sometimes stops, sometimes moves and sometimes remains still—this is why Kan is symbolized by Water.

巽為木。木發生於地下，故一陰亦在下。離為火，火出於木中，故一陰在中。兌為澤，澤鍾於地上，故一陰在上。然陰柔而陽剛，故木也始弱而終強，陽在末也。陽明而陰晦，故火也外明而內晦，陽在外也。陽燥而陰潤，故澤也外潤而內燥，陽在內也。或問：澤內燥，何也？愚日：內燥則能生金，外潤則能鍾水，金所以能生水，土所以能生金者，即澤而知之也。聖人豈苟之哉？

The Trigram Xun represents Wood, which emerges from beneath the earth, so the yin line in Xun is placed at the bottom. The Trigram Li represents Fire, which arises from Wood, so the yin line in Li is placed in the middle. The Trigram Dui represents a Lake, whose water gathers on the surface, so the yin line in Dui is placed at the top. Yin is soft and Yang is strong, so Wood starts soft and becomes strong, with Yang at the top. Yang is bright and Yin is dark, so Fire is bright on the outside and dark inside, with Yang on the outside. Yang is dry and Yin is moist, so a Lake is moist on the outside and dry inside, with Yang inside. Someone asked: If the inside of a Lake is dry, why is that? My answer is: The dryness inside allows for the generation of Metal, while the moisture outside gathers Water. The principle that Metal generates Water and Earth generates Metal is clearly shown through the image of the Lake. Could the sages have chosen these symbols by chance?

一陽生於子，二陽在丑，三陽在寅，四陽在卯，五陽在辰，六陽在巳，而乾位在西北，居子之前，故日：乾知太始。言乾以父道始天地也。

The first yang line arises in the month of Zi, the second in Chou, the third in Yin, the fourth in Mao, the fifth in Chen, and by the time of Si month, all six yang lines are complete. The trigram Qian is located in the Northwest direction, right before the position of Zi. Therefore, the Great Treatise states, "Qian knows the beginning of the Great Ultimate," referring to Qian embodying the fatherly principle that initiates the creation of heaven and earth.

一陰生於午，二陰在未，三陰在申，四陰在酉，五陰在戌，六陰在亥。而坤位在西南，蓋西南方，申也；物成於正秋，酉也。坤作於申，成於酉，故日：坤作成物。

The first yao of yin is born in the month of Wu, the second yin in the month of Wei, the third yin in the month of Shen, the fourth yin in the month of You, the fifth yin in the month of Xu, and by the month of Hai all six yins are complete. The position of the K'un hexagram is in the southwest. The earthly branch corresponding to the southwest is Shen. All things mature in the beginning of autumn, and the earthly branch corresponding to the beginning of autumn is You. Therefore, K'un begins its work in the position of Shen and achieves completion in the position of You. Hence, the Great Treatise says, "K'un brings things to completion."

自一至十，天尊於上，地卑於下。尊者乾之位，故乾為君，為父，為夫。卑者坤之位，故坤為臣，為母，為婦。皆出於天尊地卑之義也。故日：天尊地卑，乾坤定矣。

Counting from one to ten, the numbers of Heaven are superior and occupy the upper position, while the numbers of Earth are inferior and occupy the lower position. The superior position belongs to the Trigram Qian (Heaven), so Qian is taken as symbolizing the ruler, the father, and the husband. The inferior position belongs to the Trigram Kun (Earth), so Kun is taken as symbolizing the subject, the mother, and the wife. These symbolic associations all arise from the principle of "Heaven is exalted and Earth is humble." Therefore, the Great Treatise begins by saying: "Heaven is exalted and Earth is humble; thus, Qian and Kun are established."

乾元用九，參天也。坤元用六，兩地也。故日：參天兩地而倚數。九、六者，止用生數也。

The "Use of Nine" in the Qian hexagram takes "three heavens," meaning the heavenly number three is tripled; the "Use of Six" in the Kun hexagram takes "two earths," meaning the earthly number two is doubled. Therefore, the "Commentary on the Hexagrams" says: "Triple the heavens and double the earths to rely on numbers." The numbers nine and six are derived solely from the five original numbers one to five, and there is no separate basis for them.

取日月二字交配而成，如篆文日下從月，是日往月來之義，故日：陰陽之義配日月。

The character "Yi" is formed by the intermingling of the characters "sun" and "moon," just as in the seal script, "Yi" has the sun above and the moon below. This signifies the continuous alternation between day and night. Therefore, the Great Treatise states: "The principle of yin and yang corresponds to the sun and moon."

戴九履一，左三右七，二四為肩，六八為足，五為腹心，總四十五，縱橫數之，皆十五也。天五居中央，聖人觀之，遂定八卦之象。

This diagram has nine at the top and one at the bottom, three on the left and seven on the right, two and four on the shoulders, six and eight on the feet, and five in the center. The nine numbers together total forty-five. Whether counted horizontally, vertically, or diagonally, each row adds up to fifteen. The number of heaven, five, is in the center. The sage observed this diagram and thus established the images of the eight trigrams. Zhang Li followed the naming convention of Liu Mu from the Song dynasty, calling this diagram of the forty-five numbers in the nine palace arrangement the "He Tu" or "River Chart."

河圖之數四十五，蓋聖人損去天、地二、天三、地四，凡十數。獨天五居中而主乎土，至洛書則有土十之成數，故水、火、金、木成形矣。

The total number of the River Chart is forty-five, because the sage subtracted the four generating numbers, heaven one, earth two, heaven three, and earth four, which sum up to ten, from the fifty-five number. What remains is the number five of heaven in the center, governing earth. Only when the Luo Book appears does the number ten of earth become complete, allowing water, fire, metal, and wood to take form. Here, "Luo Book" refers to the diagram of fifty-five numbers, also the term used by the school of Liu Mu.

《繫辭》日：《易》有太極，是生兩儀，兩儀生四象，四象生八卦。其四象在乎天一、地二，天三、地四，天五。天一居北方坎位，為水；地二居南方離位，為火；天三居束方震位，為木；地四居西方兌位，為金，此在四正之位，而為生數也；天五居中央，則是五土數也。土無定位，然後分王四正之方，能生萬物，故北方水一得土五而成六，南方火二得土五而成七，束方木三得土五而成八，西方金四得土五而成九，此謂之四象也。

The Great Treatise says: "The Book of Changes contains the Taiji, from which the two principles arise, from which the four images arise, and from which the eight trigrams arise." Here, the four images refer to the five generating numbers: heaven one, earth two, heaven three, earth four, and heaven five. Heaven one is located in the northern position of Kan, which belongs to water; earth two is located in the southern position of Li, which belongs to fire; heaven three is located in the eastern position of Zhen, which belongs to wood; and earth four is located in the western position of Dui, which belongs to metal. These four are situated in the four cardinal directions of southeast, northwest, south, and north. They are all generating numbers. Heaven five is located in the center, which is the number five of earth. Earth does not have a fixed direction; it must be strong in the four cardinal directions to nurture all things. Therefore, the water one in the north combines with the earth five in the center to form six; the fire two in the south combines with the earth five to form seven; the wood three in the east combines with the earth five to form eight; and the metal four in the west combines with the earth five to form nine. These four groups of generated numbers are called the four images.

河圖有天一、地二，天三、地四，為象之始。至於天五，則居中而主乎土變化，但未能成形謂之四象矣。至於洛書，有土十之成數，故水、火、金、木皆相奇耦而成形矣。故河圖合四象之數，可以定八方之位；洛書有五行之數，可以備八卦之象也。是象生其卦，必俟天之變，而備於洛書土十之成數，而後成八卦矣。二者相胥，方能成卦。

The River Chart contains Tian Yi (Heavenly One), Di Er (Earthly Two), Tian San (Heavenly Three), and Di Si (Earthly Four), which mark the beginning of the Four Symbols. As for Tian Wu (Heavenly Five), it resides in the center and governs the changes of Earth, but at this stage, the four elements are still not formed into definite shapes and can only be called the "Four Symbols." When the Lo Shu appears, the number ten for Earth is completed, allowing water, fire, metal, and wood to pair with odd and even numbers to form definite shapes. Therefore, the River Chart combines the numbers of the Four Symbols to determine the directions of the eight cardinal points; the Lo Shu includes the numbers of the Five Phases, enabling the formation of the trigrams of the Eight Trigrams. This shows that the emergence of trigrams depends on the change of heavenly numbers, and only after the numbers of Earth ten in the Lo Shu are properly matched can the Eight Trigrams be established. The River Chart and the Lo Shu depend on each other, and only then can the trigrams be formed.

此八象者，始由四象所生也。伏羲氏先按河圖有八方，將以八卦位焉；次取洛書土十之成數，將以八卦象焉。乃觀陰陽而設奇偶二畫，觀天、地、人而設上、中、下三位，以三畫純陽則為乾；以六畫純陰則為坤；以一陽處二陰之下，不能屈於柔，以動出而為震；以一陰處二陽之下，不能犯於剛，乃復入為巽；以一陽處二陰之問，上下皆弱，罔能相濟，以險難而為坎；以一陰處二陽之中，上下皆強，足以自記；乃麗而為離；以一陽處二陰之上，剛以馳下，則止而為艮，以一陰處二陽之上，柔能撫下，則說而為兌。

The eight trigrams originated from the four images. Fuxi first arranged the eight trigrams according to the eight directions indicated by the River Chart. Then he used the number ten from the Lo Shu square to determine the forms of the trigrams. Observing yin and yang, he established the odd and even lines as the basic components. Observing heaven, earth, and humanity, he established the upper, middle, and lower positions of the lines. Three lines all yang form Qian (Heaven), and six lines all yin form Kun (Earth). One yang line situated below two yin lines, unwilling to yield to softness, thus vibrates and becomes Zhen (Thunder). One yin line situated below two yang lines, unable to challenge strength, thus retreats and becomes Xun (Wind). One yang line situated between two yin lines, with both above and below weak, unable to support each other, thus falls into danger and becomes Kan (Water). One yin line situated between two yang lines, with both above and below strong, sufficient for self-reliance, thus adheres and becomes Li (Fire). One yang line situated above two yin lines, using strength to control the yin below, thus stops and becomes Gen (Mountain). One yin line situated above two yang lines, using softness to comfort the yang below, thus becomes joyful and becomes Dui (Lake).

乾陽之位，共十二畫，謂乾三爻，震、坎、艮各一爻，巽、離、兌各二爻，共十二畫也。坤陰之位，其二十四畫，謂坤六畫，巽、離、兌各一畫，震、坎、艮各二畫，計二十四畫也。陽爻，君道也，故得兼之，計有三十六畫，所以四九三十六畫，陽爻則稱九也。坤，臣道也，不得僭上，故四六二十四畫，所以陰爻則稱六也。故乾三畫兼坤之六畫，成陽之九也。陽進而《乾》元用九矣，陰退而《坤》元用六矣。合此餘九、六者，蓋天地剛柔之性也。

The yang lines belonging to the trigram Qian total twelve lines in the Eight Trigrams: Qian itself has three yang lines, Zhen, Kan, and Gen each have one yang line, Xun, Li, and Dui each have two yang lines, adding up to twelve. The yin lines belonging to the trigram Kun total twenty-four lines in the Eight Trigrams: Kun itself has six yin lines, Xun, Li, and Dui each have one yin line, Zhen, Kan, and Gen each have two yin lines, totaling twenty-four. Yang lines represent the way of the sovereign, so they can encompass yin lines, totaling thirty-six lines. Four multiplied by nine equals thirty-six, so yang lines are called "nine." Kun represents the way of the minister, who cannot exceed the sovereign, so it only has four multiplied by six, twenty-four lines, hence yin lines are called "six." Thus, the three lines of Qian combined with the six lines of Kun form the number nine for yang. Since yang is progressive, the beginning of the Book of Changes (Yijing) states "use nine" for Qian. Since yin is recessive, the beginning of the Book of Changes states "use six" for Kun. In summary, the numbers nine and six reflect the nature of heaven being strong and earth being yielding.

此天地之數，十有五也，或統而取之，其旨有六，蓋合自然之數也。且其一者，始就河圖縱橫之，皆十五數也。其二者，蓋天一、地二、天三、地四、天五，凡十五數也。其三者，以其太極未分，混而為一，即是一也。一氣判而為儀，見三也；二儀分而為象，見七也；四象演而生八卦，見十五數也。

The so-called heavenly and earthly numbers, when summed up, total fifteen. If viewed as a whole, they contain six layers of meaning, all consistent with natural numbers. The first layer: according to the River Chart, whether counted horizontally or vertically, the total is fifteen. The second layer: the five generating numbers, namely heaven one, earth two, heaven three, earth four, and heaven five, when added together, amount to fifteen. The third layer: before the Taiji splits into yin and yang, it is unified as 'one'; when this single qi splits into two yin and yang, one plus two gives 'three'; when the two yin and yang further divide into four images, three plus four gives 'seven'; when the four images evolve into the eight trigrams, seven plus eight results in the number 'fifteen'.

其四者，謂五行之生數，是一水、二火、三木、四金、五土，見十五數也。其五者，將五行之數中分為之，以象陰陽，則七為少陽，八為少陰，亦見其十五數也。其六者，以少陰少陽不動，則不能變，亦且八為少陰，陰動而退，故此少陰動而為盛陰，所以退稱六也，七為少陽，陽動而進，故少陽動而為盛陽，所以進稱九也；六與九合，亦見其十五也。斯蓋一、三、五陽位為一不四間，而五居中，然配王四方也。如六、七、八、九合而周，以為四象也。

The fourth layer: The generating numbers of the Five Phases are one for water, two for fire, three for wood, four for metal, and five for earth. When added together, they total fifteen. The fifth layer: By splitting the numbers of the Five Phases to symbolize yin and yang, seven is considered lesser yang and eight is lesser yin. Adding seven and eight also results in fifteen. The sixth layer: If lesser yin and lesser yang do not move, they cannot change. Eight is lesser yin, and when yin moves, it retreats, so lesser yin moving becomes full yin, which retreats and is called 'six'. Seven is lesser yang, and when yang moves, it advances, so lesser yang moving becomes full yang, which advances and is called 'nine'. Adding six and nine still results in fifteen. Generally, the three yang numbers one, three, and five are arranged in sequence without mixing, with five in the center, allowing them to be distributed to the four directions. As for the four numbers six, seven, eight, and nine combined, they circulate through one cycle, forming the Four Symbols.

天一下降，與地六合，而生水於北。地二上駕，與天七合，而生火於南。天三左旋，與地八合，生木於束。地四右轉，與天九合，而生金於西。天五冥運，與地十合，而生土於中。以奇生者成而耦，以耦生者成而奇。天，陽也，故其數奇。地，陰也，故其數耦。奇偶相合，而五十有五之數備。

Heavenly numbers have been continuously decreasing and have combined with the earthly number six, producing water in the north. Earthly number two has been rising and has combined with heavenly number seven, producing fire in the south. Heavenly number three has been rotating left and has combined with earthly number eight, producing wood in the east. Earthly number four has been rotating right and has combined with heavenly number nine, producing metal in the west. Heavenly number five has been secretly moving in the center and has combined with earthly number ten, producing earth in the center. All things generated by odd numbers have even numbers as their completion; all things generated by even numbers have odd numbers as their completion. Heaven belongs to yang, so heavenly numbers are all odd; earth belongs to yin, so earthly numbers are all even. Odd and even numbers are paired together, and the total number of fifty-five is complete.

大衍之數，臧其五者，五行之用也；虛其一者，元氣之本也。蓋天五為變化之始，散在五行之位，故中無定象。天始生一，肇其有數也，而後生四象、五行之數。今焉虛而不用，是明元氣為造化之宗，居尊不動也。

The reason the number of the Great Derivation is fifty-five, with five subtracted, is because that five belongs to the part of the Five Phases that initiates transmission. Therefore, a 'one' is left in an empty position without being used, because one is the root of the original qi. The number of Heaven is five, which is the beginning of change, spread throughout the five phases. Therefore, in the center, there is no fixed form. Heaven first produces one, thereby initiating the concept of numbers, and then produces the four images and the numbers of the Five Phases. Now, by leaving this one in an empty position without using it, it is to indicate that the original qi is the master of creation, occupying the supreme position without moving.

六位以二、三、四、五為經，七、八、九、六為緯者，象天文也。天以龍、虎、烏、龜為經，鎮、歲、熒惑、太白為緯。六位之經，元玄武之數者，北望惟見斗樞、辰極也。故斗謂之北斗、辰謂之北辰。雖名日北，而實天中，是一、六太極之數，潛宿於五也。河圖六、一居亥、子之北，五居中央，是中央與北皆得太極之數也。

The diagram of the Six Positions of the浑天 is arranged with the numbers two, three, four, and five as the meridians, and seven, eight, nine, and six as the parallels, based on the imagery of the heavens. In the sky, the four celestial beings, the Azure Dragon, White Tiger, Vermilion Bird, and Black Tortoise, are considered the meridians, while the planet Jupiter (岁星), Mars (荧惑), Venus (太白), and Saturn (镇星) are the parallels. The meridian lines of the Six Positions do not include the number corresponding to the Black Tortoise (玄武), because looking north one can only see the Dipper (斗) and the Northern Pole (辰极). Therefore, the Dipper is called "North Dipper" (北斗), and the Northern Pole is called "North Star" (北辰). Although the term "North" is used, in reality it is at the center of the sky. This is the number one and six, the two poles of the Taiji, hidden and contained within the number five. In the River Chart (河图), the numbers six and one are located in the north, at the positions of亥 and子, while the number five is at the center. Thus, both the center and the north have received the Taiji numbers.

六位之緯，元鎮星之數者，鎮星二十八載一周天，歲、熒惑、太白、辰，皆歷鎮星所鎮之宿而行，如陰陽家所謂土居中宮，王四季之說也。故《易》爻凡三百八十四，上契天象之數；而吉凶之變，占於七、八、九、六，如五星之變焉。

The six positions along the meridian do not include the number for Zhèn Xīng, because Zhèn Xīng takes twenty-eight years to circle the sky. When the Sui Xīng, Fēng Mò, Tàibái, and Chénxīng (Water Star) move, they all pass through the star mansions guarded by Zhèn Xīng. As the Yin-Yang school explains, the Earth occupies the Central Palace and is strong in all four seasons. Therefore, the sixty-four lines in the Book of Changes total three hundred and eighty-four, exactly matching the numbers of celestial phenomena. The changes of good and bad fortune depend on the numbers seven, eight, nine, and six, just as the movements of the five planets change their positions.

右伏羲八卦圖，王豫傳於邵康節，而堯夫得之。《歸藏》初經者，伏羲初畫八卦，因而重之者也。其經初乾初爽坤，初艮初兌，初犖坎初離，初釐震初巽，卦皆六畫，即此八卦也。八卦既重，爻在其中。

The eight trigrams on the right side of the diagram were passed down to Shao Kangjie by Wang Yu, and thus Shao Yaofu obtained it. The so-called "Initial Classic" of the "Guicang" refers to the part of the classic where Fuxi first drew the eight trigrams and then transformed them into hexagrams. The hexagrams listed in that classic are called Initial Qian, Initial Shu (which is actually Kun, the original text mistakenly writes it as "Shuang"), Initial Gen, Initial Dui, Initial Luo (which is actually Kan), Initial Li, Initial Li (which is actually Zhen), and Initial Xun. Each hexagram consists of six lines, which is exactly what is referred to here as the eight trigrams. Once the eight trigrams were transformed into hexagrams with six lines, the six yao (lines) were naturally included within them.

