Six days and seven parts

《易緯》卦氣，六十四卦中，提出坎震離兌為四伯，亦曰四監，以主一年二十四氣。坎主冬至迄驚蟄，震主春分迄芒種，離主夏至迄白露，兌主秋分迄大雪。餘六十卦，以中孚起冬至，每卦主六日七分，每五卦分公闢侯大夫卿，主六候兩氣一節，六十卦共三百六十五日四分日之一，以合周天三百六十五度四分度之一。

The method of卦气 (hexagram qi) transmitted in the "Yi Wei" identifies the four hexagrams Kan, Zhen, Li, and Dui as the "Four Masters" or "Four Supervisors," used to govern the twenty-four solar terms of a year: Kan governs from Winter Solstice to Start of Spring, Zhen governs from Spring Equinox to Grain in Ear, Li governs from Summer Solstice to White Dew, and Dui governs from Autumn Equinox to Great Snow. The remaining sixty hexagrams, starting from Zhongfou at Winter Solstice, each govern six days and seven parts (a day is divided into eighty parts, and the sixty hexagrams collectively account for 365 and 1/4 days, so each hexagram governs exactly six days and seven parts). Every five hexagrams are divided into five ranks: Gong, Bi, Hou, Da Fu, and Qing, collectively governing six "hui" (periods), two "qi" (phases), and one "jie" (solar term). The sixty hexagrams together total 365 and 1/4 days, exactly matching the 365 and 1/4 degrees of the celestial sphere.

又別置復、臨、泰、大壯、夬、乾、姤、遁、否、觀、剝、坤為十二闢卦，每爻各主一候(五日五分，又六分分之，五為一候。)。自復至乾為息卦，曰太陽。自姤至坤為消卦，曰太陰。息卦所屬者曰少陽，消卦所屬者曰少陰。以四伯領十二闢，十二闢領公闢侯大夫卿五卦，以司一歲之卦氣，以推吉凶，名為六日七分之學。

In addition, the twelve hexagrams 《复》, 《临》, 《泰》, 《大壮》, 《夬》, 《乾》, 《姤》, 《遁》, 《否》, 《观》, 《剥》, and 《坤》 are set apart as the 「twelve great hexagrams」. 「Bì」 means ruler, and these twelve hexagrams are like the twelve rulers of the months in a year. Each line of the hexagrams governs one of the twenty-four solar terms, which are divided into five days each, with an additional five parts of six, making up one term. From 《复》 to 《乾》, these hexagrams represent the gradual growth of yang energy each month, known as 「the sun hexagrams」; from 《姤》 to 《坤》, they represent the gradual decline of yang energy each month, known as 「the moon hexagrams」. Those belonging to the growing yang hexagrams are called 「minor yang」, and those belonging to the declining yang hexagrams are called 「minor yin」. Using the four great trigrams to govern the twelve great hexagrams, which in turn govern the five ranks of hexagrams: public, ruler, marquis, minister, and chancellor, to manage the yin and yang energies of the year and to determine auspiciousness and inauspiciousness, this is called the 「six days and seven parts」 system.

盛於西漢，而尤於京氏為精。故後人輒稱之為京房卦氣。其實此法相傳最古。今所傳《連山》，卦雖殘缺不完，然以坎離震兌分主四季，亦復相同。可見自三代時已有此學。故孔子《繫傳》上繫起中孚，下繫起咸，亦述而不作焉。漢人去古未遠，三代遺法猶有存者。京氏之學，自必有所師承，非所能臆造者。

This discipline became popular during the Western Han dynasty, especially with Jing Fang who explained it most thoroughly. Hence, later generations often refer to it as "Jing Fang's Hexagram Qi." In fact, this method has a very ancient origin. Although the present transmission of "Lian Shan" is incomplete, it still uses Kan, Li, Zhen, and Dui to represent the four seasons, showing that this discipline existed during the Xia, Shang, and Zhou dynasties. Therefore, Confucius in the "Great Treatise" of the "I Ching" mentions the beginning of the lines in "Zhongfou" in the upper transmission and in "Xian" in the lower transmission, which is merely following the old method without introducing new ideas, as said "to narrate but not to create." Since the Han people were not far from the ancient times, the remaining practices of the Xia, Shang, and Zhou dynasties were still present, so Jing Fang's studies must have had a teacher, and it could not have been invented by him alone.

特其時讖緯之說盛行，各自為說，真贗莫辨，漸入於怪誕支離，幾不可究詁。至禁習緯書以遏其頹波，而三古僅存之遺法，亦為之湮沒不彰，良可痛也。

At that time, prophecies and interpretations of classics were widespread, with everyone offering their own views, making it difficult to distinguish truth from falsehood. Over time, these interpretations became increasingly strange and fragmented, making it almost impossible to study. Later, the government banned the study of the "Wei Shu" to curb this declining trend, and the remaining ancient methods were also gradually lost and forgotten, which is truly regrettable.

後之言卦氣者，變化百出，有自乾至未濟，依文王《序卦》，以一卦直一日，乾直甲子，坤直乙丑，迄未濟直癸亥，周而復始。六周盡三百六十日，而坎離震兌直二分二至，此焦氏之法也。有以乾坤坎離為橐龠，餘六十卦，依《序卦》一爻值一時；而周一月，又以十二闢卦，每卦管領一時。此魏伯陽之法也。

Later commentators on the hexagram energies devised various methods. Some arranged the hexagrams from Qian to Weiji, following King Wen's sequence of hexagrams, assigning each hexagram to one day: Qian corresponded to Jiazi, Kun to Yichou, and so on until Weiji corresponded to Guihai, then the cycle repeated. After six cycles, exactly 360 days were covered, with Kan, Li, Zhen, and Dui assigned to the solstices and equinoxes—this was Jiao Yanshou's method. Others used Qian, Kun, Kan, and Li as the bellows (tuo yue), symbolizing the continuous movement without itself participating in the cycle, and the remaining sixty hexagrams arranged in King Wen's sequence, with each trigram corresponding to an hour, completing a cycle in a month. They also assigned the twelve great hexagrams to each hour—this was Wei Boyang's method.

有以六十卦，一爻主一日，《上經》起乾甲子，泰甲戌，噬嗑甲申，至離三十卦，而三甲盡。《下經》起咸甲午，損甲辰，震甲寅，至癸亥而終，亦三十卦。另以中孚小過既未濟，代坎離震兌，以應分至。每爻直十五日，以應二十四氣。此史繩祖之法也。

Some use the sixty hexagrams with each line corresponding to one day: the Upper Canon starts with the hexagram Qian (Heaven) on Jiazi, Tai (Peace) on Jiaxu, and Shihe (Crushing the Bones) on Jiashen, reaching Li (Fire) after thirty hexagrams, and the three dry branches Jiazi, Jiaxu, Jiashen cycle completely; the Lower Canon starts with Xian (Salty) on Jiawu, Shen (Loss) on Jiachen, and Zhen (Thunder) on Jiayin, ending at Guihai, also covering thirty hexagrams. Additionally, they use Zhongfou (Sincerity), Xiaoguo (Minor Crossing), Ji Ji (Completion), and Weiji (Non-Completion) to replace Kan (Water), Li (Fire), Zhen (Thunder), and Dui (Lake), corresponding to the solstices and equinoxes. Each line corresponds to fifteen days, matching the twenty-four solar terms—this is the method of Shi Shengzu.

