The "Say on the Trigrams" text mentions the repetition of three trigrams in the images.

曰：否否。坎曰惟心亨，正以陽之正中也。若以陽之梗於中為病，則天下之心，殆無不病者矣。陽梗於中為耳痛，則天下之耳，將無不痛者矣。其說之誣，不待辯矣。坎為耳為心，其本象也。其為加憂，為心病，為耳痛，則因所處之時與位而言。所謂陰陽既合以後之象，陰陽合則變化生，曰憂，曰病，曰痛，明明既動以後之事，烏得以本象之陰陽言之？

It's incorrect, incorrect. The Commentary on the Judgment of the Kan hexagram says, "Only with the heart being open is there smoothness." This is precisely because a yang line is in the proper central position. If one says that a yang line obstructing in the middle is a problem, then almost everyone's heart would be diseased; if one says that a yang line obstructing in the middle causes ear pain, then everyone's ears would be painful. The absurdity of such a statement is evident without argument. Kan represents ear and heart in its fundamental form; however, its associations with added worry, heart disease, and ear pain are based on its position and timing, which belong to the images that arise after the interaction of yin and yang. Once yin and yang interact, changes arise. Speaking of worry, disease, and pain clearly refers to situations after movement has occurred. How can one explain these in terms of the fundamental yin and yang of the hexagram?

比樂師憂，同一坎焉，何為於比則樂，於師則憂？豈比之坎剛畫梗於其中，而師之坎則無剛畫梗於其中耶？豈比之坎陽陷陰中而師之坎陽出陰外耶？同一坎也，同一坎與坤也，同為一剛而五柔也，乃優樂頓異者，則惟其所處之時與位之不同耳。

The Zage Zhuan says, "Bi is joy and Shi is sorrow." Both hexagrams contain a Kan trigram, yet Bi is associated with joy while Shi is associated with sorrow. Is it because the Kan in Bi has a strong line crossing through it, while the Kan in Shi does not? Or is it because the Kan in Bi has a yang line sinking into yin, while the Kan in Shi has a yang line moving outside yin? Both are Kan, both are paired with Kun, and both consist of one yang and five yin lines. Yet joy and sorrow are completely opposite. The reason is only that their positions and contexts are different.

然憂與樂固同此心焉。處憂則憂，當樂而樂。或先憂而後樂，或先樂而後憂。時與位無定，君子處之無成心焉。故曰加憂。加者非所固有，從而加之之辭。《坎·彖》曰“惟心亨，往有尚”，尚即加之義也。物失其中為病，艮之“危薰心”，心病也。不安其中亦病，咸之“憧憧往來”，亦心病也。坎者通也，失其通為痛。噬嗑之“荷校滅耳”，《傳》曰“聰不明也”，乃耳痛也。未聞剛梗於中之為病為痛也。

However, sorrow and joy both originate from the same mind: when in a situation that calls for sorrow, one feels sorrow; when in a situation that calls for joy, one feels joy; sometimes sorrow comes first and then joy, sometimes joy comes first and then sorrow. Time and position are not fixed, and the gentleman deals with them without clinging to fixed views, so the "Say on the Hexagram" says "add sorrow" — "add" means something that was originally not there but is added later. The "Commentary on the Judgment" of the "Gua of Water" says "the mind is open and thus communication is smooth, and action is commendable," where "commendable" also means "add." When things lose the middle, they become diseased: the "Nine in the Third" of the "Gua of Stillness" says "dangerous and the heart is scorched," which is a heart disease; being unsettled in the middle is also a disease: the "Nine in the Fourth" of the "Gua of Attraction" says "confused movement," which is also a heart disease. The meaning of "Kan" is communication; losing communication leads to pain: the "Top Nine" of the "Gua of Eating the Fire" says "a wooden staff on the head and ears cut off," and the "Image Commentary" says "the ears are not clear," which is actual ear pain. I have never heard of a yang line blocking the middle being considered a disease or a pain.

腐儒不明象義，又不熟經文，僅知於一卦三畫中求象。求而不得，於是以剛柔之卦畫，以己意揣測而附會之，而不顧其理之是非。此言象者之所以授人口實也。坎之為矯輮，亦非其本象也。凡物件之矯輮者，必先炙以火，而以水定之。故坎象之為矯輮，亦必在與離相合，或在與離通變之後，而弓輪則更因矯輮推而及之者也。蓋物之有弓與輪，乃為矯輮之最著者也。《易》象有相因而及者，如艮為門闕，因更為閽寺；兌為口舌，因更為巫，皆與此一例也。

The ignorant scholar does not understand the symbolic meaning of the hexagrams and is not familiar with the classics, yet he only seeks the image within the three lines of a single hexagram. When he cannot find the image, he resorts to interpreting the yao lines, which are either hard or soft, according to his own understanding, regardless of whether the reasoning makes sense. This is precisely why those who talk about images are criticized by others. For example, the trigram Kan is said to represent "bending and straightening wood," but this is not its original image. Any process of bending and straightening wood must first be heated with fire and then fixed with water, so the image of Kan as "bending and straightening wood" only makes sense after it has interacted with Li, or after a transformation involving Li. As for "bow and wheel," this is a further derivation from the image of bending and straightening. Among objects, bows and wheels are the most obvious results of bending and straightening. In the images of the Book of Changes, there are examples where one image leads to another in a connected way: for instance, Gen represents a gate, and thus also the gatekeeper; Dui represents mouth and tongue, and thus also the shaman. These are all examples of the same pattern.

或問：象之言數，是否即“七日來復”，“八月有凶”，與“十年不字”、“十年勿用”之類？曰：非也。此乃言爻與卦之數。雖與象不盡無關，然不可即謂象之數也。然則象之倚於數者如何，可略舉其例歟？曰：《易》之為書，參天兩地而倚數。三畫成卦，參天也。因而重之，兩地也。六畫而分三才，又參天也。三才而迭用柔剛，又兩地也。用九用六，又參天而兩地也。故《易》之立言，殆無一不倚於數。詳言之，非短辭所能罄，當別論之。

Someone asked: Are the numbers mentioned in the images referring to things like the "seven days to return" in the复卦, "eight months with misfortune" in the临卦, and "ten years to be able to write" in the屯卦, as well as "ten years without use" in the蒙卦? Answer: No. Those refer to the numbers of lines and hexagrams, although they are not entirely unrelated to the images, they cannot be called the numbers of the images. Then, what numbers does the image rely on? Can you give a few examples? Answer: The Sayings of the Hexagram explains that the Book of Changes is "three heavens and two earths, relying on numbers." Forming a hexagram with three lines is "three heavens"; stacking two hexagrams to form twelve lines is "two earths"; dividing the six lines into three elements is again "three heavens"; alternating the soft and hard lines among the three elements is again "two earths"; using nine and six still follows the pattern of three heavens and two earths. Therefore, the Book of Changes is almost entirely based on numbers. To explain in detail is not possible in a few words, it should be discussed in a separate treatise.