鄭氏云：古先天圖，楊雄《太玄經》、關子明《洞極》、魏伯陽《參同契》、邵堯夫《皇極經世》而已。惜乎，雄之《太玄》、子明之《洞極》仿《易》為書，泥於文字，後世忽之，以為屋上架屋，頭上安頭也。伯陽之《參同契》，意在於鍛鍊，而入於術；於聖人之道，又為異端也。堯夫擺去文字小術而著書，天下又不願之，但以為律曆之用，難矣哉。四家之學，皆先於古先天圖。先天圖，其《易》之源乎？復無文字解注，而世亦以為無用之物也。今予作方圓圖，腳註比之四家為最簡易。而四家之意，不出於吾圖之中，於《易》之學為最要。

Zheng's view is that among ancient scholars who could follow the Heavenly Diagram, only Yang Xiong's The Classic of Supreme Mystery, Guan Ziming's The Classic of Ultimate Void, Wei Boyang's The Concordance of the Three, and Shao Yaqian's The Imperial Ultimate Classic were able to do so. Unfortunately, Yang Xiong's The Classic of Supreme Mystery and Guan Ziming's The Classic of Ultimate Void imitated the Book of Changes, being overly concerned with words, so later generations regarded them with contempt, saying they were like building another roof on top of a house or adding another head to a head. Wei Boyang's The Concordance of the Three focused on alchemical cultivation, thus leading into the realm of alchemy; from the perspective of the Way of the Sages, it became considered as heresy. Shao Yaqian wrote his book by setting aside words and minor techniques, yet the world did not sincerely accept his teachings, only treating it as a tool for the study of the calendar and music. How truly difficult it is. The learning of these four schools originated before the ancient Heavenly Diagram. The Heavenly Diagram, perhaps, is the source of the Book of Changes? Only because it lacks textual explanations, the world has regarded it as useless. Now I have drawn this diagram of mutual generation between the square and the circle, adding notes beside it, which is more concise and clear than those four schools. The intent of those four schools does not go beyond the scope of this diagram, and for the study of the Book of Changes, it is the most essential.

伏羲仰觀天文，以畫八卦，故日月星辰之行度運數，十日四時之屬，凡麗於天之文者，八卦無不統之。

Fuxi looked up to observe the patterns of heaven and stars, and based on these he drew the Eight Trigrams. Therefore, the paths and cycles of the sun, moon, and stars, as well as the ten Heavenly Stems and the four seasons, all things connected to the heavenly patterns, are comprehended by the Eight Trigrams without exception.

伏羲俯察地理，以畫八卦，故四方九州島、烏獸草木、十二支之屬，凡麗於地之理者，八卦元不統之。

Fuxi looked down at the patterns on the ground and used them to draw the Eight Trigrams. Therefore, things such as the four directions, the nine provinces, birds and beasts, plants and trees, and the twelve earthly branches, all things related to the earth's patterns, were all included within the Eight Trigrams.

乾陽居上，坤陰居下，乾自震而左行，坤自巽而右行，天左地右，故曰剛柔相摩。

Heaven's yang energy resides above, and Earth's yin energy resides below. Heaven begins from the Zhen position and moves to the left, while Earth begins from the Xun position and moves to the right. The way of Heaven turns to the left, and the way of Earth turns to the right. They move in opposite directions and rub against each other, so the Great Treatise says, "Yang and Yin rub against each other."

震盪艮，兌蕩坤，離蕩巽，坎蕩乾，八卦往來，迭相推蕩。京房日：蕩陰入陽，蕩陽入陰。

Zhen overcomes Jie Tang Gen, Dui overcomes Jie Tang Kun, Li overcomes Jie Tang Xun, Kan overcomes Jie Tang Qian; the Eight Trigrams move towards each other, taking turns to push and stir each other. Jing Fang of the Han dynasty said: to stir Yin into Yang and to stir Yang into Yin.

曹之數，七也；七而七之，其用四十九，故其德圓。卦之數，八也，八而八之，為別六十四，故其德方。圓者運而不窮，可以逆知來物。方者其體有定，可以識乎既往，故圓象神，方象知。

The number of the yarrow stalks is seven. When seven is multiplied by itself three times, the actual number used is forty-nine, so the nature of the yarrow stalks is round. The number of the hexagrams is eight. When eight is multiplied by itself three times, sixty-four hexagrams are produced, so the nature of the hexagrams is square. Round things are ever turning and never cease, thus they can foresee what is to come. Square things have fixed forms, thus they can discern what has already passed. Therefore, roundness symbolizes the "spirit" mentioned in the Great Treatise, and squareness symbolizes the "knowledge" mentioned in the Great Treatise.

本《乾》九二爻變成《同人》，次變《無妄》，次變《益》，次變《頤》，終其變至《離》而止；本《坤》六二爻變成《師》，次變《升》，次變《恆》，次變《大過》，終其變至《坎》而止，故上經始於《乾》、《坤》，終於《坎》、《離》焉。

Starting from the second line of the Qian hexagram, changing one line transforms it into the Tongren hexagram, then into the Wuwang hexagram, then into the Yi hexagram, then into the Yi hexagram, continuing until reaching the Li hexagram. Starting from the second line of the Kun hexagram, changing one line transforms it into the Shi hexagram, then into the Sheng hexagram, then into the Heng hexagram, then into the Daguover hexagram, continuing until reaching the Kan hexagram. Therefore, the Upper Canon begins with Qian and Kun and ends with Kan and Li.

本《咸》六二爻變成《大過》，次變《困》，次變《坎》，次變《師》，次變《蒙》，而終於《未濟》；本《恆》初六爻變成《大壯》，次變《豐》，次變《震》，次變《復》，次變《屯》，而入《既濟》，故下經始於《咸》、《恆》，終於《既濟》、《未濟》焉。

Starting from the second line of the Hexagram 咸 (Xian), changing one line leads to 大过 (Da Guo), then to 困 (Kun), then to 坎 (Kan), then to 师 (Shi), then to 蒙 (Meng), and finally reaching 未济 (Wei Ji). Starting from the first line of the Hexagram 恒 (Heng), changing one line leads to 大壮 (Da Zhuang), then to 丰 (Feng), then to 震 (Zhen), then to 复 (Fu), then to 屯 (Zun), and finally reaching 既济 (Ji Ji). Therefore, the lower section begins with 咸 (Xian) and 恒 (Heng), and ends with 既济 (Ji Ji) and 未济 (Wei Ji).

#1『坤』，原脫，據四庫本補。#2『定位』，原作『宅位』，據四庫本改。#3『相胥』，四庫本作『相需』，其義同。#4『自記』，四庫本作『自托』。#5『馳下』，四庫本作『馭下』。#6『而』，據四庫本補。#7『為』，據四庫本補。#8『未』，據四庫本補。

The first point: The character 「坤」 was originally missing in the base text and has been added according to the Siku Quanshu edition. The second point: The term 「定位」 was originally written as 「宅位」 in the base text and has been corrected according to the Siku Quanshu edition. The third point: 「相胥」 in the base text is the same as 「相需」 in the Siku Quanshu edition, meaning the same thing. The fourth point: 「自记」 in the base text is 「自托」 in the Siku Quanshu edition. The fifth point: 「驰下」 in the base text is 「驭下」 in the Siku Quanshu edition. The sixth point: The character 「而」 has been added according to the Siku Quanshu edition. The seventh point: The character 「为」 has been added according to the Siku Quanshu edition. The eighth point: The character 「未」 has been added according to the Siku Quanshu edition.

#9『演』原作『言』，據四庫本改。#10『動』，據四庫本補。#11『退』，據四庫本補。#12『鎮』，四庫本作『辰』。疑『鎮』字誤。#13『天象』，原作『上象』，據四庫本改。#14『堯夫』，原作『鄭夫』，據四庫本改。#15『初突』，四庫本作『初奭』。#16『未濟』，疑底本脫，據句義增補。

Article 9: The character 「演」 in the original text was 「言」, and it has been corrected according to the Siku Quanshu edition. Article 10: The character 「动」 has been added according to the Siku Quanshu edition. Article 11: The character 「退」 has been added according to the Siku Quanshu edition. Article 12: The character 「镇」 in the Siku Quanshu edition is 「辰」, and it is suspected that 「镇」 is a mistaken character. Article 13: The original text had 「上象」, which has been corrected to 「天象」 according to the Siku Quanshu edition. Article 14: The original text had 「郑夫」, which has been corrected to 「尧夫」 according to the Siku Quanshu edition. Article 15: The original text had 「初突」, but the Siku Quanshu edition has 「初奭」. Article 16: The two characters 「未济」 are suspected to be missing in the original text, and have been added according to the meaning of the sentence.

十一月《復》一陽生，黃鍾氣應；至四月，六陽為《乾》，故闢戶謂之乾。五月《娠》一陰生，蘿賓氣應；至十月，六陰為《坤》，故闔戶謂之坤。

In November, the hexagram of Fu has one yang line emerging, corresponding with the Qi of the Huangzhong pitch pipe; by April, all six lines are yang and form the hexagram of Qian, so the Great Treatise says, "Opening the door is called Qian." In May, the hexagram of Gou has one yin line emerging, corresponding with the Qi of the Rui Bin pitch pipe; by October, all six lines are yin and form the hexagram of Kun, so the Great Treatise says, "Closing the door is called Kun." The original text mistakenly writes "seng" instead of "gou," and "luobin" instead of "ruibin."

《復》十二世，《臨》二十四世，《泰》三十六世，《大壯》四十八世，《夾》六十世，《乾》七十二世，《垢》八十四世，《逐》九十六世，《否》一百八世，《觀》一百二十世，《剝》一百三十二世，《坤》一百四十四世。

This diagram matches the twelve trigrams with the numerical cycles of yuan, hui, yun, and shi: The trigram "Fu" corresponds to twelve shi, "Lin" to twenty-four shi, "Tai" to thirty-six shi, "Da Zhuang" to forty-eight shi, "Gua" to sixty shi, "Qian" to seventy-two shi, "Gou" to eighty-four shi, "Dun" to ninety-six shi, "Pou" to one hundred and eight shi, "Guan" to one hundred and twenty shi, "Bo" to one hundred and thirty-two shi, and "Kun" to one hundred and forty-four shi. Each trigram increases by twelve shi, completing a cycle that equals one yuan. The original characters "jia," "gou," and "zhu" are corrupted forms of "Gua," "Gou," and "Dun," respectively.

《乾》，一變《垢》，二變《逅》，三變《否》，至五變為《剝》而止。物不可以終盡，《剝》窮上反下，故受之以《復》。《坤》，一變《復》，二變《臨》，三變《泰》，至五變為《夫》而止。《夾》必有遇，故受之以《娠》。

The first change of the Qian hexagram becomes Gou, the second becomes Duan, the third becomes Poi, and so on until the fifth change becomes Bo, then it stops. Things cannot proceed to the extreme; when the Bo hexagram reaches the top line, it reaches its limit and returns to the lower part, so the "Xugua" text follows with the Fu hexagram. The first change of the Kun hexagram becomes Fu, the second becomes Lin, the third becomes Tai, and so on until the fifth change becomes Guai, then it stops; Guai means decision, and after decision there must be a meeting, so the "Xugua" text follows with the Gou hexagram. The original text had the characters "gou", "hou", "fu", "jia", and "shen" which are errors for "gou", "duan", "guai", "guai", and "gou" respectively.

一陽來《復》，變《臨》為二陽，變至《泰》為四陽，變至《大壯》為八陽，變至《央》為十四陽，終其變於《歸妹》，成十六陽。一陰始《娠》，變《逐》為二陰，變至《否》為四陰，變至《觀》為八陰，變至《剝》為十四陰，終其變於《隨》，成十六陰。

One yang comes from the hexagram "复" and transforms into "临," accumulating two yangs; then to "泰," accumulating four yangs; then to "大壮," accumulating eight yangs; then to "夬," accumulating fourteen yangs, and continues through "归妹" to complete sixteen yangs. One yin begins with the hexagram "姤," transforming into "遯," accumulating two yins; then to "否," accumulating four yins; then to "观," accumulating eight yins; then to "剥," accumulating fourteen yins, and continues through "随" to complete sixteen yins. This is the method of generating hexagrams layer by layer, with "复" and "姤" as the initial parents. The original characters "央," "娠," and "逐" are errors for "夬," "姤," and "遯," respectively.

一升而合九，歸五為君；十降而合六，歸二為臣，此之謂陽卦順生也。

One ascends continuously and meets with nine, returning to the fifth line position to become the ruler; ten descends continuously and meets with six, returning to the second line position to become the minister. This is called the yang trigram generating in order.

一降而合九，歸五為君；十升而合六，歸二為臣，此之謂陰卦逆生也。

One goes downward and meets with the ninth to form the ruler at the fifth line; ten goes upward and meets with the sixth to form the minister at the second line. This is called the Yin trigram generating in reverse order.

一陰五陽反對變六卦、一陽五陰反對變六卦、二陰四陽反對變十二卦、二陽四陰反對變十二卦、反對不變八卦、三陰三陽反對變二十四卦。

This diagram divides the sixty-four hexagrams into groups based on the number of yin and yang lines. Then it examines how each pair of hexagrams change when viewed as their opposites, meaning the entire hexagram is reversed. A group with one yin line and five yang lines produces six changing hexagrams through opposition. A group with one yang line and five yin lines also produces six changing hexagrams through opposition. A group with two yin lines and four yang lines produces twelve changing hexagrams through opposition. A group with two yang lines and four yin lines also produces twelve changing hexagrams through opposition. There are eight hexagrams that remain the same when reversed, meaning they do not change through opposition. A group with three yin lines and three yang lines produces twenty-four changing hexagrams through opposition. The six groups together make up the sixty-four hexagrams.

乾、坤者，數之一、二也，形之方、圓也，氣之清、濁也，理之動、靜也。故乾具兩儀之意，而分上下，坤包四象之體，而分南、北、東、西。兩儀四象，共數有六，並其乾、坤之本體，則八卦之數周備矣。此乾、坤所以去太極未遠。內貞外悔，兩儀之理也。元亨利貞，四象之道也。二、三、四、五以為經，七、八、九、六以為緯，八卦之方也。

Heavenly Stem Jia and Earthly Branch Zi represent the number one and two respectively. In form, they represent square and circle. In qi, they represent clear and turbid. In principle, they represent motion and stillness. Therefore, Heaven (Qian) contains the meaning of the two principles (two yi) and divides into upper and lower. Earth (Kun) encompasses the form of the four images (four xiang) and divides into the directions of south, north, east, and west. The two principles plus the four images make six numbers, and adding Heaven and Earth themselves, the eight trigrams (bagua) are complete. This is precisely why Heaven and Earth are not far from the Taiji. The inner trigram is called "Zhen" and the outer trigram is called "Hui," which follows the principle of the two yi. The four virtues of Yuan, Heng, Li, and Zhen follow the principle of the four xiang. Using two, three, four, and five as the jing (meridians) and seven, eight, nine, and six as the wei (woven threads) follows the directional arrangement of the eight trigrams.

所以自一而二，自二而四，自四而八，自八而十六，自十六而三十二，自三十二而六十四，六十四而天道備矣，歲功成矣，人事周矣。此《易》故六十四卦，而《乾》、《坤》居首也。學者能由六十四以歸一，由一以悟太極，則伏羲、文王、孔子皆備於我，成變化，行鬼神，亦是道也。

Therefore, from one comes two, from two comes four, from four comes eight, from eight comes sixteen, from sixteen comes thirty-two, from thirty-two comes sixty-four; when reaching sixty-four, the heavenly way is complete, the seasonal changes of a year are fulfilled, and the principles of human affairs are fully covered. This is why the Book of Changes establishes the sixty-four hexagrams, with the hexagrams of Qian (Heaven) and Kun (Earth) placed first. Those who study the Book of Changes, if they can return from the sixty-four hexagrams to one, and from one comprehend the Taiji (Supreme Ultimate), then the learning of Fuxi, King Wen, and Confucius will all be within me; what the Great Treatise says, "Achieving transformation and movement, acting like ghosts and spirits," refers precisely to this principle.

童蒙在五，擊之在上，是外學也。耳目所入，雖足以資吾，適足以賊吾之真性，故不利為寇也。包蒙在二，發之在初，是內學也。心之所造，貴於幾先，一吝也。著於心，便成機械，所以脫栓桔，利者，吾心之栓桔乎？

The "childlike ignorance" of the "Mont" hexagram is in the line six five. Those who come to strike him are in the line nine at the top, representing learning introduced from outside. What is received by the ears and eyes, although sufficient to assist me, may also harm my true nature. Therefore, the line statement of nine at the top says, "It is not advantageous to act as a plunderer." "Encompassing the ignorance" is in nine two, and "awakening the ignorance" is in six at the beginning. This represents learning arising from within. What is cultivated within is valuable when it is still in the initial stage. Once there is hesitation or attachment, it becomes cunning and deceit. Therefore, to remove the fetters—what is truly beneficial for people is not it to remove the fetters on one's own heart?

坎中之陽以為助，乾卦之陽求待上，一陽而為之援，一陰避之而興進，一陰阻之而復退，此所以為《需》之吉凶也。然聖人之意，不責於二陰而責於三陽，不責於三陽而責於坎中之陽，利所在也，故責之重也，遂繫之以酒食之象焉。酒食者，養人之具也，人之所求待也。為酒食之所困，而為害者亦有之也。始貪其利，終罹其害者，小人之常也。必有道以處之，所以貴乎貞吉也。貞者，中正之義。內中正則外固，外固則不陷矣。

In the trigram Kan, the single yang line can serve as support, while the three yang lines in the trigram Qian are seeking upward assistance. There is one yang line that supports it, one yin line that avoids it allowing it to advance, and another yin line that blocks it causing it to retreat — this is how the fortune of the hexagram Xu is determined. However, the intention of the sage is not to blame the two yin lines in the upper trigram but rather the three yang lines in the lower trigram. Nor does it stop at blaming the three yang lines but instead focuses more on the single yang line in Kan, because the benefit lies here, so the blame is heavier. Therefore, it is associated with the image of "wine and food." Wine and food are things that nourish people and are what people look forward to. However, many people are also harmed by them. Initially they desire their benefits, but eventually they suffer their misfortunes, which is the usual state of small people. Therefore, the hexagram Xu values "zheng ji" ("upright good fortune"). "Zhen" means uprightness and correctness: if the inner part is upright and correct, then the outer part will be stable; if the outer part is stable, it will not fall into danger.

乾居亥位，坎起子方，亥子皆北，皆屬於水，始無所爭也。一離於形，則天西傾，水束注；天上蟠，水下潤，於是而《訟》矣。

Qian is located at the亥 position, Kan starts from the子 direction. Both亥 and子 are in the north and belong to water, so originally there was no conflict. But once they take form, heaven inclines westward, while water flows eastward; heaven circulates above, water moistens below, moving in opposite directions, thus giving rise to the hexagram of Strife. The original text '束注' should be '东注'.

《坤》為眾，而《師》亦為眾者，《師》統眾之義也。統眾者，非德也則不可。故以《乾》之九二入於《坤》為《師》，以《乾》德在二也。律因子起，數自中出。黃鍾之律，起為度量衡，差之毫釐，則不可也。北方之坎，黃鍾之本也，故縣言丈人，爻言律。丈與律，法度之出，非有德者乎？

The hexagram Kūn is symbolized by the multitude, and the hexagram Shī is also symbolized by the multitude, because Shī signifies the leadership of a multitude. To lead a multitude, one must possess virtue. Therefore, placing the line nine in the second position from the hexagram Qián into Kūn forms the hexagram Shī, which takes the virtue of Qián at the second line. The system of pitch-pipes begins from the position Zi, and numbers originate from the center. Huangzhong is the starting point of the measures of length, capacity, and weight; even the slightest deviation is not acceptable. The northern Kan is the fundamental of Huangzhong, so the hexagram Shī's zhuang statement mentions "zhǎngrén" and its line statement mentions "lǜ". "Zhǎngrén" and "lǜ" are both sources of legal measures, so is it not appropriate that only a virtuous person can be worthy of such a position? The original text's "xiàn" is a mistaken character for "zhuāng".