至邵康節以先天圖定卦氣，以復起冬至，姤起夏至，以乾坤坎離，分主二至二分。而張理又取邵子先天方圖，以冬至起復，至泰而正月，乾四月，否七月，坤十月。又以一陰一陽至六陰六陽分列，六陽處南，自下而升；六陰處北，自上而降，則又合漢宋為一家矣。《易占經緯》又以文王八卦，依邵子先天式列為圓圖，而以渙起冬至。紛紛不一。

At the time of Shao Kangjie, the use of the Earlier Heaven diagram was employed to determine the卦气: the hexagram of Fu began at the winter solstice, and the hexagram of Gou began at the summer solstice. The trigrams Qian, Kun, Kan, and Li were assigned to the two solstices and two equinoxes. In the Yuan dynasty, Zhang Li adopted Shao's arrangement of the sixty-four hexagrams into a square diagram, starting with Fu at the winter solstice, reaching Tai for the first lunar month, Qian for the fourth lunar month, Po for the seventh lunar month, and Kun for the tenth lunar month. He also arranged them according to alternating yin and yang, with the six yang trigrams located to the south, rising from bottom to top, and the six yin trigrams located to the north, descending from top to bottom. This synthesis combined Han and Song schools of thought. The "Yi Zhan Jingwei" then arranged the Later Heaven trigrams of King Wen in a circular diagram following the pattern of Shao's Earlier Heaven diagram, starting with Huan at the winter solstice. Various interpretations abound, each differing from the others.

除焦氏為別立占法，非關卦氣；魏伯陽《參同契》，乃借《易》以演其丹經；邵子先天數，以《易》演其《皇極經世》，各自成一家，當從別論外，其餘皆模仿六日七分法以之推演者。雖具有條理，而按諸理數而無當，驗諸天時而不合。雖斥為無知妄作，亦未為不可。至因眾說之蕪雜，並卦氣而亦妄之，無乃矯枉而過其正歟！

Jiao Yanshou established a separate system of divination unrelated to the trigram calendar; Wei Boyang's "Zhou Yi Cang Tong Qi" used the Zhou Yi to elaborate his alchemical treatises; and Shao Zi's Earlier Heaven numbers employed the Zhou Yi to develop his "Huang Ji Jing Shi." These three schools formed their own distinct traditions and should be considered separately. In addition, other theories were merely imitations of the "six days and seven parts" method, which although possessing some logical structure, did not conform to the principles of numerical divination and failed to align with celestial phenomena. They could be dismissed as mere baseless inventions. However, if one dismisses the trigram calendar entirely merely because of the confusion among various interpretations, that would be an overreaction.

攻京氏之術，其占法所用月建，與近世術家之所謂月建不同。近以占日所隸節為月建，而京氏以爻直月，從世起建，佈於六位。惟乾坎二卦從初爻起，餘卦均從世爻起。如乾起甲子，坤起甲午，一卦凡六月也。積算則以爻直日，即從建所止起日，如姤之上九乙亥，即以乙亥起上九為一日，終而復始。一卦凡一百八十日。近則月為直符，日為傳符，以見於爻之卦支，合於日月者當之，與古法異矣。

Those who study Jing Fang's method should know that the "Month Builder" used in Jing's divination differs from the "Month Builder" mentioned by modern diviners. Modern practitioners determine the Month Builder based on the solar term corresponding to the day of the卦's commencement, while Jing's method uses the爻's value to determine the Month Builder, starting from the World Line and sequentially placing it on the six lines of the卦. Only the hexagrams Qian and Kan start from the first line, while all other hexagrams start from the World Line. For example, Qian starts with Jiazi and Kan starts with Jiawu, covering a total of six months for each hexagram. "Accumulated Calculation" involves using the day's value, starting from where the Month Builder ends: for instance, if the upper ninth line of the hexagram Gou is Yihai, then Yihai is taken as the first day of the upper ninth line, and this cycle repeats, covering a total of 180 days for each hexagram. Modern methods use the month as "Direct Symbol" and the day as "Transmitted Symbol," taking the earthly branch included in the line if it matches the day's branch and the Month Builder, which differs from the ancient method.

蓋京氏之學，魏晉以後，已鮮傳人。至宋時，僅存《火珠林》之法。而所謂《火珠林》者，亦不詳其所自，未知撰述者何人。要之以錢代蓍，與近世所傳相近，而《火珠林》之書卒不可見。間有傳本，又鈔寫不同，未能確辨其真偽也。

Originally, the school of Jing Fang became little known after the Wei and Jin dynasties, and by the Song dynasty only the method of the Fire Pearl Forest remained. As for the Fire Pearl Forest, its origin is unclear, and its author is unknown. In general, it uses copper coins instead of the yarrow stalks, and this method is similar to the modern practice of shaking coins to form a hexagram. However, the book of the Fire Pearl Forest is rarely seen, and when there are a few copies, they are copied differently, making it impossible to determine their authenticity with certainty.

今所傳卜筮之書，大都出於唐宋之後。溯其淵源，終不出京氏世應飛伏之範圍。而取用分類，或視昔較繁。世事紛紜，孳乳遞演，累進無已。機械之用，尤日出不窮。故推算之術，往往今密於古。但按於理而可通，徵諸道而不悖者，正不妨變通以宜民，必執舊法以相繩無謂也。

The divination texts that are passed down today mostly originated after the Tang and Song dynasties; tracing their origins, they ultimately fall within the scope of the "World and Response Lines" and "Flying and Hidden" concepts from the Jingshi school. However, the categories used are more complex than in earlier times. The world is full of confusion and change, with each generation giving rise to new developments, layer upon layer without end. The use of mechanical devices is especially endless, so the methods of calculation often become more refined in later times than in ancient times. As long as they make sense according to reason and do not contradict the Dao, they should be adaptable for the benefit of people; one must not rigidly adhere to old methods to measure everything, which would be meaningless.

