Gua (Breaking Through)

夬，決也。陽氣浸長至於五，五尊位也，而陰先之，是猶聖人積徳悅天下，以漸消去小人，至於受命為天子，故謂之夬。

"Guai" means decision and removal. Yang energy gradually increases, reaching the fifth line; five is the supreme position, yet a yin line still occupies the position before it. This is like a sage accumulating virtue and winning the hearts of the people, gradually eliminating small people, until he accepts the mandate of heaven and becomes the Son of Heaven. Therefore, the hexagram is named "Guai." According to the message hexagrams, "Guai" corresponds to the third month of the lunar calendar, when five yang lines decisively remove one yin line.

揚，越也。五互體乾，乾為君，又居尊位，王庭之象也。陰爻越其上，小人乗君子，罪惡上聞於聖人之朝，故曰夬，揚于王庭。九二，惕號，音號。莫夜，莫如字，無也。無夜，非一夜。九三，壯於頯。頯，夾面也。九五，莧陸，一名商陸。

The Hexagram Statement "Yang in the King's Court" refers to "Yang" as surpassing. The Fifth Line is located within the interacting trigrams of Qian, which represents Heaven and is associated with the ruler. It is in a position of honor and authority, symbolizing the King's Court. However, a Yin Line is above it, indicating a small person riding on the back of a superior, with wrongdoing reaching the court of the sage. Hence, it is said "Gua, Yang in the King's Court." The Line Statement for Nine in the Second "Alert cry, no night with military action" refers to "hao" as read according to its original pronunciation, and "mo ye" with "mo" read as its original character, meaning "wu," thus "wu ye" meaning not just one night, but a long night of vigilance. The Line Statement for Nine in the Third "Strong on the cheeks" refers to the cheeks on both sides. The Line Statement for Nine in the Fifth "Xian Lu Gua Gua" refers to "Xian Lu" also known as Shang Lu, a type of soft and brittle plant that is easily broken.

遘遇也。一陰承五陽，一女當五男，茍相遇耳，非禮之正，故謂之遘。女壯如是，壯健似滛，故不可娶。婦人以婉娩為其徳也。詰四方。詰，正也。九五，杞，桞也。

"Gu" means meeting. In this hexagram, one yin line is above five yang lines, which is like a woman meeting five men, which is merely a casual encounter rather than a proper marriage. Therefore, the hexagram is named "Gu." The hexagram statement says, "The woman is strong; do not take her as a wife." This is because she is too strong, almost licentious, so she should not be married. A woman should cultivate the virtue of being gentle and yielding. The "Jie" in the image commentary refers to rectifying. The line statement of nine in the fifth says, "With杞 wrapping a melon." "Qi" refers to the willow tree.

萃亨，無亨字。萃，聚也。坤為順，兌為悅，臣下以順道承事其君，悅徳居上待之，上下相應，有事而和通，故曰萃亨也。

The primary hexagram statement in the Zheng version reads "Cui亨" while another system's version omits the character "亨." "Cui" means gathering. This hexagram has the lower trigram坤 (Earth) and the upper trigram兑 (Lake):坤 represents順 (smoothness), and 兑 represents悦 (joy). Ministers use the way of gentle compliance to serve their sovereign, while the sovereign, possessing a joyful virtue, resides above to receive them. Thus, there is mutual correspondence between superior and inferior, and all matters can be harmonious and smooth, hence it is said "Cui亨."

假，至也。互有艮，巽為木，艮為闕，木在闕上，宮室之象也。四本震爻，震為長子。五本坎爻，坎為隱伏，居尊而隱伏，鬼神之象。長子入闕，升堂祭祖禰之禮也，故曰王假有廟。

The term "jià" in the hexagram statement "Wang jià yǒu miào" means "to go to." This hexagram's interacting trigrams include Gen (Mountain) and Xun (Wind), with Xun representing wood and Gen representing a gate. Wood standing on top of a gate symbolizes a palace. The fourth line, originally a Zhen (Thunder) line, represents the eldest son; the fifth line, originally a Kan (Water) line, represents concealment. Being in a high position yet concealed symbolizes the ghostly and divine. The eldest son enters the palace, ascends the hall, and performs worship for his grandfather and father, which is the ritual of the ancestral temple. Therefore, the text says "Wang jià yǒu miào."

二本離爻也，離為目，居正應五，故利見大人矣。大牲，牛也，言大人有嘉□時，可幹事，必殺牛以盟，既盟則可以行，故曰利往。除戎器。除，去也。初六，一握。握當讀為夫三為屋之屋。六二，禴，夏祭名。上六，自目曰涕，自鼻曰洟。

The second line originally belongs to the line of fire, and since fire represents the eye, the line is in a proper position and corresponds with the nine in the fifth line. Therefore, it says 'it is advantageous to see a great man.' 'Using great sacrificial animals' refers to cattle; this means that when a great man is at a time of great beauty and auspiciousness, he can take action, and it is certain that he will sacrifice cattle to conclude an alliance. Once the alliance is concluded, action can be taken, so it says 'it is advantageous to go forward.' The 'remove weapons' in the Image Commentary refers to the act of removing and repairing. The line statement of the first line 'a handful is a smile' should be read as 'wu' as in 'three men make a house' in the Zhou Li, which is the unit of land for three men. The line statement of the second line 'faithfulness is advantageous for a simple sacrifice' refers to a sacrificial rite in summer. The line statement of the sixth line 'carrying sorrow and weeping' refers to tears flowing from the eyes being called 'tears' and those from the nose being called 'snivel.'

