Yang Dao Sheng's Circular Diagram Explanation of the First Line

兩儀既判，極天下之至變，若非兩儀之妙也。則極天下之至變，莫不有兩儀之之象也。圜圖初爻三十二陽居左，三十二陰居右，合而則一陰一陽也。乾至復坤至姤之卦備而兩儀立矣。

When the two principles (yin and yang) are divided by the single principle (the One), the world undergoes extreme transformation, and nothing is not the subtle application of the two principles; the world undergoes extreme transformation, and nothing does not carry the image of the two principles. At the bottom of the circular diagram, the first line has thirty-two yang lines on the left and thirty-two yin lines on the right. When viewed together, they form one yin and one yang. From the hexagram Qian to Fu, and from Kun to Guo, all the hexagrams are complete, and the two principles are thus established in the diagram.

兩儀生四象，則極天下之至變，莫非四象之妙也。極天下之至變，莫不有四象之象也。圜圖二爻乾至臨十六陽，而間同人至復十六陰。坤至遯十六陰，而間師至姤十六陽。合之則二陽二陰，四象之象也。又合南三十二皆陽，北三十二皆陰，非即兩儀哉。

The two principles (yin and yang) give rise to the four images (the four trigrams), thus the changes in the world reach their extreme, and nothing is not the result of the subtle workings of the four images; the changes in the world reach their extreme, and nothing does not carry the form of the four images. Looking at the circular diagram, counting upward from the bottom, the second line: from the Trigram Qian to the Trigram Lin consists of sixteen yang lines, with sixteen yin lines in between, from Tongren to Fu; from the Trigram Kun to Dun consists of sixteen yin lines, with sixteen yang lines in between, from Shi to Gou. When viewed together, this is two yang and two yin alternating, which is exactly the form of the four images. If we then consider the southern half, which consists of thirty-two yang lines, and the northern half, which consists of thirty-two yin lines, combined together, this is again the two principles.

四象生八卦，則天下之至變，莫非八卦之妙也。極天下之至變，莫非有八卦之象也。圜圖三爻乾至泰八陽，而間履至臨八陰。坤至否八陰，而間謙至遯八陽。姤至升復至無妄，而間訟至師明夷至同人，八卦之象也。合之則四陽四陰，八卦而即四象也。

The four images gave rise to the eight trigrams, and thus the changes in the world reached their extreme, with nothing not being the subtle application of the eight trigrams; the changes in the world reached their extreme, and nothing failed to carry the image of the eight trigrams. Looking at the circular diagram's third line: from the trigram Qian to Tai, there are eight yang lines, with the eight yin lines from Li to Lin in between; from Kun to Po, there are eight yin lines, with the eight yang lines from Qian to Dun in between; from Gou to Sheng, and from Fu to Wuwang, these two sections are also separated by the eight lines from Song to Shi, and from Mingyi to Tongren. This is the image of the eight trigrams. When viewed together, it is four yang lines and four yin lines alternating, and the eight trigrams are essentially the doubling of the four images.

八而倍之，十六所自起也。極天下之至變，莫不有八卦之象，則亦莫不有十六之象也。圜圖四爻乾至大壯四陽也，而間小畜至泰四陰。履至歸妹、同人至豐、無妄至震之間中孚至臨、家人至明夷、益至復，法皆仝矣。坤至觀四陰也，而間豫至否四陽。謙至漸、師至渙、升至巽之間小過至遯、解至訟、恆至姤，法皆同矣。合之則八陰八陽，十六之象即八卦之象也。而以四相間，又非四象乎。

Eight trigrams doubled become sixteen, which is the origin of the number sixteen. When the changes in the world reach their extreme, nothing lacks the image of the eight trigrams, so nothing also lacks the image of sixteen. Looking at the circular diagram's fourth line: from Qian to Da Zhuang there are four yang lines, with four yin lines in between, from Xiao Xu to Tai; in addition, from Li to Gui Mei, from Tong Ren to Feng, and from Wu Wang to Zhen, each of these sections has four yin lines in between, from Zhong Fu to Lin, from Jia Ren to Ming Yi, and from Yi to Fu, and the arrangement is exactly the same. From Kun to Guan there are four yin lines, with four yang lines in between, from Yu to Pǒ; in addition, from Qian to Jie, from Shi to Huan, and from Sheng to Xun, each of these sections has four yang lines in between, from Xiao Guo to Dun, from Jie to Song, and from Heng to Gou, and the arrangement is exactly the same. When viewed together, it is eight yin and eight yang, making sixteen, which is the doubling of the image of the eight trigrams; and since it is arranged with four lines as a section, it is not also the four yin and four yang, the four images?

