An Exposition of the Zhou Changes, Volume 19 · Compiled by Hui Dong

昔者聖人之作易也。注。聖人謂庖犧。幽贊於神明而生蓍。注。幽，陰。贊，助也。乾為神明為蓍，謂乾伏坤初。聖人作易，探賾索隱，鉤深致遠，無有遠近幽深，遂知來物，是幽贊於神明而生蓍也。

The Shu Guan Zhuan says: Formerly, the sages created the Zhou Yi. Note: Here, the sages refer to Fuxi. The text says: He obtained assistance from the divine in the hidden and thus invented the method of divination with the yarrow stalks. Note: "Yong" refers to yin, and "zan" means assistance. Qian represents the divine and also the yarrow stalks, meaning that Qian is concealed beneath the first line of Kūn. The sages created the Zhou Yi, exploring the hidden and seeking the subtle, drawing out the profound and attracting the vast, thus being able to understand both near and far, deep and shallow, and foreseeing future events. This is what is meant by obtaining assistance from the divine in the hidden and thus inventing the method of divination with the yarrow stalks.

參天兩地而倚數。注。參，三。倚，立也。謂分天象為三才，以地兩之，立六畫之數，故倚數也。觀變於陰陽而立卦。注。謂立天之道曰陰與陽，乾坤剛柔，立本者卦謂六爻。陽變成震坎艮，陰變成巽離兌，故立卦六爻，三變，三六十八，則「十有八變而成卦，八卦而小成」是也。繫曰：「陽一君二民，陰二君一民。」不道乾坤者也。

The text says: Using the number three from heaven and the number two from earth as a basis to establish the number of the divination stalks. Note: "San" means three, and "yi" means to establish. This refers to dividing the heavenly phenomena into the three elements, then doubling them with the earth number two, thereby establishing the number of six lines, so it is called "yi number." The text says: Observing the changes of yin and yang to establish the hexagram. Note: This refers to establishing the principle of heaven as yin and yang; Qian and Kun, being the firm and flexible, are what the Great Treatise calls "the fundamental." Here, the hexagram refers to the six lines. Yang changes to become Zhen, Kan, and Gen, while yin changes to become Xun, Li, and Dui, so the hexagram is formed by six lines. Three changes, three multiplied by six gives eighteen, which is called "eighteen changes to form a hexagram, the Eight Trigrams are the small completion." The Great Treatise says, "Yang hexagrams have one ruler and two subjects, while yin hexagrams have two rulers and one subject," which refers to the six subordinate hexagrams and does not involve Qian and Kun themselves.

發揮於剛柔而生爻。注。謂立地之道曰柔與剛。發，動。揮，變也。變剛生柔爻，變柔生剛爻，以三為六也。因而重之，爻在其中，故生爻。和順於道德而理於義。注。謂立人之道曰仁與義。和順謂坤，道德謂乾，以乾通坤謂之理義也。窮理盡性以至於命。注。以乾推坤謂之窮理，以坤變乾謂之盡性。性盡理窮，故至於命。巽為命。

The text says: Changes arise between the soft and the strong, giving rise to lines. Note: This refers to establishing the principle of the earth, called soft and strong. "发" means to initiate, "挥" means to change. When the strong changes, it gives rise to the soft line; when the soft changes, it gives rise to the strong line. From three lines, six lines are formed. The eight trigrams are combined and overlapped, and the lines are within them, so it is said "to produce lines." The text says: To harmonize with morality and to have order in principles and meanings. Note: This refers to establishing the principle of humanity, called benevolence and righteousness. "Harmonize and be smooth" refers to the trigram of Earth, "morality" refers to the trigram of Heaven. With Heaven penetrating Earth, it is called "to be in harmony with righteousness." The text says: To investigate physical principles and human nature, ultimately reaching the mandate of heaven. Note: Using Heaven to infer Earth is called "to investigate principles"; using Earth to transform Heaven is called "to exhaust nature." When nature is exhausted and principles are investigated, one can reach the mandate. The trigram of Wind represents the mandate.

昔者聖人之作易也。注。重言昔者，明謂庖犧。將以順性命之理。注。謂乾道變化，各正性命。以陽順性，以陰順命。陰與陽，柔與剛，仁與義，所謂理也。是以立天之道曰陰與陽。注。陰謂坤，陽謂乾。立地之道曰柔與剛。注。柔謂陰爻，剛謂陽爻。立人之道曰仁與義。注。乾為仁，坤為義。

The text says again: In former times, the sage composed the Zhou Changes. Note: The repetition of "in former times" is to indicate that it still refers to Fuxi. The text says: It will be used to follow the principles of nature and destiny. Note: This refers to the changes of the Heaven's Way, which make all things establish their nature and destiny. To use Yang to follow its nature, and Yin to follow its destiny. Yin and Yang, softness and strength, benevolence and righteousness, are what is called "reason." The text says: Therefore, the Way of Heaven is established as Yin and Yang. Note: Yin refers to the Earth, and Yang refers to Heaven. The text says: The Way of Earth is established as softness and strength. Note: Softness refers to the Yin line, and strength refers to the Yang line. The text says: The Way of humanity is established as benevolence and righteousness. Note: Heaven represents benevolence, and Earth represents righteousness.

兼三才而兩之故易六畫而成卦。注。謂參天兩地，乾坤各三爻而成六畫之數也。分陰分陽迭用柔剛故易六畫而成章。注。陰陽，位也。柔剛，爻也。迭，遞也。章謂文理。乾三畫成天文，坤三畫成地理。

The classic text says: Taking together the three elements of heaven, earth, and humanity, each is paired with two lines, so the Book of Changes requires six lines to form a single hexagram. Note: This is referred to as "three heavens and two earths," with the trigrams of Heaven and Earth each occupying three lines to form the total of six lines. The classic text says: Distinguishing the positions of yin and yang, alternately using flexible and strong lines, so the Book of Changes forms its patterns with six lines. Note: Yin and yang refer to the positions of the lines, while flexible and strong refer to the nature of the lines; "迭" means alternation; "章" refers to the patterns and principles. The three lines of Heaven form the patterns of the heavens, and the three lines of Earth form the principles of the earth.

疏。聖人謂庖犧○庖犧始作八卦，故聖人謂庖犧。聖人作，故不言庖犧而言聖人也。庖犧時未有易名而稱作易者，據後言也，猶太卜三易矣。○幽陰至蓍也○此虞義也。幽陰謂坤初，太玄曰「幽遇神」，范望注云「一稱幽」是也。中庸曰「可以贊天地之化育」，鄭彼注云：「贊，助也。」乾為神明，乾伏坤初，太玄曰「崑崙天地而產蓍在崑崙之中」，故曰幽贊以通神明之德，故幽贊於神明。

The commentary says, "The sage is referring to Fuxi": Fuxi was the first to draw the eight trigrams, so the commentary refers to the sage as Fuxi. Since it is composed from the perspective of the sage, the text does not directly mention Fuxi but refers to him as "the sage." At the time of Fuxi, there was no name called "Yi," yet it says he "created Yi," which is using the later name to refer to him. This is similar to the "Three Yis" mentioned in the "Rites of Zhou" by the Grand Astrologer. The commentary from "Yin, meaning阴" to "and thus the yarrow stalks were born": this is Yu Fan's view. "Yin" refers to阴, meaning the first line of the trigram Kūn. The "Taixuan" says "Yin meets the divine," and Fan Wang's commentary says "one is called Yin," which is the same meaning. The "Zhongyong" says "it can assist in the transformation and nurturing of heaven and earth," and Zheng Xuan's commentary says, "Zan means assistance." The trigram Qian represents the divine and bright, yet Qian is hidden beneath the first line of Kūn; the "Taixuan" says "the union of heaven and earth gives rise to the yarrow stalks, which grow in the Kunlun Mountains," so it is said that it assists in the hidden and connects with the virtue of the divine, which is "Yin Zan Yu Shenming."

荀子勸學曰：「無冥冥之志者無昭昭之明。」說文曰：「冥，幽也。」是幽贊之義也。聖人作易，探嘖索隱，鉤深致遠者，嘖，初也，初隱未見，故探嘖索隱。初深，故曰鉤深。致遠謂乾。無有遠近幽深遂知來物者，遠謂天，近謂地，幽謂陰，深謂陽，乾為物，神以知來，故知來物。

Xunzi's "Encouragement of Learning" says, "Without a deep and focused mind, there can be no clear and bright understanding." The "Shuowen Jiezi" says, "Ming means y幽." This matches the meaning of "y幽 zan." The annotation says, "The sage composed the Book of Changes, exploring the hidden and seeking the concealed, drawing out the profound and reaching the distant." "Zé" refers to the first line, which is hidden and not yet revealed, so it is called exploring the hidden and seeking the concealed. The first line is at the deepest level, so it is called drawing out the profound. "Zhi yuan" refers to Qian. It says, "Without regard for distance, nearness, depth, or obscurity, one can know the coming things." "Yuan" refers to heaven, "jin" refers to earth, "y幽" refers to yin, and "shen" refers to yang. Qian represents things, and the spirit can foresee the future, so it is said, "knowing the coming things."

褚先生據傳曰：「天下和平，王道得而蓍莖長大，其叢生滿百莖。」是幽贊為贊化育之本。庖犧幽贊於神明而生蓍，創為揲蓍之法，四營而成易，十有八變而成卦，八卦而小成，引信三才，觸長爻筴，至萬一千五百二十，所謂以通神明之德，以類萬物之情也。

Chu Shaosun relied on old legends: when the world is at peace and the Way of the King is widely practiced, the stems of the yarrow grass become thick and strong, with one cluster producing a hundred stems. This shows that "you zan" is the fundamental support for the nurturing of heaven and earth. Paoxi obtained divine assistance in secrecy and invented the method of divination with yarrow stalks: four operations make one change, eighteen changes make one hexagram, and the Eight Trigrams represent the initial achievement. From here, it extends to the Three Principles, and by analogy, the number of yarrow stalks increases until it reaches the number 11,520. This is what the Great Treatise says: "To communicate the virtue of the divine and to classify the feelings of all things."

