The卦 of Footsteps, with Heaven above and Lake below.

程傳 《履序卦》：“物畜然後有禮，故受之以履。”夫物之聚，則有大小之別，高下之等，美惡之分，是物畜然後有禮，《履》所以繼畜也。履，禮也。禮，人之所履也。為卦天上澤下，天而在上，澤而處下，上下之分，尊卑之義，理之當也，禮之本也，

Cheng Yi's Yichuan Commentary on the Changes says: The "Xu Gua Zhuan" explains the sequence of the "Lv" hexagram: "Only after things have accumulated can there be propriety, hence the "Xu" hexagram is followed by the "Lv" hexagram." Once things are gathered together, there is a distinction of size, a hierarchy of high and low, and a differentiation of beauty and ugliness. This is why after accumulation there is propriety, and thus the "Lv" hexagram follows the "Xu" hexagram. "Lv" means propriety, which is something humans practice. In terms of the structure of the hexagram, Heaven is above and Marsh is below: Heaven naturally is above, and Marsh naturally is below. The distinction between above and below, and the names of respect and humility, are what should be according to reason, and this is the fundamental aspect of propriety, ... (the original text is missing from here).

履虎尾，不咥人，亨。本義 兌亦三畫卦之名，一陰見於二陽之上，故其德為說，其象為澤，“履”，有所躡而進之義也。以兌遇乾，和說以躡剛強之後，有履虎尾而不見傷之象，故其卦為《履》，而占如是也。人能如是，則處危而不傷矣。

The Hexagram Statement says: Walking on a tiger's tail, the tiger does not bite, thus it is smooth and prosperous. Zhu Xi's "Benyi" explains: Dui is also the name of the trigram composed of three lines. A single yao (line) of yin is revealed above two yang lines, so its virtue is harmony and joy, and its image is a marsh. "Lu" means to walk forward on something. When Dui meets Qian, it signifies walking behind a strong person with a harmonious and joyful attitude, symbolizing walking on a tiger's tail without being bitten. Therefore, this hexagram is called "Lu," and the divination is accordingly. If a person can act in this way, they can remain unharmed even when in a dangerous situation.

程傳 履，人所履之道也。天在上而澤處下，以柔履藉於剮，上下各得其義，事之至順，理之至當也。人之履行如此，雖履至危之地，亦無所害，故履虎尾而不見其咥齧，所以能“亨”也。

Cheng Yi in Yichuan's Commentary on the Changes says: "Lu" refers to the path that people walk. Heaven is above and marsh is below, with the soft and yielding beneath the strong and firm, thus the upper and lower each find their proper place, which is the most appropriate situation and the most correct principle. If human actions can be like this, even if one walks on the most dangerous place, one will not suffer harm. Therefore, one can step on a tiger's tail without being bitten, hence achieving "Heng."

集說《朱子語類》云：《履》上乾下兌，以陰躡陽，是隨後躡它，如踏它腳跡相似，所以云“履虎尾”。卦之三四爻，發虎尾義，便是陰去躡它陽後處。李氏簡曰：履，禮也。行之以和，故能進退履眾剛而不見傷，“禮之用和為貴”，其足之謂乎？

The "Ji Shuo" cites Master Zhu Xi's "Yu Le" saying: The "Lu" hexagram has Heaven above and Lake below, representing a yin line stepping on a yang line, like following someone and stepping on their footprints, hence the phrase "stepping on a tiger's tail." The entire hexagram, particularly the lines Six in the Third and Nine in the Fourth, expresses the meaning of stepping on a tiger's tail, which is precisely where the yin line steps behind the yang line. It also cites Li Jian saying: "Lu" means ritual, practicing it with harmony and joy, so one can step on many strong lines without being harmed. The "Analects" states "the use of ritual lies in harmony," which probably refers to this very point.

胡氏炳文曰：《程傳》訓履為踐為藉，以上下論也。《本義》云：有所躡而進，以前後論也。於尾字為切。諸家多以兌為虎，《本義》從《程傳》以乾為虎，本夫子《彖傳》意也。“不咥人亨”，大抵人之涉世，多是危機，不為所傷，乃見所履。《大傳》曰： “《易》之興也”，“其當文王與紂之事邪，是故其辭危”。危莫危於履虎尾之辭矣，故九卦處憂患，以《履》為首。

Quoting Hu Bingwen, the Yichuan Commentary on the Changes interprets "lu" as trampling or using as a cushion, which refers to the relationship between superior and inferior; the Benyi Commentary says "lu" means advancing with something beneath one's feet, which refers to the relationship between front and back, and this is more appropriate for the character "wei." Many scholars regard Dui as a tiger, but the Benyi Commentary follows the Yichuan Commentary in taking Qian as the tiger, based on Confucius' Commentary on the Judgment. As for "bu die ren heng," generally speaking, people walking through the world face dangers everywhere; only when they are not harmed can one see what they are practicing. The Xici Commentary says the origin of the Zhou Changes was probably during the time of King Wen and King Zhou of Shang, so its phrases are full of anxiety and danger. There is no greater danger than the phrase "lu hu wei." Therefore, among the nine hexagrams listed in the Xici Commentary dealing with worries and dangers, the Hexagram Lu comes first.

粱氏寅曰；履者踐履也。人之於禮，亦踐行其天理者，故履為禮也。夫虎，剛猛之獸。乾三陽，虎之象也。上為虎之首，則四為虎之尾。兌履乾之後，履虎尾之象也。虎咥人者也，然以和說履之，則不見咥而反至亨。以是觀之，人之踐履卑遜，何往而不亨乎？然和非阿容也，說非佞媚也，亦恭順而不失其正耳。兌之《傳》曰：“剛中而柔外”，此其道也。蔡氏清曰：八卦唯兌為至弱，唯乾為至健。今以至弱者而躡於至健者之後，自是危機，故獨以“履”名卦，而《彖傳》復取其德，而謂之“履虎尾，不咥人亨”也。

Quoting Liang Yin, it is said: "Lǚ" means to practice. A person's adherence to ritual is also practicing the inherent heavenly principle, so "Lǚ" is ritual. The tiger is a fierce wild beast, and the three yang lines of Qian represent the image of a tiger. The upper ninth line is the tiger's head, so the ninth line in the fourth position is the tiger's tail. Dui follows Qian, which represents the image of stepping on the tiger's tail. Although tigers usually bite people, if one approaches them with a harmonious and pleasant attitude, one may not be bitten and thus achieve success. Therefore, if a person practices with humility and modesty, where would he not find success? However, harmony does not mean without principle, and pleasantness does not mean flattery or sycophancy. It simply means respectful and compliant behavior without losing one's own proper path. The Commentary on the Judgment explains Dui as "strong in the center and soft on the outside," which is exactly this approach. Quoting Cai Qing, among the eight trigrams, only Dui is the most gentle, and only Qian is the most strong. Now, placing the most gentle after the most strong, stepping on it, is itself a danger. Hence, the name "Lǚ" is specifically given to this hexagram, and the Commentary on the Judgment also takes its harmonious virtue and states, "Stepping on the tiger's tail, not being bitten, success."

初九，素履往，無咎。本義 以陽在下，居履之初，未為物遷，率其“素履”者也。占者如是，則“往”而“無咎”也。程傳 履不處者，行之義，初處至下，素在下者也。而陽剛之才，可以上進，若安其卑下之素而往，則“無咎”矣。夫人不能自安於貧賤之素，則其進也，乃貪躁而動，求去乎貧踐耳，非欲有為也。既得其進，驕溢必矣，故往則有咎。賢者則安履其素，其處也樂，其進也將有為也，故得其進，則有為而無不善，乃守其素履者也。

The line statement for the initial yang line (Chu Jiū) says: by following one's usual conduct and moving forward, there will be no fault. Zhu Xi's "Ben Yi" states: the initial yang line is a yang element in the lowest position, located at the beginning of the "Lu" hexagram, and has not yet been influenced by external things. It is someone who follows his usual ways and moves forward in accordance with his own conduct. If a person consults the oracle in this way, then "going forward" will result in "no fault." Cheng Yi's "Yichuan Commentary on the Changes" says: "Lu" means to move forward without stopping. The initial yang line is in the lowest position, originally residing in a low position; yet it has the quality of yang strength, which allows it to advance. If one can be content with his humble position and then move forward, then "no fault" will result. If a person cannot be content with his humble and low status, then his desire to advance is merely a greedy and impetuous movement, a desire to escape poverty and low status, rather than a desire to achieve something. Once he attains success, he will inevitably become arrogant and unrestrained, so such "going forward" will result in fault. The virtuous person, however, remains content with his usual conduct: he finds joy in leisure and is ready to act when he is employed. Therefore, when he is appointed to office, he will surely accomplish something without wrongdoing. This is the person who maintains "the simple conduct."

