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

《說卦》象重出者三卦，“震為龍，艮為狗，兌為羊”，皆已見於第五章，而第八章又重出。八章“震為雷”之下，考《虞氏易》及《李氏集解》均作尨，注云幕色。震東方，故為尨。蓋馬八尺以上為尨，尨與龍，音亦同也。

In the "Say卦Transmission," the images of the hexagrams are repeated three times: "Zhen represents a dragon," "Gen represents a dog," and "Dui represents a sheep," all of which have already appeared in Chapter Five. They are repeated again in Chapter Eight. Under the entry "Zhen represents thunder" in Chapter Eight, the term "dragon" is recorded as "mang" in Yu Fan's commentary on the Zhou Changes and in Li Dingzuo's Collected Explanations of the Zhou Changes. The commentary explains that "mang" refers to a multicolored animal. Since Zhen is located in the East, "mang" is used as a symbolic image. According to Ma, a horse over eight feet tall is called "mang," and "mang" and "long" have the same pronunciation.

八章之“艮為狗”，虞氏及《李氏集解》，皆作拘。虞注云“指屈伸制物故為拘”（按：《隨·上六》“拘係之乃從維之”，即此拘也。），而朱氏《漢上易傳》曰“上言艮為狗，乃狗馬之狗。此言為狗者，熊虎子未有文猶狗也”。虞翻以兌艮為虎，艮寅位也，艮究成兌，故艮為虎子，未免迂曲矣。

Chapter Eight's "Geng Represents a Dog," both Yu Fan and the "Li Shi Ji Jie" write it as "ju." Yu Fan's commentary says, "The hand can bend and stretch to control external objects, so it is called 'ju.'" (Note: In the "Su Gu" hexagram's Sixth Line, "ju xi zhi, nai cong wei zhi," the character "ju" is used in this way.) Zhu Zhen's "Han Shang Yi Zhuan," however, says: In the fifth chapter, "Geng Represents a Dog" refers to the dog of horses and dogs; here, when it says "as a dog," it refers to the young of tigers and bears before their spots appear, which resemble dogs. Yu Fan takes You and Geng as tigers, because Geng is at the position of Yin, and when Geng is thoroughly examined, it transforms into You, so he says Geng represents tiger cubs, which is rather convoluted.

艮為羊之異說滋多，虞作“羔”，注云女使，《集解》同。鄭作“陽”，注云此陽謂養無家女行賃炊釁，今時有之，同於妾也。王氏《經義述聞》，謂“羔與羊，《書》、《傳》無訓女使”者。羔當為恙字之誤，恙亦通作養。

As for the entry 「as a sheep」 (the original text says 「Gen as a sheep」, actually referring to the Dui hexagram), there are many different interpretations. Yu Fan wrote 「gao」 and explained it as a female servant. The Li氏 Collection of Explanations agrees with this. Zheng Xuan wrote 「yang」 and explained that this 「yang」 refers to the practice of taking in an unmarried woman, employing her to cook and perform ritual sacrifices, a practice that existed at that time and was regarded as equivalent to a concubine. Wang Yinzhi's 「Narrative of Classic Interpretations」 states that there are no instances in the Shangshu or the commentaries of various schools where 「gao」 is interpreted as a female servant. Therefore, 「gao」 is likely a mistake for 「yang」, and 「yang」 can also be read as 「yang」 meaning to raise or nurture.

辛齋按以上諸說均有根據，惟無論為羔為恙為養，均須竄易經文，則不若依鄭說讀羊為陽。羊陽本通用，《春秋左氏傳》“夷養五”亦作“夷陽五”，可不必改經，而於諸家之義均可通矣。

I, Hang Xinzhai, remarked: The interpretations of the various scholars all have their basis, but regardless of whether one changes it to "gao," "yang," or "yang," it would require altering the text of the classics. Therefore, it is better to follow Zheng Xuan's interpretation and read "yang" as "yang." "Yang" and "yang" were originally interchangeable. For example, in the "Spring and Autumn Annals: Zuo Zhuan," "Yi Yang Wu" is also written as "Yi Yang Wu." This way, there is no need to alter the text of the classics, and the interpretations of all scholars can be made coherent.

八卦取象，精義入神，其微妙乃至不可思議。漢儒言《易》，不離象數，惜多散佚，已無完書。唐人以王弼為宗，言象者不著。其後如宋之邵子，及朱氏子發，與林氏黃中，鄭氏剛中，邱氏富國，黃氏東發；元之胡氏一桂，王氏申子，熊氏與可任重，龍氏仁夫；明之來氏矣鮮，黃氏道周；清之刁氏蒙吉，胡氏滄曉，惠氏仲儒定宇，萬氏彈峰諸家，皆於象義各有發明。

The eight trigrams take symbolic forms, with their subtle meanings reaching into the divine and marvelous. In their detailed aspects, they even reach an unimaginable level. Han dynasty scholars who interpreted the Book of Changes never separated from the principles of symbolic forms and numbers. Unfortunately, most of their writings have been lost, and there are no complete versions left. Tang dynasty scholars followed Wang Bi as their main authority, and those who interpreted the trigrams became less prominent. Later, figures such as Shao Yong of the Song dynasty, Zhu Zhen (zi fa), Lin Li (huang zhong), Zheng Gangzhong, Qiu Fuguo, Huang Zhen (known as Master Dongfa), in the Yuan dynasty, Hu Yigui, Wang Shenzi, Xiong Yuke (ren zhong), and Long Renfu; in the Ming dynasty, Lai Zhide (yi xian) and Huang Da Zhou; and in the Qing dynasty, Diao Bao (meng ji), Hu Xu (cang xiao), Hui Shiqi and his son Hui Dong (zhong ru, ding yu), and Wan Nianchun (tanjing) all made their own contributions to the interpretation of the symbolic meanings.

而姚氏與端木氏二家，（《姚氏易》及《周易指》）能原本經傳，發抒己見，不依傍昔賢門戶，尤為卓絕一時。雖或有所偏，其精到處皆確切不移，不可泯沒。辛齋為學日淺，僅就昔人之所未言，或言而未盡者，聊以助學《易》者之興趣也。

Among them, Yao Peizhong and Du Menguhu (i.e., the books "Yao Shi Yi" and "Zhou Yi Zhi") were able to take the classics as their foundation, express their own views, and not follow the schools of previous scholars. Their achievements were particularly outstanding at that time. Although they each had their own biases, their profound insights were accurate and unchangeable, and they should not be overlooked. My study of the Yi Jing is still shallow, so I only discuss a little on matters that previous scholars have not mentioned or have not fully explained, just to arouse the interest of those studying the Yi Jing.

凡言象者，不可忘《易》之義。《易》義不易者其體，而交易變易者其用。故八卦之象，無不交錯以見義。故乾為圜而形著於坤，離為日而光被於月。正秋者西也，而日行東陸。出震者東也，而日行西陸。執片面以言象，象不可得而見。泥一義以言象，象不得可而通也。

Anyone who talks about hexagram images must not forget the meaning of the character "Yi." "Yi" has three meanings: "Bu Yi" refers to its essence, "Jiao Yi" or "Bian Yi" refers to its function. Therefore, the images of the eight trigrams are always interrelated in expressing their meanings: Qian represents roundness, but the form of roundness is realized in Kun; Li represents the sun, but the light of the sun is applied to the moon. Dui represents the autumn season, located in the west, yet the sun in autumn moves eastward; Zhen represents the direction of spring growth, located in the east, yet the sun in spring moves westward. If one focuses only on a single aspect when discussing the images, the images will not be visible; if one rigidly adheres to a single meaning when discussing the images, the images will not make sense.

凡言象者，不可忘其數，天一地二天三地四天五地六天七地八天九地十。黃帝而後，皆以干支紀之。卦有定位，即有定數。（如坎子一，艮丑二寅三至兌酉十，乾戌亥數無。）《易》數乾元用九，乃天一不用，用地二至地十。數定而象之無定者，可因數而定。故觀象必倚數。如體物者必準諸度量，測遠者必察其角度。自舍數言象，而象茫如捕風矣。

All who discuss hexagrams must not forget the numbers behind them, which are referred to in the Great Treatise as the Heavenly One, Earthly Two, Heavenly Three, Earthly Four, Heavenly Five, Earthly Six, Heavenly Seven, Earthly Eight, Heavenly Nine, and Earthly Ten. After the Yellow Emperor, these numbers were marked with the Heavenly Stems and Earthly Branches. Since hexagrams have fixed positions, they also have fixed numbers (for example, Kan corresponds to Zi and is one, Gen corresponds to Chou and is two, and when it corresponds to Yin it is three, and so on, until Dui corresponds to You and is ten; Qian, located at Xu and Hai, is not counted). The use of numbers in the Zhou Changes is "Qian Yuan uses nine," meaning the Heavenly One is present but not used, and only the Earthly Two through the Earthly Ten are used. Once the numbers are fixed, the uncertain parts of the images can be determined by numbers, so observing images must rely on numbers, just as measuring objects requires a standard measure, and measuring distant objects requires observing angles. Since people have abandoned numbers to discuss images, the images have become indistinct, like grasping at wind.