《乾·九三》“君子終日乾乾夕惕若夤厲無咎”，舊本無“夤”字，後據《說文》所引補入。高郵王氏駁之，列舉五義，其說詳矣。然以卦象推之，乾九三爻即艮爻，《艮·九三》“艮其限列其夤厲熏心”，足以證乾九三之“夕惕若夤厲無咎”之“夤”字，決非《說文》所誤引，與後人傳寫之訛也。

The line statement of the third line of the Qian hexagram, "A gentleman remains diligent all day, and in the evening remains cautious as if something were hidden, perilous, yet without blame," originally did not include the character "yin." Later scholars added it based on the text of the Book of Changes cited in the Shuowen Jiezi. Wang Shi of Gaoyou criticized this method of supplementation, listing five reasons and explaining them in detail. However, from the perspective of the hexagram's imagery, the third line of Qian corresponds to the third line of Gen. The line statement of Gen's third line is "Restraining the waist, revealing the yin, perilous and burning in the heart." This clearly demonstrates that the character "yin" in the third line of Qian's line statement is not an error in the Shuowen Jiezi, nor a mistake in transmission.

王氏以《文言》亦無“夤”字，為所據五證之最有力者。然傳以釋經，固未必全錄經文。“坤先迷後得主利”，而《文言》曰“後得主而有常”，亦無利字，豈足以證《坤·彖》“先迷後得主利”之“利”字為衍文乎？“夤”字於卦義爻義，均極有關係，當別為說以詳之。

Wang's argument that the "Yin" character is absent in the "Wenyan Zhuan" is regarded by him as his strongest of five pieces of evidence. However, the Zhuan is used to explain the Jing, and it is not necessarily required to copy the entire text of the Jing. The "Kun" hexagram statement says "first being lost, then obtaining the master, beneficial," but the "Wenyan Zhuan" only says "after obtaining the master, there is constancy," without the character "li." Can this be used to conclude that the "li" character in the "Kun · Tuan" passage "first being lost, then obtaining the master, beneficial" is an added character? The character "Yin" is of great importance for the relationship between the hexagram meaning and the line meaning, and should be discussed in detail in a separate article.

《繫傳》“天一地二天三地四”至“所以神變化而行鬼神也”一節，原本在“《易》有聖人之道四焉”一節之前。下文所謂“參伍以變錯綜其數，通其變極其數”云云，皆根據於此。程子以之移在“大衍之數五十”之上，後人皆因之，遂將經文前後隔截，不相貫串，致發生二種錯誤。

The Great Treatise of the Upper Classic begins with "Heaven is one, Earth is two, Heaven is three, Earth is four" and continues until "so it can produce changes and act like ghosts and spirits." This section originally came before the passage "The Book of Changes contains four ways of the sage," and the following statements such as "by combining three and five, changes are made; by interweaving numbers, calculations are made" and "by comprehending changes... reaching the extreme of numbers" all rely on this section. Cheng Yi moved it above the section discussing the use of yarrow stalks for divination, "the great number of the Great Derivation is fifty," and later generations followed this move without question. As a result, the originally connected text was cut into two parts, making them disconnected and leading to two errors.

其一，“參伍錯綜”二語；無所附麗輾轉相訛，異說滋多。來瞿塘之錯綜，張乘槎之參伍，其病根皆伏於此。其二，今“大衍之數五十”，因與“天地之數五十有五”不符，發生無數異議。其實天地之數自天地之數，大衍之數自大衍之數，本不相蒙。因經文移易之後，兩節相為聯屬，遂混兩說而一之，費無限辯論駁議，於經文無所發明。

First, the phrases "San Wu" and "Cu Zhong" have lost their original context and have been passed down with errors, leading to an increasing number of conflicting interpretations. Lai Zhide discussed "Cu" and "Zhong," while Zhang Chengcha discussed "San Wu," and the root of the problem lies here. Second, the phrase "Da Yan Zhi Shu Wu Shi" (the number of the Great Derivation is fifty) has caused numerous disputes because it does not match "Tian Di Zhi Shu Wu Shi You Wu" (the number of heaven and earth is fifty-five). In reality, the number of heaven and earth is the total sum of numbers from one to ten, while the number of the Great Derivation is the actual number of yarrow stalks used in divination. These are two separate matters and originally had nothing to do with each other. However, because the passages in the text are placed next to each other, people have confused the two different concepts, leading to endless debates without any real contribution to the understanding of the text.

此皆改經之流弊也。宋儒好擅改經文，貽誤後學實多，此特其一耳。至有明喬氏黃氏，及清任釣臺等，擅將《繫辭》顛倒錯亂，尤為無知妄作，要亦宋儒之有以開其先也。

These are all the consequences of arbitrarily altering the classics. The Song dynasty scholars often made unauthorized changes to the texts, causing much confusion for later learners; this is merely one example. As for the Qiao family and Huang family of the Ming dynasty, and Ren Diaotai of the Qing dynasty, who arbitrarily rearranged the "Great Treatise," especially those who acted recklessly without knowledge, in the end, it was the Song scholars who first set the precedent.

《周易》“用九用六”。“九”“六”二字，注《易》者立說不一。《正義》云：“陽爻稱九，陰爻稱六。”其說有二：一者乾體三畫，坤體六畫。陽得兼陰，故其數九。陰不得兼陽，故其數六。二者老陽數九，老陰數六。老陰老陽皆變，《周易》以變為占。揲蓍之數，九過揲則得老陽，六過揲則得老陰。少陽稱七，少陰稱八，皆不變，為爻之本體。老陽老陰交而後變，故為爻之別名。

After the two hexagrams of Qian (Heaven) and Kun (Earth) in The Zhou Changes, there are additional sections called "Use of Nine" and "Use of Six." The characters "nine" and "six" have different interpretations among commentators of the I Ching. Kong Yingda, in his work The Correct Meaning of the Zhou Changes, explains that "a yang line is called nine, and a yin line is called six." He provides two reasons for this. First, the hexagram of Qian consists of three solid lines, while the hexagram of Kun consists of six broken lines. Yang can include yin, so its number is nine; yin cannot include yang, so its number is six. Second, the number of old yang is nine, and the number of old yin is six. Old yin and old yang both change, and The Zhou Changes uses changing lines for divination. According to the method of divination with yarrow stalks, if the number of stalks exceeds nine groups, it is considered old yang; if it exceeds six groups, it is considered old yin. Young yang is called seven, and young yin is called eight; these do not change and represent the original form of the line. Old yang and old yin interact and then change, so "nine" and "six" are alternative names for the lines.

邵子曰：“《易》有真數三而已。三天者三三而九，兩地者倍三而六。陰無一，陽無十。”楊氏萬里曰：“積天數之一三五曰九，積地數之二四曰六。”

Shao Kangjie said: The true number in the Zhou Changes is only 'three'. 'Ce Tian' (ascending to heaven) is three threes multiplied together to get nine, and 'Li Di' (two lands) is three plus one doubled to get six. Yin does not contain 'one', and Yang does not contain 'ten'. Yang Wanli said: Adding the heavenly numbers one, three, and five together gives nine, and adding the earthly numbers two and four together gives six.