象之倚數，亦不能離乎陰陽。陽數參天，陰數兩地。參兩之數，無不原本天一至地十之五十五數，而折為五行，分寄於象。故象之言數，以根於五行及九宮之數為多。而五行各有始有壯有究，數又有別也。

The numbers on which images depend cannot be separated from yin and yang: the yang numbers take "ascending to heaven" with three as the base; the yin numbers take "two lands" with two as the base. The combination of these two kinds of numbers is based on the total of fifty-five, derived from the sum of the numbers from heaven one to earth ten. This total is then divided into the Five Phases, and each phase is associated with various images. Therefore, numbers mentioned in images mostly originate from the numbers of the Five Phases and the Nine Palaces. Each of the Five Phases has three stages: beginning, flourishing, and decline, and numbers vary in each stage.

《易》窮則變，窮於數也（天數極於二十有五，地數極於三十，天地之數窮於五十有五。故生數終於五，成數始於六，天地生成之數合於五。六乃為天地之中，七則反以天之五分陰分陽。故乾之數十。以地之六迭用柔剛，故支之數十二，十三則凶。陰九陽六，六九五十四，為窮之災。而五十六為凶之始，而九十六與一百零六皆凶數。）是故欲明象之數，必先別其時位。時有三候（即始壯究也），位有三等（即初中上也），明乎此，於象倚於數之理思過半矣。

The Great Treatise says, "The Book of Changes transforms when it reaches its limit." The limit refers to numbers: the heavenly numbers reach their peak at twenty-five, and the earthly numbers reach theirs at thirty. The total of heavenly and earthly numbers is fifty-five. Therefore, the numbers of generation end at five, and the numbers of completion begin at six. The numbers of generation and completion meet at five; six is the central number of heaven and earth. Seven, on the other hand, divides the five of heaven into yin and yang. Hence, the heavenly stems have ten numbers. Using the six of earthly numbers alternately with soft and strong, the earthly branches have twelve numbers, and thirteen is considered ominous. Yin reaches its peak at nine, and yang is used at six. Multiplying six by nine gives fifty-four, which is the peak of calamity. Fifty-six is the beginning of misfortune, and ninety-six and one hundred and six are also considered ominous numbers. Therefore, to understand the numbers of the images, one must first distinguish their time and position. Time has three phases: beginning, flourishing, and ending. Position has three levels: initial, middle, and upper. Once this is understood, one will grasp a large part of the principle that images depend on numbers.

《易》象掌於太卜，周室版蕩，典章散迭。東遷而後，未能盡復故物。孔子《說卦》所傳，即為掇拾殘闕之遺，而又歷經劫火，簡策散失。比及西漢，兩篇《十翼》，猶闕《說卦》三篇。後得河內女子發於廢屋，即今之《說卦》是也。

The divination texts of the Book of Changes were originally managed by the official in charge of divination. During the turmoil of the Zhou dynasty, the rituals and systems were lost. After the Eastern Migration of the Son of Heaven, the old records could not be fully restored. The text passed down by Confucius in the "Commentary on the Hexagrams" was already collected from fragmented remains. Later, it was repeatedly damaged by wars, and the bamboo slips were lost. By the Western Han dynasty, among the ten appendices, the three chapters of the "Commentary on the Hexagrams" were still missing. Later, they were discovered by a woman from Henan in a destroyed old house, which is the version of the "Commentary on the Hexagrams" we have today.

卦象殘闕，自所不免。《荀九家》補象，乾有四，坤八，震三，巽二，坎八，離一，艮三，兌二，都三十有一。朱子已取以列入《本義》。而孟氏之逸象，文十倍於《九家》。計乾之象六十有一，坤八十一，震四十九，坎四十七，艮三十七，巽二十，離十九，兌九，共三百二十三，亦云夥矣。

The omissions in the hexagrams are inevitable. The lost images restored by the "Nine Schools of the Zhou Changes" include four for Qian, eight for Kun, three for Zhen, two for Xun, eight for Kan, one for Li, three for Gen, and two for Dui, totaling thirty-one. Zhu Xi has already included these in his "Original Meaning of the Zhou Changes." The lost images transmitted by the school of Meng Xi are ten times longer than those of the Nine Schools: Qian has sixty-one, Kun eighty-one, Zhen forty-nine, Kan forty-seven, Gen thirty-seven, Xun twenty, Li nineteen, and Dui nine, totaling three hundred and twenty-three. This is already a considerable number.

而後儒如何妥、於令升、侯果、朱震、來知德，及勝清毛錫齡，亦均有補象。要皆採自二篇《十翼》者為多。如《九家》所補之三十一象，惟坤之帛與漿，震之為鵠，巽之為鶴，未見於經，餘皆經傳所有者也。《易》道廣大，無所不包，象足以盡物，物不足以盡卦。《易·說卦》於《象》曰其於物也，其於人也，亦舉一隅而已。觸類旁通，非列舉所能盡也。

Later scholars such as Guan Bao (Zhi Sheng), Hou Guo, Zhu Zhen, Lai Zhide, and Mao Qiling of the Qing dynasty all contributed their own interpretations, though most of their additions were drawn from the two chapters of the Ten Wings. For example, among the thirty-one images added by the "Nine Schools," only the images of the Earth (Kun) "as silk" and "as soup," the Thunder (Zhen) "as a goose," and the Wind (Xun) "as a crane" are not found in the original text; the rest are already present in the classic texts. The Way of the Book of Changes is vast and encompasses everything. The images are sufficient to exhaust all things, yet all things are insufficient to exhaust a single hexagram. The "Sayings on the Hexagrams" mentions "its relation to things" and "its relation to people," but these are merely examples from one corner; the full understanding depends on drawing connections and applying principles, which cannot be exhausted by listing each case individually.

（《荀九家》者，荀慈明集九家《易》解，為書十卷，見於《班書》。而《文獻通考》引陳氏說，謂漢淮南王所聘明《易》者九人，荀爽嘗為之集解。但陸氏《釋文序錄》列九家姓氏為京房、馬融、鄭玄、宋衷、虞翻、陸績、姚信、翟子元、荀爽，與前說不同。但考陸氏所列諸家，無論時代後先，且立說各異，有相冰炭，決非可合而為一者。姑錄其說以備參考可耳。）

The so-called "Xun Jiujia" is a commentary on the Book of Changes compiled by Xun Shuang (style name Ciming) collecting the interpretations of nine schools. The entire work consists of ten volumes and is recorded in Ban Gu's "Book of Han · Catalogue of Arts and Literature." However, the "Comprehensive Survey of Literature and Records" cites Chen Zhenzun's statement, saying that it was nine scholars proficient in the Book of Changes who were hired by Prince Huainan of the Han dynasty, and Xun Shuang once made a collective commentary for them. But Lu Deming's "Sequencing of the Classics · Preface" lists the names of the nine schools as Jing Fang, Ma Rong, Zheng Xuan, Song Zhong, Yu Fan, Lu Ji, Yao Xin, Zhai Zixuan, and Xun Shuang, which differs from the previous account. Upon careful examination of the families listed by Lu, regardless of their chronological order, their doctrines are mutually conflicting, some opposing each other like water and fire, and it is impossible for them to be combined into a single work. Therefore, these different accounts are recorded here for reference only.