凡言象者，不可不明其體。體者用之主也，故卜筮者亦曰取用。（每卦六爻，先取所用者一爻為主，即體也。）以所用者為主，而後察他爻之或從或違或動或靜，為利為害，吉凶始可得而斷焉。

Anyone who discusses hexagram images must first understand the concept of "body" (体). The body is the master of the use (用), so diviners also refer to it as "taking the use" (取用). Each hexagram has six lines; first, one selects the line that will be used as the main line, which is called the body. After determining this main line, one then examines the other lines to see if they are in harmony or opposition, whether they are active or still, and whether they are beneficial or harmful to me. Only then can one judge whether the outcome is auspicious or inauspicious.

用有大小，象則因其小而小之。因其大而大之，如乾也。大則為天，小則為木果，如坤也。大則為地，小則為布為釜，坎為大川，小則為溝瀆。離日大明，小亦為螢火。小大無方，各隨其體。明體以達用，象之用乃無窮矣。

The objects used in divination can be large or small, and the images used correspond accordingly—taking a small image when the object is small, and a large image when the object is large. For example, the trigram Qian (Heaven) can be considered as the vast sky when taken large, but when taken small, it may represent a single piece of fruit. The trigram Kun (Earth) can be seen as the entire earth when large, but when small, it may be a piece of cloth or a pot. The trigram Kan (Water) can represent great rivers and streams when large, but when small, it may be a ditch or a channel. The trigram Li (Fire) can be the brilliance of the sun when large, but when small, it may be a flicker of firefly light. There is no fixed standard of size; it all depends on the nature of the object being considered. Once the nature of the object is clearly understood, its functions can be inferred, and the applications of the images are limitless.

言凡象者，不可不視其所以。以者與也，及也。（《易》曰“不富以其鄰”及“剝床以足以其國君凶”，“拔茅茹以其匯”，諸“以”字皆與“及”字同訓。）卦因而重之，重為六畫，實具兩象。兩象必以其一為主，則必有所與。而六畫之二三四五中爻之象及其變動所生之象，無一而非與也。

Anyone who discusses hexagram images must consider their "reason" or purpose. "以" means "with," "and," or "as well as." In the "Zhou Yi," examples such as "not rich with its neighbor," "bed stripped away from the foot," "with its country ruler's misfortune," and "pulling out the rhizomes in their groups" all use "以" in the same way as "及." When the eight trigrams are combined to form a hexagram with six lines, it actually contains two images, upper and lower. Among these two images, one must be the main one, and the other is the object connected to it. Similarly, the intermediate image formed by the second, third, fourth, and fifth lines in a hexagram, as well as the new images formed by line changes, are all objects connected to the main image.

所與者而善，乃吉之幾。所與者而不善，乃凶之兆。而善惡又有大小之殊，所與者又有遠近之別，《繫傳》曰“遠近相取而悔吝生”，又曰“凡《易》之情，近而不相得，則凶或害之”。悔且吝，故必觀其所與者之善惡之大小，及情偽遠近，然後吉凶生而悔吝著，庶乎可得象之用焉。

The objects connected are good, then it is a favorable omen; if they are not good, it is a sign of misfortune. Good and evil also differ in degree, and the connected objects have distinctions of nearness and distance. The Great Treatise says, "Near and far relate to each other, and regret and hardship arise," and also says, "All the situations in the Book of Changes, if near but not in harmony, then misfortune occurs, there may be harm, and regret and hardship follow." Therefore, one must clearly discern the degree of goodness or evil in the connected objects, whether they are genuine or false, near or distant, only then will fortune and misfortune become evident, and regret and hardship be clear. Only then can one roughly grasp the use of the images.

凡言象者，不可不觀其所由。《繫傳》曰：“辭也者，各指其所之。”此有所之者，即彼有所由。《文言》曰：“臣弒其君，子弒其父，非一朝一夕之故，其所由來者漸矣。”蓋於坤之第一爻“履霜堅冰”，為三百八十四爻之所由來者，舉其例焉。

Anyone who discusses hexagrams must consider their origin. The Great Treatise says: "The words of the hexagrams each point to their destination." Where one end goes, the other end comes from. The Wenyan of the Qian Hexagram says: "A minister killing his sovereign, a son killing his father, is not the result of a single day or night; it has gradually developed over time." This is an example given under the first line of the Kun Hexagram, "Treading frost, the ice is already coming," illustrating that each of the 384 lines has its origin.

觀象者先明定其體象之所在。而更觀其所由來。如乾之姤，若用乾為天，則下巽為風，此風所由來為乾。乾為西北之卦，即西北風也。乾為冰為寒，則其風必寒。若用乾為木果，則巽不取象於風，當取象於蟲。因巽所由來為乾，既用為木果矣，則木果豈能生風？自應作蟲斷焉。舉其一例，餘可類推。不觀所由，象烏乎定哉！

The person interpreting the signs first needs to determine where the fundamental image falls, and then examine its origin. For example, if the first line of the Qian hexagram changes to become the Guo hexagram, then if we take Qian as Heaven, the lower trigram Xun would be Wind, and the origin of this wind is Qian. Since Qian represents the northwest, this wind would be a northwest wind. Moreover, since Qian also represents ice and cold, this wind must be cold. However, if we take Qian as a wooden fruit, then Xun should not be taken as Wind, but rather as insects; because the origin of Xun is Qian, and since Qian has already been used as a wooden fruit, a wooden fruit cannot produce wind. Naturally, it should be interpreted as producing insects. This is just one example, and the rest can be inferred in the same way. Without considering the origin, how can the image be determined?

凡言象者，不可不察其所安。安也者，位也。《繫傳》曰：“君子安其身而後動。”觀象者既定其主體之所在矣，必察其所在之處，能否得位。位得矣，必察其位之能否得時得用，而後其象始可得而言。

Anyone who discusses hexagram images must not neglect to examine their "position." By "position," it refers to the place. The Great Treatise says: "A gentleman stabilizes himself before he acts." When observing images, after determining the main subject in which line it resides, one must check whether its position is appropriate. Once the position is appropriate, one must further examine whether this position is timely and whether it is useful. Only then can the image of the hexagram be considered valid.

如用巽為木，則必察其所處之位為甲乙。或為丙丁壬癸，或為庚辛，為甲乙則當，為丙丁則相。為壬癸則生，而庚辛則死，既當或相與生矣，則更應察衰旺。並視所與者及所由者之如何，則象之情可畢見矣，如巽木處甲為剛木，所由來為乾，必為堅強之果木；所與者為艮，必是園林；為坤而壯者（如在四季月之終或戊己日時），為廣土；其衰者（如春令或甲乙日之類），則為盆缶。其他可準此。

For example, if we take Xun as wood, we must look at the position it occupies, whether it is in the position of Jia or Yi (wood), or Bing or Ding (fire), or Ren or Gui (water), or Geng or Xin (metal). If it is in the position of Jia or Yi, it is "in season" (when the element is strongest). If it is in the position of Bing or Ding, it is "supported" (being generated by the next element and in a secondary state of strength). If it is in the position of Ren or Gui, it is "generated" (being supported by its mother element). If it is in the position of Geng or Xin, it is "dead" (being overcome by the next element). Once we know it is in season, or supported, or generated, we must further examine its strength and weakness, and look at what it is connected to and what it comes from. In this way, the full situation becomes clear. For instance, if Xun wood is in the position of Jia, it is strong wood, and its origin is Qian, which means it is hard fruitwood. If it is connected to Gen, then it represents a garden. If it is connected to Kun and is in its prime (such as at the end of the four seasons or on a Wu or Ji day or hour), then it represents broad fields. If Kun is weak (such as in spring or on a Jia or Yi day), then it represents pots and containers. Other cases can be similarly inferred.

凡言象者，不可不明消息。消則滅，息則滋。如復姤臨遁之十二卦，消息之大焉者也。乾息坤，坤消乾。陰陽之大義，造化之橐龠，物理所莫能違，人事所莫能外。故物無大小，事無鉅細。言象者必先明乎消息盈虛之故，而象始可明。

Anyone who talks about hexagrams must understand the concept of yin and yang change. "Xiao" means decline, and "Xi" means growth. For example, the twelve hexagrams of change, such as Fu, Gu, Lin, and Duan, are the greatest examples of this principle. When the yang of Qian grows, it invades Kun; when the yin of Kun grows, it declines Qian. This is the great principle of yin and yang, the windbox of nature, which cannot be violated in physical phenomena or exceptions in human affairs. Therefore, whether the subject is big or small, the matter is great or minor, those who explain hexagrams must first understand the principle of growth and decline, fullness and emptiness, in order to explain the hexagrams clearly.