《朱子語類》：“奇陽體圓，其法徑一圍三而用其全，故少之為數三。偶陰體方，其法徑一圍四而用其半，故多之為數二。歸奇積三三為九，過揲四九為三十六。積三二為六，過揲四六為二十四。積二三一二為八，過揲四八三十二。積二二一三為七，過揲四七二十八。七八九六，經緯乎陰陽。陽進陰退，故九六為老，七八為少。陽極於九，退八而為陰。陰極於六，進七而為陽。占用九六而不用七八，取其變也。”

Master Zhu Xi said: Odd numbers belong to yin and yang, and their form is round. In calculation, the diameter is one and the circumference is three, and the full number is used, so the portion with fewer counts is considered three. Even numbers belong to yin and yang, and their form is square. In calculation, the diameter is one and the circumference is four, and only half is taken, so the portion with more counts is considered two. The number of odd counts added three times as three totals nine, and the overcounting number is forty-eight. The number of even counts added three times as two totals six, and the overcounting number is twenty-four. Two threes and one two added together total eight, and the overcounting number is thirty-two. Two twos and one three added together total seven, and the overcounting number is twenty-eight. The numbers seven, eight, nine, and six interweave to form the meridians and parallels of yin and yang. Yang represents advancement, while yin represents retreat. Therefore, nine and six are considered old, while seven and eight are considered young: when yang reaches nine it is at its extreme, and when it retreats to eight, it becomes yin; when yin reaches six it is at its extreme, and when it advances to seven, it becomes yang. Divination uses only nine and six but not seven and eight, taking precisely their capacity to change.

王氏夫之曰：“於象一二函三，三奇之畫一，全具其數。三奇而成陽，三三凡九陰。左一右一，中缺其一。三二而為六。”來氏之所謂“參天兩地”，即楊氏萬里說也。其餘諸家，大約宗孔義與朱說者為多。

Wang FuZhi said: In terms of observation, one and two contain three; each of the three odd lines is considered as one, and altogether they possess the number. Three odd lines combine to form yang, and three threes make nine; for yin lines, they consist of a segment on the left, a segment on the right, and a missing segment in the middle, and three twos together make six. As for Lai Zhide's explanation of "three heavens and two earths," it is essentially the same as Yang Wanli's view. As for other scholars, most follow the interpretations of Kong Yingda and Master Zhu.

王氏夫之雖似從《正義》第一說，而實較孔氏為精。蓋數極於九，本陰陽之所同具，故二九十有八變而成卦。陰之稱六，特虛其三耳。以推之象，則惟乾九坤六，震坎艮皆七，巽離兌皆八。此《易》之獨繫二用於重乾重坤之下歟？(《易》數稱奇偶，不曰單雙。奇圓偶方稱數而形已寓其中，乾圓坤方圓周三百六十為率分四象，限為九十度。圓內容方方邊自為六十度。此數理之自然。“圓”見《易數偶得》)

Wang Fu-zhi seems to follow Kong Yingda's first explanation, but in fact he explains it more precisely. Since nine is the extreme of numbers, it is shared by both yin and yang. Therefore, two nines, making eighteen changes, form a hexagram. The reason yin is called six is simply that three of the numbers are omitted. Applying this principle to the hexagrams, only Qian (Heaven) is nine and Kun (Earth) is six. The three trigrams Zhen (Thunder), Kan (Water), and Gen (Mountain) are all seven, while the three trigrams Xun (Wind), Li (Fire), and Dui (Lake) are all eight. This is probably why the Zhou Changes alone attach the phrases "use of nine" and "use of six" to the repeated Qian and repeated Kun. In the Zhou Changes, numbers are called "odd" and "even," not "single" and "double." Odd is round and even is square. One number already implies shape: Qian is round and Kun is square. The circumference of a circle is taken as 360, divided into four trigrams, each occupying 90 degrees. The square inside the circle has each side measuring 60 degrees. This is naturally the case in numerical reasoning. For more on "circle," see my work "Notes on the Numerical Principles of the Zhou Changes."

爻有動靜，卦有貞悔。占例：內卦為貞，外卦為悔。靜卦為貞，動卦為悔。《春秋左氏傳》曰：“貞風也，悔山也。”此內貞外悔者也。貞屯悔豫，此靜貞動晦者也。向來講《易》家皆宗此說，朱子《啟蒙》言之尤詳。

Lines in a hexagram are either active or inactive, and hexagrams have a main one and a changing one. The general rule in divination is: the inner trigram is called 'Zhen,' and the outer trigram is called 'Hui'; an unchanging hexagram is called 'Zhen,' and a changing hexagram is called 'Hui.' The 'Zuo Shi Chuan' of the 'Spring and Autumn Annals' records divination statements saying 'Zhen is wind, Hui is mountain,' which refers to the inner trigram as 'Zhen' and the outer trigram as 'Hui.' It also says 'Zhen is the hexagram 'Zun,' Hui is the hexagram 'Yu,'' which refers to the original hexagram as 'Zhen' and the changing hexagram as 'Hui.' All those who have interpreted the 'Yi' have followed this explanation. Master Zhu's 'Yi Xue Ming Tong' explains this in detail.

而不知《易》之經文，已明明自舉其例。《坤·六三》曰“可貞”，明內卦之為貞也。《乾·上九》曰“有悔”，明外卦之為悔也。如《乾·初九·傳》曰“陽在下也”，《坤·初六·傳》曰“陰始凝也”，亦為陽九陰六自舉其例也。

But he did not know that the text of The Zhou Changes itself clearly presents these meanings. The hexagram Kūn (Earth) at line six three says "It is proper to be firm," which clearly indicates that the inner trigram is called "Zhen" (firmness). The hexagram Qián (Heaven) at line upper nine says "There is regret," which clearly indicates that the outer trigram is called "Hui" (regret). Another example is the Small Image Commentary of Qián hexagram at line initial nine, which says "Yang is at the bottom," and the Small Image Commentary of Kūn hexagram at line initial six, which says "Yin begins to condense." These are also examples given by the text itself to explain why Yang is called "nine" and Yin is called "six."