《坤·彖》曰“君子有攸往”。讀者於此一句，往往忽略，順口讀過。而自漢以後，講《易》者無慮千數百家，亦均未著眼於此。宋儒或以為占辭，以君子指筮者，則更為無稽。須知此卦為六十四卦之第二卦，上承六十四卦第一卦之乾卦。

The Hexagram Statement of the Qian Hexagram says, "The gentleman has a course to take." Readers often overlook this sentence, reading it carelessly; since the Han dynasty, there have been more than a thousand scholars interpreting the Book of Changes, but none have focused on this point. Some Song dynasty Confucian scholars took it as a divination statement, considering "the gentleman" to refer to the person casting the divination, which lacks proper basis. One must understand that the Qian Hexagram is the second among the sixty-four hexagrams, following the first hexagram, Qian.

文王於《乾·彖》，只繫以“元亨利貞”四字，以概括乾德，即以概括六十四卦。以乾為天行，蕩蕩莫名。舍此四字，實無可以表示乾德而概括無遺者。坤以承乾，故亦首繫以“元亨利牝馬之貞”。“牝馬”二字，綰合乾坤，以示陰陽合德，剛柔有體。所謂立天之道，立地之道者，皆以此“元亨利貞”四字挈其綱矣。

King Wen attached only the four characters "Yuan, Heng, Li, Zhen" to the Hexagram Statement of Qian. He used these four characters to summarize the virtue of Qian, and also to summarize the entire sixty-four hexagrams. Since Qian represents the movement of Heaven, which is vast and beyond description, there are no other words besides these four that can fully express the virtue of Qian without omission. K'un follows Qian, so the Hexagram Statement of K'un also begins with "Yuan, Heng, Li, Zhen of the female horse." The two characters "female horse" connect Qian and K'un, indicating the union of yin and yang, and the distinct nature of yang and yin. The "establishing the way of Heaven" and "establishing the way of Earth" mentioned in the "Shuo Gua Zhuan" are all summarized and guided by these four characters "Yuan, Heng, Li, Zhen."

然天地之道，非人莫明；天地化育，非人莫參。先聖作《易》，原以明人道以立人極。故於《坤·彖》“貞”字之下，即大書特書曰“君子”，所以正名定分，乃《周易》開宗明義之第一特筆也。

However, the way of heaven and earth cannot be made clear without people; the nurturing and transformation of heaven and earth cannot be participated in without people. The sage ancestors composed the Zhou Changes, originally to clarify human conduct and establish the standards of being a person. Therefore, in the Hexagram Statement of the Qian Hexagram, immediately following the character "Zhen," they prominently inscribe the term "junzi" (gentleman), to properly name and define roles—this is the first distinctive emphasis in the Zhou Changes.

讀者疑吾言乎？試即文王六十四卦之《彖辭》索之，可比較而得之矣。謙為人道之卦，曰“君子有終”。否曰“不利君子貞”，同人曰“利君子貞”，皆此君子也。周公繫爻於乾三之“君子終日乾乾”。孔子贊《易》，六十四卦《大象》之“君子”，皆述文王之意，所以闡發此一句“君子”兩字者也。乃後人猶不注意，不將前聖後聖垂教之苦心，一筆抹煞乎？

Does the reader doubt my words? Just check the sixty-four hexagram statements of the hexagrams systematized by King Wen, and a comparison will make it clear. The hexagram of Humility discusses human conduct, and its statement says, "The gentleman has a proper end." The hexagram of Non-Alignment says, "It is not advantageous for the gentleman to be steadfast." The hexagram of Fellowship says, "It is advantageous for the gentleman to be steadfast." All of them refer to this term "the gentleman." The Duke of Zhou composed the line statements, and in the third line of the hexagram of Heaven, he wrote, "The gentleman remains diligent all day." Confucius commented on the Book of Changes, and in the Great Image Commentary of the sixty-four hexagrams, the term "the gentleman" is also used to convey the meaning of King Wen, explaining the two characters in the statement of the hexagram of Earth. How could later generations still fail to pay attention, thereby wiping out the sincere efforts of the sages past and present in imparting teachings and guiding people?

“有攸往”者，乃鄭重指導之辭，三字具有無窮深意，亦不當忽略讀過。此“有”字，乃全《易》開卷第一“有”字，即《序卦》“有天地然後有萬物”與“有男女有夫婦有父子及禮義有所錯”之有。言既有“乾元亨利貞”，既有“坤元亨利牝馬之貞”，而後君子始“有攸往”之可言矣。

"The 'There is something to go toward' (you you wang)" is a solemn word of guidance. These three characters contain infinite meaning and should not be overlooked. The character 'you' here is the first 'you' in the entire I Ching, that is, in the "Xugua Zhuan" (the "Sequence of Changes" commentary), "When Heaven and Earth exist, then all things come into being," and also "There are men and women, there are husband and wife, there are father and son," up to "Rites and righteousness have their place." The meaning is that first there is the "Yuan, Heng, Li, Zhen" (the four virtues) of Qian (Heaven), then there is the "Yuan, Heng, Li, the贞 of the female horse" of Kun (Earth), and only then can the gentleman speak of "there is something to go toward."

攸者，安也，久也；往者，進也。上言乾坤之“元亨利貞”，乃天地之道，循環而無端者也。而君子以參贊天地，乃進化而不已者也。故曰“有攸往”。與近世哲學家所謂天行之往復為循環線，人治之進化為螺旋線，其理正相吻合。以下六十四卦皆根此立言，以明人事之是非得失而定吉凶。

"Yu" means to be secure and enduring, "wang" means to advance forward. The "yuan heng li zhen" of Qian and Kun mentioned earlier represent the way of heaven and earth, which is cyclical and continuous without beginning or end. However, the gentleman's participation in the nurturing of heaven and earth is a constant process of advancement, hence it is said "there is a proper direction to go." This aligns with the modern philosopher's statement that "the movement of heaven is a circular cycle, while human governance is a spiral ascent." All sixty-four hexagrams are based on this principle, used to explain the right and wrong of human affairs and to determine fortune and misfortune.

自讀者將此重要之經文滑口讀過，宋人不得其解，更以君子二字為指筮者而言。於是全《易》，《彖》、《象》，皆索然毫無生氣。孔子之《大象》所謂“君子以”者，亦味同嚼蠟矣。

Since readers have lightly passed over this most important passage, the Song scholars found it difficult to understand, so they simply took the term "junzi" to mean the person performing the divination. As a result, the entire Zhou Yi along with the Commentary on the Judgment and the Image Commentary have become dull and lifeless; even the "junzi yi" phrases in Confucius' Great Image Commentary read like tasteless wax.