集說 胡氏炳文曰：初未交於物，有素象。案《本義》與蔡氏皆曰：居《履》之初，

"The Collection of Sayings" cites Hu Bingwen's statement: "Initial Nine has not yet interacted with external things, so it has the image of 'simple' (素)." Li Guangdi comments: "The original meaning and Cai Qing both say that it is at the beginning of the "Walking" hexagram, ..." (the original text is missing from here onwards)

九二，履道坦坦，幽人貞吉。本義 剛中在下，無應於上，故為履道平坦，幽獨守貞之象。幽人履道而遇其占，則貞而吉矣。程傳 九二居柔，寬裕得中，其所履坦坦然平易之道也。雖所履得坦，《易》之道亦必幽靜安恬之，人處之則能貞固而吉也。九二陽志上進，故有幽人之戒。集說 梁氏寅曰：行於道路者，由中則平坦，從旁則崎險。九二以剛居中，是履道而得其平坦者也。持身如是，不輕自售，故為“幽人貞吉”。

The line statement for the second line (Nine Two) says: the path one is taking is smooth and level, and the person who lives in seclusion and maintains quietude attains good fortune by upholding the right path. Zhu Xi's "Original Meaning" states: the Nine Two, being a yang line, is located in the middle of the lower trigram and is situated in the lower trigram. There is no corresponding line above it, so the path is smooth, and the person who lives in seclusion and maintains quietude is in a position that reflects the image of upholding the right path. If a person who lives in seclusion follows the right path and comes across this line, they will uphold the right path and attain good fortune. Cheng Yi's "Yichuan Commentary on the Changes" says: the Nine Two, being a yang line, is in a yin and flexible position, is broad-minded and "holds the center," and is walking on a smooth and easy path. Although the path is smooth, it is only when a person who is quiet and tranquil is in this position that they can maintain firmness and attain good fortune (the original text mistakenly split the phrase "tanjie zhi dao" into two parts). The Nine Two is still a yang line, and its mind is inclined towards advancement, so it is given the warning of "the secluded person." The "Collected Sayings" cites Liang Yin, who says: when walking on a path, walking in the middle makes the path smooth, while walking on the sides makes it rugged and dangerous. The Nine Two, being a yang line in the central position, is the one who is walking on the path and attains smoothness. Holding onto oneself in this way, not easily giving oneself away, is what is meant by "the secluded person upholds the right path and attains good fortune."

六三，眇能視，跛能履，履虎尾，咥人凶，武人為于大君。本義 六三不中不正，柔而志剛，以此履乾，必見傷害，故其象如此，而占者凶。又為剛武之人，得志而肆暴之象，如秦政、項藉，豈能久也？

The Line Statement for the third line says: One eye is blind yet it tries to see, one leg is lame yet it tries to walk; stepping on the tiger's tail, the tiger bites, which is dangerous; a brave person acts for the great ruler. Zhu Xi's "Original Meaning" says: The sixth line is neither in the center nor in the proper position, is inherently gentle yet has a stubborn will, and with such a nature it steps on Qian, inevitably suffering harm, so the image is taken in this way, and the divination results in a凶 (dangerous) outcome. It also has the image of a brave person who, once successful, acts tyrannically, like Qin Shi Huang Ying Zheng or Xiang Yu of the Western Chu, how could they last long?

程傳 三以陰居陽，志欲剛而體本陰柔，安能堅其所履？故如盲眇之視，其見不明。跛躄之履，其行不遠。才既不足，而又處不得中，履非其正，以柔而務剛，其履如此，是履於危地，故曰“履虎尾”。以不善履履危地，必及禍患，故曰“咥人凶”。“武人為于大君”，如武暴之人，而居人上，肆其躁率而已，非能順履而遠到也。不中正而志剛，乃為群陽所與，是以剛躁蹈危而得凶也。

Cheng Yi in Yichuan's Commentary on the Changes says: The sixth line in the third position holds a yin line in a yang place. Her heart desires strength, but her nature is inherently soft and weak. How can she hold on to her path? Therefore, it is like a person who has lost one eye, unable to see clearly; or a person with a limp, unable to walk far. Her ability is insufficient, and she is in a position of disadvantage. The path she follows is not correct. With her weakness, she insists on being strong, and her actions reach this point, which is like stepping on a tiger's tail. Therefore, it is said 'to tread on a tiger's tail.' Using improper methods to enter a dangerous place will certainly bring calamity, hence 'the tiger bites someone and it is凶.' As for 'the warrior serves the great lord,' it is like a fierce warrior in a position of authority, who only knows to indulge his impetuousness and recklessness, and cannot follow the correct path to go far. He is neither upright nor balanced, yet his will is stubborn and rigid, and he is supported by many yang lines. Therefore, his bold and reckless actions lead to misfortune.

集說 耿氏南仲曰：視欲正，視而不正，則眇者也。行欲中，行而不中，則跛者也。故《歸妹》初九不中則為“跛”，九二不正則為“眇”。履，六三不中又不正，故跛眇兼焉。《歸妹》、《履》，皆兌下也。

"The Collected Sayings" cites Geng Nanzhong's explanation: looking should be done properly; if looking is not correct, it becomes one-eyed. Walking should be done in the middle; if walking is not in the middle, it becomes lame. Therefore, the "Initial Nine" of the "Return of the Maiden" hexagram says "lame" because it does not occupy the central position. The "Nine in the Second" is not in the proper position, so it says "one-eyed." The "Six in the Third" of the "Foot" hexagram is neither in the middle nor in the proper position, so it has both "lame" and "one-eyed." The "Return of the Maiden" and "Foot" hexagrams both have the same lower trigram, which is Dui."

王氏申子曰：三以陰居陽，以柔履剛，謂其明耶？則眾陽而獨陰。謂其不明耶？則又居於陽。眇能視之象也。謂其能行耶，則眾剛而獨柔。謂其不能行耶？則又履乎剛，跛能履之象也。是體暗而用明，才弱而志剛者也，而又不中不正，故不自度量而一於進，敢於蹈危而取禍，如“履虎尾”而受咥人之凶也。若不顧強弱，勇猛直前，唯武人用之以有為于大君之事則可。然彖亦主三而言，曰“不咥人亨”，此曰“咥人凶”，何也？蓋彖總言一卦之體，爻則據其時與位而言，所以不同。

Wang Shenzi said: The sixth line in the third position is a yin line occupying a yang position, using softness to tread on strength. If we say it is clear-sighted, the whole hexagram is composed of yang lines, yet it is alone yin; if we say it is not clear-sighted, it is yet occupying a yang position. This is the image of "one eye can see." If we say it can walk, the whole hexagram is composed of strong lines, yet it is alone weak; if we say it cannot walk, it is yet treading on strong lines. This is the image of "limping but able to walk." Thus, its physical condition is weak but its function is evident, its ability is soft but its will is strong. Moreover, since it is neither in the middle nor in the proper position, it acts without measure, advancing recklessly, daring to take risks and inviting misfortune, like stepping on a tiger's tail and suffering a bite. If we say it is bold and advances without regard for strength, then only warriors can use this kind of spirit to serve the great sovereign. However, the "tiger's mouth" statement is mainly based on the sixth line in the third position, yet it says "not biting people is beneficial," while here it says "biting people is ominous." Why is this? Because the "tiger's mouth" statement discusses the whole hexagram in general, while the line statement discusses each line according to its time and position. Thus, the two are different.

吳氏澄曰：彖通指一卦而言，則上九虎之首也。虎口實而合，有“不咥”之象。此專據一爻而言，則三為兌之上畫也，兌口虛而開，故有“咥人”之象。胡氏炳文曰：凡卦辭以爻為主，則爻辭與卦同。如《屯》卦“利建侯”，而初爻亦“利建侯”。以卦上下體論，則爻辭與卦不同。如此卦云“履虎尾不咥人”，而六三則曰“咥人”是也。卦書“不咥人”，兌三爻說體，自與乾三爻健體相應也。爻書“咥人”，六三一爻，與上九一爻獨相應，“履虎尾”而首應也。

Wu Cheng said: "The '彖辞' generally refers to the entire hexagram. Therefore, the top line, 'Nine at the Top', is like the tiger's head. When the tiger's mouth is closed and full, it has the image of 'not biting'. Here, however, it refers specifically to one line. The third line, 'Six in the Third', is the top line of the '兑' trigram. Since '兑' has an open and empty mouth, it has the image of 'biting people'. Wu Cheng also cited Hu Bingwen, saying that if a hexagram's statement focuses on a particular line, then the line statement will be the same as the hexagram statement. For example, the hexagram '屯' says 'favorable to establish a feudal lord', and the first line also says 'favorable to establish a feudal lord'. However, if the hexagram statement is based on the upper and lower trigrams, then the line statement will differ from the hexagram statement. For instance, this hexagram's statement says 'walking on a tiger's tail without being bitten', but the third line says 'biting people'. The hexagram statement says 'not biting people' because the third line of '兑' belongs to the harmonious and joyful trigram, naturally corresponding to the third line of '乾', which belongs to the strong and vigorous trigram. The line statement says 'biting people' because the third line corresponds specifically to the top line, and stepping on the tiger's tail just happens to meet the tiger's head."

