Revolutionary governance establishes the calendar and clarifies the time.

《乾·九四·文言》曰“或躍在淵，乾道乃革”，以九四去內卦之終，而居外卦之始，為新陳代謝之際。故《雜卦傳》曰：“革去故也。”（乾二之坤五，乾成同人，坤成比。再以乾四之坤初，乾成家人，坤成屯。屯反蒙，蒙通革。家人反睽，睽上下交錯亦為革。）

The *Wenyan Zhuan* of the *Qian Hexagram* says: "Sometimes leaping in the abyss, the Qian path then changes." Because the Nine in the Fourth line has left the end of the Inner Trigram and is now at the beginning of the Outer Trigram, it is at the turning point of renewal, so the *Zagua Zhuan* says: "Change, abandoning the old." (The Second line of Qian and the Fifth line of Kui exchange positions, resulting in Qian becoming *Tongren* and Kui becoming *Bi*. Then the Fourth line of Qian and the First line of Kui exchange positions, resulting in Qian becoming *Jiaoren* and Kui becoming *Zun*. *Zun* reverses to become *Meng*, and *Meng* is connected with *Ge*; *Jiaoren* reverses to become *Kui*, and *Kui* with its upper and lower lines crossing becomes *Ge*.)

革上兌下離，《象》曰“澤中有火革，君子以治曆明時”。其所以治曆明時者，仍在九四之一爻，與乾之九四爻，實互相發明者也。（《周易折中》以革九五為成卦之主，於《彖》、《象》之義無當也。）

The Gé hexagram has Dui above and Li below. The Image Commentary says: "There is fire in the marsh, this is transformation; the superior man uses this to regulate the calendar and clearly distinguish the four seasons." Its ability to "regulate the calendar and clearly distinguish the seasons" depends crucially on the fourth line, which is mutually illuminating with the fourth line of the Qian hexagram. (The Yongzuan Zhouyi Zhizhong states that the fifth line of the Gé hexagram is the main line of the hexagram, but this does not align with the meaning of the Commentary on the Judgment and the Image Commentary.)

乾坤二策，合三百有六十，當期之日。變通在四時，時各九十日。八卦分值一年。一卦盡，得四十五日。（五日為一候，三候為一氣，八卦一爻主一氣，三氣四十五日而一卦畢。）

The combined number of策 (counting units) for the trigrams Qian and Kun is 360, exactly matching the number of days in a year. The principle of change and adaptability is reflected in the four seasons, with each season consisting of 90 days. The eight trigrams take turns to guard the year, each trigram taking charge for 45 days. (Five days make a候 (period), three候 make an气 (climate), each yao of the eight trigrams governs one气, and three气 total 45 days, completing the term of one trigram.)

乾九四已入外卦，內卦三爻之氣已盡，故曰“乾道乃革”。兌離為西南之卦，金火相乘，（四時：春木生夏火，秋金生冬水，冬水又生春木，惟夏秋為火克金，故金曰“從革”。）志不相得乃革，故《象》曰“己日乃孚”。己者土也，以坤土行離兌之間，孚而信之，革道乃成。《彖傳》曰：“天地革而四時成”。虞仲翔氏云：“曆象謂日月星辰。離為明，坎為月，離為日，蒙艮為星，（革通蒙）四動成坎離。日月得正，謂四爻動外卦變坎，成水火既濟。日月得正，曆象正而時序明矣。”王弼云：“曆數時會存乎變。”則渾括其意，義雖當，初學視之益蕩然矣。

The Nine in the Fourth of the Qian hexagram has already entered the outer trigram, and the energy of the third line of the inner trigram has been exhausted, so it is said, "The way of Heaven is transformation." The Dui and Li hexagrams belong to the western and southern trigrams respectively, and metal and fire mutually overpower each other. The sequence of the five phases is: spring wood generates summer fire, autumn metal generates winter water, and winter water generates spring wood; only between summer and autumn is fire overcoming metal. Therefore, the "Classic of Documents: Hongfan" says that the nature of metal is called "from transformation." Since the two trigrams have conflicting intentions, there is transformation, hence the hexagram "Gai" says, "Only on the day of Ji does trust arise." "Ji" belongs to the earth element, and the earth element moves between Li and Dui, thus gaining people's trust and completing the way of transformation. The Commentary on the Judgment says, "Heaven and Earth transform, and the four seasons are formed." Yu Fan (styled Zhongxiang) says, "Lixiang refers to the sun, moon, and stars. Li represents brightness, Kan represents the moon, and Li represents the sun. The mountain in the "Meng" hexagram represents the stars (the "Gai" and "Meng" hexagrams are yin-yang counterparts), and when the fourth line moves, it becomes Kan and Li. The phrase 'the sun and moon are in their proper places' means that when the fourth line moves, the outer trigram becomes Kan, and the whole hexagram becomes Water and Fire "Ji Ji." The sun and moon are each in their proper places, the Lixiang is correct, and the sequence of time becomes clear." Wang Bi says, "The reckoning of years and the conjunction of the seasons depend on transformation." This statement is only a general remark, though the meaning is correct, beginners may find it more confusing.

蓋革象下離為日，上坎為月，而九四一爻奇於其間，致日與月，不能相齊。日有餘而月不足，三為終，四連於三，歸餘於終之象，歸日之餘於終，積而成月，則閏也。積閏為章，（七閏十九年為一章）積章為蔀。（四章為一蔀，二十蔀為一遂，三遂為一首，七首為一極。詳《周髀算經》。）章蔀之名，不見於革而見於豐。豐六二、九四皆云“豐其蔀”，上六“蔀其家”，六五“來章”，蓋豐五變則成革也。孔子贊《易》，於一字一義，無不與卦爻往來脈絡貫通。非參互錯綜以求之，又烏能得其意之所在哉！（凌銳按：革五爻皆當位，惟九四一爻不當位。故曰“革而當其悔乃亡”。）

The image of the "Revolution" hexagram is formed by the lower trigram Li (Fire) representing the sun and the upper trigram Kan (Water) representing the moon, which has changed. The line nine in the fourth position is isolated in the middle, preventing the sun and moon from being properly aligned. The sun has an excess of days while the moon lacks sufficient days. The third line is called "the end," and the fourth line follows immediately after, symbolizing the transfer of the excess days to the end position. Accumulating these excess days forms a month, which is called "leap month." Accumulating leap months forms a "chapter" (a cycle of nineteen years with seven leap months), and accumulating chapters forms a "section" (four chapters make a section, twenty sections make a "sui," three "sui" make a "shou," and seven "shou" make a "ji," as detailed in the "Zhou Bi Suan Jing"). The terms "chapter" and "section" do not appear in the "Revolution" hexagram but appear in the "Brightness" hexagram: the line six in the second position and nine in the fourth position of "Brightness" both say "brightening the section," and the line six at the top says "sectioning the family," while the line six in the fifth position says "coming to the chapter." This is because the fifth line of the "Brightness" hexagram transforms into the "Revolution" hexagram. Confucius interpreted the Book of Changes, ensuring that every word and every level of meaning was connected with the flow of the hexagram lines. Without referring to mutual relationships and transformations, how could one understand his intent? (Ling Rui's note: The "Revolution" hexagram has five lines in proper position, except for the line nine in the fourth position, which is not in proper position. Therefore, the "Commentary on the Judgment" says, "Revolution in proper position, its regret will vanish.")