十六又倍之，三十二所自起也。則有十六之象也，莫不有三十二之象也。圜圖五爻履兌二陽而間二陰之睽歸妹，謙艮二陰而間二陽之蹇漸。餘五十六卦之相間，莫不皆然。合之則十六陽十六陰，十六之象即三十二之象也。而相間以二，亦即兩儀之象也。

Sixteen doubled is thirty-two, which is the origin of the number thirty-two. Since there is the image of sixteen, there is no reason it should not also carry the image of thirty-two. Looking at the circular diagram's fifth line: The hexagrams "Zhu" and "Dui" are two yang lines, with the hexagrams "Kui" and "Gui Mei" in between, which are two yin lines; the hexagrams "Qian" and "Gen" are two yin lines, with the hexagrams "Jian" and "Jian" in between, which are two yang lines. The remaining fifty-six hexagrams are also arranged in this alternating pattern. When viewed as a whole, there are sixteen yang lines and sixteen yin lines. The image of sixteen is half of the image of thirty-two; and the arrangement of two lines as a section alternately is the image of the two principles.

卦之有六十四，生於三十二也。推而上之，生於一。一與二，三十二與六十四，卦之終始也。圜圖上爻一陰一陽相間而列。合之則三十二陽、三十二陰，六十四之象即三十二之象也。而陰陽相間以一為率，兩儀之象即太極之象也。

There are sixty-four lines in the hexagrams, which come from doubling thirty-two; tracing back layer by layer, they ultimately originate from 'one'. One and two correspond to thirty-two and sixty-four, representing the end and beginning of the hexagrams. Looking at the top line of the circular diagram, it shows yin and yang alternating; when viewed together, it consists of thirty-two yang lines and thirty-two yin lines. The image of sixty-four is simply the image of thirty-two doubled. Yin and yang alternate in one line as a section, and the image of the two principles ultimately comes down to the image of the Taiji.

《周易》始於乾坤，終於既濟未濟，一經之終始也。上經始於乾坤，終於坎離。下經始於咸恆，終既濟未濟。一分為二而各有終始也。始於乾坤，中於泰否，終於坎離，為上經。始於咸恆，中於損益，終於既濟未濟，為下經。上下經之各有始各有中各有終，所以成一經之始於乾坤終於既濟未濟也。

The Zhou Changes begins with the trigrams Qian (Heaven) and Kun (Earth), and ends with Ji Ji (Completion) and Wei Ji (Not Yet Completed), forming the beginning and end of the entire book. The Upper Classic starts with Qian and Kun, and ends with Kan (Water) and Li (Fire); the Lower Classic starts with Xian (Mutual Attraction) and Heng (Permanence), and ends with Ji Ji and Wei Ji. The entire book is divided into two parts, each with its own beginning, middle, and end. The Upper Classic begins with Qian and Kun, has in the middle Tai (Harmony) and Po (Opposition), and ends with Kan and Li. The Lower Classic begins with Xian and Heng, has in the middle Shen (Loss) and Yi (Gain), and ends with Ji Ji and Wei Ji. Each part has its own beginning, middle, and end, and together they form the overall structure of the entire book, which begins with Qian and Kun and ends with Ji Ji and Wei Ji.

而始於乾坤終於既濟未濟者何也。上經言乾坤坎離，實則乾為主坎用事，宗陽也。下經言震巽艮兌，實則坤為主離用事，宗陰也。乾坤坎離，萬象之樞也。故始於乾坤而終於既濟未濟，即始於乾坤而終於坎離也。然不終於坎離而終於既濟未濟何也。

Then why do we begin with Qian and Kun and end with Ji Ji and Wei Ji? The Upper Canon appears to discuss Qian, Kun, Kan, and Li, but in reality it centers on the Qian hexagram with Kan hexagram in charge, emphasizing Yang; the Lower Canon appears to discuss Zhen, Xun, Gen, and Dui, but in reality it centers on the Kun hexagram with Li hexagram in charge, emphasizing Yin. Qian, Kun, Kan, and Li are the fundamental pillars of all phenomena. Therefore, "beginning with Qian and Kun and ending with Ji Ji and Wei Ji" is equivalent to "beginning with Qian and Kun and ending with Kan and Li." But if that is the case, why end with Kan and Li directly, rather than with Ji Ji and Wei Ji?