大衍之數五十，其用四十有九，其太極以一持萬，其初幽贊於神明，其極至於贊化育參天地，皆是物也。○參三至數也○此虞義也。參讀為三，故云參三也。倚立，廣雅文。虞注繫上極其數云：「數謂六畫之數。」揲蓍之法分而為二以象兩，掛一以象三，足分天象為三才也。

The number of the Great Derivation is fifty, but only forty-nine are actually used; the one not used is the Taiji, which unifies all things. In terms of its origin, it assists the divine in the hidden; in its ultimate function, it assists in the process of generation and is ranked alongside heaven and earth as the three. All these statements refer to the same thing. The commentary from "参, three" to "therefore, it is based on numbers" is Yu Fan's interpretation. "参" is read as "three," hence "参, three." The character "倚" is interpreted as "establish," based on the "Guangya." Yu Fan's commentary on the sentence "extreme number" in the "Great Treatise" says: "Number refers to the number of six lines." The method of divination with yarrow stalks first divides the yarrow into two to represent the two principles, then adds one to represent the three elements. This clearly shows that the division of heaven into the three elements has a solid basis.

五歲再閏再扐而後掛以成一爻之變。耦以承奇，故云以地兩之。立六畫之數謂乾坤各三爻為六畫也。參兩之說諸儒不同。馬融王肅等據天數五地數五，五位相得而各有合，雲五位相合，以陰從陽，天得三合謂一三與五也，地得兩合謂二與四也。一三五凡三，參之而九。二四凡二，兩之而六。謂參天兩地而立九六之數也。鄭氏云：天地之數備於十，三之以天，兩之以地，而倚托大衍之數五十。是諸說不同也。

Within five years there are two leap months, so when divining with yarrow stalks, the remainder must be placed twice into the palm, then hung to form one line of change. Even numbers are used to receive odd numbers, so the commentary says 'to take the earth's two'. The term 'establishing the six lines' refers to the combination of the three lines of Heaven and Earth to form six lines. Regarding 'three heavens and two earths', there are differing interpretations among scholars. Ma Rong and Wang Su, among others, based their views on 'the heavenly number is five, the earthly number is five, the five positions correspond and each has its match', stating that the five positions correspond, with yin following yang: Heaven receives three harmonies, referring to one, three, and five; Earth receives two harmonies, referring to two and four. One, three, and five total three, tripled to make nine; two and four total two, doubled to make six. This is to say that 'three heavens and two earths' is used to establish the numbers nine and six. Zheng Xuan, however, said that the numbers of Heaven and Earth are complete in ten, using the heavenly number threefold and the earthly number doubled to derive the fifty numbers of the Great Derivation. It is evident that there are differing views among the various schools.

○謂立至者也○此虞義也。三畫稱卦，卦有陰陽，故云立天之道曰陰與陽。下繫云：「剛柔者，立本者也。」虞彼注云：「乾剛坤柔為六子父母，乾天稱父，坤地稱母，本天親上，本地親下，故立本者也。」乾坤各三爻，合為六爻而成六子，故卦謂六爻。

The passage from "Shuzheng Zhuwen" "Wèi lì tiān zhī dào yuē yīn yǔ yáng" to "bù dào qiān kūn zhě yě" refers to Yu Fan's interpretation. Three lines are called a hexagram, and hexagrams are distinguished by yin and yang. Therefore, establishing the principle of heaven is called yin and yang. The "Xici Xia" says, "Yang and yin are the fundamental principles." Yu Fan explained there: "Qian is yang and Kun is yin, and they are the parents of the six subsidiary hexagrams. Qian, representing heaven, is called the father; Kun, representing earth, is called the mother. Those originating from heaven are attached above, and those originating from earth are attached below, so it is called establishing the fundamental principle." Qian and Kun each have three lines, combining to form six lines, which produce the six subsidiary hexagrams. Therefore, the "hexagram" mentioned in the commentary refers to the six lines.

陽變成震坎艮謂之陽卦，陰變成巽離兌謂之陰卦，故觀變於陰陽而立卦也。震坎艮乾三索而得，巽離兌坤三索而得，故六爻三變，三六十八，所云十有八變而成卦也。乾坤與六子俱名八卦而小成，謂天三爻，故云小成也。

When yang changes to form Zhen, Kan, and Gen, these are called yang hexagrams; when yin changes to form Xun, Li, and Dui, these are called yin hexagrams. Thus it is said, "Observing the changes of yin and yang to establish the hexagrams." Zhen, Kan, and Gen are formed when Qian seeks Kuan three times, while Xun, Li, and Dui are formed when Kuan seeks Qian three times. Therefore, each of the six lines undergoes three changes, three multiplied by six equals eighteen, which is referred to as "eighteen changes to form the hexagram." Qian, Kuan, and the six sons are collectively called the Eight Trigrams, known as "small completion," because they only reach the three lines of heaven, hence called small completion.

陽一君二民謂震坎艮，陰二君一民謂巽離兌。揲蓍之時尚未有畫，止稱陰陽，故云不道乾坤者也。若然，天有八卦之象，聖人因天制作，震巽已下六子亦從後名之也。○謂立至生爻○此虞義也。六畫稱爻，爻有剛柔，故云立地之道曰柔與剛。道有變動，故曰爻，故云發動揮變也。剛柔相推，變在其中，謂九六相變，故云變剛生柔爻，變柔生剛爻。參重三才以為六爻，故云以三為六，謂六畫以成六十四卦。爻在重卦之中，故生爻也。

"The phrase 'Yang one, King two, People' refers to the trigrams Zhen, Kan, and Gen, while 'Yin two, King one, People' refers to Xun, Li, and Dui. When divining with yarrow stalks, the hexagram form has not yet been drawn, so only Yin and Yang can be referred to, hence it does not involve the names of Qian and Kun. If this is the case, then Heaven originally had the images of the Eight Trigrams. The sage followed the heavenly images to create the hexagram figures. The names of the six subsidiary trigrams below Zhen and Xun were also added later. The passage from the commentary 'It is said that establishing the principle of Earth is called soft and hard' to 'thus generating the lines' refers to Yu Fan's view. The six lines are called 'yao', and 'yao' has distinctions of hardness and softness, so establishing the principle of Earth is called soft and hard. The principle has movement, hence it is called 'yao'. Therefore, the commentary says 'Fa means movement, hui means change'. Hardness and softness alternate, and change is thus generated, referring to the transformation between the numbers nine and six. When the three elements are each doubled to form two lines, they make up the six lines, so it is said 'using three to make six', meaning the six lines are stacked to form the sixty-four hexagrams. The 'yao' is within the stacked hexagram, hence it is said 'generating the lines'.

○謂立至義也○此虞義也。乾鑿度曰：「易始於一，分於二，通於三。」大衍之數五十，三才之合，效三才為六畫。爻辭有仁義，故立人之道曰仁與義。陰陽相應為和，坤，順也，故和順謂坤。乾為道為德，故道德謂乾。以坤順乾，是和順於道德。乾鑿度曰：「天動而施曰仁，地靜而理曰義。」以乾通坤，故謂之理義也。

The passage from "Shuzheng Zhuwen" stating "to establish the way of human beings is called benevolence and righteousness" up to "is called reason and righteousness": this is Yu Fan's view. The "Qian Zao Du" says "The Book of Changes begins with one, differentiates into two, and unifies through three." The number fifty of the Great Derivation is the number where the three principles converge, imitating the three principles to form six lines. The line statements originally contain the concepts of benevolence and righteousness, so establishing the way of human beings is called benevolence and righteousness. The mutual感应 of yin and yang is called "harmony," and the virtue of the earth is to be yielding, so "harmony and yielding" refers to the earth. The heaven represents the way and virtue, so "morality" refers to the heaven. Yielding to the heaven is called "harmony and yielding to morality." The "Qian Zao Du" says "heaven moves and gives, which is called benevolence; earth is still and orderly, which is called righteousness." By the heaven penetrating the earth, it is called "reasoned in righteousness."

○以乾至為命○此虞義也。坤為理，以乾推坤故謂之窮理。乾為性，以坤變乾故謂之盡性。乾伏坤初，巽為命，性盡理窮，故至於命，謂贊天地之化育也。繫上曰：「易簡而天下之理得矣。天下之理得而易成位於其中矣。」

This is Yu Fan's view. The earth (Kun) represents principle, and using the heaven (Qian) to infer the earth is called "exhausting principle." The heaven represents nature, and using the earth to transform the heaven is called "exhausting nature." The heaven is hidden beneath the first line of the earth, and the wind (Xun) represents destiny. When nature is fully understood and principle is thoroughly explored, one can reach destiny—that is, to assist in the transformation and nurturing of heaven and earth. The Great Treatise says: "Heaven and earth are easy and simple; thus all the principles of the world are grasped. When the principles of the world are grasped, the function of the Book of Changes is established within heaven and earth."

虞彼注云：「乾坤變通窮理以盡性，故天下之理得。天下之理得而易成位乎其中，天地位，萬物育，此既濟之事。」蓋為下陳明堂大道張本也。○重言至庖犧○此虞義也。○謂乾至理也○坤下有伏乾，所謂性也。乾下有伏巽，所謂命也。乾變坤化，參天兩地，六耦承奇，是各正性命。乾為性，故以陽順性。巽為命，故以陰順命。此上虞義也。

Yu Fan remarked: "The transformations of Heaven and Earth are interconnected and thorough, investigating physical principles to exhaust human nature, so that the principles of the world can be grasped. When the principles of the world are grasped, the Book of Changes establishes its place. Thus, Heaven and Earth each occupy their proper positions, and all things flourish in their respective ways, which is precisely the state described in the 'Already Achieved' hexagram." Hui Dong's exposition seems to be setting the stage for the subsequent explanation of the Great Hall doctrine. The annotation "repeating 'in the past,' meaning 'Paoxi'" is Yu Fan's view. The passage from "the way of the乾 (Heaven) changing" to "what is called principle" states: beneath the坤 (Earth) lies the乾 (Heaven), which is called "nature"; beneath the乾 (Heaven) lies the巽 (Wind), which is called "destiny." The乾 (Heaven) governs transformation, the坤 (Earth) governs transformation through change, combining Heaven and Earth, with six even numbers following the three odd numbers, which is "each establishing its nature and destiny." The乾 (Heaven) represents nature, so the yang follows its nature; the巽 (Wind) represents destiny, so the yin follows its destiny. All of the above are Yu Fan's views.

