the original explanation of the trigrams second

朱子答袁樞曰：伏羲之《易》，初無文字，只有一圖以寓其象數，而天地萬物之理，陰陽始終之變具焉。文王之《易》，即今之《周易》，而孔子所為作《傳》者是也。孔子既因文王之《易》以作《傳》，則其所論，固當專以文王之《易》為主，然不推本伏羲作《易》畫卦之所由，則學者只從中半說起，不識向上根原矣，故“十翼”之中，如“八卦成列”“因而重之”，太極兩儀四象八卦，而天地山澤雷風水火之類，皆本伏羲畫卦之意。今新書原卦畫一篇，亦分兩義，伏羲在前，文王在後。

In a letter to Yuan Shu, Zhu Xi said: Fuxi's Book of Changes originally had no written text, only a diagram to express its images and numbers. The principles of heaven and earth and all things, as well as the changes of yin and yang, were all contained within it. King Wen's Book of Changes is the present text of the Zhou Yi, which Confucius later explained with his commentaries. Since Confucius explained the Book of Changes based on King Wen's, his discussions naturally focused on King Wen's Book of Changes. However, if we do not trace back to the origin of Fuxi's diagramming of the trigrams, scholars can only start from the middle part and cannot understand the deeper source. Therefore, in the "Ten Wings," such as the "Great Treatise" saying "the eight trigrams are arranged in order" and "therefore they are repeated," as well as the concepts of the Supreme Ultimate, the dual aspects, the four images, the eight trigrams, and the categories of heaven, earth, mountain, marsh, thunder, wind, water, and fire, all these ideas are based on Fuxi's intention in drawing the trigrams. Now, this newly compiled book includes an article called "Original Trigram Diagram," which is divided into two parts: Fuxi's comes first, and King Wen's comes later.

古者包羲氏之王天下也，仰則觀象於天，俯則觀法於地，觀鳥獸之文與地之宜，近取諸身，遠取諸物，於是始作八卦，以通神明之德，以類萬物之情。《大傳》又言包羲畫卦所取如此，則《易》非獨以《河圖》而作也，蓋盈天地之間，莫非太極陰陽之妙，聖人於此，仰觀俯察，遠求近取，固有以超然而默契於其心矣。

The Great Treatise says: In ancient times, Fu Xi ruled the world. He looked up to observe the phenomena in the heavens, looked down to observe the principles on the earth, observed the patterns of birds and beasts and the suitability of the land. He took inspiration from his own body nearby and from all things in the world afar. Thus he began to draw the Eight Trigrams, using them to connect with the virtue of the divine and to classify the forms of all things. The启蒙 text says: The Great Treatise also explains the sources from which Fu Xi derived the trigrams, showing that the Book of Changes was not solely based on the Yellow River Chart. All things in the universe are merely the subtle workings of the Supreme Ultimate and yin and yang. The sage observed from above and below, sought far and near, and inherently possessed an intuitive understanding beyond form and a silent harmony with the mind.

故自兩儀之末分也，渾然太極，而兩儀四象六十四卦之理，已粲然於其中。自太極而分兩儀，則太極固太極也，兩儀固兩儀也，自兩儀而分四象，則兩儀又為太極，而四象又為兩儀矣，自是而推之，由四而八，由八而十六，由十六而三十二，由三十二而六十四，以至於百千萬億之無窮。

Therefore, when the two principles had not yet separated, it was a single Taiji, and the principles, the four images, and the sixty-four hexagrams were already fully contained within it. When Taiji divides into the two principles, then Taiji remains Taiji and the two principles remain the two principles; then, when the two principles divide into the four images, the two principles again become Taiji, and the four images again become the two principles. Continuing in this way, from four to eight, from eight to sixteen, from sixteen to thirty-two, from thirty-two to sixty-four, and so on, it can be extended to countless numbers without end.

雖其見於摹畫者，若有先後而出於人為，然其已定之形，已成之勢，則固已具於渾然之中，而不容毫髮思慮作為於其間也。程子所謂加一倍法者，可謂一言以蔽之，而邵子所謂畫前有《易》者，又可見其真不妄矣，世儒於此，或不之察，往往以為聖人作《易》，蓋極其心思探索之巧而得之，甚者至謂凡卦之畫，必由蓍而後得，其誤益以甚矣。

When these trigrams appear on paper, they seem to have a sequence and arrangement as if planned by human effort. In reality, their definite forms and established trends were entirely present within the unified Taiji, leaving no room for human thought or artificial intervention. Cheng Hao's phrase "adding one more" can be used to summarize this idea. Shao Yong's statement "before drawing the trigrams, the Book of Changes already exists" also clearly shows that it is not empty talk. Many scholars fail to recognize this, often believing that the sages created the Book of Changes through painstaking effort and clever insight. Worse still, some even claim that all trigrams must be obtained through divination with yarrow stalks, which is a far greater mistake.

集說 謝氏良佐曰：堯夫《易》數甚精，明道聞說甚熟，一日因監試無事，以其說推算之皆合，出謂堯夫曰：堯夫之數，只是加一倍法，以此知《太玄》都不濟事。朱子答虞大中曰：太極兩儀四象八卦，此乃《易》學綱領，開卷第一義，孔子發明伏羲畫卦自然之形體，孔子而後；千載不傳，唯康節明道二先生知之，蓋康節始傳先天之學而得其說，且以此為伏羲之《易》也。《說卦》天地定位一章，“先天圖”乾一至坤八之序皆本於此，然康節猶不肯大段說破《易》之心髓全在此處。不敢容易輕說，其意非偶然也。明道以為加一倍法，其發明孔子之言，又可謂最切要矣。

Collected Commentaries: Xie Liangzuo said that Shao Yaofu explained the Book of Changes with extreme precision. Cheng Mingdao listened to his explanations thoroughly. One day, when Mingdao was supervising the imperial examination, having nothing else to do, he calculated according to Shao's method and found everything to match perfectly. When he came out, he told Yaofu: "Your system of numbers is merely a method of doubling." From this we can see that Yang Xiong's Taixuan was entirely ineffective. Zhu Xi wrote in a letter to Yu Dazhong that the Taiji, two principles, four images, and eight trigrams are the main points and the first essential of the study of the Book of Changes. These were used by Confucius to explain the natural forms of the trigrams drawn by Fuxi. After Confucius, for over a thousand years, this knowledge was not passed down, except for two gentlemen, Shao Kangjie and Cheng Mingdao. Shao Kangjie was the first to master the earlier heaven system and its explanation, and he regarded this as the Book of Changes of Fuxi. The order of the eight trigrams from Qian one to Kun eight in the chapter "Heaven and Earth are positioned" of the Shuigua transmission is based on this. However, Shao was still unwilling to fully reveal it. The essence of the Book of Changes lies entirely in this, yet he did not dare to speak it out lightly. His carefulness was not accidental. Mingdao summarized it as the "method of doubling," using it to explain Confucius' words, and it can be said to be the most essential explanation.