升，上也。坤地巽木，木生地中，日長而上，猶聖人在諸侯之中，明徳日益髙大也，故謂之升。升，進益之象。六四，王用亨于岐山。亨，獻也，許兩反。

"Sheng" means ascending. This hexagram has Wind below and Earth above: Earth represents the land, Wind represents wood, and trees growing in the land gradually grow taller upward, just as a sage, situated among the feudal lords, cultivates his virtue day by day, making it increasingly prominent. Therefore, the hexagram is named "Sheng" — "Sheng" precisely symbolizes gradual progress. The line statement of the fourth line, "The king offers sacrifices at Qishan," refers to "Heng" as offering, with the reverse-sounding pronunciation "Xu Liang Fan," read as "Xiang."

坎為月，互體離，離為日，兌為闇昧，日所入也。今上掩日月之明，猶君子處亂世，為小人所不容，故謂之困也。君子雖困居險，能悅，是以通而無咎也。

The hexagram "Goon" consists of the lower trigram Kan (Water) and the upper trigram Dui (Lake). Kan represents the moon, and the lines two to four form the trigram Li (Fire), which represents the sun; Dui signifies darkness and obscurity, the place where the sun sets. Now the upper trigram obscures the brightness of the sun and moon, just like a gentleman who is in a chaotic world and is not accepted by petty men, hence the name of the hexagram is "Goon." Although a gentleman is confined in a dangerous situation, he can still remain cheerful and content, thus ultimately achieving success without error.

九二，困于酒食，朱韍方來，利用享祀。二據初，辰在未，未為土，此二為大夫，有地之象。未上值天廚，酒食象。困于酒食者，采地薄不足已用也。

The Line Statement of the Second Line says, "Confined by wine and food, the vermilion sash is about to come, and it is advantageous to offer sacrifices." Zheng Xuan explains using the concept of爻辰: The Second Line relies on the First Line, and the爻辰 of the First Line is "Wei." Wei belongs to the Earth element in the Five Phases, indicating that the Second Line represents a nobleman with a territory. Above Wei is the star "Tianchu," which symbolizes wine and food. The phrase "confined by wine and food" suggests that the territory is poor and insufficient even for the nobleman's own needs.

二與日為體，離為鎮霍。爻四為諸侯，有明徳，受命當王者。離為火，火色赤。四爻辰在午時，離氣赤，又朱是也。文王將王，天子制用朱韍。朱，深於赤。九五，劓刖，當為倪□。

Nine in the Second shares the same nature as the sun, and Li (Fire) represents the planet Jupiter and the mountain Heshan. Nine in the Fourth represents a feudal lord, who possesses virtue and is destined to become king by receiving the mandate of heaven. Li is Fire, and the color of fire is red; the yao (line) of Nine in the Fourth is associated with the hour 'Wu', when the energy of Li is intensely red. The text refers to 'Zhu' (red), which is deeper than 'Chi' (red). When King Wen of Zhou was about to become king, the color used for the ceremonial sash of the Son of Heaven was 'Zhu', which is darker than 'Chi'. The line statement of Nine in the Fifth mentions 'Ni Yue' (nose and foot amputations); Zheng Xuan explains it as 'Ni', but the original character is missing and can only be recorded as is.

井，法也。坎，水也。巽木，桔槔也。互體離兌，離外堅中虛，瓶也。兌為暗澤，泉口也。言桔槔引瓶，下入泉口，汲水而出井之象也。井以汲人，水無空竭，猶人君以政教養天下，惠澤無窮也。

"The well" represents regulation. This hexagram has the trigram Zhen (Wind) below and Kan (Water) above: Kan is water, Zhen is wood, symbolizing the lever used for drawing water. Within the hexagram, the interacting trigrams form Li (Fire) and Dui (Lake): Li is solid on the outside and hollow in the middle, like a clay jar; Dui is a hidden water pool, like a spring source. This describes using the lever to lift the jar, lowering it into the spring source, drawing water, and then lifting it up to the wellhead. The well provides water for people to draw without ever drying up, just as a ruler governs with laws and moral education, benefiting the people without end.

九二，井谷射鮒。九二，坎爻也，坎為水，上直巽。九三，艮爻也，艮為山，山下有井，必因谷水所生魚，無大魚但多鮒魚耳。夫感動天地，此魚之至大；射鮒井谷，此魚之至小，故以相況。甕，停水器也。井渫不食，謂已浚渫也，猶臣修正其身以事君也。

The line statement for the second line, "Well in the valley shooting small minnows," refers to the second line being the Kan line. Kan represents water, and above it is Xun. The third line is the Gen line, which represents mountain, with a well beneath the mountain. The mountain valley has water, and thus small fish are born from it; such water does not produce big fish, only small minnows. What can move heaven and earth is the largest fish; to shoot small minnows in the well is the smallest among fish—Zheng Xuan contrasts the large and the small, showing the smallness of the action of the second line. "Weng" is a vessel for holding water. "The well is cleaned but not used" means the well has been cleaned but no one comes to draw water, just as a minister who has corrected himself to serve the sovereign is not appointed.

革，改也。水火相息而更用事。猶王者受命，改正朔，易服色，故謂之革也。

"Revolution" refers to change. This hexagram has the trigram Li (Fire) below and Dui (Lake) above. Water and fire mutually destroy each other and take turns to be dominant. This is like a king receiving the mandate of heaven, changing the calendar and the beginning of the year, altering the colors of his chariots, clothing, and banners. Therefore, the hexagram is named "Revolution." Zheng Xuan directly associates the hexagram of Revolution with the institutional changes of replacing a dynasty, rather than discussing change in an abstract sense.