京氏卦納甲：乾貞子，坤貞未；乾納甲壬，內子外午；坤納乙癸，內未外丑；六子之卦，各按其所納之幹，而依乾坤之爻以為序。震貞子，坎貞寅，艮貞辰。巽從坤而內外相易，貞丑。離貞卯，兌貞己。乾子寅辰午申戌，左轉；坤未己卯丑亥酉，右行。陰陽相間，而周十二辰。

Jing Fang's method of assigning Heavenly Stems to hexagrams: The first line of the Qian hexagram is assigned to Zi, and the first line of the Kun hexagram is assigned to Wei. Qian hexagram is assigned the Heavenly Stems Jia and Ren, with the inner trigram starting at Zi and the outer trigram starting at Wu. Kun hexagram is assigned the Heavenly Stems Yi and Gui, with the inner trigram starting at Wei and the outer trigram starting at You. The remaining six hexagrams each follow their own assigned Heavenly Stems, arranging their lines according to the sequence of lines in Qian and Kun hexagrams: Zhen hexagram's first line is assigned to Zi, Kan hexagram's first line is assigned to Yin, Gen hexagram's first line is assigned to Chen. Xun hexagram follows Kun, with its inner and outer trigrams swapped, and its first line assigned to You. Li hexagram's first line is assigned to Mao, and Dui hexagram's first line is assigned to Si. Qian hexagram's lines are assigned in the order Zi, Yin, Chen, Wu, Shen, Xu, turning left in sequence. Kun hexagram's lines are assigned in the order Wei, Si, Mao, You, Hai, You, turning right in sequence. One yin and one yang alternate, exactly circling the twelve Earthly Branches.

鄭氏爻辰：乾貞於子左轉，子寅辰午申戌。間時而治六辰，與納甲同。坤貞於未亦同。乃由未而酉亥丑己卯，則與乾同為左轉。後學因此，每多歧誤。或謂康成說《易》本《乾鑿度》，故與京氏不同。然《乾鑿度》云“乾貞於十一月子，左行陽時六。坤貞於六月未，右行陰時六。歲終次從於屯蒙，屯蒙主歲。屯為陽，貞於十二月丑，其爻左行。以間時而治六辰。蒙為陰，貞於正月寅，其爻右行。亦間時而治六辰，歲終則從其次”云云。乃以六十四卦依《序卦》之次，前卦為陽，後卦為陰，每兩卦分主一歲。故三十二歲而一周，與爻辰之說不相蒙也。

Zheng Xuan's method of yao chen: The first line of the Qian hexagram is fixed at Zi, and moving left in a clockwise direction, it goes through Zi, Yin, Chen, Wu, Shen, Xu, assigning each line to one of six zhi, which is the same as Jing Fang's Najia method. The first line of the Kun hexagram is fixed at Wei, starting from the same point, but moving left in a clockwise direction as well, going through Wei, You, Hai, Chou, Si, Mao. Later scholars often made mistakes because some claimed Zheng Xuan's interpretation of the Book of Changes was based on the "Yi Wei Gan Zao Du," which is different from Jing Fang. However, the "Gan Zao Du" says: "The first line of the Qian hexagram is fixed at Zi in the eleventh month, moving left in a clockwise direction through the six yang positions; the first line of the Kun hexagram is fixed at Wei in the sixth month, moving right in a counterclockwise direction through the six yin positions. After one year, the order proceeds to the two hexagrams Zun and Meng: Zun belongs to yang, and its first line is fixed at Chou in the twelfth month, moving left, assigning each line to one of six zhi; Meng belongs to yin, and its first line is fixed at Yin in the first month, moving right, also assigning each line to one of six zhi; after one year, the order continues in sequence." This shows that the "Gan Zao Du" arranges the sixty-four hexagrams in the order of "Xu Gua," with the first hexagram being yang and the second being yin, each pair of hexagrams governing one year, completing a cycle of thirty-two years, which has nothing to do with Zheng Xuan's yao chen theory.

錢溉亭《述古錄》謂“京氏本律呂之合聲，鄭氏本月律”。其說具見《周官·太師》鄭氏注：“太師掌六律六同，（疏云：六律左旋，六同右轉）以合陰陽之聲。陽聲黃鐘子，太簇寅，姑洗辰，蕤賓午，夷則申，無射戌。子寅辰午申戌，其次與乾六爻左旋同也。陰聲大呂丑，應鐘亥，南呂酉，林鐘未，小呂己，夾鐘卯，則丑亥未酉己卯，其次與坤六爻不相合矣。鄭氏以律呂相生為主，則六律六同皆左旋。以律為夫，以呂為婦。婦從夫，故皆左旋。”是京氏之納甲，與《乾鑿度》同主合聲。而鄭之爻辰，則主相生，非本於《乾鑿度》者也。

Qiantang (nominated Gaiting) in his "Shu Gu Lu" said: "Jing Fang's theory is based on the harmonious sounds of the pitch pipes, while Zheng Xuan's theory is based on the monthly pitch pipes." This complete explanation appears in the Zheng Xuan commentary on "The Rites of Zhou · Spring Officials · Tai Shi": "The Tai Shi is in charge of the six pitch pipes and the six same pitch pipes (Jia Gongyan's commentary says: the six pitch pipes turn to the left, and the six same pitch pipes turn to the right), used to harmonize the sounds of yin and yang. The yang sounds are Huangzhong paired with Zi, Taicuo paired with Yin, Guxi paired with Chen, Rui Bin paired with Wu, Yizhe paired with Shen, and Wuyue paired with Xu. The order of Zi, Yin, Chen, Wu, Shen, Xu corresponds to the six yao of the Qian hexagram turning to the left. The yin sounds are DaLv paired with Chou, Yingzhong paired with Hai, Nanlv paired with You, Linzhong paired with Wei, XiaoLv paired with Si, and Jiazhong paired with Mao. The order of Chou, Hai, Wei, You, Si, Mao does not correspond to the six yao of the Kun hexagram turning to the right. Zheng Xuan takes the mutual generation of the pitch pipes as the main principle, so the six pitch pipes and the six same pitch pipes all turn to the left. This is because the pitch pipes are regarded as the husband and the same pitch pipes as the wife, with the wife following the husband, hence turning to the left." From this, we can see that Jing Fang's Najia and the "Qian Zao Du" both focus on "harmonious sounds," while Zheng Xuan's yao chen focuses on "mutual generation," and is not based on the "Qian Zao Du."

辛齋按：陰從於陽，陰陽之體也。河圖一三七九、二四六八皆左行者是也。（若陰陽分言，則陰逆陽順。陽自一三五七九，而陰則從四起，為四二十八六。故五位相得而各有合。若如舊說，則五與十無相合之理。詳見《易數偶得》）陽左旋陰右轉，陰陽之用也。洛書之一三九七左旋、二四八六右轉是也。非順行不能相生，非逆行不能相合，《易》之體用無不如是，明乎此，則聚訟不決之懸案，可片言而斷矣。

Xin Zhai says: Yin follows Yang, which is the "body" of yin and yang. In the Yellow River Chart, the generating numbers and the completed numbers are paired in pairs, with one, three, seven, and nine paired with two, four, six, and eight, all moving to the left, which is the reason for this. (If yin and yang are considered separately, then yin moves in reverse while yang moves in regular order: Yang is arranged as one, three, five, seven, nine, while Yin starts from four and proceeds as four, two, ten, eight, six, so that the five directions are paired in pairs and each has its match. If following the traditional arrangement, five and ten would not be compatible. See my work "Accidental Insights on the Changes".) Yang rotates to the left while Yin rotates to the right, which is the "use" of yin and yang. In the Luo Writing, one, three, nine, and seven rotate to the left, while two, four, eight, and six rotate to the right, which is the reason for this. Without moving in the proper direction, mutual generation cannot occur; without moving in the reverse direction, mutual compatibility cannot be achieved. The "body" and "use" of the Changes are all like this. Once this is understood, those cases that are in dispute can be decided with one sentence.