乾坤立坎離之體，坎離妙乾坤之用。因乾坤之交不交以生坎離之用，因坎離之交不交以章乾坤之體。坎離一乾坤也。乾坤得坎離，則每於不交者正其位。坎離繼乾坤，則必於交其[文瀾本“其”作“者”]呈其能。未言離坎坎[文瀾本“離坎坎”作“坎離首言”]乾坤，曰乾曰坤曰坎曰離，乾坤坎離之不交者也。乾坤之不交，即坎離之不交也。既言泰否，終言既濟未濟。曰泰曰否曰既濟曰未濟，乾坤坎離之交者也。坎離之交，即乾坤之交也。《周易》雖分上下經，雖各有終始。實則始於乾坤，中於坎離，終於既濟未濟。坎離不交即乾坤，而交即既濟未濟。

Heavenly Stems and Earthly Branches form the basis of Kan and Li, and Kan and Li elaborate the functions of Heaven and Earth in a refined manner. The interaction or non-interaction of Heaven and Earth gives rise to the functions of Kan and Li; the interaction or non-interaction of Kan and Li reveals the nature of Heaven and Earth. In the end, Kan and Li are essentially Heaven and Earth. When Heaven and Earth have Kan and Li, they remain in a state of non-interaction, each maintaining its proper position. When Kan and Li take up the role of Heaven and Earth, they must demonstrate their abilities in the place where they interact (here, "交其" is in the Wenlan edition written as "交者"). The opening of the Upper Classic first mentions Heaven, Earth, Kan, and Li (the original text reads "未言离坎坎乾坤," which has an error; in the Wenlan edition, the three characters "离坎坎" are written as "坎离首言"). It discusses Heaven, Earth, Kan, and Li, and these four trigrams all represent the state where Heaven and Earth and Kan and Li do not interact with each other. The non-interaction of Heaven and Earth is also the non-interaction of Kan and Li. Later, it discusses Tai and Po, and finally Ji Ji and Wei Ji, discussing Tai, Po, Ji Ji, and Wei Ji, which all represent the state where Heaven and Earth and Kan and Li interact with each other. The interaction of Kan and Li is also the interaction of Heaven and Earth. Although the Zhou Changes are divided into Upper and Lower Classics, each with their own beginning and end, in reality, they start with Heaven and Earth, proceed through Kan and Li, and conclude with Ji Ji and Wei Ji. When Kan and Li do not interact, they are Heaven and Earth; when they do interact, they become Ji Ji and Wei Ji.

凡震巽艮兌錯行於其間，以成乾坤既濟未濟之終始。乾坤既濟未濟，誠萬象之樞也。盍觀乎圜圖之互卦乎。以六十四卦互得三十二卦。左右八分列，實得一十六卦。曰乾曰夬曰睽曰歸妹曰家人曰既濟曰頤曰復曰姤曰大過曰未濟曰解曰漸曰蹇曰剝曰坤。兩卦而互一卦，亦四卦而互一卦也。又以其三十二卦互之得十六卦。左右重列，實得四卦。曰乾曰既濟曰未濟曰坤。

The trigrams Zhen, Xun, Gen, and Dui are interwoven among them, forming the beginning and end structure of Qian and Kun, as well as Ji Ji and Wei Ji. This shows that Qian, Kun, Ji Ji, and Wei Ji are indeed the overall hub of all phenomena. Why not look again at the "Nuclear Hexagram" on the circular diagram (a hexagram formed by the second to fifth lines of another hexagram)? Taking the Nuclear Hexagram from each of the sixty-four hexagrams results in thirty-two hexagrams. When arranged on both sides, they actually consist of only sixteen hexagram names: Qian, Gua, Kui, Gui Mei, Jia Ren, Ji Ji, Yi, Fu, Guo, Da Guo, Wei Ji, Jie, Zhen, Jian, Po, and Kun. Two hexagrams generating one hexagram is equivalent to four hexagrams generating one hexagram. Taking the Nuclear Hexagram from these thirty-two hexagrams results in sixteen hexagrams. When arranged on both sides, they actually consist of only four hexagram names: Qian, Ji Ji, Wei Ji, and Kun.