案 “武人為于大君”，王氏之說得之。蓋三非大君之位，且為於兩字語氣亦不順也。子曰：“暴虎馮河，死而無悔者，吾不與也。”即此句之意。

Li Guangdi comments: Regarding the phrase "wu ren wei yu da jun," Wang Shenzi's interpretation is most appropriate. Since the sixth line in the third position is not in the position of the great sovereign, and the two characters "wei yu" do not read smoothly when connected. Confucius said, "I do not wish to serve with a man who would fight a tiger with bare hands or cross a river on foot, even if he dies without regret." This is exactly the meaning intended.

本義 九四亦以不中不正，履九五之剛，然以剛居柔，故能戒懼而得“終吉”。程傳 九四陽剛而乾體，雖居四，剛勝者也。在近君多懼之地，無相得之義，五復剛決之過，故為“履虎尾”。“愬愬”，畏懼之貌，若能畏懼，則當“終吉”。蓋九雖剛而志柔，四雖近而不處，故能兢慎畏懼，則終免於危而獲吉也。

The original text is missing the statement of the fourth line. Zhu Xi's "Benyi" says: Nine in the fourth is also neither central nor upright, yet it follows nine in the fifth, which is strong and firm. However, since it is a yang line in a yin position, it can be cautious and vigilant, thus achieving "final good fortune." Cheng Yi's "Yichuan Commentary on the Changes" says: Nine in the fourth is strong and belongs to the Qian trigram, though it is only in the fourth position, it still has the dominant strength of yang. It is in a position close to the sovereign, where suspicion and fear are greatest, and it does not have a harmonious relationship with nine in the fifth. Moreover, nine in the fifth has the flaw of being overly decisive, hence the phrase "treading on the tiger's tail." "Susu" means a state of fear; if one remains cautious and reverent, then "final good fortune" is achieved. This is because nine, though strong, has a gentle will, and four, though close to the sovereign's position, does not claim it, thus being careful and reverent, ultimately avoiding danger and achieving good fortune.

集說 王氏弼曰：逼近至尊，以陽承陽，處多懼之地，故口“履虎尾，愬愬”也。然以陽居陰，以謙為本，雖處危懼，終獲其志，故“終吉”也。王氏宗傳曰：《經》曰“四多懼”，處多懼之地，而復以恐懼自處，所謂愬愬也。四處三陽之後，故亦曰“履虎尾”。無忘其愬愬之戒，故曰“終吉”，在卦德曰“履虎尾，不咥人，亨”，其九四之謂乎？

The "Collected Sayings" cites Wang Bi's explanation: Nine in the Fourth is close to the position of the Supreme Sovereign, with a Yang line following another Yang line, situated in a place where doubt and fear are most prevalent. Therefore, it says "treading on a tiger's tail, with anxiety" (the original text "gù kǒu" should be "gù yuē"). However, since it is a Yang line in a Yin position, it is based on humility and modesty. Although it is in a dangerous and fearful situation, it ultimately realizes its aspirations, hence "eventually auspicious." It also cites Wang Zong's explanation: The "Great Treatise" states "Four is often fearful"; being in a position of frequent fear, yet being mindful of fear, is what is meant by "with anxiety." Nine in the Fourth is behind three Yang lines, so it is also said "treading on a tiger's tail"; not forgetting the warning of "with anxiety," hence "eventually auspicious." Regarding the卦德 explanation of "treading on a tiger's tail, the tiger does not bite, and it is smooth," this is probably referring to someone like Nine in the Fourth.

《朱子語類》云：履三爻正是躡它虎尾處，四上躡五，亦為虎尾之象。胡氏炳文曰：《本義》於三之“履虎尾”，曰不中不正以履乾，是以乾為虎而三在其後也。於四之“履虎尾”，則曰亦以不中不正履九五之剛，是以九五為虎，而四在其後也。三四皆不中正，而佔有不同者，“三多凶”，以柔居剛，其凶也宜。“四多懼”，以剛居柔，所以“終吉”。

Master Zhu Xi says in the "Collected Sayings of Master Zhu" that the sixth line in the third position of the "Lu" hexagram is exactly where one steps on the tiger's tail; the ninth line in the fourth position steps upward onto the ninth line in the fifth position, which also represents the image of the tiger's tail. He cites Hu Bingwen, who explains that the "Original Meaning" interprets the "stepping on the tiger's tail" of the sixth line in the third position as not being in the center or correct position, and stepping onto the Qian trigram, taking Qian as the tiger and the sixth line in the third position as being behind the tiger. For the ninth line in the fourth position, it says that it also is not in the center or correct position, but steps onto the strong and firm ninth line in the fifth position, taking the ninth line in the fifth position as the tiger and the ninth line in the fourth position as being behind the tiger. The third and fourth lines are both not in the center or correct position, but their interpretations differ: the "Great Treatise" says "the third line is often凶 (dangerous)", because the sixth line in the third position, being yin and soft, occupies a yang and strong position, so it is appropriate for it to be凶 (dangerous). It also says "the fourth line is often fearful", because the ninth line in the fourth position, being yang and strong, occupies a yin and soft position, so it can ultimately be吉利 (auspicious).

九五，夬履，貞厲。本義 九五以剛中正履帝位，而下以兌說應之，凡事必行，無所疑礙，故其象為夬決其履，雖使得正，亦危道也，故其占為雖正而危，為戒深矣。

The Line Statement of the Fifth Line (Nine Five): A strong and decisive movement, maintaining correctness still involves danger. Zhu Xi's "Original Meaning" states: Nine Five, with the quality of being strong, vigorous, central, and upright, is situated on the throne. Below it is the Joyful Lake (兑), responding to it. Therefore, everything can be done promptly without doubt or obstruction, hence the image of decisive action. Even though the path is correct, it is still dangerous, so the divination indicates that although it is upright, it is perilous, and the warning within is profound.

程傳 夬，剛決也。五以陽剛乾體，居至尊之位，任其剛決而行者也。如此則雖得正，猶危厲也。古之聖人，居天下之尊，明足以照，剛足以決，勢足以專。然而未嘗不盡天下之議，雖芻蕘之微必取，乃其所以為聖也，履帝位而光明者也。若自任剛明，決行不顧，雖使得正，亦危道也，可固守乎？有剛明之才，苟專自任，猶為危道，況剛明不足者乎？《易》中云“貞厲”，義各不同，隨卦可見。

Cheng Yi in his commentary Yichuan's Commentary on the Changes says: "Guai" means decisive strength. The Nine in the Fifth, possessing the quality of yang strength and the body of heaven's strength, holds the supreme position, and is a person who acts decisively on his own. In this way, even if his actions are correct, they are still dangerous. The ancient sages, who occupied the highest position in the world, had wisdom sufficient to perceive everything, strength sufficient to decide everything, and power sufficient to act alone. Yet they never failed to widely listen to the opinions of the people, even those of the humblest individuals such as those who cut grass or gathered firewood. This is precisely how they became sages, and it is the way of being upright and open while standing on the throne. If one relies on his own strength and insight, and acts alone without considering others, even if his actions are correct, it is a dangerous path. How can one remain firm and unchanging? Those who possess strength and insight, once they act alone, are already on a dangerous path. What then of those who lack even this strength and insight? The Zhou Changes mentions "Zhen Li" in various places, and the meaning varies according to the different hexagrams.

集說 項氏安世曰：六三於彖辭為“亨”者，以下卦言之，有和說之德也，於本爻為凶者，資本陰柔，履位不正，宜其凶也。九五於彖辭為不疚者，以上卦言之，有剛健中正之德也。於本爻為厲者，以剛行剛，志在夬決，其理雖正，其事則危也。凡彖多言卦德，凡爻多論爻位。王氏申子曰：《履》之卦義，履剛也。履剛之道，尚柔不尚剛也。五雖中正以履帝位，然以剛居剛，是一於尚剛者也。夬履，謂決於行也。一於任剛，決行而不顧，則於中正之道，豈能無咎乎？若貞固守此，危道也，故曰“貞厲”。

"The Collection of Sayings" cites Xiang Anshi's view: In the "Tu Cí" (彖辞), the line "Six in the Third" is interpreted as "Heng" (smooth), which refers to the lower trigram, as it possesses a harmonious and pleasant virtue. However, in the specific line statement, it is judged as凶 (misfortune), because the line itself is originally of a yin and soft nature, and its position is not proper, so it is appropriate for it to be misfortune. The line "Nine in the Fifth" is called "Bu Jiu" (without guilt) in the "Tu Cí," which refers to the upper trigram, as it possesses the virtue of being strong, upright, and proper. However, in the specific line statement, it is judged as "Li" (danger), because it acts with strength and decisiveness, and is determined to act, though the principle is correct, the matter is very dangerous. Generally, the "Tu Cí" discusses the virtue of the whole hexagram, while the "Yao Cí" (爻辞) discusses the positions of each line. Quoting Wang Shenzi's view: The meaning of the "Lü" (履) hexagram is to walk on strength; the way of walking on strength is to value gentleness and not to value strength. Although "Nine in the Fifth" is upright and occupies the position of the sovereign, it is a yang line in a yang position, and thus is one-sidedly valuing strength. "Gua Lü" (夬履) means to act decisively; acting decisively and proceeding without looking back, how can there be no mistake regarding the path of uprightness? If one insists on this approach, it is a dangerous path, hence it is said "Zhen Li" (keeping firmness in danger).