北主幽陰殺伐之象，南主嚮明朝會之象。六爻分二、三、四、五之數。二居南方，離明之地也，故以比為南面。五居中央，非北也。天北望，惟見斗樞、辰極。辰曰北辰，斗曰北斗，雖名曰北，實中天也。《師》北向，故有五人為伍之意。比南面，故有五等分爵之象。上居五位，後其君者也，故曰：後夫凶。

The north is associated with darkness, coldness, and military campaigns, while the south is associated with brightness and governance, as well as the assembly of feudal lords. Among the six lines, there are positions numbered two, three, four, and five. Position two is in the south, which is the place where the bright fire trigram resides, so the hexagram "Comparison" takes the image of facing south. Position five is in the center and is not in the north. When a person looks northward on the ground, they can only see the pole star and the Big Dipper; the pole star is called "North Star," and the Big Dipper is called "Northern Dipper," although they are named north, they are actually at the center of the sky. The hexagram "Army" faces north, hence the meaning of five people forming a unit. The hexagram "Comparison" faces south, hence the image of five ranks of feudal lords: duke, marquis, viscount, count, and baron. The sixth line is after position five, located behind the ruler, so the hexagram statement says "the one who comes after is凶 (unfavorable)."

巽居東南之方，乾氣自子至於巳，入於巽方，為巽所畜，名曰《小畜》，以陰生於巽。巽，陰之微也，故曰小。艮居束北方，乾氣自子至寅，入於艮方，為艮所畜；名曰《大畜》者，陽終於艮。艮，陽之究也，故曰大。自子至寅，三畫之乾也；自子至巳，六畫之《乾》也，是艮畜《乾》貞，巽畜《乾》悔也。《大畜》之所以得權者，變《小畜》之九五而六五耳，謙虛下人，所以得權而畜人也。《小畜》之所以失權者，變《大畜》之六五而九五耳，滿假自大，所以失權而為人所畜也。

The trigram Xun is located in the Southeast direction. The energy of Qian starts from the Zi position and moves through the Si position, entering Xun, where it is restrained. This is called "Xiao Xu" (Small Accumulation). Since Yin energy originates from Xun, which is where Yin energy first begins to emerge, it is called "small." The trigram Gen is located in the Northeast direction. The energy of Qian starts from the Zi position and moves through the Yin position, entering Gen, where it is restrained. This is called "Da Xu" (Great Accumulation). Since Yang energy ends at Gen, which is where Yang energy reaches its ultimate point, it is called "great." From Zi to Yin, it is only the three lines of Qian; from Zi to Si, it is the six lines of Qian. Thus, Gen restrains the inner trigram (Zhen) of Qian, while Xun restrains the outer trigram (Hui) of Qian. "Da Xu" is able to take authority because it replaces the Nine in the Fifth of "Xiao Xu" with the Six in the Fifth—being humble and willing to be below others, thus gaining authority and being able to restrain others. "Xiao Xu" loses authority because it replaces the Six in the Fifth of "Da Xu" with the Nine in the Fifth—being self-satisfied and arrogant, thus losing authority and being restrained by others.

乾居亥位，初爻本室、壁，二爻方起奎；奎擊之者，見其履虎尾也。坤居申位，參本坤之初爻；以參繫兌者，見虎尾之啞人也。乾居兌下，則無履虎啞與不啞之象矣。以乾乘兌，所以履虎之象明也。《履》卦自兌入乾，由戌達亥，以人應天之道乎。

Heavenly Stem乾 is located at the亥 position, with the first line originally belonging to Encampment mansion and Wall mansion, and the second line beginning at Legs mansion; since Legs mansion has the meaning of striking, it shows the image of 'treading on a tiger's tail'. Earthly Stem坤 is located at the申 position, with参宿 originally belonging to the first line of坤; by associating参宿 with兑, the image of a tiger's tail biting appears. If乾 were below兑, there would be no image of treading on a tiger's tail, nor would there be an image of biting or not biting; precisely because乾 is above兑, the image of 'treading on a tiger' becomes clear. The卦《履》 moves from兑 to乾, passing from the戌 position to the亥 position, which is probably the meaning of aligning human affairs with the heavenly way. The original text's '哑' is a corrupted form of '咥'.

觀《泰》之象，則見《否》之所生；觀《否》之象，則見《泰》之所起，是陰陽之氣上下升降以成象也，故《否》、《泰》之卦，皆曰往來。

Observing the image of the Qie hexagram reveals where the Po hexagram originates; observing the image of the Po hexagram reveals where the Qie hexagram arises. This is the image formed by the interaction of yin and yang energies rising and falling, ascending and descending. Therefore, both the Qie and Po hexagrams mention "going" and "coming" in their interpretations.

乾居上三十六策，變其中爻，則同乎離。離居下二十四策，變其中爻，則同乎乾。是謂二人同心，言外貌不同，而心同也。

Heaven is above, with an old yang line that represents thirty-six strategies. By changing its middle line, it becomes the same as Fire. Fire is below, with an old yin line that represents twenty-four strategies. By changing its middle line, it becomes the same as Heaven. This is called the Great Treatise saying, "Two people with the same heart"—meaning that although their appearances are different, their hearts are the same.

《大有》之卦眾陽盛時，而五以六居之，人君體元以居正，可不知守位之仁乎？推而明之，四為侍從，則曰匪其旁；三為三公，則曰公用亨于天子；二為侯牧，則曰大車辦載；初遠於君位，有要荒蠻夷之象，則曰無交害。皆發政施仁之道也。如是，則福及宗廟，而永有萬世之業矣。

The hexagram Da You comes at a time when many yang forces are flourishing, yet the fifth line holds a yin and flexible six in the position of the ruler. How can the sovereign, who understands the principle of Qian and occupies the correct position, fail to recognize the virtue of upholding his position with benevolence? Extending this idea: the fourth line represents a servant official, so the line statement says "Fmi qi Peng"; the third line represents the three ministers, so the line statement says "Gong yong heng yu tianzi"; the second line represents the feudal lords and governors, so the line statement says "Da che yi zai"; the first line is farthest from the ruler's position, symbolizing the distant territories, the vassals, and the barbarians, so the line statement says "Wu jiao hai". These all illustrate the principles of issuing decrees and practicing benevolent governance. If this is done, the blessings will reach the ancestral temples, and the great foundation of a thousand generations can be preserved. The original text mistakenly writes "Fmi qi pang" instead of "Fmi qi Peng", and "Ban zai" instead of "Yi zai".

艮居寅，屬木，仁也。坤居申，屬金，義也。故五上有殺伐之象。謙者，以至誠為本也，言心聲也。不情之言，則不出於誠，非心之本也，是為偽也。故嗚謙居中者為至誠，居外者為不情，是以謙為嗚耳，外謙而內好勝也。

The trigram Gen (Mountain) is located at the position of Yin, which belongs to wood and represents benevolence. The trigram Kun (Earth) is located at the position of Shen, which belongs to metal and represents righteousness. Therefore, the lines Six in the Fifth and Six at the Top in the hexagram Qian (Humble) carry the image of killing and warfare. The virtue of humility is based on utmost sincerity. Words are the voice of the heart; false words do not come from sincerity, nor do they originate from the true heart, but are instead hypocrisy. Therefore, "humane humility" resides in the inner trigram as utmost sincerity, but in the outer trigram it is insincerity—this is merely using humility as a verbal expression, appearing humble on the outside while being competitive within. The original text uses "wu" which is the same as "ming."

震居坤下，是謂一陽之《復》，天地之心也。今出於坤上，是謂出地之《豫》，亦天地之心也。坤中之爻，靜中之靜也，故曰：介于石。震中之爻，動中之靜也，故曰：貞疾，恆不死。

The Trigram Zhen is below the Trigram Kun, which forms the hexagram Fu, meaning "Returning," also referred to as the "Heart of Heaven and Earth" as mentioned in the Commentary on the Judgment. Now, when Zhen is above Kun, it forms the hexagram Yu, meaning "Joy," which is also the "Heart of Heaven and Earth." The central line of Kun is a stillness within stillness, so the Line Statement of line six in the second position says "Between the stones." The central line of Zhen is stillness within movement, so the Line Statement of line six in the fifth position says "Remaining steadfast in illness, yet never dying."

自震達兌，由東祖西，春作秋成之義也。夫是之謂《隨》，陽自陰中而起，陰隨陽動也。陰來迎陽而說之，陽隨陰聚也。故兌之上爻，有羈摩之象。

From Zhen to Dui, moving from the east to the west, it embodies the meaning of spring coming to life and autumn achieving maturity, which is called "Following." Yang arises from Yin, and Yin follows Yang; Yin also comes to meet Yang and delights in it, so Yang follows Yin to gather. Therefore, the top line of Dui carries the image of restraint and binding. The original text "zu xi" refers to "cu xi," meaning going west.

巽居巳位，金之所生也。至酉金王，而巽之功成矣，故巽五爻言庚。今在艮下，猶居寅位木之鄉也，故言甲。甲庚分子午之位，循環無窮，行權之道也。金克於木，今居於木下，是蠹生於木中也。有蠱，自然之象。上九居山之高，有高上之志，足以振蠱壞之風使懦夫有立焉。

The trigram Xun is located at the position of Si, which is where metal is generated; when it reaches the position of You, the metal energy is at its peak, and thus the function of Xun is fulfilled, so the line statement of the hexagram Xun at the fifth line mentions "Geng." Now, Xun is below Gen and still in the position of Yin, which is the territory of wood, so the statement of the hexagram Gu mentions "Jia." Jia and Geng live apart at the positions of Zi and Wu respectively, continuing in a cycle, which is precisely the principle of flexible adaptation. Metal usually overcomes wood, but now it is located below wood, like a worm living inside the wood, resulting in the phenomenon of "Gu," which symbolizes decay and corruption. The top line, located at the highest point of the mountain, represents a lofty aspiration, sufficient to revive the corrupted atmosphere, enabling the weak to become self-reliant.

《臨》卦之象，本指為人主者，以臨乎下也。臨下之術，在施德於下，而存心於上。施德於下，則二陽在下，如天氣感地焉。存心於上，則行中以智，而敦樸為先，如高明柔克焉。彼兌口之甘，是區區能言而不能行，如王者空降詔諭丁寧，而仁澤實不行也。何足以論施德存心之道哉？

The imagery of the hexagram "Approach" refers to a ruler standing high and looking down upon the people. To approach effectively, one should extend benevolence to the people below and maintain one's mind above. Extending benevolence to the people below is represented by two yang lines at the lower position, like the heavens responding to the earth. Maintaining one's mind above means acting with moderation and employing wisdom, prioritizing sincerity and simplicity, as mentioned in the "Book of Documents · Hongfan" as "high and noble yet gentle in overcoming." As for the image of sweetness taken from the trigram Dui (Joy), it is merely a superficial ability to speak well without actual practice, like a king issuing empty decrees and giving earnest instructions, yet actually not implementing benevolence. How can this be considered true benevolence and sincerity?

四陰生，陰侵陽之卦也。比之於陽侵陰，乃《大壯》之理也。不曰《小壯》，而曰《觀》者，陰順巽而無侵陽之意也。下既順巽，上必以中正，然後足以使下觀而化焉；下觀而化矣，則安有侵陽之事乎？

The "Guan" hexagram has four yin lines growing, which represents a situation where yin is pressing upon yang. Comparing this to the situation where yang invades yin, it corresponds to the meaning of the "Da Zhuang" hexagram. However, it is not called "Xiao Zhuang" but "Guan," because yin is gentle, compliant, and humble, and there is no intention of invading yang. Since the lower part is gentle, compliant, and humble, the upper part must maintain uprightness and correctness, so that the people below may look up and be influenced; once the people below have looked up and been influenced, how could there be any invasion of yang?

《噬嗑》本以口為象，而趾、鼻、耳、目亦繫之者，蓋一身賴口以為養也。養之有道，噬嗑之福；養不以道，噬嗑之禍。禍多福少，小人貪嗜者多也。《噬嗑》，先電而後雷也，電揚而雷震，舌動而齒咀，此自然之理也。《噬嗑》與《賁》，皆《頤》中有物。一為《賁》，一為《噬嗑》者，噬嗑得《頤》之下動，《賁》得《頤》之上止。惟下動，則《噬嗑》矣。

The hexagram Shìkè originally takes the mouth as its image, but the line statements associate even toes, nose, ears, and eyes with it, because the whole body depends on the mouth for sustenance. Sustaining in accordance with the Dao brings the blessings of Shìkè; sustaining in violation of the Dao brings the calamities of Shìkè. Calamities are more frequent than blessings, because small people are mostly greedy for delicious food. Shìkè is like lightning coming before thunder, with the electric light preceding the thunderous sound, just as the tongue moves first and the teeth follow in chewing, which is a natural principle. The hexagrams Shìkè and Bēn both contain something within the mouth of Yí. One becomes Bēn and the other becomes Shìkè, because Shìkè takes the lower trigram of Yí in motion, while Bēn takes the upper trigram of Yí in stillness; only when the lower trigram moves does Shìkè come into being.

柔文剛以成離，離為日，日運於天，其亨之意也。剛文柔以成艮，艮，山也；山不動，而云出為雨，木伐以為用，其小利有攸往乎。然孔子皆謂之天文，而不及地者，蓋觀象以作《象》也，象有日月迦明之象也。日月因迦明而合朔，朔晦相循而四時成矣，此所以察時變也。《離》有繼明之意，而《賁》變《離》之四爻，日月相抱持也，此所以為天文之要道焉。

Heavenly Stems: Jia, Yi, Bing, Ding, Wu, Ji, Geng, Xin, Ren, Gui Earthly Branches: 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) Glossary: Hexagram Statement = Gua Ci Commentary on the Judgment = Tuan Zhuan Fourth Line = Si Yao Confucius = Kongzi The soft comes to adorn the strong and becomes Li, which represents the sun. The sun moves across the sky, which is the meaning of the Hexagram Statement "Prosperous." The strong ascends to adorn the soft and becomes Gen, which represents the mountain. The mountain remains still yet can produce clouds and rain, and its timber can be cut and used, which is the meaning of "Minor advantage in going somewhere." However, Kongzi in the Tuan Zhuan refers to it as "celestial phenomena" without mentioning the earth, because he observed the hexagram images to compose the Tuan. The hexagram image contains the image of the sun and moon alternately shining. The sun and moon meet on the new moon day due to their alternating illumination, and the new moon and the dark moon alternate, thus forming the four seasons. Therefore, it is said to "observe the changes of time." The hexagram Li has the meaning of continuous illumination, while the hexagram Bie is derived by changing the fourth line of Li. The sun and moon embrace each other, which is the reason it becomes the essential principle of celestial phenomena. The original term "Jaming" is actually "Dieling."

《復》卦之下陽，即《剝》之上陽落於地也，故有碩果不實之象。其陽氣之種乎，所以《乾》為木果，而生木於亥也。亥者，《乾》之位也。木有生而未芽，芽則生子者，孳也。未芽之果，本於《剝》上之陽，如果在木末焉。

The yang line at the bottom of the hexagram "Fu" is the same yang line at the top of the hexagram "Bo" that has fallen into the earth, hence the image of "a large fruit not being eaten" in the line "Shang Ji" of "Bo." This yang line is probably the seed of yang energy, so the "Shuo Gua" says "Qian" represents fruit trees, and trees grow in the亥 position, which is the direction of "Qian." Fruits have a stage where they are already formed but not yet sprouted; once they sprout, they bear fruit. The sprout refers to the process of growth. The fruit that has not yet sprouted originates from the yang line at "Shang Ji" of "Bo," like a fruit still hanging on the branch.

爻位者，實數之六也。太極者，虛數之六也。虛數之六，本於含三之積算。含三之積籌，本於園物之徑一。故天下之數十、百、千、萬，莫不出乎六。六數進則為七，退則為五，是五為六之未盈，六為五之已滿，過則為七矣。六為極矣。

The concept of yao positions refers to the actual number six, while the concept of the Taiji (Supreme Ultimate) refers to the hypothetical number six. The hypothetical number six originates from the cumulative calculation of 'one containing three'; this cumulative calculation itself originates from the fact that the diameter of a circular object is one and its circumference is three. Therefore, all numbers such as ten, hundred, thousand, and ten thousand in the world arise from the number six. When the number six advances, it becomes seven; when it retreats, it becomes five. This shows that five is six that has not yet been completed, and six is five that has already been completed, and moving forward from six becomes seven. Thus, six is the extreme number.

一陽生，則七日來復也；二陽生，則八月有凶也。七為少陽，八為少陰。日為震，月為兌。《臨》雖陽長，而實得八兌之數也，故日有凶於八月也。《復》卦一陽來復，曰七日者，蓋《坤》陰極於亥，六數盡於一，復出於坎，並而得七也。數周六甲，運周三統，而復為元，亦七日來復之義云耳。

At the beginning of the first yang, it is said "seven days of return"; when two yangs grow, it is said "danger in the eighth month." Seven is the number of the minor yang, and eight is the number of the minor yin; the day belongs to Zhen, and the month belongs to Dui. Although the hexagram "Qing" (Approaching) represents yang growing, it actually receives the number eight from Dui, so it is said that danger occurs in the eighth month. The hexagram "Fu" (Return) is called "seven days" because the yin energy of K'un reaches the亥 position and reaches its extreme, the number six is used up on the one, and yang re-emerges from Kan. Six plus one makes seven. The numbers cycle through the sixty Jiazi, the energies cycle through the three principles of heaven, earth, and humanity, and then return to form a new beginning, which still refers to the meaning of "seven days of return."

《中孚》，信也。而《元妄》，亦信也。《中孚》之信，其自然之誠乎。《元妄》之信，是或使之也。故曰：剛自外來，而為主於內。誠信之道，本自中出。而中者，亦中之為主也。自外來，而為內主，安得自然哉？以異乎《中孚》也。

The *Zhongfu* hexagram discusses "trust," and the *Wuwang* hexagram also discusses "trust." The trust in *Zhongfu* is probably a natural sincerity; the trust in *Wuwang*, however, is something that causes it to be so. Therefore, the *Tuanchuan* says, "The strong comes from outside, and becomes the master within." The way of sincerity should originate from within; the term "zhong" (center) means to take the center as the main principle. Now, it is something coming from outside that has become the master within, how can this be considered natural? This is the difference between *Zhongfu* and *Wuwang*. The original text "yuan wang" (originally "wu wang") is a change made in the *Daozang* edition.

《頤》中虛，虛則靈龜之象。君子見之，以靈龜自警。小人見之，以朵頤垂涎。三為下齒，噬之動者也，故凶甚於二、五。三之所以動者，因初有震象耳。

The颐 hexagram has a hollow center, and the emptiness resembles the image of a spiritual turtle. The superior person sees it and uses the spiritual turtle to warn himself; the inferior person sees it and only opens his mouth with greed. The sixth line three is the lower tooth, which moves most vigorously when gnawing, so its danger exceeds that of the sixth line two and the sixth line five. The sixth line three moves because the first line nine carries the image of movement.

《大過》一卦，吉凶在初與上也。棟之隆，以應藉地之茅，慎之至也；棟之橈，以應滅木之水，乃大過也，故《大過》之縣辭見於九三也。陽氣驕為大者過。九二配以少陰，故能發生枯楊之梯者，揚之茅擠耳。九五配以老陰，發生之理窮矣。遂有枯楊生華象，象楊不能結實，為萌芽也。

The hexagram "Great Excess" has good or bad fortune determined by the first line and the top line. When the main beam rises high, it corresponds to the first line "using white reed grass," which indicates extreme caution. When the main beam bends downward, it corresponds to the top line "exceeding the head in crossing a river," which is truly "great excess." Therefore, the meaning of the "Great Excess" hexagram is reflected in the third line. Excessive yang energy is called "great excess." The second line pairs with the initially weak yin line, so it can make a withered poplar tree sprout new branches, but this is merely the tender shoots of the poplar tree. The fifth line pairs with the fully developed yin line at the top, and the principle of growth has reached its limit, so there is only the image of a withered poplar tree blooming flowers—flowers appear, but the poplar tree does not bear fruit or sprout new buds. The original text "tai" should be "tiri," and "xuan" should be "tuan."