或問：既如子言，則京氏既主合聲矣，何以坤之未己卯丑亥酉，又與陰聲之丑亥酉未己卯不同也？曰：此即洛書七與九、二與八易位之理也。故巽之六爻則為丑亥酉未己卯矣。此中玄妙，具有至理。神而明之，非言所能盡焉。

Someone asked: According to your explanation, since Jing Fang advocates 'harmonizing tones,' then why do the hexagrams of the Kūn hexagram, which include the earthly branches of Wei, Si, Mao, Chou, Hai, and You, differ from the yin tones of Chou, Hai, You, Wei, Si, and Mao? The answer is: This is precisely the principle of the Luo Writing where the numbers seven and nine, and two and eight, exchange positions. Therefore, the order of the six lines of the Xun hexagram is exactly Chou, Hai, You, Wei, Si, and Mao. The subtlety here has extremely profound reasons, which can only be understood by individuals through inner realization, and cannot be fully expressed in words.

或問鄭康成氏爻辰說《易》，以星象證爻辭，而原注已佚。從《禮》注與《乾鑿度》注搜輯者，寥寥無幾。近世戴棠氏，撰《鄭氏爻辰補》。而全《易》三百八十四爻，各取《甘石星經》及《開元占經》所載諸星名，以印證爻辭，無不恰合。詎伏羲之播爻，文王之繫辭，果一一仰觀天文以取象乎，何巧合若是？

Someone asked: Zheng Xuan used the theory of yao chen to explain the Book of Changes, using celestial phenomena to verify the line statements. However, his original annotations have been lost, and only a few fragments have been collected from his commentaries on the Rites and his annotations on the Qian Zao Du. Recently, Dai Tang wrote the "Supplement to Zheng's Yao Chen," in which he matched each of the 384 lines of the Book of Changes with the names of stars recorded in the Gan Shi Star Classic and the Kaiyuan Treatise on Astrology, and found that they all coincided perfectly. Could it be that Fuxi arranged the line diagrams and King Wen composed the line statements of the upper trigrams by observing the heavens and taking their images? Otherwise, how could such a perfect coincidence occur?

曰：伏羲畫卦之時，文字未作，器用未備，又何有星名？蓋一畫開天，奇偶以生。仰觀俯察，法象於天地，變通乎四時。陰陽剛柔，動靜變化，而洽於造化數理之自然。而天地之運行，人物之遞演，自不能出此常軌之外。故先天而天不違。至黃帝以黃鐘定律，準度量，定權衡，悉本於伏羲之卦。而窺天測地，定日月星辰以紀歲時。

The response was: When Fuxi drew the trigrams, writing had not yet been invented, and utensils were not yet complete, how could there be the names of the star mansions? He merely drew the first trigram to open up the heavens, from which the odd and even lines originated. He looked up to observe the celestial phenomena and looked down to examine the geographical features, taking inspiration from the images of heaven and earth, and adapting to the order of the four seasons. The yin and yang, the firm and the flexible, the movement and stillness, all harmonize with the natural principles of creation and numbers. The operation of heaven and earth, and the successive transformation of human affairs and all things, have always followed this constant pattern. Therefore, it is said, "Before heaven, heaven does not violate." Later, the Yellow Emperor used the Huangzhong to establish the musical scale, calibrated measures and weights, and established standards, all based on Fuxi's trigrams. Afterwards, people explored the heavens and earth, determined the sun, moon, and stars to mark the passage of time.

然天廣無垠，既以象限立儀（象限儀分圓周為四，即法乎四象。儀者，分陰分陽，即法乎兩儀。），以分躔度次舍，而不可無以名之以資識別也。於是各按八卦之象數以定其名。故天星之名，大都出自卦象，非卦象之強合星名也。鄭氏爻辰以星名證其爻義，已不免倒果為因。必逐爻求象於星，而以爻辭附會之，以期或有一字一義之合；無論其未必盡合，即合矣，於經義仍未必有所發明。是亦可以不必矣。

But the heavens are vast and boundless; having already established a system using the quadrant instrument (which divides the circumference into four parts, thus following the principle of the Four Symbols; "instrument" refers to dividing yin and yang, thus following the principle of the Two Principles), it distinguishes the degrees of the sun and moon's movement and the sequence of the Twenty-Eight Mansions (where the sun and moon temporarily halt in their course). Therefore, it is necessary to have names for identification. Hence, they are named according to the numerical symbolism of the Eight Trigrams. Therefore, the names of the star mansions in the heavens mostly originate from the trigrams, and it is not the case that the trigrams are forced to conform to the names of the stars. Zheng Xuan used the names of the stars to verify the meaning of the lines, which already involves reversing cause and effect. If one insists on seeking symbolic correspondences from the star mansions for each line, and then force the line statements to fit, hoping for a one-to-one correspondence—regardless of whether such correspondences can actually be found, even if they can, it does not necessarily contribute to the elucidation of the classic's meaning. Therefore, such an approach is certainly unnecessary.

《易·彖傳》言“陰陽上下往來”，後儒或主卦變，或主錯綜，（此指來氏之所謂錯綜）眾論紛若，莫衷一是。而卦變之例，荀虞以下既各不同，而同一虞《易》，其為圖也又參差不一。朱子既圖卦變，又取《彖傳》之言往來者十九卦，編為歌訣。然與其圖，已不相符合。且《彖傳》之言往來上下者，亦不僅此十九卦。故證以經文，參諸卦象，自以主兩卦之一往一來者，（即來氏錯綜）其說較優。

The Commentary on the Judgment in the Book of Changes speaks of "yin and yang moving up and down." Later Confucian scholars have proposed different interpretations, some advocating the use of "changing hexagrams" and others advocating "interchange and reversal" (here referring to the concept of interchange and reversal as discussed by Lai Zhide). There are many conflicting views, and no consensus has been reached. As for the method of changing hexagrams, from Xun Shuang and Yu Fan down to other scholars, their approaches have varied greatly. Even within Yu Fan's own interpretation of the Book of Changes, later generations have drawn different diagrams. Zhu Xi both drew a diagram of changing hexagrams and compiled a mnemonic verse based on the nineteen hexagrams from the Commentary on the Judgment that discuss movement. However, the verse does not align with his own diagram. Moreover, the Commentary on the Judgment discusses movement up and down not only in these nineteen hexagrams. Therefore, using the text to verify and referring to the hexagrams for examination, it is still more reasonable to argue based on the mutual reversal of two hexagrams, one moving and one returning (which is what Lai Zhide called interchange and reversal).