兩卦而互一卦，亦四卦而互一卦，且八卦而互一卦也。推之六十四卦。則四卦而互一卦，亦八卦而互一卦，且一十六卦而互一卦也。互至於乾坤既濟未濟而窮，蓋互之而仍得乾坤既濟未濟也。以四卦而畫六十四卦，故乾坤既濟未濟為萬象之樞也。故《周易》始於乾坤終於既濟未濟也。既濟未濟一坎離也，坎離一乾坤也。《周易》之始於乾坤，終於既濟未濟。即始於乾坤，終於乾坤也。至[“至”當作“互”、從文瀾本]卦云者，即孔子之所謂雜物撰德也。

This refers to whether two trigrams produce one trigram, or four trigrams produce one trigram, or eight trigrams produce one trigram. When considering the sixty-four trigrams, it is four trigrams that produce one trigram, or eight trigrams that produce one trigram, or sixteen trigrams that produce one trigram. When reaching the four trigrams of Qian, Kun, Ji Ji, and Wei Ji, the process comes to an end, because further mutual interaction results in the same four trigrams. These four trigrams can be used to generate the sixty-four trigrams, so Qian, Kun, Ji Ji, and Wei Ji are the fundamental trigrams of all phenomena. Therefore, the Zhou Yi begins with Qian and Kun and ends with Ji Ji and Wei Ji. In the end, Ji Ji and Wei Ji are essentially Kan and Li, and Kan and Li are essentially Qian and Kun. Thus, the Zhou Yi begins with Qian and Kun and ends with Qian and Kun. The concept of 'mutual trigrams' (originally written as 'to zhi gua', according to the Wenlan edition it should be 'mutual trigrams') is what Confucius refers to as 'combining various things to compose virtue' in the Xici Zhuan.

乾坤，大父母也。乾坤正而八卦正矣，六十四卦俱正矣。陽生於北而極於南，陰生於南而極於北，天之道也。圜圖法天，故乾南而坤北。陽始於東北而盛於西北，陰始於西南而盛於東南，地之道也，方圖法地，故乾西北而坤東南。乾坤運卦體於無窮，圜圖之義也。乾坤交卦體以變化，方圖之義也。此其所異也。由是次乾坤而兌艮，次兌艮而離坎，次離坎而震巽，八卦之位不既正乎。由是一一統八，八其八而六十四卦之位，不俱正乎。

Heaven and Earth are the great parents of the sixty-four hexagrams. When Heaven and Earth are properly positioned, the eight trigrams are properly positioned, and the sixty-four hexagrams are all properly positioned. Yang energy originates from the north and reaches its peak in the south; Yin energy originates from the south and reaches its peak in the north. This is the way of Heaven; the circular diagram follows the pattern of Heaven, so Heaven is placed in the south and Earth in the north. Yang energy originates from the northeast and reaches its peak in the northwest; Yin energy originates from the southwest and reaches its peak in the southeast. This is the way of Earth; the square diagram follows the pattern of Earth, so Heaven is placed in the northwest and Earth in the southeast. Heaven and Earth move the hexagram structure endlessly, which is the purpose of the circular diagram; Heaven and Earth combine to generate change, which is the purpose of the square diagram—the difference between the two diagrams lies here. Following Heaven and Earth come Dui and Gen; following Dui and Gen come Li and Kan; following Li and Kan come Zhen and Xun. Has the position of the eight trigrams not already been properly arranged? From here, one trigram governs the eight trigrams; eight eights multiplied together form sixty-four, so the positions of the sixty-four hexagrams are also properly arranged.

六十四卦成列，相交變化而八卦各居其本位，以為卦主。從計之則乾一兌二離三震四巽五坎六艮七坤八不少紊也。衡計之，則亦乾一兌二離三震四巽五坎六艮七坤八不少紊也。以從衡之間斜計之，仍為乾一兌二離三震四巽五坎六艮七坤八，不少紊也。此其為卦之正，以統夫眾卦也。

The sixty-four hexagrams are arranged in an eight-by-eight square, intersecting with each other to produce changes. The eight trigrams each remain in their original positions, acting as the sovereign of their respective areas. Counting vertically, they are Qian one, Dui two, Li three, Zhen four, Xun five, Kan six, Gen seven, and Kun eight, in perfect order. Counting horizontally, they are also Qian one, Dui two, Li three, Zhen four, Xun five, Kan six, Gen seven, and Kun eight, in perfect order. Counting diagonally across the square, they remain Qian one, Dui two, Li three, Zhen four, Xun five, Kan six, Gen seven, and Kun eight, in perfect order. This is the 'correct position' of the eight pure trigrams, which serves to govern the other hexagrams.

