A Plain Account of the Zhou Changes, Volume Eight · A Plain Account of the Zhou Changes Diagrams

按易繫辭傳曰，天一地二，天三地四，天五地六，天七地八，天九地十。此即所謂河圖，理數之大原也。天以一生水，地以六成之。地以二生火，天以七成之。天以三生木，地以八成之。地以四生金，天以九成之。天以五生土，地以十成之。此河圖五行生成之數也。

According to the Great Treatise section of the Zhou Changes, it says: "Heaven is one, Earth is two; Heaven is three, Earth is four; Heaven is five, Earth is six; Heaven is seven, Earth is eight; Heaven is nine, Earth is ten." Odd numbers belong to Heaven, and even numbers belong to Earth. These ten numbers are called the Yellow River Chart, which is the source of both meaning and numerical symbolism. Heaven uses one to generate water, and Earth uses six to complete it; Earth uses two to generate fire, and Heaven uses seven to complete it; Earth uses four to generate metal, and Heaven uses nine to complete it; Earth uses three to generate wood, and Heaven uses eight to complete it; Heaven uses five to generate earth, and Earth uses ten to complete it. The numbers one, two, three, four, and five are called "generative numbers," while the numbers six, seven, eight, nine, and ten are called "completed numbers." Each set consists of one odd and one even number, which is how the Yellow River Chart's five elements are generated through numbers.

一為太陽，居北。二為少陰，居南。三為少陽，居東。四為老陰，居西。東北陽分，故一三皆位陽。西南陰方，故二四皆位陰。東南物之始生，故二少位於東南。西北物之收成，故二老位於西北。此河圖四象之位也。

The four trigrams are arranged as follows: the first is the Sun, located in the north; the second is the Lesser Yin, located in the south; the third is the Lesser Yang, located in the east; and the fourth is the Old Yin (Great Yin), located in the west. The east and north belong to the yang aspect, so the first and third, which are odd numbers, are placed on this side; the west and south belong to the yin aspect, so the second and fourth, which are even numbers, are placed on that side. The east and south are the places where all things begin to grow, so the Lesser Yang and Lesser Yin, both marked with '少', are placed in the southeast; the west and north are the places where all things converge and mature, so the Sun and Great Yin, both marked with '老', are placed in the northwest. This is the arrangement of the four trigrams in the Yellow River Chart.

一六為水居北。左旋而東，則水生木。又旋而南，則木生火。又旋而中，則火生土。又旋而西，則土生金。又旋而北，則金生水。此以其運行之序言之，左旋而相生也。北方一六之水尅南方二十之火，西方四九之金，又尅東方三八之木。此以其對待之位言之，又未嘗不相尅也。

One and the Six Harmony belong to water, located in the north. Following the direction from north clockwise to the east, water generates wood; then turning to the south, wood generates fire; then moving to the center, fire generates earth; then turning to the west, earth generates metal; and finally returning to the north, metal generates water. This describes the sequence of the Yellow River Chart's operation: rotating left once, the Five Phases generate each other in order. However, looking at the opposing positions: northern water (one and six) directly faces southern fire (two and seven), and water controls fire; western metal (four and nine) directly faces eastern wood (three and eight), and metal controls wood. This refers to the opposing positions: there is also mutual control among them. (The original text mistakenly says 'twenty fire' instead of 'two and seven fire'.)

要而論之，理數之原一而已矣。一者，太極也。二之則為兩儀。四之則為四象。四象變化而庶類繁生，數至四而備矣。一合四即為五，為五行。故五者，數之中也。自五以後，生數皆合五以為成數。一合五為六，二合五為七，三合五為八，四合五為九，成數至九而備矣。而五備五則為十。小衍之為十，大衍之為五十，即為蓍策之數所起。故十者，數之終也。

In summary, the origin of both principles (yi li) and numerical calculations (xiang shu) is a single 'one'. One is the Taiji. When one doubles, it becomes two yi, and when doubled again, it becomes four xiang. When the four xiang change, myriad things arise, so the number four is complete. One plus four is five, which is the Five Phases. Therefore, five is the central number of the sequence. From five onwards, each generating number is added to five to form the completing numbers: one plus five is six, two plus five is seven, three plus five is eight, four plus five is nine, and the completing numbers reach nine. Five itself plus another five makes ten. The small derivation reaches ten, and the great derivation reaches fifty, which is the starting point of the numbers used in the divination with yarrow stalks. Therefore, ten is the end of the number sequence.

五為數之中，故於成數之中減其生數皆得五。十為數之終，故以生數合成數又皆得十。蓋太陽居一而連九，太陰居四而連六，少陰居二而連八，少陰居三而連七。就其三居之位言之。則生數太陽，成數配以太極。生數太極，成數配以太陽。生數少陽，成數配以少陰。生數少陰，成數配以少陽。而就陰陽老少各分計之，皆得十焉。此皆天地之自然，非人力所能損益也。

Five is the central number, so when any number is subtracted from its corresponding generating number, the result is always five (six minus one, seven minus two, eight minus three, nine minus four all result in five). Ten is the terminal number, so when the generating numbers and mature numbers of old and young yin and yang are paired and added together, the result is always ten. The generating number one of the sun yang is connected with nine, the generating number four of the great yin is connected with six, the generating number two of the lesser yin is connected with eight, and the generating number three of the lesser yang is connected with seven. In terms of their positions: the generating numbers belonging to the sun yang are paired with the mature numbers of the great yin; the generating numbers belonging to the great yin are paired with the mature numbers of the sun yang; the generating numbers belonging to the lesser yang are paired with the mature numbers of the lesser yin; and the generating numbers belonging to the lesser yin are paired with the mature numbers of the lesser yang. When calculated separately according to yin and yang, old and young, their sums are always ten. All these are natural phenomena of heaven and earth, not something that human beings can add to or subtract from. (The original text says 「少阴居三而连七」 should be 「少阳」; 「成数配以太极」 and 「生数太极」 both have 「太极」 which should be 「太阴」, but we retain the original text.)

萬物統乎天，數始乎一。乃以一二三四分屬於天地何也。天地之大，不外乎陰陽。陽奇陰偶分之，自各有所屬也。五行皆生於天地。乃或天生而地成之，或地生而天成之何也。萬物皆陰陽合而有生，而所以又各自有陰陽，皆由得氣之初，陰陽或先或後。

Someone asked: All things are included within heaven, and numbers all begin with one. So why are the numbers one, two, three, and four assigned to heaven and earth respectively? Answer: The vastness of heaven and earth does not go beyond the two aspects of yin and yang. Odd numbers belong to yang, and even numbers belong to yin. Thus, one and three belong to heaven, and two and four belong to earth, each having its proper place, which is natural. Another question: The five phases are all produced by heaven and earth. Why is it that some are produced by heaven and formed by earth, while others are produced by earth and formed by heaven? Answer: All things are generated through the union of yin and yang. Each thing itself also divides into yin and yang. This depends on the initial moment when it receives the qi. The arrival of yin and yang has a先后 order.