韓非子曰：「理者，方圓短長麤靡堅脆之分也。」立天之道曰陰與陽，不言陰陽而言陰與陽，是陰陽之理。立地之道曰柔與剛，是柔剛之理也。立人之道曰仁與義，是仁義之理也。陰陽柔剛仁義原本於性命，所謂性命之理。下雲兼三才而兩之，是順性命之理也。

The "Han Feizi · Jie Lao" says: "What is called 'reason' is the distinction between square and round, short and long, coarse and fine, hard and brittle." The classic text says that establishing the way of Heaven is called "yin and yang," not directly calling it "yin and yang" but saying "yin and yang," which is precisely to point out the order between yin and yang. It says that establishing the way of Earth is called "flexible and strong," which refers to the order between flexibility and strength; it says that establishing the way of humanity is called "benevolence and righteousness," which refers to the order between benevolence and righteousness. Yin and yang, flexibility and strength, benevolence and righteousness all originate from the nature and destiny, which is called "the reason of nature and destiny." The following text says "combining the three elements and dividing them into two," which is precisely following the way of nature and destiny.

○陰謂至為義○陰謂坤，陽謂乾者，謂坤三畫為陰，乾三畫為陽也。柔謂陰爻，剛謂陽爻者，謂以三為六，二四上為陰爻，初三五為陽爻也。管子曰：「天仁地義。」故乾為仁，坤為義。○謂參至數也○此虞義也。上雲參天兩地而倚數，是天地本有兼才之理。聖人設卦，因而重之，以地兩三而成六畫，所謂順性命之理也。

The passage "Yin refers to Kun, Yang refers to Qian" up to "Kun represents meaning": What is meant by Yin referring to Kun and Yang referring to Qian is talking about the three-line trigrams. The three lines of Kun belong to Yin, and the three lines of Qian belong to Yang. What is meant by softness referring to Yin lines and strength referring to Yang lines is talking about the process of deriving the six-line hexagrams from the three-line trigrams: the second, fourth, and top lines are Yin lines, while the first, third, and fifth lines are Yang lines. The "Guanzi" says "Heaven governs benevolence, Earth governs righteousness," so Qian represents benevolence and Kun represents righteousness. The passage "called参天两地" up to "the number of six lines": This is Yu Fan's view. The previous text says "by combining three and two," indicating that Heaven and Earth originally contain the principles of the three elements. The sage established the trigrams based on this principle, by doubling the Earth number two with the Heaven number three to form six lines, which is exactly what is meant by following the principles of nature and destiny.

○陰陽至地理○位有陰陽，故云陰陽位也。爻有剛柔，故云剛柔爻也。「迭，遞也」已下虞義也。釋言曰：「遞，迭也。」遞迭同訓，故云迭遞也。剛柔更用事，故云迭用柔剛。繫上曰：「仰以觀於天文，俯以察於地理。」故章謂文理。

The passage from "Shuzheng Zhuwen" "Yin and Yang, positions" to "Kun's three lines form the geography": There are distinctions between yin positions and yang positions, hence "Yin and Yang, positions." There are also distinctions between strong lines and flexible lines, hence "Strong and flexible, lines." From "Alternating, meaning successive" onwards, the explanation follows Yu Fan's interpretation. The "Erya · Xiyán" states "Successive means alternating," and since "successive" and "alternating" have the same meaning, it says "Alternating, meaning successive." Strong and flexible alternate in dominance, hence "alternating the use of flexible and strong." The "Xici Shang" says "Looking up to observe the patterns of heaven, looking down to examine the order of earth," so "chapter" refers to patterns and order.

文理者，間雜之義。昭廿五年春秋傳曰「五章」，杜預注云：「青與赤謂之文，亦與白謂之章，白與黑謂之黼，黑與青謂之黻，五色備謂之繡。」所謂五章是也。韓非子曰：「理者成物之文也。」天地人各有陰陽剛柔仁義，即上文性命之理也。

The term "wen li" refers to the interwoven patterns. In the "Zuo Zhuan" of Duke Zhao's twenty-fifth year, it mentions "wu zhang," and Du Yu's commentary explains: "The combination of blue and red is called wen, the combination of red and white is called zhang (the original "yi" is a mistake for "chi"), the combination of white and black is called fu, the combination of black and blue is called fu, and the combination of all five colors is called xiu." This is what is referred to as the five zhang. The "Han Feizi" states, "Li is the pattern that forms things." Heaven, Earth, and humanity each possess yin and yang, hardness and softness, and benevolence and righteousness, which is the principle of life and nature mentioned earlier.

天地定位山澤通氣雷風相薄水火不相射八卦相錯。注。此明二篇之次也。天地定位，乾坤泰否也。山澤通氣雷風相薄，咸恆損益也。水火不相射，坎離既未濟也。薄，入也。射，厭也。所陳凡八卦相錯而成上下二篇也。

The Shuo Guà Zhuàn says: Heaven and Earth establish their positions above and below, mountains and marshes communicate their energies, thunder and wind mutually stir each other, water and fire do not despise each other. The eight trigrams are arranged in sequence. Note: This explains the order of the two parts of the Zhou Yi. "Heaven and Earth establishing their positions" refers to Qian, Kun, Tai, and Po; "mountains and marshes communicating their energies, thunder and wind mutually stirring" refers to Xian, Heng, Shen, and Yi; "water and fire not despising each other" refers to Kan, Li, Ji Ji, and Wei Ji. "Bó" means mutual entry, and "shè" means despising. What is stated here is only the eight trigrams. When the eight trigrams are interwoven and overlapped, they form the upper and lower parts.

易說陽道純而奇，故上篇三十，所以象陽也。陰道不純而偶，故下篇三十四，所以法陰也。上經象陽，故以乾為首，坤為次，先泰而後否。下經法陰，故以咸為始，恆為次，先損而後益。又曰離為日，坎為月，日月之道，陰陽之經，所以終始萬物，故以坎離為終。既濟未濟為下篇終者，所以明戒慎而全王道。

The cited text from the "Commentary on the Changes" states: The principle of yang is pure and belongs to the odd number, hence the upper section contains thirty hexagrams, symbolizing yang; the principle of yin is not pure and belongs to the even number, hence the lower section contains thirty-four hexagrams, following the pattern of yin. Since the upper section symbolizes yang, it begins with the hexagram Qian (Heaven) and follows with Kun (Earth), and arranges Tai (Harmony) before Po (Obstruction); since the lower section follows yin, it starts with Xian (Mutual Influence) and follows with Heng (Permanence), and arranges Shen (Loss) before Yi (Gain). The "Commentary on the Changes" also states: Li (Fire) represents the sun, and Kan (Water) represents the moon. The movement of the sun and moon is the constant way of yin and yang, used to bring about the beginning and end of all things. Hence, the last two hexagrams of the upper section are Kan and Li. As for using Ji Ji (Completion) and Wei Ji (Non-Completion) to conclude the lower section, it is to indicate that only through vigilance and caution can the Way of the Sovereign be preserved.

數往者順知來者逆是故易逆數也。注。坤為數往，乾為知來。坤消從午至亥，上下故順。乾息從子至巳，下上故逆。易氣從下生，故云易逆數也。雷以動之風以散之雨以潤之日以烜之艮以止之兌以說之乾以君之坤以藏之。注。烜，乾也。乾坤三索而得六子，六子自下生。六子既成各任生物之功，乾為之君，坤受而藏之以成十二闢卦也。

The text says: Pushing numbers backward is called following the trend, while predicting the future is called reversing the trend, so the Book of Changes is based on reversing the trend. Note: The Earthly element (Kun) governs pushing numbers backward, and the Heavenly element (Qian) governs predicting the future. The energy of Kun wanes from the month of Wu to the month of Hai, moving from top to bottom, hence called following; the energy of Qian grows from the month of Zi to the month of Si, moving from bottom to top, hence called reversing. The energy of the Book of Changes arises from the bottom upward, so it is called reversing numbers. The text says: Thunder is used to stir up all things, wind is used to scatter all things, rain is used to nourish all things, sun is used to dry all things, Mountain (Geng) is used to stop them, Lake (Dui) is used to make them joyful, Heaven (Qian) is used to govern them, and Earth (Kun) is used to collect them. Note: "Xuan" means drying. Heaven and Earth interact three times to produce the six sons, and all six sons arise from the bottom. Once the six sons have been generated, each takes on its role in nurturing all things. Heaven serves as their sovereign, and Earth receives and collects them, thus forming the twelve trigrams of division.

疏。此明至王道○此承參兩來釋文王分上下二經，乾坤泰否坎離咸恆損益既未濟終始相次之義，而六十四卦之序亦可知矣，故云二篇之次也。天地定位，天地，乾坤也。乾下坤上為泰，坤下乾上為否，故云乾坤泰否也。

The passage "This explains the order of the two chapters" to "completing the Way of the King" continues from the previous text "participating in heaven and dividing into two." It explains the meaning of the sequence of the hexagrams in the division of the Book of Changes into upper and lower parts by King Wen. The relationship between the pairs of hexagrams, such as Qian and Kun, Tai and Po, Kan and Li, Xian and Heng, Shen and Yi, Ji Ji and Wei Ji, shows their mutual continuation and completion. Understanding this allows one to know the order of the sixty-four hexagrams, hence it is called "the order of the two chapters." "Heaven and earth are positioned" refers to heaven and earth being Qian and Kun. Qian below and Kun above form Tai, while Kun below and Qian above form Po, hence Qian Kun Tai Po.

山澤通氣雷風相薄，山上有澤，咸。山下有澤，損。雷風恆，風雷益。故云咸恆損益也。水火不相射，水火，坎離也。水在火上既濟，火在水上未濟，故云坎離既未濟也。薄入，馬鄭義。射厭，虞陸義也。射厭，釋詁文。以上所陳凡八卦耳，因參重三才之後，故相錯雜而成六十四卦為上下二篇也。

"Mountains and marshes communicate, thunder and wind contend with each other": a marsh on top of a mountain is the hexagram "Xian," a marsh below a mountain is the hexagram "Sun"; thunder above wind below is the hexagram "Heng," wind above thunder below is the hexagram "Yi," hence "Xian," "Heng," "Sun," and "Yi." "Water and fire do not shoot at each other": water and fire refer to Kan and Li; water above fire is the hexagram "Ji Ji," fire above water is the hexagram "Wei Ji," hence "Kan" and "Li" are "Ji Ji" and "Wei Ji." Taking "bo" as "ru" (enter) follows the interpretation of Ma Rong and Zheng Xuan; taking "she" as "yan" (saturate) follows the interpretation of Yu Fan and Lu Ji. "She, yan also" is found in the "Erya · Xiguzhu." The above merely refers to the eight trigrams. Because after each of the three elements (Heaven, Earth, Humanity) has two lines, the eight trigrams intermingle to form the sixty-four hexagrams, divided into upper and lower sections.