《易》有太極太極者，象數未形，而其理已具之稱，形器已具，而其理無聯之目，在《河圖》、《洛書》，皆虛中之象也。周子曰：“無極而太極。”邵子曰：“道為太極。”又曰：“心為太極。”此之謂也。

The Great Treatise says, "The Book of Changes contains the Supreme Ultimate." The启蒙 explains that the Supreme Ultimate is a term established when the images and numbers have not yet taken form but its principles are already complete, and also a term established when the physical forms and objects are already present but its principles are imperceptible (the original text mistakenly reads "wu lian" instead of "wu zhen"). In the Yellow River Chart and the Luo Writing, it is represented by the central image that is left unused. Zhou Dunyi said, "From the absence of extremes comes the Supreme Ultimate," Shao Yong said, "the Dao is the Supreme Ultimate," and also said, "the mind is the Supreme Ultimate," all referring to this meaning.

案 太極之在《易》書者雖無形，然乾即太極也，偏言之，則可以與坤對，亦可以與“六子”並列，專言之，則地一天也，“六子”亦一天也。故程子曰：夫天，專言之則道也，以形體言謂之天，以主宰言謂之帝，以妙用言謂之神，以性情言謂之乾，其言可謂至矣。雖然畫卦之初亦未有乾之名，其始於一畫者即是也，摹作圓形者，始自周子，朱子蓋借之以發《易》理之宗，學者不可誤謂伏羲畫卦，真有是象也。

The case is: The Taiji is not given a physical form in the book of The Zhou Changes, but Qian is Taiji. When considered separately, Qian can be contrasted with Kun, or placed alongside Zhen, Kan, Gen, Xun, Li, and Dui, the six sons; when considered together, Kun is merely this one Heaven, and the six sons are also this one Heaven (the original text mistakenly says "earth is one Heaven" instead of "Heaven is one Heaven"). Therefore, Cheng Yi said: "When discussing Heaven, when considered together it is the Dao; when considered in terms of form it is called Heaven, when considered in terms of sovereign it is called the Emperor, when considered in terms of subtle function it is called the Divine, and when considered in terms of nature and disposition it is called Qian." These words can be said to have reached the extreme. Although this is the case, when drawing the trigrams, there was actually no name called "Qian" at that time; the first line was simply Taiji. Drawing Taiji as a circle was first done by Zhou Dunyi, and Zhu Xi merely used it to emphasize the fundamental principle of the Book of Changes; scholars should not mistakenly think that Fuxi actually had a circular image when drawing the trigrams.

太極之判，始生一奇一偶，而為一畫者二，是為兩儀，其數則陽一而陰二，在《河圖》、《洛書》則奇偶是也。周子所謂“太極動而生陽，動極而靜，靜而生陰，靜極復動，一動一靜，互為其根，分陰分陽，兩儀立焉”，邵子所謂“一分為二”者，皆謂此也。

The Taiji once divided into two, producing one odd and one even, forming two symbols in a single line, which are called the two principles (Wuji and Yijing). In terms of numbers, Yang is one and Yin is two; in the Yellow River Chart and the Luo Writing, these correspond to the odd and even numbers. Zhou Dunyi's "Taiji Tu Shuo" states, "Taiji moves to generate Yang; when movement reaches its extreme, it becomes stillness, and stillness generates Yin; when stillness reaches its extreme, it again becomes movement; movement and stillness alternate, forming the fundamental basis of each other; thus, Yin and Yang are separated, and the two principles are established." Shao Yong's concept of "dividing one into two" refers to this very idea.

集說 朱子答袁樞曰：如所論兩儀，有曰乾之畫奇，坤之畫偶，只此乾坤字便未穩當，蓋儀，匹也，如俗語所謂一雙一對云耳，自此再變至第三畫，八卦已成，方有乾坤之名。當其為一畫之時，方有一奇一偶，只可謂之陰陽，未得謂之乾坤也。

Collected Commentary: Zhu Xi answered Yuan Shu saying: Like your discussion of the two principles, explaining that "the line of Qian is odd, and the line of Kun is even," the mere use of the words "Qian" and "Kun" is inappropriate. "Yi" means matching, like the saying of a pair. Only when it develops to the third line do the Eight Trigrams become complete, and then the names Qian and Kun are used. When it is only one line, it is merely one odd and one even, which can only be called yin and yang, and not yet Qian and Kun.

兩儀生四象“兩儀”之上，各生一奇一偶，而為二畫者四，是謂“四象”，其位則太陽一；少陰二；少陽三；太陰四。其數則太陽九；少陰八；少陽七；太陰六。以《河圖》言之，則六者一而得於五者也，七者二而得於五者也，八者三而得於五者也，九者四而得於五者也。以《洛書》言之，則九者十分一之餘也，八者十分二之餘也，七者十分三之餘也，六者十分四之餘也。周子所謂“水火木金”，邵子所謂“二分為四”者，皆謂此也。

The Great Treatise says, "The two principles give rise to the four images." The启蒙 explains that above the two principles, each generates one odd and one even, forming four symbols of two lines, which is called the "four images." In terms of position, the sun comes first, the lesser yin comes second, the lesser yang comes third, and the greater yin comes fourth. In terms of numbers, the sun is nine, the lesser yin is eight, the lesser yang is seven, and the greater yin is six. Referring to the Yellow River Chart, six is derived by adding one to the central five, seven is derived by adding two to five, eight is derived by adding three to five, and nine is derived by adding four to five. Referring to the Luo Writing, nine is what remains after subtracting one from ten, eight is what remains after subtracting two from ten, seven is what remains after subtracting three from ten, and six is what remains after subtracting four from ten. The "water, fire, wood, metal" four elements discussed in Zhou Dunyi's "Tian Ji Tu Shuo" and the "two divided into four" mentioned by Shao Yong both refer to this principle.

集說 朱子答程迥曰：所謂“兩儀”為乾坤初爻，“四象”為乾坤初二，相錯而成，則恐立言有未瑩者，蓋方其為“兩儀”，則未有“四象”也，方其為“四象”，則未有八卦也，安得先有乾坤之名，初二之辨哉？“兩儀”只可謂之陰陽，“四象”方有太少之別，其序以太陽少陰少陽太陰為次，此序既定，遞升而倍之，適得乾一兌二離三震四巽五坎六艮七坤八之序也。

Collected Commentaries: Zhu Xi answered Cheng Jing, saying: You say that "two principles" (liang yi) are the first lines of Qian and Kun, and "four images" (si xiang) are formed by the mutual crossing of the first and second lines of Qian and Kun. This explanation may not be clear enough. When it was still "two principles," there was no "four images"; when it was still "four images," there was no Eight Trigrams. How could there be the names of Qian and Kun and the distinction between the first and second lines before that? "Two principles" can only be called yin and yang. It is only when reaching "four images" that there is a distinction of "great" (tai) and "small" (shao). The order is Sun (Taiyang), Shao Yin, Shao Yang, Tai Yin. Once this order is established, it doubles at each level, resulting in the sequence of the Eight Trigrams: Qian one, Dui two, Li three, Zhen four, Xun five, Kan six, Gen seven, Kun eight.