水先天陽而後天陰，故體陽而用陰。火先天陰而後天陽，故體陰而用陽。木由滋潤而後焦枯，先天同水而後天同火也。金由煅煉而後融液，先天同火而後天同水也。以至人道有男女，飛走之有雌雄、牝牡，其先後天皆可類推也。

Taking the Five Phases as an example: Water first receives the yang from Heaven (Heaven generates water with one), then receives the yin from Earth (Earth completes water with six), so its essence belongs to yang but its function belongs to yin. Fire first receives the yin from Earth (Earth generates fire with two), then receives the yang from Heaven (Heaven completes fire with seven), so its essence belongs to yin but its function belongs to yang. Wood first needs moisture to grow, then later becomes dry and withered; its earlier heaven nature is similar to water, while its later heaven nature is similar to fire. Metal first needs to be smelted by fire, then later becomes liquid; its earlier heaven nature is similar to fire, while its later heaven nature is similar to water. Extending this principle, human beings are divided into male and female, birds have male and female, and beasts have male and female; their earlier heaven and later heaven yin and yang attributes can all be inferred in the same way.

五行之生有先後，數有多寡何也。凡物之生皆自微而著，由清而濁，數之生皆自少而多。五行，水最輕清火次之，故一六水而二七火也。木則形堅，金則質重，土則最大而最濁矣。故三八木，四九金，而五十土也。

The generation of the Five Phases has a definite order, and the numbers assigned to them vary in quantity. What is the reason for this? All things originate from subtle and hidden to manifest and prominent, from light and clear to heavy and turbid. The emergence of numbers also follows a similar pattern, starting from few and accumulating to many. In the case of the Five Phases, water is the lightest and clearest, followed by fire. Therefore, "Heaven produces one, Earth completes it with six," so water is paired with one and six. "Earth produces two, Heaven completes it with seven," so fire is paired with two and seven. Wood has already formed a solid body, and metal is even heavier. Earth has the largest form and is the heaviest and most turbid. Therefore, "Heaven produces three, Earth completes it with eight," so wood is paired with three and eight; "Earth produces four, Heaven completes it with nine," so metal is paired with four and nine; "Heaven produces five, Earth completes it with ten," so earth is paired with five and ten. The light and clear comes first, thus receiving a smaller number; the heavy and turbid comes later, thus receiving a larger number. The order of precedence and quantity is never confused.

太陽以一為生數最少，以九為成數則最多。太陰以四為生數最多，而以六為成數又最少。少陽以三為生數多（「數多」當作「數次多」，從文瀾本），以七為成數又次少。少陰以二為生數次少，以八為成數又次多。何也。蓋生數主氣，成數主形。生數先天，而成數後天。論氣，則太陽清輕而太陰重濁，故太陽一而太陰四。論形，則太陽有餘而太陰不足，故太陰六而太陽九也。論先天，則少陽強而少陰弱，故少陽三而少陰二。論後天，則少陽主洩而少陰主收，故少陽七而少陰八也。

The sun is associated with the number one as its generating number, the smallest among the four generating numbers, yet it is associated with nine as its completed number, the largest among the completed numbers. The moon is associated with four as its generating number, the largest among the generating numbers, yet it is associated with six as its completed number, the smallest among the completed numbers. The lesser yang is associated with three as its generating number, the second largest among the generating numbers (the original text says "the largest," while the Wenlan text says "the second largest"), yet it is associated with seven as its completed number, the second smallest among the completed numbers. The lesser yin is associated with two as its generating number, the second smallest among the generating numbers, yet it is associated with eight as its completed number, the second largest among the completed numbers. Why is this so? Because generating numbers govern "qi," while completed numbers govern "form." Generating numbers belong to the Earlier Heaven, and completed numbers belong to the Later Heaven. In terms of qi, the sun is light and clear, while the moon is heavy and turbid, so the sun is associated with one and the moon with four. In terms of form, the sun is abundant while the moon is deficient, so the moon is completed at six while the sun is completed at nine. In terms of the Earlier Heaven, the lesser yang is strong while the lesser yin is weak, so the lesser yang is associated with three and the lesser yin with two. In terms of the Later Heaven, the lesser yang governs dispersion and release, while the lesser yin governs gathering and storage, so the lesser yang is completed at seven and the lesser yin at eight.

老少陰陽之位，從一二三四而不論六七八九何也。由太極生兩儀，由兩儀生四象，皆先天之事也，故當從生數也。揲筮老少陰陽之數，取六七八九而不取一二三四又何也。由分二而掛一而揲四，皆後天之事也。故當從成數也。揲筮老陽取九而不取七，而老陰則取六不取八又何也。即太陽有餘太陰不足之說也。而不止此也。

Why are the positions of old yang, old yin, young yang, and young yin determined by the numbers one, two, three, and four rather than six, seven, eight, and nine? This is because the generation of the Taiji into the two principles, and the two principles into the four images, are natural processes of the Earlier Heaven, so they should be based on the generating numbers. However, when performing the divination method called "xie shi," the numbers used to represent old and young yin and yang are six, seven, eight, and nine, not one, two, three, and four. Why is this so? Because the procedures in the divination method, such as "fen er" (dividing the yarrow stalks into two bundles), "gua yi" (setting aside one stalk), and "xie si" (counting four stalks), are human-made actions of the Later Heaven, so they should be based on the completed numbers. As for why old yang is taken as nine rather than seven and old yin is taken as six rather than eight, this is precisely the reason mentioned earlier, that the sun has an excess and the moon has a deficiency. However, there are more reasons for this.