“坤利西南得朋，東北喪朋”二語，註解不一。王肅以下，大概以朋為陰類，西南離巽兌皆陰卦，故“得朋”。東北震坎艮皆陽卦，故“喪朋”。以喻女子在室得朋，猶迷而失道；出嫁喪朋，乃順而得常。陰必從陽，離喪其朋類，乃能成化育之功，而有安貞之吉。史徵、崔憬，及程朱《傳》、《義》之解釋，大略如此。其於文義，終覺牽強。言虞氏學者，以納甲為言。以坤之得朋，為月之得明，則以朋為陽矣。辛齋以為欲解釋此二語，必先定朋字之確詁。究竟指陽說，抑指陰言？

The hexagram statement of the "Kun" hexagram, "In the southwest we gain companions, in the northeast we lose companions," has had various interpretations by commentators. Since Wang Su of the Wei dynasty, most have regarded "companions" as referring to like elements of yin. The hexagrams associated with the southwest direction, Li (Fire), Xun (Wind), and Dui (Lake), are all yin hexagrams, hence called "gaining companions"; those in the northeast direction, Zhen (Thunder), Kan (Water), and Gen (Mountain), are yang hexagrams, hence called "losing companions." This is used as an analogy for a woman who, while unmarried and living at home, is with her peers, which is called "gaining companions," yet this is seen as straying from the right path; when she marries and leaves her peers, which is called "losing companions," she becomes gentle and conforms to the norm. Yin must follow yang, and by abandoning her own kind, she can achieve the function of nurturing all things, thus resulting in the auspiciousness of "safety and sincerity." The explanations of Tang dynasty scholars such as Shi Zheng and Cui Jing, as well as Cheng Yi's "Yichuan Commentary on the Changes" and Zhu Xi's "Original Meaning of the Zhou Changes," largely follow this approach, but when compared with the literal text of the classic, they still seem forced. Those who follow Yu Fan's school of thought, however, reinterpret the statement using the "Najia" system, interpreting "gaining companions" as the moon receiving light, thus making "companions" refer to yang. Hang Xinzhai believes that to make sense of these two sentences, one must first determine the exact meaning of the character "companions": does it refer to yang or yin?

按西南固坤之本位，坤中爻二三四為益坤(益卦二三四爻為坤)，三四五為損坤(損卦二三四爻為坤)。故損之五，益之二，皆曰“十朋之龜”。此十朋，即《坤·象》“得朋”“喪朋”之朋也。而損之六三，曰“三人行則損一人，一人行則得其友，”以損之義為損下益上。損泰下卦之三，以益上卦之上，泰變為損，下乾(乾，子丑寅三人)去其一爻，故曰“三人行則損一人”。損此一爻以益坤上，雖成損，而上與三仍得陰陽相應，故日“則得其友”。據此以觀，則陰以得陽為朋，陽以得陰為友，其例甚明。

His analysis begins with the trigram images. The southwest direction is originally the position of the Trigram Earth (Kun); and the Trigram Earth has another source: the Trigram Increase (Yi) with its second, third, and fourth lines forms the Trigram Earth, and the Trigram Decrease (Sun) with its third, fourth, and fifth lines also forms the Trigram Earth. Therefore, the line statements of the sixth line of the Trigram Decrease and the second line of the Trigram Increase both mention "ten tortoises," and the "ten friends" in this context refers to the "friends" mentioned in the "Tuan" statement of the Trigram Earth. Now looking at the third line of the Trigram Decrease: "If three people walk, one is lost; if one walks, he gains a friend." The meaning of the Trigram Decrease is to reduce the lower trigram to increase the upper trigram: by removing the third line of the lower trigram Tai, it is added to the top line of the upper trigram, transforming Tai into Sun. Originally, the lower trigram was Heaven (Qian), which corresponds to the stems Zi, Chou, and Yin, matching the "three people." Now one line is removed, hence "three people walk and one is lost." This line is added to the upper trigram Earth (Kun), so although the trigram becomes Sun, the top line and the third line still correspond in yin and yang, hence "then he gains a friend." From this we can see that when yin receives yang, it is called "friend," and when yang receives yin, it is called "friend" as well. The principle is clear. This is the key point where his interpretation differs from the old commentaries: the old commentaries interpreted "friend" as a kind of yin, but he deduced from the line statements of the Trigrams Decrease and Increase that "friend" must refer to yang.

而《坤·彖》之“朋”可得言矣。坤方於十二辰為未申之位，於消息卦為否為遁。否下卦坤，故“先迷”。上卦乾，故“後得主”。坤間辰六爻，未巳卯逆行，自西至南，由遁至乾，皆陽爻日增，故曰“西南得朋”。自乾以後，而東而北，夬壯泰臨復。陽爻遞減，故曰“喪朋”。至戌亥歸坤，純陰無陽，朋喪盡矣。更逆行至酉，為坤之終位(兌酉數十，十亦為終)。值兌之正位，兌九四之喜有慶也。故曰“乃終有慶”。

Once the grammatical meaning is established, the word "friend" in the "Tuan" statement of the "Kun" hexagram makes sense. The "Kun" hexagram is located in the western-southwest direction, corresponding to the Earthly Branches "Wei" and "Shen," and in the twelve changing hexagrams, it corresponds to "Pu" and "Dun." The lower trigram of "Pu" is "Kun," so the hexagram statement says "first being lost"; the upper trigram is "Qian," so it says "later obtaining a master." The six lines of the "Kun" hexagram correspond to the Earthly Branches "Wei," "Si," and "Mao" in reverse order, moving from west to south, and the hexagram image progresses from "Dun" to "Qian," with the number of yang lines gradually increasing, hence "friendship is found in the southwest." After "Qian," moving east and north, the sequence is "Gua," "Da Zhuang," "Tai," "Lin," and "Fu," with the number of yang lines gradually decreasing, hence "friendship is lost." When reaching "Xu" and "Hai," they return to "Kun," which is entirely yin with no yang, and friendship is completely lost. Reversing again to "You," this is the final position of "Kun" ("Dui" corresponds to "You," and its number is ten, which signifies the end), and it coincides with the proper position of "Dui." This matches the "Nine in the Fourth" line of "Dui" saying "there is joy," hence the hexagram statement continues with "finally there is celebration."

則自“先迷後得主”以下，可一氣貫串，無一字不腳踏實地矣。至“十朋”之義，原為天一至地十之數，各相有合。在坤言坤，以陰得陽，故曰“十朋”，與前說亦相合也。(以消息言之，“得”者息也，“喪”者消也。得喪者，即消息二字之代名也。以坤消乾至東北而乾陽消盡，反為純坤。喪朋之為消陽，可無疑義矣。)

According to this, the hexagram statements from "First losing then gaining the master" onwards can be connected in a continuous manner, with no single character left hanging without a concrete meaning. As for the meaning of "ten friends," it originally refers to the set of numbers from heaven one to earth ten, paired two by two with each having a corresponding match; in the context of the Hexagram Kūn, it refers to the attainment of yang by yin, hence called "ten friends," which also fits perfectly with the previous explanations. Hang Xinzhai added a comment saying: if viewed from the perspective of the message hexagrams, "gaining" is "rest," meaning the growth of yang energy; "losing" is "decline," meaning the retreat of yang energy; the two characters "gaining" and "losing" are actually substitutes for the two characters "message" and "decline." Using the Hexagram Kūn to decline the Hexagram Qián, when reaching the northeast direction, the yang lines of Qián are completely declined, and the entire hexagram becomes pure Kūn. Thus, "losing friends" is indeed the decline of yang, and there is no doubt about this.