又答袁樞曰：“四象”之名，所包甚廣，大抵須以兩畫相重四位成列者為正，而一二三四者其位之次也，七八九六者，其數之實也。其以陰陽剛柔分之者，合天地而言也，其以陰陽太少分之者，專以天道而言也，若專以地道言之，則剛柔又自有太少矣，推而廣之，縱橫錯綜，凡是一物，無不各有四者之象，不但此數者而已矣。《語類》云：《易》中七八九六之數，向來只從揲蓍處推起，雖亦吻合，然終覺曲折太多，疑非所以得數之原。因看“四象”次第，偶得其說，極為捷徑，蓋因一二三四，

Zhu Xi also answered Yuan Shu saying: "The term 'Four Categories' includes a wide range. Basically, the correct interpretation is that they are formed by combining two lines, arranged in a sequence of four positions. One, two, three, and four represent their order of precedence, while seven, eight, nine, and six represent their actual numerical values. When divided by yin, yang, strength, and softness, it refers to both heaven and earth together. When divided by the major and minor of yin and yang, it refers specifically to the heavenly aspect. If referring specifically to the earthly aspect, strength and softness also have their own major and minor distinctions. Extending this further, in all directions and crosswise, any thing will have the images of these four categories, and it is not limited to the several mentioned above." The "Shu Lei" of Zhu Xi says: In the Book of Changes, the numbers seven, eight, nine, and six were originally derived from the process of divination with yarrow stalks. Although they are consistent, it always seemed that the process was too convoluted, and there was doubt about whether these numbers were the original source. Later, by looking at the order of the "Four Categories," he suddenly understood a straightforward explanation, which is based on one, two, three, four... There is a missing text here, and this passage is incomplete. The next part directly follows the text from the "Boming" section titled "The Four Categories Generate the Eight Trigrams."

四象生八卦“四象”之上，各生一奇一偶，而為三畫者八，於是三才略具，而有八卦之名矣，其位則乾一兌二離三震四巽五坎六艮七坤八。在《河圖》，則乾坤離坎分居四實，兌震巽艮分居四虛。在《洛書》，則乾坤離坎分居四方，兌震巽艮分居四隅。《周禮》所謂三《易》“經卦皆八”，《大傳》所謂“八卦成列”，邵子所謂“四分為八”者，皆指此而言也。

The Great Treatise says, "The four images give rise to the eight trigrams." The启蒙 explains that on top of each of the four images, one odd and one even are added, forming the eight trigrams with three lines each. Thus, the positions of heaven, earth, and humanity are roughly complete, and the names of the eight trigrams are established. Their positions are: Qian (Heaven) one, Dui (Lake) two, Li (Fire) three, Zhen (Thunder) four, Xun (Wind) five, Kan (Water) six, Gen (Mountain) seven, and Kun (Earth) eight. In the Yellow River Chart, Qian, Kun, Li, and Kan occupy the four real positions corresponding to the numbers of generation, while Dui, Zhen, Xun, and Gen occupy the four empty positions without numbers. In the Luo Writing, Qian, Kun, Li, and Kan are located in the four cardinal directions of southeast, northwest, northeast, and southwest, while Dui, Zhen, Xun, and Gen are located in the four corners. The Zhou Li discusses the three books of the Yi, namely Lianshan, Guicang, and Zhouyi, all of which have "eight basic trigrams." The Great Treatise says, "The eight trigrams are arranged in order," and Shao Yong says, "four are divided into eight," referring to this.

八卦之上，各生一奇一偶，而為四畫者十六，於經無見，邵子所謂“八分為十六者”是也，又為‘兩儀”之上，各加八卦，又為八卦之上，各加“兩儀”也。案 四畫十六者，為八卦之上，各加“兩儀”，又為“四象”之上，各加四象也。

On top of each of the eight trigrams, one odd and one even are added, forming sixteen symbols of four lines. This is not explicitly stated in the classic texts, which is what Shao Yong referred to as "eight divided into sixteen." Alternatively, one might say that it is adding a pair of trigrams on top of each of the two principles, or adding a pair of trigrams on top of each of the eight trigrams. Note: the sixteen symbols of four lines can be viewed either as adding two principles on top of each of the eight trigrams, or as adding four trigrams on top of each of the four principles.

於經雖無見，然及六十四卦既成之後，以其自二至五，四爻互之，或自初至四，或自三至上，或自四而又至初，或自五而又至二，或自上而又至三，錯綜顛倒互之，皆得《乾》、《坤》、《既濟》、《末濟》、《剝》、《復》、《垢》、《夬》。《漸》，《歸妹》、《大過》、《頤》、《解》、《蹇》、《睽》、《家人》諸卦適合十六之數，孔子於雜卦發其端矣。漢儒互卦之說，蓋本諸此也。邵子詩云：四象相交，成十六事。即以此四畫者，為四象相交者爾，學者誤以上文天地否泰十六卦當之，失其指矣。

The hexagram composed of four lines is not explicitly mentioned in the classic text, but after the sixty-four hexagrams are drawn, the four lines from the second to the fifth are taken as the interacting lines, or the lines from the first to the fourth, or from the third to the top line, or from the fourth line back to the first, or from the fifth line back to the second, or from the top line back to the third. By taking these lines in a reversed and inverted way, the resulting hexagrams are all among the following: Qian, Kun, Ji Ji, Wei Ji, Bo, Fu, Gou, Guai, Zhen, Gui Mei, Da Guo, Yi, Jie, Jian, Kui, Jia Ren. These hexagrams exactly match the number sixteen. (The original text mistakenly writes "Wei Ji" as "Mo Ji" and "Gou" as "Gou".) Confucius in the "Zagua Zhuan" already introduced this idea, and the Han scholars' explanation of the interacting hexagrams is based on this. Shao Yong's poem says, "Four images intersecting, forming sixteen matters," which refers to using these sixteen symbols of four lines as the intersection of the four images. Scholars mistakenly take the sixteen hexagrams of Tian Di Pihui and Tai as the meaning, thus misunderstanding his original intention.