凡一卦本體之消息，或因時言之，或以位論之。當其消焉，象雖吉而未可言福。當其息焉，象若凶而益長其禍。其時值消而位當息，或位據息而時見消，則須辨其重輕，而異而分劑。或可亭毒均處而劑其平，或雖截短補長終莫齊其數。則又勢為之，未可泥於一端也。蓋勢之所趣，每善不敵惡，福不勝禍，一薰一蕕，十年尚猶有臭。一朝失足，而畢生之功盡棄。此君子之所以戒惡念之萌，而《易》道之所以扶陽而抑陰，嚴堅冰之防於履霜之始也。

The growth and decline of a hexagram's essence can be considered either in terms of the season or in terms of the yao positions. When the essence is in decline, even if the image is auspicious, it cannot bring about good fortune; when the essence is in growth, even if the image is ominous, it may instead increase misfortune. If the season indicates decline while the yao position suggests rest, or if the yao position indicates rest while the season indicates decline, one must distinguish between the two and handle them accordingly. Some cases can be balanced to achieve equilibrium between the two, while others, even with adjustments, cannot fully match the numbers. This is due to the situation at hand, and one must not be rigid in approach. Generally, the trend of circumstances often leads to good being overcome by evil, and fortune being surpassed by misfortune—just as a fragrant herb and a foul weed placed together will, after ten years, still leave the foul smell; a single misstep can cause the loss of a lifetime's achievements. This is precisely why a gentleman must be cautious and vigilant when evil thoughts first arise, and it is why the principles of the Book of Changes emphasize supporting yang and restraining yin, and why it warns against the formation of solid ice even at the beginning of a frosty step.

言象之大要如此。故夫陰陽之順逆，五行之休廢，氣數之盛衰，均不可不辨焉。向之言《易》者，曰吾治經，非以談休咎，奚用此術數為？而不知《易》以道陰陽，原本天地之數，以著天地之象，以通神明之德，以類萬物之情。非數則無以見《易》，非數即無以見象，未有象不明而能明《易》者也。

The main points of explaining the images (xiàng) are these. Therefore, the reversal and order of yin and yang, the decline and decline of the Five Phases, and the rise and fall of qi and numbers must all be distinguished. Previously, those who interpreted the Yi often said: "I am studying the classics, not coming to discuss good fortune, misfortune, blessings, and curses. What use is this system of numerology?" But they did not realize that the Zhuangzi's "Tianxia" had already said, "The Yi explains yin and yang." The Zhou Yi is originally dedicated to elucidating yin and yang; it originates from the numbers of heaven and earth, used to display the images of heaven and earth, used to connect with the virtue of the divine, and used to classify the forms of all things. Without numbers, one cannot see the Yi; without numbers, one cannot see the images. There has never been a person who could explain the Yi clearly without first understanding the images.

舍象以言《易》，故宋儒之性理，往往流於禪說而不自知。舍《易》以言象，方士之鼎爐，每每陷於魔道而殺其身。唯之與阿，相去幾何？然方士之說，不足以惑人，尚其為害之小者也。

Discarding the images to discuss the Yi, so the Song Confucian scholars who discussed principles of nature often fell into the path of Chan Buddhism without realizing it; discarding the Yi to discuss images, so the alchemists played with cauldrons and refined elixirs, repeatedly falling into wrong ways and losing their lives. The Dao De Jing says, 'Yes and Ah, how far apart are they?' The distance between these two is actually not far. However, the practices of the alchemists are not enough to confuse the people, so their harm is relatively minor.

易學自邵子以前，無八卦之圖。故言象者，除納甲以外，皆卦自為象。其有通兩卦又言者，即卦變及覆卦（來氏曰綜）耳。未有求之於八卦者，先天八卦無論矣。即後天八卦方位，亦鮮探索。惟“西南得朋”，“先甲”“先庚”等《彖》、《象》，注家或求諸卦位，餘則罕見矣。至先天八卦，更為言漢學者眾矢之的。焦氏之《易通釋》亦只以旁通貫串各卦，終不承認八卦之有先天也。

Before Shao Yong, there was no diagram of the eight trigrams with directional positions in the study of the Book of Changes. Therefore, those who discussed the images of the trigrams, apart from the method of assigning heavenly stems, considered each trigram to form its own image. Occasionally, there were discussions that connected two trigrams, but these were merely about changes between trigrams and their reversals, which Lai Zhide called 'comprehensive' or 'zong'. No one sought the positions of the eight trigrams. The Earlier Heaven Trigrams were even less considered. Even the directional positions of the Later Heaven Trigrams were rarely explored by predecessors. Only a few sentences in the Commentary on the Judgment and Image Commentary, such as 'southwest is where friends are found' in the Qian hexagram, 'three days before the first day of the month' in the Gu hexagram, and 'three days before the seventh day of the month' in the Xun hexagram, were occasionally used by commentators to find support from the trigram positions. As for the Earlier Heaven Trigrams, they became a target of criticism among scholars of the Han dynasty tradition. Jiao Xun's work 'Yi Tong Shi' only used 'parallel transmission' to connect the hexagrams and never acknowledged that the eight trigrams had an Earlier Heaven arrangement.

今按之六十四卦之《彖》、《爻》，其取象之所由，無不原本於先天後天兩圖。苟明其例，則逐卦逐爻象義相合。如按圖而索驥。否則各爻之象，有決非本卦與互卦及旁通所有者。如山風蠱，六爻有四爻言父，一爻言母。而父母之象，從何而來？不於先後兩圖求之，雖輾轉穿鑿，終不能得。迨考諸先後天，則知先天艮巽之位，即後天乾坤之位。乾父坤母，其所由來了如指掌矣。

Now that we use the sixty-four hexagrams' "Tuan Ci" and "Yao Ci" for comparison, their symbolic references all originate from the Earlier Heaven and Later Heaven diagrams. Once we understand this system, the images and meanings of each hexagram and its lines can be matched accordingly, just like finding a horse by following a map; otherwise, some of the images in the lines cannot be explained by the primary hexagram, the nuclear hexagram, or the related hexagrams. For example, in the hexagram "Gǔ" (Mountain Wind), four lines mention "father" and one mentions "mother." Where do the images of parents come from? Without referring to the Earlier Heaven and Later Heaven diagrams, no amount of interpretation can explain it. Only when we compare the Earlier Heaven and Later Heaven diagrams do we realize that the positions of Kūn (Earth) and Gèn (Mountain) in the Earlier Heaven correspond exactly to the positions of Qián (Heaven) and Kūn (Earth) in the Later Heaven—Qián represents father and Kūn represents mother, thus the source becomes clear.

又如《象傳》天火同人九五，曰“同人之先，以中直也”，“先”字從何而來？無從索解。考諸先後天，則後天離位，即先天乾位，更明析矣。故先天後天二圖，實闡發全《易》之秘籥。非但無可駁議，而先後二字，亦決不可易。或改先天為天地定位圖，後天為帝出乎震圖，乃昧於先後之義者也。

For example, the "Image Commentary" of "Heavenly Fire, Unity with Others" (Hexagram 13) explains the "Nine in the Fifth" as "The one who unites with others comes first, because of uprightness and centrality." Where does the character "first" (先) come from? According to traditional interpretations, there is no way to find an explanation. However, by comparing the Earlier Heaven and Later Heaven diagrams, we see that the position occupied by the Fire trigram (离) in the Later Heaven corresponds exactly to the position occupied by the Heaven trigram (乾) in the Earlier Heaven. Since the Heaven trigram is "first," the origin of "first" becomes clear. Therefore, the Earlier Heaven and Later Heaven diagrams are actually the key to understanding the entire "Zhou Changes" (I Ching). Not only are they irrefutable, but the terms "Earlier Heaven" and "Later Heaven" should not be changed. Those who would rename the Earlier Heaven diagram as the "Diagram of Heaven and Earth in Position" and the Later Heaven diagram as the "Diagram of the Emperor Emerging from the Thunder" do not understand the meaning of the words "earlier" and "later."

惟邵子以先天圖為伏羲所畫，後天圖為文王所定，則殊可議。蓋兩圖實體用相生，不能離拆。伏羲既作先天八卦，決不能無後天卦以通其用，故先天後天，與重卦六十四，皆一時並有。其六十四卦之大圓圖與方圖，或為邵子所發明，未必為伏羲氏之所畫也。

Only Shao Yong claimed that the Earlier Heaven Trigrams were drawn by Fuxi and the Later Heaven Trigrams were established by King Wen. This point is highly questionable. In fact, the two diagrams are mutually generative in essence and function, and cannot be viewed separately. Since Fuxi created the Earlier Heaven Trigrams, he certainly could not have failed to establish the Later Heaven Trigrams to realize their practical applications. Therefore, the Earlier Heaven Trigrams, the Later Heaven Trigrams, and the sixty-four hexagrams formed by their superposition all coexisted simultaneously. As for the circular and square diagrams of the sixty-four hexagrams, they might have been invented by Shao Yong himself, and were not necessarily drawn by Fuxi in ancient times.