《坤·初六》：“履霜堅冰至”。舊說尚無悖於義，惟以“堅冰”二字為疑。於是臆說紛紜，妄相揣測。而於聖人立言之本旨，相去愈遠矣。須知此爻乃坤卦初爻，乃六十四卦陰爻之第一爻，亦即以陰消陽之第一爻也。剛柔始變，陰陽大化根本所自立之初，豈可輕易忽略看過？周公繫艾，鄭重言之曰“履”。履者何？踐履也。以“履”冠六十四陰爻之初，以明人生涉世之初步也。

The line statement of the first line of the Hexagram Kūn says, "When you walk on frost, you know ice is coming." Previous interpretations have not entirely deviated from the meaning, but they have doubted the word "ice," leading to many speculative interpretations. These guesses have only moved further away from the original intention of the sage. We must realize that this line is the first line of the Hexagram Kūn, which is the first line among all the yin lines in the sixty-four hexagrams. It is also the first line where yin begins to overcome yang. Here the transformation between hardness and softness starts, and the fundamental principle of yin and yang is established. How can we lightly dismiss this? The Duke of Zhou attached this line statement with great seriousness, using the character "履" ("to walk"). What does "履" mean? It means to walk with firm steps, to tread the ground. By placing the character "履" at the beginning of all the yin lines in the sixty-four hexagrams, it clearly points out the first step one takes in entering the world.

離卦之初曰“履錯然”，以殿《上經》，以示有始必有終。兩“履”字遙相呼應，非泛文也。孔子韋編三絕，深能契合文周之心，故《繫傳》於三陳九德，獨舉一履。再三反覆，推勘盡致。以明立德之本。雖僅舉九卦，而六十四卦可以意推之矣。故“履”之一字，即以為全《易》之綱領，為聖人以《易》立教精義之所在，亦無不可也。豈可輕易忽略看過哉！

In correspondence with this, the line statement of the initial line of the "Li" hexagram says, "To tread in disorder," which is used to conclude the Upper Canon, indicating that there must be an end to any beginning. The two instances of the character "履" (tread) echo each other from beginning to end, clearly not mere incidental words. Confucius, having studied the "Zhou Yi" so thoroughly that he wore out the thongs of his satchel, deeply understood the intent of King Wen and the Duke of Zhou. Therefore, in the "Great Treatise" section of the "Xici Zhuan," the part discussing "three presentations and nine virtues" uniquely places the "Lv" hexagram first, elaborating it repeatedly and thoroughly exploring the principle until its full meaning is revealed. This is done to clarify the fundamental aspect of establishing virtue. Although only nine hexagrams are mentioned there, the principles of the sixty-four hexagrams can be inferred from them. Therefore, considering the character "履" as the main idea of the entire "Zhou Yi" and as the essential meaning of the sages' teaching through the "Yi" is not unreasonable. Such an important character, how could it be easily overlooked!

“堅冰至”，原非坤初爻之候，乃周公以繫於初爻者。雖曰防微杜漸之意，然實《周易》之一種特別筆法，學者更不可不知也。陽順陰逆，坤乃陰卦之宗。故聖人繫辭，皆用逆筆，特由“至”字反說到“初”。觀乾曰“元亨利貞”，坤曰“元亨利牝馬之貞”，其文氣亦皆一順一逆。孔子贊坤，亦以“至”字開口，真能與文王周公心心相印者矣。觀象玩辭，不可不於此等處加之意也。

The time referred to by "坚冰至" does not originally belong to the first line of the Hexagram坤 (Earth). It was intentionally attached by the Duke of Zhou. Although old interpretations viewing it as a warning against neglecting small matters are correct, this is also a special writing style in the Zhou Yi. Those studying the Yi should be aware of it. The movement of yang is smooth, while that of yin is reverse. Since坤 is the master of all yin hexagrams, the sage used reverse expressions in its commentary. It deliberately starts from the result "至" and goes back to the beginning "初". For example, the Qian hexagram says "元亨利贞", while the坤 hexagram says "元亨利牝马之贞". The style is one smooth and one reverse. When Confucius wrote the Commentary on the Judgment for the坤 hexagram, he began with the word "至" in "至哉坤元", truly reflecting the mind of King Wen and the Duke of Zhou. When observing the hexagram and contemplating the line statements, one must pay special attention to such points.

《坤·六二》“習”之一字，亦《周易》最要之眼目也，亦不可忽略看過。初曰“履”，以明人生涉世之始也。二曰“習”，以明涉世後必至之一境也。繫接上文，一氣而來。霜猶履也，堅冰至則已習矣。人之生性相近也，習則遠矣。善惡分途，積微成著，無不由習之一字而來。聖人慎所習，惟立教以濟之，故坎特著曰“習坎”(坤二爻坎位也)。孔子《大象》曰“君子以常德行習教事”，而《論語》曰“學而時習之”，此皆善用其習以立人道者也。

The character "xi" in the second line of the "Kun" hexagram is also one of the most important elements in the "Zhou Yi," and should not be overlooked. The first line mentions "lu," highlighting the beginning of a person's entry into the world. The second line mentions "xi," indicating the inevitable state one enters after becoming involved in the world. The meaning of these two lines continues in a connected manner: stepping on frost is still "lu," but when solid ice forms, it becomes "xi." Human nature is originally similar, but once habits are formed, they become very different; good and evil then diverge, accumulating from small beginnings into obvious distinctions, and all of this comes from the character "xi." The sage understands the danger of habits and can only remedy this through education, so the "Kan" hexagram specifically names its hexagram "Xi Kan" ("Practice of Difficulty"), as the second line of the "Kun" hexagram is precisely in the position of the "Kan" hexagram. Confucius in his "Great Image Commentary" says, "The superior man uses constant virtue and practices teaching and affairs." The opening of the "Analects" says, "Learning and reviewing it from time to time," which are examples of using "xi" to establish the way of human beings.

自世運遞遞降，天德王道已成故事(蠱，故事也)。後世雄才大略之君相，恆利用“習”之一字，為操縱斯民之具。非常之原，黎民懼焉。乃施之以漸，今習而安之，則習非且可以勝是矣！(如革命之說，初聞者無不掩耳卻走，駭為非常。乃一再試之輿論，和之。曾幾何，時昔之掩耳卻走者，或且醉心從之矣。此即習之說也。近世歐美大政治家，欲有所設施，恆先建議以造成輿論，使人民習見習聞而後行之。舉重若輕矣。)

However, the world's circumstances have gradually declined through generations, and the Heavenly Virtue and the Way of the King have long become outdated matters (the image taken from the "Guzh" hexagram precisely represents accumulated old practices). Later rulers and ministers with great talent and ability often reversed this, using the concept of "habit" as a tool to control the people. Whenever extraordinary measures were taken, the people at first were always fearful; thus, they would gradually implement them step by step, allowing people to become accustomed to them and accept them as normal, eventually leading to the wrong becoming dominant over the right. Hang Xinzhai, in his own notes, gave an example: when the idea of revolution was first proposed, those who heard it would all cover their ears and flee, shocked and horrified; but after repeated trials and endorsements by public opinion, soon those who had once covered their ears and fled were even沉迷 and followed it, which is precisely the effect of "habit." In modern times, great politicians in Europe and America also often begin by proposing bills to create public opinion, allowing the people to become accustomed to seeing and hearing about it before implementing it, thus making heavy tasks seem light.