案 凡《彖傳》中所讚美，則其置辭無凶厲者，何獨此爻不然？蓋履道貴柔。九五以剛居剛，是決於履也。然以其有中正之德，故能常存危厲之心，則雖決於履，而動可無過舉矣。《書》云：心之憂危，若蹈虎尾，此其所以“履帝位”而“不疚”也與。凡《易》中貞厲、有厲，有以常存危懼之心為義者，如《噬嗑》之”貞厲無咎”，《夬》之“其危乃光”是也。然則此之“貞厲”，兌五之“有厲”，當從此例也。

Li Guangdi remarked: Whenever the Commentary on the Judgment praises something, its wording does not include words of misfortune or danger. Why is this particular line different? Because the practice of walking with caution values the use of softness. The Nine in the Fifth is strong in a strong position, acting decisively. However, because it possesses the virtue of being both central and upright, it can always maintain a sense of danger and vigilance. Thus, even though it acts decisively, its actions do not result in mistakes. The Book of Documents says that inner fear and vigilance are like walking on a tiger's tail. This is precisely why it can "walk upon the imperial throne" without regret. In the Zhou Changes, whenever the term "zhengli" or "youli" appears, it often refers to maintaining a constant sense of danger and vigilance. For example, "zhengli wu jiu" in the噬嗑 hexagram and "qi wei na guang" in the夬 hexagram. Therefore, the "zhengli" here, as well as the "youli" in the兑 hexagram's Nine in the Fifth, should be understood in this way.

本義 視履之終，以考其樣，周旋無虧，則得“元言”，占者禍福視其所履而未定也。程傳 上處《履》之終，於其終視其所履行，以考其善惡禍福，若其旋則善且吉也。旋，謂周旋完備，無不至也。人之所履，考視其終，若終始周完無疚，善之至也，是以“元吉”。人之吉凶，繫其所履，善惡之多寡，占凶之小大也。

The text for the top line (上九) is missing in the original. Zhu Xi's "Benyi" says: Looking back at the final outcome of one's entire life journey, one can examine its signs of good or bad fortune; if all aspects are complete and nothing is lacking, then it is "yuanji" (the original text mistakenly says "kao qi yang" instead of "kao qi xiang," and "yuan yan" instead of "yuan ji"). Whether a person's fortune or misfortune is determined by their actions, and this is not yet decided. Cheng Yi's "Yichuan Commentary on the Changes" says: The top line is at the end of the "Lv" hexagram, so at this final point, one looks back at the entire journey, using it to examine goodness and badness, fortune and misfortune; if all aspects are complete, then it is both good and fortunate. "Xuan" refers to completeness in all directions. A person's actions should be examined at the end; if they are fully complete and without flaw from beginning to end, then goodness has reached its peak, hence "yuanji." A person's good or bad fortune depends on the path they take, and the amount of goodness or evil determines the degree of good or bad fortune (the original text mistakenly says "zhan xiong" instead of "ji xiong").

集說 王氏弼曰：禍福之祥，生乎所履。處履之極，履道成矣，故可“視履”而“考樣”也。居極應說，高而下危，是其旋也，履道大成，故“元吉”。梁氏寅曰：上，《履》之終也。人之所履，觀之於始，則誠偽未可見，惟觀之於終，然後見也。故視其所履以考其善，若周旋無虧，則其吉大矣。是爻也，豈非動容周旋中禮之至與？

"The Collection of Sayings" cites Wang Bi's explanation: signs of misfortune and good fortune arise from one's own actions. The upper ninth line is at the extreme of the "Foot" hexagram, having completed the path of proper conduct, so it can "look back at one's steps" and "examine the auspicious signs." It occupies the highest position yet corresponds with the harmonious and joyful nature, thus although it is at the top, it can descend to the lower positions and be mindful of caution, which is its "turning around"; having fully completed the path of proper conduct, it achieves "supreme good fortune." It also cites Liang Yin's explanation: the upper ninth line is the end of the "Foot" hexagram. Human conduct, when viewed at the beginning, is difficult to distinguish between sincerity and falsehood; only when viewed at the end can it be clearly discerned. Therefore, looking back at what he has done to examine his virtue, if his movements are complete without any deficiency, then the good fortune is great. This line is not precisely the ultimate of what Mencius said about one's movements and behavior being entirely in accordance with propriety?

總論項氏安世曰：一陰一陽之卦，在下者為《復》、《姤》，在上《夬》、《剝》，具義主於消長也。在二五者，陽在二為《師》之將，在五為《比》之主，陰在二為《同人》之君子，在五為《大有》之君子，其義主於得位也。在三四者，陽在三，則以剛行柔為“勞謙”，在四則以剛制柔為“由豫”，陰在三，則以柔行剛為《履》，在四，則以柔制剛為《小畜》，其義主於用事也。大抵用事之爻，在下者為行己之事，在上者為制人之事。

"The General Discussion" cites Xiang Anshi's statement: those hexagrams with only one yin or only one yang line, the line that is at the very bottom is the hexagram of Fu and Guo, and the line that is at the very top is the hexagram of Guai and Po. The meaning is mainly about the waxing and waning of yin and yang. When the line is in the second or fifth position: a yang line in the second position is the general of the hexagram Shi, and in the fifth position is the ruler of the hexagram Bi; a yin line in the second position is the gentleman of the hexagram Tongren, and in the fifth position is the gentleman of the hexagram Dayou. The meaning is mainly about being in the proper position. When the line is in the third or fourth position: a yang line in the third position is to act with strength in a yielding situation, forming the "lao qian" (modest humility) of the hexagram Qian; in the fourth position, it is to control yielding with strength, forming the "you yu" (joyful ease) of the hexagram Yu; a yin line in the third position is to act with yielding in a strong situation, forming the hexagram Liu; in the fourth position, it is to control strength with yielding, forming the hexagram Xiaoxu. The meaning is mainly about being in authority and taking responsibility. Generally, the line that is taking responsibility, if it is in the lower trigram, is about matters concerning oneself, and if it is in the upper trigram, is about matters concerning others.

又曰：《履》之六爻，皆以履柔為吉，故九二為“坦坦”，九四為“愬愬終吉”，上九為“其旋元吉”，皆履柔也。六三卦辭本善，終以履剛為凶。初九九五所履皆正，然初僅能“無咎”，五不免於“厲”，皆履剛也。是故初則懼其失初心之正，而教之以保其素。五則懼其恃勢位之正，而教之以謹其決。蓋剛者，喜動而好決，任剛而行者，後多可悔之事也。

He also said that all six lines of the "Gua" hexagram "Lu" (Following) emphasize the advantage of following the soft and yielding, so line nine at the second position is "Tantant" (level and straightforward), line nine at the fourth position is "Susu zhongji" (cautiously and finally auspicious), and line nine at the top is "Qixuan yuanji" (its turning back is originally auspicious), all of which belong to following the soft. Line six at the third position was originally good in the hexagram statement, but eventually became inauspicious because it followed the hard. Lines nine at the beginning and nine at the fifth position both acted properly, yet line nine at the beginning could only achieve "wu jiao" (no blame), and line nine at the fifth position still had to bear the word "li" (danger), all because they followed the hard. Therefore, for line nine at the beginning, it is feared that it might lose its original purity, so it is taught to remain steadfast. For line nine at the fifth position, it is feared that it might rely on the legitimacy of its position and power, so it is taught to be cautious in its decisions. Because strong people like to act and enjoy making decisions, if they act solely based on their strength, there are often regrettable outcomes afterwards.

程傳《泰序卦》；“履而泰然後安，故受之以泰。 ”履得其所則舒泰，泰則安矣，《泰》所以次《履》也。為卦坤陰在上，乾陽居下，天地陰陽之氣，相交而和，則萬物生成，故為通泰。

Cheng Yi in Yichuan's Commentary on the Changes says that the "Sequence of Hexagrams" explains the order of the hexagram Tai: "Only after proper conduct and practice can one achieve prosperity and ease; only after prosperity and ease can one attain stability, hence the hexagram Lu is followed by the hexagram Tai." Proper conduct and practice lead to openness and prosperity, and prosperity leads to stability, which is why the hexagram Tai comes after the hexagram Lu. In terms of the structure of the hexagram, the yin of Kūn is above and the yang of Qián is below, with the two energies of heaven and earth, yin and yang, interacting and harmonizing, allowing all things to grow and flourish, hence it is called prosperity and ease.