凡陽屬天，天形圓。圓者，徑一而圍三。凡陰屬地，地形方。方者，徑一而圍四。揲筮以四為數。所扐之數，以四為奇以象天，以八為偶以象地。如三扐皆奇，取徑一圍三之義。則三三為九，為天矣。天用其全，故不用七而用九也。如三扐皆偶，取徑一圍四之義。則三四為十二，為地矣。地用其半故不用八而用六也。且所扐者九，而過揲之數亦為四九三十六。所扐者六，而過揲之數亦為四六二十四。

All yang elements belong to heaven, which is round in shape. The proportion of a circle is a diameter of one and a circumference of three. All yin elements belong to earth, which is square in shape. The proportion of a square is a side of one and a circumference of four. When divining with yarrow stalks, they are counted in groups of four. Each change is counted between the fingers as "tou" (a bundle). If four stalks are obtained, it is called "qi", symbolizing heaven; if eight stalks are obtained, it is called "ou", symbolizing earth. If all three changes are "qi", the meaning of "a diameter of one and a circumference of three" is taken, and three threes combined make nine, which is the number of heaven. Heaven uses its full number, so old yang does not use seven but nine. If all three changes are "ou", the meaning of "a diameter of one and a circumference of four" is taken, and three fours combined make twelve, which is the number of earth. Earth uses only half of it, so old yin does not use eight but six. Moreover, if the "tou" results in nine, the remaining stalks after counting are exactly thirty-six, which is four times nine. If the "tou" results in six, the remaining stalks after counting are exactly twenty-four, which is four times six. The two ends correspond exactly.

是揲筮老陽老陰，不必皆因河圖，而自與河圖暗合，此所以為理數之自然也。至若河圖言五行，而伏羲因之以畫八卦。河圖五方，而先後天之八卦分為八方。皆與河圖各有所合。又當即橫圖圓圖方圖，詳析兮疏，其義始見，故姑總其大略如此。而諸圖仍即楊子道聲《圖卦闡義》所分，備列於後雲。

It is evident that the counting methods for old yin and old yang in the process of divination with yarrow stalks are not necessarily directly derived from the Yellow River Chart, yet they naturally correspond with it. This precisely demonstrates that they arise from the natural order of principles and numbers. As for the Yellow River Chart, which deals with the Five Phases, Fuxi used it to draw the Eight Trigrams; the Yellow River Chart divides the five directions, while the Earlier Heaven and Later Heaven Trigrams divide the eight directions, and each has its own correspondences with the Yellow River Chart. These principles require further analysis through the "horizontal diagram," "circular diagram," and "square diagram" to be fully explained, so that their meanings can become clear. Therefore, here we will first provide a general overview. The following diagrams will still follow the order as presented in Yang Daosheng's "Explanations of Diagrams and Trigrams."

楊子道聲《洛書別論》曰。洛書之數起於一，中於五，窮於九。五建極於中，為眾數所取法。自五為以下皆為生數，為一為二為三為四。自五以上皆為成數，為九為八為七為六。生數與成數相間而立，以成右轉之形。夫數始於一，一合中五而生六，六合一而生七，七合中五去十而生二，二合七而生九，九合中五去十而生四，四合九去十而生三，三合中五為八，八合三去十而復生一，運行無窮焉。

Yang DaoSheng's "A Different Discussion on the Luo Writing" says: The numbers of the Luo Writing begin with one, reach the center at five, and end at nine. Five establishes the central pole and is located in the center, serving as the standard for the other numbers. The numbers below five are called the generating numbers, which are one, two, three, and four; the numbers above five are called the forming numbers, which are nine, eight, seven, and six. The generating and forming numbers alternate in arrangement, forming a pattern of rotation to the right. The numbers start from one: one plus the central five gives six, six plus one gives seven, seven plus the central five gives twelve, subtract ten to get two, two plus seven gives nine, nine plus the central five gives fourteen, subtract ten to get four, four plus nine gives thirteen, subtract ten to get three, three plus the central five gives eight, eight plus three gives eleven, subtract ten and return to one, thus cycling endlessly without end.

而其相合相生之法，凡奇數則合中五以生下數，耦則合前位之奇以生下數。耦從奇，奇不從耦也。奇必生耦，耦必生奇，陰陽互根也。中五建極，奇耦相生而自右至左，法自然之運。此不同於河圖之不奇耦（文瀾本「不奇耦」作「不生奇耦」），耦之合中五而為數也。至其對待之法，更有大異於河圖者。河圖奇耦重列以相對，洛書則單列以相對。奇對必奇，耦對必耦。以中五為之綱，而餘數相伍以列。

Their principle of mutual generation and addition is: whenever an odd number is encountered, add the central five to produce the next number; whenever an even number is encountered, add the previous odd number to produce the next number. This is the way even numbers follow odd numbers, while odd numbers do not follow even numbers. Odd numbers must generate even numbers, and even numbers must generate odd numbers, which is exactly the principle of yin and yang as fundamental forces. The central five establishes the ultimate standard, and odd and even numbers alternate in generation, moving from right to left, following the natural movement of heaven. This differs from the Yellow River Chart, which does not add the central five to both odd and even numbers to form numbers (this sentence has an error or omission in the original text; the Wenlan edition reads 'not generating odd and even' as 'not producing odd and even'). As for the arrangement of 'opposites,' the difference is even greater: the Yellow River Chart arranges odd and even numbers in overlapping pairs facing each other, while the Luo Writing arranges single odd numbers facing each other and single even numbers facing each other; odd numbers always face odd numbers, and even numbers always face even numbers, all taking the central five as the main axis, with the other numbers arranged in sequence accordingly.

及計其對待之共數，莫不各倍中五以成十，而十已默寓於眾數之中矣。楊子道聲之論如此。今按，《易·繫辭傳》曰，河出圖，洛出書，聖人則之，是圖書相為表裡，夫子之言可據。後人以洛書至禹始出，其訛固不俟辨。至若天一地二章，所言皆河圖而不及洛書，蓋緣蓍數取於五十，故獨引河圖為言。至由兩儀四象而生八卦，則圖書皆其根本。而先後天八卦之位配之洛書，尤其易見者也。

When the corresponding numbers are added together, they always amount to twice the central number five, making ten. This shows that the number ten is implicitly contained within the numbers of the Luo Book. This is the view of Yang Daosheng. Now, according to the commentary in the "Xici" chapter of the "Yijing," it says, "The river produced the diagram, and the Luo produced the book; the sage followed them as a model." This shows that the He Tu and the Luo Shu are complementary to each other. Confucius' words can be trusted. Later people claimed that the Luo Shu appeared only during the time of Yu the Great controlling the floods; such a mistaken tradition is unnecessary to refute. As for the passage in the "Xici" chapter that says "Heaven is one, Earth is two," it discusses the He Tu and does not mention the Luo Shu. This is because the number used in the big yarrow stalk divination is fifty, so it only refers to the He Tu. As for the generation of the eight trigrams from the two principles and the four images, both the He Tu and the Luo Shu are its foundation. Especially when matching the positions of the Earlier Heaven and Later Heaven trigrams with the Luo Shu, it becomes particularly clear.