朱子以河圖洛書及先天卦位圓方各圖，弁於《周易》之首，為後世言漢學者所抨擊，幾於體無完膚。然趙宋以前，雖未有先天之圖，而乾坤坎離震巽艮兌之卦位，固早散見於漢人之《易》注。荀慈明之升降，虞仲翔之納甲，細按之殆無不與先天之方位相合。即以經文上下二篇之卦論之，《上經》首乾坤終坎離，非四正之卦乎？《下經》首上兌下艮之咸，上震下巽之恆，非四隅之卦乎？至《說卦》“天地定位山澤通氣”之一章，兩兩對舉者，更無論矣。

Zhu Xi placed the "Yellow River Chart," "Luo Writing," and the circular and square diagrams of the Earlier Heaven trigrams at the beginning of the "Zhou Changes" (I Ching). Later scholars of the Han learning school criticized him heavily, almost refuting him completely. However, before the Song dynasty, although the diagram of the Earlier Heaven trigrams had not yet been drawn, the relative positions of the eight trigrams—Qian, Kun, Kan, Li, Zhen, Xun, Gen, and Dui—were already scattered in the commentaries of Han scholars on the "Book of Changes." Xun Shuang's concept of "ascending and descending" and Yu Fan's theory of "Najia stem assignment" correspond closely with the positions of the Earlier Heaven trigrams. Even if we look only at the sequence of trigrams in the upper and lower parts of the "Book of Changes": the upper part begins with Qian and Kun and ends with Kan and Li, which are exactly the four cardinal trigrams of the Earlier Heaven diagram. The lower part starts with the "Xian" trigram, which has Dui above and Gen below, followed by the "Heng" trigram, which has Zhen above and Xun below, which are precisely the four intercardinal trigrams. As for the passage in the "Shuo Gua Zhuan" that says "Heaven and Earth are positioned, mountains and marshes communicate through the air," which lists the eight trigrams in pairs, this is even more obvious.

乃漢學家必一概抹煞，謂經傳無乾南坤北離東坎西之文。然先王制禮，推本於《易》，固漢學家所公認焉。乾天坤地，離日坎月，亦漢學家所公認焉。《祭義》“祀天南郊，祭地北郊。朝日東門，夕月西門”，豈亦“帝出乎震”一章之方位乎？

However, Western scholars tend to dismiss these clues altogether, claiming that the classics and their commentaries contain no mention of "Qian in the south, Kun in the north, Li in the east, Kan in the west." Yet it is acknowledged by Western scholars themselves that the ancients established rituals based on the Yi Jing. It is also acknowledged by them that Qian represents Heaven, Kun represents Earth, Li represents the sun, and Kan represents the moon. The Li Ji · Ji Yi states: "In the southern suburbs, we worship Heaven; in the northern suburbs, we worship Earth; at the eastern gate, we pay homage to the sun; at the western gate, we pay homage to the moon." Heaven is in the south, Earth in the north, the sun in the east, and the moon in the west. Is this arrangement of directions the Later Heaven arrangement mentioned in the Shuo Gua Zhuan's chapter "The Emperor arises from Zhen"? It is clearly the Earlier Heaven arrangement.

“河出圖洛出書”，明見於《繫傳》，是否即今所傳之河圖洛書？誠不敢必。但天地之數五位相得而各有合，既為孔子所明言；一六二七三八四九之位數，又為鄭康成揚子雲所列舉；而兩數之經緯錯綜，加減乘除，又極盡陰陽變化之妙，悉出造化之自然，非人力所能造作。乃亦以經所未載，訾議亦駁斥不留餘地？

The saying "The Yellow River produced the chart, the Luo River produced the book" is clearly recorded in the Great Treatise. As for whether it refers to the two diagrams known today as the Yellow River Chart and the Luo Writing, one cannot be certain. However, the matching of the five numbers with the five positions in the cosmos, each having its own pairing, was clearly explained by Confucius in the Great Treatise. The numerical positions such as one and six, two and seven, three and eight, four and nine, were also listed by Zheng Xuan (styled Kangcheng) and Yang Xiong (styled Ziyun). These two sets of numbers, when arranged in cross and vertical directions and subjected to addition, subtraction, multiplication, and division, are consistent everywhere, revealing the profound mysteries of yin and yang changes to the fullest extent. This arises naturally from the workings of the universe itself, not from human invention. Yet Han scholars, merely because the classics do not explicitly mention them, have一味ly criticized and rejected them without leaving any room for consideration.

毛西河改河圖為天地生成圖，洛書為太乙九宮圖。夫此二名，詎為經文所載乎？鄭康成之爻辰，所謂子寅辰午申戌，亦經所未載。乃一則據為典要，一則斥為異端。豈得謂是非之平，黨同伐異之見，不能為賢者諱矣。

Ma Qilin, who styled himself as Xihé, renamed the "Heavenly River Chart" as the "Diagram of Heaven and Earth Generating Each Other" and the "Luo Writing" as the "Diagram of Taiyi Nine Palaces." However, are these new names found in the canonical texts? Zheng Xuan's theory of "Yao Chen" paired the six lines of the Qian hexagram with the earthly branches Zi, Yin, Chen, Wu, Shen, and Xu, which are also not found in the canonical texts. Western scholars treat Zheng Xuan's Yao Chen theory as an unshakable principle, yet they condemn the Heavenly River Chart and Luo Writing as heretical. Both are not found in the canonical texts, yet they are treated so differently. How can there be any fair judgment? This kind of favoritism toward one's own group and hostility toward outsiders is a prejudice that cannot be justified even if it comes from respected elders.

許叔重《說文》云：“《秘書》日月為《易》，象陰陽也。”所謂“秘書”者，當時必有傳本。許與魏伯陽同時，決非指《參同契》也。杜預《春秋左氏傳集解後序》曰：“汲郡有發舊塚者，大得古書。《周易》上下篇與今本同。別有陰陽說，而無《彖》、《象》、《文言》、《繫辭》。疑於時仲尼造之於魯，尚未播之於遠國也。”由是觀之，《周易》上下二篇外，必尚有類於圖說之簡篇。漢時猶有流傳，或稱為“秘書”，亦未可知。

Xu Shen, whose courtesy name was Shuzhong, in his work Shuo Wen Jie Zi said: "The Secret Collection explains that the characters 'sun' and 'moon' combined form the character 'yi', which is taken as an image of yin and yang." The work he cited, the Secret Collection, must have had another existing version at that time. Xu Shen and Wei Boyang were contemporaries, so what he referred to could not have been Wei Boyang's Zhou Yi Cang Tong Qi. Du Yu, in his postscript to the Spring and Autumn Zuo Zhuan Ji Jie, said: "There was a person in Ji Jun who dug up an ancient tomb and found a large number of ancient books. Among them were the upper and lower parts of the Zhou Yi, which were the same as the current version, and another book that discussed yin and yang, but did not include the Commentary on the Judgment, the Image Commentary, the Wenyan, or the Great Treatise. It is inferred that when Confucius was in Lu State composing the Ten Wings, they had not yet spread to distant countries." From this, it can be seen that in addition to the upper and lower parts of the Zhou Yi, there must have been other documents similar to diagrams, which might have been still in circulation in the Han dynasty and referred to as 'secret collection'.