卦有經，必有緯。經正則緯正，緯正則經緯之間無弗正。圜圖以南北為經，則東西為緯。方圖以西北東南為經，則東北西南為緯。乾坤交得否泰，繼而兌艮交得咸損，故次否泰。繼而離坎交得未既濟，故又次咸損。繼而震巽交得恆益，故又次未既濟。皆為緯。緯合經而一十六，邵子所謂四象相交成十六事也。而各卦之交咸取諸此矣。

The hexagrams have a main line (jing) and a secondary line (wei); when the main line is properly arranged, the secondary line is also properly arranged, and where the main and secondary lines intersect, everything is correctly aligned. In the circular diagram, the north-south line serves as the main line, and the east-west line is the secondary line. In the square diagram, the line from northwest to southeast is the main line, and the line from northeast to southwest is the secondary line. The trigrams Qian (Heaven) and Kun (Earth) intersect to form the hexagrams "Pu" (Obstruction) and "Tai" (Peace), followed by Dui (Lake) and Gen (Mountain) intersecting to form "Xian" (Attraction) and "Sun" (Loss), so they come after "Pu" and "Tai". Then Li (Fire) and Kan (Water) intersect to form "Wei Ji" (Not Yet Completed) and "Ji Ji" (Completed), so they follow "Xian" and "Sun". Then Zhen (Thunder) and Xun (Wind) intersect to form "Heng" (Permanence) and "Yi" (Benefit), so they follow "Wei Ji" and "Ji Ji"—these are the secondary lines. The secondary lines combined with the main lines total sixteen hexagrams, which is what Shao Yong referred to as "the four trigrams intersecting to form sixteen events." The rules for the intersection of hexagrams are all based on this principle.

六十四卦生於八卦之相交，而八卦之相交其法有七。有隔六交者，有比肩交者，乃至隔一、隔二、隔三、四、五交者。其隔六，則乾坤相交是也。隔五，則乾艮、坤兌相交是也。隔四，則乾坎、艮離、兌艮相交是也。

The sixty-four hexagrams are produced by the mutual interaction of the eight trigrams. There are seven ways in which the trigrams interact: some intersect with trigrams six positions apart, some intersect with trigrams adjacent to them, and there are also intersections with trigrams separated by one, two, three, four, or five positions. The term "separated by six" refers to the trigrams at the beginning and end of the sequence,乾 and 坤, which are six positions apart. The term "separated by five" refers to the intersections between 乾 and 艮, and 坤 and 兑. The term "separated by four" refers to the intersections between 乾 and 坎, 艮 and 离, and 兑 and 艮 (the last pair in the original text is written as "兑艮," which does not match the number for separation by four, suggesting a possible error in the text).

乾巽、兌坎相交，坤震、艮離相交，則隔三也。乾震、兌巽相交，則隔二也。交以離乾、兌震，交以離巽、震坎，交以巽艮、坎坤，非隔一乎。交以乾兌、兌離，交以離震、震巽，交以巽坎、坎艮及艮坤，非比肩乎。剛柔往來，貞悔變易盡之矣。

Heavenly Stems and Earthly Branches intersect in the following ways: Qian and Xun, Dui and Kan intersect with a gap of three. Qian and Zhen, Dui and Xun intersect with a gap of two. Using Li with Qian, Dui with Zhen, Li with Xun, Zhen with Kan, Xun with Gen, and Kan with Kun intersect with a gap of one. Using Qian with Dui, Dui with Li, Li with Zhen, Zhen with Xun, Xun with Kan, Kan with Gen, and Gen with Kun intersect directly. The movement and transformation of yao, both yin and yang, and the change between inner and outer trigrams are all included in these seven methods of intersection.

方圖之形衡八而從八。計其衡，則自下而上，乾一兌二離三震四巽五坎六艮七坤八皆居貞卦之位。計其從，則自右而左，一乾二兌三離四震五巽六坎七艮八坤皆居悔卦之位。各以一卦為主而從有八悔，衡有八貞。縱衡貞悔，犬牙相錯。分之而其體成八。八縱八衡，卦各據其一行也。合之而其用有九。縱二衡二，虛中而得九也。先王九州別壤，九井均田蓋取諸此。

The figure is arranged in eight rows horizontally and eight columns vertically. Counting by the horizontal rows, from bottom to top, they 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; this sequence occupies the positions of the inner trigram (Zhen trigram). Counting by the vertical columns, from right to left, they are one Qian, two Dui, three Li, four Zhen, five Xun, six Kan, seven Gen, and eight Kun; this sequence occupies the positions of the outer trigram (Hui trigram). Each trigram has its own position: vertically there are eight outer trigrams, horizontally there are eight inner trigrams. The intersection of the vertical and horizontal lines results in the interweaving of Zhen and Hui trigrams, like the teeth of a dog interlocking. When viewed separately, the figure forms eight: eight vertical lines and eight horizontal lines, each trigram occupying one line. When viewed together, it results in nine: cutting vertically twice and horizontally twice, leaving one square empty in the middle, thus forming the nine numbers of the Nine Squares. The ancient kings of old divided the land into nine regions and measured land with nine units of land, probably based on this principle.