易說者，乾鑿度文，所以釋二篇諸卦之次正與此合，故引之。彼文云：「陽三陰四，位之正也，故易六十四分而為上下，象陰陽也。」陽道純而奇者，鄭注謂「陽道專斷，兼統陰事，故曰純也」。三法天，故上篇三十，所以象陽也。陰道不純而偶者，陰制於陽，故不純。四法地，故下篇三十四，所以法陰也。

The text cited in the commentary refers to the words of the "Yi Shuo" (Commentary on the Changes), specifically from the "Qian Zao Du" (The Opening of the Qian). Its explanation of the order of the sixty-four hexagrams in the upper and lower sections coincides exactly with this, so it is quoted. The "Qian Zao Du" states: "Yang belongs to three, Yin belongs to four; this is the proper order of positions, so the sixty-four hexagrams are divided into upper and lower sections to symbolize Yin and Yang." The phrase "Yang's path is pure and odd" is explained by Zheng Xuan as "Yang's path is exclusively about decision-making and also oversees Yin's affairs, hence it is called pure." Three is taken as a model from Heaven, so the upper section contains thirty hexagrams, symbolizing Yang. The phrase "Yin's path is not pure but even" is because Yin is controlled by Yang, hence it is not pure; four is taken as a model from Earth, so the lower section contains thirty-four hexagrams, symbolizing Yin.

上篇象陽，乾陽坤陰，故乾為首，坤為次。乾鑿度又云：「乾坤者，陰陽之本始，萬物之祖宗，故為上篇。始者，尊之也。」泰陽息卦，否陰消卦，故先泰而後否。鄭注謂「先尊而後卑，先通而後止者，所以類陽事也」。下篇法陰，鄭注謂「咸則男下女，恆則陽上而陰下」，故以咸為始，恆為次。先陰而後陽者，以取類陰事也。

The upper section represents yang. The trigram Qian belongs to yang and Kun belongs to yin, so the hexagram Qian comes first and Kun comes second. The "Qian Zuo Du" says: "Qian and Kun are the origins and beginnings of yin and yang, the ancestors of all things, so they are placed in the upper section. They are placed at the beginning to show respect for them." The hexagram Tai represents yang's growth, while the hexagram Po represents yin's decline, so Tai comes before Po. Zheng Xuan's commentary says, "First the noble, then the humble; first the open, then the closed. This is used to compare with yang's affairs." The lower section follows the pattern of yin. Zheng Xuan's commentary says, "Xian represents a man yielding to a woman, while Heng represents yang above and yin below." Therefore, Xian comes first and Heng comes next. First yin, then yang, to compare with yin's affairs.

乾鑿度曰：「損者陰用事，益者陽用事。」故先損而後益。鄭注謂「損象陽用事之時，陰宜自損以奉陽者，所以戒陰道以執其順者也。益當陰用事之時，陽宜自損以益陰者，所以戒陽道以弘其化者也」。鄭知然者，損自泰來，故象陽用事之時，陰自損以奉陽。益自否來，故當陰用事之時，陽當自損以益陰也。

The *Qian Zao Du* says: "The *Dun* hexagram signifies the time when Yin is in authority, while the *Yi* hexagram signifies the time when Yang is in authority." Therefore, *Dun* comes before *Yi*. Zheng Xuan's commentary states: "The *Dun* hexagram symbolizes the time when Yang is in authority, and Yin should reduce itself to serve Yang; this is a warning to Yin to maintain its gentleness. The *Yi* hexagram signifies the time when Yin is in authority, and Yang should reduce itself to benefit Yin; this is a warning to Yang to promote its nurturing power." Zheng Xuan could make this determination because the *Dun* hexagram arises from *Tai*, thus symbolizing the time when Yang is in authority and Yin reduces itself to serve Yang; the *Yi* hexagram arises from *Po*, thus signifying the time when Yin is in authority and Yang reduces itself to benefit Yin.

日月之道，陰陽之經，所以終始萬物者，五六三十乃天地之數，故曰陰陽之經。乾彖傳曰「大明終始」，荀注云：「乾起坎而終於離，坤起離而終於坎。離坎者，乾坤之家而陰陽之府，故終始萬物。」是上篇終坎離之義也。

The commentary says, "The movement of the sun and moon follows the constant way of yin and yang, thus bringing about the beginning and end of all things." Five multiplied by six gives thirty, which is exactly the number of heaven and earth, hence it is called "the classic of yin and yang." The Commentary on the Judgment of the Qian hexagram says, "Great brightness brings about the beginning and end." Xu Shuang's commentary says, "The Qian hexagram begins with Kan and ends with Li, while the Kun hexagram begins with Li and ends with Kan. Li and Kan are the dwellings of Qian and Kun, the repositories of yin and yang, thus they can bring about the beginning and end of all things." This is the reason why the previous section concludes with Kan and Li.

雲既濟未濟為下篇終者，所以明戒慎而全王道者，上篇天道，下篇人事。王者體中和贊化育而成既濟定。既濟象傳曰「君子以思患而豫防之」，荀注云：「六爻既正，必當復亂，故君子象之思患而豫防之。」治不忘亂，故云所以戒慎而全王道。序卦曰：「物不可窮也，故受之以未濟終焉。」是下篇終既未濟之義也。

The commentary says, "Using the hexagrams of Ji Ji and Wei Ji as the conclusion of the lower section is to indicate the need for vigilance and caution in preserving the Way of the King." The upper section discusses the Way of Heaven, while the lower section discusses human affairs. The King, by observing the virtue of harmony and balance and assisting the transformation and nurturing of Heaven and Earth, can achieve the fixed state of the hexagram Ji Ji, where all six lines are properly aligned. The image of Ji Ji says, "The gentleman thus contemplates dangers and prepares in advance." Xun Shuang's commentary says, "Since all six lines have already been properly aligned, it is certainly going to turn toward disorder again, so the gentleman takes this image as a model, contemplates dangers, and prepares in advance." A time of peace should not forget the time of chaos, hence it is said to be about vigilance and caution in preserving the Way of the King. The "Xu Guan Zhuan" says, "Things cannot be exhausted, so the hexagram Wei Ji is used to follow and conclude," which is the reason why the lower section concludes with Ji Ji and Wei Ji.

○坤為至數也○繫上曰：「神以知來，知以藏往。」虞彼注云：「乾神知來，坤知藏往。」故坤為數往，乾為知來。坤消已下虞義也。坤消自午，右行至亥，從上而下，故順。乾息自子，左行至巳，從下而上，故逆。易氣從下生，乾鑿度文。鄭彼注云：「易本無形，自微及著，氣從下生，以下爻為始。」故十二辰之法坤雖自上而下，然消遘及亦自下生，故云易逆數也。

The commentary from "Kun Governs the Past" to "Therefore it is said that the Book of Changes is inverse in counting" states: The Great Treatise says, "The divine can foresee the future, and wisdom can collect the past." Yu Fan comments, "The divine of Qian foresees the future, and the wisdom of Kun collects the past." Therefore, Kun governs the past, and Qian governs the future. From "Kun declines" onwards are Yu Fan's remarks: The qi of Kun declines starting from the month of Wu, moving right to the month of Hai, which is from top to bottom, hence called "smooth." The qi of Qian grows starting from the month of Zi, moving left to the month of Si, which is from bottom to top, hence called "inverse." The phrase "the qi of the Book of Changes arises from below" comes from the "Qian Zuo Du." Zheng Xuan comments there: "The Book of Changes originally has no form, emerging from subtle to manifest, its qi arises from below, starting with the lower trigrams." Therefore, according to the twelve earthly branches, although Kun moves from top to bottom, the decline of yin still begins from below, hence it is said that the Book of Changes is inverse in counting.

○烜乾至卦也○烜乾，京義也。乾道成男，一索再索三索而得震坎艮。坤道成女，一索再索三索而得巽離兌。皆自下而上，以明易之為逆數也。九家云：「乾坤交索，既生六子，各任其才往生物。」故云六子既成，各任生物之功，謂動之散之之類是也。乾為之君，謂息卦自子至巳。坤受而藏之，謂消卦自午至亥，是謂十二闢卦。著此者為下陳明堂十二月之法也。

The passage from "Shuzheng Zhuwen" "Xuan, Qian also" to "to form the twelve trigrams of the sun" states that interpreting "Xuan" as drying is in line with Jing Fang's method. The principle of Qian (Heaven) produces the male trigrams, with one, two, and three searches resulting in Zhen (Thunder), Kan (Water), and Gen (Mountain); the principle of Kun (Earth) produces the female trigrams, with one, two, and three searches resulting in Xun (Wind), Li (Fire), and Dui (Lake): all are formed from the bottom up, indicating that the Book of Changes operates through reverse reasoning. The "Nine Schools of the Book of Changes" says: "Qian and Kun interactively seek, thus producing the six sons, who each, according to their nature, nurture all things." Therefore, the commentary states that the six sons have already been generated, each taking on the responsibility of nurturing all things, which refers to actions such as stirring and dispersing. "Qian as the sovereign" refers to the trigrams of yang energy from the first lunar month to the fourth lunar month; "Kun receiving and storing it" refers to the trigrams of yin energy from the fifth lunar month to the tenth lunar month: this is the twelve trigrams of the sun. Hui Dong specifically points this out here to serve as a prelude for the following explanation of the twelve months of the Bright Hall.

帝出乎震齊乎巽相見乎離致役乎坤說言乎兌戰乎乾勞乎坎成言乎艮。注。帝，上帝也。上帝五帝在太微之中，迭生子孫，更王天下，故四時之序，五德相次。聖人法之以立明堂，為治天下之大法也。

The Sayings on the Trigrams states: The Supreme Deity starts from the Zhen position, arranges all things in order at the Xun position, meets all things at the Li position, subdues all things at the Kun position to nurture them, makes all things joyful and speak at the Dui position, and has yin and yang contend at the Qian position. At the Kan position, the Supreme Deity comforts all things; at the Gen position, the Supreme Deity establishes the beginning and end. Note: "Deity" refers to the Supreme Deity. The Supreme Deity is the Five Emperors, residing in the Taiwei垣, taking turns to produce children and rule the world, hence the four seasons proceed in order and the five virtues succeed one another. The sage modeled this and established the Bright Hall as the fundamental principle for governing the world.