泰，小往大來，吉亨。本義 ”泰”，通也，為卦天地交而二氣通，故為《泰》，正月之卦也。“小”，謂陰。“大”，謂陽。言坤往居外，乾來居內。又自《歸妹》來，則六往居四，九來居三也。占者有剛陽之德，則“吉”而“亨”矣。

The Hexagram Statement says: "The Great Communication," the small has gone away and the great has come in, auspicious, smooth and unimpeded. Zhu Xi's "Original Meaning" states: "Tai" means communication. In terms of the hexagram structure, heaven and earth intersect and the two energies are connected, hence it is called "The Great Communication." It corresponds to the first month of the summer calendar. "Small" refers to yin, "great" refers to yang; it means the earth trigram moves upward to occupy the outer trigram, while the heaven trigram moves downward to occupy the inner trigram. Furthermore, in terms of "hexagram transformation," the hexagram "Tai" comes from "Returning to the Maiden," which is when the line six in the third position moves upward to the fourth position, and the line nine in the fourth position moves downward to the third position. If the person divining possesses the virtue of yang strength, then it is "auspicious" and "smooth."

程傳 “小”，謂陰。“大”，謂陽。“往”，往之於外也。“來”，來居於內也。陽氣 集說 劉氏牧曰：往來者，以內外卦言之，由內而之外為往，由外而復內為來。蔡氏清曰：卦名曰《泰》，以天地交而二氣通，就造化之本不可相無上取也。卦辭曰“小往大來”，以內君子外小人而言，就淑慝之分上取也。然則《泰》有二乎？曰：一也。但是天地交而二氣通，則決然內陽而外陰矣。

Cheng Yi's Yichuan Commentary on the Changes says: "Small" refers to yin, "great" refers to yang; "going" is moving to the outer trigram, "coming" is coming into the inner trigram. Yang energy... (the original text here is missing). "Collected Sayings" cites Liu Mu's view: the concept of coming and going refers to the inner and outer trigrams, moving from inner to outer is called going, moving from outer to inner is called coming. It also cites Cai Qing's view: the name of the hexagram is Tai, which is derived from the mutual interaction of heaven and earth and the communication of the two energies, establishing the idea from the fundamental source of creation that neither can be missing. The hexagram statement says "small goes and great comes," which refers to the inner being the gentleman and the outer being the petty person, taking meaning from the distinction between good and evil. So does the hexagram Tai have two meanings? Answer: It has only one. As long as heaven and earth interact and the two energies communicate, it must necessarily be that yang is inside and yin is outside.

初九，拔茅茹以其匯，征吉。本義 三陰在下，相連而進，拔茅連茹之象，征行之占也。占者陽剛，則其征吉矣。郭璞《洞林》讀至匯字絕句，下卦放此。

Initial line statement: Pulling up wild grass, the roots and tendrils come up together, similar things follow each other, and proceeding is auspicious. Zhu Xi's "Original Meaning" says: The three yang lines below are connected and advancing together (the original text "three yin below" should be "three yang below"), this is the image of pulling up wild grass with roots and tendrils connected, it is a divination for traveling; if the person consulting the hexagram possesses yang strength, then proceeding is auspicious. The Jin scholar Guo Pu in his "Dong Lin" reads the character "hui" and breaks the sentence, and the same sentence in the initial line of the "Pu" hexagram is read in the same way.

程傳 初以陽爻居下，是有剛明之才而在下者也。時之否，則君子退而窮處。時既泰，則志在上進也。君子之進，必與其朋類相牽援，如茅之根然，拔其一則牽連而起矣。“茹”，根之相牽連者，故以為象。“匯”，類也。賢者以其類進，同志以行其道，是以“吉”也。君子之進，必以其類，不唯志在相先，樂於與善，實乃相賴以濟。故君子小人，未有能獨立不賴朋類之助者也。自古君子得位，則天下之賢，萃於朝廷，同志協力，以成天下之泰。小人在位，則不肖者並進，然後其黨勝而天下否矣。蓋各從其類也。

Cheng Yi in Yichuan's Commentary on the Changes says: The initial line, which is a yang line at the very bottom, represents a person with strong and wise abilities who is in a low position. When the situation is blocked, the gentleman retreats and remains in obscurity; when the situation is open and favorable, his aspirations are to advance. The advancement of the gentleman must be supported by those of the same kind, just as the roots of reed grass are connected; if one is pulled up, others are pulled up along with it. "Ru" refers to the interconnected roots, so it is used as a symbol; "Hui" means the same kind. The virtuous person brings his kind together for advancement, and with like-minded people, they promote their ideas, hence "good fortune." The advancement of the gentleman must be accompanied by his kind, not only because he wishes to let others go first and is kind to others, but because they rely on each other to accomplish things. Therefore, whether gentleman or petty person, none can succeed in isolation without the support of their kind. Since ancient times, when the gentleman holds power, the virtuous people of the world gather at court, working together to achieve the prosperity of the world; when the petty person holds power, the wicked gather together, and thus their faction dominates and the world becomes blocked: all of this is due to following their own kind.

集說 劉氏向曰；賢人在上位，則引其類，而聚之於朝，在下位則思與其類俱進。在上則引其類，在下則推其類。故湯用伊尹，不仁者遠，而眾賢至類相致也。《朱子語類》云：以其匯屬上文，嘗見郭璞《洞林》，亦如此作句，便是那時人已自恁地讀了。蓋拔茅連茹者，物象也，以其匯者，人也。林氏希元曰：《程傳》曰：茹，根之相牽者。以《本義》三陽在下，相連而進推之，乃別茅之根，非本茅之根也。蓋一陽進而二陽與之相連，猶一茅拔而別茅之根與之相連也。

"The Collection of Sayings" cites Liu Xiang's view: when the virtuous are in high positions, they recommend their own kind and gather them to the court; when in lower positions, they think of promoting their own kind together. When in high positions, they recommend their own kind; when in low positions, they recommend their own kind. Therefore, King Tang of Shang appointed Yi Yin, and the unvirtuous were far away, while many virtuous people came one after another, which is the mutual attraction among the same kind. The "Zhu Zi Yu Le" says: connect "qi yi hui" with the previous text, and I have seen Guo Pu's "Dong Lin" also make this division, showing that people at that time had already read it this way. Because "ba mo lian ru" refers to the image of things, while "qi yi hui" refers to people. Quoting Lin Xi Yuan's view: "Yichuan's Commentary on the Changes" says "ru is the roots that connect with each other"; according to the "Ben Yi" "three yang are below, connected and advancing," this refers to the root of another mo, not the root of this mo itself. Because one yang line advances, the other two yang lines follow and connect, like pulling up one mo, and the roots of other mos are also pulled up together.

九二，包荒，用馮河，不遐遺，朋亡，得尚于中行。本義 九二以剛居柔，在下之中，上有六五之應，主乎《泰》而得中道者也。占者能包容荒穢，而果斷剛決，不遺遐遠，而不暱朋比，則合乎此爻中行之道矣。

The Line Statement for the Second Line (Nine Two): It can embrace disorder and filth, dare to walk alone across the river, not neglect distant people, and not favor one's own faction. Thus, it is in harmony with the middle path. Zhu Xi's "Original Meaning" says: Nine Two, with a Yang line in a Yin position, is in the middle of the Lower Trigram, and above it is Six Five, which corresponds with it. This is a person who takes charge of the situation of the Book of Changes (Tai) and can maintain the middle path. If those who divinate can embrace disorder and act decisively and resolutely, and do not neglect distant people while not favoring their own faction, then they conform to the principle of the middle path in this line.

程傳 二以陽剛得中，上應於五，五以柔順得中，下應於二。君臣同德，是以剛中之才，為上所專任，故二雖居臣位，主治泰者也，所謂上下交而其志同也。

Cheng Yi in Yichuan's Commentary on the Changes says: Nine in the Second, with its yang strength, attains the center and connects upward with Six in the Fifth; Six in the Fifth, with its flexibility and compliance, attains the center and connects downward with Nine in the Second. The virtue of ruler and minister is the same, so Nine in the Second, with its strong and upright ability to maintain the center, gains the ruler's exclusive trust. Therefore, although Nine in the Second holds the position of a minister, it is the one who governs the flourishing era. This is what the Commentary on the Judgment refers to as the mutual communication between superior and inferior, with aligned aspirations.