朱子謂“先天各圖，決非後儒所能偽造，必當初所本有，後來散佚，流入道家。至希夷傳出，得復還儒家之舊”云云，殊非無所見而云然也。後人或據劉長民之說，以九為河圖，十為洛書。或欲避先後天之名，以先天為伏羲八卦，後天為文王八卦；或以先天為天地定位圖，後天為帝出乎震圖。舍其實而鶩於名，是更可以不必矣。

Zhu Xi said: "The earlier heaven diagrams were certainly not fabricated by later Confucian scholars, but must have originally existed, then scattered and passed into Daoism; until Chen Tuan (who was known as Xiyi) transmitted them again, they were able to return to Confucianism as their original possession." This statement is not without basis. As for later scholars, some followed Liu Mu's (who was known as Changmin) view, calling the nine palace numbers "the Yellow River Chart" and the ten number diagram "the Luo Writing"; others wished to avoid the terms "earlier heaven" and "later heaven," instead calling the earlier heaven "the Fuxi Eight Trigrams" and the later heaven "the King Wen Eight Trigrams"; still others renamed the earlier heaven as "the Diagram of Heaven and Earth Positioned" and the later heaven as "the Diagram of the Emperor Emerging from the Thunder." All of these are abandoning the substance and competing over names, which is even more unnecessary.

易學於西漢為盛。乃至東京，幾成絕響。施孟梁丘三家之學，若存若亡。費氏高氏，亦罕傳述。至漢季始有馬鄭荀虞諸氏，繼緒而興。陸績劉表宋衷諸氏，均有撰著。然習費氏古文者為多。三家之《易》，僅虞翻延孟氏一線，餘子皆湮沒無聞矣。嘗疑東西二京，相去非遙，何以易學之驟然衰落，一至於是？此其中必有原因。

Yi studies flourished greatly during the Western Han dynasty, but by the Eastern Han dynasty, they had almost become a thing of the past. The three official schools of study, led by Shi Chou, Meng Xi, and Liang Qiu He, were either still existing or on the verge of extinction. The two other schools, led by Fei Zhi and Gao Xiang, were scarcely transmitted by anyone. It was not until the end of the Han dynasty that figures such as Ma Rong, Zheng Xuan, Xun Shuang, and Yu Fan resumed the tradition and revived Yi studies. Lu Ji, Liu Biao, and Song Zhong also wrote their own works, but most of their studies were based on the ancient text version of Yi transmitted by Fei Zhi. The schools of Yi from Shi, Meng, and Liang Qiu had only the lineage of Yu Fan continuing the tradition of Meng Xi, while all the other schools had completely disappeared. I have always been puzzled: the Western Han and Eastern Han dynasties were not far apart, so why did Yi studies suddenly decline to such an extent? There must be some reason behind this.

嗣據金石家所探索，謂西漢無碑，因王莽惡稱頌漢德，故剷除殆盡。間有存者，非伏藏土中，或深埋窮谷，為搜剔所不及者耳。於是悟《易》注之亡，亦或莽之所為。蓋西漢易學既盛，而讖緯之說，又成俗尚。西京士大夫，往往侈言陰陽。觀馬班諸書所錄書疏，可見其概。莽初則利為己用，名位既成，惡而去之，乃勢所必然。竄改五經之作用，亦此物此志焉。

Later, when I read the investigations of numismatologists and epigraphers, I learned that few stone inscriptions from the Western Han dynasty have survived. This was because Wang Mang detested the inscriptions that praised the Han dynasty's achievements and had them destroyed completely. Occasionally, some inscriptions did survive, but they were buried underground or hidden deep in remote mountains and valleys, beyond the reach of search. From this I realized that the loss of the Western Han commentaries on the Book of Changes may also have been due to Wang Mang. Since the study of the Book of Changes was very flourishing in the Western Han, and the doctrine of "portents and omens" had become a prevailing trend, scholars in the capital often discussed yin and yang and portents of disaster and auspicious signs. This can be seen from the memorials collected in the works of Sima Qian and Ban Gu. At first, Wang Mang skillfully used this doctrine to build up his own authority, but once he had secured his position, he turned against it, detesting and destroying it, which was inevitable. His intention to alter the Five Classics was driven by the same mindset.

又據《班書·儒林傳》，高相子康以明《易》為郎，王莽居攝。東郡太守崔誼，謀舉兵誅莽。事未發，康候知東郡有兵亂，私語門人，門人上書言之。後數月崔誼兵起，莽召問，對受師高康，莽惡之。以為惑眾斬康，亦足為莽摧殘易學之一證焉。行篋無書，他日當詳考之。

According to Ban Gu's "Book of Han, the Transmission of the Confucian Schools," Gao Kang, the son of Gao Xiang, became an official because he was skilled in the study of the Book of Changes. When Wang Mang was acting as regent, the governor of Dongjun, Cui Yi, plotted to raise an army to kill Wang Mang. Before the plot was carried out, Gao Kang, through divination, foresaw that there would be military unrest in Dongjun and secretly told his disciples. However, the disciples reported this to the authorities. A few months later, Cui Yi indeed raised an army, and Wang Mang summoned Gao Kang for questioning. Gao Kang claimed that he had learned this from his teacher. Wang Mang therefore resented him and had him executed on charges of spreading false prophecies. This incident serves as evidence of Wang Mang's suppression of the study of the Book of Changes. I did not bring any books with me, and I will examine this matter more thoroughly in the future.

嗚呼，《易》幸不亡於暴秦，乃厄於偽新。殆所謂美新劇秦也歟？（按：呂政不知書，故儕《易》於卜筮，不甚注意。而王莽則深於經學者也，知《易》道廣大，必為小人之憂。乃陽奉而陰沮之。一手遮天，直欲盡掩天下後世之耳目。諺曰：家賊之禍，倍烈於盜寇哉！）

Alas! The Zhou Changes (I Ching) luckily escaped destruction by the brutal burning of books under the Qin dynasty, but instead suffered hardship under Wang Mang's fabricated "Xin" dynasty. This is probably the result of Yang Xiong's approach in his work "Ju Qin Mei Xin," which criticized the brutal Qin and praised Wang Mang. (Original note: Emperor Qin Shi Huang did not read books, so he classified the I Ching under divination and did not pay much attention, allowing the I Ching to be preserved. Wang Mang, however, was deeply knowledgeable in Confucian classics and understood that the principles of the I Ching were vast and would inevitably become a tool for villains. Therefore, he outwardly honored it but secretly obstructed its spread, trying to block the eyes of the world. A proverb says: the祸 of family thieves is twice as severe as that of bandits!)