鼎象也。卦有木火之用，互體乾兌。乾為金，兌為澤，澤鍾金而含水，□以木火，鼎烹熟物之象。鼎烹熟以養人，猶聖君興仁義之道以教天下也，故謂之鼎矣。凝命，凝成也。

"The hexagram 'Ding' derives its name from the image of a vessel. This hexagram embodies the functions of wood and fire, and its interacting elements form the trigrams Qian (Heaven) and Dui (Lake). Qian represents metal, and Dui represents a marsh. Metal accumulates in water and contains water, (the original text here is missing one character and cannot be conjectured) plus wood and fire, which together form the image of a cooking pot used to prepare food. The cooking pot cooks food to nourish people, just as a wise ruler promotes the way of benevolence and righteousness to educate the world. Therefore, the hexagram is named 'Ding'. The 'Image Commentary' states 'neng ming', where 'neng' means accomplishment."

初六，鼎顛趾。顛，踣也。趾，足也。無事曰趾，設陳曰足。爻體巽為股。初爻在股之下，足象也。足所以承，正鼎也。

The Line Statement for the First Line, "Initial Six," says, "The tripod is overturned at the foot." "Overturned" means to fall backward, and "foot" refers to the lower part. When an object is unused and stored away, it is called "foot," but when it is set up and used, it is called "foot" as well. The trigram associated with this line is Xun (Wind), which represents the thigh. The First Line is located below the thigh, corresponding to the foot. The foot is used to support and stabilize the entire tripod.

初陰爻而柔與乾同體，以否正承乾。乾為君，以喻君。夫人事君，若失正禮，踣其為足之道，情無怨，則當以和，義出之然。如否者，嫁於天子，雖失禮，無出道，廢逺之而已。

Chu Liu is a yao of yin nature, soft in character and sharing the same body as Qian. It uses an improper position to serve Qian. Qian represents the sovereign, symbolizing the ruler. In human affairs, when subjects serve the sovereign, if they lose proper decorum, it is as if they have destroyed their own role as the tripod's foot. However, as long as there is no resentment in reason and sentiment, they should be dealt with through harmony and righteousness. In such an improper situation, if a woman has already married the Son of Heaven, even if she is disrespectful, there is no grounds for divorce; she can only be demoted and distanced.

若其無子，不廢逺之，后尊如故其犯。六出則廢之逺之，子廢。坤為順，又為子，母牛。在后妃之旁，側妾之例也。有順徳，子必賢，賢而立以為世子，又何咎也。

If she did not give birth to a son, she would not be dismissed or distanced, and her status as a consort would remain as before. Only if she violated six of the seven conditions for dismissal would she be dismissed, distanced, and even her sons would be discarded. The trigram坤 represents order, as well as sons and mother cows, and its position beside the queen consort symbolizes the status of concubines and secondary wives. Since she possesses the virtue of flexibility and obedience, the son she bears must be virtuous. If he is virtuous and appointed as the heir, what fault could there be? Zheng Xuan interpreted the first line, Six at the Beginning, directly as the ritual regulations concerning the appointment and dismissal of the queen consort and her concubines.

九二，我仇有疾。怨耦曰仇。九三，雉膏，食之美者。九四，鼎折足，覆公餗，其刑屋（釋文剭，周禮注云其刑剭，音屋）。糝，謂之餗。震為竹，竹萌曰筍，筍者，餗之為菜也。餗，美饌，具八珍之食。

Nine in the Second Line Statement says, "My enemy is ill": "Enemy" refers to a spouse with whom there is resentment. Nine in the Third Line Statement says, "Chicken fat": this refers to the finest type of food. Nine in the Fourth Line Statement is commonly transmitted as "The tripod breaks its foot, spills the food, and its form is stained," while the Zheng version says "Its punishment is like a roof." (The Classic Interpretation says "zhu," and the Zheng annotations in the Zhou Li say "its punishment is zhu," which is pronounced like "wu.") A meat soup made with rice flour is called "tu." Zhen represents bamboo, and the tender shoot of bamboo is called "sun," which is the vegetable used in "tu." "Tu" is a delicious dish that requires the completeness of the eight delicacies.

鼎三足，三公象。若三公傾覆王之美道，屋中刑之（一雲臣下曠官，失君之美道，當刑之於屋中）。餗，一作蔌。注，一蔌為八珍所用。六五，金鉉，喻明道能舉君之官職也。

The tripod has three legs, symbolizing the Three Grand Ministers. If the Three Grand Ministers overturn the virtuous ways of the sovereign, they should be executed within the hall (another interpretation says: if ministers occupy positions without performing duties, corrupting the sovereign's virtuous path, they should be executed within the hall). "Fei" is sometimes written as "Su"; the commentary also says that "Su" refers to vegetables used in the eight delicacies. The line statement of the fifth line, "Jin Xuan," metaphorically means that a person who understands the Way can promote the sovereign's official duties and affairs, just as the Xuan (a metal bar) connects the tripod's ears to lift the tripod.

震驚百里，不喪匕鬯。震為雷，雷動物之氣也。雷之發聲，猶人君出政教以動國中之人也，故謂之震。人君有善聲教，則嘉會之禮通矣。

The hexagram statement says, "The thunder shakes a hundred miles, and the ritual vessel is not lost." Zhen represents thunder, which is the vital energy that moves all things. Thunder produces sound, just as a ruler issues decrees and moral teachings to move the people of the state. Therefore, the hexagram is named Zhen. If a ruler possesses virtuous prestige and moral influence, then joyful gatherings and proper rites will flow smoothly without obstruction.