故治泰之道，主二而言。“包荒，用馮河，不遐遺，朋亡”，四者處泰之道也。人情安肆，則政舒緩而法度廢弛，庶事無節，治之之道，必有包含荒穢之量，則其施為寬裕詳密，敝革事理，而人安之。若無含弘之度，有貧疾之心，則無深遠之慮，有暴擾之患，深敝未去，而近患已生矣，故在“包荒”也。“用馮河”，泰寧之世，人情習於久安，安於守常，惰於固

Cheng Yi's Commentary on the Changes continues: the principle of governing a time of great harmony and prosperity mainly focuses on the second line, line nine. The four lines of the line statement, "Include the desolate and the abandoned, cross the river with confidence, not neglect the distant, and have no companions," are the four proper approaches one should take when in a time of great harmony. Once human feelings become indulgent and unrestrained, government orders become slack, and laws and regulations gradually fall into disuse, leading to the loss of control over all affairs. To rectify such a situation, one must first possess a broad and inclusive spirit, which will allow governance to be broad and thorough, removing accumulated evils and restoring order, thus bringing peace to the people. If one lacks a magnanimous spirit and instead harbors aversion and resentment, there will be no far-reaching plans, only the calamities of hasty and oppressive measures. Deep-rooted problems remain unresolved while immediate troubles arise, hence the four lines should begin with "Include the desolate and the abandoned." As for "cross the river with confidence," it refers to the fact that in times of peace and security, people have become accustomed to long-term ease, content with following old ways, and lazy about... The original text here is missing, and Cheng Yi's passage is incomplete.

集說 胡氏炳文曰：若有包容而無斷制，非剛柔相濟之中也。必包容荒穢，而又果斷剛決，則合乎中矣。雖不遺遐遠，而或自私於吾之黨類，則易至偏重，非輕重不偏之中也。唯不遺遐遠，而又不暱朋比，是不忘遠又不洩邇，合乎中矣。《本義》兩而字當細玩。

Collecting various interpretations, Hu Bingwen says: if there is only inclusion without discernment, it is not the 'center' which is the harmonious balance of firmness and flexibility. One must be able to include the coarse and the vulgar, and at the same time be resolute and decisive, only then can it be considered as center. Although not abandoning distant people, yet favoring one's own faction, is easy to become biased, and thus not the impartial center. Only when one neither abandons distant people nor favors one's own faction, is it both not forgetting the distant and not neglecting the near, thus conforming to the center. Zhu Xi's "Ben Yi" uses two "er" particles consecutively when explaining this line, which should be carefully considered.

龔氏煥曰：初九“以其匯”，九二則欲其“朋亡”，何也？初九在下之賢，則欲其引類而進，九二大臣，所以進退天下之人才者，故欲亡其朋類。唯亡其朋類則能用天下之賢，若獨私其朋，則天下之賢，有不得進用者矣。此其所以不同也。

Collecting interpretations cite Gongs Huan's view: In the Tai hexagram, the line 'Initial Nine' says 'with its kind,' meaning to move forward together with like-minded people; but at 'Nine in the Second,' it says 'friends disappear,' meaning to abandon one's own group. Why is this so? The 'Initial Nine' is a virtuous person in a low position, so he wishes to bring in like-minded people to advance together; 'Nine in the Second' is in the position of a high official, responsible for recommending and dismissing talents throughout the country. Therefore, he must abandon his own group. Only by abandoning his own faction can he employ talents from all over the country; if he only favors his own group, then talents throughout the country will not be employed. This is the reason why two lines in the same hexagram have different meanings.

案 此爻以夫子《象傳》觀之。須以“包荒”兩字為主。蓋聖賢之心無棄物，堯舜之道欲並生，非包荒則不足以體天地之心，而盡君師之道矣。然“包荒”，非混而無別之謂，故必斷以行之，明以周之，公以處之，然後用舍舉措無不合於中道。《魯論》所謂寬信敏公者，意蓋相似也。四者以寬為本，故曰居上不寬，吾何以觀之哉！

Li Guangdi remarked: According to Confucius' Image Commentary, this line must be interpreted with the two characters "bao huang" as the main focus. The sage and virtuous person's heart does not abandon any person or thing. The way of Yao and Shun requires that all things grow together. Without the ability to embrace and include the wild and untamed, one cannot comprehend the heart of heaven and earth that generates and nurtures all things, nor can one fulfill the responsibility of being a ruler or a teacher. However, "bao huang" does not mean to mix everything together without distinction. Therefore, one must also use decisiveness to implement, clarity to examine thoroughly, and impartiality to handle matters. In this way, the selection and rejection, the actions and arrangements, will all conform to the middle way. The four virtues of "kuan" (broad-mindedness), "xin" (trustworthiness), "min" (diligence), and "gong" (impartiality) mentioned in the Analects, are likely intended to be similar in meaning. These four virtues take "kuan" as their foundation, so Confucius said: How can I observe a person in a position of authority who is not broad-minded?

九三，無平不陂，無往不復，艱貞無咎，勿恤其孚，于食有福。本義 將過乎中，《泰》將極而《否》欲來之時也。“恤”，憂也。“孚”，所期之信也。戒占者艱難守貞，則“無咎”而“有福”。

The line statement of the Third Line of the Qian trigram in the Tai hexagram says: There is no constant levelness without turning into incline, no constant going forward without turning back; to maintain uprightness in hardship will not result in error, there is no need to worry about the sincerity one expects, and in enjoying the sustenance one receives, there is inherent blessing. Zhu Xi's "Ben Yi" says: The Third Line is about to cross the central position of the lower trigram, which is precisely the time when Tai is about to reach its peak and Pi is about to arrive. "Xu" means worry, and "Fu" refers to the sincerity one expects. This is a warning to the person consulting the oracle to maintain uprightness in hardship, thus achieving "no error" and "blessing."

程傳 三居泰之中，在諸陽之上，泰之盛也。物理如循環，在下者必升，居上者必降。《泰》久而必《否》，故於《泰》之盛，與陽之將進，而為之戒曰：無常安平而不險陂者，謂無常《泰》也。無常往而不返者，謂陰當復也。平者陂，往者復，則為《否》矣。當知天理之必然，方《泰》之時，不敢安逸，常艱危其思慮，正固其施為，如是則可以“無咎”。處《泰》之道，既能“艱貞”，則可常保其泰，不勞憂恤，得其所求也。

Cheng Yi in Yichuan's Commentary on the Changes says: Nine in the Third is located in the middle of the Tai hexagram and is at the top of the three yang lines, which is the position of Tai reaching its peak. The principle of things is like a cycle; what is below must rise, and what is above must descend. When Tai is prosperous for a long time, it will inevitably turn into a blocked state. Therefore, when Tai is at its peak and the yang energy is still advancing, the sage gives this warning: there is no permanently flat and unslanted path, meaning there is no permanent Tai; there is no permanently going forward without returning, meaning the yin energy will eventually return. The flat becomes slanted, the going away returns, and thus it becomes the Po hexagram. People should understand this as the inevitable principle of heaven. Even when Tai is prosperous, one should not be complacent, but always keep in mind the difficulties and dangers, and act with integrity and firmness. In this way, one can achieve 'no fault'. When one can practice 'difficult yet firm' in the state of Tai, one can maintain the prosperity of Tai for a long time, without needing to worry, and can also attain what one seeks.

不失所期為孚。如是，則於其祿食有福益也。祿食，謂福祉。善處《泰》者，其福可長也。蓋德善日積，則福祿日臻，德逾子祿，則雖盛而非滿。自古隆盛，未有不失道而喪敗者也。

Cheng Yi continued to say: Not disappointing expectations is called "fu." Being able to do so brings blessings and increases one's俸禄 and sustenance.禄 and 食 are forms of blessings. Those who are good at living in a prosperous time can maintain their blessings for a long time. Because virtue and good deeds accumulate day by day, blessings and禄 also come day by day; when virtue surpasses one's position, even if one's status is great, it is not considered full. Since ancient times, those who have prospered greatly have never failed because they lost the right path.

集說 項氏安世曰：“無平不陂”，為三陽言之；“無往不復”，為三陰言之。兩言“無”“不”者，明此皆天道之必至，而“有孚”者也。人能知此，則當《泰》之極，不可不

Collected Commentaries cite Xiang Anshi's statement: "Without level there is slope" refers to the three yang lines in the lower trigram, while "Without going there is return" refers to the three yin lines in the upper trigram. Both phrases use the double negative structure "without... not..." to emphasize that these are matters certain to occur according to the heavenly way, which is what the line statement refers to as "having sincerity." When people understand this, then when Tai reaches its extreme, they must not... the original text here is missing, and Xiang's remarks are incomplete.

徐氏直方曰：小人所以勝君子者，非乘其怠，則攻其隙，艱則無怠之可乘，貞則無隙之可攻，如此則町以“無咎”，可以勿憂其孚矣。或曰：陰陽交運，《否》《泰》相仍，時勢然也，雖“艱貞”，“勿恤”如之何？曰：平陂住復者，天運之不能無；“艱貞”“勿恤”者，人事之所當盡。天人有交勝之理，處其交履其會者，必有變化持守之道，若一諉之天運，以為無預於人事，則聖人之《易》，可無作矣。

Collecting sayings cites Xu Zifang's statement: A petty person can overcome a gentleman, either by taking advantage of the gentleman's slackness or by attacking the gentleman's weaknesses. If one can endure hardship, there will be no slackness to take advantage of; if one can maintain integrity, there will be no weakness to attack. In this way, one can achieve "no fault," and thus need not worry about the reliability of one's expectations (the original text "町以" should be "可以"). Someone asks: Yin and Yang alternate, and the states of "non-communication" and "communication" follow one another, which is natural due to the times. Even if one achieves "endurance through hardship" and "no anxiety," what difference does it make? The answer is: When flat ground becomes steep and then returns to flat, this is inevitable in the heavenly course; however, "endurance through hardship" and "no anxiety" are duties that human beings should fulfill. Heaven and humanity inherently have the principle of mutual overcoming. Those who are in such alternating situations and experience these times must surely have the ability to adapt and remain firm. If one merely attributes everything to heavenly course, believing it has nothing to do with human affairs, then the sage's Book of Changes would not have been written.