洛書自北之西，一六之水尅二七之火。火南行，尅四九之金。金東行，尅三八之木。木轉中，尅中英（「英」當作「央」，從文瀾本）之土。土北行，又尅一六之水。此洛書之右轉相尅，異於河圖之左旋相生者也。至以其相對待言之，則東南四九之金，生西北一六之水。而東北三八之木，生西南二七之火。是洛書之對（「對」當作「之」，從文瀾本）對待相生，又異於河圖之對待相尅者也。

The numbers of the Luo Book turn from the north to the west. The water of the north and northwest (one and six) control the fire of the west and southwest (two and seven). The fire then moves south to control the metal of the south and southeast (four and nine). The metal then moves east to control the wood of the east and northeast (three and eight). The wood then moves to the center to control the central earth. The earth then moves north again to control the water of one and six. This is how the Luo Book rotates to the right and successively controls, differing from the He Tu which rotates to the left and successively generates. If we consider the opposite directions, the metal of the southeast (four and nine) generates the water of the northwest (one and six); the wood of the northeast (three and eight) generates the fire of the southwest (two and seven). This is how the Luo Book's opposite positions generate each other, differing from the He Tu's opposite positions which control each other.

要之，生之中有尅，尅之中有生。十之數，不外九之用。九之用，已備十之體。四正已備乎四隅，四隅不外乎四正。四正四隅皆本於中宮，兩儀四象皆根於太極。此則河圖洛書之所同，而實未嘗異者。要之，言乎理則一，言乎氣則二，言乎象則四，言乎行則五。由是即一奇一耦，以生八卦六十四卦，而先天後天，為方為圓，皆從此起焉。是又當即諸圖分析求之，以詳其義者也。

In summary, mutual generation contains mutual control, and mutual control contains mutual generation. The 'body' established by the ten numbers of the Yellow River Chart cannot be separated from the 'function' expressed by the nine numbers of the Luo Writing; the 'function' of the nine numbers of the Luo Writing itself already includes the 'body' of the ten numbers. The four cardinal directions already encompass the four corners, and the four corners do not go beyond the four cardinal directions. Both the four cardinal directions and the four corners originate from the Central Palace, and the two principles, four elements, all originate from the Supreme Ultimate. These are the common aspects of the Yellow River Chart and the Luo Writing, and there is indeed no difference. In summary: from the perspective of 'principle' it is one; from the perspective of 'energy' it is two, that is yin and yang; from the perspective of 'image' it is four, that is the four elements; from the perspective of 'movement' it is five, that is the Five Phases. By using one odd and one even number, layer by layer, we generate the Eight Trigrams and then the sixty-four Trigrams. The Earlier Heaven and Later Heaven, the square diagram and the circular diagram, all originate from here. These should be analyzed and explored in detail through the following diagrams in order to fully explain their meanings.

河圖以十為數，洛書以九為數。河圖列四正五十居中，洛書列四正四隅而五居中。於八卦似各異，要之本太極而為陰陽奇偶，則一而已矣。陽大陰小，則陽先陰後。故伏羲先畫一奇以陽，畫一偶以象陰而兩儀具。兩儀各生一陽一陰而四象形。四象又各生一陽一陰而八卦列。卦既成，見其具天地人三才之象，非有取於三才強畫之也。卦既列，而乾一兌二至坤八有自然之序，非有意於先後強分之也。卦備於八，是謂小成。

The Yellow River Chart uses ten as its ultimate number, while the Luo Writing uses nine as its ultimate number. The Yellow River Chart arranges only the four cardinal directions with five and ten in the center, whereas the Luo Writing includes all four cardinal directions and four corners with five in the center. Although the way they combine with the Eight Trigrams seems different, they both ultimately originate from the Taiji and divide into yin and yang, odd and even. Since yang is greater and yin is smaller, yang comes first and yin follows. Therefore, Fuxi first drew a single line to represent yang, then a double line to symbolize yin, and the two principles were formed. Each of the two principles then generated one yang and one yin, forming the Four Symbols. The Four Symbols each generated one yang and one yin, and the Eight Trigrams were arranged. After the trigrams were formed, it became clear that each trigram consists of three lines, which naturally contain the images of heaven, earth, and humanity. It was not that the concept of the three principles was first established and then forced into three lines. Once the positions of the trigrams were arranged,乾 is one, 兑 is two, and so on up to 坤 being eight, with a natural order, not deliberately arranged in sequence. When the trigrams reach eight, they are complete, which is called "small completion."

八卦未畫之先，則太極生八卦。八卦既畫之後，則八卦皆可以為太極。所謂物物各具一太極者，此也。由是而兩儀得十有六。由是而四象得三十有二。由是而八卦得六十有四。六畫之上無可加，六十四卦之外亦無可益，此理數之自然也。六十四卦之中，八卦各居其本位。乾一兌二離三震四巽五坎六艮七坤八，分陰分陽，萬變畢具。陽生於復而極於乾，陰生於姤而極於坤。論卦體之相生，則自乾而復為順，自姤而坤為逆。論陰陽之升降，則自姤而坤為順，自乾而復為逆。奇偶順逆循環，而圓圖方圖皆自此出矣。

Before the eight trigrams were drawn, the Taiji gave rise to the eight trigrams; once the eight trigrams were drawn, each trigram could be considered as a Taiji on its own. The phrase "each thing possesses its own Taiji" refers exactly to this. From this, each trigram gives rise to two yin and yang, resulting in sixteen; then each of these gives rise to four images, resulting in thirty-two; then each of these gives rise to eight trigrams, resulting in sixty-four. The trigram lines cannot be added beyond six, and the number of trigrams cannot exceed sixty-four, which is the natural limit of the principles and numbers. Among the sixty-four trigrams, the eight original trigrams each occupy their own position: Qian one, Dui two, Li three, Zhen four, Xun five, Kan six, Gen seven, Kun eight. Yin and yang are clearly divided, and all kinds of changes are included within. Yang energy arises from Fu and reaches its peak in Qian; yin energy arises from Gu and reaches its peak in Kun. If we consider the mutual generation of trigram structures, counting from Qian to Fu is in the order, and counting from Gu to Kun is in reverse; if we consider the rising and falling of yin and yang, counting from Gu to Kun is in the order, and counting from Qian to Fu is in reverse. The odd and even, the order and reverse, the going and returning, the circular and square diagrams are all derived from this.