蓋文王之《易》，本以兩卦反覆一往一來。則《彖傳》以釋《彖》，自必於此兩卦推勘其義，理至當也。上卦為外為上為往，下卦為內為下為來。（此卦之下即彼卦之上，此往則彼來，彼上則此下。）上卦二陽一陰者，陰上進而往。二陰一陽者，陽上進而往。下卦之為來亦然。

The original "Book of Changes" by King Wen was arranged by repeatedly reversing two trigrams, with movement going and coming. Since the "Commentary on the Judgment" explains the hexagram statements, it naturally seeks meaning between the two reversed trigrams, which is the most reasonable approach. The upper trigram belongs to the outside and is "going," while the lower trigram belongs to the inside and is "coming" (the lower trigram of this hexagram is the upper trigram of the other, so when one goes, the other comes; when one is above, the other is below). If the upper trigram has two yang lines and one yin line, the yin line moves upward and is considered "going"; if it has two yin lines and one yang line, the yang line moves upward and is considered "going." The situation for "coming" in the lower trigram follows the same pattern.

故《孔疏》云“凡言往來者皆據異類而言。”若三陰三陽之卦，則上下並言。泰否之兼言往來，咸蠱之兼言上下，噬嗑賁渙節言來言上言分是也。四陰四陽之卦，則以一陰一陽之在上下者言，晉升無妄大畜訟需是也。二陰二陽，則以陰陽之在上卦者言，賽解鼎睽是也。五陰五陽者，以一陰一陽言，復姤是也。似較卦變之茫無一定者，差可依據。

Therefore, Kong Yingda in The Correct Meaning of the Zhou Changes says: "Whenever there is talk of coming and going, it refers to the yao that differs from the majority." If the hexagram consists of three yin and three yang lines, then both the upper and lower trigrams are mentioned: The Tai and the Pi hexagrams both discuss coming and going, the Xian and the Gu hexagrams both discuss upper and lower, and the Shihe, Ben, Huan, and Jie hexagrams discuss coming, upper, and division, all belonging to this category. If the hexagram consists of four yin and four yang lines, then the yao in the upper or lower trigram is referred to: the Jin, Sheng, Wuwang, Daxu, Song, and Xu hexagrams are examples. If the hexagram consists of two yin and two yang lines, then the yao in the upper trigram is referred to: the Jian, Jie, Ding, and Kui hexagrams are examples. If the hexagram consists of five yin and five yang lines, then the single yin or yang line is referred to: the Fu and Guu hexagrams are examples. This is more grounded than the indeterminate nature of the theory of hexagram transformation.

然此但以上下兩象而言，間有以專重之一爻為主者，則又不在此例。乾坤為《易》之門，往來者必於此門。二陽一陰者坤體，而陰往來上下於其間也。二陰一陽者乾體，而陽往來上下於其間也。上下無常，剛柔相易，原非可執一例以求之。但初學者不可不先求一隅之可舉者以為根據耳。

However, this is only referring to the images of the two upper and lower trigrams; there are also cases where a particular important line is the focus, which are not included in this category. Qian and Kun are the gateways of the Book of Changes, and movement must pass through this gate. For a trigram with two yang lines and one yin line, the yin line is the main element, moving up and down within it. For a trigram with two yin lines and one yang line, the yang line is the main element, moving up and down within it. Since movement up and down is ever-changing, and the qualities of yang and yin constantly shift and transform, it is naturally impossible to follow a fixed rule. But for beginners, they cannot avoid using a concrete example as a reference.

《周禮·太卜》：“掌三《易》之法，《連山》、《歸藏》、《周易》。其經卦皆八，其別卦皆六十有四。”段若膺云：“《連山》、《歸藏》、《周易》三《易》，每《易》有八，每八分為六十四，故云其別卦。經卦即乾坤震巽坎離艮兌，別卦即因而重之之六十四卦也。”

The Zhou Li · Chun Guan · Tai Bu says: "The three books of Yi, namely the Lian Shan, Gui Cang, and Zhou Yi, all use the method of divination with yarrow stalks. They all have eight primary trigrams and sixty-four derived trigrams." Duanyucai (style name Ruoying) says: "The Lian Shan, Gui Cang, and Zhou Yi each have eight primary trigrams. Each set of eight trigrams is further combined in pairs to form sixty-four derived trigrams, which is called 'derived trigrams.' The primary trigrams are Qian, Kun, Zhen, Xun, Kan, Li, Gen, and Dui. The derived trigrams are formed by stacking two primary trigrams on top of each other to create the sixty-four trigrams."

楊用修《丹鉛錄》云：“別當作□。從重八。八八六十四，故云別卦。”蓋別訓分，八亦訓分。□從八八，謂分而又分。八八為六十四，正合八卦重為六十四卦之義。可見古人修辭之學，其用字之精當，迥非後人所可及也。

Yang Shen (style name Yongxiu) in his "Danqian Lu" said: "The character 'bie' should be written as '□', composed of two 'ba' characters superimposed. Since eight eights make sixty-four, it is called 'bie gua'. " Originally, the character 'bie' means to divide, and the character 'ba' also means to divide. The character '□' is made up of two 'ba's, meaning divided again and again. Eight times eight equals sixty-four, which exactly corresponds to the meaning of the eight trigrams being superimposed to form the sixty-four hexagrams. This shows that the rhetorical skills of ancient people were precise and appropriate in their word choice, far beyond what later generations can match.

《說卦傳》：震其究為健為蕃鮮，巽其究為躁卦。健為乾，蕃鮮指巽。躁卦即震也。考其他六卦，皆不稱究，獨於震巽兩卦言之何也？物有始有壯有究，震巽陰陽變化之始也。震以一陽變於坤，坤成震而乾成巽。原始要終，可得其究。至於坎離，為陰陽之壯，又得乾坤之中，不至極於一偏。艮兌已為陰陽之究，所謂其上易知。故艮成言，兌說言，皆無須推極其究者也。

The *Sayings on the Hexagrams* says: When the *Zhen* trigram is examined to its extreme, it becomes "strong" and "abundant and bright"; when the *Xun* trigram is examined to its extreme, it becomes "restless trigram." "Strong" refers to *Qian*, "abundant and bright" refers to *Xun*, and "restless trigram" refers to *Zhen*. The other six trigrams do not mention "examination," but only *Zhen* and *Xun* do. Why is this so? All things have three stages: beginning, flourishing, and culmination. *Zhen* and *Xun* are precisely the beginning of yin and yang transformation: *Zhen* is when one yang enters *Kun*, and *Kun* thus becomes *Zhen*; *Qian* thus becomes *Xun*. By tracing the origin and seeking the end, one can see its "culmination." As for *Kan* and *Li*, they are the flourishing stage of yin and yang, and they have the middle lines of *Qian* and *Kun*, so they do not reach an extreme. *Gen* and *Dui* have already reached the culmination of yin and yang, which is what the *Great Treatise* calls "easily known." Therefore, the *Sayings on the Hexagrams* says "it is fully expressed in *Gen*" and "it is explained in *Dui*," and there is no need to further examine their culmination.

惟巽之究為躁，似與其木性相反。而震之究為健，則為復其本性。為蕃鮮則為極其功用，其究同而究不同，則陰陽之分際然也。蓋陽為萬物之本，（天地五十五數，陽奇陰隅，而陰陽合數則仍為奇。一六合為七，二七合為九，三八合為十一，四九合為十三，總數五十五皆奇也。故曰陰必歸陽。）非若陰之為用有限也。

The trigram Xun reaches its extreme and becomes "zao" (restlessness), which seems to contradict its inherent gentle and flexible nature as wood. In contrast, the trigram Zhen reaches its extreme and becomes "jian" (strength), which restores its original yang nature. "Fan xian" (abundance and brightness) represents the full expression of its function. The same character "jiu" (to investigate to the extreme) leads to different results, which is due to the difference between yin and yang. Yang is the fundamental principle of all things (the total number of heavenly stems and earthly branches is fifty-five, with yang being odd numbers and yin even numbers; however, the combination of yin and yang still results in an odd number: one combined with the six harmonies makes seven, two combined with seven makes nine, three combined with eight makes eleven, four combined with nine makes thirteen, and the total number fifty-five is also odd, thus yin must return to yang). Unlike yin, whose function is limited, yang's function is boundless.