六四，翩翩，不富以其鄰，不戒以孚。本義 已過乎中，《泰》已極矣，故三陰翩然而下復，不待富而其類從之，不待戒今而信也。其占為有小人合交以害正道，君子所當戒也。陰虛陽實，故凡言不富者，皆陰爻也。

The Line Statement of the Sixth Line of the fourth position in the Tai hexagram says: Light and graceful, descending swiftly, without relying on wealth, it moves together with nearby like elements, without needing instruction, they trust each other. Zhu Xi's "Ben Yi" says: The sixth line has already passed the central position of the upper trigram, Tai has reached its extreme, so the three yin lines gracefully descend back, without waiting for wealth, similar elements follow, without needing a command, they trust each other (the original text "bu dai jie jin" should be "bu dai jie ling"). The divination for this line indicates that small people associate in groups to harm the correct path, and the gentleman should be cautious. Yin lines are empty while yang lines are substantial, so in the "Book of Changes," whenever it says "not rich," it refers to yin lines.

程傳 六四處《泰》之過中，以陰在上，志在下復，上二陰亦志在趨下。“翩翩”，疾飛之貌，四翩翩就下，與其鄰同也。“鄰”，其類也，謂五與上。夫人富而其類從者，為利也，不富而從者，其志同也。三陰皆在下之物，居上乃失其實，其志皆欲下行，故不富而相從，不待戒告而誠意相合也。

Cheng Yi in Yichuan's Commentary on the Changes says: The sixth line in the fourth position is located beyond the central position in the Tai hexagram. It is a yin line in the upper trigram, with a mind inclined to return downward. The two yin lines above it also desire to move downward. "Pian pian" refers to a swift and eager flight. The sixth line in the fourth position flies swiftly downward, aligning with its neighboring lines. "Neighboring" refers to similar elements, meaning the sixth line in the fifth position and the sixth line at the top. People follow others because they are wealthy, seeking benefit; but those who are not wealthy still follow others because their hearts are in harmony. Originally, these three yin lines belong to the lower position, but by occupying the upper position, they have lost their proper place. Their minds all desire to move downward, so they follow each other without relying on wealth, and their sincerity naturally aligns without waiting for admonition.

夫陰陽之升降，乃時運之《否》、《泰》，或交或散，理之常也。《泰》既過中，則將變矣，聖人於三，尚云“艱貞”則“有福”，蓋三為將中，知戒則可何，四已過中矣，理必變也，故專言始終反覆之道。五，《泰》之主，則復言處《泰》之義。

Cheng Yi continued to say: The rising and falling of yin and yang correspond to the times of fortune and misfortune. Sometimes they come together, sometimes they separate, which is the normal course of things. When the state of Tai (Prosperity) has passed the central position, it is about to change. The sage, in the line nine in the third position, says "difficult but firm" and then "there is blessing," because nine in the third is approaching the central position, and knowing caution is still possible. However, when six in the fourth has passed the central position, according to principle, it must change, so it focuses on the principle of beginning and reversal. Six in the fifth is the main line of the Tai hexagram, so it goes back to explain the meaning of dealing with prosperity.

集說 沈氏該曰：四處上體，在近君之位。三陽既進，樂與賢者共之，志同願得，是以不富以鄰，不戒而孚也。趙氏彥肅曰：從六五下賢，其心休休焉者也。李氏簡曰：陰氣上升，陽氣下降，乃天地之交《泰》也。上以謙虛接乎下，下以剛直事乎上，上下相孚，乃君臣之交泰也，君臣交泰，則天下泰矣。故下三爻皆以剛直事其上，上三爻皆以謙虛接乎下，四當二卦之交，故發此義。

The collected interpretations cite Shen Gai's view: the sixth line in the fourth position is located in the upper trigram, close to the position of the ruler. The three yang lines in the lower trigram have already advanced upwards. The sixth line in the fourth position delights in working with virtuous people, sharing the same aspirations and achieving their goals, so it does not rely on wealth to travel with similar kinds, and does not need to be instructed to gain mutual trust. The collected interpretations also cite Zhao Yansu's view: this follows the manner of the sixth line in the fifth position, which shows respect and honor to virtuous people, displaying a broad-minded and inclusive attitude. The collected interpretations also cite Li Jian's view: the yin energy rises and the yang energy descends, which is how heaven and earth interact to form harmony; the superior ones humbly accept the inferior ones, while the inferior ones uprightly serve the superior ones, and thus the superior and inferior trust each other, forming harmony between ruler and minister. When ruler and minister are in harmony, the world is also in harmony. Therefore, the three lines in the lower trigram all uprightly serve their superiors, and the three lines in the upper trigram all humbly accept their inferiors. The sixth line in the fourth position is precisely at the junction of the upper and lower trigrams, so this meaning is explained in this line.

俞氏琰曰：“翩翩”，降以相從之貌。《易》以陰虛為不富，六四陰爻，故曰“不富”。何氏楷曰：此正陰陽交《泰》之爻也。“翩翩”，群飛而下貌。陰虛陽實，凡言不富者皆陰爻。“鄰”，指五上，四能挾其並居之鄰，相從而下者，以三陰皆欲求陽，故不待教戒，而能以之下孚乎陽也。

The collected interpretations cite Yu Yan's view: "Pian pian" describes the appearance of descending and following each other. The Book of Changes regards the emptiness of a yin line as "not rich," and since the sixth line in the fourth position is a yin line, it says "not rich." The collected interpretations also cite He Kai's view: this is exactly one line of yin and yang meeting in harmony. "Pian pian" describes the appearance of a group flying down together. Yin is empty and yang is full; whenever "not rich" is mentioned, it refers to a yin line. "Neighboring" refers to the sixth line in the fifth position and the sixth line at the top; the fourth line can lead the neighboring line downward together because the three yin lines all desire to unite with yang, so they do not wait for instruction or warning and can gain trust from the yang line by moving downward.

案 《傳》義皆以此爻為小人復來，然以《彖傳》“上下交而其志同”觀之，則四五正當君相之位，下交之主，兩爻《象傳》所謂“中心願也”，中以行願也，則正所謂“志同”者也。爻辭“不富”，與《謙》六五同，皆言其謙虛而不自滿足爾。沈氏趙氏以下諸說，義皆可從。

Li Guangdi remarked: Both Yichuan's Commentary on the Changes and the Benyi treat this line as the return of a petty person. However, from the Commentary on the Judgment, "the superior and inferior are in mutual communication and their aspirations are the same," it can be seen that the lines six in the fourth and six in the fifth are in positions of prime ministers and the sovereign, and are the ones leading the downward communication. The statements in the Image Commentary, "the center's wish" and "the center carries out the wish," are exactly what is meant by "their aspirations are the same." The line statement "not rich" is the same as line six in the fifth of the Qian hexagram, and merely indicates that he is humble and not self-satisfied. The interpretations of Shen Cai and Zhao Yansu and later scholars can all be accepted.

六五，帝乙歸妹，以祉元吉。本義 以陰居尊，為《泰》之主，柔中虛已，下應九二，吉之道也。而“帝乙歸妹”

The Line Statement of the Fifth Line in the Tai hexagram says: "The Emperor Yi married off his young maiden, thus obtaining blessings, which is a great auspicious omen." Zhu Xi's "Benyi" states: "The Fifth Line, being a yao of Yin in a noble position, is the main line of the Tai hexagram. It is gentle, compliant, and maintains the middle, remaining humble and open to others. It reaches down to correspond with the Second Line, which is the way to auspiciousness." As for "Emperor Yi marrying off his maiden"..., the original text here is missing. Zhu Xi's passage in "Benyi" is incomplete, and the text directly continues with Yichuan's Commentary on the Changes.