理，一而已矣。一而二，則為乾坤。二而四，則乾得離而坤得坎。四而八，則乾得兌離震，坤得艮坎巽。乾坤動乎一者也。離坎繼乾坤而代之者也。兌震艮巽妙坎離之用者也。乾坤之位正而離坎正矣。離坎之位正而八卦正矣。坤之居北而配一六者何，一為數始而生物之始，六所以成之也。

Reason is simply one. From one, it divides into two, which are Heaven and Earth. From two, it divides into four; Heaven receives Fire, and Earth receives Water. From four, it divides into eight; Heaven encompasses the trigrams of Lake, Fire, and Thunder, while Earth encompasses the trigrams of Mountain, Water, and Wind. Heaven and Earth originate from the single "one" of the Supreme Ultimate. Fire and Water follow Heaven and Earth, carrying out their functions. Lake, Thunder, Mountain, and Wind are what make the functions of Fire and Water subtle and varied. When the positions of Heaven and Earth are properly arranged, the positions of Fire and Water are also properly arranged; when the positions of Fire and Water are properly arranged, the positions of the eight trigrams are all properly arranged. Why is Earth positioned in the north and paired with the numbers one and six? Because one is the beginning of numbers and the beginning of life, while six is used to complete it.

則所重在一。一，陽也。乾象而非坤象。然坤不能自生而生於乾，是以居北。乾之居南而配二七者何。二為一之匹，而亦生物之數。則所重在二。二，陰也。坤象而非乾象。然乾亦不能自生而生於坤，是以居南。乾南坤北，亦所以法天，天陽南而陰北也。離居東而配三八何，天三生木，地八成之，火生於木也。坎居西而配四九者何。地四生金，天九成之，水生於金也。四卦正位，一經一緯。不居其位而位乎其所自生，故曰先天也。

The group of one and six focuses on one. One is an odd number, belonging to yang, and originally represents the image of Qian rather than Kun. However, Kun cannot generate itself, and it comes from Qian, so Kun is located in the north. Why is Qian located in the south and paired with the numbers two and seven? Two is the spouse of one, and it is the number of generation, so this group focuses on two. Two is an even number, belonging to yin, and originally represents the image of Kun rather than Qian. However, Qian cannot generate itself, and it comes from Kun, so Qian is located in the south. Qian in the south and Kun in the north follow the pattern of the heavenly way, with the yang energy of heaven in the south and the yin energy in the north. Why is Li located in the east and paired with three and eight? Because "heavenly three generates wood, and earthly eight completes it," and fire is generated from wood. Why is Kan located in the west and paired with four and nine? Because "earthly four generates metal, and heavenly nine completes it," and water is generated from metal. The four trigrams, Qian, Kun, Li, and Kan, are fixed in their positions. They intersect with each other, one as a vertical line and one as a horizontal line, forming a pattern. They do not occupy the directions corresponding to their own five elements, but instead the directions from which they are generated. This is called "Earlier Heaven."

震兌艮巽之居四維者何。以乾坤離坎之定位位之也。陽之運自南而北，陰之運自北而南。南為老陽乾居之。乾之上爻變而為兌，居東南。中爻變而為離，居東。兩爻俱變而震，居東北。以極於北。則乾爻盡變矣。北為老陰坤居之。坤之上爻變而為艮，居西北。中爻變而為坎，居西。兩爻俱變而為巽，居西南。以極於南。則坤爻盡變矣。陰陽相摩，迭為終始。八卦正位，萬象森列。故曰乾坤離坎正而八卦正矣。

Why are the trigrams Zhen, Dui, Gen, and Xun located in the four corners? They are arranged according to the positions of the trigrams Qian, Kun, Li, and Kan. The movement of yang energy proceeds from south to north, while the movement of yin energy proceeds from north to south. The south is old yang, occupied by Qian: the top line of Qian changes to become Dui, located in the southeast; the middle line changes to become Li, located in the east; when both the top and middle lines change, it becomes Zhen, located in the northeast; continuing this process until the north, all the lines of Qian have changed. The north is old yin, occupied by Kun: the top line of Kun changes to become Gen, located in the northwest; the middle line changes to become Kan, located in the west; when both the top and middle lines change, it becomes Xun, located in the southwest; continuing this process until the south, all the lines of Kun have changed. Yin and yang interact and alternate between beginning and end. Each of the eight trigrams occupies its proper position, and thus all phenomena are orderly arranged. Therefore, when Qian and Kun, Li and Kan are properly positioned, the eight trigrams are all properly placed.

易逆數也而順以行之，聖人所以善法天也。《說卦》，帝出乎震，成言乎艮，後天之卦位也。先天乾坤為經，離坎為緯。今則離坎進而為經，震兌繼而為緯。一六為水故坎在北，二七為火故離在南。三八為木。四九為金。故震東而兌西。水火金木，各正其位。經正則緯正，緯正則八卦亦靡不正。夫震為木為春。離為火為夏。帝出乎震，歲之始也。春夏之交，百物暢茂。

The original method of the Book of Changes (Yi) was to predict backwards towards the future, but the sages applied it in accordance with the sequence of time, which is exactly how they emulated the way of Heaven. The "Commentary on the Hexagrams" says, "The Emperor arises from Zhen" and "The completed statement is in Gen," which refers to the Later Heaven arrangement of the hexagrams. In the Earlier Heaven arrangement, Qian and Kun form the main axis, while Li and Kan form the cross-axis. In the Later Heaven arrangement, Li and Kan rise to become the main axis, while Zhen and Dui take over the cross-axis. One and six belong to water, so Kan is located in the north; two and seven belong to fire, so Li is located in the south; three and eight belong to wood, four and nine belong to metal, so Zhen is located in the east and Dui in the west. Water, fire, metal, and wood each return to their proper positions. When the main axis is correct, the cross-axis is correct; when the cross-axis is correct, all eight trigrams are properly placed. Zhen belongs to wood and corresponds to spring, while Li belongs to fire and corresponds to summer. "The Emperor arises from Zhen" marks the beginning of the year; by the time summer comes, all things flourish and grow vigorously.