或問：《說卦傳》“坎為血卦”，《荀氏易》作“血衄”。說者謂血為人身之水，以病故衄然歟？曰：否。坎為血卦，猶離之為乾卦也。六子惟坎離得乾坤之中，特稱卦以別之。離為乾體，故曰“乾卦”。坎為坤體，故曰“血卦”。血坤也。《坤·上六》曰“其血玄黃”，《傳》曰“猶未離其類也，故稱血焉”。以見血為坤之類，是坎之稱血卦，與離之稱乾卦為例正同，未可以血衄改之也。

Someone asked: The "Commentary on the Hexagrams" says "Kan is the Blood Hexagram," but the "Xunshi Yi" of Xun Shuang's school writes it as "blood and nosebleed." Interpreters of the classics think that blood is the water in the human body, and nosebleeds occur when one is sick, so Kan also governs blood. Is this interpretation correct? Answer: No. The term "Blood Hexagram" for Kan is consistent with the term "Dry Hexagram" for Li. Among the six sub-hexagrams generated by Qian and Kun, only Kan and Li inherited the middle line from Qian and Kun, so they are specially named with the word "hexagram" to distinguish them from the other four sub-hexagrams. The outer two lines of Li are yang, and the middle line is yin, so its essence belongs to Qian, hence it is called the "Dry Hexagram." The outer two lines of Kan are yin, and the middle line is yang, so its essence belongs to Kun, hence it is called the "Blood Hexagram" — "blood" refers to Kun. The "Yao Ci" of the "Upper Sixth" line of the "Kun Hexagram" says "its blood is black and yellow," and the "Wenyan Zhuan" explains that "it has not yet separated from its category, hence it is called blood." This shows that blood belongs to the category of Kun. Therefore, the naming of Kan as the "Blood Hexagram" follows the same example as Li being called the "Dry Hexagram," and it is not correct to change it to "blood and nosebleed" as in the "Xunshi Yi."

或曰：離之為乾卦，乾讀若干，乃燥萬物者莫熯乎火，故曰乾卦。與乾坤之乾，音訓其可通乎？曰：鄭注云乾當為乾，陽在外作幹正也。虞《易》亦同。而張湛雲乾音乾，則音固可通。《易》之用字，恆以形聲相類者，分見互用，以相鉤貫。焦氏《通釋》言之詳矣。而《說卦》言象，尤往往舉甲以概乙，又或對舉相互以見意者。如乾為圓，則坤之為方可知。巽為臭，則震為聲可知。

Someone asked: The trigram 'Li' is called 'Qian', and the 'Qian' here should be read as 'Gan', based on the meaning in the 'Shuo Gua Zhuan' that 'the thing that dries all things is none other than fire', meaning fire can dry out all things, so it is called 'Qian' trigram. However, can the 'Qian' in 'Qian and Kun' be considered as the same in pronunciation and meaning? Answer: Zheng Xuan in his commentary said that 'Qian' should be read as 'Gan', with the yang line outside, and the character 'Gan' is considered correct. Yu Fan's commentary on the 'Zhou Yi' is also the same. However, Zhang Zhan of the Jin dynasty said that 'Gan' and 'Qian' have the same pronunciation, indicating that the pronunciation has always been the same. The use of characters in the 'Zhou Yi' often separates similar characters with similar radical and phonetic components, using them interchangeably to connect and link them, as explained in detail by Jiao Xuan's 'Yi Tong Shi'. As for the 'Shuo Gua Zhuan' discussing the images of the trigrams, it often uses one character to represent another, or pairs them to show their meanings: once it says 'Qian represents roundness', 'Kun represents earth', we can infer the rest; once it says 'Xun represents smell', 'Zhen represents sound', we can also infer the rest.

此以離為乾卦，以與坎之血卦相對。貞者事之幹也。乾貞在坎，而著乾之義於離，離其類為血，而存血之文於坎，交互見意，錯綜成文，可謂極天下之至精至變者矣！故《易》之為書，廣大悉備。孔子贊《易》之文，悉與相稱。一名一字，於形聲訓義，均鉤深致遠，無不各有精義存乎其間，非言語所能形容也。舉一三反，是在讀者之神而明之。

Here, the trigram Li is called "Qian" (Heaven), which is meant to contrast with Kan's "Xue" (Blood) trigram. The "Wenyan" section of the "Qian Hexagram" says, "Zhen refers to the main stem of a matter," where "Zhen" signifies the main part of something. The "Zhen" position of Qian falls on Kan (in the Later Heaven arrangement, Kan is located in Due North, which is precisely where Qian's "Zhen" position is). Yet the meaning of "dry" is assigned to Li; Li's category is originally associated with blood, but the character "blood" is preserved in Kan. The meanings are interchanged and interwoven, creating a complex and intricate text, truly exhausting the most subtle and changeable principles in the world. Therefore, the book of The Zhou Changes is vast and comprehensive, covering everything. Confucius' commentary on the Changes is also in harmony with it: each term and each character is deeply explored in both sound and meaning, each containing profound significance, beyond the reach of words. By understanding one, one can infer the rest, and it is up to the reader to grasp the meaning intuitively.

或問《說卦》之取象，震坎皆言馬，合之乾共三卦。巽為木，而坎於其木也堅多心，離其於木也為科上稿，艮於其木也為堅多節，凡四卦。乾又為木果，而震為蒼筤竹，又其於稼也為反生，亦木之類。何馬與木之取象獨多也？

Someone asked: The "Sayings on the Trigrams" mentions the image of a horse in both Zhen and Kan, and also mentions it in Qian, making a total of three trigrams that use the image of a horse. Xun represents wood, and Kan says "its image for wood is firm with many hearts" (the wood is hard with many knots), Li says "its image for wood is hollow in the middle and withered at the top" (the middle is hollow and the top is dry), and Gen says "its image for wood is firm with many knots" (the wood is hard with many knots), making a total of four trigrams that refer to wood. Qian also represents fruit trees, Zhen represents young bamboo, and Zhen also says "its image for crops is reverse growth" (the seeds of grain sprout in reverse), which also belongs to the category of wood. Why does the imagery of the eight trigrams focus so much on horses and wood?

曰：此為切於人生日用者言之。行者以馬，居者以木，為用廣，故取象多也。又周以火德王，馬為離午之精，行地無疆，周乎天下。故乾坤坎離皆言馬。伏羲以木德王，木者火之母也。損上益下，木道乃行。天施地生，其益無方者木也。故《易》言馬與木為獨多也。

This is talking about things most closely related to the daily lives of the people. Travel depends on horses, and dwellings depend on wood, both of which have the widest range of uses, so they are represented in many symbolic forms. Moreover, the Zhou dynasty ruled with the virtue of fire, and horses are the essence and qi of the fire element, corresponding to the午 position. The Commentary on the Judgment of the坤卦 says, "moving on the earth without boundaries," which means being able to travel everywhere, so the four trigrams Qian, Kun, Kan, and Li all mention horses. Fuxi ruled with the virtue of wood, and wood is the mother of fire; the Commentary on the Judgment of the益卦 says, "reducing from above to benefit below," "the way of wood is then established," and also says, "heaven gives, earth produces, its benefit has no limits." The thing capable of bearing the responsibility of nurturing all things without limit is wood. Therefore, the Zhou Changes speak extensively about horses and wood.