《坎》之《象》曰：維心亨。是心無善惡之思，無喜怒哀樂之動。一入於習，則同者變為異也，故《坎》卦始終象小人習險以自陷其身，戒人用心之惡也。且陰陽者，善惡之端也，動靜之分也。心之動，則惡萌矣。陽動而陰靜，陽善而陰惡，六三以陰居陽，所以為惡之大也；又陷於二陰之中，是染習皆惡也。

The Commentary on the Judgment of the Kan hexagram says, "The mind is harmonious." This means that the mind originally has no good or evil thoughts, nor does it experience fluctuations of joy, anger, sorrow, or joy. Once it falls into the habit of practice, what was originally the same becomes different. Therefore, the Kan hexagram throughout symbolizes small people who are accustomed to danger and thus entrap themselves. Its intention is to warn people not to use their minds for evil. Moreover, yin and yang are the beginnings of good and evil, and the boundaries between movement and stillness. When the mind moves, evil arises. Yang belongs to movement and is associated with good, while yin belongs to stillness and is associated with evil. The sixth line in the third position, which is a yin line occupying a yang position, is the greatest of evils, and it is also trapped between two yin lines, indicating that it is entirely influenced by evil.

六四以陰居陰，靜之至也，是復性而反誠也，又居於二陽之問，是染習皆善也。故樽酒、篡貳用缶，有簡率敦樸之象。二五雖以陽中，然未免陷二陰之黨，染習之氣不能免也。孔子所以指之以未出中，中未大之象也。

Six four has a yin line in a yin position, which is extremely still, indicating a return to its true nature and a return to sincerity. It is also located between two yang lines, showing that it has been influenced entirely by goodness. Therefore, the line statement of six four mentions 'a cup of wine, two bowls, and a jar,' reflecting an image of simplicity, sincerity, and modesty. Although nine two and nine five have yang strength in the center, they are inevitably surrounded by two yin lines, and cannot completely avoid being influenced. Therefore, Confucius points out in the 'Small Image' that they 'have not yet emerged from the center' and 'the center is not yet great.'

下卦《離》之貞也，上卦《離》之悔也，是下卦為貞明，而上卦為繼明也。月者，趨日以明也。合朔之時，月包於日，而後趨其明也。此上卦所以包下卦，有日月趨明之象也。離為日而不為月，在重離則月象生焉。故曰明兩也；又曰日月麗乎天也。六二黃離，是自中而明也，所謂誠明之性也。六五有哀悲之象者，是既望之月，而將遠於日也，亦明極而晦生也。

The lower trigram is the inner trigram of 《Li》, called "Zhen"; the upper trigram is the outer trigram of 《Li》, called "Hui"; thus the lower trigram represents the inherent brightness, and the upper trigram represents the continuing brightness. The moon attains brightness by approaching the sun; when the moon is new, it is enclosed by the sun, and then it draws its light from it. This is why the upper trigram encompasses the lower trigram, symbolizing the mutual approach of sun and moon for brightness. Although 《Li》 originally represents the sun and not the moon, within the double 《Li》, the image of the moon emerges. Therefore, the 《Commentary on the Judgment》 says "two lights shining" and also "the sun and moon shining upon the heavens." The line 《Six in the Second》 "Yellow 《Li》" emits brightness from the middle path, which is the nature of sincerity leading to clarity. The line 《Six in the Fifth》 carries the image of sorrow, representing the moon after the full moon, which is gradually moving away from the sun, precisely the moment when brightness reaches its peak and darkness begins to appear.

一氣居中，故澤之雲蒸于山，而山之泉入於澤，是山澤之相感也。卦有三陽，而九四居中，中心象也。惜乎朋於二陽，未免有意有必，有固有我，故僮憧而往來也。九五上連於上六，是用在上六也，故上六為頰、舌，而五為脾。九三下連於六二，是用在六二也，故六二為腓，而三為股。股隨腓而動，脾則不隨頰、舌以發言，此吉凶所以異也。

A single force flows through the center, so the clouds above the marsh rise up to the mountains, and the spring water from the mountains flows back into the marsh. This is the mutual response between the mountain and the marsh. The hexagram Xian has three yang lines, and the line nine in the fourth position is in the center, which represents the "center." Unfortunately, it forms a clique with the other two yang lines, inevitably leading to four kinds of private intentions: intention, necessity, firmness, and self. Therefore, the line statement says "tongtong coming and going." The line nine in the fifth position connects upward with the line six at the top, and its effect falls upon the line six at the top, so the line six at the top is taken as the cheek and tongue, and the line nine in the fifth position is taken as the flesh on the back. The line nine in the third position connects downward with the line six in the second, and its effect falls upon the line six in the second, so the line six in the second is taken as the calf muscle, and the line nine in the third position is taken as the thigh. The thigh follows the movement of the calf muscle, but the flesh on the back does not follow the cheek and tongue to speak. Therefore, their fortune and misfortune differ. The original text mistakenly uses "pi" instead of "mei," and "tongtong" is actually "chongchong."

六爻惟取九二一爻，得一剛一柔之道而居中，孔子與之以能久中之象。六五雖一剛一柔而居中，然與共天位者亦柔也，故有婦人之貞從一之象，所以異於二矣。九三以剛居剛，動而過中，不恆之象，固不符言也。初、上爻二爻，一浚以趣下，一振而向上，皆迷塗之甚者，不得其中，故皆凶。

In the hexagram of "Constancy," only the second line, nine two, is selected because it combines both a strong and a gentle quality and is positioned in the center. Therefore, Confucius in the "Small Image" gives it the image of "being able to maintain constancy in the center." Although the fifth line, six five, also combines a strong and a gentle quality and is in the center, it shares the heavenly position with a gentle line, thus carrying the image of a woman maintaining purity and remaining faithful to one person, which is different from nine two. The third line, nine three, is a strong yang line in a strong position; once it moves, it exceeds the center, thus embodying the image of "not being constant," which naturally needs no further explanation. The first line and the top line, six initial and six above, each move excessively downward and upward respectively, both straying too far and failing to reach the center, hence both are ominous.

二以中順之德，而取象於黃牛。牛之所以能負重者，革之堅也。牛無革，則機上肉耳，何能為或？九三以剛居外，有革之象，三苟隨《乾》以遯，則二遇禍矣。此所以勸其執之也。

Six Two, relying on the virtue of being in the center and yielding, takes the image of a yellow ox. An ox is able to carry heavy loads because of the toughness of its hide; if the ox had no hide, it would be nothing more than meat on a chopping board, and would be of no use. Nine Three, with its yang strength in an external position, takes the image of 'change' ('ge'). If Nine Three follows the hidden retreat of the Upper Trigram Qian, then Six Two will suffer misfortune. This is why the Line Statement of Six Two advises one to fasten it securely with the hide of the yellow ox.

四陰以九居之，下應於初六，故曰好。好者，交好也，是陰位下交於陰爻也。五陽以九居之，下應於六二，故曰嘉。嘉妃也，是陽位之陽爻下妃於陰位之陰爻也。陰妃於我，交於我；小人不可交，則與之絕，此所以吉矣。妃則吾正偶耳，是不能絕也，故但正其志焉。吾之志正，則淫邪非僻不能入矣。此所以為貞吉雲。

The fourth position is originally a yin position, but it is occupied by a yang line, which corresponds downward with the initial line, so the line statement says, "Good retreat." "Good" means to be friendly, indicating that a yang line residing in a yin position interacts downward with a yin line. The fifth position is originally a yang position, occupied by a yang line, which corresponds downward with the second line, so the line statement says, "Blessed retreat." "Blessed" refers to marriage, meaning a yang line in a yang position interacts downward with a yin line in a yin position. When a yin line comes to associate with me, to marry me, or to interact with me, small people are not to be associated with, so we should cut off such connections, which is auspicious. However, the one who is to be married to me is my proper spouse, and I cannot cut off this connection, so I only need to maintain the right mindset. When my mindset is upright, corrupt and perverse influences cannot enter, which is the meaning of "upright auspiciousness."

《大壯》之卦，下累四陽，有棟宇基北之象，故云壯也。其卦上震下乾，震為蒼食竹，故有藩象。《乾》之九三變則入兌，故有羊象。兌西而震束，卯酉正沖，故有羊觸藩之象。初者，羊之足趾也。羊以角觸，而趾用其力；角贏，則趾困矣。九四實吾之同類，苟決其藩以開大塗，容羊進而贏之，則下三陽反為壯輿之轅矣。此九二、九四所以有貞吉之縣矣。

The hexagram "Da Zhuang" has four accumulating yang lines below, symbolizing the beams of a house and its foundation, hence the name "Zhuang" (strength). This hexagram consists of Zhen above and Qian below. Zhen represents young bamboo, hence the image of a fence; the third line of Qian changes to Dui, hence the image of a sheep. Dui is in the west and Zhen in the east, with卯 and酉 directly opposing each other, hence the image of a ram colliding with a fence. The first line represents the ram's toe; the ram uses its horn to push, but the effort comes from the toe. If the horn is caught, the toe is also trapped. The fourth line is actually of the same kind as the ram. If it were to break the fence and open a path, allowing the ram to advance without being caught, then the three lower yang lines would become the yoke of a cart carrying the ram forward. This is why the lines nine two and nine four have the judgment "Zhen Ji" (upright and auspicious). The original text "Cang shi zhu" refers to "Cang lang zhu" (young bamboo), and "xuan" is actually "tuan."

八卦之象，乾實為馬。《晉》以坤之貞，而陰爻居五位，豈有馬象哉，蓋乾錫之馬耳，因錫馬以致蕃庶，諸侯之象明矣。《易》以明出地上象諸侯者，以火在天上為《大有》，象天子故耳。天子與諸侯，皆南面之君也，必有明德以安民，民安則位安矣，故曰康侯也。

In the symbolic representations of the Eight Trigrams, Qian (Heaven) is indeed associated with a horse. The hexagram Jin (Progress) uses Kun (Earth) as its inner trigram, and the fifth line is a yao (line) of yin, so where is the image of a horse? It is the horse given by Qian; because having received the horse, there are many horses and carriages, thus the image of the feudal lords becomes evident. The Book of Changes uses "light emerging from the earth" to symbolize the feudal lords, because "fire in the sky" from the hexagram Dàyǒu (Great Possession) has already been used to symbolize the Son of Heaven. Both the Son of Heaven and the feudal lords are rulers facing south, and they must have bright virtue to govern the people. When the people are at peace, the ruler's position is secure, so the hexagram statement refers to him as "the healthy lord."

《明夷》之卦，聖人贊之，以《象》、《象》最顯最著，於人事最明。五為箕子，則上為紂矣。九三有南狩而得大首之辭，豈非武王乎？拯馬壯者，又豈非武王之輔相亂臣乎？六四本《坤》畫，而下與三同居人位，又豈非微子、太公之歸周乎？初九與上六同乎坎水，將飛而翼垂，將行而喂根不繼，豈欲拯之而力不能如伯夷、叔齊之徒乎？

The hexagram Mingyi is the one where the sage's commentary in the Commentary on the Judgment and the Image Commentary is most clear and explicit, corresponding most clearly to human affairs. The line six five is Ji Zi, and the line six at the top is Shang Zhou. The line nine three has the line statement "Southward hunting, capturing the great leader," which is not precisely King Wu of Zhou? The line six two "Using aid, the horse is strong," is not precisely the ministers who assisted King Wu, those who governed and brought order? The line six four originally belongs to the hexagram Kun, and it is placed downward in the same human position as nine three, which is not precisely Wei Zi and Jiang Taigong joining the Zhou dynasty? The line nine one and the line six at the top both belong to the hexagram Kan water, one about to rise with low wings, the other about to move forward but not eating for three days, unable to continue, is this not like those people such as Bo Yi and Shu Qi, who wanted to help but lacked the strength? The original text here "The Image, The Image" should be "The Commentary on the Judgment, The Image."

或問文中子《家人》之象，明內而齊外，蓋離、巽之卦也。象一然子象日在：陰一陽，相妃於中，有父母夫婦之，意本於夫子之《象》。焦延壽以上爻為宗廟，五為君；今用之於《家人》，則君位為父矣。孔子曰：家人有嚴君焉，父母之謂也。

Someone asked about Wang Tong (Wenzǐ), of the Sui dynasty, view on the imagery of the hexagram "Family." The hexagram "Family" is clear within and orderly without, which corresponds to the hexagram with lower trigram Li (Fire) and upper trigram Xun (Wind). Within the hexagram, one yin and one yang line are in harmony in the central position, thus expressing the meaning of parents and husband and wife. This meaning originally comes from Confucius' Commentary on the Judgment. (The original text has some errors and omissions, making the phrase "xiàng yī rán zǐ xiàng rì zài" difficult to read.) Jiao Yanshou of the Han dynasty took the top line as the ancestral temple and the fifth line as the ruler. Now applying this method to the hexagram "Family," the ruler's position becomes the father's position. Therefore, Confucius said, "The family has a strict ruler, who is the parents."

《睽》之為卦，六爻相疑者，陰陽相疑也。陽居陰位，是以位相疑。二應五而五連於上，上應三而三連於二，是以應相疑。疑則睽而不合矣。故聖人於六爻之辭，莫不解其疑也，而使陰陽各安其位焉。所以《睽》卦物象，比之他卦最盛，蓋欲盡意而已。

The hexagram Kui involves six lines that are all suspicious of each other, actually representing the mutual suspicion between yin and yang. A yang line occupying a yin position is the suspicion arising from the positions of the lines; the line six two should correspond to nine five, but nine five is connected to upper nine, and upper nine should correspond to six three, but six three is connected to nine two. This is the suspicion arising from the correspondences. Once suspicion arises, they become discordant and fail to unite. Therefore, the sage in the line statements of the six lines is constantly trying to resolve the suspicions so that yin and yang can each remain in their proper positions. This is why the hexagram Kui uses more symbolic images than any other hexagram, simply to fully express its meaning.

《蹇》之二陽，皆陷於陰中，故曰賽。《蹇》之象，往來者四，而不繫往來之象者二。四者皆失中，而二者皆得中也。聖人得中道以自養，故雖處蹇中，而素患難，行乎患難也。何往來之有，五在上位之中，是得中而居上者也；善處賽而不凌下，使人樂歸之，此所以致朋來，而不終孤立於險中矣。二在下位之中，是得中而居下者也。善處賽而不援上，匪其躬而自任其責，此所以致終無尤過，而獲應於上矣。

The hexagram "Jian" has two yang lines that are trapped among yin lines, hence the name "Jian," meaning difficulty in advancing, like a lame person. Among the six lines of the hexagram "Jian," four lines have the term "wanlai" (coming and going), while two do not. The four lines that have "wanlai" all lose the central position, and the two that do not have "wanlai" both hold the central position. The sage cultivates himself by following the middle path, so even though he is in a difficult situation, he remains content with hardship and continues to follow the right way, so where is there any need for coming and going? The line "Ji Wu" is in the upper trigram, holding the central position while occupying the upper position. It is good at dealing with difficulties without oppressing the lower lines, making people willing to follow, thus attracting friends and not remaining isolated in danger. The line "Li Er" is in the lower trigram, holding the central position while occupying the lower position. It is good at dealing with difficulties without clinging to the upper position, not thinking of itself but taking responsibility, thus ultimately having no mistakes and gaining the support from above. The original text "Sai" is the same as "Jian."

三陽之失中也，故勸之反身修德也。四陰之失中也，故勸其連接乎二陽也。初在下，故勉之以養其聲譽，而無苟往。上近五，故勖之以就於充實，而從大人，如四之連耳。

Nine in the Third has lost the central position, so it is advised to turn back and cultivate virtue. Six in the Fourth has lost the central position, so it is advised to connect with the yang line below. Six at the Beginning is at the very bottom, so it is encouraged to first cultivate its reputation and not act rashly. Six at the Top is close to Nine in the Fifth, so it is encouraged to move toward fulfillment and follow the great person, just as Six in the Fourth connects with the yang line.

坎中之一陽，即震下之一陽，始包於坎中，既而出於坎上，動而震下也，若果核之仁變而為芽也，故曰：得黃矢。矢者，中直也。中直，則芽達矣。《解》之為卦，陰陽悖亂而不當其位，上爻故有解悖之象，震之在坎也。君子屈墊於下，混邊於小人之時，而發生敷大易象數布之心不忘也。一曰一脫邊而去，遂伸其志，此九四之與六三所以有拇象。

The yang line in the middle of Kan becomes the yang line below Zhen: at first it was enclosed within Kan, but later it emerged from above Kan, and once it moved, it became Zhen. This is like the sprout within a fruit seed transforming into a shoot, so the line statement of nine in the second says "obtaining a yellow arrow." An arrow is something that is both central and straight; being central and straight allows the sprout to grow. The hexagram "Jie" has yin and yang in disorder and none in the proper position, so the line six at the top has the image of removing disorder, which is exactly the meaning of Zhen being above Kan. When a gentleman bends his body and remains hidden below, mingling with petty people, his mind of growth and spreading never ceases. Once he escapes, his aspirations are fulfilled, which is why nine in the fourth and six in the third have the image of "the thumb."

二卦之《象》，皆言與時偕行。二卦之爻，皆言十朋之龜。言時者，謂時當損而損，天下不以為儉嗇；當益而益，天下不以為驕奢也。言龜者，謂龜筮協從，臣民無逆也。

The Commentary on the Judgment of the hexagrams "Loss" and "Gain" both mention "moving in harmony with the times." The line statements of both hexagrams refer to "ten tortoises." Speaking of "time" means that when reduction is appropriate, one should reduce, and the people will not consider it stingy; when increase is appropriate, one should increase, and the people will not consider it extravagant. Speaking of "tortoises" means that divination by tortoise shells and by yarrow stalks both act in harmony, and ministers and common people do not act against them.

五陽而決一陰，五君子而去一小人，不為難矣。然陰附五位，五與四皆屬之，是謂兌卦。所謂包陽之陰，挾君子之小人，所以難決難去耳。《大壯》之羊，施壯於震。震，同類也。《夬》之羊，施壯於兌。兌，非類也，變我則與同。此四爻所以有牽羊之象，此三爻變有羊象耳。

Five yang lines remove one yin line, and five gentlemen remove a petty person; this is originally not difficult. However, this yin line is attached to the fifth position, and both nine five and nine four are involved, forming the trigram Dui. This is called a yin line that wraps around yang, and a petty person that holds back the gentlemen. Hence, it is difficult to decide and difficult to remove. The sheep in the hexagram Dazhuang places its strength on Zhen, which is of the same kind; the sheep in the hexagram Guai places its strength on Dui, which is not of the same kind, but after a change it becomes the same. This is why nine four has the image of "leading a sheep," and nine three, after a change, shows the image of a sheep.