四畫之上，各生一奇一偶，而為五畫者三十二，邵子所謂“十六分為三十二者”是也，又為“四象”之上，各加八卦，又為八卦之上，各加四象也。案 五畫三十二者，自初至三，可互一卦，自三至五，又可互一卦，六十四卦既成之後，依此法錯綜，顛倒互之，則得《復》、《垢》、《頤》、《大過》、《屯》、《鼎》、《恆》、《益》、《豐》、《渙》、《坎》、《離》、《蒙》、《革》、《同人》、《師》、引臨》，《遯》、《成》、《損》、《節》、《旅》、《中孚》、《小過》、《大壯》、《觀》、（大有》、《比》、《夾》、《剝》、（乾》、《坤》諸卦亦適合三十二之數，先儒亦有以是說互卦者，如《損》、《益》皆互《頤》，《頤》象離為龜，故《損》、《益》二五言“十朋之龜”之類。

The four trigrams each generate one odd and one even line above them, forming five lines and thirty-two symbols, which is what Shao Yong called "sixteen divided into thirty-two." Seen from another perspective, this can also be understood as adding one trigram to each of the four trigrams, or adding one trigram to each of the eight trigrams. According to the text, after the sixty-four hexagrams are drawn, by using this method of reversal and inversion, one can derive the following hexagrams: The Reversal, The Meeting, The Nourishing, The Great Exceeding, The Sprouting, The Cauldron, The Perseverance, The Gain, The Abundance, The Dispersing, The Water, The Fire, The Enlightenment, The Change, The Union, The Army, The Approaching, The Retreat, The Sincerity, The Loss, The Moderation, The Traveler, The Middle Trust, The Small Exceeding, The Great Strength, The Observing, The Great Possession, The Following, The Parting, The Breaking, The Heaven, and The Earth. These hexagrams exactly match the number thirty-two. (The original names of the hexagrams have some errors; "gou" should be "gou," "cheng" should be "shan," and "jia" should be "guai.") Previous scholars have also used this method to explain the nuclear hexagram. For example, both the hexagrams The Loss and The Gain produce the hexagram The Nourishing. The image of the hexagram The Nourishing takes the trigram Li (Fire) as the tortoise, so the fifth line of The Loss and the second line of The Gain both mention "ten tortoises," which belongs to this category.

五畫之上，各生一奇一偶，而為六畫者六十四，則“兼三才而兩之”，而八卦之乘八卦亦周，於是六十四卦之名立而《易》道大成矣。《周禮》所謂三《易》之別，皆六十有四，《大傳》所謂“因而重之，爻在其中矣”，邵子所謂“三十二分為六十四者”是也。

In the five lines above, each is further supplemented by one odd and one even line, forming six lines of sixty-four hexagrams, which is what the Great Treatise says "combining the three elements and doubling them." The eight trigrams multiplied by each other reach this completeness. Thus the names of the sixty-four hexagrams are established, and the Way of the Book of Changes is completed. The Zhou Li mentions that the three kinds of hexagrams in the Book of Changes are all sixty-four. The Great Treatise says "thereby doubling them, the lines are included within," and Shao Yong says "thirty-two divided into sixty-four," all referring to this same principle.

若於其上各卦，又各生一奇一偶，則為七畫者百二十八矣；七畫之上又各生一奇一偶，則為八畫者二百五十六矣；八畫之上，又各生一奇一偶，則為九畫者五百十二矣；九畫之上，又各生一奇一偶，則為十畫者乾二十四矣；十畫之上，又各生一奇一偶，則為十一畫者二乾四十八矣；十一畫之上，又各生一奇一偶，則為十二畫者四千九十六矣。

If each trigram is further divided into one odd and one even, it becomes 7 lines with 128 combinations; if each of these 7-line combinations is again divided into one odd and one even, it becomes 8 lines with 256 combinations; if each of these 8-line combinations is again divided into one odd and one even, it becomes 9 lines with 512 combinations; if each of these 9-line combinations is again divided into one odd and one even, it becomes 10 lines with 1024 combinations (the original text mistakenly writes '干' instead of '千'); if each of these 10-line combinations is again divided into one odd and one even, it becomes 11 lines with 2048 combinations; if each of these 11-line combinations is again divided into one odd and one even, it becomes 12 lines with 4096 combinations. Each additional line doubles the number of combinations, which is exactly the case of extending the 'doubling method' beyond six lines.

此焦贛《易林》變卦之數，蓋亦六十四乘六十四也，今不復為圖於此，而略見第四篇中。若自十二畫上，又各生一奇一偶，累至二十四畫，則成千六百七十七萬七千二百一十六變，以四千九十六自相乘，其數亦與此合，引而伸之，蓋未知其所終極也，雖未見其用處，然亦足以見《易》道之無窮矣。

This is exactly the number of changing hexagrams in Jiao Gong's "Yi Lin," which is sixty-four multiplied by sixty-four. No further diagrams are drawn here, as they are briefly mentioned in the fourth section. If one adds one odd and one even number to each of the twelve lines, continuing this process up to twenty-four lines, it results in sixteen million seven hundred seventy-seven thousand two hundred sixteen variations; multiplying four thousand and nine十六 by itself also gives the same number. If we continue to extend and deduce in this way, no one can know where the ultimate limit lies. Although these variations may not show practical use, they demonstrate the boundless nature of the principles of the Book of Changes.

案 《易林》之數，蓋古占筮之法，《洪範》占法，“曰貞曰悔”，夫以八卦變為六十四言之，則八卦貞也，重卦悔也，《春秋傳》“貞風悔山”是也。以六十四卦變為四千九十六言之，則六十四卦貞也，變卦悔也，《春秋傳》“貞屯悔豫”是也，因卦畫之生生無盡，故占筮之變化無窮，焦贛能知其法，而至各綴之以辭則鑿矣，邵朱二子，所為傳心之要者在此。

The "Easy Forest" (Yi Lin) originally refers to the method of divination used in ancient times. The "Hong Fan" mentions the method of divination as "Zhen and Hui." In the case of the eight trigrams transforming into the sixty-four hexagrams, the lower trigrams are called "Zhen," and the upper trigrams, which are superimposed, are called "Hui." The "Zuo Zhuan" records "Zhen Feng Hui Shan" in this manner. In the case of the sixty-four hexagrams transforming into four thousand and nine十六 hexagrams, the primary hexagram is called "Zhen," and the resulting hexagram is called "Hui," as recorded in the "Zuo Zhuan" as "Zhen Tun Hui Yu." Because the hexagram lines are ever-renewing and endless, the changes in divination are also infinite. Jiao Gong understood this method, but he added a short explanation for each hexagram, which was excessive. The reason why Mr. Shao Yong and Mr. Zhu Xi valued and regarded this as essential for transmitting the mind is precisely because of the ever-renewing nature of the hexagram lines.

集說 朱子答林栗曰：太極兩儀四象八卦，生出次第，位置行列，不待安排，而粲然有序，以至於第四分而為十六，第五分而為三十二，第六分而為六十四，則其因而重之，亦不待用意推捧，而與前之三分焉者，未嘗不吻合也。比之並累三陽以為乾，連疊三陰以為坤，然後以意交錯而成“六子”，又先畫八卦於內，復畫八卦於外+以旋相加而

Collected Commentary: Zhu Xi answered Lin Li, saying: The order in which the Taiji, two principles, four images, and eight trigrams arise, as well as their arrangement in sequence, do not require human intervention; they naturally appear in an orderly manner. Up to the fourth division, which results in sixteen, the fifth division resulting in thirty-two, and the sixth division resulting in sixty-four, the process of "superimposing" them does not require deliberate arrangement (the original text mistakenly writes "pushing" instead of "arranging"), and it is consistent with the results of the previous three divisions in every aspect. This is in contrast to the method of first combining three yang lines to form Qian and three yin lines to form Kun, then arranging the six sons—Zhen, Kan, Gen, Xun, Li, and Dui—by human intention. Furthermore, one first draws the eight trigrams within the inner trigram and then draws the eight trigrams outside the outer trigram, adding them sequentially... The original text here has a missing passage, and this section is incomplete. The text directly continues with another passage from Zhu Xi's answer to Yuan Chu.