輔嗣說《易》，陳誼甚高。而文辭雋逸，超乎物外，故能得意忘象。司空表聖所謂超於象外得其環中者，其斯之謂歟？惟必超乎象之外，方可以忘象。如探驪龍之領而既得其珠，則龍亦廢物，更何論乎魚兔之筌蹄？

Wang Bi (style name Fusi) explained the Yi, establishing his arguments at a high level, and his writing was clear, elegant, and detached from worldly concerns. Therefore he could "grasp the meaning and forget the image" — once he understood the principles, he could set aside the hexagrams. The phrase "transcend the image and grasp the center of the circle" from Si Kong Tu's Twenty-Four Poetic Styles probably refers to this kind of realm. However, one must truly transcend the hexagrams before one can forget the images. It is like the person who retrieves a pearl from the dragon's jaw; once the pearl is in hand, the dragon itself becomes useless, let alone the bamboo baskets for fishing or the nets for catching rabbits.

後之言《易》者，既畏象數之繁頤奧衍，莫窺其蘊，喜王氏之學，可以避去繁頤奧衍之象數而說《易》也。於是群焉奉之為圭顳，而又病輔嗣陳義之過高，未能企而及焉，乃曰此玄談也。非孔子之道，為王《易》之微疵焉。吾輩舍其短而取其長，斯盡善盡美白圭無玷矣。因之空談性命，不著邊際。但讀“一陰一陽之謂道”一句，卦爻盡屬贅疣。《彖》、《象》十翼，望文生義以解之，而《易》之能事畢矣。

Later scholars who interpreted the Book of Changes were originally afraid of the complexity and depth of the study of images and numbers, which made it difficult to grasp its essence. Therefore, they favored Wang Bi's approach, as it allowed them to discuss the Book of Changes without relying on the intricate and profound study of images and numbers. They gathered together to regard Wang Bi's scholarship as the standard, yet they found his theories too lofty for themselves to reach, so they said: this is "abstruse discussion," not in line with Confucius' way, and it is a minor flaw in Wang's interpretation of the Book of Changes. They claimed that by discarding its shortcomings and taking its strengths, they had achieved perfection, like a white jade without blemish. Thus, they engaged in empty discussions about the mind, nature, and principles, entirely off the mark: they only read the sentence "a combination of Yin and Yang is called the Dao," and regarded all the hexagrams and lines as superfluous appendages; they superficially interpreted the Commentary on the Judgment and Image Commentary and the other ten appendices, and thought that they had exhausted the entire study of the Book of Changes.

不知王《易》之所以能掃象而仍無礙其說者，正惟其深得玄理，故能獨超乎意象之表也。乃以玄談為病而去之，則所存之不病者，皆糟粕耳。猶冥然自侈為輔嗣之功臣，致令後世宗漢《易》者以掃象為王氏罪，曰“輔嗣學行無漢《易》”，輔嗣豈任受哉？

They do not realize: Wang Bi's ability to eliminate the images of the hexagrams and still maintain his reasoning is precisely because he deeply understood the profound principles. Thus, he could transcend the realm of meaning and image on his own. Now, if we regard "xuāntán" (discourse on the profound) as a flaw and remove it, the remaining "wu bing" (without illness) parts are all dross. These people are still blindly proud of themselves as contributors to Wang Bi, resulting in later scholars who venerate the Han dynasty's "Yi" (Book of Changes) recording the "sǎo xiàng" (elimination of images) as part of Wang Bi's work, saying "With Yixing's study, the Han dynasty's Yi learning has been cut off." This accusation is surely not something Wang Bi could bear.

《坤·彖傳》“坤厚載物德合無疆”，“牝馬地類行地無疆”，“安貞之吉應地無疆”。《程傳》雖已分晰言之，殊未悉當。郭氏云雍曰：“坤合乾德之無疆，馬行類地之無疆，聖人應坤之無疆。”

In the Commentary on the Judgment of the Qian hexagram, the term "wujiang" appears three times: first, "Kun's thick bearing of things, its virtue harmonizing with boundless limits"; second, "the female horse, a creature of the earth, moves without bound"; third, "the auspiciousness of maintaining sincerity lies in responding to the boundless nature of the earth." Although Cheng Yi's Commentary on the Changes explains these separately, his interpretations may not all be entirely appropriate. Guo Yong, also known as Master Baimo, said: the first instance refers to the boundless harmony between the virtue of Kun and that of Qian; the second refers to the female horse's movement following the boundless nature of the earth; and the third refers to the sage's response to the boundless nature of Kun.

邱建安富國曰：“德合無疆，乾之無疆也。行地無疆，坤之無疆也。應地無疆，君子之無疆也。無疆，天德也。地能合天之德。君子法地，地法天。”郭邱二說，似較《程傳》為勝。此與“大哉乾元”“至哉坤元”“元者善之長也”三“元”字，為例正同，所謂三才之道也。

Jian'an person Qiu Fuguo said: "Dehe wujiang" refers to the boundless nature of Qian, "Xingdi wujiang" refers to the boundless nature of Kun, and "Yingdi wujiang" refers to the boundless nature of the gentleman. Wujiang originally belongs to Tiande, the earth can harmonize with the virtue of Heaven, and the gentleman follows the earth, while the earth in turn follows Heaven." Guo Yong and Qiu Fuguo's interpretations seem to be more refined than Yichuan's Commentary on the Changes. The use of "wujiang" in these three instances corresponds exactly to the three instances of "yuan" in the Changes, which belong to Heaven, Earth, and humanity respectively, following the principle of贯通 the three elements of Heaven, Earth, and Humanity.

經傳用字，往往含有廣狹二義。如天，以狹義言之，則與地對。而廣義之天，則廣大無垠，非地可並擬者也。如陽之狹義，則與陰對，而廣義則陽可統陰，陰生於陽，非陰可同論矣。如乾之狹義，則與坤對，而廣義則乾可包坤。乾之一卦，實統轄乎六十四卦。上下篇六十四卦，為三十六卦之反覆，實得二百一十有六爻，為重乾一卦之策。如坤之百四十有四策，悉歸納於乾之內矣。此意義廣狹之最顯者也。

The terms used in the classic texts often carry both broad and narrow meanings. Take the character "heaven" (天) for example: in a narrow sense, it refers to the sky opposite the earth; in a broad sense, it is boundless and cannot be compared with the earth. Similarly, the character "yang" (阳) also has both narrow and broad meanings: in a narrow sense, it is opposite to "yin" (阴); in a broad sense, yang encompasses yin, since yin originates from yang and cannot be equated with yang. The character "qian" (乾) is also the same: in a narrow sense, it is opposite to "kun" (坤); in a broad sense, qian encompasses kun. The hexagram qian actually governs all sixty-four hexagrams— the upper and lower sections of the sixty-four hexagrams are formed by viewing thirty-six hexagram bodies in reverse, resulting in a total of 216 lines, which exactly matches the number of lines in the hexagram qian. In this way, the 144 lines of the hexagram kun are entirely included within qian. This is the most obvious example of the distinction between broad and narrow meanings of characters.