巽為木為風。振動而長養之，以相見乎離。繼之兌為金為秋，方受夏制伏而不起。交中央土，土以生金，坤卦當之，厥象為母。逮入北坎。西北之野，龍以戰焉，此天地之尊嚴氣也，乾卦當之，為君為父。冬之卦坎，百物告成。貞以起元，冬之季也，故艮以成之。艮，止也。歲聿云暮，功用止矣。正離坎以正發斂。正離坎震兌以正四時。正震巽離坤兌乾坎艮以正八節。天時以行，人事以遂，王者治平之道以弘。彌綸天地，各正性命，所謂後天而奉天時者乎。

The trigram Xun belongs to wood and represents wind. Wind causes movement and stimulation, nurturing all things, thus meeting with Li, as mentioned in the "Shuo Gua Zhuan" saying "they meet at Li." Next comes Dui, which belongs to metal and corresponds to autumn, when it is subdued by the summer fire and cannot act. Then comes the central earth, which generates metal. The trigram Kun is at this position, symbolizing the mother. Then comes the trigram Kan in the north. The northwest wilderness is the place of "Long Zhan Yu Ye" in the upper sixth line of the trigram Kun, representing the solemn and fierce energy of heaven and earth. The trigram Qian is at this position, representing the sovereign and father. The winter trigram is Kan, where all things reach completion. From "Zhen" it turns to "Yuan," which occurs at the end of winter, so the trigram Gen completes it. Gen means "to stop," as the year is about to end and its function ceases. By placing Li and Kan correctly, one places the aspects of growth and gathering; by placing Li, Kan, Zhen, and Dui correctly, one places the four seasons; by placing Zhen, Xun, Li, Kun, Dui, Qian, Kan, and Gen correctly, one places the eight seasonal divisions of the year. Thus the heavenly time moves, human affairs are accomplished, and the great way of the sovereign governing the state and pacifying the world becomes grand. It encompasses heaven and earth, enabling all things to correct their destiny and nature, which is probably the meaning of the "Wen Yan" of the "Qian" hexagram saying "after the later heaven, it follows the heavenly time."

洛書之數，奇者居正，耦者居隅，尊陽也。卦以配之，各從其類。乾為純陽而配九。九，陽之極也。於河圖之位為二七。二合七非九乎，故乾稱用九。坤匹乾為純陰。厥配為一，陽饒而陰乏也。亦河圖天一之本位也。以九一截數之終始，以乾坤定卦之陰陽，則六子均可計焉。

The numbers of the Luo Shu are arranged so that odd numbers occupy the four cardinal positions and even numbers the four corners, which is due to the reverence for Yang. When the Eight Trigrams are paired with the Luo Shu, each is matched according to its kind. Qian is entirely Yang and is paired with nine; nine is the extreme of the Yang numbers. In the He Tu, Qian originally occupies the position paired with two and seven, and two plus seven is exactly nine. Therefore, the use of the line in the Qian hexagram is called "use nine." Kun, which matches with Qian as the entirely Yin trigram, is paired with one; this signifies that Yang numbers are abundant while Yin numbers are deficient. One is also the original position of "Heavenly One" in the He Tu. "Use nine" and one take the end and beginning of numbers respectively, and with Qian and Kun establishing the Yin and Yang of the hexagram, the order of the six subsidiary trigrams—Zhen, Kan, Gen, Xun, Li, and Dui—can then be deduced.

乾一交於坤得震，故次乾曰震，次九曰八。再交於坤得坎，故次震曰坎，次八曰七。三交於坤得艮，故次坎曰艮，次七曰六。而三男之位定矣。坤一交於乾得巽，故次坤曰巽，次一曰二。再交於乾得離，故次巽曰離，次二曰三。三交於乾得兌，故次離曰兌，次三曰四。而三女之位亦定矣。是以論其位，則乾一兌二離三震四巽五坎六艮七坤八。論其數，則乾九震八坎七艮六坤一巽二離三兌四。以卦之生得其數，以數之位序其卦云爾。

Heavenly Stem Jia first combines with Earthly Branch Zi to produce Zhen, so after Qian comes Zhen, nine follows eight; secondly, Jia combines with Zi to produce Kan, so after Zhen comes Kan, eight follows seven; thirdly, Jia combines with Zi to produce Gen, so after Kan comes Gen, seven follows six—thus the positions of Zhen, Kan, and Gen, the three male trigrams, are established. Earthly Branch Zi first combines with Jia to produce Xun, so after Zi comes Xun, one follows two; secondly, Zi combines with Jia to produce Li, so after Xun comes Li, two follows three; thirdly, Zi combines with Jia to produce Dui, so after Li comes Dui, three follows four—thus the positions of Xun, Li, and Dui, the three female trigrams, are also established. Therefore, if we consider the earlier Heaven trigram positions, they are Qian one, Dui two, Li three, Zhen four, Xun five, Kan six, Gen seven, and Kun eight; if we consider the numbers of the Luo Square, they are Qian nine, Zhen eight, Kan seven, Gen six, Kun one, Xun two, Li three, and Dui four. This is merely determining the numbers based on the generation of the trigrams and then arranging the trigrams according to the numerical positions.

先天乾坤為父母，以生六子之用。後天坎離為繼體，共生四子以還歸乎大父母之用。此卦位之所以異也。乾坤之體，體純陰純陽。相交而生，生之用已弘。離坎之體，襍陽襍陰。必互異而生，生之用乃顯。此尤卦位之所以異也。夫離陽儀所生，繼乾故居南而當九。坎陰儀所生，繼坤故居北而當一。離坎即父母也。坎之初爻易乎離，則中女生男。故離之次艮，九之次八。即以離之初爻易乎坎，則中男生女。故艮之次兌，八之次七。

In the Earlier Heaven arrangement, the trigrams Qian (Heaven) and Kun (Earth) are considered the parents, from which six children are generated. In the Later Heaven arrangement, the trigrams Kan (Water) and Li (Fire) inherit the main structure, and together they produce four children, eventually returning to the function of the original parents Qian and Kun. This is one reason for the difference between the Earlier Heaven and Later Heaven arrangements. The essence of Qian is pure yang, and the essence of Kun is pure yin. When they interact, they can generate and transform, and their function of generation and transformation is already great. However, the essence of Li contains yin within yang, and the essence of Kan contains yang within yin. They must exchange and differ in their lines to generate and transform, and only then does their function of generation and transformation become evident. This is another reason for the difference between the Earlier Heaven and Later Heaven arrangements. Li is generated from the yang symbol and inherits Qian, so it is located in the south and corresponds to the number nine. Kan is generated from the yin symbol and inherits Kun, so it is located in the north and corresponds to the number one. In the Later Heaven arrangement, Kan and Li are regarded as the parents. Exchanging the first line of Kan with the first line of Li produces Gen (Mountain), which represents a woman giving birth to a man, so Li is followed by Gen, and nine is followed by eight. Conversely, exchanging the first line of Li with the first line of Kan produces Dui (Lake), which represents a man giving birth to a woman, so Gen is followed by Dui, and eight is followed by seven.