兩儀既判，陰固不可無陽，陽亦不可無陰。實則陰施而陰受，陽信而陰屈，陽尊而陰卑。此相輔以為用，而聖人所以垂教萬世也。乾兌離震陽卦也，合所生之二十八卦而得陽卦三十二。坤艮坎巽陰卦也，合所生二十八卦而得陰卦三十二。於衡圖，則陽卦皆居前而陰卦皆居後。於圜圖，則陽卦居左而陰卦皆居右。於方圖，則陽卦皆居內而陰卦居外。尊陽也。

The two principles, yin and yang, are divided into one fundamental principle. Yin cannot exist without yang, and yang cannot exist without yin. In practical terms, yang acts while yin receives, yang expands while yin contracts, and yang is exalted while yin is humble. The two complement each other and each has its own function. The sages used this principle to teach the world. The trigrams Qian, Dui, Li, and Zhen are yang trigrams, and together with the twenty-eight trigrams they generate, there are thirty-two yang trigrams in total. The trigrams Kun, Gen, Kan, and Xun are yin trigrams, and together with the twenty-eight trigrams they generate, there are thirty-two yin trigrams in total. In the horizontal diagram, all yang trigrams are placed before all yin trigrams; in the circular diagram, yang trigrams are placed on the left and yin trigrams on the right; in the square diagram, yang trigrams are all inside and yin trigrams outside— all to honor yang.

故觀方圖者，分之則六十四卦，合之則一卦也。三十二卦為貞，三十二卦為悔。一貞一悔，非一卦之象乎。以六十四卦觀之，則其文燦然而有章也，以一卦觀之，則其體寂然而不動也。陰陽變化不可以智知，不可以識識，其斯之謂歟。若乃各爻之相對相間，不少異於圜圖，知圜圖而方圖有可知者。

Therefore, those who study the square diagram should understand: when viewed separately, it consists of the sixty-four hexagrams, but when viewed together, it forms a single hexagram. The thirty-two hexagrams serve as the inner trigram (Zhen), and the other thirty-two hexagrams serve as the outer trigram (Hui). One Zhen and one Hui combined do not they form exactly the image of a single hexagram? When viewing the sixty-four hexagrams, their patterns are brilliant and clearly connected; when viewing a single hexagram, its essence is quiet and motionless. What is said about yin and yang changes being unable to be measured by cleverness or grasped by knowledge, is probably referring to this. As for the relative and alternating arrangement of each line, it is entirely the same as the circular diagram. Once the circular diagram is understood, the square diagram can also be inferred.

按，祝氏曰。初爻內三十二陽，外三十二陰。二爻內外皆可六陽間十六陰。三爻內外各八陰八陽相間。四爻內外各四陰四陽相間。五爻內外各二陰二陽相間。上爻內外各一陰一陽相間。今按，初二三爻相配如祝氏說。其各悔卦左右中分之。則四爻右三十二陽，左三十二陰。五爻左右各十六陰間十六陽。上爻左右各八陰八陽相間。蓋貞卦分內外，悔卦分左右以配陰陽。此異於圜圖，祝氏諸家所未悉也。

Chen noted: Zhu said that in the square diagram, the first line consists of thirty-two yang lines inside and thirty-two yin lines outside; the second line has sixteen yang lines and sixteen yin lines alternating both inside and outside (the original text says "all can be six yang," where "can" should be "ten"); the third line has eight yin and eight yang alternating inside and outside; the fourth line has four yin and four yang alternating inside and outside; the fifth line has two yin and two yang alternating inside and outside; and the top line has one yin and one yang alternating inside and outside. Now it seems that the arrangement of the first, second, and third lines indeed matches Zhu's description. However, the outer trigram (the悔卦) should be viewed as left and right halves: the fourth line has thirty-two yang lines on the right and thirty-two yin lines on the left; the fifth line has sixteen yin lines alternating with sixteen yang lines on both sides; and the top line has eight yin and eight yang alternating on both sides. Generally, the inner trigram (the贞卦) divides inside and outside to match yin and yang, while the outer trigram divides left and right to match yin and yang. This differs from the circular diagram and is something that Zhu and other scholars have not fully explained.