驚之言，警戒也。雷發聲聞於百里，古者諸侯之象。諸侯之出教令，能警戒其國疆之內，則守其宗廟社稷，為之祭主，不亡其匕與鬯也。

"The meaning of '惊' is alarm. The sound of thunder can travel a hundred miles, which is the symbolic reference for the ancient feudal lords' territorial boundaries. When a feudal lord issues commands, he can alert people within his territory, thus being able to protect his ancestral temple and state sacrifices, and not lose the dagger and the fragrant wine used in worship — 'not losing the dagger and the fragrant wine' refers precisely to his position as the master of the sacrifice remaining unshaken."

人君於祭之禮，匕牲體薦鬯而已，其餘不親為也。升牢於俎，君匕之，臣載之。鬯，秬酒，芬芳條鬯，因名焉。啞啞，樂也。六二，億，喪貝十萬曰億，於力反。六三，蘇蘇，不安也。上六，索索，猶縮縮，足不正也。矍矍，目不正。

The sovereign personally uses a ladle to take the sacrificial animal and offers the wine called "Chang." The rest of the rituals are carried out by the ministers. When the sacrificial animal is placed on the俎, the sovereign uses the ladle to take it, while the ministers carry it. "Chang" is a type of wine made from black millet, which has a fragrant and smooth aroma, hence its name. The "Xiang Zhuan" of the first line says, "Laughing and cheerful," where "yayayā" refers to the sound of joy. The "Yao Ci" of the second line says, "Lost the shell," where "yi" means ten thousand, and the reverse pronunciation of "yi" is "yu li fan." The "Yao Ci" of the third line says, "Zhen Susu," where "susu" describes a state of mental unease. The "Yao Ci" of the sixth line says, "Zhen Sosuo," where "sosuo" is equivalent to "suosuo," meaning unsteady steps; "shì Juju" refers to "juju," meaning wandering eyes.

艮之言很也。艮為山，山立峙各於其所，無相順之時。猶君在上，臣在下，恩敬不相與通，故謂之艮也。九三，限，要也。列其腰。

The meaning of "Gèn" (艮) is harsh and unyielding, lacking harmony. "Gèn" represents a mountain, where mountains stand independently in their respective positions, never harmonizing with each other. This is like a ruler above and a minister below, where benevolence and respect do not communicate. Hence, the name of the hexagram is "Gèn." The third line statement says, "Gèn its limit, breaking its loin." "Limit" refers to the waist, the place where the upper and lower parts of the body meet. "Breaking its waist" means the waist is split apart.

初六，乾，謂大水之傍，故停水處。九三，婦孕不育。九三上與九五互體為離，離為大腹，孕之象也。又互體為坎，坎為大夫。坎為水，水流而去，是夫征不復也。夫既不復，則婦人之道顛覆，故孕而不育。孕猶娠也。

The Line Statement for the first line, "Initial Six" (初六), says, "The wild goose progresses to the dry land." "Dry land" here refers to the area by the big water, where water had previously accumulated and then dried up, meaning the edge of the water. The Line Statement for the third line, "Nine in the Third" (九三), says, "The wife is pregnant but does not give birth." The third line interacts with the fifth line, "Nine in the Fifth," to form the trigram Li (Fire), which symbolizes a large belly, representing pregnancy. At the same time, the interaction between the third and fifth lines also forms the trigram Kan (Water), which represents a gentleman or a military officer. Kan also symbolizes water, which flows away and does not return, hence the Line Statement "the husband goes on a campaign and does not return." Since the husband does not return, the way of the wife is overturned, so even though she is pregnant, she cannot give birth. "Pregnant" is equivalent to "pregnant."

六三，歸妹以須。須，有才智之稱（天文有須女，屈原之姊名女須。姊，一作妹）。上六，女承筐無實。宗廟之禮，主婦奉筐米。

The line statement for the third line, "Six in the Third," says, "Returning to marriage, one waits." "Wait" refers to a person of talent and wisdom. There is a star called "Xu Nu" in the sky, and Qu Yuan's sister was named Nu Xu. The character "zhi" (姊) is also written as "mei" (妹) in some texts. The line statement for the sixth line at the top, "Six at the Top," says, "The woman carries a basket but finds it empty." According to the rites of ancestral worship, the wife should personally carry a bamboo basket filled with rice. Now the basket is empty, indicating that this marriage cannot fulfill the responsibility of honoring the ancestors.

豐之言，腆充滿意也。初九，遇其妃主。嘉耦曰妃。雖曰無咎，初修禮上朝四，四以匹敵恩厚待之，雖留十旬，不為咎。

"The word '丰' means full and abundant. The line statement of the initial line in the通行本 reads 'meeting its matching master,' while in the Zheng version it reads 'fei zhu,' where 'fei' refers to a beautiful spouse. Although the line statement says 'no blame,' it is because the initial line, by properly observing the etiquette between guest and host, goes to meet the fourth line. The fourth line also receives him with equal courtesy and deep affection. Therefore, even though he stays for ten days, it is not considered a fault."

正以十日者，朝聘之禮止於主國以為限，聘禮畢歸。大禮曰：旬而稍。旬之外為稍，久留非常。六二，豐其菩。菩，小席。九三，豐其芾。芾，祭祀之蔽膝。

The reason it is fixed at ten days is because the ceremony of state visits follows the set period determined by the host state, and after the visitation ceremony is completed, the envoy should return home. The Classic of Great Rituals says, "After ten days, it is called 'sao'"; exceeding ten days is called "sao," and staying too long is against the proper etiquette. The line statement of the second line in the hexagram is commonly printed as "Feng qi pu," but in the Zheng version it is "Pu," which refers to a small mat. The line statement of the third line is commonly printed as "Feng qi pai," but in the Zheng version it is "Fui," which refers to the ceremonial apron worn around the knees during worship.