若更進一層言之，則廣義狹義之中，又各有大小或淺深精粗之不同，非詳察其上下之文義，及所聯綴之名詞。逐字剖析，則與經傳之本意，便大有出入。往往因一字之牽連混合，而誤會經旨，輾轉謬誤，歧中又歧，遂致乖戾不可究詁。

If we go a step deeper, in a broad sense there are distinctions between major and minor aspects, and within a narrow sense there are differences in depth, refinement, and coarseness. If one does not carefully examine the meaning and flow of the context along with the connected terms, and analyze each word thoroughly, the interpretation will differ greatly from the original intent of the classics. Often, a single word's confusion or misinterpretation leads to misunderstanding the main purpose of the entire text, resulting in errors that spread and multiply, eventually leading to interpretations that are so distorted that they become untraceable.

如道德等，皆經傳中最主要之字也，而道字之意義，其範圍廣狹大小，各各不同。老子曰“有物無形先天地生，無以名之強名之曰道”者，此道字範圍最大。乃立乎天地之先，孕育萬有之根。此先天之道，無可比擬也。《易》以有立教，從“《易》有太極”說起。故《易》之道，皆一陰一陽之謂道，此《易》中道字廣義之界說也。

For example, the characters "Dao" and "De" are among the most important in the classics. If we consider the character "Dao" alone, its scope varies in size. The "Dao" mentioned in the "Laozi" refers to something without form, existing before heaven and earth, which cannot be named and is given the name "Dao" by force. This "Dao" has the broadest scope, existing prior to the generation of heaven and earth, serving as the fundamental source of all things, belonging to the Dao of the Earlier Heaven, incomparable in its nature. The "Zhou Yi" establishes its teaching based on the concept of "having" or "being." It begins with the statement, "The Book of Changes has the Taiji." Therefore, the "Dao" discussed in the "Zhou Yi" refers to the "Dao" defined as "the way is the interplay of Yin and Yang," which represents the broad definition of the term "Dao" within the "Zhou Yi."

經文“道”字凡四見，皆屬此義。《十翼》中如“未失道焉”，“道大悖也”，“其道光明”等道字，皆廣義也。其狹義者，如“天道”“地道”“人道”“君子之道”“小人之道”是也。而“夫婦之道”、“陰陽之道”、“三極之道”，則又狹隘義中之廣義矣。

In the text, the character "道" appears four times, all of which belong to this broad meaning. In the "Ten Wings," instances such as "未失道焉," "道大悖也," and "其道光明" also refer to this broad meaning. As for the narrow usage, it refers to terms like "天道" (heavenly way), "地道" (earthly way), "人道" (human way), "君子之道" (the way of the gentleman), and "小人之道" (the way of the petty person). Meanwhile, expressions such as "夫妇之道" (the way between husband and wife), "阴阳之道" (the way of yin and yang), and "三极之道" (the way of the three ultimate principles) represent a layer that is narrower yet relatively broader within the narrow usage.

德字如“通神明之德”，德之盛也。“和順於道德”之“德”字，皆廣義之德也。如“陰陽合德”、“位乎天德”、“而德不孤”之“德”字則狹義矣。但無論廣義狹義，又各有內外之別。如健順動入為卦德，乃德之見於外者，為才德之德，如“三陳九德”之德（即“履德之基也”一章），及“進德修業”“神明其德”等德字，乃德之蓄乎內者，為“道德”之德。類乎此者，不勝枚舉。非極深研幾，逐字衡量而剖析之，則差以毫釐，謬以千里矣。

The character "de" (德) is also like this: in phrases such as "communicating the virtue of heaven and earth," "the fullness of virtue," and "harmonious with morality and virtue," the term "de" refers to a broad sense of virtue. In expressions such as "yin and yang combine in virtue," "standing in the virtue of heaven," and "virtue is never isolated," the term "de" refers to a narrow sense of virtue. Whether referring to broad or narrow sense, there is also a distinction between internal and external aspects: for example, the nature of the eight trigrams such as "Qian" representing strength, "Kun" representing docility, "Zhen" representing movement, and "Xun" representing entry—these are called "guade" (卦德), which refers to the external manifestation of virtue, belonging to the category of "cai de" (才德, talent and virtue). As for the three times in the "Xici Zhuan" (Great Treatise) that elaborate on the virtue of the nine trigrams (such as the chapter "Lu, the foundation of virtue"), and expressions like "advancing virtue and cultivating one's career" and "the virtue of the divine," these refer to the internal cultivation of virtue, belonging to the category of "moral virtue." Similar situations are countless. "Extremely profound and exploring subtle details" is a phrase from the "Xici Zhuan," referring to the practice of delving into the most subtle aspects. Without such effort, carefully weighing and analyzing each word, one would make a small mistake and end up with a great error.

此猶就一字言之，更有兩字互相為用。而彼此迭相發明者，如《乾·九五》曰“位乎天德”，《坤·六三》曰“地道光也”。此“道”“德”二字，實互相關聯。各卦之類此者，亦不勝枚舉。蓋聖人作《易》，實與造化同功。其神妙不可思議，而文字亦非常理可以測度。故有以非同一之字，而以形聲之相同而通之為一者，如弟娣梯涕、爤籣連漣之類是也。即有以同一之字，同一意義，而大小內外分際各殊，絕不相假借者，二四三五同功異位，同人以同而異，睽以異而同，神而明之，存乎其人，先聖已一言以蔽之矣。

The above discussion is only about individual characters; there are also cases where two characters are used together, complementing and explaining each other. For example, the "Wenyan" section of the "Qian Hexagram" at line nine five says "positioned in Heavenly Virtue," while the "Xiangzhuan" of the "Kun Hexagram" at line six three says "the way of the earth shines." The "Qian" speaks of "De" and the "Kun" speaks of "Dao," but the characters "Dao" and "De" are actually closely related and have overlapping meanings. There are countless such examples in each hexagram. The sages who composed the Book of Changes have a function similar to the workings of nature, their methods being so mysterious and profound that they cannot be fully understood by ordinary reasoning. Therefore, there are cases where two characters are not the same, yet they are used interchangeably because they have the same form and sound, such as "Di, Di, Ti, Ti," or "Ran, Lan, Lian, Lian." There are also cases where two characters are the same and have the same meaning, yet they are not interchangeable because they differ in size or in their internal and external distinctions. The lines two and four, as well as three and five, have the same function but different positions. The "Tongren" hexagram shows "difference" through "sameness," while the "Kui" hexagram shows "sameness" through "difference." The subtle distinction between these two concepts is exactly as the "Xici Zhuan" says, "the divine and clear understanding lies in the person," and the ancient sages have already summarized this in one sentence.