又答袁樞曰：若要見得聖人作《易》根原直截分明，不如且看卷首橫圖，自始初只有兩畫時，漸次看起，以至生滿六畫之後，其先後多寡既有次第，而位置分明不費辭說，於此看得，方見六十四卦全是天理自然挨排出來，聖人只是見得分明，便只依本畫出，元不曾用一豪智力添助。蓋本不繁智力之助，亦不容智力得以助於其間也。

Zhu Xi also answered Yuan Shu saying: If one wants to see clearly and directly the origin of the Book of Changes as interpreted by the sages, it is better to first look at the horizontal diagram at the beginning of the text. Start from the time when there were only two lines, and proceed step by step until all six lines are formed. The order of succession, the number of lines, and their positions are originally clear and orderly, requiring no verbal explanation. Only after understanding this can one realize that all sixty-four hexagrams are naturally arranged according to the principles of heaven and earth. The sages merely saw clearly and drew them according to their original form, without adding anything at all. Because there was no need for intelligence to help, and there was no room for intelligence to interfere.

及至卦成之後，逆顧縱橫，都成義理，千般萬種，其妙無窮，卻在人看得如何，而各因所見為說，雖若各不相資，而實未嘗相悖也。蓋自初未有畫時，說到六畫滿處者，邵子所謂“後天之學”也，卦成之後，各因一義推說，邵子所謂“先天之學”也。先天後天既各自為一義，而後天說中，取義又多不同，彼此自不相妨，不可執一而廢百也。

After the hexagram has been drawn, looking at it vertically and horizontally, everywhere there is meaning and principle, with countless variations and infinite applications, depending on how one looks at it. Each person establishes their own interpretation according to their own understanding. These interpretations may seem to be mutually unhelpful, but in reality they do not contradict each other. Generally speaking, the approach that starts from the beginning before the hexagram is drawn and continues until the six lines are fully drawn is what Shao Yong called "Earlier Heaven Learning." The approach that, after the hexagram is completed, derives meaning and establishes explanations based on a single principle is what Shao Yong called "Later Heaven Learning" (the original text here reverses the terms "Earlier Heaven" and "Later Heaven"). Since "Earlier Heaven" and "Later Heaven" each form their own system of principles, and the meanings derived in the "Later Heaven" approach vary, they do not interfere with each other. One should not rigidly adhere to one interpretation and discard all others.

《浯類》問自一陰一陽，見一陰一陽又各生一陰一陽之象，以圖言之，兩儀生四象，四象生八卦，節節推去，固容《易》見，就天地間著實處，如何駿得？曰：一物上又自各有陰陽，如人之男女陰陽也，逐人身上，又各有這血氣，血陰而氣陽也，如晝夜之間，晝陽而夜陰也，而晝陽自午後又屬陰，夜陰自子後又屬陽，便是陰陽各生陰陽之象。

The Shu Leiclass by Master Zhu records that someone asked, if from the principle of yin and yang, one can further observe that each yin and yang gives rise to another yin and yang, then in terms of diagrams, two principles (two yi) generate four images (four xiang), four images generate the eight trigrams, and so on, which is easy to understand. However, when considering actual things in the world, how can this be verified? (The original text mistakenly wrote 'easy' as '容《易》' and 'verified' as '骏得'.) Master Zhu answered: Each thing has its own yin and yang. For example, distinguishing between male and female is yin and yang; each person has blood and qi within their body, where blood belongs to yin and qi belongs to yang. Another example is day and night, where day belongs to yang and night belongs to yin. However, the yang of the day turns into yin from noon onwards, and the yin of the night turns into yang after midnight — this is the image of yin and yang giving rise to yin and yang again.

又云：先天圖直是精微，不起子康節，希夷以前元有，只是秘而不傳，次第是方士輩所相傳授，《參同契》中，亦有些意思相似，揚雄《太玄》，全模仿《易》，他底用三數，《易》卻用四數，他本是模《易》，故就他模底句上看《易》，也可略見得《易》意思。

Master Zhu said again that the Earlier Heaven diagram is really subtle and profound. It was not started by Shao Kangjie. The original version existed before Chen Xiyi, but it was kept secret and not passed on outside. It was probably handed down secretly by generations of practitioners of divination. There are also some similar ideas in the "Compendium of the Three" from the Zhou Changes. Yang Xiong's "Ta Xuan" is entirely imitating the Zhou Changes. His system uses a ternary counting method, while the Zhou Changes uses a quaternary counting method. Since he was imitating the Zhou Changes, by looking at his imitative passages, one can roughly understand some meaning of the Zhou Changes.

又云：自有《易》以來，只有邵子說得此圖如此齊整，如揚雄（太玄》，便零星補湊得可笑。若不補，又卻欠四分之一，補得來，又卻多四分之三，如《潛虛》之數用五，只似如今算位一般，其直一畫則五也，下橫一畫則為六，模二畫則為七，蓋亦補湊之書也。

The Master Zhu said again that since the Book of Changes came into being, only Shao Yong has explained this diagram so clearly and systematically. For instance, Yang Xiong's Tai Xuan is pieced together in a haphazard way, which is quite laughable: if you do not complete it, it is missing a quarter; if you do complete it, you have added three quarters more. As for Sima Guang's Potentia Vacua, the numbers used are based on five, which is like arranging counting rods today: a vertical stroke represents five, and adding a horizontal stroke below makes it six, and another stroke makes it seven — it is also a work that has been compiled by patching together.

黃氏瑞節曰：先天圖與太極圖同時而出，周邵二子不相聞，則二圖亦不相通，此勿論也。陳瑩中云：司馬文正與康節同時友善，而未嘗有一言及先天之學，邵伯溫云，伊川在康節時，於先天之學非不問，不語之也。即二先生之論，則先天圖在當時，豈猶未甚著邪，陳瑩中云，先天之學，以心為本，其在《經世書》者，康節之餘事耳。又曰：闡先聖之幽，微先天之顯，不在康節之書乎，然則朱子以前表章尊敬此圖者，了翁為有見也。

Huang Ruijie said: The Earlier Heaven diagram and the Taiji diagram appeared at the same time. Zhou Dunyi and Shao Yong did not communicate with each other, so the two diagrams could not have been mutually connected. Let us not discuss this point. Chen Guan said that Sima Guang and Shao Kangjie were contemporaries and had a good relationship, yet they never mentioned the study of Earlier Heaven. Shao Bowen said that Cheng Yi, before Shao Kangjie's death, did not fail to ask about the study of Earlier Heaven, but Shao Kangjie was unwilling to tell him. From the remarks of these two scholars, can we not see that the Earlier Heaven diagram was not very prominent at that time? Chen Guan also said that the study of Earlier Heaven takes the mind as its foundation, and what is recorded in The Supreme Principles Governing the World is merely a secondary matter for Shao Kangjie. He also said that explaining the hidden teachings of the ancients and revealing the clear meaning of Earlier Heaven is precisely found in Shao Kangjie's writings. Thus, among those who praised and honored this diagram before Zhu Xi, Chen Laojun was the most insightful.