及坎之中爻易乎離，則中女之用還歸乎大父。故兌之次乾，七之次六。而乾兌艮之位定矣。即以離之中爻易位坎，則中男之用還歸乎大母。故坎之次坤，一之次二。坎之上爻易乎離，則中女又生男。故坤之次震，二之次三。即以離之上爻易乎坎，則中男更生女。故震之次巽，三之次四，而坤震巽之位定矣。先天正乾坤而八卦正。後天正離坎而八卦亦正。至八卦正乎離坎，而乾坤垂拱無為以董厥成，則又乾坤之妙其用，而離坎之神其能也。

When the middle line of the Kan trigram exchanges with the middle line of the Li trigram, the function of the middle daughter "Li" returns to the great father "Qian," so after Dui trigram comes Qian trigram. Following the numerical sequence, after seven comes six, and the positions of Qian, Dui, and Gen trigrams are thus determined. Conversely, when the middle line of the Li trigram exchanges with the middle line of the Kan trigram, the function of the middle son "Kan" returns to the great mother "Kun," so after Kan trigram comes Kun trigram. Following the numerical sequence, after one comes two. When the upper line of the Kan trigram exchanges with the upper line of the Li trigram, the middle daughter gives rise to a son trigram, so after Kun trigram comes Zhen trigram. Following the numerical sequence, after two comes three. Conversely, when the upper line of the Li trigram exchanges with the upper line of the Kan trigram, the middle son gives rise to a daughter trigram, so after Zhen trigram comes Xun trigram. Following the numerical sequence, after three comes four, and the positions of Kun, Zhen, and Xun trigrams are thus determined. In the Earlier Heaven diagram, placing Qian and Kun trigrams in their proper positions corrects the positions of all eight trigrams. In the Later Heaven diagram, placing Li and Kan trigrams in their proper positions also corrects the positions of all eight trigrams. When all eight trigrams are properly aligned with Li and Kan, Qian and Kun can govern by simply observing the results, without personally acting. This is precisely how Qian and Kun skillfully apply their functions, and how Li and Kan remarkably display their abilities.

學後天者，亦正其離坎而已。

Therefore, those who study the Later Heaven system begin their practice by properly placing the two trigrams Li (Fire) and Kan (Water). The Earlier Heaven diagram uses Qian (Heaven) and Kun (Earth) as the meridians of north and south, with the focus on aligning Qian and Kun. In the Later Heaven diagram, Li and Kan take the place of Qian and Kun, occupying the positions of north and south, so the focus shifts to aligning Li and Kan. Once the pair of trigrams Li (south) and Kan (north) are correctly positioned, the other four trigrams Zhen (Thunder), Dui (Lake), Xun (Wind), and Gen (Mountain) along with Qian and Kun will naturally return to their proper places. The key to the entire Later Heaven system lies in this alignment.

南北為經，東西為緯，夫人而知之矣。而八卦之經緯更有異焉。先天以震巽為經，後天以坤艮為經，而諸卦皆為緯。先天者，天地之生氣也。後天者，天地之成氣也。震巽為木為春為發生，一氣互乾東北西南，而凡緯於其間皆主生。於是乾生坎，艮生兌，離生坤，以成先天之位。

The north-south direction is called the meridian, and the east-west direction is called the latitude, which is common knowledge. However, the Eight Trigrams have their own system of meridians and latitudes, different from this. In the Earlier Heaven diagram, the trigrams Zhen and Xun are considered the meridians, while in the Later Heaven diagram, the trigrams Kun and Gen are the meridians. The other trigrams are regarded as latitudes. The Earlier Heaven diagram represents the vital energy of the generation of heaven and earth, while the Later Heaven diagram represents the vital energy of the formation of things. Zhen and Xun belong to wood and are associated with spring, governing the process of growth. This energy runs along a line from the Northeast to the Southwest. All trigrams lying across this line are considered to be related to 'generation'. Thus, Qian generates Kan, Gen generates兑, and Li generates Kun, and the positions of the trigrams in the Earlier Heaven diagram are determined in this way.

坤艮為土為季氣為收藏，一氣互於東北西南，而凡緯乎其間者皆主尅。於是坎尅離，兌尅震，乾克巽，以成後天之位。先天主生，故人之飲食、衣服、醫藥之屬咸取法焉。後天主尅，故人之祭祀、棺槨之屬咸取法焉。有後天而無先天則無本，有先天而無後天則不成。至生之中未嘗無尅，尅之中未嘗無生。觸類而長之可耳。

The trigrams K'un and Gen belong to earth and correspond to the final months of the four seasons, known as the 'seasonal qi', which governs storage and gathering. This particular qi flows along the line from the northeast to the southwest. All trigrams lying across this line are characterized by 'overcoming' (ke). Thus, Kan overcomes Li, Dui overcomes Zhen, and Qian overcomes Xun. The arrangement of the later heaven trigrams is thus established. The earlier heaven trigrams focus on generation, so matters related to human sustenance, clothing, and medicine, which pertain to nourishing life, are modeled after the earlier heaven diagram. The later heaven trigrams focus on overcoming, so matters related to worship and funerary practices, which pertain to the end of life, are modeled after the later heaven diagram. Without the earlier heaven, things would lose their root; without the later heaven, things would be unable to be completed. Moreover, within generation there is also overcoming, and within overcoming there is also generation. Following this principle, one can proceed to deduce further.

圜，天象也。卦之有圜圖，法天也。天之可見者，莫如陰陽。陰陽之可見者，莫如四時。天之陰極於冬，陰極陽生為冬至。天之陽極於夏，陽極生為夏至。故二至為陰陽之樞紐。卦之陽極於乾，陽極陰生而為姤。卦之陰極於坤，陰極陽生而為復。故乾坤姤復亦為陰陽之樞紐。知此可與言圜圖矣。歲一而已，二之為冬夏，四之為春夏秋冬，八之為八節者，陰陽迭運以成其寒暑也。卦各一而已，倍之十六，再倍之三十二，又倍之六十四者，陰陽迭運以成其貞悔也。

The circle represents the image of Heaven; the reason why the hexagram diagram is made in a circular form is because it follows the pattern of Heaven. In the way of Heaven, the most visible is yin and yang. Within yin and yang, the most visible is the four seasons. The yin energy of Heaven reaches its end in winter, and when yin reaches its extreme, yang begins to return, which is the winter solstice. The yang energy of Heaven reaches its end in summer, and when yang reaches its extreme, yin begins to emerge, which is the summer solstice. Therefore, the winter and summer solstices are the main turning points of yin and yang. The yang energy in the hexagrams reaches its extreme in the hexagram Qian, and when yang reaches its extreme, yin begins to emerge, forming the hexagram Gou. The yin energy in the hexagrams reaches its extreme in the hexagram Kun, and when yin reaches its extreme, yang begins to emerge, forming the hexagram Fu. Therefore, the four hexagrams Qian, Kun, Gou, and Fu are also the main turning points of yin and yang. Only when one understands this can one discuss the circular diagram. A year is originally a single whole; when divided into two parts, it becomes winter and summer; when divided into four parts, it becomes the four seasons; when divided into eight parts, it becomes the eight solar terms. This is how the alternation of yin and yang creates cold and heat. Each hexagram is originally a single whole; when doubled, it becomes sixteen; when doubled again, it becomes thirty-two; when doubled again, it becomes sixty-four. This is how the alternation of yin and yang divides the inner trigram 'Zhen' and the outer trigram 'Hui'.