初與本爻觀之，則有豕象，而九三突其臀。初、二、四觀之，則有魚象，言陽包陰也。於九五觀之，則有瓜葛滋長之象。《姤》本《乾》也，一陰變其初，有龍反化魚象，龍化魚而角無用矣。此《妮》之角所以上窮也。《乾》之一陽，起子而終於巳，巳實居巽方，是《乾》之六陽與巽相遇於巳位，而巽之一陰遂萌矣。此一陰之生，故名曰《姤》也。

Looking at the first line and the present line, there is an image of a pig, and the third line directly hits its hindquarters. Looking at the first, second, and fourth lines together, there is an image of fish, indicating yang enclosing yin. Looking at the fifth line, there is an image of vines and tendrils growing. The hexagram "Gou" originally comes from "Qian," but when the first line changes from yin to yang, there is an image of a dragon transforming into a fish. Once the dragon transforms into a fish, its horn becomes useless, which is why the top line says "Gou its horn" and it reaches the top position in a state of exhaustion. The yang of "Qian" begins at the Zi position and ends at the Si position. The Si position actually resides in the Xun direction, so the six yang lines of "Qian" meet the Xun at the Si position, and the yin of Xun then emerges. Because of the emergence of this yin, the hexagram is named "Gou," meaning "meeting." The original character "ni" is the same as "gou."

《萃》之成卦，則物各以類聚。而陽據南面之位，一為天子，一為諸侯，下統三公、二十七大夫、八十一元士，上奉宗廟之嚴，防眾亂之道，寄於初爻；懲失眾之象，寓於上畫。萃者，物之秋成而後萃也。秋本主於兌，兌卦本以上爻為主。今西南之坤氣，運至西方，而陰畫眾矣，故二陽統之，而上爻失眾焉。

Once the hexagram "Cui" is formed, all things gather according to their categories. Two yang lines occupy the southern positions, one representing the Son of Heaven and the other the feudal prince, governing below the three dukes, twenty-seven great officials, and eighty-one lesser officials, while above they guard the solemnity of the ancestral temple. The principle of preventing disorder among the people is embodied in the first line; the warning against losing the people's support is contained in the top line. The term "Cui" refers to the gathering of all things after they have matured in autumn. Autumn is originally governed by the hexagram Dui, which usually emphasizes the top line. Now, the yin energy from the southwest direction of the earth (Kun) has moved westward, increasing the yin lines, so two yang lines are needed to control the situation, and thus the top line loses the people's support.

巽下之一陰，與坤之三陰一體也。陰沉滯，而陽升騰。升騰者，二陽也。初附二陽而升，三陰又與之一體，故有允升之象。允者，見信於人。

The yin line below Xun is originally one body with the three yin lines of Kun. Yin nature tends to be heavy and sinks downward, while yang nature rises upward. The two yang lines above Xun are capable of rising. The initial line (Chu Liu) relies on these two yang lines to rise upward, and since the three yin lines of Kun are integrated with it, there is an image of "trustworthy ascent" ("Yun Sheng"). "Yun" means being trusted by others.

坤用事於亥，而亥亦木之生，而未成形者也。至於子位，則震居坤下，震亦木也，是木之始芽根耳。若巽居坤下，則有二陽，非震一陽之比，故曰《升》也。《升》居丑位，及乎卯，則木王矣。外卦以位言也，而五天位，是不可以階升也。然貞者，正也。堯、舜、禹、湯昇天位以正，如升階焉。不以貞者，寧免於顛躋乎。

The trigram坤 is in the position of亥, which is the time when wood first begins to grow but has not yet taken shape. When reaching the position of子, the trigram震 is below坤, and since震 also belongs to wood, it is merely the time when wood starts to sprout and take root. If the trigram巽 were below坤, it would have two yang lines, which is not comparable to震 with only one yang line. Therefore, the hexagram is called《升》. The hexagram《升》 is in the position of丑. When reaching the position of卯, wood is at its peak. The outer trigram refers to the position of the lines. The fifth line is the position of the Son of Heaven. The position of heaven is not something that can be reached by climbing steps. However, '贞' means 'correct' or 'righteous'. Yao, Shun, Yu, and Tang ascended to the heavenly position by following the righteous path, just as one ascends step by step. Those who do not follow the righteous path will inevitably fall and be injured.

#1『阻之』，原作『祖之』，據四庫本改。#2『復退』，原作『彼退』，據四庫本改。#3『三陽』，四庫本作『二陽』。#4斗利』，四庫本作『權』字。#5『非德也』，四庫本作『非德』。#6『居』，據上下文義例增補。#7『上下』，原作『上上』，據四庫本改。#8『為嗚耳，外謙』，底本原缺，據《道藏》本《周易圖》卷中及其上下文義補之。

The first item: the original text reads "zǔ zhī" but is corrected to "zǔ zhī" according to the Siku Quanshu edition. The second item: the original text reads "fù tuì" but is corrected to "bǐ tuì" according to the Siku Quanshu edition. The third item: "sān yáng" in the Siku Quanshu edition reads "èr yáng". The fourth item: the character "lì" is changed to "quán" according to the Siku Quanshu edition. The fifth item: "fēi dé yě" in the Siku Quanshu edition reads "fēi dé". The sixth item: the character "jū" is added according to the textual examples in the surrounding context. The seventh item: the original text reads "shàng xià" but is corrected to "shàng shàng" according to the Siku Quanshu edition. The eighth item: the words "wéi wū ěr, wài qiān" are missing in the original text but are added according to the middle section of the "Zhou Yi Tu" in the Daozang and the surrounding context.

#9『地』，底本和四庫本皆作『治』，據《道藏》本《周易圖》卷中及其上下文義改正。#10『猶』原作『尤』，據四庫本改。#11『子』，據四庫本補。#12『乎』，四庫本作『也』字，疑底本誤。#13『朵頤』，原作『孕頤』，據四庫本改。#14『梯』，底本和四庫本皆誤作『梯』。#15『脾』，原作『晦』，據四庫本改。#16『上爻』，四庫本略作『上』字，義同。

Article 9: The character "地" in both the original edition and the Siku Quanshu edition is "治," which is corrected to "治" according to the Zhouyi Tu in the Daozang and the context. Article 10: The character "犹" in the original edition was originally "尤," which is corrected according to the Siku Quanshu edition. Article 11: The character "子" is added according to the Siku Quanshu edition. Article 12: The character "乎" in the Siku Quanshu edition is "也," suggesting that the original edition may have an error. Article 13: The character "朵颐" in the original edition was originally "孕颐," which is corrected according to the Siku Quanshu edition. Article 14: The character "梯" in both the original edition and the Siku Quanshu edition is mistakenly written as "梯," and should be "稊." Article 15: The character "脾" in the original edition was originally "晦," which is corrected according to the Siku Quanshu edition. Article 16: The character "上爻" in the Siku Quanshu edition is abbreviated as "上," with the same meaning.

#17『趣下』，四庫本作一趨下』。#18『之』，據四庫本補。#19『基北』，四庫本作『基兆』，而據《道藏》本《周易圖》卷中疑當作『基址』。三稱何者為是，待考。#20『正沖』，原作『正衡』，四庫本亦是，據此句文義改正。《道藏》本《周易圖》卷中亦作『正沖』。#21『援上』，原作『授上』據四庫本改。#22『震下』，四庫本作一震上』。#23『矢』，原脫，今據其文義補之。#24『有拇象』，四庫本作『有解拇象一。

Article 17: "Quxia" is written as "Quxia" in the Siku Quanshu edition. Article 18: The character "Zhi" is added according to the Siku Quanshu edition. Article 19: "Jibei" is written as "Jizhao" in the Siku Quanshu edition, and according to the "Zaocang" edition of "Zhouyi Tu" in the middle volume, it is suspected to be "Jizhi"; which of the three readings is correct remains to be determined. Article 20: The original text reads "Zhengheng", and the Siku Quanshu edition also reads "Zhengheng". Now it is corrected according to the meaning of this sentence; the "Zaocang" edition of "Zhouyi Tu" in the middle volume also reads "Zhengchong". Article 21: The original text reads "Shoushang", which is corrected according to the Siku Quanshu edition. Article 22: "Zhensha" is written as "Zhenshang" in the Siku Quanshu edition. Article 23: The character "Shi" was originally missing in the text, and is now added according to the meaning of the text. Article 24: "Youmuxiang" is written as "Youjiamuxiang" in the Siku Quanshu edition.

#25『儉嗇』，原作『險嗇』，於義不妥；據四庫本改。#26『於震』，原作『子震』，據四庫本改。#27『壯』，據上文義例補之。#28『變我』，四庫本作『變坎』。#29『初二四』，四庫本作『初於四』。#30『據』，四庫本作『居』。#31『本以』，原作『未於』，據四庫本改。#32『三陰』，原作『三陽』，四庫本亦是。今據《周易圖》卷中。

Article 25: The original text read "xiansae" but this does not make sense; it is corrected according to the Siku Quanshu edition to "jianse". Article 26: The original text read "zi zhen" but it is corrected according to the Siku Quanshu edition to "yu zhen". Article 27: The character "zhuang" is added according to the textual example in the preceding text. Article 28: "bian wo" in the original text is "bian kan" according to the Siku Quanshu edition. Article 29: "chushisi" in the original text is "chuyusi" according to the Siku Quanshu edition. Article 30: The character "ju" in the original text is "ju" according to the Siku Quanshu edition. Article 31: The original text read "weiyu" but it is corrected according to the Siku Quanshu edition to "benyu". Article 32: The original text read "san yin" but it is also "san yang" in the Siku Quanshu edition; now it is corrected according to the middle volume of "Zhou Yi Tu" — the text of this article in the original edition is not yet complete here.

《困》之為卦，屬乎九月兌氣用事，而臨於戌土；澤水為土所壅，故《大象》曰：澤無水，困也。《困》因兌、坎相重而成也。兌正秋，而坎為冬。兌之一陰，象乎始得秋氣而蔓草未殺。故為葛萬之困。六三則秋冬之交，蔓草葉脫而刺存焉，故為漢藥之困。若初六則在坎之下，正大寒之時也，蔓草為霜殺而靡有孑遺，而所存者株木而已。此《困》三陰爻故繫以草木象也。

The hexagram "Kun" (Obstruction) belongs to the time when the Qi of Dui (Lake) is dominant in September, and it is right above the earth element Xu (Earth Dog). The water in the marsh is blocked by the earth, so the "Great Image" says, "A marsh without water, obstruction." The hexagram "Kun" is formed by stacking Dui on top of Kan: Dui corresponds to the beginning of autumn, and Kan belongs to winter. The upper yin line of Dui symbolizes the time when the autumn Qi has just begun and the weeds have not yet been killed by frost, hence the image of "Gelaizi" (a type of vine). The line six in the third position corresponds to the transition between autumn and winter, when the leaves of the weeds have fallen but their thorns remain, hence the image of "Jilizi" (a type of thorny plant). As for the line six at the beginning, it is at the very bottom of Kan, which is the time of great cold, when all the weeds have been killed by frost and nothing remains but the bare stumps of trees, hence the image of "Zhu Mu" (tree stumps). This is why the three yin lines of the hexagram "Kun" are associated with images of plants and trees. The original text "Ge Wan" refers to "Gelaizi," and "Han Yao" refers to "Jilizi."

《井》以陽為泉者，水因天一之陽而生也。坎中之陽出於坎方寒泉也，所謂北方生寒，寒生水之義也。故又日太陽寒水。巽之二陽，一在地位，而趣下是谷，而非井矣；一陽雖在人位，居梵之下，汲之不及，不若五爻浮溢於梵上也。井欲溢，而鼎戒盈，此德為器之辨也。《鼎》卦鉉、耳、趾皆全，而趾欠其一，所以初爻言鼎顛趾，言鼎倒而趾在上也。下一陰反有兩耳之象，五爻故曰黃耳，以別初焉。

The hexagram of Well uses a yang line to represent the spring, because water arises from the yang of heaven. The single yang line in the center of Kan represents the cold spring, which is the meaning of the "Su Wen" saying "the north produces cold, and cold produces water." Therefore, it is also called "sun yang cold water." The two yang lines of Xun, one located at the position of the earth and tending downward, represent a valley rather than a well; the other, although located at the position of humans, is situated beneath the well wall and cannot be drawn up, unlike the nine in the fifth line, which allows water to overflow above the well wall. A well is considered good when it can overflow, while a tripod should be cautious of being full, which is the difference between "de" and "qi." The hexagram of Tripod has all its parts, the handle, the ear, and the legs, but lacks one leg, so the first line says "the tripod overturns its foot," meaning the tripod is overturned with the foot facing upward. The yin line below has the image of two ears, so the line of six in the fifth says "yellow ears," distinguishing it from the first line. The original text "fan" should be "zhou," referring to the well wall.

《革》雖有鼎鬲革生為熟之象，然以爐輪之象為正，蓋以離火鼓鑄兌金，而金從革也。革而後鼎者，以鼓鑄而成鼎也。夏后氏鑄鼎，而湯、武因之，以寶其器，故有湯、武革命之象。

The Hexagram of Revolution, although it also refers to the image of using cauldrons and cooking vessels to transform raw materials into mature ones, is primarily interpreted as representing the image of a furnace and bellows. This is because it depicts the use of fire from the trigram Li (Fire) to blow and melt the metal from the trigram Dui (Lake), which corresponds exactly to the statement in the "Book of Documents · Hongfan" that "metal is called from revolution." The "Xugua" arranges the Hexagram of Cauldron after the Hexagram of Revolution because casting metal is necessary to make cauldrons. The Xia Dynasty cast nine cauldrons, which were continued by the Shang Tang and King Wu of Zhou, who regarded them as precious objects. Therefore, this hexagram also symbolizes the revolution of Shang Tang and King Wu of Zhou. The original term "lu lun" refers to "lu bei," meaning the leather bellows used for blowing air.

《震》之六爻，初勸之以有戒懼之心，而後言笑；二又戒之以喪貝而勿逐，是欲人內無妄動於一心，而外無貪其利也；三爻則言震蘇蘇，是欲人修慝而辨惑，無終入於迷塗也。皆動心之要也。外卦論動之邇，故四言遂泥，以表事之凝滯而不決；五言無喪，以表事之成；上言征凶，以表事之敗。

The hexagram Zhen has six lines. The first line advises people to first hold a cautious and respectful attitude before they can speak or laugh. The second line warns that even if one loses money or property, there is no need to chase after it, teaching people to keep their minds calm and not be greedy for external gains. The third line speaks of "Zhen Su Su," which means one should eliminate wrong thoughts and clarify doubts, so as not to eventually become lost. These are all key points about "moving the heart." The outer trigram discusses the traces left by movement: the fourth line mentions "Sui Ni," indicating that things become stagnant and cannot be decided. The fifth line says "Wu Sang," meaning that things are successfully accomplished. The sixth line states "Zheng Xiong," indicating that the matter ends in failure.

《艮》之象，言輔、頰不言口，言身不言腹，言夤、限不言臍，有背面而立之象，故曰艮其背也。統一卦而觀之，下不分其腓、趾，上不別其身、輔，四陰排布，宛有背骨之狀。上一陽為肩膊，中一陽而為脊膂也。脊膂，取其貫中而已。

The hexagram of "Mountain" (Gèn) describes the yao (lines) in terms of the cheek and jawbone but not the mouth, the body but not the abdomen, the back muscles and waist but not the navel. Everywhere it conveys the image of standing with one's back to others. Therefore, the hexagram statement says, "Gèn its back." When considering the entire hexagram, the lower part does not distinguish between the lower leg and toes, and the upper part does not differentiate between the body and the jawbone. The four yin lines arranged together resemble the shape of a spinal column: the top yang line represents the shoulders, and the middle yang line represents the spine. The image of the spine is taken only for its function of connecting through the center.

《艮》之九三，《艮》之主也，以陽居陽，其性躁動，譬之於腰焉，俯仰罄折，起居行止，莫不因之；然其運動，實繫於心也，故聖人繫之以熏心之象。六二以陰居陰，其性靜矣，有腓象；心欲動而腓不能舉行，其心安有快意乎？故聖人又繫之以其心不快之辭。

The ninth line in the third position is the main line of the entire hexagram. A yang line in a yang position indicates a restless nature. Using the body as an analogy, it is like the waist: whether bowing down, raising up, bending, or moving about, nothing can be done without it. However, its movement actually originates from the heart, so the sage gives it the image of 'dangerous and troubling the heart.' The sixth line in the second position is a yin line in a yin position, indicating a quiet nature, with the image of the calf muscle. If the mind wants to move but the calf muscle cannot lift, how can the heart be happy? Therefore, the sage also gives it the line statement 'its heart is not joyful.'

《漸》卦，下艮而上巽，時當正月立春之後，鴻漸來之候矣，故六爻皆係以鴻也。鴻者，隨陽之烏，而艮、巽限乎子、午之陽，方繫之以鴻，豈不宜哉？三居艮卦之上，上居巽卦之上，是南北二陸也。三以一陽限於群陰之闖，當鴻雁北來之際，烏獸將孳尾之時，故有夫征婦孕之象也。三與四，氣交於人位，故孕也。若五與二，一居於天，一處於地，遠應而雌雄有別，故不孕耳。

The "Gradual Progress" hexagram has the lower trigram艮 (Mountain) and the upper trigram巽 (Wind). This corresponds to the time of the beginning of spring in the first lunar month, when geese gradually begin to fly from the south. Therefore, all six lines are associated with the character "geese." Geese are birds that migrate with the yang energy, and the trigrams艮 and巽 are precisely located between the yang energies of the子 (Rat) and午 (Horse) positions. It is indeed appropriate to associate the image of geese with this hexagram. The line nine in the third position is at the top of the Mountain trigram, and the line nine at the top is at the top of the Wind trigram, representing the northern and southern landmasses. The line nine in the third position, with a single yang line among a group of yin lines, corresponds to the time when geese are flying north and animals are about to mate, hence the image of a husband going to war and a woman becoming pregnant. The lines nine in the third and six in the fourth interact in the human position, hence the possibility of pregnancy. However, the lines nine in the fifth and six in the second are located in the heavenly and earthly positions respectively, being far apart and thus not corresponding, with distinct male and female characteristics, hence no pregnancy. The original text uses "wu" for "bird" and "chuang" for "between."

震為蒼筧竹，下實而上虛，筐象也。《歸妹》之卦與《泰》相類，而人位二爻兩相交互，有掩袂之象。人之一身，左陽而右陰；陰陽之交，如兩袂之交也。娣，位乎下，其畫陽也；君，位乎上，其畫陰也。《易》以陽善而陰惡，陽貴而陰賤，此君之袂不如娣之袂矣。

The trigram Zhen is symbolized by young green bamboo, with the lower part solid and the upper part hollow, resembling a bamboo basket. The hexagram Guimei is similar in form to the hexagram Tai, but the two lines in the human position are interwoven, symbolizing the overlapping of sleeves. A person's body has the left side belonging to yang and the right side belonging to yin; the interweaving of yin and yang is like the overlapping of two sleeves. The position of the娣 (a younger sister accompanying in marriage) is at the lower position, which is yang; the position of the君 (the main wife) is at the upper position, which is yin. The Book of Changes considers yang as good and yin as evil, yang as noble and yin as lowly, so the line statement of the sixth line in the fifth position says that the sleeve of the main wife is not as good as that of the娣.

蓋以《歸妹》安行非正也。其卦乃遷東方之陽，以就西方之陰，是震氣入於兌，木為金之剋制也。故必月幾望而後吉。月望，則陰敵陽，有少陵長，賤易貴之變矣。所以《歸妹》之縣唯曰：征凶，無攸利。以行不以正者，非聖人之事也。

This is because the hexagram "Gui Mei" (Return of the Maiden) does not follow the correct path. This hexagram involves moving the yang from the east to accommodate the yin of the west, meaning the energy of Zhen (Thunder) enters Dui (Lake), and wood is restrained by metal. Therefore, it is favorable only when the moon is full but not yet complete. When the moon is fully round, yin and yang are equal, leading to disturbances such as the young oppressing the old and the low replacing the high. Hence, the "Tuan Ci" (Discourse) of "Gui Mei" only states "Traveling brings danger; there is no benefit." Acting without following the correct path is not what the sage would do. The original text "xuan" refers to "tuan."