漢《易》家駁先天圖者，曰：“離南坎北，《說卦傳》明定之方位也。乃以西北之乾置之南，西南之坤移之北。離為火故南方熱，坎為水故北方寒。今以乾居南方，則乾為寒為冰，豈不大謬？”當時以為名言。孰知南極北極，固皆為冰洋，今則三尺之童亦知之矣。駁議已不值一笑。然南北冰洋之發見，近三百年內事耳。乃何以伏羲畫卦時，已預有是象，謂非天下之至神乎？

The Han learning school refuted the Earlier Heaven diagram by saying: "Li is in the south, Kan is in the north, this is clearly established by the 'Sayings of the Guiguzi' regarding directions; yet the Earlier Heaven diagram places Qian, which should be in the northwest, in the south, and Kun, which should be in the southwest, in the north. Li is fire, so the south is hot; Kan is water, so the north is cold. Now placing Qian in the south, while the 'Sayings of the Guiguzi' also says Qian represents cold and ice, is this not a great mistake?" These words were once regarded as a famous argument. Who would have thought that the north and south poles were originally frozen seas, and today even a child knows that this argument is no longer credible. However, the discovery of the frozen seas in the north and south poles happened only within the last three hundred years. Why did Fuxi's diagram already contain this image? This is not precisely the most marvelous thing in the world?

乾為圜。圜者，渾圓，非平圓也。故《易》道之圓象，直四面凌空，不能僅觀其一面。鄉之言象者，目光不出於書外，泥於紙上之一圈，以為圓。錢竹汀至以地勢北高南下，駁乾南坤北之圖。具此目光以觀象，何異鄉愚觀李思訓山水。雖尺幅千里，以為不如春牛圖之得情，豈不辜負良工心苦！

The "Say on the Hexagrams" says, "Qian represents the circle." What is meant by "circle" here is a three-dimensional spherical shape, not a flat circular line. Therefore, the concept of "circle" in the "Book of Changes" refers to a sphere that extends in all directions, not merely a single plane. In the past, those who interpreted symbols were confined by books, fixating on the circle drawn on paper as the representation of a circle. Even Qian Daxin (pen name Zhuting) used the uneven terrain of north being higher than south to refute the "Earlier Heaven diagram" which places Qian in the south and Kun in the north. Observing symbols with such a narrow perspective is no different from a country bumpkin looking at a mountain landscape painting by Tang dynasty artist Li Sizhen. The painting captures a vast landscape within a small space, yet he prefers the familiar spring ox diagram posted in the government office, thus failing to appreciate the artist's painstaking effort.

乾為天，亦渾圓之天。故初潛而上亢。南極入地不見，潛也。北極出地，亢也。若在赤道以南觀之，則北極入地，而南極出地。若於正中赤道下觀之，則南北極皆不見，而成大過象。故大過曰“顛也，本末弱也”。

"Qian represents Heaven," which is also a round sphere. Therefore, the first line of the Qian hexagram is called "Qian" (hidden), and the top line is called "Kang" (exalted). When viewed from the northern hemisphere where China is located, the South Pole is buried underground and not visible, which is "Qian." The North Pole is above the ground, which is "Kang." If one were to view it from south of the equator, it would be reversed: the North Pole is buried underground, and the South Pole is above the ground. If one stands exactly on the equator, neither pole is visible, forming the image of the Da Guo hexagram, where the top and bottom lines are yin and the middle four lines are yang. Thus, the Commentary on the Judgment of Da Guo says, "Da Guo means overturning," and also says, "the beginning and end are weak."

六爻以三四兩爻為人爻，合言之，則上天下地中人。三極之道，與天地參者也。分言之，則人於天地間，只估三分之一。故乾以六爻言天行，則六龍皆為星象。言人道，則六龍以喻君子。言地勢，則中二爻為人居之地。初九、九二、九五、上九，皆龍之所宅。龍所宅，則海洋耳。即一卦分合言之，無不各具至理。舉乾而他卦可隅反矣。

In the six lines of a hexagram, the third and fourth lines are referred to as the human line. When considered together, the upper part represents heaven, the lower part represents earth, and the middle part represents humanity, which is exactly what the Great Treatise says: "the way of the three extremes." Humanity is thus placed on equal footing with heaven and earth as the third element. When viewed separately, humanity occupies only one-third of the space between heaven and earth. If the Qian hexagram is interpreted as describing the movement of celestial bodies, then the six lines represent the constellations of the eastern dragon (the Seven Stars of the Azure Dragon). If interpreted as describing human virtue, the six lines symbolize the gentleman. If interpreted as describing terrain, the middle two lines represent the land where humans reside, while the first, second, fifth, and top lines represent the places where dragons dwell—places that are the sea. In considering a single hexagram, whether viewed separately or together, there are always profound meanings to be found. Taking the Qian hexagram as an example, the same reasoning can be applied to all other hexagrams.

坎陷也，險也。說者謂以一陽陷兩陰之中，故險也。似矣，而未盡也。論卦象，坎為坤體，坤為順，何險之有？然正以上下皆順，如一人處至順之境，則陷溺其中而不自知。上下皆順，惟我是從，則更無匡弼輔導之資，其險莫險於是矣。反觀夫離，以一陰陷二陽之中，厥狀相等，何以不曰陷曰險，而乃曰麗？則離為乾體，乾德剛健，能匡輔之，乃剛柔相濟，自無險陷之虞矣。聖人取象之精，意極深遠。徒以陰陽言之，不免皮相之論也。

The trigram Kan represents a pit or a dangerous situation. Commentaries explain that because a yang line is trapped between two yin lines, it becomes dangerous. This seems plausible, but it does not fully capture the meaning. Considering the trigram itself, Kan is fundamentally associated with Kun, which represents compliance and smoothness. How then does danger arise? However, precisely because both upper and lower parts are compliant, it is like a person in a completely smooth and favorable environment, unaware of being trapped. When everyone follows one's will and there is no one to correct or support, there is no greater danger than this. In contrast, the trigram Li has a yin line trapped between two yang lines, which is the same shape as Kan. Why is it not called "trapping" or "danger," but instead "attachment" (li)? Because Li is fundamentally associated with Qian, which represents strength and vigor. Qian can correct and support Li, thus achieving a balance between yin and yang, and there is no danger of being trapped. The subtlety of the sage's use of imagery is profound; merely discussing the positions of yin and yang lines is superficial.

巽為雞，離為雉。雉俗呼為野雞，亦雞類也。巽既為雞，何不足以概雞，又特著於離？似近煩複矣。乃細察象義，則巽二陽在上，陽以象雞之翅。二陽重疊不分，故雞不能飛。離則兩陽在外，兩翅開張，故雉能飛。取象之妙，其細微不遺如此。

The *Shuogua* says that the trigram *Xun* represents a chicken and the trigram *Li* represents a pheasant. A pheasant is commonly known as a wild chicken and also belongs to the chicken family. Since *Xun* already represents a chicken, why is there a need to specially mention a pheasant under *Li*? It seems redundant. However, upon careful examination of the symbolic meanings, it becomes clear: the *Xun* trigram has two yang lines at the top, which symbolize the chicken's wings. The two yang lines are stacked together without separation, so a domestic chicken cannot fly. The *Li* trigram, on the other hand, has two yang lines arranged on the outside, resembling spread wings, so a wild pheasant can fly. The symbolism is so subtle and precise that even such fine distinctions are not overlooked.

兌為羊，說者謂羊性外柔內剛，故《陰符》曰“猛如虎狠如羊”。羊見死絕下畏避，且不號呼，切齒瞪目以就刃，剛狠極矣。而外極柔順，故以象兌之外柔內剛是也，猶未盡焉。兌，正秋也，五行屬金。土能生金，兌金為羊，故土可種羊，而土之怪亦曰羵羊。象理物理之妙合。實不可思議。

The *Shuo Gua* says that the trigram Dui represents a sheep. Interpreters explain that sheep are outwardly gentle and inwardly strong, hence the *Yin Fu Jing* says, "Fierce like a tiger, fierce like a sheep." When a sheep sees itself about to be slaughtered, it does not retreat or cry out, but instead clenches its teeth and stares bravely at the knife, showing extreme firmness while appearing extremely gentle on the outside. Therefore, it is used to symbolize the trigram Dui, which embodies outer softness and inner strength—this interpretation is correct, though not complete. Dui is the trigram of autumn, and it belongs to the metal element. Earth generates metal, so the image of the sheep is derived from the earth. The *Guoyu* records that Ji Hanzi dug a well and found a strange creature in the earth, and Confucius called it a "fengyang," which is a sheep found in the earth. The symbolic meaning and physical reality coinciding in this way is truly astonishing.