神農曰天府，黃帝曰合宮，唐曰五府，虞曰總章，夏曰世室，殷曰重屋，周曰明堂。明堂者有五室四堂，二九四七五三六一八，四正四維皆合於十五。室以祭天，堂以佈政。王者承天統物，各於其方以聽事謂之明堂。月令，虞夏商周四代行之，今所傳月令是也。

The name of the Bright Hall has varied through different dynasties: during the time of the Divine Farmer it was called the Imperial Mansion, during the Yellow Emperor's time it was called the Combined Palace, during the reign of the Yao Dynasty it was called the Five Palaces, during the Shun Dynasty it was called the General Hall, during the Xia Dynasty it was called the World Hall, during the Shang Dynasty it was called the Heavy Roof, and it was only during the Zhou Dynasty that it was called the Bright Hall. The Bright Hall consists of five rooms and four halls, with the numbers of the nine squares being 2, 9, 4; 7, 5, 3; and 6, 1, 8. The sum of the four cardinal directions and the four secondary directions, when added together, all total fifteen. The rooms are used for worshiping Heaven, while the halls are used for issuing decrees and governing the state. The sovereign governs all things according to the heavenly way, and each ruler attends to state affairs in the corresponding hall according to the appropriate direction, which is called the Bright Hall. The system of the Monthly Orders was practiced by the Yu, Xia, Shang, and Zhou dynasties, and the version of the Monthly Orders that is passed down today is derived from it.

古之聖人生有配天之業，沒有配天之祭，故太皥以下歴代所禘。太皥以木德，炎帝以火德，黃帝以土德，少昊以金德，顓頊以水德。王者行大享之禮於明堂謂之禘祖宗，其郊則行之於南郊。禘郊祖宗四大祭而總謂之禘者，禘其祖之所自出故也。一帝配天，功臣從祀，故禘禮上遡遠祖，旁及毀廟，下逮功臣。

Ancient sages, while alive, had meritorious deeds worthy of Heaven, and after their death, they received worship equal to that of Heaven. Therefore, since the time of Tai Hao, successive generations have received the rites of禘. Tai Hao was associated with the Wood virtue, the Flame Emperor with Fire, the Yellow Emperor with Earth, Xiao Hao with Metal, and Zhuan Xu with Water. The king holds a grand ceremony in the Bright Hall called "禘 the ancestors"; as for the ceremony at the southern suburb, it is held at the southern outer altar. The four great rites of禘,郊, 祖, and 宗 are collectively called "禘" because they all involve the worship of the heavenly emperor from whom the ancestors originated. One heavenly emperor is paired with Heaven, and meritorious ministers are included in the worship. Thus, the rites of禘 can trace back to distant ancestors, include those of destroyed temples, and extend to meritorious ministers.

聖人居天子之位，以一德貫三才，行配天之祭，推人道以接天，天神降，地示出，人鬼格。夫然而陰陽和，風雨時，五穀孰，草木茂，民無鄙惡，物無疵厲，群生咸遂，各盡其氣，威厲不試，刑措不用，風俗純美，四夷賓服，諸福之物，可致之詳，無不畢至，所謂既濟定也。庖犧畫八卦以贊化育，其道如此。

The sage holds the position of the Son of Heaven, using a pure and unified virtue to connect the three elements of heaven, earth, and humanity. He conducts rituals to match the heavens, extending human morality to connect with heaven. Thus, heavenly spirits descend, earth deities emerge, and human spirits come to respond. In this way, yin and yang harmonize, winds and rains come at the proper time, grains mature, and grass and trees flourish. The people do not commit crude or evil deeds, and all creatures are free from defects and calamities. Each being fulfills its life according to its nature, and the power of punishment is not needed, nor are punishments applied. Customs become refined, and the surrounding tribes submit. All blessings and auspicious signs arrive together—this is called the established order of "The Final Completion" where each thing is in its proper place. The Yellow Emperor drew the Eight Trigrams to assist in the nurturing of heaven and earth, and the principle is exactly the same.

萬物出乎震震東方也。注。出，生也。東方者，青陽太廟也。齊乎巽巽東南也齊也者言萬物之絜齊也。注。東南者，東青陽個，南明堂個也。巽陽藏室，故絜齊。離也者明也萬物皆相見南方之卦也。注。離為日為火，故明。日出照物，以日相見，故萬物皆相見。南方者，明堂太廟也。

The classic text says: All things originate from the Zhen position, and Zhen is located in the east. Note: "Originating" means being born. Here, the east refers to the Bright Hall's Qingyang Temple. The classic text says: At the Xun position, things are orderly arranged; Xun is located in the southeast. The term "orderly arranged" means that all things are clean and well-organized. Note: The southeast refers to the eastern Qingyang Temple and the southern Bright Hall. The yang line of Xun is hidden indoors, hence it is clean and orderly. The classic text says: Li represents brightness, and all things meet here, which is the southern trigram. Note: Li represents the sun and fire, hence it signifies brightness. The sun rises and shines upon all things, allowing them to be visible to each other through sunlight, hence all things meet. Here, the south refers to the Bright Hall Temple.

聖人南面而聽天下向明而治蓋取諸此也。注。負斧扆南面而立，故南面而聽天下。聽，聽朔也。乾為治，天子當陽，故嚮明而治。蓋取諸此者，言明堂之法取諸此也。蔡氏謂人君之位莫正於此，故雖有五名而主以明堂也。

The classic text says: "The sage faces south to govern the world, facing the light to administer the state and rites, which is derived from this." The annotation explains: the king stands facing south with a screen depicting an axe behind him, thus "facing south to hear the world." Here, "hearing" refers to "listening to the new moon," meaning that on the first day of each month, the emperor issues decrees in the Bright Hall. The trigram Qian represents governance, and the Son of Heaven stands in the center, facing the light to administer the state and rites. The phrase "taking from this" indicates that the method of the Bright Hall is derived from this passage. Cai Yong believed that there is no more appropriate position for a ruler than this, so although the Bright Hall has five names such as Qingyang and Zongzhang, it is still primarily called the Bright Hall.

坤也者地也萬物皆致養焉故曰致役乎坤。注。坤位未而王四季，故用事於西南而居中央。西總章個，南明堂個，中央太廟太室也。明堂月令中央土，土爰稼穡，故萬物皆致養役事也。坤為事。王者四時迎氣於四郊，其中央之帝乃方澤也，合圜丘之帝為六天。

The text says: "Kun represents the earth, and all things are nurtured here, so it is said 'to serve under Kun'." Commentary: The position of Kun is at Wei, and earth rules over the four seasons. Therefore, it exercises authority and governs in the southwest and resides in the center. In terms of the Bright Hall, it refers to the total chapter in the west, the Bright Hall in the south, and the Great Temple and Great Chamber in the center. The "Bright Hall Monthly Order" assigns the center to earth, and the "Hóng Fàn" states "earth governs crops and farming," so all things are nurtured and subjected here. Kun represents affairs. The king observes the seasonal changes at the four outer areas during the four seasons, while the temple of the central emperor is at the square marsh; the emperor of the square marsh combines with the emperor of the round hill, making a total of six heavens.

兌正秋也萬物之所說也故曰說言乎兌。注。兌主酉，故正秋。總章，太廟也。兌為雨澤，故說萬物。震為言，震二動成兌，言從口出，故說言也。戰乎乾乾西北之卦也言陰陽相薄也。注。西北者，西總章個，北玄堂個也。坤十月卦，乾消剝入坤，故陰陽相薄也。

The text says: "The trigram Dui is appropriate for the autumn season, which is the time when all things are joyful, hence it is said 'speech is related to Dui.'" Note: Dui governs the month of You, hence it is the proper autumn; in terms of the Bright Hall, it refers to the Total Chapter Temple. Dui represents rain and dew, which can make all things joyful. Zhen represents speech, and when the second line of Zhen moves, it becomes Dui. Dui represents the mouth, and speech comes from the mouth, hence it is said "speech is related to Dui." The text says: "In the position of Qian, there is a struggle. Qian is the trigram of the northwest, which refers to yin and yang approaching each other closely." Note: Northwest refers to the Total Chapter in the west and the Xuan Hall in the north. Kun is the trigram of the tenth month, and Qian is consumed and enters Kun, hence yin and yang approach each other closely.

坎者水也正北方之卦也勞卦也萬物之所歸也故曰勞乎坎。注。正北方者，玄堂太廟也。勞，動也。水性動而不舍，故曰勞卦。歸，藏也。艮東北之卦也萬物之所成終而所成始也故曰成言乎艮。注。東北者，東青陽個也，故曰成始。北玄堂個也，故曰成終。

The text says: Kan is water, the trigram of the north, representing diligence, for all things are gathered and hidden here, hence it is called "diligence in Kan." Note: The north, in terms of the bright hall, is the dark hall and the ancestral temple. "Diligence" refers to ceaseless movement. Water's nature is to flow ceaselessly, hence it is called the diligence trigram. "Gather" means to collect. The text says: Gen is the trigram of the northeast, where all things complete their end and begin anew, hence it is called "completion in Gen." Note: The northeast is connected to the east's Qingyang, hence "completion of the beginning"; and connected to the north's dark hall, hence "completion of the end."