伏羲畫震於束，而置離於南方者，表少陽之氣動於束方，太陽之明盛於南方也。文王以震重離，遂名日《豐》，言少陽之震運至於南方，合太陽之離明，而為豐盛耳。所以文王於《豐》縣，明盛極必衰之理，日宜日中；於《豐》爻，明明極必昏之理，日日中見斗與沬也。文王所繫卦爻之辭，唯日與斗也。

Fuxi placed Zhen in the east and Li in the south to indicate that the energy of the young yang begins to move in the east and the bright yang reaches its peak in the south. King Wen placed Zhen on top of Li, and named the hexagram "Feng," meaning that the young yang Zhen moves to the south and combines with the bright yang Li, thus achieving fullness and abundance. Therefore, in the "Tuan Ci" of "Feng," King Wen pointed out the principle that when something reaches its peak, it must decline, saying "It is appropriate at noon." In the "Yao Ci" of "Feng," he explained the principle that when brightness reaches its peak, darkness must follow, saying "The Big Dipper appears at noon" and "A mist appears at noon." The hexagram statements and line statements that King Wen attached to the hexagrams mention only the sun and the Big Dipper.

孔子之《象》，遂論及月，何哉？蓋《豐》卦在五、六月之交，日在柳宿之度，而斗指午、未之分。柳宿之度，實通三辰，故有見斗之理。

Then why does Confucius mention the moon in the Commentary on the Judgment? Because the time corresponding to the卦 of Fullness is around the intersection of the fifth and sixth months, when the sun reaches the degree of Willow Mansion, and the handle of the Big Dipper points between Wu and Wei. The degree of Willow Mansion actually connects the three celestial bodies: sun, moon, and stars, which is why the Big Dipper can be seen during the day.

六二以中道，遂懷資得童僕。九四以剛柔相濟而有應，遂得資斧。皆近利，不若六五也。離之所以明者，順以行其智也，故曰畜牝牛吉。上九之喪牛，是喪其明也。《旅》當《夫》之後，《乾》之前也，陽盛皆客氣，所以反日《旅》也。

The second line holds to the middle path, thus possessing wealth and gaining a servant; the fourth line, being flexible and strong, with mutual support, thus obtains tools. These two lines are both close to seeking profit, but they are not as good as the fifth line. The brightness of the hexagram Li comes from the use of its wisdom through flexibility and gentleness, so the hexagram statement of Li says 'keeping a female ox is auspicious'; the top line 'losing the ox' means losing this brightness. The hexagram Lü comes after Guai and before Qian, with strong yang energy but encountering only polite people wherever it goes, so it is called Lü, meaning to dwell as a guest. The original text 'fu' refers to 'Guai'.

《旅》之上九得勢而主權者，寄一身於炎炎之上，而不知有焚巢之禍。九三趨炎而躁進，而不知有焚次之災。六二、九四雖以柔道而旅，或懷資，或得斧，獲利於時，而二必以身而後兔過，四之心尤不快也。豈非戒旅以求利之事乎？若六五者，始以離雉有文明之美，而射之，而亡其矢，而不獲，是道不行而利不得也。

The upper nine of the Travel卦 holds power and is in a strong position, relying on the blazing fire at a high place, but does not realize the danger of burning its nest. The nine three follows the heat and rushes forward hastily, but does not realize the disaster of burning the lodging. The six two and the nine four, although they are in a foreign place with a gentle and compliant approach, either hide wealth or obtain tools, gaining some advantage temporarily. However, the six two must be careful in self-restraint to avoid mistakes, while the nine four is even more dissatisfied. Is this not a warning to travelers not to pursue profit alone? As for the six five, it initially admires the fire as a symbol of civilization and beauty, and goes to shoot it, but misses an arrow and fails to hit it—this indicates that the path is not feasible and no benefit is obtained. The original text 'rabbit passing' refers to 'avoiding mistakes'.

《巽》以陽為肺簣，而以陰為林足者，以肺下有足之象，四陽行列，有簣之象也。九二林之束壁，而上九將之西壁也，故皆云《巽》在林下，以林足附之也。九五為龍飛，而為虎變者也。飛龍為甲，虎變為庚，是以一氣之變更耳。上九喪斧，剛過也。九二用史、巫，剛中而未得位也。九三之頻蹙，又無位而失中也。由是觀之，則權以有位而得中者行矣。非九五，而誰乎？

The hexagram of Xun uses yang lines as the bed boards and reed mats, and yin lines as the bed legs, because beneath the bed boards there must be legs; four yang lines arranged side by side resemble a spread-out bamboo mat. The line Nine in the Second is at the eastern wall of the bed, and the line Nine at the Top is at the western wall, so both lines say "Xun is beneath the bed," referring to the bed legs from this perspective. The line Nine in the Fifth is both a flying dragon and a tiger transformation: the flying dragon corresponds to Jia, and the tiger transformation corresponds to Geng, but they are merely a change of the same qi. The line Nine at the Top "losing his tools and axe" indicates excessive yang; the line Nine in the Second inviting the historian and the shaman to pray shows yang that is strong but not in the correct position; the line Nine in the Third being repeatedly pressed is even more so, lacking both position and the center. Therefore, authority should be exercised by someone who is both in the correct position and in the center — besides the line Nine in the Fifth, who else could it be? The original text "Lin" refers to "bed," and "shu bi" refers to "eastern wall."

《坎》之初六，主於冬至。《離》之初九，主於夏至。《震》、《兌》之初，則主於春、秋之分也。故以《兌》之下二爻陽氣尤盛，為七月之象；中二爻陰陽中分，為八月之象；上二爻陰過於陽，為九月之象。此《兌》卦所以四爻為言商兌，以見《震》角、《離》徵、《坎》羽之音；五爻言孚剝，以見《震》、《央》、《離》、《娠》、《坎》、《復》之理也。

The first line of the hexagram Kan governs the winter solstice, while the first line of the hexagram Li governs the summer solstice. The first line of the hexagrams Zhen and Dui respectively govern the spring equinox and the autumn equinox. Therefore, the two lower lines of the hexagram Dui represent the time when yang energy is most vigorous, corresponding to the seventh month; the middle two lines represent the time when yin and yang are equal, corresponding to the eighth month; and the upper two lines represent the time when yin has already surpassed yang, corresponding to the ninth month. This is why the line nine in the fourth position of the hexagram Dui says "Shang Dui"—using the Shang tone to express the tone of Zhen (Jue), Li (Zheng), and Kan (Yu). The line nine in the fifth position of the hexagram Dui says "Fu Yu Bo," which is used to illustrate the mutual relationship between Zhen and Guai, Li and Gou, and Kan and Fu. The original text "yang" refers to "Guai," and "shan" refers to "Gou."

一陽生於子，而六陽亢於巳。子屬坎，而巳屬巽，以巽重坎，所以為《渙》也。渙者，散也。卦氣當夏至之後、大暑之前也，是陽氣散於外也。陽雖散於外，而有生生不窮者在其中，是坎中之一陽也。一元之氣，是坎中之一陽也。

One yin is born at the Zi position, and six yins reach their peak at the Si position. Zi belongs to Kan, and Si belongs to Xun; when Xun is superimposed over Kan, it forms the hexagram "Huan." "Huan" means dispersion. The qi of this hexagram corresponds to the period after the summer solstice and before the great heat, which is the time when yang qi is dispersing outward. Although yang is dispersing outward, there is something that continues to generate endlessly within, which is the single yang in Kan. This is called the original qi of the universe, which is precisely that single yang in Kan.

陽主氣，陰主形。一陽散於外，故言汗、血也。二陰分於中，故言群、躬也。躬分而為四支，群分而為五臟、六腑形也，是皆一元之氣分散而成也。人之生也，本於元氣。元氣出於坎水，是為天一之精也，蒸而為汗，流而為血，以養四肢五臟。

Heavenly Stem governs energy, while Earthly Branch governs form. One Yang spreads outward, so the Line Statement says 'sweating' and 'dispersing blood'. Two Yins live apart in the middle, so the Line Statement says 'dispersing the group' and 'dispersing the body'. The body, when separated, becomes limbs, and the group, when separated, becomes the five viscera and six腑. All of these are formed from the dispersion of the original energy. Human life fundamentally depends on original energy; original energy comes from the Water Trigram Kan, which is the essence produced by the first Heaven Stem. This essence rises up, vaporizes to become sweat, flows to become blood, and is used to nourish the limbs and internal organs.

巽之上爻，兌之下爻，變皆成坎。坎氣蒸上，為巽木之枝葉潤也。坎氣下濡，為兌澤之中聚水草也。澤水竭，則為困矣，是水下洩也。兌之一陽下洩，則有戒欲之象。坎之一陰上缺，則有戒嗜之象。戒欲二不出戶庭。戒嗜，故云甘、苦之味。

The top line of Xun and the bottom line of Dui both change to Kan. The energy of Kan rises upward, moistening the branches and leaves of Xun wood; the energy of Kan descends downward, nurturing water plants in the marsh of Dui. When the water in the marsh dries up, it becomes the hexagram of Guan, which represents water leaking downward. The single yang line of Dui leaking downward signifies the image of restraining desires; the single yin line of Kan at the top opening up signifies the image of restraining habits. Restraining desires is expressed as 'not going out of the gate'; restraining habits is expressed as tasting sweet and bitter flavors.

初爻言不出戶庭無咎，二爻言不出戶庭凶者，是戒欲之義也。初爻變為坎，天一之水是為真精之原，君子能知通塞之理，慎密而不出，閉其精戶，是養生之要也。坎二則火也，門庭者是開竅為心也。心火貴乎下濟於水，心明貴乎外明於物，不出則失中道矣，亦戒欲之義也。六三言嗟者悔嘆而不節，六四言安者安於能節，是皆明告利害於人也。養生之道，盡此二卦。

The first line says, "Without going out of the gate, there is no blame," and the second line says, "Without going out of the courtyard, there is misfortune." Both are talking about the principle of restraining desires. The first line changes into Kan, which represents water under heaven, the source of true essence. A gentleman who understands the principle of openness and closure, being cautious and not easily going out, keeping the gate of essence closed, is the key to cultivating life. When Kan reaches the second line, it becomes fire. The term "door and courtyard" refers to the opening of the senses and connection to the heart. Heart fire is valuable for descending to nourish kidney water, and a clear mind is valuable for illuminating external things. If one is overly closed and does not go out, one loses the middle path, which is again the principle of restraining desires. The third line says, "Alas, if only," indicating failure to control and later regret. The fourth line says, "Resting in moderation," meaning being at ease with the ability to control. These clearly explain the advantages and disadvantages. The principles of cultivating life are all contained in the hexagrams of "Huan" and "Jie."

《中孚》生陽，羽族卵生也。《咸》卦生陰，血肉之物胎生也。故《中孚》為生陽之始，《小過》為生陽之成也。烏雀四時生卵而春盛，故為立春之象，冬至之卵焉。《中孚》有烏卵之象，烏炎上之性，必以豚魚而後吉。豚魚，潤下之物也。北方子位，豚魚之地也。

The hexagram Zhongfu belongs to the category of generating yang, symbolizing a bird laying eggs with feathers; the hexagram Xian belongs to the category of generating yin, symbolizing a flesh-and-blood animal conceiving and giving birth. Therefore, Zhongfu marks the beginning of generating yang, while Xiaoguo signifies the completion of generating yang. Birds lay eggs in all four seasons, but most especially in spring, so Zhongfu takes the image of the beginning of spring, which corresponds to the eggs formed at the winter solstice. Zhongfu has the image of a bird's egg; birds have a nature that ascends, so they must be paired with pigs and fish, which are moist and descend, and the northern position of the first earthly branch corresponds to where pigs and fish reside. The original text's "wu" is actually "niao" (bird).

《小過》之飛烏離之凶者，由東行而中，南方之網罟也。網罟取離陽，至離而太盛，陰氣生矣。黃帝之律呂，分為乾、坤，妃為坎、離。乾、坤即分六陰、六陽，坎、離則成。

The hexagram Xiao Guo discusses a bird encountering danger because it flew from the east toward the center and collided with a net in the south. The net represents the yang energy of Li; when it reaches the position of Li, the yang energy becomes excessive, and yin energy then arises. The Yellow Emperor established the laws and tones, dividing them into Qian and Kun, and pairing them into Kan and Li: Qian and Kun produce the six yin and six yang lines, while Kan and Li form... the original text here is incomplete.

《既濟》、《未濟》。坎中之陽，將升而至於仲呂，闢卦為《乾》，是謂《乾》盈九不見其首。離內之陰，已入於坎，至於應鍾，闢卦為《坤》，是謂《坤》虛十以導潛龍之氣。《既濟》之首，《乾》之首也。《未濟》之尾，《坤》之尾也。《乾》尾續於《坤》尾，九而後十也。《坤》首繼於《乾》首，二而先一也。

Here we discuss the hexagrams of "Already Completed" (既济) and "Not Yet Completed" (未济). The single yang line in Kan is about to rise and reach the tone of Zhonglü, corresponding to the hexagram Qian, which is called "Qian full to nine and 'its head is not seen'"; the single yin line in Li has already entered Kan and reached the tone of Yingzhong, corresponding to the hexagram Kun, which is called "Kun empty to ten, guiding the hidden dragon's energy." The head of "Already Completed" is the head of Qian; the tail of "Not Yet Completed" is the tail of Kun. The tail of Qian follows the tail of Kun, which is first nine then ten; the head of Kun follows the head of Qian, which is two coming before one.

離巽繩離目。網目謂之罟，兩目相連，結繩為之網罟也。離，雉佃也。兌、巽為魚，漁也。

The hexagram Li (Fire) says: Xun (Wind) is the rope, and Li (Fire) is the eye. The eye holes on a net are called "gu," and with two eyes connected, tying ropes together makes a net. Li is also the wild chicken, which can be hunted; Dui (Lake) and Xun (Wind) are fish, which can be caught. This is what the Great Treatise says about Fuxi making ropes into nets to hunt and fish, which is derived from the hexagram Li.

益乾金斷巽，斷木也，四之上成坎，坎為益揉之初成。震，揉木也，入坤土而巽於前，斷木為耜也。動於後，揉木為未也。

The hexagram Yi (Benefit): The metal of Qian cuts the wood of Xun, which is called 'cutting wood'; the fourth line moves upward to form Kan, which is the beginning of Yi hexagram's action of shaping wood. Zhen is the action of shaping wood, the wood is inserted into the earth of Kun, with Xun hidden in front, which is cutting the wood to make a plowshare; when it moves forward, it is shaping the wood into a plow. This is what the Great Treatise says about Shen Nong 'carving wood into a plowshare and bending wood into a plow, which is derived from the hexagram Yi'. The original text 'wei' is actually 'le'.

噬嗑眾離日在上，為日中。坤眾在下，為市眾為民。離有伏，兌為羸，具坤往之致天下之民，聚大下之貨也。以坤交乾，交易也。

The hexagram Shihhe states: The trigram Li (Fire) with the sun in the upper position signifies 'noon'; the trigram Kun (Earth) with the multitude in the lower position signifies a market, where 'multitude' refers to the people. Within Li is concealed Dui (Lake), which represents goods that can be carried, and with the multitude moving towards it, it attracts people from all over the world and gathers goods from everywhere. Using Kun to meet Qian (Heaven) signifies trade. This is what the Great Treatise says: Shennong established the market at noon, gathering the people from all over the world and collecting goods from everywhere, engaging in trade and then departing, each returning to their proper place. This is derived from the hexagram Shihhe. The original text '大下' is actually '天下'.

乾乾，坤無為，六子自用，垂衣裳而天下乾在上為衣。

The Qian hexagram: Qian remains at ease in its position, while Kun does nothing. The six subordinate hexagrams each perform their functions, thus achieving the state of "governing the world by wearing robes and keeping a simple demeanor." Qian occupies the upper position, symbolizing the upper garment.

坤坤在下為裳。裳，下體之飾也。

The sixth hexagram, K'un, is associated with the lower position, symbolizing the lower garment. The lower garment is clothing that covers the lower part of the body. Together with the previous statement, this forms what the Great Treatise says about the Yellow Emperor, Yao, and Shun: "They governed the world by simply wearing robes, which was derived from the hexagrams of Qian and K'un."

渙乾金剖巽，浮於坎上，剖木為舟也。火上銳，刻木為楫也。

The Hexagram of Dispersing: Heaven metal splits Wind wood, allowing it to float on Water. This is making a boat by hollowing out wood. The shape of fire is pointed at the top, which is making an oar by carving wood. This is what the Great Treatise says: "Hollowing out wood to make a boat, carving wood to make an oar; the usefulness of boats and oars in crossing water that is not passable, is derived from the Hexagram of Dispersing."

隨坤牛而震足，驅之服牛也。震作足馬，上六引之。引，重也。內卦近，外卦遠，上六在外卦之外，致遠也。

The hexagram "Following" states: Earth (Kun) represents the ox and Zhen represents the foot, driving it forward is like harnessing an ox cart; Zhen also represents a good-running horse, with the sixth line at the top pulling it. "Pulling" means bearing a heavy load. The inner trigram is near, the outer trigram is far, and the sixth line is outside the outer trigram, hence "reaching far away." This is what the Great Treatise says: "Harnessing oxen and riding horses, bearing heavy loads and reaching far away, benefiting the world, is derived from the hexagram 'Following.'"

豫《豫》，《謙》之反也。《謙》，艮為門，九三之四又為門，重門也。艮為手，坎為堅，震為聲，手擊堅木而有聲，擊柝也。坤為闔戶，而坎盜逼之，暴客也。

The hexagram Yu: Yu is the reverse of the hexagram Qian. In Qian, Gen represents a gate, and the line nine in the third position moves up to the fourth position to form another gate, making two gates stacked on top of each other, which is called "chong men" (double gates). Gen represents the hand, Kan represents a hard object, and Zhen represents sound; using the hand to strike a hard wooden block and produce a sound is called "ji tuo" (striking a wooden block), which is the act of beating a drum to signal the night watch. Kun represents a tightly closed gate, while the thief represented by Kan approaches forcefully, which is called "bu ke" (sudden intruders). This is what the Great Treatise says: "Chong men ji tuo, yi dai bu ke, ge qu zhu Yu."

小過兌金斷巽木，斷木為杵也。巽木入坤土，掘地為臼也。坎，陷也。臼之象，杵動於上，臼止於下，四應初，三應上，上下相應，杵、臼之利也。坎變巽股，萬民濟也。

The "Small Crossing" hexagram: The metal of the Trigram Dui cuts the wood of the Trigram Xun, which is made into a pestle; the wood of Xun is inserted into the earth of the Trigram Kun, which is dug into to make a mortar. The Trigram Kan represents a depression, which matches the image of a mortar. The pestle is above and moves, while the mortar is below and remains still; the line Six in the Fourth corresponds to Six at the Beginning, and Nine in the Third corresponds to Six at the Top, with upper and lower parts corresponding, thus forming the benefit of pestle and mortar for pounding rice. When the Trigram Kan changes to the "thigh" of the Trigram Xun, all the people receive sustenance. This is what the Great Treatise says: "Cutting wood to make a pestle, digging the earth to make a mortar, the benefit of pestle and mortar sustains the people, which is taken from the 'Small Crossing' hexagram."

睽《睽》，《家人》之反也。《家人》，巽為木，巽、離為絲，坎為弓，弦木為弓也。兌金刻木而銳之，刻木為矢也。兌庾乾剛，威天下也。

The hexagram Kui is the reverse of the hexagram Jiaoren. In Jiaoren, Xun represents wood, Xun and Li represent silk threads, and Kan represents the bow. When silk threads are strung on wood, a bow is formed. The metal of Dui sharpens the wood into an arrow. The solemnity of Dui combined with the strength of Qian is sufficient to subdue the world. This is what the Great Treatise says: "To make a bow from wood and string, to make an arrow by sharpening wood, the utility of bows and arrows to subdue the world, is derived from the hexagram Kui."