難者曰：坤土為牛，火能生土，何以火不能種牛？巽木為雞，水能生木，何以水不能種雞？曰：物各有理，非可概論。羊於辰屬未，坤貞未土，故土之生羊，不盡因於土金之相生焉。他物之生，各有原理。恨吾人學識尚淺，未能悉知之耳。

Someone raised a question: The Earth (Kun) represents soil and cattle, and fire generates earth, so why can't cattle grow out of fire? The Wind (Xun) represents wood and chickens, and water generates wood, so why can't chickens grow out of water? The answer is: All things have their own principles, and they cannot be treated in the same way. Sheep belong to the Earthly Branch 'Wei' and the correct position (Zhen) of the Kun hexagram is exactly at 'Wei' soil, so earth can generate sheep, not entirely because of the generation between earth and metal. The generation of other creatures also follows their own principles. We only regret that our knowledge is still shallow and we cannot understand them all.

坎為水，離為火。水火天地之大用，道家謂為人生之至寶。修道之功，歸結於取坎填離。而平時所致力者，所謂龍虎升降。二五交媾，皆不越坎離之功用。古來傳記，所載物類能煉形修道者，惟狐為最多。且其收效之易且速，恆為人類所不及。雖為經史所未載，然不盡為荒唐無稽之語，可斷言也。

Kan represents water, and Li represents fire. Water and fire are the greatest functions in the universe, and Daoist teachings regard them as the most precious treasures for human life. The practice of Daoist cultivation ultimately comes down to "taking Kan to fill Li." The daily efforts of so-called dragon and tiger rising and falling, and the union of the two five, all fall within the scope of the functions of Kan and Li. Throughout history, the records of creatures that can refine their forms and cultivate Dao are most commonly about foxes. Moreover, the effectiveness and speed of their transformation often surpass that of humans. Although these events are not recorded in official historical texts, they cannot all be dismissed as nonsense. This can be firmly stated.

要皆未能證明其理，乃考之於《易》，狐為坎象（《荀九家補》）。而水火既濟、火水未濟之兩卦，皆取象於狐。夫既濟未濟，非道家之乾坤，《參同契》之關鍵乎？乃文王作《彖》，周公繫《爻》，皆取象於狐。則狐之性靈形體，必與人近。或其內體有特異之機能，合於水火升降之作用，有非為人所及者，故能事半而功倍。古聖必已確知其故，因以繫諸離坎交媾之兩卦，非偶然也。

But no one has ever been able to prove the reasoning behind it. So we examine the Zhou Yi: the fox is the image of the Kan trigram (as seen in the supplementary images in the Xun Jiua Yi), and both the Ji Ji and Wei Ji hexagrams take their images from the fox. Are Ji Ji and Wei Ji not exactly the key concepts of the Daoist theory of Qian and Kun, as discussed in the Cang Tong Qi? King Wen composed the Tai Cis and the Duke of Zhou connected the line statements, yet they specifically took the image of the fox for these two hexagrams. Therefore, the fox's spirit and form must be very close to humans; perhaps it has some special function within its body that precisely corresponds to the rising and falling of water and fire, something beyond human capability, thus making cultivation much more effective. The ancient sages must have certainly known this reason beforehand, and that is why they connected the fox to these two hexagrams of mutual interaction between Li and Kan. It was certainly not by chance.

但非詳於動物生理學者，不能剖此疑團。在北京時，會以質諸大學教習日耳曼人沙某。沙亦向喜中國古學。而精於生理解剖者也。辛齋詳語其故，而沙乃鼓掌狂喜曰：“此足與吾國學者之研究相印證矣！近年解剖之學日精，凡人類與動物之身體之結構，無不明晰其作用：如人之腦筋有十二對，若者司觀，若者司聽司嗅，無不條分縷析。獨狐之腦筋，異常繁複。經多數博士之考驗，迄今尚未能解決。今由《易》象，可得其端倪。即從心腎兩臟以探察之，或可得其要領乎？”即此以觀，可見吾人於科學知識未能充分，而《易》象之精深奧衍，則斷非一知半解之腐儒所可擬議矣。

But if one is not an expert in animal physiology, one cannot unravel this mystery. When I was in Beijing, I once asked a German professor at the university, Mr. Sha, about this question. Mr. Sha had always been fond of Chinese antiquities and was skilled in anatomical studies. I explained the matter in detail to him, and he clapped his hands in delight, saying, "This is sufficient to corroborate the research of our scholars! In recent years, the study of anatomy has become increasingly precise, and the structure and functions of the human and animal bodies have all been clearly understood. For example, human cranial nerves are twelve pairs, and which pair controls vision, which hearing, which smell, are all clearly defined. However, the cranial nerves of the fox are exceptionally complex, and after many doctors have examined them repeatedly, the issue remains unsolved. Now, through the imagery of the Book of Changes, we may gain some insight—perhaps we should start by investigating the heart and kidney organs, and thus grasp the key to this mystery." From this incident, we can see that our scientific knowledge is still insufficient, and the depth and richness of the Book of Changes' imagery are far beyond the reach of those who only have a superficial understanding and dare to make hasty comments.

凡卦之象，合言之各有陰陽剛柔之別。陰陽以氣言，剛柔以形言。如乾為天為剛，坤為地為柔，坎為水為氣之形，離為火為形之氣，是也。而分言之，每卦又各自有其剛柔氣形之用。如乾為天為圜為父為君，又為玉為金為寒為冰，又為大赤，為良馬為老馬為瘠馬為駁馬，又為木果。

The images of all hexagrams, when considered together, each have distinctions of yin and yang, and of hardness and softness. Yin and yang refer to the nature of qi, while hardness and softness refer to form. For example, Qian represents Heaven and is considered hard, while Kun represents Earth and is considered soft. Kan represents water, which is a form condensed from qi, and Li represents fire, which is qi transformed into form. This is the meaning. When viewed separately, each hexagram also possesses various functions of hardness and softness, and of qi and form. For example, Qian is listed in the "Commentary on the Hexagrams" as representing Heaven, a circle, a father, a ruler, jade, metal, coldness, ice, a bright red color, a fine horse, an old horse, a thin horse, a spotted horse, and a tree fruit.

說者謂乾元資始，天與圜乾之體也，父與君，人之元也。玉與金，物之元也。寒與冰，氣之元也。大赤，色之元也。馬與木果，動物植物之元也。又來瞿唐云：“乾為馬，良馬其本體也。時變為老，形變為瘠，色變為駁，皆能得觀象之要者也。”學者由此類推，更可得無窮之精義。

Interpreters explain that Qian Yuan is the origin of all things, and Heaven and roundness are the essence of Qian; father and ruler are the fundamental elements in human relationships; jade and metal are the fundamental elements in material substances; cold and ice are the fundamental elements in qi; great red is the fundamental element in color; horse and fruit trees are the fundamental elements in animals and plants. Lai Zhide (also known as Qu Tang) further says: "Qian represents the horse, and a fine horse is its essence; as time changes, it becomes an old horse; as form changes, it becomes a thin horse; as color changes, it becomes a horse with mixed colors." These interpretations capture the essential principles of observing phenomena. Scholars can further infer from these and gain infinite profound meanings.

如為玉為金，金玉乃物質之最堅最精最純正者。《乾·文言》曰“剛健中正，純粹精也”，故以金玉象之。然物質之發明，日進無窮。近世所寶貴之金剛石，在畫卦時未必有是物也。而乾之剛純粹精，已酷肖其象。故自金剛石出世，而金玉失其貴。擬乾之象，當亦以金剛石為最肖矣。

For example, the Qian trigram is associated with "jade" and "metal." Metal and jade are the hardest, most refined, and most pure substances. The "Wenyan" section of the Qian hexagram states, "It is strong and upright, pure and refined." Therefore, metal and jade are used to symbolize it. However, discoveries in material substances are constantly evolving. Diamond, which is considered a treasure in modern times, may not have existed in the era when the hexagrams were drawn. Yet the virtue of Qian, being strong, upright, pure, and refined, has already closely resembled its form. Therefore, since the discovery of diamond, jade and metal have lost their former prestige. Today, when seeking to symbolize the image of Qian, diamond is the most appropriate representation.

蓋乾乃純粹之氣，而凝合成形，又極剛極堅，無物足以比擬。據近世化學家所考驗，金剛石乃純粹之炭氣所凝結，化之仍散而為氣，絕無渣滓。夫至精至純至剛至堅，又光明通達，聚之成質，而散仍復為氣。非乾之全德，又烏足以肖之？此象之可以物理之確當而補之者也。

The Trigram Qian represents pure qi condensed into form, and is extremely firm and hard, with nothing comparable to it. According to recent chemical analysis, a diamond is formed by pure carbon condensed, and when burned, it reverts back to gas without any residue. It is most refined, most pure, most firm, and most hard, yet also bright and transparent. When condensed, it forms a solid body; when dispersed, it returns to gas. Without possessing all these qualities of Qian, how could it be compared to it? This is an example where modern physical knowledge can be used to supplement the meaning of the hexagram.