日中見昧，折其右肱。三艮爻，艮為手，互體為巽，巽又為進退，手而便於進退，右肱也。猶大臣用事於君，君能誅之，故無咎。上六，闃，無人貌。天際翔也。際，當為瘵。瘵，病也。自戕也。戕，傷也。

The line statement for the third line, "Nine in the Third," says, "At noon, the mist appears; the right arm is broken." The Zheng edition reads "mist" as "confusion." The third line is the Qian trigram, representing the hand. Here, the interacting trigrams form Xun, which signifies movement and retreat. The hand that is convenient for movement and retreat is the right arm. This is like a minister who acts independently before the king, and the king is able to eliminate him, hence it is said "there is no blame." The line statement for the sixth line at the top, "Empty and no one is there," refers to the state of being empty and deserted. The character "际" in "flying at the sky's edge" should be read as "瘵," which means disease. The character "戕" in "self-inflicted injury" means harm.

初六，瑣瑣，猶小小也。爻互體艮，艮，小石，小小之象。三為聘客，初與二其介也。介當以篤實之人為之，而用小人，瑣瑣然。客主人為言，不能辭曰非禮，不能對曰非禮。每者不能以禮行之，則其所以得罪。

The Line Statement for the first line, "Initial Six" (Chu Liu), says "traveling in a petty way." "Petty" refers to something small. The interaction of this line forms the trigram Gen (Mountain), which represents small stones, thus symbolizing something small. The ninth line is the guest who has come to visit, while the first and second lines are the attendants "Jie" who accompany him. Those who serve as attendants should be chosen as sincere and trustworthy people, but now they are petty people, hence appearing petty and trivial. When the guest interacts with the host, if he cannot speak appropriately when he should be courteous, it is unbecoming; if he cannot respond appropriately when he should be answering, it is also unbecoming. Being unable to act in accordance with propriety in all matters is precisely the reason for his wrongdoing.

九四，商兌。商，隱度也。

The Line Statement for Nine in the Fourth says, "Shang Dui Wei Ning": "Shang" means to secretly consider or privately deliberate. It indicates that Nine in the Fourth, situated between Nine in the Fifth and Six in the Third, is repeatedly weighing things and cannot find peace of mind.

節以制度，空府藏則傷財，力役繁則害民。二者奢泰之所致。

The Image Commentary of the "Moderation" hexagram says, "Moderation is achieved through established rules." Zheng Xuan explained from the perspective of governance: when the treasury is exhausted, it harms resources; when labor service is excessive, it harms the people. These two outcomes are both results of extravagance and excess. Therefore, it is necessary to establish regulations for moderation, so that resources are not completely depleted and people's strength is not exhausted.

豚魚吉。三辰在亥，亥為豕，爻失正，故變而從小名，言豚耳。四辰在丑，丑為鱉蟹，鱉蟹，魚之微者，爻得正，故變而從大名，言魚耳。

The Hexagram Statement says "a pig and fish are auspicious." Zheng Xuan still uses the concept of爻辰 to explain it: the爻辰 of line six in the third position is "Hai," which belongs to the pig, but since this line is not in the correct position, it takes a smaller name, referring only to "豚," which means a small pig. The爻辰 of line six in the fourth position is "Chou," which belongs to turtles and crabs, which are a minor category among aquatic animals; since this line is in the correct position, it takes a larger name, directly calling it "鱼," meaning fish. The size of the name depends entirely on whether the line is in the correct position or not.

互體兌，兌為澤。四上值天淵，二五皆坎爻，坎為水。二侵澤則豚利，五亦以水灌淵則魚利。豚魚以喻小民也，而為明君賢臣恩意所供養，故吉。乘木舟虛也。舟謂集板，如今自空大木為之曰虛。

This hexagram's interacting lines form Dui, which represents a marsh. The sixth line in the fourth position faces directly the star "Heavenly Depth." The ninth line in the second position and the ninth line in the fifth position are both Kan lines, which represent water. The ninth line in the second position moistens the marsh, benefiting the pig; the ninth line in the fifth position waters the Heavenly Depth, benefiting the fish. The pig and the fish symbolize the common people, who are nourished by the grace of a wise ruler and virtuous minister, hence the auspiciousness. The "Commentary on the Judgment" says, "riding on a wooden boat is empty." "Boat" refers to a vessel made by joining planks together, or a large piece of wood hollowed out, which is called "empty."

不宜上。上如字，謂君也。中孚為陽，貞於十一月子；小過為陰，貞於六月，法於乾坤。

The Hexagram Statement of 《Xiao Guo》 says "Not suitable to go up, suitable to go down": "Up" is read according to the original character, referring to the sovereign. Zheng Xuan also matched the hexagram energies with months: 《Zhong Fu》 belongs to yang, and its fixed month is the eleventh month, Zi month; 《Xiao Guo》 belongs to yin, and its fixed month is June—this follows the precedent set by the hexagrams Qian and Kun, each governing one month respectively with one yang and one yin.

濟，既已也，盡也。濟，度也。六二，茀，車蔽也。九三，憊，劣弱也。九五，東鄰殺牛，不如西鄰之禴祭。互體為坎，又互體為離。離為日，坎為月，日出東方，東鄰象；月出西方，西鄰象也。

The original title of this section was written as "未既," with the two characters reversed, and the actual subject being the hexagram "Both Completion." "济" means completion or exhaustion, and also refers to crossing a river. The line statement for the second line, "The woman loses her veil," refers to the veil on a carriage. The line statement for the third line, "fatigue," means weakness and exhaustion. The line statement for the fifth line, "The eastern neighbor sacrifices an ox, but the western neighbor's simple offering is better," refers to the fact that the interacting lines form the trigram Kan (Water) and also the trigram Li (Fire). Li represents the sun, and Kan represents the moon. The sun rises in the east, symbolizing the eastern neighbor; the moon appears in the west, symbolizing the western neighbor.