然聖人之化民成俗，尚道德不尚事功。操縱之術，非所屑焉。端民習於就學之始，薰陶而善良之，化行而俗美，則施之於事。不習自無不利，此豈一朝一夕之故哉！周公繫“習”於坤之二爻，以承“履霜堅冰”之後，其用意至深遠矣！

But the sage cultivates the people and shapes the customs, valuing morality rather than achievements. Such manipulative tactics are beneath him. The sage's approach is to correct the people's learning from the very beginning of their schooling, using gradual influence to guide them toward goodness. Once education is widely implemented, the customs will naturally become refined. Only then can governance be applied. At that point, there is no need for deliberate practice, and everything will naturally proceed smoothly. How could such a thing be achieved in a day or two! The Duke of Zhou associated the character "习" with the Second Line of the "Kun" hexagram, following "Footsteps of frost, ice forms," intending something profoundly significant.

乾，天行也。坤，地道也。天運於虛，地徵諸實。故乾以言道，坤以言德。道運於虛，德徵諸實也。詳玩兩卦《彖》、《象》，乾曰“元亨利貞”，坤則曰“元享利牝馬之貞”。全卦六爻，乾則象以“潛見躍飛亢”及“乾乾”“惕若”，皆用虛筆。而坤則曰“履”，曰“習”曰“可貞”，曰“括囊”曰“黃裳”，曰“血”，筆筆皆徵實矣。

The hexagram Qian discusses the movement of heaven, and the hexagram Kun discusses the principles of earth. Heaven operates in the void, while earth manifests in the tangible, so Qian is used to explain "the Way" and Kun to explain "virtue." The Way operates in the void, while virtue must be verified through actual deeds. Looking closely at the Commentary on the Judgment and the Image Commentary of these two hexagrams: Qian speaks of "origin, prosperity, advantage, and uprightness," while Kun adds a specific image, "origin, prosperity, advantage, and the uprightness of a mare." The wording of the six lines is also similar: Qian uses "hidden," "emergent," "leaping," "flying," "excess," and "diligently striving" and "cautious vigilance," all abstract expressions; Kun, however, uses "walking," "practice," "suitable uprightness," "binding the bag," "yellow undergarment," and "blood," each phrase grounded in reality.

聖人之筆，妙極神化。孔子贊《易》，為衰世之救濟，略天道而言人事，由下學以希上達。故首重立德，由立德以明道。然明道與立德，均非辭無以見焉。是以《文言》曰“修辭立其誠”。上下兩篇之《繫辭》，又各為之傳，又特表而出之曰“以言者尚其辭”，又曰“所樂而玩者爻之辭焉”，皆教人以學《易》之方也。卦有小大，辭有險易，言小大而陰陽可知，言險易而順逆虛實可知。學者必潛心玩索，始能微顯闡幽。茲略舉乾坤兩卦之字法，餘卦可類推，而《十翼》之辭亦可類及矣。

The precision with which the sage writes is so subtle that it seems supernatural. Confucius composed the "Commentaries on the Changes," originally intending to seek relief for a time of decline and disorder, so he omitted discussions on heavenly principles and focused more on human affairs. He started from practical learning to pursue higher understanding, thus emphasizing moral cultivation first, and then using moral cultivation to explain the Way. However, whether seeking to understand the Way or cultivating virtue, it cannot be expressed without words. Therefore, the "Commentary on the Literary Changes" says, "Refine your expressions and establish sincerity." Both the Upper and Lower "Great Treatises" specially emphasize "those who speak should value words," and also say, "what they enjoy and play with is the words of the hexagrams," all teaching the way to study the Changes. Hexagrams have small and great ones, and their words have dangerous and easy ones: speaking of small and great allows one to understand yin and yang; speaking of danger and ease allows one to understand order and disorder, emptiness and reality. Those who study the Changes must deeply ponder and explore, so as to move from the obvious to the subtle and reveal hidden meanings. Here we only briefly mention the use of words in the hexagrams of Qian and Kun; the other hexagrams can be understood in the same way, and the writings of the Ten Wings can also be compared similarly.

《乾·彖》曰：“首出庶物，萬國咸寧。”《坤·彖》曰：“含弘光大，品物咸亨。”此以贊乾坤化育之功，皆陰陽合德，交相為用。乾用九以變坤，坤用六以承乾。僅一咸字，已將乾坤兩卦綰合，有天地絪縕之妙。咸者上兌下艮之卦，乾在坤中，所謂二氣感應以相與，天地感而萬物化生者也。

The Commentary on the Judgment of the Qian hexagram says, "It leads all creatures and brings peace to all nations." The Commentary on the Judgment of the Kun hexagram says, "It contains and expands, and all things are able to flourish." Both sentences praise the nurturing power of Qian and Kun. Yet both are based on the harmonious union of yin and yang, and their mutual use: Qian transforms into Kun through the use of all nines, and Kun receives Qian through the use of all sixes. The single character "xian" (all) connects the Qian and Kun hexagrams together, embodying the subtle intermingling of the energies of heaven and earth. "Xian" itself is the hexagram composed of Dui above and Gen below, and its structure is precisely Qian within Kun. This is what the Commentary on the Judgment of the Xian hexagram says: "The two energies respond to each other," and "Heaven and earth feel each other and all things are generated."

夫庶物與萬國，皆坤象焉。乾元首出，久道化成。於是乎有咸寧之慶。弘與大，皆乾象焉，而坤能含之光之(凡陽必得陰而始光。如日，必遇地與月，或其他能受光之質，而光始見也。)，於是乎品物有咸亨之象。然而乾之咸寧，寧於坤焉。而坤之咸亨，亨於乾焉。交互錯綜，妙合無間。神哉化工之筆也！至臨之“咸臨”，姤之“咸章”，皆以一“咸”字以形容陰陽構合之妙。臨數一二，一二為子丑，子丑陰陽始合。姤數七八，七八為午未，午未天地相遇，為陰陽中合。與乾坤兩卦之“咸”字，互相印證，互相發明者也。

Looking at them separately: "Shu wu" and "wan guo" both belong to the image of the Hexagram Kun. The principle of the Hexagram Qian, which is at the beginning and leads to enduring and nurturing, thus brings about the auspiciousness of "xian ning" (peace and stability). "Hong" and "da" both belong to the image of the Hexagram Qian, while the Hexagram Kun can contain and illuminate them. (For any yang, it must be combined with yin to show light. For example, the sun must meet the earth, the moon, or other objects that can receive light, for the light to be seen.) Thus, all things have the image of "xian heng" (harmonious and prosperous). However, the "xian ning" of the Hexagram Qian is actually peace resting upon the Hexagram Kun; the "xian heng" of the Hexagram Kun is actually prosperity arising from the Hexagram Qian. They interact and interweave in a perfect and seamless way, truly a marvel of nature. As for the "xian lin" in the line statement of the Hexagram Lin and the "xian zhang" in the line statement of the Hexagram Guo, they both use the character "xian" to describe the subtlety of the union between yin and yang. The Hexagram Lin corresponds to the numbers one and two, which correspond to the earthly branches Zi and Chou, the very beginning of the union between yin and yang. The Hexagram Guo corresponds to the numbers seven and eight, which correspond to the earthly branches Wu and Wei, the very point where heaven and earth meet and yin and yang meet halfway. These instances of the character "xian" along with the "xian" in the Hexagrams Qian and Kun can be used to confirm and illuminate each other.