凡卦之擬象，有自其陰陽之本體言者，有自其陰陽既合以後言者。如乾道成男，坤道成女，為男為女，是各就其本體言也。若乾為父，坤為母為婦，則自其陰陽既合以後而言也。凡卦之擬象，有取其全體者，有取三畫中之一畫者。乾坤為陰陽之宗，故取象皆以其全體。六子各分乾坤之一爻，故取象亦各就其一爻而言。如震巽以下爻，坎離以中爻，艮兌以上爻是也。

All divination hexagrams take their symbolic forms either from the fundamental nature of yin and yang or from their combination after they have interacted. For example, the Great Treatise says, "The principle of Heaven gives birth to the male, and the principle of Earth gives birth to the female," referring to their nature as male and female in terms of their fundamental essence. However, when it says Heaven represents the father and Earth represents the mother or wife, this refers to their interaction after yin and yang have combined. Furthermore, the symbolic forms of hexagrams may be taken from the entire hexagram or from a single line within the three lines. Heaven and Earth are the ultimate sources of yin and yang, so their symbolic forms are taken as a whole. The six subsidiary trigrams each receive one line from Heaven or Earth, so their symbolic forms are based on that particular line: Zhen and Xun take the lower line, Kan and Li take the middle line, and Gen and Dui take the upper line. This is the reasoning behind it.

六子既各分乾坤之一爻，故即分乾坤之象。如乾為馬，震坎皆言馬。坤為牛，離亦為牛。坤為腹，離為大腹。乾為首，坎為大首。“大腹”見於《傳》而不見於《經》，“大首”見於《經》而不見於《傳》，此尤見經傳互相發明之妙也。

The six sons each received one line from the trigrams Qian and Kun, thus each received part of the trigram imagery. For example, Qian represents a horse, and both Zhen and Kan also refer to a horse; Kun represents an ox, and Li also represents an ox; Kun represents the abdomen, and Li represents the great abdomen; Qian represents the head, and Kan represents the great head. The term "great abdomen" appears only in the Commentary on the Hexagrams but not in the classic text, while "great head" appears only in the classic text but not in the Commentary. One is in the Commentary, the other in the classic text, complementing each other perfectly. This clearly demonstrates the ingenious mutual clarification between the classic text and its Commentary.

震為聲。凡天下之聲，無不由動而發者也。震為群動之宗，故又為聲。然《說卦傳》未言震為聲者，以巽之為臭對照而可得者也。《說卦》一言象，往往於相對待者舉其一端。如舉坤為眾，知乾之為一。舉乾為寒，知坤之為暑。舉坎為憂，知離之為樂。此以對卦互見其義者也，亦有反對互見其義者。如震為大塗，而艮為徑路。巽為疑而兌為決。此皆《說卦》所明言者，則其未明言者可類推而知矣。如舉巽為長為高，則知兌為渺小為纖細。舉艮為門闕，則知震為盤桓。非神而明之，象義莫能見矣。

The trigram Zhen represents sound. All sounds in the world arise from movement; Zhen is the ultimate source of all movement, hence it also represents sound. However, the "Commentary on the Hexagrams" does not explicitly state that Zhen represents sound. This must be inferred by comparing it with Xun, which represents scent. The "Commentary on the Hexagrams" often explains the symbolic meanings by referring to one of two opposing or related trigrams. For example, it mentions Kun as multitude, so we know Qian as unity; it mentions Qian as cold, so we know Kun as heat; it mentions Kan as sorrow, so we know Li as joy. This is using the concept of mutual reference between opposing trigrams to understand their meanings. There are also cases where the meanings are understood through the opposition of trigrams: Zhen represents a broad road, while Gen represents a narrow path; Xun represents doubt, while Dui represents decision. These are explicitly stated in the "Commentary on the Hexagrams." Therefore, things not explicitly mentioned can be inferred by analogy. For example, since Xun represents length and height, we can infer that Dui represents smallness and fineness; since Gen represents gates and thresholds, we can infer that Zhen represents lingering or wandering. Without the ability to grasp the meaning intuitively, the symbolic meanings of the trigrams cannot be understood.

坎為水，離為火，其單象也。而陰陽既合，而離又為電為光為熱。物理之作用，非水不能溶解，非光熱不能融合。無論動物之生，不能離水火與光力熱力，為循環之挹注。既礦物諸質，其凝結之初，亦無不由此。故以電光熱之力，無物不可化分，亦無物不可以化合。故《易》以坎離為六十四卦之中樞，而殿之以水火既濟火水未濟。

The trigrams Kan (water) and Li (fire) represent their simple forms. But when yin and yang interact, Li becomes electricity, light, and heat. In terms of physical functions: without water, there can be no dissolution; without light and heat, there can be no fusion. Not only do animals depend on the continuous cycle of water, fire, light, and heat for their growth, but even the initial formation of various minerals comes from this process. Therefore, with the power of electricity, light, and heat, nothing can remain undecomposed, and nothing can fail to combine. For this reason, the Zhou Changes take Kan and Li as the central trigrams of the sixty-four hexagrams, and use Ji Ji (water and fire in harmony) and Wei Ji (water and fire not yet in harmony) as the concluding hexagrams of the entire book.

或問：乾為天，又為木果。小大之不倫，何懸絕若是？曰：天者元也，元無所不至。木果雖小，即乾之貞，而為元之所伏也。剝之上九曰“碩果不食”，反而為復，貞下起元，故終則有始也。其取象於木果者，以其形圓。圓內有核，核內有仁，仁內即元之所存，物雖小而生意無窮。至初爻變為巽，則元已不可見。故巽為不果，又為伏。伏者即謂元之伏藏而不可見，即無首之義也。《易》象之妙，極深研幾，無一字不有精義存乎其間。

Someone asked: The trigram Qian represents both Heaven and a fruit tree, yet the size is so different, why is there such a big difference? The answer: Heaven is "Yuan," which is everywhere. Although the fruit is small, it is precisely the "Zhen" of Qian, which is where Yuan is hidden. The upper ninth line of the Bao hexagram says "the large fruit is not eaten," and when Bao is exhausted, it returns to Fu, meaning that when Zhen is exhausted, Yuan arises again. Therefore, there must be a beginning when there is an end. The image of a fruit tree is taken because its shape is round: within the roundness is a kernel, within the kernel is the kernel, and within the kernel is where Yuan resides. Though the thing is small, its vitality is endless. When the first line of Qian changes to Xun, Yuan becomes invisible, so the Commentary on the Hexagrams says Xun "is not a fruit" and "is hidden." The term "hidden" means that Yuan is concealed and not visible, which is the meaning of "seeing a group of dragons without a leader" in the use of nine in Qian. The subtlety of the Book of Changes lies in exploring the profound and examining the subtle, with no single character lacking in profound meaning.

或問：乾為木果，即乾上爻之象乎？曰：碩果不食，上爻之象也。而窮上反下，則為初爻。故“木果”二字，須合兩爻以見義。經於剝上曰“碩果”，曰“不食”，二字均有分寸，不可不深思熟察也。

Someone asked: "The Qian hexagram is represented as 'wooden fruit,' is this the image of the top line of the Qian hexagram?" The answer: "The phrase 'large fruit not eaten' indeed represents the image of the top line, but when it reaches the top it must return to the bottom, thus becoming the first line again. Therefore, the two characters 'wooden fruit' must be understood in conjunction with both the top line and the first line to reveal their meaning. The classic text in the Bao hexagram's top line says 'large fruit,' and also says 'not eaten.' The expressions 'large' and 'not eaten' are both very precise, and one cannot help but think deeply and examine carefully."

或問：乾乃純陽，何以為寒為冰？曰：陽畜於陰，寒與冰，皆以陰畜陽。乾居西北，固陰沍寒。陰陽相薄，凝而為冰（所謂陰陽既合以後之象也）。故乾西北對東南巽。乾巽曰小畜，乾居西北，於先天之位為艮，艮乾曰大畜，大畜小畜而陽始生，猶必潛以養之，勿用以守之。剛健純粹，夫豈一朝一夕之故哉！

Someone asked: Qian is pure yang, so why does the "Shu Gu" say it represents cold and ice? The answer is because yang is restrained by yin - cold and ice both involve yin restraining yang. In the later heaven arrangement, Qian is located in the northwest, which is naturally cold and closed off due to the gathering of yin energy. The interaction between yin and yang leads to the formation of ice (this is precisely what is meant by the image after the union of yin and yang). Therefore, Qian being in the northwest corresponds to Xun in the southeast. With Xun above and Qian below, we have the hexagram Xiao Xu. In the earlier heaven arrangement, the position of Qian is艮 (Gen). With Gen above and Qian below, we have Da Xu. Only after going through Da Xu and Xiao Xu can yang energy begin to grow. Even then, it is still necessary to conceal it as in the first line of Qian, "Initial Nine," to nurture it, and to guard it by "not using" it. The strong and pure virtue of Qian cannot be achieved in a day or two!