天地定位，山澤通氣，雷風相薄，水火不相射，八卦相錯，數往者順，知來者逆，是故《易》，逆數也。雷以動之，風以散之，雨以潤之，日以晅之，艮以止之，兌以說之，乾以君之，坤以藏之。

The Sayings on the Trigrams states: Heaven and Earth each take their proper position, mountains and marshes communicate with each other through their energies, thunder and wind interact with each other, water and fire do not despise each other, and the Eight Trigrams thus interconnect in pairs. When numbers have already passed, they are deduced in a forward direction; when knowing what is to come, they are deduced in a reverse direction. Therefore, the Book of Changes is a discipline that reverses to foresee the future. It also says: Thunder is used to move all things, wind is used to scatter all things, rain is used to nourish all things, the sun is used to dry all things, mountain is used to stop all things, lake is used to please all things, heaven is used to rule over all things, and earth is used to gather all things.

邵子曰：此一節，明伏羲八卦也。八卦相錯者，明交相錯而成六十四也，“數往者順，若順天而行，是左旋也，皆已生之卦也，故云“數往”也。“知來者謹”，若逆天而 自震之初為冬至，離兌之中為春分，以至於乾之末而交夏至焉，皆進而得其已生之卦，猶自今日而追數昨日也，故曰“數往者順”。其右方，自巽之初為夏至，坎艮之中為秋分，以至於坤之末而交冬至焉，皆進而得其未生之卦，猶自今日面逆計來日也，故曰“知來者逆”，然本《易》之所以成，則其先後始終，如橫圖及圓圖右方之序而已，故曰“《易》逆數也。”

Shao Yong said: The section of "Shuo Gua" is about the eight trigrams of Fuxi. The phrase "the eight trigrams are intermingled" means that the eight trigrams are interwoven to form the sixty-four hexagrams. "Counting the past in the direction of the heavens" refers to following the direction of the heavens' movement, which is a leftward rotation, and the hexagrams counted in this way are those that have already been formed, hence called "counting the past." "Knowing the future by going against the heavens" refers to moving against the direction of the heavens... the original text here has a missing character ("jin" is a miswriting of "ni," which means "against"). The following part continues with the right half of the circular diagram. Starting from the trigram Zhen, which corresponds to the beginning of the winter solstice, passing through Li and Dui in the middle corresponds to the spring equinox, and continuing up to the end of Qian, which connects to the summer solstice, the hexagrams obtained by following this path are all those that have already been formed, like counting backwards from today to yesterday, hence called "counting the past." The right half of the circular diagram starts from the trigram Xun, which corresponds to the beginning of the summer solstice, passing through Kan and Gen in the middle corresponds to the autumn equinox, and continuing up to the end of Kun, which connects to the winter solstice, the hexagrams obtained by following this path are all those that have not yet been formed, like calculating forward from today to tomorrow (the original text has "er" miswritten as "mian"). Therefore, it is said "the Book of Changes is counted in reverse."

集說 《朱子語類》云：若自乾一橫排至坤八，此則全是自然，故《說卦》云： “《易》逆數也。”皆自己生以得末生之卦，若如圓圖，則須如此，方見陰陽消長次第，震一陽，離兌二陽，乾三陽，巽一陰，坎艮二陰，坤三陰，雖似稍涉安排，然亦莫非自然之理。

Collected Commentaries: Master Zhu said that if the trigrams from Qian one to Kun eight are arranged in a straight line, this is entirely in the natural order of generation. Therefore, the "Commentary on the Trigrams" states that "The Book of Changes is inverse in its numbering," which refers to deriving the ungenerated trigrams from the already generated ones. If arranged in a circular diagram, such an arrangement is necessary to show the sequence of the waxing and waning of yin and yang: Zhen is one yang, Li and Dui are two yang, and Qian is three yang; Xun is one yin, Kan and Gen are two yin, and Kun is three yin. Although this arrangement appears to have some artificiality, it is entirely in accordance with natural principles.

附錄 項氏安世曰：“數往者順”，以指上文，“知來者逆”，以指下文，“是故《易》逆數也”，此一句以起下文八句也。上文據八卦已成之後，對面數之，其序順而理明，故曰“數往者順”。下文據八卦始畫之初，左右對畫，而上下逆生，故曰“知來者逆”。非聖人於順之外別為逆象也，此之逆象，即上文之順象。

Appendix: Xiang Anshi says, "To count the past is to follow the order" refers to the previous sentences "Heaven and Earth are positioned," and "To know the future is to go against the order" refers to the following sentences "Thunder moves it." The sentence "Therefore, the Book of Changes is inverse in its counting" is used to introduce the following eight sentences. The previous part refers to the situation after the Eight Trigrams have already been drawn, counting them face to face in a sequential order, which is clear in its reasoning, hence "To count the past is to follow the order." The following part refers to the situation when the Eight Trigrams were first drawn, with strokes written from left to right and from bottom to top in an inverse manner, hence "To know the future is to go against the order." It is not that the sage created an inverse image in addition to the natural order; the so-called inverse image here is actually the same as the previous natural order.

章氏潢曰：自乾純陽，歷兌離以至一陽之震，自坤純陰，歷艮坎以至一陰之巽，非數往之順乎？自震一陽，歷離兌以至乾之純陽，自巽一陰，歷坎艮以至坤之純陰，非知來之逆乎？左旋則總為“知來”，有旋則總為“數往”，但《易》以“知來”為主，生生不窮，是以逆而數之。

Zhang Huang said: Starting from Qian, the pure yang trigram, passing through Dui and Li to reach Zhen, the trigram of one yang; starting from Kun, the pure yin trigram, passing through Gen and Kan to reach Xun, the trigram of one yin—this is not precisely the "numbering the past" in sequence? Starting from Zhen, the trigram of one yang, passing through Li and Dui to reach Qian, the trigram of pure yang; starting from Xun, the trigram of one yin, passing through Kan and Gen to reach Kun, the trigram of pure yin—this is not precisely the "knowing the future" in reverse? Turning to the left, overall it is "knowing the future"; turning to the right (the original text mistakenly says "you" instead of "right"), overall it is "numbering the past." However, the Book of Changes mainly focuses on "knowing the future," because it reflects the endless generation and transformation, so it requires counting in reverse.