《咸·彖傳》曰“咸，感也。(舊說：咸感無心，兌說無言。無心之感，其感始至。無言之說，其說乃大。)二氣感應以相與”。蓋物理必異性者乃能相感，而善感者莫如人。人之善感者，莫如男女，尤莫如少女少男。故以少女少男之卦名之曰咸。而咸卦六爻，又均取象於人身，則以感覺之最靈且捷者，更莫過於一身焉。

The Commentary on the Judgment of the Hexagram Xian says: "Xian means感应 (response). ... Two energies respond to each other and interact." (Old interpretations point out that the character "Xian" lacks a "heart" component compared to "gan" (response), and the character "Dui" lacks a "speech" component compared to "shuo" (speech); without a heart, the response is most sincere; without speech, the joy is most extensive.) In general, physical phenomena require things of different natures to respond to each other, and among all things, humans are most adept at responding. Among humans, the most sensitive to sensation are men and women, especially young girls and young boys. Therefore, the Book of Changes takes the hexagram with the young girl Dui above and the young boy Gen below, and names it Xian. Moreover, all six lines of the hexagram Xian are taken as symbols of the human body, because nothing is more sensitive and quick in sensation than one's own body.

六爻初拇，二腓，三股，五脢，六輔頰舌。四當為心，乃不曰心，而曰“憧憧往來”。以心不可見，且咸之感，本無心也。卦爻取象之精細，可謂剖拆毫芒。至義蘊之妙，更有非言語所能形容。細玩逐爻之辭，見深見淺，必有所得焉。(物理：異性則相感相吸。兩性既感而吸合，則原有之兩性相消而等於無。故咸又為無。又咸從戌從口，戌亥數無。先天卦艮居戌口，與兌相對，故兌艮為咸，而咸為無。後天卦乾居戌亥，故乾亦為無。)

The six lines of a hexagram correspond to specific parts of the body: the first line (initial six) represents the big toe, the second line (six in the second) represents the calf, the third line (nine in the third) represents the thigh, the fifth line (nine in the fifth) represents the back muscles, and the sixth line (six at the top) represents the cheek and tongue. In order, the fourth line (nine in the fourth) should represent the heart, but the line statement does not mention the heart, instead saying "chong chong wai lai" (a state of confusion and coming and going), because the heart is invisible, and thesympathetic response (response or mutual influence) of "Xian" (咸) is originally a feeling without a specific object. The detailed imagery used in the hexagram lines can be analyzed down to the finest detail; as for the profound meaning contained within, it is beyond words, and one can only carefully contemplate each line's wording, whether seeing it deeply or shallowly, and eventually gain some understanding. Hang Xinzhai added in his commentary: from a physical perspective, opposite elements attract and respond to each other; once the two elements have responded and combined, their original dual nature cancels each other out and becomes nothing. Therefore, "Xian" (咸) also has the meaning of "nothing." Furthermore, looking at the character "Xian," it is composed of "Xu" and "Kou." The numbers associated with Xu and Hai are "nothing." In the Earlier Heaven arrangement, the trigram "Gen" (Geng) is located at Xu, facing "Dui" (De), so "Dui" and "Gen" together form "Xian," and thus "Xian" represents "nothing." In the Later Heaven arrangement, "Qian" (Qian) is located at Xu and Hai, so "Qian" also represents "nothing."

“大哉乾元！萬物資始”，“至哉坤元！萬物資生”。此言盈天地間之事事物物而約其大數，即上下二篇之策，萬有一千五百二十以當萬物之數者是也。《乾·彖》曰“品物流形”，《坤·彖》曰“品物咸亨”。品物者，物之既成，可以類而別之，故曰“品”。“品物流形”者，乾流坤形也，坎也。“品物咸亨”者，坤承乾亨也，離也。可見乾坤二《彖》，無一字不互文見義者也。

The Commentary on the Judgment of the Qian hexagram says, "How great is the Qian Yuan! All things draw their origin from it." The Commentary on the Judgment of the Kun hexagram says, "How profound is the Kun Yuan! All things draw their sustenance from it." Here, "all things" refers to the generalization of everything existing between heaven and earth as a single number, which is the total of the counts in the Upper and Lower Classics mentioned in the Great Treatise. The number is eleven thousand five hundred and twenty, used as the number representing all things. Furthermore, the Commentary on the Judgment of the Qian hexagram also says, "The myriad things flow into form," while the Commentary on the Judgment of the Kun hexagram says, "The myriad things all achieve success." The term "myriad things" refers to things that have already taken form and can be classified into categories, hence the term "category" or "kind." "The myriad things flow into form" signifies the movement of the Qian energy and the shaping by the Kun, symbolizing the trigram Kan. "The myriad things all achieve success" indicates the Kun receiving the Qian and achieving success, symbolizing the trigram Li. Thus, every word in the Commentaries on the Judgment of the Qian and Kun hexagrams is interdependent and mutually explanatory.

至“首出庶物”，不曰“萬”，不曰“品”者，乃合萬與品而兼言之，對於首而言也。通言萬物，未分類也。物而曰品，則“方以類聚物以群分”矣。既類聚以群分，則必有一焉超乎其類統乎其群者。即首出之義，而不為首者皆庶也。故曰“庶”者，對於首而言也。不曰“首出萬物”，“首出品物”，而必曰“首出庶物”。可見聖人修辭之精，無一字虛設，無一字苟且焉。

As for the phrase "shou chu shu wu," it does not say "wanwu" (all things) or "pinwu" (classified things), but instead uses "shu wu" (common things). This combines the meanings of "wan" (ten thousand) and "pin" (categories), and it is in contrast with the character "shou" (first). To refer generally to "wanwu" is to speak without classification; to call them "pinwu" is as the "Xici Zhuan" says, "things are grouped by their kind, and objects are categorized by their class." Once things are grouped and categorized, there must be one that transcends the category and leads all others, which is the meaning of "shou chu" (first to emerge). Those that are not in the leading position are all called "shu" (common). Therefore, using the word "shu" is precisely in contrast with "shou." It does not say "shou chu wanwu" or "shou chu pinwu," but insists on "shou chu shu wu." This shows the meticulousness of the sage's rhetoric; no word is superfluous, and no word is used carelessly.