程傳 史謂湯為天乙，厥後有帝祖乙，亦賢王也。後又有帝乙。《多士》曰：自成湯至於帝乙，罔不明德恤祀。稱“帝乙”者，未知誰是。以爻義觀之，帝乙制王姬下嫁之禮法者也。自古帝女雖皆下嫁，至帝乙然後制為禮法，使降其尊貴，以順從其夫也。六五以陰柔居君位，下應於九二剛明之賢，五能倚任其賢臣而順從之，如帝乙之歸妹然，降其尊而順從於陽，則以之受祉，且元古也。“元吉”，大吉而盡善者也，謂成治《泰》之功也。

Cheng Yi in Yichuan's Commentary on the Changes says: Historical records refer to Shang Tang as Tianyi, and later there was Emperor Zuyi, who was also a virtuous ruler, and later Emperor Yi. The Book of Documents, Dushì, says: From Cheng Tang to Emperor Yi, none did not strive to practice virtue and conduct solemn worship. It is unclear which emperor the line statement refers to as 'Emperor Yi'. Considering the meaning of the line, Emperor Yi should be the one who established the rites for the marriage of royal daughters. Since ancient times, royal daughters were all married off, but it was Emperor Yi who formalized the rites, making them descend from their noble status to obey their husbands. The line refers to the sixth line, which is a yin line occupying the position of the ruler, and it corresponds to the second line, a yang line representing a virtuous minister. The sixth line can rely on and appoint this virtuous minister and obey him, just as Emperor Yi married his sister, descending from her noble status to obey the yang. Therefore, it receives blessings and great good fortune (the original text 'qi yuan gu' should be 'qi yuan ji'). 'Yuan ji' means great good fortune and complete virtue, indicating the accomplishment of the governance of the prosperous era.

集說 項氏安世曰：帝女，下嫁之札，至湯而備。湯嫁妹之辭曰：無以天子之富而驕諸侯。陰之從陽，女之順夫，天下之義也。往事爾夫，必以禮義。湯稱天乙。或者亦稱帝乙乎？

Collected Sayings cites Xiang Anshi's statement: The ritual for a royal daughter marrying down, in the proper way, was only fully established during the time of King Tang of Shang (the original text says "down marriage document" but should be "down marriage ritual"). When King Tang married his sister, the words of instruction said: Do not rely on the wealth and prestige of the Son of Heaven to be arrogant toward the feudal lords. Yin follows Yang, and the woman follows her husband, which is the universal principle of the world; when you serve your husband, you must do so according to propriety and righteousness. King Tang was called Tianyi, perhaps also referred to as Diyi?

上六，城復于隍，勿用師，自邑告命，貞吝。本義 《泰》極而《否》，“城復于隍”之象。戒占者不可力爭，但可自守，雖得其貞，亦不免於羞吝也。

The Line Statement of the Sixth at the Top of the Tai hexagram says: The city walls collapse and fall into the dry ditch below the city. Do not mobilize the army; only issue commands from your own territory. Although you maintain uprightness, you cannot avoid regret. Zhu Xi's "Benyi" says: When Tai reaches its extreme, it transforms into Pi. This is the image of "the city walls returning to the dry ditch." This warns the person consulting the oracle not to strive for contention, but to hold fast to self-restraint; even if one maintains uprightness, one cannot avoid feelings of shame and regret.

程傳 掘隍土積累以成城，如治道積累以《泰》。及《泰》之終，將反於《否》，如城土頹圯，復反於隍也。上，《泰》泰之終，六以小人處之，行將否矣。“勿用師”，君之所以能用其眾者，上下之情通心從也。今《泰》之將終，失《泰》之道，上下之情不通矣。民心離散，不從其上，豈可用也？用之則亂。

Cheng Yi in Yichuan's Commentary on the Changes says: digging up the soil from the moat and piling it up to build the city wall is like the way of governing the country, which accumulates layer by layer to achieve prosperity. When prosperity reaches its end, it will return to blockage, just as the soil on top of the city wall collapses and falls back into the moat. The Sixth at the Top is the end of prosperity. A person of Yin flexibility and weakness is in this position, and prosperity is about to turn into blockage. The phrase 'do not use the army' is because the ruler can mobilize people by having harmony between superiors and inferiors and the people's obedience. Now that prosperity is about to end, the way of prosperity has already been lost, and harmony between superiors and inferiors is broken, the people are scattered and unwilling to obey the ruler. How can one still use the army? If one does, chaos will arise.

眾既不可用，方自其親近而告命之，雖使所告命者得其正，亦可羞吝。“邑”，所居，謂親近，大率告命必自近始。凡“貞凶”“貞吝”有二義，有貞固守此則凶吝者，有雖得正亦凶吝者，此不云貞凶而云“貞吝”者，將否而方告命，為可羞吝，否不由於告命也。

Cheng Yi continued to say: since the people cannot be moved, one can only issue commands to those close to oneself; even if the content of the command is in accordance with the right path, it is still a matter of shame and regret. "Yi" refers to one's own dwelling place, meaning those close to oneself; generally, when issuing commands, one should start from the near. All divination phrases such as "Zhen Xiong" and "Zhen Lin" have two meanings: one is that adhering to this path will bring misfortune and poverty, and the other is that even if one attains the right path, misfortune and poverty are still unavoidable. Here, instead of saying "Zhen Xiong," it says "Zhen Lin," because the command is issued when the time is about to be blocked, and it is merely a matter of shame and regret; the blockage itself is not caused by the command.

集說 《朱子語類》：問：《泰》卦“無平不陂，無往不復”，與“城復于隍”。曰：此亦事勢之必然，冶久必亂，亂久必治，天下無久而不變之理。子善遂言天下治亂，皆生於人心，治久則人心放肆，故亂因此生。亂極則人心恐懼，故治由此起。曰：固是生於人心，履其運者，必有變化持守之道可也。案 “貞”者，常也。爻義言當此之時，只可告邑，未可用師。若守常而用師則吝，非以告邑為可吝也。

Quoted from "Ji Shuo" citing "Zhu Zi Yu Lue": Someone asked about the meaning of "There is no level ground without slope, no going without return" in the Tai hexagram and "The city returns to the moat" in the line "Six at the Top." Zhu Xi said: This is also a natural course of events. A long period of peace will inevitably lead to chaos, and a long period of chaos will inevitably lead to restoration. There is no such thing as a state that remains unchanged forever (the original text "Ye jiu bi luan" should be "Zhi jiu bi luan"). A disciple named Zi Shan continued: The rise and fall of the world come from the people's hearts. When peace lasts long, people's hearts become unrestrained, and chaos thus arises; when chaos reaches its peak, people's hearts become fearful, and restoration thus emerges. Zhu Xi said: It is indeed rooted in the people's hearts, but those who are in the midst of such times must have the ability to adapt to changing circumstances and maintain self-discipline. Li Guangdi commented: "Zhen" means constant. The meaning of the line is that at this time, one can only issue orders within the city, but not yet deploy troops; if one rigidly adheres to conventional methods and uses military force, there will be regret, but this does not mean that issuing orders within the city itself is shameful or regrettable.

總論劉氏定之曰；《泰》取天地交而萬物通，上下交而其志同、故六爻之中，相交之義重。初與四相交，《泰》之始也。故初言“以其匯”，如茅之連茹。四言“以其鄰”，如鳥之連翩，二與五相交，《泰》之中也，故五言人君降其尊貴以任夫臣，二言大臣盡其職任以答夫君。三與上相交，《泰》之終也，故三言平變而為陂，上言城復而於隍。

In summary, Liu Dingzhi explains that the hexagram Tai derives its meaning from the mutual interaction between heaven and earth, allowing all things to communicate, and the mutual interaction between above and below, leading to harmony of hearts and minds. Therefore, among the six lines, the significance of mutual interaction is most important. The six lines are paired in pairs of 'responding' lines, forming exactly three pairs: the first and fourth, the second and fifth, and the third and sixth. The interaction between Chou and Si represents the beginning of Tai, so Chou says 'by its convergence,' like the roots of reeds connected together; Si says 'by its neighbor,' like a flock of birds descending in unison. The interaction between Er and Wu represents the middle of Tai, so Wu speaks of the ruler descending from his lofty position to employ ministers, and Er speaks of ministers fulfilling their duties to repay the ruler. The interaction between San and Liang represents the end of Tai, so San speaks of flat ground turning into a steep slope, and Liang speaks of the city walls collapsing back into the moat.

蓋君子進而小人退，所以致《泰》也。君委任而臣效忠，所以致《泰》也。抑天運之循環，《泰》極而《否》，有必然者，而保泰之意，隱然有不容不恐懼焉，則平陂城隍，其旨嚴哉！

Liu Dingzhi continued saying: When the virtuous advance and the petty men retreat, this is the cause of the prosperity of Tai; when the sovereign entrusts authority freely and the ministers serve with loyalty, this is also the cause of the prosperity of Tai. However, the heavenly course is cyclic, and when Tai reaches its extreme, it turns into Pi, which is inevitable. Within the intention of maintaining the prosperity of Tai, there is implicitly a necessity for vigilance. Thus, looking at the two line statements "Without level there is slope" and "The city returns to the moat," how severe their intent is!

吳氏曰慎曰：初四以氣類言，二體之始也。三上以時運言，二體之終也。二五以主

In summary, Wu Yueshen said: "Chu Ji and Liu Si refer to those with the same nature, they are respectively the beginnings of the upper and lower parts; Ji San and Shang Liu refer to the change of time, they are respectively the endings of the upper and lower parts; Ji Er and Liu Wu, however, refer to..." The original text here is missing, and Wu's statement is incomplete. The text then directly proceeds to the hexagram of "Pu."