案 邵子所謂左旋者，猶言向左而旋耳。所謂右行者，猶言向右而行耳，與歷家所謂左旋右轉，義正相反，各為一說也。其所謂“已生一未生”，正指陰陽生生而言，如章氏之說，而項氏說尤得前後聯貫語氣。蓋其順數者，既如上文所列矣，而圖之作，主於逆數，故其終始生成，又如下文之所敘也。朱子之解似又自為一說，學者分別觀之。

The "left rotation" mentioned by Shao Yong merely refers to rotating to the left, and the "right movement" simply means moving to the right. These are exactly opposite in meaning to the left and right movements described by astronomers. Each represents a different way of expressing the concept. The "already born" and "not yet born" mentioned by him refer to the continuous generation of yin and yang, which aligns with Zhang Huang's explanation. Xiang Anshi's interpretation is even more consistent with the coherent tone. Generally speaking, the sequence of the count in the correct order has already been listed above. However, the purpose of drawing the diagram is based on the reverse counting, so the order of generation from beginning to end is as described below. Zhu Xi's explanation seems to form its own separate view, and scholars should examine them separately.

又曰：太極既分，兩儀立矣，陽上交於陰，陰下交於陽，而四象生矣。陽交於陰，陰交於陽，而生天之四象。剛交於柔，柔交於剛，而生地之四象。八卦相錯，而後萬物生焉，是故一分為二，二分為四，四分為八，八分為十六，十六分為三十二，三十二分為六十四。猶根之有乾，乾之有枝，愈大則愈小，愈細則愈繁。

Shao Yong also said: After the Taiji has been divided, the two principles are established. Yang goes upward to meet Yin, and Yin goes downward to meet Yang, thus the four images are generated. When Yang meets Yin and Yin meets Yang, the heavenly four images are produced. When strength meets flexibility and flexibility meets strength, the earthly four images are produced. The eight trigrams interact and intertwine, then all things are generated. Therefore, one divides into two, two into four, four into eight, eight into sixteen, sixteen into thirty-two, and thirty-two into sixty-four. This is like the roots of a tree producing the trunk, and the trunk producing branches: the whole becomes larger as it grows, while the branches become smaller as they divide. The more detailed the division, the more numerous the branches become.

集說 《朱子語類》：問：程《易》乾辭下解云，聖人始畫八卦，三才之道備矣，因而重之，以盡天下之變，故六畫而成卦。或疑此說卻是聖人始畫八卦，每卦便是三畫，聖人因而重之為六畫，似與邵子一分為二，而至六十四為六畫，其說不同。曰：程子之意，只雲三畫上疊成六畫，八卦上疊成六十四耳，與耶子說誠異，蓋康節此意，不曾說與程子，程於亦不曾問之，故一向只隨他所見去。但程子說聖人始畫八卦，不知聖人畫八卦時，先畫甚卦，此處便曉不得。

Collected Commentaries: The "Collected Sayings of Master Zhu" records that someone asked: In the "Commentary on the Book of Changes" by Cheng Yi, under the Hexagram Statement of the Qian Hexagram, it says, "When the sage first drew the Eight Trigrams, the principles of the three realms were complete, and then they were overlapped to exhaust all changes in the world, thus forming a hexagram with six lines." Someone doubted that this explanation suggests that the sage drew the Eight Trigrams at once, with each trigram consisting of three lines, and then overlapped them to form six lines, which seems different from Shao Yong's explanation that starts from one divided into two, continuing until sixty-four, resulting in six lines. Master Zhu answered: Cheng Yi's meaning was simply that three lines were overlapped to form six lines, and the Eight Trigrams were overlapped to form the sixty-four Hexagrams. This is indeed different from Shao Yong's view. Kangjie did not explain this point to Cheng Yi, and Cheng Yi also did not ask him about it, so he continued to explain according to his own understanding. However, Cheng Yi said that the sage first drew the Eight Trigrams, but he did not know which trigram the sage first drew — this part does not make sense.

是故乾以分之，坤以翕之，震以長之，巽以消之。長則分，分則消，消則翕也，乾坤定位也，震巽一交也，兌離坎艮再交也，故震陽少而陰尚多也，巽陰少而陽尚多也，兌離陽浸多也，坎艮陰浸多也。

Shao Yong continued to say: Therefore, Qian is used to differentiate and expand, Kun is used to gather and collect. Zhen is used to promote growth, Xun is used to retreat and dissipate. When growth occurs, differentiation follows; when differentiation occurs, retreat follows; when retreat occurs, gathering follows. Qian and Kun establish the positions of upper and lower. Zhen and Xun represent the first interaction of yin and yang. Dui, Li, Kan, and Gen represent the second interaction. Therefore, the Zhen hexagram has few yang lines and many yin lines, while the Xun hexagram has few yin lines and many yang lines; the Dui and Li hexagrams have gradually increasing yang lines, while the Kan and Gen hexagrams have gradually increasing yin lines.

又曰：無極之前，陰含陽也，有象之後，陽分陰也。陰為陽之母，陽為陰之父，故母孕長男而為《復》，父生長女而為《姤》，是以陽起於《復》，陰起於《垢》也。案 周子所謂“無極而太極”者，以陰陽之奉體言之，《中庸》所謂“天命之性”也。邵子所謂“無極”者，以動靜之樞紐言之，<中庸》所謂“未發之中”也。天命之性，固周流而無不在，然人生而靜，天之性也，則沖漠無暇之時，乃本體之真之所以具，故周子亦言主靜，程子言其本也，真而靜，三子之說，實相發明而不相悖也。

Shao Yong also said: Before the ultimate void, yin contained yang; after there was form, yang differentiated into yin. Yin is the mother of yang, and yang is the father of yin. Therefore, the mother gave birth to the eldest son and formed the hexagram of Fu, and the father gave birth to the eldest daughter and formed the hexagram of Guo. Thus, yang energy begins with Fu, and yin energy begins with Guo (the original text mistakenly wrote 'Gou' instead of 'Guo'). Note: Zhou Dunyi's statement 'from the ultimate void comes the supreme ultimate' refers to the essence of yin and yang, which is the same as the 'heavenly mandate is called nature' in the Zhongyong. Shao Yong's concept of 'ultimate void' refers to the pivot of movement and stillness, which corresponds to the 'unexpressed middle' in the Zhongyong. Although the heavenly mandate and nature are pervasive and present everywhere, the 'human being is born in stillness, which is the nature of heaven' from the Liji's Yujì says that when there is nothingness and no trace (the original text mistakenly wrote 'wu xia' instead of 'wu zhen'), that is the place where the true essence of the original nature is fully complete. Therefore, Zhouzi also advocated 'maintaining stillness,' and Chengzi said 'its origin is truly and still.' The views of these three masters actually complement each other and do not contradict.