漢《易》之存於今者，惟虞氏注未盡亡佚。經勝清惠定宇、張惠言二氏之搜輯演繹，儼然首尾貫串，而規模畢具矣。顧宋學家及同為漢學之馬鄭者，悉力攻擊之。或謂其納甲之說，以魏伯陽《參同契》而擅改聖經之卦位；或謂其之正之說，全背《彖》、《象》傳義。王氏《經義述聞》，辯駁尤甚。

Han dynasty commentary on the Book of Changes has survived to the present day only in the works of Yu Fan. Through the efforts of Zhang Huiyan and Hui Dong of the Qing dynasty in collecting and deducing, Yu's commentary on the Book of Changes has become coherent and has a substantial framework. However, scholars of the Song dynasty school, as well as those following the Han school who revered Ma Rong and Zheng Xuan, all strongly criticized it. Some claimed that his theory of "Najia" was borrowed from Wei Boyang's Dan Classic, using alchemical correspondences, and that he arbitrarily altered the positions of hexagrams in the sacred classics. Others said his theory of "zhizheng" completely contradicted the meaning of the Commentary on the Judgment and the Image Commentary. Among them, Wang Yinzhi's refutation in his work "Jingyi Shuwén" was the most intense.

略謂仲翔發明卦爻，多以之正為義。陰居陽位為失正，則之正而為陽。陽居陰位為失正，則之正而為陰。蓋本《彖傳》之言位不當者而增廣之，變諸卦失正之爻以歸於既濟，可謂同條共貫矣。然經云位不當者，惟論爻之失正，以決其悔吝之由，示觀象玩辭、觀變玩占者，知所警耳。

Wang's general meaning is that Yu Fan (style name Zhongxiang) explained the hexagram lines by using the concept of 'returning to the correct position'—a yin line in a yang position is considered incorrect and should change to a yang line to return to correctness; a yang line in a yin position is considered incorrect and should change to a yin line to return to correctness. This is an extension of the Commentary on the Judgment's statement 'position is not appropriate.' It applies the idea of correcting incorrect lines to all hexagrams, changing all incorrect lines to the pattern of the hexagram Ji Ji, where all six lines are in their proper positions, making the reasoning coherent. However, the 'position is not appropriate' mentioned in the classics refers only to a single line being incorrect, used to determine the origin of regret and hardship, serving as a warning for those observing phenomena and interpreting divination.

夫爻因卦異，卦以爻分，各有部居，不相雜廁。若爻言初六、六三、六五，而易六以九；言九二、九四、上九，而易九以六言，則爻非此爻，卦非此卦矣。虞氏以為變而之正，實自失其本體，不且紊亂而無別乎？遍考《彖》、《象》傳文，絕無以之正為義者。既已無所根據，乃輒依附於經之言貞者，而以之正解之。

The statements of the lines vary according to the hexagram, and the hexagrams are distinguished by their lines, each having its own position, and they cannot be mixed up. If the line statements clearly mention initial six, sixth three, or fifth six, yet one changes 'six' to 'nine'; or if it mentions nine two, nine four, or top nine, yet one changes 'nine' to 'six', then the line is no longer that line, and the hexagram is no longer that hexagram. Yu Fan thought that 'changing to the correct' was the meaning, but in reality he lost the original essence, is it not causing confusion and disorder in the hexagrams and lines, making them indistinguishable? A thorough examination of the texts in the Commentary on the Judgment and the Image Commentary shows that there is not a single instance where 'changing to the correct' is used as a meaning. Since there is no basis for this, he simply attached himself to instances where the character 'zheng' appears in the classic text, and used 'changing to the correct' to explain everything.

如注“坤利牝馬之貞”，云“坤為牝，震為馬。初動得正，故利牝馬之貞”。注“安貞吉”，云“復初得正故貞吉”。案《彖》曰“牝馬地類，行地無疆，柔順利貞”，又曰“安貞之吉，應地無疆”，皆以坤純陰言之，未嘗以為初爻之正也。且如其說，文王於復卦繫於“利牝馬之貞”，不更合耶？何為紛紛然由此之彼，乃以彼釋此耶？以下逐卦指駁，斥謂盡亂聖人之成法。

For example, in commenting on the Hexagram Statement of the坤 (Earth) hexagram, "Beneficial to the faithful mare," Yu Fan said, "Kun represents the female, Zhen represents the horse, and the first line moves to become correct, hence it is beneficial to the faithful mare." In commenting on "Steadfastness brings good fortune," he said, "It transforms into the Fu hexagram, and the first line becomes correct, hence steadfastness brings good fortune." However, the Commentary on the Judgment of the坤 hexagram clearly states, "The female horse is of the earth kind, moving on the earth without boundaries, flexible, smooth, and faithful," and also says, "The good fortune of steadfastness is due to the earth having no boundaries." These statements are based on the overall nature of the pure yin lines in the坤 hexagram, never considering the first line changing to become correct. Moreover, according to Yu's interpretation, King Wen would have been better off directly associating "Beneficial to the faithful mare" with the Fu hexagram, which would have been more appropriate. Why go through the trouble of using one hexagram to explain another? Later scholars such as Wang criticized Yu's annotations for thoroughly disrupting the established methods of the sages.

又駁其旁通之說，謂《易》《彖》及《大象》惟取義於本卦。健順動巽陰明止說之德，天地風雷水火山澤之象，無不各如其本卦，義至明也。虞仲翔以卦之旁通釋之，雖極竟彌縫，究與《經》相牴牾。

Wang's school further refutes Yu Fan's theory of "parallel transmission," arguing that the Commentary on the Judgment and the Great Image in the Zhou Changes only derive meaning from the primary hexagram, taking the eight virtues of strength, smoothness, movement, entering, sinking, adhesion, stillness, and joy, and the eight natural phenomena of heaven, earth, wind, thunder, water, fire, mountain, and marsh, none of which fail to correspond with the primary hexagram. The meaning is originally very clear. Yu Fan, however, uses the "parallel transmission" of complete reversal of yin and yang between two hexagrams to explain it. Although he tries hard to reconcile the theory, it ultimately conflicts with the text of the classic.