神也者妙萬物而為言者也。注。神謂易，即一也。妙，微也。聖人飭明堂，以一偶萬，明者以為法，微者以是行，不見其事而見其功，故妙萬物而為言。動萬物者莫疾乎雷撓萬物者莫疾乎風燥萬物者莫熯乎火說萬物者莫說乎澤潤萬物者莫潤乎水終萬物始萬物者莫盛乎艮。注。四時分而效職。故水火相逮雷風不相悖山澤通氣。注。六子合而成物。然後能變化既成萬物也。注。變化謂乾坤。乾道變化，各正性命，成既濟定，故既成萬物矣。不言乾坤而言變化者，以見神之所為。

The text says: The term "spirit" refers to the subtle transformation of all things. Note: "Spirit" refers to the Book of Changes, which is "one"; "subtle" means subtle and invisible. The sage established the system of the Bright Hall, using "one" to govern all things: the manifest part is for people to follow, while the subtle part operates silently within, unseen yet its effects are visible. Therefore, it is said that the spirit subtly transforms all things. The text says: Nothing is more vigorous in stirring all things than thunder, nothing more powerful in shaking all things than wind, nothing more intense in drying all things than fire, nothing more pleasing to all things than marshes, nothing more nourishing to all things than water, and nothing more comprehensive in ending and beginning all things than mountain. Note: The four seasons each have their respective roles and fulfill their functions. The text says: Therefore, water and fire pursue each other, thunder and wind do not contradict each other, and mountains and marshes exchange their energies. Note: The six sons combine to create all things. The text says: Only then can transformation occur, and all things are completed. Note: "Transformation" refers to the trigrams Qian and Kun. The way of Qian brings about transformation, enabling all things to establish their nature and destiny, achieving the fixed state of the "Already Completed" hexagram. Therefore, it is said that all things are completed. Not directly referring to Qian and Kun but using "transformation," is to highlight that this is the work of the "spirit."

疏。帝上至如此○此陳明堂之法。六子成而生物之功備，十二消息具而乾坤之用宏，夫然而既濟之治可得而言矣。帝即五帝，五帝稱上帝者，孝經曰「周公宗祀文王於明堂以配上帝」，周以木德，謂配木德之帝，是五德之帝皆稱上帝也。上帝五帝在太微之中迭生子孫更王天下者，此何休義也。劉歆七略曰：「王者師天地，體天而行，是以明堂之制內有太室象紫微，南出明堂象太微。」援神契亦謂五精之神實在太微，故知五帝在太微之中。

The passage from "Shu Zheng Zhu Wen" "Emperor, meaning the Heavenly Emperor" to "its way is like this": Here, Chen is talking about the method of the Bright Hall. Once the six sons are complete, their function of generating and nurturing all things is fully established; once the twelve messages are complete, the functions of Heaven and Earth become grand. At this stage, a world governed like the "Ji Ji" hexagram can be discussed. "Emperor" refers to the Five Emperors. The Five Emperors are called "Heavenly Emperor" because the "Xiao Jing" says "the Duke of Zhou in the Bright Hall honored King Wen to be paired with the Heavenly Emperor." The Zhou dynasty belonged to the wood virtue, and the one paired with it was the wood virtue emperor, thus showing that the emperors of the five virtues can all be called Heavenly Emperor. The commentary says that the Heavenly Emperor and the Five Emperors take turns giving birth to children and ruling the world, which is the view of He Xiu. Liu Xin's "Qi Lue" says: "The king takes the heavens and earth as his teacher, observing the heavenly way to act, so the system of the Bright Hall includes Tai Shi symbolizing the Purple Micro垣, and the southern extension of the Bright Hall symbolizing the Tai Wei垣." The "Xiao Jing Yuan Shen Qi" also says that the five vital spirits actually dwell in the Tai Wei垣, thus knowing that the Five Emperors dwell in the Tai Wei.

乾彖傳曰「大哉乾元，萬物資始乃統天」，郊特牲曰「萬物本乎天」，聖人而為天子，尤天所篤生者，故云迭生子孫更王天下，如下所云五德相次是也。四時之序木火土金水，五行之德用事者王，所生相，故王廢，勝王囚，王所勝死，故云五德相次。家語孔子曰：「天有五行木火金水土，分時化育以成萬物，其神謂之五帝。」又曰：「五行用事先起於木。木東方萬物之初皆出焉，是故王者則之而首以木德王天下，其次則以所生之行轉相承也。」

The Commentary on the Judgment of the Qian hexagram says, "Majestic is the Qian yuan, by which all things begin, and it governs heaven." The "Rites of the Sacrificial Offering to the Ancestral Spirits" states, "All things originate from heaven." A sage becomes a king, especially one born by heaven's favor, so it is said that they successively produce descendants and take turns ruling the world, as explained below, where the five virtues succeed one another in order. The sequence of the four seasons is wood, fire, earth, metal, and water; the virtue of the current element is called "king," the one it generates is called "minister," the previous one is called "abandoned," the one that overcomes it is called "captured," and the one overcome is called "dead." Therefore, the five virtues succeed one another in order. The "Discourses of the Master Kong" records that Kongzi said, "Heaven has the five elements, wood, fire, metal, water, and earth, which govern the four seasons and nurture all things. Their spirits are called the Five Emperors." It also says, "When one of the five elements is in charge, it begins with wood. Wood is in the east, and all things first arise from here, so the ruler takes the virtue of wood first, ruling the world, and then follows the order of the element it generates."

大戴禮盛德云「明堂天法」，故聖人法之以立明堂，謂庖犧作八卦，聖人法之。故宇文愷據黃圖曰：「堂方百四十四尺，法坤之筴也，方象地。屋圓楣徑二百一十六尺，法乾之筴也，圓象天。室九宮，法九州島。太室方六丈，法陰之變也。十二堂法十二月。三十六戶法極陰之變數。七十二牖法五行所行日數。八達象八風，法八卦。」

The "Da Dai Li Ji · Sheng De" says, "The Bright Hall is modeled after Heaven." Therefore, sages modeled it to establish the Bright Hall—that is,庖牺 drew the Eight Trigrams, and sages then modeled themselves after the Eight Trigrams. Therefore, the Sui dynasty person Yuwen Kai, based on the "San Fu Huang Tu," said: "The hall is a square, with each side measuring 144 chi, modeled after the number 144 of the Earth Trigram, symbolizing the square shape. The circular eaves of the roof have a diameter of 216 chi, modeled after the number 216 of the Heaven Trigram, symbolizing the circular shape of Heaven. The room is divided into nine palaces, modeled after the nine states. The main hall is square with six zhang on each side, modeled after the transformation of the yin number. Twelve halls are modeled after the twelve months. Thirty-six doors are modeled after the extreme transformation of yin. Seventy-two windows are modeled after the number of days each of the Five Phases governs. Eight directions being accessible symbolize the Eight Winds, modeled after the Eight Trigrams."

通天台徑九尺，法乾以九覆六。高八十一尺，法黃鍾九九之數。二十八柱象二十八宿。堂高三尺，土階三等，法三統。堂四向五色，法四時五行。水四周於外，象四海，圓法陽也。水闊二十四丈，象二十四氣。水內徑三丈，應覲禮經。是言所法之事。蔡氏明堂月令論其說略同。尋明堂之制，備於冬官，冬官亡，故黃圖月令論所稱不盡與古合，為袁準所駁，然其取法於易則同也。

The Heavenly Platform has a diameter of nine feet, following the principle of the Trigram Qian (Heaven) which uses nine to cover six. The platform is eighty-one feet high, following the number of the Huangzhong (Yellow Bell) which is nine multiplied by nine, resulting in eighty-one. Twenty-eight pillars symbolize the Twenty-Eight Mansions. The hall is three feet high with three steps of earth, following the system of the Xia, Shang, and Zhou dynasties. The hall opens to four sides and is decorated with five colors, following the four seasons and the Five Phases. Water surrounds it on all sides, symbolizing the four seas, and the circular shape follows the principle of Yang. The width of the water surface is twenty-four zhang, symbolizing the twenty-four solar terms; the inner diameter of the water is three zhang, corresponding with the description in the Book of Rites: The Rites of the Audience. All these are matters concerning the principles followed in the construction of the Bright Hall. Cai Yong's discussion in his Treatise on the Monthly Ordinances of the Bright Hall is roughly similar. Investigating the system of the Bright Hall, it was originally fully recorded in the Book of Rites: The Works of the Winter Official, but the chapter on the Winter Official is now lost, so the descriptions in the Sanfu Huangtu and the Treatise on the Monthly Ordinances may not all conform to the ancient system, as pointed out by Yuan Zhuan. However, they all trace the principles of the Bright Hall back to the Book of Changes, which is consistent among them.

又先儒戴德戴聖韓嬰孔牢馬宮劉歆賈逵許慎服虔盧植潁容蔡雍高誘諸人皆以明堂上有靈臺，下有辟雍，四門有太學。故蔡氏論云：「謹承天順時之令，昭令德宗祀之禮，明前功百辟之勞，起養老敬長之義，順教幼誨稚之學，明諸侯選造士於其中，以明制度。生者乘其能而至，死者論其功而祭，故為大教之宮。」周書大匡曰：「明堂所以明道，明道惟法。」是言治天下之大法也。

In addition, previous scholars such as Dai De, Dai Sheng, Han Ying, Kong Lao, Ma Gong, Liu Xin, Jia Kui, Xu Shen, Fu Qian, Lu Zhi, Ying Rong, Cai Yong, Gao You, and others all believed that the Bright Hall had the Lingtai above, the Biyong below, and the Taixue set up at the four gates. Therefore, Cai Yong's "Discussion on the Bright Hall and the Monthly Ordinances" says: "Here, we carefully abide by the political orders that follow heaven and the seasons, clarify the virtue of honoring ancestors, commend the merits of predecessors and officials, promote the principles of respecting the elderly and caring for the young, implement the educational system for children, enable the feudal lords to select and cultivate scholars, and use this to clarify the system. The living come here by their abilities, and the deceased are honored according to their merits, so it is the palace where great education is practiced." The "Yi Zhou Shu · Da Kuang" says: "The Bright Hall is used to clarify the great way, and clarifying the great way lies in establishing the laws and regulations." This clearly indicates that the Bright Hall is the fundamental law for governing the country.