坊記疏云：東鄰謂紂國中也，西鄰謂文王國中也。既濟，離下坎上，離為牛，坎為豕。西鄰禴祭則用豕，與言殺牛而凶，不如殺豕受福，喻奢而慢不如儉而敬也，與易注不同。禴，夏祭之名。

The Commentary by Kong Yingda on the Li Ji · Fang Ji says: the eastern neighbor refers to the kingdom of Zhou, and the western neighbor refers to the kingdom of Wen. The hexagram Ji Ji has the lower trigram Li (Fire) and the upper trigram Kan (Water): Li represents cattle, and Kan represents pigs. The western neighbor performed the summer sacrifice using pigs; compared to the scripture's statement that killing cattle leads to misfortune, using pigs instead brings blessings—this is a metaphor meaning that extravagance and negligence are worse than frugality and respect. (Wang Yinglin notes: this statement differs from Zheng Xuan's commentary in the Yi Jing.) "Yue" is the name of a summer sacrifice.

汔幾也。凡卦爻二至四，三至五，兩體交互，各成一卦。先儒謂之互體。

The hexagram "Wei Ji" (The Unfinished) has the hexagram statement "Xiao Hu Qi Ji," meaning "a small fox is almost crossing the river." Below this line, Wang Yinglin added a note on the general practice of Zheng Xuan's interpretation of the Book of Changes. For any hexagram with six lines, the second to fourth lines and the third to fifth lines form two groups of three lines each. These two groups of three lines interact with each other and also form separate hexagrams. Earlier scholars called this method of taking images "hu ti" (interchangeable structures). Zheng Xuan frequently used this method in interpreting the Book of Changes, which is fundamentally different from the approach of interpreting based solely on the upper and lower trigrams of the primary hexagram. The references to "hu ti" in the previous hexagrams all come from this general principle.

君臣尊卑之貴賤，如山澤之有髙卑也，動靜雷風也。類聚群分，謂水火也。成象日月星辰也。成形謂草木鳥獸也。乾以易知，音亦。翫其辭。震無咎，震懼也。

The Great Treatise says, "Heaven is exalted, Earth is humble, thus the trigrams Qian and Kun are established." This refers to the distinction between ruler and subject, honor and disgrace, just as mountains and marshes have high and low positions. "Motion and stillness follow their regular patterns" refers to thunder and wind. "Things of the same kind gather together, objects of the same class group together" refers to water and fire. "In heaven, images are formed" refers to the sun, moon, and stars; "in earth, forms are formed" refers to grasses, trees, birds, and beasts. The "Yi" in "Qian is known through Yi" is pronounced the same as "also." The "wan" in "deliberate its words" means to ponder. The "Zhen" in "Zhen without blame lies in regret" refers to fear and caution.

原始及終，精氣為物，游魂為變。精氣謂七八也，游魂謂九六也。七八，木火之數；九六，金水之數。木火用事而物生，故曰精氣為物；金水用事而物變，故曰游魂為變。

The commonly circulated version of the Great Treatise states "returning to the beginning and concluding at the end," while Zheng's version reads "returning to the beginning and reaching the end." The following text says, "The vital energy becomes things, and the wandering soul causes change." Zheng Xuan explains this using the numbers of divination paired with the Five Phases: "vital energy" refers to the numbers seven and eight, and "wandering soul" refers to nine and six. Seven and eight are the numbers of wood and fire, while nine and six are the numbers of metal and water. When wood and fire are dominant, things come into being, hence "the vital energy becomes things." When metal and water are dominant, things undergo transformation and decay, hence "the wandering soul causes change." This approach directly connects the principles of life and death to the numbers of the four seasons and the Five Phases, without engaging in abstract discussions about human nature and moral principles.

游魂謂之鬼，物終所歸；精氣謂之神，物生所信也。言木火之神生物東南，金水之鬼終物西北。二者之情其狀，與春夏生物、秋冬終物相似（一雲二物變化，其情與天地相似），故無所差違之也。

Wandering souls are called "ghosts," which are where all things return to at the end of their existence; vital energies are called "spirits," which are what all things rely on during their growth. This means that the spirits of wood and fire are in the southeast, giving birth to all things, while the ghosts of metal and water are in the northwest, bringing about the end of all things. These two phenomena are similar to the way life flourishes in spring and summer and things come to an end in autumn and winter. (Another interpretation is: the changes of these two things are similar to those of heaven and earth.) Therefore, the text continues, "They are similar to heaven and earth, hence they do not violate."

道濟天下，道當作導。範圍，範法也。故君子之道尟矣。臧諸用。臧，善也。言天下之至賾，賾當為動。慎斯術也。術，道。有功而不置，置當作志。野容誨滛，言妖野容儀。

The "dao" in "知周乎万物而道济天下" should be read as "dao" meaning guidance. The "fan" in "范围天地之化" refers to principle. In "故君子之道鲜矣," the Zheng version uses "xuan" meaning few. "臧诸用" (the common version reads "藏诸用") has "臧" meaning good. In "言天下之至赜," "赜" should be read as "dong" meaning movement. The "shu" in "慎斯术也以往" refers to path. In "有功而不德," the Zheng version reads "不置," and "zhi" should be read as "zhì" meaning mind. "冶容诲淫" in the Zheng version is "野容," meaning a vulgar and unrestrained appearance that leads to licentiousness.