如《履·彖》曰“履，柔履剛也”，虞曰“坤柔乘剛，謙坤藉乾，故柔履剛”。又“履帝位而不疚”，虞曰“謙震為帝，坎疾為病，至履帝位坎象不見，故履帝位而不疚”。此謂履與謙通，謙上體有坤，互體有震坎也。然《經》云說而應乎乾，謂下兌上乾也。若取義於下艮上坤之謙，則是止而應乎坤矣，豈說而應乎乾之謂乎？亦逐卦指駁，謂《彖》、《象》釋《易》也，不合於《彖》、《象》，尚望其合於《易》乎？

For example, the Commentary on the Judgment of the "Gua of Walking" says, "Walking, it means the softness walking upon the firmness." Yu Fan interprets this as "the yao of the softness in the坤 (Earth) trigram is riding upon the yao of the firmness, and the Gua of Humility, which is坤 on top, borrows from the乾 (Heaven), so it is called softness walking upon firmness." The Commentary on the Judgment also says, "Walking upon the imperial throne without guilt." Yu Fan interprets this as "the Zhen (Thunder) trigram in the Gua of Humility represents the emperor, and the Kan (Water) trigram represents illness. When reaching the position of the imperial throne, the Kan image disappears, so walking upon the imperial throne brings no pain." These are all explanations that the Gua of Walking and the Gua of Humility are connected through their mutual trigrams, since the Gua of Humility has the坤 trigram on top and contains Zhen and Kan in its interacting trigrams. However, the Commentary on the Judgment of the Gua of Walking clearly states, "It is said and corresponds to the乾 (Heaven)." This refers to the lower trigram being Dui (Lake) and the upper trigram being Qian (Heaven). If instead we take the meaning from the Gua of Humility, which has the lower trigram as Gen (Mountain) and the upper trigram as坤 (Earth), it would become "Stopping and corresponding to the坤 (Earth)." How could this still mean "It is said and corresponds to the乾 (Heaven)"? Wang also criticizes each hexagram in this way, saying that the Commentary on the Judgment and the Image Commentary were originally meant to explain the Zhou Changes. If even the Commentary on the Judgment and the Image Commentary do not align, how can we expect them to align with the Zhou Changes?

王氏之說，辨而詳矣。然六爻發揮旁通情也，辭也者各指其所之，而變卦以不當位之爻變而當位，又古今說《易》家所不廢，則旁通與之正，要不可謂非《易》中之一例。第必執此一例以概全《易》，其所不通者亦必強而通之，不得不謂虞氏之一蔽。必如王氏之說，則《彖》、《象》之外，更不容有一義之引伸比附，則廣大悉備之《易》象，恐學者更未易明也。

Wang Yinzhi's rebuttal is thorough and clear. However, the original text of the Wenyan section of the Qian hexagram says, "The six lines unfold, expressing the circumstances of the world." The Xici section also states, "The words each refer to their respective meanings." When changing hexagrams, moving an improperly positioned line to a proper position is a method that has never been abandoned by scholars throughout history. This shows that "bypassing" and "returning to the correct position" are indeed part of the structure of the Zhouyi. However, if one insists on using this structure to explain the entire Zhouyi, forcing explanations where they do not fit, then it cannot be denied that Yu Fan's interpretation has obscured the truth. But if one insists on Wang's view, allowing only interpretations from the Tuanchuan and Xiangchuan, and forbidding any further analogy or inference, then the vast and comprehensive imagery of the Yi would become even more difficult for scholars to understand.

況《彖》、《象》所釋，或含意待申，或僅舉一隅，或專重一事者，其例正多。故孔子曰“觀其彖辭則思過半矣”，又曰“書不盡言”，未嘗以《彖》、《象》所釋為已盡，更不容他人置喙也。

Moreover, the explanations in the Commentary on the Judgment and the Image Commentary are sometimes waiting for later scholars to elaborate on their meanings, sometimes only mention a single aspect, and sometimes focus on a particular matter. Such situations are quite common. Therefore, Confucius said in the Great Treatise, "Observing the judgment statements, one can think through more than half of it," and also said, "Written words cannot fully express speech." This shows that he never thought the explanations in the Judgment and Image Commentaries had exhausted all meanings, still less did he prohibit others from adding their own comments.

虞仲翔生於易代之際，世道人心，江河日下。說《易》大師，有曲說阿時以聖經為羔雁者矣。（如荀慈明輩是也。）故憤時疾俗，或不免有過激之論。如以坤初為“子弒其父臣弒其君”，謂坤陰漸而成遁弒父，漸而成否弒君，於象義亦未允當，（坤消至剝而乾象滅迷不復，常大變以其國君，凶方為家滅國滅之象。近書《周易指》已辨正之。）要皆有為而言。

Yu Fan was born during a period of dynastic change, when the world and people's morals were deteriorating day by day. Among the masters of the Zhou Changes at that time, some distorted the meaning of the classics and catered to the prevailing situation, using the sacred scriptures as gifts to gain favor and advancement (people like Xun Shuang were among them). Therefore, he was cynical about the world and his criticisms often went to extremes. For example, he interpreted the first line of the Kun hexagram, "Walking on frost, firm ice," as "a son killing his father, a minister killing his sovereign." He claimed that the gradual increase of the yin line in the Kun hexagram leading to the Duan hexagram represented a son killing his father, and the gradual increase leading to the Pǒ hexagram represented a minister killing his sovereign. This interpretation in terms of symbolic meaning is indeed not appropriate (according to reason, the yin should gradually decrease the yang until the Bo hexagram, with the yang image disappearing completely and not returning, thus producing the ominous image of a great change in the sovereign, the destruction of the state and family. Modern scholar Du Mu Guo Hu in his work "Zhou Yi Zhi" has already corrected this). However, what he said was all motivated by a purpose.

其納甲消息，皆與荀氏升降之說針鋒相對，意尤顯然。以之正立論，明天地大義。以既濟定也為歸，期人心之不正者胥歸於正，於是乎世亂或可少定。此虞氏之或苦心孤詣，千載而下猶皦然可見者也。

He discussed Najia and the concept of transmission and reception, constantly opposing Xu Shuang's theory of rising and falling. His intention was especially clear. He used the term "zhizheng" to argue for elucidating the great principles between heaven and earth; taking the six lines of the hexagram Ji Ji and establishing their respective positions as the ultimate goal, he hoped that all people with unrighteous hearts would return to the right path, so that the chaotic world might be somewhat stabilized. This was precisely Yu Fan's sincere and painstaking effort, and even a thousand years later, it remains clearly visible.

嗚乎！今之時何時乎？世道人心，視三國紛爭之際為何如？人材之消乏，視三國紛爭之際又何如？仲翔以梗直不見容流俗，被擯嶺表，尚不忘情於世，欲以《易》道濟之。相傳廣州六榕寺，猶仲翔講《易》之遺趾，流風未沫。今有其人，吾願執鞭以從之矣。

Alas! What kind of era is this today? How does the current state of the world and people compare to the time of the Three Kingdoms? How does the decline of talent compare to that time? Yu Fan was dismissed to Lingnan because of his upright nature, not being accepted by the prevailing customs, yet he never ceased to care about the world, wanting to use the principles of the Book of Changes to help it. It is said that the old site where he once explained the Book of Changes still remains at the Liu Rong Temple in Guangzhou, and his influence has not ceased. If there were such a person today, I would willingly take up the whip and drive the carriage to follow him.

虞仲翔氏說《易》，有半象與兩象易之兩例，後人多非議之。如解“小有言”為震象半見，解小畜“密雲不雨”為坎象半見，蓋皆以三畫卦之上兩畫，或下兩畫言之。後之說《易》者，駁詁非難，不勝備記。

Yu Fan interpreted the Yi Jing, establishing two methods: "half image" and "two images Yi." Later scholars often criticized these approaches. For example, he interpreted "small words" in the Gao卦 (Strife Hexagram) as a half-exposed Zhen image, and "thick clouds without rain" in the Xiao Xu卦 (Small Accumulation Hexagram) as a half-exposed Kan image. These interpretations focused on the upper two lines or the lower two lines of the three-line trigrams. Later commentators on the Yi Jing criticized and refuted these two methods extensively, making it impossible to list them all.