大壯《大壯》自《還》來，一變《中孚》。艮為居，兌為口穴之象。穴，居也。再變大《大畜》，乾在上，天際也，野之象。巽入變艮，而止野處也。三變《大壯》，震壯木在上，棟也。乾天在下，宇也。巽風隱，兌澤流，待風雨也。《大壯》則不橈矣。

The hexagram Great Strength comes from the hexagram Retreat, with the first change leading to the hexagram Middle Trust. The mountain (Gèn) represents stopping and dwelling, and the lake (Duì) represents the mouth, which is the image of a cave; the cave is the dwelling place. The second change leads to the hexagram Great Accumulation. Heaven (Qián) at the top represents the sky's edge, which is the image of the open field; the wind (Xùn) enters and transforms into the mountain, indicating stopping in the open field to rest. The third change leads to the hexagram Great Strength. The strong wood (Zhèn) above represents the beams, and Heaven (Qián) below represents the house; the wind (Xùn) is blocked, and the marsh (Duì) water flows away, indicating protection against wind and rain. With the hexagram Great Strength, the roof beams will not bend. This is what the Great Treatise says: "In ancient times people dwelled in caves and lived in the open fields, but later sages replaced this with houses and buildings, with beams above and eaves below, to guard against wind and rain, which is derived from the hexagram Great Strength." The original text's "return" should be "Retreat."

大過《大過》自《遯》，一變《訟》，乾見坤隱，不封也。再變巽木，而兌金毀之，不樹也。三變《鼎》，離為目，兌澤流喪也。上九變而應三，坎兌為節，不變喪期，無數也。木在澤下，中有乾人，棺槨也。葬則棺周於身，槨周於瓪棺，土周於槨，大過也。

The hexagram Great Excess comes from the hexagram Retreat. The first change produces the hexagram Strife, with Heaven appearing and Earth hidden, hence "not sealing," meaning not piling earth to form a tomb. The second change sees the Wood of Xun destroyed by the Metal of Dui, hence "not planting trees," meaning not planting trees as markers. The third change produces the hexagram Cauldron, with Li representing the eye and the water from Dui's marsh flowing out, which signifies weeping. The upper nine changes to correspond with the lower nine three, with Kan and Dui combining to form "Regulation," which remains unchanged, so the mourning period is "without number." Wood is beneath the marsh, with the figure of Heaven in the center, representing the coffin. At burial, the coffin surrounds the body, the outer case surrounds the coffin, and earth surrounds the case, layer by layer, exactly "Great Excess." This is what the Great Treatise says about ancient burial practices: "Not sealing, not planting trees, mourning without number; later sages replaced this with coffins and outer cases, taking the meaning from the hexagram Great Excess."

夬《夬》自《姤》，四變《大有》。《姤》，巽為繩，結繩也。巽變成離、坤。離為文書也。兌金刻木契也。

The hexagram Guai is derived from Guo, with the fourth line changing to Dàyǒu. In Guo, Xun represents a rope, which is "binding with ropes"; when Xun changes into Li and Kun, Li represents documents. The trigram Dui (metal) carves wood, which is "carving contracts". This is what the Great Treatise says: "In ancient times, they governed by binding with ropes; later sages replaced this with written contracts. Thus, officials could govern and people could be examined. This is taken from Guai."

一：《履》，德之基；《謙》，德之柄；《復》，德之本；《恆》，德之固；《損》，德之修；《益》，德之裕；《困》，德之辯；《井》，德之地；《巽》，德之制。

The first explanation discusses which part of virtue each of the nine trigrams represents: The trigram "Xu" (Progress) is the foundation of virtue, "Qian" (Humility) is the handle of virtue, "Fu" (Return) is the origin of virtue, "Heng" (Perseverance) is the stable place of virtue, "Sun" (Loss) is the cultivation of virtue, "Yi" (Gain) is the abundance of virtue, "Kun" (Obstruction) is the discernment of virtue, "Jing" (Well) is the dwelling place of virtue, and "Xun" (Wind) is the restraint of virtue.

二：《履》和而至；《謙》尊而光；《復》小而辨於物；《恆》雜而不厭；《損》先難而後易；《益》長裕而不設；《困》窮而通；《井》居其所而遷；《巽》稱而隱。

The second explanation discusses the characteristics of these nine trigrams: The trigram "Xu" (Progress) is harmonious and can achieve its purpose; The trigram "Qian" (Humility) is modest and thus becomes more esteemed; The trigram "Fu" (Return) arises from small beginnings and can discern things; The trigram "Heng" (Perseverance) remains steadfast even in complex situations without tiring; The trigram "Sun" (Loss) starts with difficulty but becomes easy later; The trigram "Yi" (Gain) maintains long-term abundance without artificiality; The trigram "Kun" (Obstruction) remains in hardship yet its path is clear; The trigram "Jing" (Well) does not move itself but benefits others; The trigram "Xun" (Wind) measures things and remains hidden.

三：《履》以和行；《謙》以制禮；《復》以自知；《恆》以一德；《損》以遠害；《益》以興利；《困》以寡怨；《井》以辨義；《巽》以行權。

The third explanation discusses the respective uses of these nine trigrams: using the trigram "履" (Foot) to make conduct harmonious, using "谦" (Modesty) to establish propriety, using "复" (Return) for self-examination, using "恒" (Perseverance) to maintain steadfast virtue, using "损" (Loss) to avoid calamity, using "益" (Gain) to promote benefit, using "困" (Obstruction) to reduce grievances, using "井" (Well) to discern righteousness, and using "巽" (Wind) to exercise flexibility.

上經卦三三敘而九，下經卦六三叔而十八。《履》十，《謙》十五，《復》二十四，《恆》二，《損》十一，《益》十二，《困》十七，《井》十八，《巽》二十七，九卦之數，總一百三十有六。凡三求之，四百有八也。周天三百六十成數也，餘四十八，陰陽所以進退也。陽進於《乾》，六月各四十八，《復》至《乾》也。陰退於《坤》，六月亦四十八，《娠》至《坤》也。

The upper section of the Classic contains nine trigrams arranged in groups of three, and the lower section contains eighteen trigrams arranged in six groups of three. The nine trigrams in their respective sections are: The Trigram of Progress at the tenth position, The Trigram of Humility at the fifteenth, The Trigram of Return at the twenty-fourth, The Trigram of Constancy at the second, The Trigram of Loss at the eleventh, The Trigram of Gain at the twelfth, The Trigram of Obstruction at the seventeenth, The Trigram of Well at the eighteenth, and The Trigram of Wind at the twenty-seventh. In total, there are one hundred and thirty-six trigrams. When multiplied by three, this gives four hundred and eight. The full cycle of the heavens is three hundred and sixty, and the remaining forty-eight corresponds to the movement of yin and yang. Yang advances toward the Trigram of Heaven, advancing six months, which totals forty-eight, from the Trigram of Return to the Trigram of Heaven. Yin retreats toward the Trigram of Earth, retreating six months, which also totals forty-eight, from the Trigram of Encounter to the Trigram of Earth. The original text uses 'shu' for 'xu' and 'sen' for 'gou'.

天一下生地六，地二上生天七；天三左生地八，地四右生天九。

The heavenly numbers descend to produce the earthly numbers six, and the earthly numbers two ascend to produce the heavenly number seven; the heavenly number three generates the earthly number eight to the left, and the earthly number four generates the heavenly number nine to the right. These four pairs of generating numbers and forming numbers are paired up in the up-down and left-right directions, forming the basic structure of this diagram.

參，合也。配，偶也。天地之數，各相參配，錯綜往來而相生，故生成之數大備，而天地之文生焉。《繫辭》日：參伍以變，錯綜其數，通其變，遂成天地之文。此之謂也。

"San" means to come together, and "pei" means to pair. The heavenly numbers and earthly numbers each come together and pair with each other, interweaving and combining, alternating and generating each other, so that the generated numbers and completed numbers are fully complete, and thus the cultural patterns of heaven and earth are produced. The Great Treatise says: "By combining three and five, changes occur; numbers are interwoven and combined. By comprehending these changes, the cultural patterns of heaven and earth are formed." This is exactly the meaning being explained.

男女合者，上、下經惟十二位。正位《乾》、《坤》、《坎》、《離》、《咸》、《恆》、《損》、《益》八卦，分為十八位。《乾》、《坤》變《頤》、《大過》，《頤》、《大過》變《坎》、《離》，《坎》、《離》變《中孚》、《小過》，《中孚》、《小過》變《咸》、《恆》，成人倫也。

In terms of matching male and female, there are only twelve positions in the Upper and Lower Classics. The trigrams that take the correct positions are Qian, Kun, Kan, Li, Xian, Heng, Shen, and Yi, arranged separately to form eighteen positions. Qian and Kun generate Yi and Da Guo, Yi and Da Guo generate Kan and Li, Kan and Li generate Zhong Fu and Xiao Guo, Zhong Fu and Xiao Guo generate Xian and Heng, and thus the principles of human relationships are established. This successive transformation is referred to as 'eighteen changes'.

六十四卦，一陰一陽，始《乾》終《坤》。先自《乾》、《坤》一陰一陽，排六十四，次自《乾》二陽二陰，次四陽四陰，次十六陽十六陰，次三十二陽三十二陰，即成六十四卦也。故曰一陰一陽之謂道。

The sixty-four hexagrams alternate between one yin and one yang, starting with Qian (Heaven) and ending with Kun (Earth). First, they are arranged beginning with Qian and Kun, alternating one yin and one yang until all sixty-four positions are filled. Then, starting again with Qian, they are arranged in pairs of two yangs and two yins, then in groups of four yangs and four yins, then sixteen yangs and sixteen yins, and finally thirty-two yangs and thirty-two yins. Thus, the sixty-four hexagrams are arranged. Therefore, the Great Treatise says: "To alternate one yin and one yang is called the Way."

自甲午至癸亥三十日。起申至巳。先甲。黑暈。自甲子至癸巳三十日。起寅至亥。後甲。白暈。

From the day of Jiawu to the day of Guisi, a period of thirty days, beginning at Shen and ending at Si, this section is classified as "Xian Jia," marked with a black halo on the diagram. From the day of Jiazi to the day of Guisi, another period of thirty days, beginning at Yin and ending at Hai, this section is classified as "Hou Jia," marked with a white halo on the diagram. This arrangement distributes the Hexagram Statement of "Gǔ" ("Guilt") which states "Xian Jia three days, Hou Jia three days" across the sixty Jiazi cycles.

陽卦以奇為君，故一陽而二陰，陽為君，陰為民也。陰卦以偶為君，故二陽而一陰，陰為君，陽為民也。陽，一畫為君，二畫為民，其理順，故日君子之道。陰，二畫為君，一畫為民，其理逆，故曰小人之道。

In a yang trigram, the odd number line is considered the ruler, so it is one yang line paired with two yin lines, with yang as the ruler and yin as the people. In a yin trigram, the even number line is considered the ruler, so it is two yang lines paired with one yin line, with yin as the ruler and yang as the people. In a yang trigram, the single line is the ruler and the two lines are the people, which follows the natural order, so the Great Treatise calls it "the way of the superior man." In a yin trigram, the two lines are the ruler and the single line is the people, which goes against the natural order, so it is called "the way of the inferior man."

震、坎、艮，陽卦也。曷為而多陰？自坤而索也。其卦皆一陽二陰，凡五也，故曰陽卦奇。巽、離、兌，陰卦也。曷為而多陽？自乾而來也。其卦皆一陰二陽，凡四也，故日陰卦耦。

Zhen, Kan, and Gen are yang hexagrams, yet they have more yin lines. This is because they are obtained by seeking from Kun. These three hexagrams each consist of one yang line and two yin lines, totaling five strokes. Five is an odd number, so it is said "yang hexagrams are odd." Xun, Li, and Dui are yin hexagrams, yet they have more yang lines. This is because they come from Qian. These three hexagrams each consist of one yin line and two yang lines, totaling four strokes. Four is an even number, so it is said "yin hexagrams are even."

第一揲、第二揲、第三揲。第一卦於小指間，不五則九；第二卦於中指間、第三卦於食指間，皆不四則八。

To determine one line of the divination, the process involves three steps: the first, second, and third divinations. In the first step, the remaining stalks are held between the little finger, resulting in either five or nine. In the second step, they are held between the middle finger, and in the third step, between the index finger, resulting in either four or eight each time.

五四四，此係三少，計十三策，四十九策中除十三，餘三十六，即四九之數也，是為老陽。

Three throws of the yarrow stalks resulted in five, four, and four, which constitutes a "three few" combination, totaling thirteen lines. Subtracting these thirteen lines from the forty-nine, leaves thirty-six, which is four times nine. Therefore, this line is determined to be an old yang.

九八八，此係三多，計二十五策，四十九中除二十五，餘二十四，即四六之數，是為老陰。

Three throws of the yarrow stalks resulted in nine, eight, and eight, which constitutes a group of 'three multiples,' totaling twenty-five lines. Subtracting these twenty-five lines from the total of forty-nine leaves twenty-four, which is exactly four times six. Therefore, this line is determined to be old yin.

五八八，少陽。九四八，並係兩多一少，各計二十一策，四十九中除二十一，餘二十八，即四七之數也，是為少陽。九八四，少陽。

Obtaining five, eight, and eight, it is considered a minor yang. Obtaining nine, four, and eight, it is the same as the previous case, belonging to 'two many and one few,' with each total amounting to twenty-one counts; subtracting twenty-one from forty-nine leaves twenty-eight, which is four times seven, so it is determined as minor yang. Obtaining nine, eight, and four, it is also minor yang.

九四四，少陰。五八四，並係兩少一多，各計十七策，四十九中除十七，餘三十二，即四八八之數也，是為少陽。五四八，少陰。

The numbers obtained are nine, four, and four, which belong to the category of "few yin." The numbers five, eight, and four also fall into the same "two fews and one many" category, each totaling seventeen counts. Subtracting seventeen from forty-nine leaves thirty-two, which is the product of four multiplied by eight. According to this, it should be determined as "few yin" — the original text mistakenly writes it as "few yang," and "four eight eight" should be corrected to "four eight." The numbers five, four, and eight also belong to "few yin."

以三因天地十五數，得四十五。以五因天地十五數，得七十五。以七因天地十五數，得一百五。九宮數止一百五，故百六為極數。用三、五、七者，取陽數中者用之。

By multiplying three by the number of heaven and earth, which is fifteen, we get forty-five; by multiplying five by fifteen, we get seventy-five; by multiplying seven by fifteen, we get one hundred and five. The numbers in the Nine Stars system do not exceed one hundred and five, so one hundred and six is taken as the extreme number. The reason we only use three, five, and seven for multiplication is that we are selecting several middle numbers from the yang numbers to use.

乾職生覆，坎司寒化，艮司溼化，震司動化，巽司風化，離司暑化，坤職形載，兌司燥化。

The function of Qian is to generate and cover, Kan governs the transformation of cold energy, Gen governs the transformation of dampness, Zhen governs the transformation of movement, Xun governs the transformation of wind, Li governs the transformation of heat, and Kun's function is to form and carry. This diagram arranges the eight trigrams, each responsible for a specific type of energetic transformation.

坎北，震束，乾西北，艮束北，四卦皆陽也。離南，兌西，巽束南，坤西南，四卦皆陰也。故日：方以類聚。一聚於六而分乾、坎，四聚於九而分坤、兌，二聚於七而分離、巽，三聚於八而分震、艮，故日：物以群分。得朋則吉，乖類則凶，此吉凶所以生也。

Heavenly Stems: Jia, Yi, Bing, Ding, Wu, Ji, Geng, Xin, Ren, Gui Earthly Branches: 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) Glossary: Northeast, Southeast, Northwest, Southwest, Due East, Due South, Due West, Due North, Great Treatise Kan is located in the north, Zhen in the east, Qian in the northwest, and Gen in the northeast; these four trigrams are all yang. Li is located in the south, Dui in the west, Xun in the southeast, and Kun in the southwest; these four trigrams are all yin. Therefore, the Great Treatise says, "Things gather by their kind." One gathers to six and distinguishes Qian and Kan, four gathers to nine and distinguishes Kun and Dui, two gathers to seven and distinguishes Li and Xun, three gathers to eight and distinguishes Zhen and Gen. Therefore, the Great Treatise says, "Things separate by their group." To associate with similar things brings good fortune, while separating from similar things brings misfortune, and thus good and bad fortune arise.

子者，乾之始，而終於巳。午者，坤之始，而終於亥。陽爻二百九十二，晝數也，其數一千七百二十八。陰爻一百九十二，夜數也，其數一千一百五十二。總而言之，二千八百八十九，四求之合，萬有一千五百二十，故日：通乎晝夜之道而始。

Zi is the beginning of Qian, and it ends at Si; Wu is the beginning of Kun, and it ends at Hai. Among the sixty-four hexagrams, there are 192 yang lines, which belong to the number of day, and their total is 1728; there are 192 yin lines, which belong to the number of night, and their total is 1152. Altogether, they total 2880. Then using four to find their combined number, it becomes 11520. Therefore, the Great Treatise says: "To understand the principle of day and night." The original text "two hundred ninety-two" should be "one hundred ninety-two," "two thousand eight hundred eighty-nine" should be "two thousand eight hundred eighty," and "while beginning" should be "while knowing."

上經三十，下經三十四。

This diagram is arranged according to the "Xu Gua" (Sequence of the Hexagrams): the Upper Classic contains thirty hexagrams, and the Lower Classic contains thirty-four hexagrams, making a total of sixty-four hexagrams.

《雜卦》者，雜揉眾卦，錯綜其義，以暢無窮之用，故其義專以剛柔、升降、反覆取義，與《序卦》不同。故韓康伯云：或以同相類，或以異相明，雜六十四卦以為義是也。

The so-called "Zage" (Miscellaneous Hexagrams) combines and blends the various hexagrams, interweaving their meanings to demonstrate infinite applications. Therefore, it focuses on aspects such as hardness and softness, rising and falling, and right and wrong. This approach differs from that of the "Xugua" (Order of Hexagrams). Hence, Han Kangbo of the Jin Dynasty said that some group similar ones together, while others contrast differing ones to illuminate each other, and by combining all sixty-four hexagrams into one meaning, this is exactly what is referred to.

一玄生三方，用三乘一。三方生九州島，用三乘三。九州島生二十七部，用三乘九。二十七部生八十一家，用三乘二十七。八十一家生二百四十三表，用三乘八十一。二百四十三表生七百二十九贊，用三乘二百四十三。七百二十九贊生二萬六千二百四十四策，用三十六乘七百二十九。凡一玄為一歲，七十二策為一日，起十一月。

Yang Xiong's "Tai Xuan" is structured in layers as follows: one "Xuan" gives rise to three "Fang," which is three times one; three "Fang" give rise to nine "Zhou," which is three times three; nine "Zhou" give rise to twenty-seven "Bu," which is three times nine; twenty-seven "Bu" give rise to eighty-one "Jia," which is three times twenty-seven; eighty-one "Jia" give rise to two hundred forty-three "Biao," which is three times eighty-one; two hundred forty-three "Biao" give rise to seven hundred twenty-nine "Zan," which is three times two hundred forty-three; seven hundred twenty-nine "Zan" give rise to twenty-six thousand two hundred forty-four "Ce," which is thirty-six times seven hundred twenty-nine. In total, one "Xuan" corresponds to one whole year, and seventy-two "Ce" correspond to one day, starting from November. The original "Jiu Zhou" refers to "Jiu Zhou," and the diagram title "Wan Xuan" refers to "Tai Xuan."

右律曆之元，始於冬至，卦氣起於《中孚》。

The diagram above indicates that the calculation of the laws and calendar begins at the winter solstice, while the卦气 (gua qi) starts from the hexagram Zhongfou.