大衍之數五十。天地之數五十有五，以五行氣通。凡五行減五，大衍又減一，故四十九也。衍，演也。揲，取也。

"The number of great derivation is fifty." Zheng Xuan's calculation is: the original number of heaven and earth is fifty-five. Because the five phases' energies are interconnected, each phase reduces by five. The great derivation further reduces by one, so only forty-nine stalks are actually used for divination. "Derivation" refers to deduction or inference, and "揲" refers to selecting or dividing.

天一生水於北，地二生火於南，天三生木於東，地四生金於西，天五生土於中。陽無耦，陰無配，未得相成。地六成水於北，與天一併；天七成火於南，與地二並；地八成木於東，與天三並；天九成金於西，與地四並；地十成土於中，與天五並也。

The numbers generating the Five Phases are arranged as follows: Heaven One (天一) in the north produces water, Earth Two (地二) in the south produces fire, Heaven Three (天三) in the east produces wood, Earth Four (地四) in the west produces metal, and Heaven Five (天五) in the center produces earth. At this point, yang has no counterpart, and yin has no match, so they cannot complement each other. Therefore, Earth Six (地六) in the north completes water, joining with Heaven One; Heaven Seven (天七) in the south completes fire, joining with Earth Two; Earth Eight (地八) in the east completes wood, joining with Heaven Three; Heaven Nine (天九) in the west completes metal, joining with Earth Four; and Earth Ten (地十) in the center completes earth, joining with Heaven Five. One generation and one completion form pairs, and the Five Phases are thus fully established.

大衍之數五十有五，五行各氣並，氣並而減五，惟有五十。以五十之數不可以為七八九六卜筮之占以用之，故更減其一，故四十有九也。

The original number of the Great Derivation is fifty-five: the generating numbers and the forming numbers of the Five Phases are paired together, and when their energies are combined, five is subtracted, leaving fifty. However, this number of fifty cannot be directly used to determine the numbers of lines obtained by divining with yarrow stalks, such as seven, eight, nine, and six. Since actual divination requires practical operation, one more stalk is subtracted, resulting in forty-nine.

天數五，地數五，五位相得而各有合。天地之氣各有五，五行之次，一曰水，天數也；二曰火，地數也；三曰木，天數也；四曰金，地數也；五曰土，天數也。此五者，陰無匹，陽無耦，故又合之。

"Heaven has five numbers, Earth has five numbers, the five positions correspond to each other and each has its match." The heavenly energies and earthly energies each have five. The order of the Five Phases is: the first is water, belonging to the heavenly numbers; the second is fire, belonging to the earthly numbers; the third is wood, belonging to the heavenly numbers; the fourth is metal, belonging to the earthly numbers; the fifth is earth, belonging to the heavenly numbers. These five numbers, the yin ones have no match, the yang ones have no partner, so they need to be matched one by one.

地六為天一匹也，天七為地二耦也，地八為天三匹也，天九為地四耦也，地十為天五匹也。二五陰陽各有合，然後氣相得施化行也。研機，機當作幾。幾，微也。蓍之徳圓而神，蓍形圓而可以立變化之數，故謂之神也。

The method of pairing is: the Earthly Branch number six pairs with the Heavenly Stem number one, the Heavenly Stem number seven pairs with the Earthly Branch number two, the Earthly Branch number eight pairs with the Heavenly Stem number three, the Heavenly Stem number nine pairs with the Earthly Branch number four, and the Earthly Branch number ten pairs with the Heavenly Stem number five. These two groups of five numbers, with yin and yang each having their pairings, allow the energies to harmonize and enable the process of generation and nurturing. "Yan Ji" is in the Zheng edition written as "Yan Ji," and "Ji" should be "Ji," meaning subtle. "The virtue of the divining rod is round and divine": the form of the divining rod is round, and it can establish the numbers of change, hence it is called "divine."

四象，布六於北方以象水，布八於東方以象木，布九於西方以象金，布七於南方以象火。河出圖，洛出書，聖人則之。春秋緯云：河以通乾出天苞，洛以流坤吐地符。河龍圖發，洛龜書感。河圖有九篇，洛書有六篇，有以尚賢也。

The four images derived from the two principles, as interpreted by Zheng Xuan, are explained through the numbers associated with directions: arranging six in the north to symbolize water, eight in the east to symbolize wood, nine in the west to symbolize metal, and seven in the south to symbolize fire. "The river produces the diagram, the Luo produces the book, and the sage follows them": According to the "Chunqiu Wei," the Yellow River, by connecting with the virtue of Heaven, produces the heavenly embryo, while the Luo River, by flowing with the virtue of Earth, produces the earthly symbol. The dragon diagram appears in the Yellow River, and the turtle book emerges from the Luo River in response. The "He Tu" contains nine chapters, and the "Luo Shu" contains six chapters. The sage takes them as models, which contain the meaning of valuing capable people.

樞，戸樞也。機，弩牙也。戸樞之發，或明或闇；弩牙之發，或中或否，以譬言語之發，有榮有辱。包犧，包，聚也。鳥獸全具曰犧。蓋取諸乾坤，乾為天，其色元；坤為地，其色黃。但土無正位，托於南方，南方色赤，黃而兼赤，故為纁也。

"Words and deeds are the key points for a gentleman": "Shu" refers to the pivot of a door, and "ji" refers to the trigger of a crossbow. When the door pivot turns, it may open toward the bright or the dark; when the crossbow trigger is pulled, it may hit the target or miss. This is used to illustrate that once words are spoken, they may bring honor or bring disgrace. "Baoxi Shi" refers to "bao" meaning to gather together, and "xi" refers to animals with complete and unbroken bodies. "Huangdi, Yao, and Shun governed the world by simply wearing robes, which was derived from the hexagrams Qian and Kun": Qian represents Heaven, whose color is Xuan; Kun represents Earth, whose color is Huang. However, soil does not have a specific direction, so it is associated with the south, whose color is red. Therefore, the color of the lower garment became "Xun".