先王定城郭宮室甸服之制，以辨內外，朝聘以時，至寒暑不怨諮，叛亂備而民生遂。何其慎邪。庖羲氏之方圖，誘厥矣。夫乾坤視八卦，故凡與乾坤並列者皆居外。次乾坤而為兌艮，故凡與兌艮並列者皆居次外。次兌艮為離坎，故凡與離坎並列者皆居次內。次離坎為震巽，故凡與震巽並列者皆居內。內以應外，外以衛內。內外之辨不亦詳且密哉。

In ancient times, the sovereigns established the rules for cities, palaces, and the graded system of the land, to distinguish between inner and outer areas. They held court ceremonies and diplomatic visits according to the seasons, so people did not complain even when they had to travel through the cold and heat. Rebellion was prevented and the people's livelihood was smoothly carried out — how careful was their intention. The square diagram drawn by Fuxi had already revealed this principle. The trigrams Qian and Kun govern all the eight trigrams, so those trigrams listed together with Qian and Kun are placed at the outermost layer. Then come Dui and Gen, so those trigrams listed together with Dui and Gen are placed at the second outer layer. Then come Li and Kan, so those trigrams listed together with Li and Kan are placed at the second inner layer. Then come Zhen and Xun, so those trigrams listed together with Zhen and Xun are placed at the innermost layer. The inner layer corresponds with the outer layer, and the outer layer guards the inner layer — is this not sufficiently detailed and meticulous in distinguishing inner and outer?

天氣上升，地氣下降，則不交而物不生。地氣上升，天氣下降，則相交而物生。相交者，天交乎地，地交乎天也。其不交者，天與天交而地與地交也。不交乎此，則交乎彼矣。不交，則天地或幾乎息矣。相交而生物者，天地之用也。不交而不生物者，天地之體也。有體而後有用，故有貞而後有元，有不生物而後有生物。

Heavenly Qi rises continuously while earthly Qi descends constantly; when they move apart and do not meet, all things cannot be generated. When earthly Qi rises and heavenly Qi descends, they meet and thus all things are generated. By meeting, it means that heaven meets with earth and earth meets with heaven. By not meeting, it means that heaven meets only with heaven and earth meets only with earth. If it does not meet here, it must meet there. If there is no meeting at all, heaven and earth would almost cease to function. The generation of all things comes from their meeting; the essence of heaven and earth is their not meeting. First there is the essence, then there is the function. Therefore, first there is the 'Zhen' of winter concealment, then there is the 'Yuan' of spring generation. First there is the aspect of not generating things, then there is the aspect of generating things.

天之卦乾兌離震，自相交而生無妄、大壯十二卦，天交天也。即為天之體。地之坤卦艮巽坎自相交而生觀、升十二卦，地交地也。即為地之體。天之卦而交坤艮坎巽得恆、否、豫、姤十六卦，天交乎地也。地之卦而交乾兌離震得泰、益、復、小畜十六卦，地交乎天也。即為天地之用。於是，即此得聲音色味與夫飛走草木情性形體之變，此邵子前知之學也。

The four trigrams belonging to Heaven are Qian, Dui, Li, and Zhen. They interact with each other to produce twelve hexagrams such as Wuwang and Dazhuang. This is the interaction of Heaven with Heaven, representing the essence of Heaven. The four trigrams belonging to Earth are Kun, Gen, Xun, and Kan. They interact with each other to produce twelve hexagrams such as Guan and Sheng. This is the interaction of Earth with Earth, representing the essence of Earth. The four trigrams of Heaven interact with Kun, Gen, Kan, and Xun to produce sixteen hexagrams such as Heng, Pinyin, Yu, and Gou. This is the interaction of Heaven with Earth. The four trigrams of Earth interact with Qian, Dui, Li, and Zhen to produce sixteen hexagrams such as Tai, Yi, Fu, and Xiaoxu. This is the interaction of Earth with Heaven. These two categories represent the functions of Heaven and Earth. From this, one can derive sounds, colors, smells, and the various changes in the nature and forms of birds, beasts, plants, and trees. This is exactly the system of knowledge that Shao Yong used to foresee the future.