又曰：震始交陰而陽生，巽始消陽而陰生。兌，陽長也，艮，陰長也，震兌，在天之陰也，巽艮，在地之陽也，故震兌上陰而下陽，巽艮上陽而下陰。天以始生言之，故陰上而陽下，交泰之義也。地以既成言之，故陽上而陰下，尊卑之位也。乾坤定上下之位，坎離列左右之門，天地之所闔闢，日月之所出入，春夏秋冬，晦朔弦望，晝夜長短，行度盈縮，莫不由乎此矣。震始交陰而陽生，是說圓圖震與坤掛而一陽生也，巽始消陽而陰生，是說圓圖巽與乾接而二陰生也。

Shao Yong also said: Zhen represents the beginning of the meeting with yin and the emergence of yang energy; Xun represents the beginning of the decline of yang and the emergence of yin energy. Dui represents the growth of yang energy, and Gen represents the growth of yin energy. Zhen and Dui belong to the side of heaven and are yin, while Xun and Gen belong to the side of earth and are yang. Therefore, the two trigrams Zhen and Dui have yin lines above and yang lines below, while the two trigrams Xun and Gen have yang lines above and yin lines below. Heaven refers to the initial birth of all things, so yin is above and yang is below, representing the harmonious union of heaven and earth. Earth refers to the completion of all things, so yang is above and yin is below, representing the established hierarchy. Qian and Kun fix the positions of above and below, while Kan and Li form the left and right gates. The opening and closing of heaven and earth, the rising and setting of the sun and moon, the four seasons of spring, summer, autumn, and winter, the phases of the moon such as waning, full, and crescent, the length of day and night, and the waxing and waning of movement all originate from this. The phrase "Zhen begins to meet yin and yang is born" means that in the circular diagram, Zhen is connected to Kun and one yang line is generated. The phrase "Xun begins to decline yang and yin is born" means that in the circular diagram, Xun is connected to Qian and one yin line is generated (the original text mistakenly writes "two yin lines" instead of "one yin line").

集說 邵子曰：陽爻，晝數也；陰爻，夜數也。天地相銜，陰陽相交，故晝夜相離，剛柔相錯。春夏，陽也，故晝數多，夜數少。秋冬，陰也，故晝數少，夜數多。胡氏方平曰：此一節先論震巽艮兌四維之卦，而後及於乾坤坎離四正之位。震始交陰而陽生，以震接坤言也，至兌二陽，則為陽之長。巽始消陽而陰生，以巽接乾言也，至艮二陰則為陰之長。震兌在天之陰者，邵子以震為天之少陰，兌為天之太陰，唯其為陰，故陰爻皆在上，而陽爻皆在下。天以生物為主，始生之初，非交泰不能，故陰上陽下，而取交泰之義。

Collected Explanations: Shao Yong said that a yang line represents the number of day, while a yin line represents the number of night. Heaven and earth connect with each other, and yin and yang interact, so day and night are separated, and the strong and the gentle are intermingled. Spring and summer belong to yang, so the number of day is more and the number of night is less; autumn and winter belong to yin, so the number of day is less and the number of night is more. Hu Fangping said: this passage first discusses the four trigrams located at the four corners, namely Zhen, Xun, Gen, and Dui, and then proceeds to mention the four trigrams located at the four cardinal directions, namely Qian, Kun, Kan, and Li. "Zhen begins to meet yin and yang is generated" refers to the connection between Zhen and Kun, and when Dui becomes two yang lines, it signifies the growth of yang. "Xun begins to eliminate yang and yin is generated" refers to the connection between Xun and Qian, and when Gen becomes two yin lines, it signifies the growth of yin. Zhen and Dui are called "yin in heaven" because Shao Yong regarded Zhen as the lesser yin of heaven and Dui as the greater yin of heaven. Since they belong to yin, the yin lines are above and the yang lines are below. Heaven is primarily about generating life, and at the beginning of the birth of all things, mutual interaction is essential, so the yin is above and the yang is below, symbolizing the meaning of mutual interaction.

巽艮在地之陽者，邵子以巽為地之少剛，艮為地之太剛，唯其為剛，故陽爻皆在上，而陰爻皆在下。地以成物為主，既成之後，則尊卑定，故陰下陽上，而取尊卑之位。乾坤定上下之位，天地之所闔闢也，坎離列左右之門，日月之所出入也。歲而春夏秋冬，月而晦朔弦望，日而晝夜行度，莫不胥此焉出，豈拘拘爻畫陰陽之間哉。

The trigrams Xun and Gen are called "the yang of the earth," because Shao Yong regarded Xun as the minor yang of the earth and Gen as the major yang of the earth. Because they belong to yang, the yang lines are all above and the yin lines are all below. The earth is mainly about forming things; after all things are formed, the hierarchy is established, so yin is below and yang is above, taking the positions of hierarchy. Qian and Kun fix the positions of above and below, which are the place where heaven and earth open and close; Kan and Li form the left and right gates, which are the places where the sun and moon rise and set. The seasons of spring, summer, autumn, and winter in a year, the phases of the moon in a month, and the day and night in a day, all arise from here. How could it be confined merely to the forms and traces of the lines and yin and yang?

又曰：乾四十八而四分之，一分為陰所克也，坤四十八而四分之，一分為所克之陽也，故乾得三十六，而坤得十二也。兌離以下更思之。今按，兌離二十八陽二十陰，震二十陽二十八陰，艮坎二十八陰二十陽，巽二十陰二十八。

Shao Yong also said: The number of Qian is forty-eight, which is divided into four parts, one part being taken away by yin, so Qian actually has thirty-six. The number of Kun is also forty-eight, which is divided into four parts, one part being taken away by yang, so Kun actually has twelve. As for Dui and Li and the following trigrams, they need to be further carefully considered. Now according to the text: Dui and Li trigrams consist of twenty-eight parts of yang and twenty parts of yin, Zhen trigram consists of twenty parts of yang and twenty-eight parts of yin, Gen and Kan trigrams consist of twenty-eight parts of yin and twenty parts of yang, Xun trigram consists of twenty parts of yin and twenty-eight parts of yang—the last sentence of the original text is missing the character 'yang'.

又曰：乾坤縱而六子橫，《易》之本也。又曰：陽在陰中，陽逆行，陰在陽中，陰逆行，陽在陽中，陰在陰中，則皆順行，此真至之理，按圖可見之矣。又曰：《復》至《乾》凡百一十有二陽，《垢》至《坤》凡八十陽，《垢》至《坤》凡百一十有二陰，《復》至《乾》凡八十陰。

Shao Yong also said: The trigrams Qian and Kun are arranged vertically, while the six sons are arranged horizontally. This is the fundamental principle of the Book of Changes. He also said: When Yang is in the middle of Yin, Yang moves in reverse; when Yin is in the middle of Yang, Yin moves in reverse; when Yang is in the middle of Yang and Yin is in the middle of Yin, they both move in the correct direction. This is the true and unchanging principle. Looking at the diagram will make it clear. He also said: Counting from the Fu hexagram to the Qian hexagram, there are a total of 112 Yang lines; counting from the Gou hexagram to the Kun hexagram, there are a total of 80 Yang lines; counting from the Gou hexagram to the Kun hexagram, there are a total of 112 Yin lines; and counting from the Fu hexagram to the Qian hexagram, there are a total of 80 Yin lines (the original text mistakenly writes 'Gou' twice as 'Gou').