重門擊柝，豫，坤下震上。九四體震，又互體有艮。艮為門。震日所出，亦為門，重門象。艮又為手，巽爻也，應在四，皆木也，手持二木也。手持二木以相敲，是為擊柝，擊柝為守備警戒也。

"Guarding the gates with the sound of a wooden staff to ward off robbers, this is derived from the hexagram of Joy." Zheng Xuan carefully analyzes the hexagram: The hexagram of Joy has the Earth below and Thunder above. The line nine in the fourth position belongs to Thunder. Within the hexagram, there is also an interacting trigram of Mountain, which represents a gate. Thunder is also the place where the sun rises, which can also be considered a gate. Two gates overlapping correspond to the image of "double gates." Mountain also represents hands; and the line six at the beginning, corresponding to nine in the fourth, is the trigram of Wind, which represents wood. Both places belong to wood, thus forming the image of holding two pieces of wood in the hands. Holding two pieces of wood and striking them together is called "striking the wooden staff," which is done for guarding and vigilance.

四又互體為坎，坎為盜，五離爻為甲冑戈兵，盜謂持兵，是暴客也。又以其卦為豫，有守備則不可自逸。

Nine in the Fourth also forms the trigram Kan through mutual interaction, and Kan represents thieves. Six in the Fifth is the trigram Li, and Li represents armor and weapons. Thieves holding weapons correspond to the passage's mention of 'violent guests.' Furthermore, the name of this hexagram is 'Yu,' which means ease. Since there is a need to set up defenses, one should not seek ease. The hexagram name and its symbolic meaning here serve as a warning.

結繩為約，事大大其繩，事小小其繩。書契，書之於木，刻其側為契，各持其一，後以相考。合以制器者尚其象，存於器，象可得而用，一切器物及造立皆是。

"During the ancient times, people used knots on ropes to manage affairs: large matters were marked with large knots, and small matters with small knots." Later, "bookkeeping with written contracts" emerged, where characters were carved on wooden slips, and notches were made on the sides as a form of verification, with each party holding half. Later, they could compare them to confirm the truth. "The making of objects relies on their forms": the form is preserved within the object, so taking the form can be made practical; all objects and the establishment of systems fall into this category.

一君二民，君子之道也。二君一民，小人之道也。一君二民，謂黃帝，堯，舜。謂地方萬里為方千里者百，中國之民居七千里，七七四十九，方千里者四十九。夷狄之民居千里者五十一，是中國夷狄二民共事一君。

"Yang has one ruler and two subjects, which is the way of the superior man; Yin has two rulers and one subject, which is the way of the inferior man." Zheng Xuan calculated using territorial boundaries and population figures: "one ruler and two subjects" refers to the time of the Yellow Emperor, Yao, and Shun. The entire world was square and measured ten thousand li on each side, which was divided into one hundred square areas each one thousand li on a side. The population of the Central States occupied a square area of seven thousand li, which was seventy times seven, resulting in forty-nine square areas of one thousand li each. The population of the夷狄 (barbarians) occupied fifty-one square areas of one thousand li each. Thus, both the Central States and the夷狄 shared one ruler, which is why it is called "one ruler and two subjects."

二君一民，謂三代之末，以地方五千里，一君有五千里之土，五五二十五，更足以一君，二十五始滿千里之方五十，乃當堯舜一民之地，故云二君一民。

The term "two kings and one person" refers to the late period of the Three Dynasties. A single ruler's territory was considered to be five thousand li square, with five such areas making up a thousand li square, resulting in twenty-five such regions. Adding another ruler's twenty-five regions brings the total to fifty regions of a thousand li square, which exactly matches the land area previously occupied by one person during the time of Yao and Shun. Therefore, two rulers were needed to correspond to the land area of one person, hence the term "two kings and one person."

男女覯精。覯，合也。男女以陰陽合其精氣。因貳以濟民行，貳當為弍。損，徳之修也。修，治也。困，徳之辯也。辯，別也。遭困之時，君子固窮，小人窮則濫，徳於是別也。益，長裕而不設。設，大也。雜物算徳。算，數也。居可知矣，居音基。知者，觀其彖辭。彖辭，爻辭也。亹亹，汲汲也。

"The union of male and female essence" is from the Zheng version as "gou jing": "gou" means to meet and unite, indicating that men and women unite their vital energies through yin and yang. "Because of 'er' to benefit human conduct" should be "because of 'er' to benefit human conduct" where "er" should be read as "er" meaning two. "Loss, is the cultivation of virtue": "cultivate" means to govern. "Difficulty, is the distinction of virtue": "distinction" means to differentiate—when encountering hardship, the gentleman remains steadfast in poverty, while the petty person becomes reckless when in poverty, thus the difference in virtue is revealed here. "Increase, is long abundance without exaggeration": "exaggeration" means to overstate. "Mixing various things to cultivate virtue," the Zheng version reads "calculate virtue": "calculate" means to count. "Residence is known" where "residence" is pronounced like "ji."the so-called "know" refers to observing the line statements; and here, the term "line statements" actually refers to the line statements. "Weiwei" describes a state of diligence and tireless effort.