或問：艮為虎，兌亦為虎。艮為虎，乃荀九家之說。按之於《經》，則履之“虎尾”，革之“虎變”，皆似兌象。究何從乎？曰：履與革，固有兌象。而頤之“虎視眈眈”，則艮象也。此即前文所謂以對卦而相通之一例也。

Someone asked: "Geng (Gon) represents the tiger, and Dui also represents the tiger. The representation of Geng as the tiger comes from the supplementary imagery in the Xun Jiye Yi. But if we check the classic texts, the phrase 'stepping on a tiger's tail' in the Lu卦 and 'the great man's tiger transformation' in the Ge卦 seem to be Dui imagery. So which one should we follow?" The answer is: The Lu卦 and Ge卦 indeed both contain Dui imagery, while the phrase "the tiger stares intently" in the Yi卦's line six in the fourth position is Geng imagery. This is exactly the example mentioned earlier, demonstrating how one can use the mutual correspondence between related trigrams.

考八卦之象，艮為狗，因艮外剛而內柔，狗之性似之，故為狗。然艮有成終成始之德，能與剛德相終始，則為虎。兌之本象為羊，履之“虎尾”，革之“虎變”，曰“尾”曰“變”，明非兌之本象也。至兌之為虎，乃另屬一義。兌居西方，上直昂宿白虎之位，亦如乾卦之取象蒼龍，則因位而取象。與剛柔之說無與矣。

Examining the symbolic representations of the Eight Trigrams: The Trigram Gen is associated with the dog because Gen is externally strong and internally gentle, and the dog's nature is similar, hence the dog is used as its symbol. However, Gen also possesses the virtue of "completing the beginning and the end," being able to maintain harmony with strong virtue throughout, so it can also be associated with the tiger. The original symbol of Dui is the sheep; the Book of Changes says "tiger's tail" in the hexagram Li and "tiger's transformation" in the hexagram Ge. One mentions "tail" and the other "transformation," clearly not referring to Dui's original symbol. As for why Dui is associated with the tiger, it is due to another reason: Dui is located in the west, precisely corresponding to the White Tiger constellation, the seven stars ofHairy Head mansion. This is similar to how the Trigram Qian is associated with the Eastern Blue Dragon, based on directional association, and has nothing to do with the idea of being externally gentle and internally strong.

或問：坤為布為釜，乃坤之本象乎？曰：非也。此皆陰陽化合而生之象也。坤與乾合，則陰陽經緯而有布象。坤得離坎，則水火濟用而有釜象或缶象。缶亦釜也。《易》有缶而無釜，因上古火化之始，未有釜也。觀比之盈缶，坎用缶，離鼓缶，可會通其義矣。曰：陰陽經緯，既乾坤相合之象，何獨於坤言之？曰：陽氣而陰質也。曰：乾亦有稱布乎？曰：有諸。乾施坤受，施亦布也。布五行於四時，乾之布也。布同而義殊矣。妙哉！《易》之為書也。

Someone asked: "Is 'Kun' associated with 'cloth' and 'vessel', which are its original images?" The answer was: No. These are images that arise after the combination of yin and yang. When Kun combines with Qian, yin and yang intermingle vertically and horizontally, thus producing the image of cloth. When Kun combines with Li and Kan, water and fire interact, thus producing the image of a vessel or a gu. A gu is also a vessel. The text of the Zhou Yi only mentions 'gu' and not 'fu', because when ancient people first learned to use fire for cooking, there was no such thing as a 'fu'. Looking at the line 'There is sincerity in the gu' from the top line of the Bi hexagram, 'Wine and food in two vessels, using the gu' from the sixth line of the Kan hexagram, and 'Singing without beating the gu' from the third line of the Li hexagram, one can understand the meaning. Another question: If the intermingling of yin and yang is the image of the combination of Qian and Kun, why is the image of cloth specifically mentioned under Kun? The answer is: Because yang is only qi, while yin is the substance. Another question: Can Qian also be called 'cloth'? The answer is: Yes. Qian gives out, and Kun receives. 'Giving out' is also 'cloth'. Distributing the five elements throughout the four seasons is precisely the action of Qian. The same character 'cloth' has different meanings. The Zhou Yi is truly marvelous.

或問：離為鼈、為蟹、為蠃、為蚌、為龜。此五者，惟龜象見於頤與損益，餘象皆不見經傳，其義何居？曰：五者皆水族也。不屬諸坎而屬諸離，以見陰陽互藏之妙焉。舊說以五者皆甲蟲，外剛內柔，故以取象。是矣，而未盡也。離中虛能受，故能納五行之精。得巽木之精為鱉，得震雷之精為蟹，得兌月之精為蚌，得乾金之精為蠃，得坎艮之精為龜，而畢受化於坤土。觀象於頤可得其義。推而廣之，其象可見也。（焦氏《易通釋》謂《易》之言敝即鱉也，言解即蟹也，言贏即蠃也，言邦即蚌也，於義亦通。）

Someone asked: The "Say on the Trigrams" says that the trigram Li (Fire) represents turtle, crab, snail, mussel, and tortoise. Among these five, only the tortoise is mentioned in the "Yi" (I Ching) and its commentaries, while the other four are not found in the classical texts. What is the purpose of using these as symbols? The answer: These five are all aquatic creatures, yet they are not associated with Kan (Water) but with Li (Fire), which clearly shows the profound mystery of yin and yang intermingling and containing each other. The old view considered these five to be creatures with hard shells and soft insides, so they were used as symbols—this is partly correct, but not entirely. The trigram Li is hollow in the center, and emptiness allows it to contain and receive. Therefore, it can hold the essence of the Five Phases: it receives the essence of Xun wood to become a turtle, the essence of Zhen thunder to become a crab, the essence of Dui metal to become a mussel, the essence of Qian metal to become a snail, and the essence of Kan mountain to become a tortoise. Finally, all of them are nurtured by the essence of Kun earth. Observing the images in the "Yi" (I Ching) in the "Yi" hexagram can clarify this meaning. Extending this understanding, these images can all be recognized. (Jiao Xun's "Yi Tong Shi" says that the character "bi" in the "Yi" text refers to turtle, "jie" refers to crab, "ying" refers to snail, and "bang" refers to mussel. These interpretations are also reasonable in terms of meaning.)

或曰：坎為月，今以兌為月，是非邵子之象乎？曰：非也。卦之言象，以相對見義。坎離相對，離為日，則坎為月。離為火，則坎為水。兌之為月，對於震巽取義。《易》之言月者，除日月對舉者則指坎。餘皆指兌言也。

Some people say: "Cann is the moon, but now it is Dui that is taken as the moon. Is this not the way of Shao Yong's school?" The answer is: No. In divination, the meaning is derived from the relations between the trigrams. Cann and Li are opposite to each other: since Li represents the sun, Cann represents the moon; since Li represents fire, Cann represents water. As for Dui being taken as the moon, it is in relation to Zhen and Xun. In the text of the Zhou Changes, whenever the moon is mentioned, it refers to Cann in cases where the sun and moon are mentioned together, but in other cases, it refers to Dui.

或問：《繫下傳》“龍蛇之蟄以存身焉”，是否指乾卦之象？曰：然。咸卦三爻至五爻互乾，乾四爻之“上不在天下不在田中不在人”者，以此四爻乃在乾卦之中。《咸·象》曰“君子以虛受人”者，即此一爻，故稱龍蛇。龍蛇者，未確指其為龍為蛇，與“或躍在淵”之或字相應者也。蓋乾之對宮為巽，巽於十二辰，貞在辰巳，辰為龍，巳為蛇。躍者，超越而上之名，言四爻能超躍越過巳之一位，即及於離午而為飛龍。不能及於離午，則在巳而為蛇。辭意極為明析。按之於象數，無不絲絲人扣者。聖人之文，真與造化同一工也！

Someone asked: The "Xici Xia Zhuan" says, "The dragon and snake hibernate to preserve themselves," does this refer to the image of the Qian hexagram? Answer: Yes. The third to fifth lines of the Xian hexagram together form the structure of the Qian hexagram. The Nine in the Fourth line of the Qian hexagram is said to be "not above Heaven, not below the field, not in the middle of people," precisely because this line is in a transitional position within the Qian hexagram. The "Great Image" of the Xian hexagram says, "The gentleman receives others with humility," which refers exactly to this line, hence it is called "dragon and snake." The term "dragon and snake" does not specifically refer to either a dragon or a snake, corresponding to the "or" in the line statement "or leap into the abyss." Originally, the opposite hexagram of Qian is Xun. In the twelve earthly branches, the position of Xun falls on the hours of Chen and Si: Chen is the dragon, and Si is the snake. "Leap" is a term meaning to transcend upward. It means that the Nine in the Fourth line can leap over the position of Si and reach Li and Wu to become a flying dragon; if it cannot leap over, it remains in the position of Si and is merely a snake. The meaning of the line statement is very clear. When verified with the principles of numbers and positions, everything fits perfectly. The words of the sage are truly in harmony with the workings of nature!