天何依乎，依乎地也。地何附乎，附乎天也。天地相依附，而天地之內千變萬化。所謂不貳不測者，不外乎一經一緯、一方一圓、一動一靜間也。先天圖圜乎外方乎內。夫子欲取方圖於外以別地，而虛圜圖之內以象天。實不若天包地外，地居天中，有依附之勢為不易也。天圜於外，圜則運行而不息。地方於內，方以相交而成功。於是陰陽之妙用大無外小無內，悉包舉於斯而莫之或遺矣。

What does heaven rely on? It relies on earth. What does earth depend on? It depends on heaven. Heaven and earth rely on each other, thus generating myriad changes within them. The "Middle Way" says, "Its nature is not dual, so its generation of things is unpredictable," which is no different from the interplay of one vertical and one horizontal, one square and one circle, one movement and one stillness. The Earlier Heaven diagram has a circular pattern on the outside and a square pattern inside. A senior master once wanted to move the square pattern to the outside to represent earth, and leave the center of the circular pattern empty to symbolize heaven. In reality, this is not as fixed as the current arrangement where heaven is outside and earth is inside, with heaven encompassing earth and earth residing in the center of heaven, forming a mutual reliance and embracing relationship. Heaven is circular on the outside, allowing it to move ceaselessly; earth is square on the inside, enabling it to interconnect and produce all things. In this way, the subtle workings of yin and yang, vast without boundaries and minute without limits, are all encompassed within this diagram, with nothing left out.

《麻衣易》謂卦有反對。反者，即綜卦之謂也。正則為屯，倒則為蒙。正則為需，倒則為訟。諸卦相綜悉視此。其不得綜者凡八。曰乾、坤、坎、離、頤、大過、中孚、小過。《麻衣》所謂對卦，即錯卦也。合錯綜而言得三十六卦，邵子所謂三十六宮也。以此言之也，方圖圓圖橫圖之外，不可不知錯綜之圖。

The Ma Yi Yi says that in the "Say卦" there are "reverse" and "opposite" hexagrams.the so-called "reverse" refers to what later scholars call the "inverted hexagram" — turning a hexagram upside down. Looking at it normally, it is Zhun; turning it upside down, it becomes Meng. Looking at it normally, it is Xu; turning it upside down, it becomes Song. The principle of hexagrams being inverted is like this for each hexagram. Among them, there are eight hexagrams that remain the same when turned upside down and thus cannot form an inverted hexagram, namely Qian, Kun, Kan, Li, Yi, Da Guo, Zhong Fu, and Xiao Guo. The "opposite hexagram" mentioned in the Ma Yi refers to what later scholars call the "opposite hexagram" — exchanging the yin and yang of all six lines. When combining the opposite and inverted hexagrams, the sixty-four hexagrams reduce to thirty-six different forms, which is what Shao Yong called the "Thirty-six Palaces." According to this, in addition to the square diagram, circular diagram, and horizontal diagram, one must also understand the opposite and inverted diagrams.

十翼之有《雜卦傳》，固專為錯綜卦言之也。《彖傳》《本義》以卦變言者十有五卦，曰訟、隨、蠱、噬嗑、賁、無妄、大畜、晉、睽、蹇、解、升、鼎、漸、渙是也。《程傳》論卦變，多本於乾坤。《本義》但取兩爻相比為變。渙卦柔得位乎外則不合，朱子自亦疑之。今照咸恆二卦剛上柔下柔上剛下之例，皆以卦綜言之，於十五卦皆合。然兩卦雖有錯綜，至錯綜之或先或後，自當因名以求其義。如《序卦》所云，不可易也。

The inclusion of the "Zagua Transmission" in the "Ten Wings" was originally specifically for explaining the opposite and inverted hexagrams. In Zhu Xi's "The Original Meaning of the Zhou Changes," fifteen hexagrams are explained using the concept of "hexagram transformation," namely: "Strife," "Following," "Restlessness," "Breaking the Bones," "Brightness," "No False Movement," "Great Accumulation," "Progress," "Strife," "Obstruction," "Resolution," "Rising," "Tripod," "Gradual Progress," and "Dispersal." Cheng Yi's "Yichuan Commentary on the Changes" discusses hexagram transformation, mostly tracing its origin to the hexagrams of Heaven and Earth. However, "The Original Meaning" only uses the exchange of adjacent lines as transformation. But the "Judgment" of the "Dispersal" hexagram says "the flexible line is in the outer position," which cannot be explained by this method, and Zhu Xi himself had doubts about it. Now, following the precedent of the "Salty" and "Constant" hexagrams, which state "the strong above and the flexible below" and "the flexible above and the strong below," if we universally use the inverted hexagram to explain these fifteen hexagrams, none of them will be difficult to understand. However, although two hexagrams may have opposite and inverted relationships, the question of which comes first and which comes later among these relationships should still be determined by examining the meaning of the hexagram names, just as the "Sequence of Hexagrams" has established the order, which should not be arbitrarily changed.