《下經》之損益，猶《上經》之泰否也。《上經》始乾坤，至小畜履凡十卦。陰陽爻各三十，而繼之以泰否，為乾坤變。《下經》始咸恆至蹇解亦十卦。陰陽爻各三十，而繼之以損益。咸恆為乾在坤中，損益乃坤在乾中也。天行人事，均不外乎否泰往來損益盈虛而已。舊說泰損下益上，(損下卦之九三以益上卦之上六)則成損。否損上益下，(損上卦之上九以益下卦之六三)則成益。然則否泰往來，損益盈虛，其所以轉移變化之機關，俱在三爻。三爻者，人爻也。以明否泰損益皆在於人，而天地無與焉。天行之否泰，人得而轉移之。人事之否泰，天地無如何也。

The two hexagrams "Xin" and "Yi" in the Lower Classic are equivalent in status to the two hexagrams "Tai" and "Pou" in the Upper Classic. The Upper Classic begins with "Qian" and "Kun," proceeding through "Xiao Xu" and "Lv," totaling ten hexagrams, with thirty yao of yin and thirty yao of yang. Following these are "Tai" and "Pou," which are variations of "Qian" and "Kun." Similarly, the Lower Classic starts with "Xian" and "Heng," proceeding through "Jian" and "Jie," also totaling ten hexagrams, with thirty yao of yin and thirty yao of yang. Following these are "Xin" and "Yi." "Xian" and "Heng" represent "Qian" within "Kun," while "Xin" and "Yi" represent "Kun" within "Qian." The operation of heaven and the affairs of the world cannot escape the alternation of "Tai" and "Pou" and the waxing and waning of "Xin" and "Yi." According to old interpretations, "Tai" hexagram involves reducing the third line of the lower trigram to increase the sixth line of the upper trigram, transforming into "Xin"; "Pou" hexagram involves reducing the sixth line of the upper trigram to increase the third line of the lower trigram, transforming into "Yi." Thus, the transformation between "Tai" and "Pou," and between "Xin" and "Yi," hinges entirely on the third line. The third line is the human line, indicating that "Tai," "Pou," "Xin," and "Yi" all depend on human actions and have nothing to do with heaven and earth. The operation of heaven's Tai and Pou, can be altered by human effort; the Tai and Pou of human affairs, however, are beyond the control of heaven and earth. This is the key point of Hang Xinzhai's argument—he seeks to transfer the responsibility for disorder and order from heavenly fate to human affairs, hence emphasizing that the pivot lies in the human line rather than in heaven and earth.

孔子於乾之九三，反覆申明其義。曰“與時偕行”，在損曰“與時偕行”，在益曰“與時偕行”。否泰者時也，損益者人也。與時偕行，則否可轉泰。不能與時偕行，而與時偕極，則無泰而非否矣。與時偕行者何？即所謂“終日乾乾，乾行”者是也。然而經文於損，獨曰“有孚元吉”者何也？曰“損上益下”，其理近而易明，其事順而易行。故否泰之轉移尚易，然否轉為泰，泰復轉為否，泰否往復循環不已。又烏能日進無疆？

Confucius repeatedly emphasizes this point in the "Wenyan" section of the "Qian" hexagram's Nine in the Third, saying "to move in harmony with the times." He also mentions "to move in harmony with the times" in the "Commentary on the Judgment" of the "Sun" hexagram and again in the "Commentary on the Judgment" of the "Yi" hexagram. "Po" and "Tai" belong to "time," while "Sun" and "Yi" belong to "human action." If one moves in harmony with the times, "Po" can be transformed into "Tai"; if one does not move in harmony with the times and instead follows the trend to an extreme, then there will be no place of "Tai" and everywhere will be "Po." What does "to move in harmony with the times" mean? It refers to the continuous effort described in the "Qian" hexagram as "to be diligent day and night." However, the classic text only mentions "having sincerity and original good fortune" in the "Sun" hexagram. Why is that? Because the principle of "reducing from above to benefit below" is simple and easy to understand and carry out, so the transformation between "Po" and "Tai" is relatively easy. However, "Po" transforms into "Tai," and "Tai" turns back into "Po," and the cycle between "Tai" and "Po" continues without end. How then can we talk about continuous progress without bounds?

吾國數千年曆史皆一治一亂，循環往復致人事永無進步，不能與世界列強相抗衡者，正以吾人只知以益求益，而不能以損求益。故極其功只能轉否，而不能化否。能化否，則否變同人。同人而進於大有，世運始有進步。始避泰否之循環線而入於傾否之螺旋線，然後得合於進化之正軌也。故孔子又於益之《彖傳》申明之。曰“益動而巽，日進無疆”。此損益之大道，(天行先泰而後否，人事先損而後益)先聖之象已明示之。

The history of our country for thousands of years has always been characterized by cycles of peace and chaos, with human affairs never making real progress, and thus unable to compete with the world's major powers. The root of the problem lies in our tendency to pursue gain only through "benefit" (益), without understanding the necessity of "loss" (损) in order to achieve gain. Therefore, even when the effects of such efforts reach their peak, they can only lead to a reversal of the unfavorable situation (转否), but not a transformation of it (化否). If we can transform the unfavorable situation, then the hexagram of "Opposition" (否) would become "Harmony with Others" (同人); from there, we could progress to "Great Possession" (大有), and the world would indeed make real progress, escaping the cycle of alternation between peace and chaos (泰否循环), and entering an upward spiral, such as the line "Inverting Opposition" (倾否) in the upper ninth line of the hexagram of "Opposition." Only then would we be on the correct path of evolution. Therefore, Confucius explicitly states in the "Commentary on the Judgment" (彖传) of the hexagram of "Benefit" (益): "Benefit is dynamic and compliant, advancing daily without limit." This is the great principle of gain and loss (天道运行是先泰而后否, 人事经营则应先损而后益). The ancients, through the hexagrams, have clearly indicated this. What he seeks to refute is the ingrained habit of seeking only benefit without understanding the necessity of loss. The evidence he relies on is the line "Inverting Opposition" (倾否) in the upper ninth line of the hexagram of "Opposition" and the statement "Advancing daily without limit" (日进无疆) from the "Commentary on the Judgment" of the hexagram of "Benefit."

孔子贊《易》，又一再言之。乃三千年來竟無一人能察聖人之象，昧聖人之言，以求日進而無疆，坐令錦繡之乾坤，困於一治一亂之輪迴，而無發展之機，不亦深可痛哉！辛齋何人，於古先大師大儒之學，會不能仰望其肩背，詎謂能發前人所未發，明前人所未明，以補數千年之罅漏？或者時事相催，劫運當復，天誘其衷，困諸囹圄，導諸良師，開其一隙之明，畀引其端。庶聖意不致終晦，後人得藉此發揮而光大之，以臻世界之大同，未可知也。九仞之山，成於螘垤。辛齋其亦一蟻而已。

Confucius wrote the "Commentaries on the Book of Changes," and he repeatedly spoke about this matter. However, for three thousand years, no one has been able to understand the sage's hexagrams or grasp the sage's words, to pursue continuous progress without limit. Instead, the splendid mountains and rivers have been trapped in the cycle of peace and chaos, without the opportunity for development. Is it not deeply regrettable? Hang Xinzhai modestly said: Who am I? I have not even been able to look up to the shoulders of the great scholars and sages of the past, how dare I claim to have discovered what others have not discovered or clarified what others have not clarified, to fill the gaps of thousands of years? Perhaps it is due to the urgency of the times and the turning of the calamitous era, that Heaven has guided my aspirations, putting me in prison and bringing me good teachers who have enlightened me, opening a small ray of light and handing over this thread to me. Perhaps the intention of the sages will not ultimately remain obscure, and later generations may be able to use it to develop and expand, achieving world-wide harmony. This is also possible. A mountain nine li high is built up by small heaps of earth like an ant's hole. I, Hang Xinzhai, am no more than one ant among them.