或問：《說卦》“離為龜”，乃六十四卦之有離者，均不言龜，獨見之於頤與損益何也？曰：頤與損益，皆剛外柔內，有離之象。來氏所謂大象是也。頤與損益，大象似離，故言龜。亦即聖人示人以取象之一例焉。

Someone asked: The "Sayings on the Trigrams" says "Li represents the tortoise," but among the sixty-four trigrams, none of the ones containing the trigram Li mention the tortoise, except for the trigrams Yi, Shen, and Yi. Why is this? The answer is: The trigrams Yi, Shen, and Yi all have a hard outer part and a soft inner part, and they have the shape of Li. This is what Lai Zhide referred to as "the great image." Since these three trigrams as a whole resemble Li, they are associated with the tortoise. This is exactly the example of taking a symbolic image that the sage demonstrated to people.

曰：在損益皆稱“十朋之龜”何也？曰：十者，取其最多之數，即天一至地十之數也。朋者，陰陽相合。以天一地二天三地四，數各有合，故曰朋。此“龜”字與震卦“億喪貝”之貝字同。古人無錢布，龜與貝皆寶貨之一類也，故以象言之。頤之龜乃活龜，而損益之龜則龜版耳。

Another question: Both the hexagrams "Zhen" (Loss) and "Yi" (Gain) mention "ten tortoises," why is this so? The answer is: "Ten" refers to the largest number, which is the end of the sequence from heavenly one to earthly ten. "Peng" refers to the pairing of yin and yang: heavenly one pairs with earthly two, heavenly three pairs with earthly four, and each number has its counterpart, hence called "peng." The word "gu" (tortoise) here is of the same category as the "bei" (shell money) in the line "yi sang bei" (countless loss of shell money) in the hexagram "Zhen." In ancient times, there were no copper coins or metal currency; tortoise shells and shells were considered valuable items, so they were used as symbols. The tortoises mentioned in the hexagram "Yi" (Nourishment) are live tortoises, but those mentioned in "Zhen" (Loss) and "Yi" (Gain) are merely the turtle shells used for divination.

或問：巽為寡髮，《李氏集解》作宣髮。虞注曰巽為白，故宣髮。將何說之從？曰：兩說皆可通也，巽為長女。凡女之愆時未嫁。及早嫁而生育過多者。血皆失其經而髮禿。故曰寡髮。禿必於前額，故亦可曰宣髮。《考工記》“半矩謂之宣”，似宣之義更能形容酷肖，較寡字尤周到也。

Someone asked: The "Say on the Trigrams" says that Xun is "of sparse hair," but Li Dingzuo's "Collected Explanations of the Zhou Changes" says "of spreading hair." Yu Fan's commentary says that Xun is associated with white, hence "spreading hair." Which should be followed? The answer is that both interpretations are reasonable. Xun is the elder sister, and any woman who has not married before her time or who has married early and given birth many times will lose her blood balance, leading to thinning hair, hence "sparse hair." However, baldness always begins at the forehead, so it can also be called "spreading hair." The "Rites of Zhou · Records of the Master of Works" says "half the square is called 'Xuan'," and "Xuan" implies a broad forehead, which seems to describe the condition more accurately and comprehensively than the word "sparse."

或問：巽為近利市三倍，其於象也何居？曰：此象之微妙，非通全卦而觀之，僅就巽之三畫以探索之，無從得其義焉。巽為入，有入而無出，得坤吝嗇之性。然坤柔順，故雖吝音，尚不致為貪。而巽之體，則乾體也。以乾體之健，行坤性之吝，更兼其本性之人。三者合之，所謂三倍也。

Someone asked: The "Say on the Trigrams" says that Xun represents "a profit threefold." What is the basis for this image? The answer: This image is very subtle. If one does not observe the entire trigram but only examines the three lines of Xun, one cannot understand its meaning. Xun represents "entering," which is only entering and not exiting, thus acquiring the nature of Kūn, which is stingy. However, Kūn is flexible and yielding, so although it is stingy, it does not become greedy. The original nature of Xun, however, is the nature of Qian: with the strength and vigor of Qian, acting with the stinginess of Kūn, and adding its own nature of "entering," the combination of these three is what is called "threefold." (The original text says "lìn yīn" should be read as "lìn sè" [stingy], and "běn xìng zhī rén" should be read as "běn xìng zhī rù" [nature of entering].)

然則近利市三字之象，又從何而來也？曰：此則須索之於八卦方位也。八卦巽居東南，其前則東震也，其後則南離也。離與震，火雷噬嗑。日中為市，致天下之民，聚天下之貨，交易而退，各得其所，蓋取諸噬嗑。今巽之方位，適介於噬嗑上下卦之間，非近利市而何？故聖人之於象，一字一義，必有根據。潛心以求之，多方以索之，方能知其妙。若以不解解之，其奧義終莫能得也。

So where does the image of "near profit and market" come from? The answer is to look for it in the positions of the Eight Trigrams. Among the Eight Trigrams, Xun is located in the southeast. In front of it is Zhen in the due east, and behind it is Li in the due south. Li and Zhen combine to form the Hexagram 21, Fire Over Thunder, Shi Ke. The "Xici Xia Zhuan" says: "At noon the market is held, gathering the people from all over the world and collecting goods from all over the world. They trade and then depart, each getting what they need. This is derived from Shi Ke." Now, the position of Xun is exactly between the upper and lower trigrams of Shi Ke. Is this not "near profit and market"? Thus, the sage established images, each character and each meaning must have its basis. One must diligently seek and search from many sides to understand its subtlety. If one explains it with partial knowledge and superficial understanding, those profound meanings will never be grasped.

或曰：宣髮與近利市三倍，其象義之妙既聞之矣。而巽又為多白眼，亦必有妙義，可得聞歟？曰：此則前人已有言之者矣。曰離柔居中，為目之正。巽陰反下，而二陽上，故多白眼。似為來氏之說。於義頗近，尚未明暢。請申言之。

Some people said: I have already understood the subtle meanings of the two divination lines "宣发" and "近利市三倍"; since the trigram Xun is said to "represent many white eyes," there must be some profound meaning, could you explain it to me? The answer was: this point has already been discussed by previous scholars. They said: the trigram Li has a yin line in the middle, which represents the upright eyes; while the trigram Xun has a yin line at the bottom and two yang lines above, thus representing many white eyes. This seems to be the view of Lai Zhide, and the meaning is quite similar, but not clearly explained. I will now elaborate further.

離為目，巽之下，即離之上也。離之下，即兌之上也。此即虞氏所謂半象。故經文於兌稱“眇目”，履與歸妹皆兌，皆曰“眇能視”是也。以兌例巽，則巽亦眇耳。惟巽又為白。白者，上二陽也。是巽之眇，白且占三分之二。非多自眼而何？“多白眼”二字，不啻將巽之眇活畫出來。神哉化工之筆也！

The trigram Li represents the eye. The lower half of Xun is exactly the upper half of Li; the lower half of Li is exactly the upper half of Dui — this is what Yu Fan referred to as "half-trigrams." Therefore, the classic text refers to "眇目" (blind eye) in the Dui hexagram: both the hexagram "Lu" (Following) and "Gui Mei" (Return of the Maiden) contain the structure of Dui, and both mention "眇能视" (blind in one eye yet able to see). By comparing Dui to Xun, Xun also possesses the quality of "眇." However, Xun is also associated with "white," referring to the two yang lines at the top. Thus, the "眇" in Xun is dominated by white, occupying two-thirds of it. It is not called "多白眼" (many white eyes) for nothing (the original text says "多自眼," where "自" is a mistake for "白"). The term "多白眼" vividly portrays Xun's eye that appears pale. Truly, it is a masterpiece of divine craftsmanship!

或問：坎，其於人為加憂，為心病，為耳痛。舊解為陽陷陰中，心危慮深，故加憂。憂之甚為心病，心以虛為體。剛畫梗於其中故病。惟耳亦然。坎為耳，外陰內陽，取象陽之總也。又為耳痛，象陽畫之梗於其中也。其說當乎？

Someone asked: The "Say on the Trigrams" says about Kan (Water): "It represents added worry, heart disease, and ear pain." Old commentaries explain that a yang line is trapped within yin lines, causing inner anxiety and deep thinking, hence "added worry"; when worry reaches its extreme, it becomes "heart disease," because the heart is based on emptiness, and a single strong yang line blocking in the middle causes illness. The ear is similar: Kan represents the ear, with outer yin and inner yang, symbolizing the gathering of yang energy; saying it "represents ear pain" also symbolizes that yang line blocking in the middle. Is this explanation appropriate?