大戴禮盛德曰「明堂者古有之也」，盧辯注云：「案淮南子言神農之世祀於明堂，明堂有蓋四方，蓋始於此。」尸子曰：「黃帝曰合宮，有虞曰總章，周人曰明堂，皆所以明休其善。」又曰：「欲觀黃帝之行於合宮，觀堯舜之行於總章。」故知黃帝曰合宮，虞曰總章。尚書帝命驗曰：「帝者承天立五府，以尊天重象。」注云：「象五精之神也。天有五帝集居太微，降精以生聖人，故帝者承天立五帝之府，是為天府。」桓譚新論曰：「明堂，堯謂之五府。」府，聚也，言五帝之神聚於此。

The "Da Dai Li Ji · Sheng De" says, "The Bright Hall has existed since ancient times." Lu Bian's commentary says, "Examining the 'Huainanzi,' it states that in the time of Shen Nong, sacrifices were performed in the Bright Hall, and the Bright Hall had a roof covering all four directions, so it was probably started at this time." The "Shizi" says, "In the time of the Yellow Emperor, it was called He Gong; in the time of Yu Shun, it was called Zong Zhang; in the time of the Zhou dynasty, it was called Ming Tang. These were all used to publicize and honor good deeds." It also says, "If one wishes to examine the deeds of the Yellow Emperor, one should look at He Gong; if one wishes to examine the deeds of Yao and Shun, one should look at Zong Zhang." Therefore, it is known that in the time of the Yellow Emperor it was called He Gong, and in the time of Yu Shun it was called Zong Zhang. The "Shangshu · Dì Mìng Yàn" says, "Emperors who inherited the Mandate of Heaven established five palaces, using them to honor Heaven and pay attention to celestial phenomena." The commentary says, "Xiang refers to the five spirits of the essence. Heaven has five Emperors residing in the Ta Wei Yuan, descending their vital energies to produce sages, so emperors who inherited the Mandate of Heaven established the palaces of the Five Emperors, which is called the Tian Fu." Huan Tan's "Xin Lun" says, "The Ming Tang, Yao called it the Wu Fu." "Fu" means gathering, meaning that the five spirits of the Emperors gathered here.

古文尚書堯典曰「正月上日受終於文祖」，鄭彼注云：「文祖，五府之大名，如周之明堂。」故知唐曰五府，皆明堂異名也。考工記曰：「夏后氏世室，殷人重屋，周人明堂。」是三代明堂亦異名也。五室謂中太室，東青陽，南明堂，西總章，北玄堂。四堂各有室，兼中央為五，故有五室四堂也。

The ancient text "Shangshu · Yaodian" says, "On the first day of the first month, the position of succession is accepted in the Wenzu Temple." Zheng Xuan notes there, "Wenzu refers to the general name of the five halls, equivalent to the Mingtang of the Zhou dynasty." Therefore, it is known that during the Tang Yao period, they were called the five halls, all of which are alternative names for the Mingtang. The "Kaogong Ji" states, "The Xia dynasty called it the Shishi, the Shang dynasty called it the Chongwu, and the Zhou dynasty called it the Mingtang." This shows that the Mingtang of the three dynasties also had different names. The term "wushì" refers to the central Taishi, the eastern Qingyang, the southern Mingtang, the western Zongzhang, and the northern Xuantang. Each of the four directional halls has a room, plus the central room, making a total of five rooms, hence it is said there are five rooms and four halls.

二九四七五三六一八者，大戴禮盛德文。坤二離九巽四，故云二九四。兌七中央五震三，故云七五三。乾六坎一艮八，故云六一八。凡九謂之九宮。一二三四得五為六七八九，故乾鑿度曰「太一取其數以行九宮，四正四維皆合於十五」。

"Erjiu si, qiwu san, liuyi ba" comes from the "Daidai Li Ji · Shengde." The second position in the Kun palace is two, the ninth in the Li palace is nine, and the fourth in the Xun palace is four, hence "erjiu si." The seventh in the Dui palace is seven, the central position is five, and the third in the Zhen palace is three, hence "qiwu san." The sixth in the Qian palace is six, the first in the Kan palace is one, and the eighth in the Gen palace is eight, hence "liuyi ba." In total, there are nine positions, called the nine palaces. One, two, three, and four each added to the central five become six, seven, eight, and nine. Therefore, the "Qianzaodu" says, "Taiyi follows this numerical sequence to tour the nine palaces, and the four directions and four diagonals all add up to fifteen."

鄭彼注云：「太一，主氣之神。四正四維以八卦神所居，故亦名之曰宮。太一下行，猶天子出巡狩省方嶽之事，每率則復。太一下行八卦之宮，每四乃還於中央。中央者，北辰之所居，故因謂之九宮。始坎次坤次震次巽次中央次乾次兌次艮次離，行則周矣，乃反於紫宮。出從中男，入從中女，亦因陰陽男女之偶為終始雲。」

Zheng Xuan explained: "Taiyi is the deity who governs qi. The four cardinal directions and four intermediate directions are the positions where the deities of the Eight Trigrams reside, so they are also called palaces. Taiyi moves downward, touring in sequence, just as the Son of Heaven goes out on a tour to inspect the mountains and rivers of the four directions, returning after each tour. Taiyi moves through the palaces of the Eight Trigrams, returning to the center after every four palaces. The center is the dwelling place of Beichen, so the whole is called the Nine Palaces. The journey begins at Kan, then proceeds in order through Kun, Zhen, Xun, then enters the center, followed by Qian, Dui, Gen, and Li, completing one cycle and returning to the Purple Palace. The journey starts from Zhongnan at Kan and ends at Zhongnü at Li, which is also determined according to the relationship of yin and yang and the pairing of male and female."

坎離震兌為四正，乾坤艮巽為四維。一九六四二八七三乘五皆為十五，故云皆合於十五。室以祭天，堂以佈政者，後魏封軌明堂議文。軌又云：「依行而祭，故室不過五。依時佈政，故堂不踰四。」是也。王者承天統物，各於其方以聽事者，禮記明堂陰陽録文。彼文云：「明堂之制，周旋以水，水左旋以象天。內有太室象紫垣，南出明堂象太微，西出總章象五潢，北出玄堂象營室，東出青陽象天市。上帝四時各治其室，故王者法之也。」統物，統萬物也。

The trigrams Kan, Li, Zhen, and Dui are the four cardinal trigrams. The trigrams Qian, Kun, Gen, and Xun are the four corner trigrams. One and nine, six and four, two and eight, seven and three, each combined with the central five, total fifteen. Therefore, the four cardinal and four corner trigrams all add up to fifteen. "The hall is used for worshipping Heaven, and the hall is used for announcing government orders" is from the "Discussion on the Bright Hall" by Feng Ji of the Northern Wei dynasty. Feng Ji also said, "Following the Five Phases for worship, so the hall does not exceed five; following the four seasons for governance, so the hall does not exceed four." This is exactly the meaning. "The sovereign follows the Heavenly Way to govern all things, each according to its proper direction to listen to political affairs" is from the "Record of the Bright Hall and Yin-Yang" in the "Rites of Zhou." The text says, "The form of the Bright Hall is surrounded by water, which flows from the left to symbolize Heaven. Inside, the Tai Shi represents the Purple Micro垣, extending southward to represent the Tai Wei垣, westward to represent the Wu Huang stars, northward to represent the Yan Tang stars, and eastward to represent the Tian Shi垣. The Supreme Deity governs the corresponding hall in each of the four seasons, so the sovereign follows this example." The term "governing all things" refers to governing all things.

蔡氏章句曰：「月令所以順陰陽，奉四時，效氣物，行王政也。成法具備，各從時月藏之。明堂所以示承祖考神明，明不敢洩瀆之義，故以明堂冠月令。」虞夏商周四代行之，故禮記明堂位兼陳四代之服器。其文在周書五十三，大戴採以為明堂月令，馬氏附月令於小戴而刪明堂字，故止謂之月令也。

Cai Yong's "Chapter on the Monthly Orders" says: "The 'Monthly Orders' is used to follow yin and yang, observe the four seasons, examine climatic and natural phenomena, and implement the king's policies. Once the established practices are complete, they are stored according to the appropriate month and season. The Bright Hall is used to express reverence for ancestors and deities, showing a sense of respect and not being disrespectful or careless, hence the term 'Bright Hall' is placed before the 'Monthly Orders.' The Yu, Xia, Shang, and Zhou dynasties all practiced this system, so the 'Book of Rites' includes the ceremonial attire and objects of all four dynasties. This text originally appeared in the fifth十三 chapter of the 'Lost Book of Zhou,' which was later adopted by Da Dai and titled 'Bright Hall and Monthly Orders.' Ma Rong removed the term 'Bright Hall' when he included the 'Monthly Orders' in Xiao Dai's 'Book of Rites,' so now it is only known as the 'Monthly Orders.'"

中庸言「唯天下至聖為能聰明睿知足以有臨也」，下云「凡有血氣者莫不尊親」，故曰配天，是生有配天之業也。古文尚書伊訓篇曰：「惟太甲元年十有二月乙丑朔，伊尹祀於先王，誕資有牧方明。」劉歆釋之曰：「言太甲雖有成湯太丁外丙之服，以冬至越茀祀先王於方明以配上帝。」方明者，放明堂之制。太甲行吉禘之禮，宗祀成湯於明堂以配上帝，是沒有配天之祭也。

The Doctrine of the Mean says, "Only the supreme sage of the world is capable of ruling the world with his wisdom and intelligence." The following text says, "All beings with life and breath do not fail to honor and attach themselves to him," so he is called "matching Heaven." This is the achievement of living in harmony with Heaven. The ancient text Shangshu · Yixun says: "In the first day of the twelfth month of the first year of Taijia, Yi Yin worshipped the former kings and held a great assembly of the feudal lords at Fangming." Liu Xin explains: "This refers to Taijia, although still mourning for Chengtang, Tai Ding, and Waijing, having crossed the limits of mourning on the winter solstice to worship the former kings at Fangming to match the Heavenly Emperor." Fangming is a structure modeled after the Bright Hall. Taijia performed the ritual of Ji Di at the Bright Hall, honoring Chengtang to match the Heavenly Emperor—this is the posthumous honor of being worshipped in accordance with Heaven.