一一：元之元，日之日，乾之乾，一。二一：會之元，月之日，兌之乾，一十二。一二：元之會，日之月，乾之兌，卜十二。二二：會之會，月之月，兌之兌，一百四十四。一三：元之運，日之星，乾之離，三百六十。二三：會之運，月之星，兌之離，四千三百二十。一四：元之世，日之辰，乾之震，四千三白二十。二四：會之世，月之辰，兌之震，五萬一千八百四十。

This diagram is from Shao Yong's "Huang Ji Jing Shi," representing the full numerical table of the interactions between the yuan, hui, yun, and shi, as well as the sun, moon, stars, and the eight trigrams. Each row first lists two position numbers, followed by the corresponding pairings of yuan, hui, yun, and shi, the pairings of the sun, moon, stars, and the eight trigrams, and finally the number for that row. The first row "yi yi" refers to yuan within yuan, day within day, and Qian within Qian, with the number being one. "Er yi" refers to yuan within hui, day within moon, and Dui within Qian, with the number being twelve. "Yi er" refers to hui within yuan, day within moon, and Qian within Dui, with the number being twelve (the original text's "bu" is a misinterpretation). "Er er" refers to hui within hui, moon within moon, and Dui within Dui, with the number being one hundred forty-four. "Yi san" refers to yun within yuan, star within day, and Li within Qian, with the number being three hundred sixty. "Er san" refers to yun within hui, star within moon, and Li within Dui, with the number being four thousand three hundred twenty. "Yi si" refers to shi within yuan, chen within day, and Zhen within Qian, with the number being four thousand three hundred twenty (the original text's "bai" is a misinterpretation of "bai"). "Er si" refers to shi within hui, chen within moon, and Zhen within Dui, with the number being five thousand one hundred eighty-four.

一五：元之歲，日之石，乾之巽，一十一萬九千六百。二五：會之歲，月之石，兌之巽，一百五十五萬五千二百。一六：元之月，日之土，乾之坎，一百五十五萬五千二百。二六：會之月，月之土，兌之坎，一千八百六十六萬二千四百。一七：元之日，日之火，乾之艮，四千六百六計五萬六千。二七：會之日，月之火，兌之艮，五萬五千九百八十七萬二千。一八：元之星，日之水，乾之坤，五萬五千九百八十七萬二千。二八：會之辰，月之水，兌之坤，六十七萬一千八百四十六萬四千。

「One Five」: The first five, the beginning in the middle of the year, the stone in the middle of the day, the wind in the middle of heaven, the number is eleven million nine thousand six hundred. 「Two Five」: The second five, the gathering in the middle of the year, the stone in the middle of the month, the wind in the middle of lake, the number is one million five hundred and fifty-five thousand two hundred. 「One Six」: The first six, the beginning in the middle of the month, the soil in the middle of the day, the water in the middle of heaven, the number is one million five hundred and fifty-five thousand two hundred. 「Two Six」: The second six, the gathering in the middle of the month, the soil in the middle of the month, the water in the middle of lake, the number is eighteen million six hundred and sixty-six thousand two hundred and forty. 「One Seven」: The first seven, the beginning in the middle of the day, the fire in the middle of the day, the mountain in the middle of heaven, the number is forty-six million six hundred and fifty-five thousand six hundred (the original text mistakenly writes 'count' instead of 'ten'). 「Two Seven」: The second seven, the gathering in the middle of the day, the fire in the middle of the month, the mountain in the middle of lake, the number is five million five hundred and ninety-eight thousand seven hundred and twenty. 「One Eight」: The first eight, the beginning in the middle of the star, the water in the middle of the day, the earth in the middle of heaven, the number is five million five hundred and ninety-eight thousand seven hundred and twenty. 「Two Eight」: The second eight, the gathering in the middle of the hour, the water in the middle of the month, the earth in the middle of lake, the number is sixty-seven million one hundred and eighty-four thousand six hundred and forty.

三一：運之元，星之離，日之乾，三百六十。四一：世之元，辰之日，震之乾，四千三百二十。三二：運之會，星之月，離之兌，四千三百二十。四二：世之會，辰之月，震之兌，八萬五千一百四十。三三：運之運，星之星，離之離，一十二萬九千六百。四三：世之運，辰之星，震之離，一百五十五萬五千二百。三四：運之世，星之辰，震之震，一百五十五萬五千二百。四四：世之世，辰之辰，震之震，一千八百八十六萬二千四百。

"The Three One": The beginning of the cycle, the day of the star, the Heaven in the Fire, the number is three hundred and sixty (the original text has a misplacement in the columns "star's Fire" and "day's Heaven"). "The Four One": The beginning of the world, the day of the hour, the Heaven in the Thunder, the number is four thousand three hundred and twenty. "The Three Two": The meeting in the cycle, the month of the star, the Lake in the Fire, the number is four thousand three hundred and twenty. "The Four Two": The meeting in the world, the month of the hour, the Lake in the Thunder, the number should be fifty-one thousand eight hundred and forty (the original text says "eighty-five thousand one hundred and forty"). "The Three Three": The cycle in the cycle, the star in the star, the Fire in the Fire, the number is one hundred twenty-nine thousand six hundred. "The Four Three": The cycle in the world, the star in the hour, the Thunder in the Fire, the number is one hundred fifty-five thousand five hundred and twenty. "The Three Four": The world in the cycle, the hour in the star, the Thunder in the Fire, the number is one hundred fifty-five thousand five hundred and twenty (the original text says "Thunder's Thunder" but should be "Fire's Thunder"). "The Four Four": The world in the world, the hour in the hour, the Thunder in the Thunder, the number should be one million eight hundred and sixty-six thousand two hundred and forty.

三五：運之歲，星之石，離之巽，四千六百六十五萬六千。四五：世之歲，辰之石，震之巽，五萬九千九百八十七萬二千。三六：運之月，星之土，離之坎，五萬五千九百八十七萬二千。四六：世之月，辰之土，震之坎，六十萬一千八百四十六萬四千。三七：運之日，皋之火，離之艮，一百六十七萬九千六百一十六萬。四七：世之日，辰之火，震之艮，二千一十五萬五千三百九十二萬。三八：運之辰，星之水，離之坤，二千一十五萬五千三百九十二萬。四八：世之辰，辰之水，農之坤，二萬四千一百八十六萬四千七百四萬。

"Three and five": In the cycle of years, among the stars, in the fire trigram, the number is forty-six million six hundred and fifty-six thousand six hundred. "Four and five": In the cycle of years, among the celestial stems, in the thunder trigram, the number should be fifty-five million nine hundred and eighty-seven thousand two hundred. "Three and six": In the cycle of months, among the earthly branches, in the water trigram, the number is fifty-five million nine hundred and eighty-seven thousand two hundred. "Four and six": In the cycle of months, among the earthly branches, in the water trigram, the number should be sixty-seven million one hundred and eighty-four thousand six hundred and forty. "Three and seven": In the cycle of days, among the stars, in the mountain trigram, the number is one hundred and sixty-seven million nine hundred and sixty-one thousand six hundred. "Four and seven": In the cycle of days, among the celestial stems, in the mountain trigram, the number is twenty million one hundred and fifteen thousand five hundred and thirty-nine thousand two hundred. "Three and eight": In the cycle of days, among the stars, in the earth trigram, the number is twenty million one hundred and fifteen thousand five hundred and thirty-nine thousand two hundred. "Four and eight": In the cycle of days, among the earthly branches, in the earth trigram, the number is twenty-four million one hundred and eighty-six thousand four hundred and seventy thousand four hundred.

五一：歲之元，石之日，巽之乾，一十二萬九千六百。六一：月之元，土之日，坎之乾，一百五十五萬五千二百。五二：歲之會，石之月，巽之兌，一百五十五萬五千二百。六二：月之會，土之月，坎之兌，一千八百六十六萬二千四百。五三：歲之運，石之星，巽之離，四千六百六十五萬六千。六三：月之運，土之星，坎之離，五萬五千九百八百八十七萬二千。五四：歲之世，石之辰，巽之震，五萬五千九百八十七萬二千。六四：月之世，土之辰，坎之震，六十七萬一千八百四十六萬四千。

"Five One": The beginning of the year, the day in stone, the乾 in wind, the number is twelve million nine thousand six hundred. "Six One": The beginning of the month, the day in earth, the乾 in water, the number is one million five hundred fifty-five thousand two hundred. "Five Two": The meeting of the year, the month in stone, the兑 in wind, the number is one million five hundred fifty-five thousand two hundred. "Six Two": The meeting of the month, the month in earth, the兑 in water, the number is eighteen million six hundred sixty-six thousand two hundred forty. "Five Three": The movement of the year, the star in stone, the离 in wind, the number is four million six hundred sixty-five thousand six hundred. "Six Three": The movement of the month, the star in earth, the离 in water, the number is five million five hundred ninety-eight thousand seven hundred twenty (the original text has an addition of 'eight hundred' characters). "Five Four": The era of the year, the hour in stone, the震 in wind, the number is five million five hundred ninety-eight thousand seven hundred twenty. "Six Four": The era of the month, the hour in earth, the震 in water, the number is sixty-seven million one hundred eighty-four thousand six hundred forty.

五五：歲之歲，石之石，巽之巽，一百六十七萬九千六百一十六萬。六五：月之歲，土之石，坎之巽，二千一十五萬五千三百九十二萬。五六：歲之月，石之土，巽之坎，二千一十五萬五千三百九十二萬。六六：月之月，土之土，坎之坎，二萬四千一百八十六萬四千七百四萬。五七：歲之日，石之火，巽之艮，六萬四百六十六萬一千七百六十萬。六七：月之日，土之火，坎之艮，七十二萬五千五百九十四萬一千一百二十萬。五八：歲之辰，石之水，巽之坤，七十二萬五千五百九十四萬一千一百二十萬。六八：月之辰，土之水，坎之坤，八百七十萬七千一百二十九萬三千四百四十萬。

"Five-Five": Within the year within the year, stone within stone, wind within wind, the number is one hundred sixty-seven million nine thousand six hundred sixteen thousand. "Six-Five": Within the month within the year, earth within stone, water within wind, the number is twenty million fifteen thousand five hundred thirty-nine thousand two hundred. "Five-Six": Within the year within the month, stone within earth, wind within water, the number is twenty million fifteen thousand five hundred thirty-nine thousand two hundred. "Six-Six": Within the month within the month, earth within earth, water within water, the number is two million four hundred eighteen thousand six thousand four hundred seventy-four thousand. "Five-Seven": Within the year within the day, stone within fire, wind within mountain, the number is six million forty-six thousand six hundred seventeen thousand six hundred. "Six-Seven": Within the month within the day, earth within fire, water within mountain, the number is seventy-two million five hundred fifty-nine thousand four hundred eleven thousand two hundred. "Five-Eight": Within the year within the hour, stone within water, wind within earth, the number is seventy-two million five hundred fifty-nine thousand four hundred eleven thousand two hundred. "Six-Eight": Within the month within the hour, earth within water, water within earth, the number is eight hundred seventy million seven hundred twenty-nine thousand three hundred forty-four thousand.

七一：日之元，火之日，艮之乾，四千六百六十五萬六千。八一：辰之元，水之口，坤之乾，五萬五千九百八十七萬三千。七二：日之會，火之月，艮之兌，五萬五千九百八十七萬二千。八二：辰之會，水之月，坤之兌，六千七萬一千八百四十六萬四千。七三：日之運，火之星，艮之離，一百六十七萬九千六百一十六萬。八三：辰之運，水之星，坤之離，一千一十五萬五千三百九十二萬。七四：日之世，火之辰，艮之震，一千一十五萬五千三百九十二萬。八四：辰之世，水之辰，坤之震，二萬四千一百八十六萬四千七百四萬。

「Seven One」: The origin in the middle of the day, the day in the fire, the dry earth in the mountain, the number is four million six hundred and sixty-five thousand six hundred. 「Eight One」: The origin in the middle of the morning, the day in the water, the earth in the mountain, the number should be five million five hundred and ninety-eight thousand seven hundred and twenty. (The original text mistakenly wrote 「mouth」 instead of 「day」, and the ending 「three thousand」 should be 「two thousand」.) 「Seven Two」: The gathering in the middle of the day, the month in the fire, the mountain in the lake, the number is five million five hundred and ninety-eight thousand seven hundred and twenty. 「Eight Two」: The gathering in the middle of the morning, the month in the water, the earth in the lake, the number should be sixty-seven million one hundred and eighty-four thousand six hundred and forty. (The original text mistakenly wrote 「six million seven thousand」.) 「Seven Three」: The movement in the middle of the day, the star in the fire, the mountain in the fire, the number is one hundred and sixty-seven million nine thousand six hundred and sixteen. 「Eight Three」: The movement in the middle of the morning, the star in the water, the earth in the fire, the number should be twenty million one hundred and fifteen thousand five hundred and thirty-nine hundred and twenty. 「Seven Four」: The era in the middle of the day, the time in the fire, the mountain in the thunder, the number should be twenty million one hundred and fifteen thousand five hundred and thirty-nine hundred and twenty. 「Eight Four」: The era in the middle of the morning, the time in the water, the earth in the thunder, the number is two million four hundred and eighteen thousand six hundred and forty-seven hundred and four.

七五：日之歲，火之石，艮之巽，六萬四百六十六萬一千七百六十萬。八五：辰之歲，水之石，坤之巽，七十二萬五千五百九十四萬一千一百二十萬。七六：日之月，火之土，艮之坎，七十二萬五千五百九十四萬一千一百二十萬。八六：辰之月，水之土，坤之坎，八百七十萬七千一百二十九萬三千四百四十萬。七七：日之日，火之火，艮之艮，二百一十七萬六千七百八十二萬三千五百。八七：辰之日，水之火，坤之艮，二千六百一十一萬千三百八十八萬二千。七八：日之辰，火之水，艮之坤，二千六百一十一萬一千三百八十八萬二千。八八：辰之辰，水之水，坤之坤，三萬一千三百四十五萬六千六百五十八萬四千。

"75": In the middle of the day, stone in fire, mountain in wind, the number is six million and four hundred sixty-six thousand one hundred seventy-six thousand. "85": In the middle of the morning, stone in water, earth in wind, the number is seventy-two million five thousand five hundred ninety-four thousand one hundred twenty thousand. "76": In the middle of the month, earth in fire, mountain in water, the number is seventy-two million five thousand five hundred ninety-four thousand one hundred twenty thousand. "86": In the middle of the month, earth in water, earth in water, the number is eight hundred seventy million seven hundred twenty-nine thousand three thousand four hundred forty thousand. "77": In the middle of the day, fire in fire, mountain in mountain, the number is two hundred seventeen million six thousand seven hundred eighty-two thousand three thousand five hundred. "87": In the middle of the day, fire in water, earth in mountain, the number is twenty-six million one hundred eleven thousand one hundred thirty-eight thousand eight hundred twenty thousand (the original text lacks one 'one' character). "78": In the middle of the day, water in fire, mountain in earth, the number is twenty-six million one hundred eleven thousand one hundred thirty-eight thousand eight hundred twenty thousand. "88": In the middle of the day, water in water, earth in earth, the number is three million one hundred thirty-five thousand six hundred fifty-eight thousand four hundred. The entire table ends here, with eight columns both horizontally and vertically, making a total of sixty-four sections, exactly matching the sixty-four hexagrams.

凡性之序，先列十純。十純既浹，其次降一，其次降二，其次降三，其次降四，最後五配而性備矣。始於純，終於配，天地之道也。

Sima Guang's "Potent Hidden Emptiness" arranges the order of human nature in this way: first listing ten "pure" categories. After the ten pure ones have been fully arranged, the next level is one step lower, then two steps lower, then three steps lower, then four steps lower, and finally the five "complementary" categories are used to conclude. Thus, the categories of human nature are complete. Starting from "pure" and ending with "complementary," this precisely reflects the principle of the generation of heaven and earth.

造化之一氣，即聖人之一心也。造化之氣本於發生，而聖人之心亦將以濟世也。故不兔由靜以之動，自無而入有，使萬物得以遂其生，安其業。天下之人，終不見其邇者，其故何哉？蓋造化之氣，與聖人之心，雖動而不離，雖有而不舍無，被萬物與萬民也。齊、見、役、說、戰、勞於其問，而不自覺知耳。此八卦之序，所以出乎震，而成乎艮也。謂之帝者，豈非造化之氣，與聖人之心一乎？

The vital energy of creation and transformation is the same as the sincere heart of the sage. The energy of creation and transformation originates from growth and development, while the heart of the sage is also used to relieve the suffering of the world. Therefore, both inevitably move from stillness to activity, from nothingness to existence, enabling all things to follow their natural growth and remain in their proper roles. Yet people throughout the world have never seen its form or traces. Why is this so? Because the energy of creation and transformation and the heart of the sage, although active, have not departed from their original nature; although they have entered into existence, they have not abandoned nothingness. It covers and supports all things and all people. All things and all people carry out their activities within the process described in the "Say on the Trigrams" as "moving forth from Zhen, reaching completion with Gen." They themselves are unaware of this. This is why the sequence of the Eight Trigrams begins with Zhen and ends with Gen. The "Say on the Trigrams" refers to it as "the Emperor," which clearly indicates that the energy of creation and transformation and the heart of the sage are fundamentally one. The original text says "不兔" meaning "inevitably," and "其问" meaning "among them."

#1『未殺』，原作『末殺』，據四庫本改。#2『大寒之時』，原作『大正之時』，據四庫本改。#3『臍』，原作『躋』，據四庫本改。#4『陵』，四庫本亦是，疑為『稜』字之誤。#5『沬』，原作『沐』，據四庫本改。#6『焚次』，原作『炎次』，據四庫本改。#7『至』，據四庫本補。#8『四肢』，原作『四支』，據四庫本改。#9『戶庭』，四庫本作『門庭』。

The first item: the original text reads "末杀", but it is corrected to "未杀" according to the Siku Quanshu edition. The second item: the original text reads "大正之时", but it is corrected to "大寒之时" according to the Siku Quanshu edition. The third item: the original text reads "跻", but it is corrected to "脐" according to the Siku Quanshu edition. The fourth item: the character "陵" in the Siku Quanshu edition is suspected to be a mistake for "棱". The fifth item: the original text reads "沐", but it is corrected to "沬" according to the Siku Quanshu edition. The sixth item: the original text reads "炎次", but it is corrected to "焚次" according to the Siku Quanshu edition. The seventh item: the character "至" is added according to the Siku Quanshu edition. The eighth item: the original text reads "四支", but it is corrected to "四肢" according to the Siku Quanshu edition. The ninth item: the Siku Quanshu edition reads "门庭" instead of "户庭".

#10『成坎』，原作『戊坎』，據四庫本改。#11『後易』，原作『復易』，據四庫本改。#12『辨義』，原作『辯義』，據四庫本改。#13『怛』，原作『常』，據四庫本改。#14『求』，原作『永』，據四庫本改。#15『而始』，四庫本作『而知』。#16『三』，據四庫本補。#17『被萬物與萬民也』，四庫本作『彼萬物與萬物已』。

Article 10: The original text of "cheng kan" was "wu kan," which is corrected according to the Siku Quanshu edition. Article 11: The original text of "hou yi" was "fu yi," which is corrected according to the Siku Quanshu edition. Article 12: The original text of "bian yi" was "bian yi," which is corrected according to the Siku Quanshu edition. Article 13: The character "da" in the original text was "chang," which is corrected according to the Siku Quanshu edition. Article 14: The character "qiu" in the original text was "yong," which is corrected according to the Siku Quanshu edition. Article 15: The original text says "er shi," while the Siku Quanshu edition says "er zhi." Article 16: The character "san" is added according to the Siku Quanshu edition. Article 17: The original text says "bei wanwu yu wanmin ye," while the Siku Quanshu edition says "bi wanwu yu wanwu yi."