如焦理堂說《易》，固主虞氏旁通者也。乃於半象亦攻之甚力，謂“乾之半，亦巽兌之半；坤之半，亦艮震之半。震之下半，何異於坎離之上半？坎之半，又何異於兌艮之半？求其故而不得，造為半象，又造為三變受上之說。試思半象之說興，則履姤之下，均堪半坎；師困之上，皆可半震。究何從乎？朱漢上譏其牽合，非過論也”云云。

Jiao Xun, who originally advocated Yu Fan's theory of "pan tong" in interpreting the Yi Jing, strongly criticized the concept of "ban xiang." He said that half of Qian is also half of Xun and Dui, and half of Kun is also half of Gen and Zhen; what is the difference between the lower half of Zhen and the upper half of Kan and Li? Or between half of Kan and half of Dui and Gen? Yu Fan could not find the reason, so he invented the concept of "ban xiang" and also proposed the idea of "san bian shou shang." Imagine if the theory of "ban xiang" were established, then the lower trigrams of the Lu and Gou hexagrams could be considered half of Kan, and the upper trigrams of the Shi and Kun hexagrams could be considered half of Zhen. In the end, which one should be followed? Zhu Zhen, known as the Han Shang Master, criticized him for being forced and artificial, and his criticism was not unwarranted.

嗚呼！漢上固宋人之深於象數者，而焦理堂之《易通釋》，亦能貫串全經確有心得，非一知半解人云亦云者比，乃亦有此似是而非之論，可見解人難索。象學之發明，正未易言矣。焦氏所指駁者，驟觀之似極有理，實於象學茫然未辨也。虞氏半象之名，未能達意，且別無詳析之釋文，宜淺近者之詫為無理焉。

Alas! Zhu Zhen was a scholar of the Song dynasty who was particularly skilled in the imagery and numbers of the Yi Jing. Jiao Xun's "Yi Tong Shi" can connect the entire text and indeed has genuine insights, not someone who merely knows a little and follows others' opinions. Yet he still made such ambiguous remarks, showing how rare it is to find someone who truly understands the essence. It is indeed very difficult to clarify the study of imagery. What Jiao Xun criticized seems at first glance very reasonable, but in reality he did not clearly distinguish the principles of imagery study. Yu Fan's term "half imagery" did not clearly express his meaning, and he left no detailed explanatory writings, so it is not surprising that those with shallow learning find it strange and unreasonable.

蓋八卦之象，惟乾坤坎離，反覆皆同。震艮巽兌四卦，則為二卦之反覆。震反即艮，兌反即巽。故孔子《雜卦》，曰“震起，兌見，巽伏，艮止”，又曰“離上而坎下也”。坎離雖不可反易，實即震艮巽兌之中體。下震起而上艮止即為離，下巽而上兌見即為坎。八卦之變化，皆此震起艮止巽伏兌見所往來。若去此四者，乾坤坎離皆為死物，無易可言矣。

The images of the Eight Trigrams are such that only Qian (Heaven) and Kun (Earth), along with Kan (Water) and Li (Fire), remain the same when turned upside down. The other four trigrams—Zhen (Thunder), Gen (Mountain), Xun (Wind), and Dui (Lake)—are paired and turn into each other when inverted: Zhen becomes Gen, and Dui becomes Xun. Therefore, Confucius said in the "Zagua Zhuan" that "Zhen initiates movement, Dui reveals, Xun conceals, and Gen stops." He also said, "Li is above and Kan is below." Although Kan and Li cannot be inverted, they are actually the intermediate forms of Zhen, Gen, Xun, and Dui. The lower part of Li is Zhen initiating movement, and the upper part is Gen stopping, forming Li. The lower part of Kan is Xun concealing, and the upper part is Dui revealing, forming Kan. All changes of the Eight Trigrams depend on the interaction of these four elements: Zhen initiating movement, Gen stopping, Xun concealing, and Dui revealing. If these four are removed, Qian, Kun, Kan, and Li would all become static and there would be no "Yi" (Change) to discuss.

故六爻之卦，初爻為震爻，二為坎爻，三為艮爻，四為巽丈，五為離爻，上為兌爻。虞氏所謂震體半見者，即震爻也。坎象半見者即坎爻也。六爻皆乾坤之體，故乾坤不可分爻。焦氏謂乾之半坤之半，正見其於卦象未通，未足以闢虞氏也。虞之失，在半象二字之辭不達意，謂其立名未當則可，謂為無所適從不可也。

Therefore, the six-line hexagram has the first line as the Zhen line, the second line as the Kan line, the third line as the Gen line, the fourth line as the Xun line (the original text says 'Xun zhang', where 'zhang' is a mistake for 'yao'), the fifth line as the Li line, and the top line as the Dui line. Yu Fan's statement 'Zhen body is half visible' refers to the Zhen line; 'Kan image is half visible' refers to the Kan line. All six lines of the hexagram are essentially composed of the Qian and Kun lines, so Qian and Kun themselves do not have separate lines. Zhao Xun's questioning with 'half of Qian and half of Kun' clearly shows his lack of thorough understanding of the hexagram images, making him insufficient to refute Yu Fan. Yu Fan's mistake lies only in the term 'half image' being imprecise; it is acceptable to say his naming is inappropriate, but it is not acceptable to say this approach leaves people confused.

至虞氏之所謂兩象易，實即上下錯。孔子《雜卦》亦即兩卦之上下交錯。六十四卦以交錯見義者，不勝枚舉。如履上下錯（上天下澤易上澤下天）為姤，履柔履剛也，姤柔遇剛也。屯上下錯為解，屯雷雨之動滿盈，解雷雨作而百果草木皆甲坼。恆上下錯為益，恆立不易方，益為益無方，皆兩象易也。苟以為非，則孔子之《彖傳》亦盡非乎？辛齋非宗虞氏《易》者，但以是非為去取，絕無成見。恫向之言《易》者，蔽於門戶之見，動輒是己而非人。故特著之，亦以自警焉。

As for Yu Fan's concept of "two images exchange," it simply refers to the reversal of the upper and lower parts of the hexagram. Confucius also used the method of interchanging the upper and lower trigrams in his "Commentary on the Miscellaneous Hexagrams." There are numerous examples in the sixty-four hexagrams where the meaning is revealed through such reversal: reversing the upper and lower trigrams of the "Gua" hexagram (changing upper Qian and lower Dui to upper Dui and lower Qian) results in the "Gou" hexagram. The "Commentary on the Judgment" of the "Gua" hexagram says "the soft follows the strong," while that of the "Gou" hexagram says "the soft meets the strong." Reversing the upper and lower trigrams of the "Zun" hexagram results in the "Jie" hexagram. The "Commentary on the Judgment" of the "Zun" hexagram says "the movement of thunder and rain fills the world," while that of the "Jie" hexagram says "thunder and rain arise, and all fruits and plants split open." Reversing the upper and lower trigrams of the "Heng" hexagram results in the "Yi" hexagram. The "Great Image" of the "Heng" hexagram says "standing firm without change," while the "Commentary on the Judgment" of the "Yi" hexagram says "the benefit has no fixed direction." These are all examples of the "two images exchange." If one insists that this method is wrong, can Confucius's "Commentary on the Judgment" be entirely incorrect? I, Hang Xinzhai, do not follow Yu's school of thought in interpreting the "Book of Changes," but I judge matters based on right and wrong, without any preconceived notions. I merely regret that those who interpreted the "Book of Changes" in the past were blinded by factionalism, often asserting their own views as correct and others as wrong. Therefore, I have written this explanation to clarify this point, and also as a warning to myself.