夏少康中興，伍員亦云「祀夏配天」。三代受命、中興之主及繼世有德之君沒皆行配天之祭。禹湯文武，受命之主也。夏之少康，周之宣王，中興之主也。殷之三宗，周之成康，繼世有德之君也。雲太皥以下歴代所禘者，禮運云「大道之行也，天下為公」，鄭注祭法云：「有虞氏以上尚德，禘郊祖宗配用有德者而已，自夏已下稍用其姓氏代之。」禮運所謂「大道既隱，天下為家，禹湯文武成王周公由此其選」，言禹湯以下雖用明堂之法而大道稍隱也。若然，太皥炎帝當亦黃帝以下所禘，其黃帝以下乃四代所禘，見於魯語及祭法也。

In the Xia Dynasty, Shao Kang revived the dynasty, and Wu Yuan once said, "Worship the former kings of Xia and offer them to Heaven." Among the three dynasties, the sovereigns who received the mandate of Heaven, the rulers who revived the dynasty, and the kings who inherited the throne and possessed virtue all held ceremonies to offer sacrifices to Heaven. Yu, Tang, King Wen, and King Wu were sovereigns who received the mandate of Heaven; Shao Kang of Xia and Xuan Wang of Zhou were rulers who revived the dynasty; the three ancestors of Yin and Cheng Wang and Kang Wang of Zhou were kings who inherited the throne and possessed virtue. The commentary says, "From Tai Hao onwards, each dynasty held the ceremony of禘 (a type of ancestral worship)." The "Li Yun" says, "In the time of the Great Way, the world was held in common." Zheng Xuan's commentary on "Ji Fa" says, "From the time of Yu the Great onwards, the rites of禘, jiao, zu, and zong were offered only to those who possessed virtue; since the Xia Dynasty, they gradually began to replace them with ancestors of the same clan." The "Li Yun" says, "After the Great Way had disappeared, the world became the property of one family, and Yu, Tang, Wen, Wu, Cheng Wang, and Zhou Gong were outstanding figures of that time." This means that although Yu and Tang onwards still used the method of the Ming Tang, the Great Way had gradually disappeared. Therefore, Tai Hao and the Flame Emperor were also the objects of the禘 ceremony in the generations following Huangdi, and Huangdi's descendants were the objects of the禘 ceremony for the four dynasties of Yu, Xia, Shang, and Zhou, as recorded in "Guoyu · Lu Yu" and "Ji Ji · Ji Fa."

蔡氏獨斷曰：「易曰帝出乎震，震者木也，言宓犧氏始以木德王天下也。木生火，故宓犧氏沒，神農氏又以火德繼之。火生土，故神農氏沒，黃帝以土德繼之。土生金，故黃帝氏沒，少昊氏以金德繼之。金生水，故少昊氏沒，顓頊氏以水德繼之。」是言五德相次自太皥以下也。

Cai Yong's "Duduan" says: "The Book of Changes speaks of 'The Emperor arises from Zhen,' and Zhen belongs to the Wood element among the Five Phases. This means Fu Xi first ruled the world with the virtue of Wood. Wood generates Fire, so after Fu Xi's death, Shen Nong ruled with the virtue of Fire; Fire generates Earth, so after Shen Nong's death, the Yellow Emperor ruled with the virtue of Earth; Earth generates Metal, so after the Yellow Emperor's death, the Xiaohao ruled with the virtue of Metal; Metal generates Water, so after Xiaohao's death, Zhuan Xu ruled with the virtue of Water." This passage explains how the five virtues succeed each other in the order of mutual generation, and this sequence begins from Tai Hao onwards.

獨斷又云：「水生木，故顓頊氏沒，帝嚳以木德繼之。木生火，故帝嚳氏沒，帝堯以火德繼之。火生土，故帝舜氏以土德繼之。土生金，故夏禹氏以金德繼之。金生水，故殷湯氏以水德繼之。」亦皆五德相次。故帝嚳雖不列五帝，商周以下禘之，堯舜禹湯文武咸列祖宗之祭也。若明堂月令以太皥相次者，蓋唐虞已前之制，其實歴代皆有損益也。

The "Duduan" also says: "Water generates wood, so after the death of Zhuanxu, Emperor Ku inherited the virtue of wood. Wood generates fire, so after the death of Emperor Ku, Emperor Yao inherited the virtue of fire. Fire generates earth, so after the death of Emperor Shun, the earth virtue was inherited. Earth generates metal, so after the death of Xia Yu, the metal virtue was inherited. Metal generates water, so after the death of Yin Shang, the water virtue was inherited." These are all examples of the five virtues succeeding one another in order. Therefore, although Emperor Ku is not listed among the Five Emperors, the Shang and Zhou dynasties still performed the ancestral rites of禘 (a type of sacrificial rite) for him. Yao, Shun, Yu, Shang Tang, King Wen, and King Wu were all included in the ancestral and lineage sacrifices. As for the "Mingtang Yueling" which places Taihao first and follows the sequence, that is probably the system before the Xia, Shang, and Zhou dynasties; in reality, each dynasty made its own modifications to it.

禮器曰：「大饗其王事與？三牲魚臘，四海九州島之美味也。籩豆之薦，四時之和氣也。內金示和也。束帛加璧尊德也。龜為前列先知也。金次之見情也。丹漆絲纊竹箭與眾共財也。其餘無常貨，各以其國之所有則致遠物也。」禮器云「大饗其王事」，大饗者，明堂之大禘也。王者行大饗之禮於明堂謂之禘祖宗。禘者，圜丘之大禘與春夏之時禘及喪畢之吉禘也。祖者如周之祖文王也，宗者如周之宗武王也，皆配天之祭，又皆蒙禘之名，謂禘其祖之所自出故也。

The Book of Rites, Volume on Ritual Objects says: "The great feast offering is probably a major affair for the sovereign. The three sacrificial animals, fish, and dried meat presented are the delicious foods from the four seas and nine provinces; the food offered in the bamboo trays and ceramic bowls comes from the harmonious energies of the four seasons. Presenting metal signifies harmony, and wrapping silk with jade tablets signifies respect for virtue. The tortoise comes first because it is capable of foreknowledge, and bronze comes next because it can reveal truth. Cinnabar, lacquer, silk, cotton, bamboo, and arrows are common goods shared by the people; other items without fixed rules are presented according to what each country produces, which is to attract distant treasures." The Book of Rites says, "The great feast is the sovereign's affair," and the great feast refers to the grand sacrifice held in the Bright Hall. When the sovereign holds the great feast offering in the Bright Hall, it is called the "Dì," "Zu," or "Zong." "Dì" refers to the grand sacrifice on the circular mound, as well as the seasonal sacrifices in spring and summer and the joyful sacrifices after mourning is completed. "Zu" is like the Zhou people taking King Wen as their ancestor, and "Zong" is like the Zhou people taking King Wu as their ancestor. All these belong to sacrifices in honor of Heaven, and they are all prefixed with "Dì" because they all involve the worship of the original Heaven God from whom the ancestors originated.

后稷之祀在南郊，郊特牲曰「兆於南郊，就陽位也」，又云「於郊，故謂之郊」，故云唯郊行之於南郊，其三大祭皆在明堂也。爾雅祭名曰：「禘，大祭也。」禘郊祖宗四大祭而總謂之禘者，楚語「禘郊」，郊也。鄭注大傳「不王不禘」及詩長發大禘箋皆云「郊祀天」，是郊稱禘也。周頌雝序云「禘，大祖也」，鄭箋云「大祖謂文王」，是祖稱禘也。劉歆云「大禘則終王」，是宗稱禘也。禘者，禘其祖之所自出。董子曰：「天地者，先祖之所出也。」故四大祭皆蒙禘之名也。

The worship of Hou Ji is held at the southern suburbs. The "Rites of Zhou: Special Rites" says, "Building a platform at the southern suburbs is because it is on the yang position," and also says, "Because it is outside the city, it is called a suburban sacrifice." Therefore, only the suburban sacrifice is held at the southern suburbs, while the other three major sacrifices are held at the Bright Hall. The "Erya" explains the names of sacrifices, saying, "Dì is a major sacrifice." The four major sacrifices, Dì, Jiao, Zu, and Zong, are collectively called "Dì." The "Guoyu: Chu Language" refers to "Dì Jiao" as meaning the Jiao sacrifice. Zheng Xuan's commentary on "Rites of Zhou: Da Zhuan" "Not the king may perform Dì" and the annotation of "Shi Jing: Shang Song: Chang Fa" "Great Dì" both say "sacrificing to heaven at the suburban area," showing that Jiao is also called Dì. The small preface of "Shi Jing: Zhou Song: Yong" says, "Dì sacrifice to the great ancestor," and Zheng Xuan's annotation says, "The great ancestor refers to King Wen," showing that Zu is also called Dì. Liu Xin says, "Great Dì extends to all previous kings," showing that Zong is also called Dì. So, Dì refers to the ancestral worship of the origin of the ancestors, which is the heavenly deity. Dong Zhongshu says, "Heaven and earth are the origin of the ancestors." Therefore, all four major sacrifices are prefixed with the term "Dì."

般庚曰：「茲予大享於先王，爾祖其從與享之。」故云一帝配天，功臣從祀。禘禮上遡遠祖者，謂如周始祖之上又有遠祖嚳，虞喜曰「終禘及郊宗石室」是也。旁及毀廟者，謂四廟二祧之外又及毀廟，皆升合食，序昭穆，故韓詩內傳曰「禘取毀廟之主，皆升合食於太祖」是也。下逮功臣者，謂功臣從祀，周書大匡曰「勇如害上，不登於明堂」，高堂隆釋之云「謂有勇而無義，死不登堂而配食」。故蔡氏據禮記太學志曰「善人祭於明堂，其無位者祭於太學」，是言禘祭下逮功臣之事也。

The Book of Documents, Pan Geng, says: "I am holding a great sacrifice to the former kings, and your ancestors are also included in this sacrifice." Therefore, a heavenly emperor is paired with heaven, and meritorious ministers are included in the sacrifice. The so-called禘 ritual traces back to distant ancestors, meaning that for the Zhou people, there was a distant ancestor, Emperor Ku, above their first ancestor Hou Ji. Yu Xi said, "The final禘 ritual extends to the ancestral spirits enshrined in the temple of the ancestral spirits, the ancestral temple, and the stone chamber," which is the meaning of this. The so-called including the ruined temples refers to the spirits of the ancestors from temples beyond the four immediate ancestral temples and the two secondary temples, as well as those from the ruined temples, being brought up to the main ancestral temple for joint sacrifice, arranged according to the order of昭 and穆. Therefore, the Inner Transmission of the Han Poetry says, "The禘 ritual brings the spirits from the ruined temples out and includes them all in the main ancestral temple for joint sacrifice." The so-called including meritorious ministers refers to meritorious ministers being included in the sacrifice. The Yi Zhou Shu, Da Kuang, says, "Those who are brave but harmful to those above are not allowed to be sacrificed in the Bright Hall." Gao Tang Long explains, "This refers to those who are brave but without righteousness, who after death cannot be enshrined in the hall for sacrifice." Therefore, Cai Yong, based on the Li Ji Tai Xue Zhi, says, "The virtuous are sacrificed in the Bright Hall, and those without rank are sacrificed in the Tai Xue," which refers precisely to the inclusion of meritorious ministers in the禘 ritual.