夫天道流行始乎陽，而陽之初生又始之始也。陽則生於極陰，坤爰生復為陽始，冬至配焉。盡震宮八卦至明夷，離為貞卦。一陰又生於三爻，立春配焉。盡離宮八卦至於臨，兌為貞卦。一陽又生於二爻，春分配焉。盡兌宮八卦至於泰，貞卦三陽，立夏配焉。盡乾宮八卦至於乾，貞悔皆陽。陽極陰生得姤卦，夏至配焉。盡巽宮八卦至於訟，坎為貞卦。一陰又生於三爻，立秋配焉。盡坎宮八卦至於遯，艮為貞卦。一陰又生於二爻，秋分配焉。盡艮宮八卦至於否，貞卦三陰，立冬配焉。盡坤宮八卦至於坤，貞悔皆陰。陰極陽生，又得復卦配冬至。卦氣相配，循環無端。

Heavenly movement begins with yang energy, and the initial emergence of yang energy is the beginning of the beginning. Yang energy arises in the extreme yin place, after the Kun trigram comes the Fu hexagram, which marks the beginning of yang energy, corresponding to the winter solstice. After completing the eight trigrams of the Zhen palace to Mingyi, the lower trigram (Zhen hexagram) becomes Li, which is when the third line changes from yin to yang (the original text says 'one yin', but according to hexagram transformation it should be 'one yang'), corresponding to the beginning of spring. After completing the eight trigrams of the Li palace to Lin, the lower trigram becomes Dui, which is when the second line generates another yang, corresponding to the spring equinox. After completing the eight trigrams of the Dui palace to Tai, the lower trigram has all three lines as yang, corresponding to the beginning of summer. After completing the eight trigrams of the Qian palace to Qian, both the inner and outer trigrams are all yang lines, and when yang reaches its extreme, yin arises, resulting in the Guo hexagram, corresponding to the summer solstice. After completing the eight trigrams of the Xun palace to Song, the lower trigram becomes Kan, which is when the third line generates another yin, corresponding to the beginning of autumn. After completing the eight trigrams of the Kan palace to Dun, the lower trigram becomes Gen, which is when the second line generates another yin, corresponding to the autumn equinox. After completing the eight trigrams of the Gen palace to Pǐ, the lower trigram has all three lines as yin, corresponding to the beginning of winter. After completing the eight trigrams of the Kun palace to Kun, both the inner and outer trigrams are all yin lines, and when yin reaches its extreme, yang arises, regaining the Fu hexagram and corresponding to the winter solstice. The hexagram energies correspond with the solar terms in this way, cycling endlessly without beginning or end.

蓋天道左旋而卦則之。以陰陽之升降言，則復至乾姤至坤皆順。以卦體之初生言，則復至乾姤至坤皆逆。以衡圖相配言，則姤至坤為順，復至乾為逆。運行無窮而乾南坤北離東坎西之位不失。先天之八卦，得此益彰矣。按，此篇以衡圖相配之順逆與《說卦傳》所稱順逆不同。《說卦傳》以豫推未生之卦為逆，數已生之卦為順。以合衡圖之序為順，逆衡圖之序為逆也。

The general principle is that the heavenly way moves to the left, and the trigram diagram follows this pattern. In terms of the rising and falling of yin and yang, moving from the trigram of "Return" to "Heaven" and from "Meeting" to "Earth" is considered correct; in terms of the order of the initial emergence of the trigrams, moving from "Return" to "Heaven" and from "Meeting" to "Earth" is considered reverse; in terms of matching the order of the horizontal diagram, moving from "Meeting" to "Earth" is correct, while moving from "Return" to "Heaven" is reverse. This continuous movement ensures that the positions of Heaven in the south, Earth in the north, Fire in the east, and Water in the west remain unchanged. Thus, the meaning of the Earlier Heaven Trigrams is more clearly understood through this diagram. Chen's note: The concept of correct and reverse order mentioned in this passage regarding the matching with the horizontal diagram is not the same as the correct and reverse order discussed in the "Explanation of the Trigrams." The "Explanation of the Trigrams" refers to calling a trigram that has not yet been generated as reverse, and a trigram that has already been generated as correct. In contrast, this passage considers matching the order of the horizontal diagram as correct and going against it as reverse.

天左旋，日月星辰右轉。一順一逆，變化見矣。圜圖陰陽之升降則左旋以法天，六十四卦之相生則右轉以法七政。乾卦生兌離震，坤卦生巽坎艮。六子之所生，皆乾坤之所生也。故生卦之本，惟乾坤雲。乾坤而六十四卦之位以正，三百八十四爻之變以章章焉。夬至坤皆生於乾，剝至乾皆生於坤。貞卦以宰之，悔卦以動之。悔卦之變一周而貞卦一變，貞悔之變一周而乾坤一變，六十四卦所以全乾坤之用也。

The celestial bodies rotate to the left, while the sun, moon, and stars move to the right. In this interplay of clockwise and counterclockwise motion, change becomes evident. In the circular diagram, the rising and falling of yin and yang follow the leftward rotation, modeled after the heavens; the mutual generation of the sixty-four hexagrams follows the rightward movement, modeled after the sun, moon, and the five planets (the seven celestial bodies, or "seven ministers"). The Qian hexagram gives rise to Dui, Li, and Zhen; the Kun hexagram gives rise to Xun, Kan, and Gen. All the hexagrams generated by the six subsidiary hexagrams ultimately originate from Qian and Kun. Therefore, the fundamental source of all hexagrams is only Qian and Kun. With Qian and Kun, the positions of the sixty-four hexagrams are properly arranged, and the changes of the 384 lines become clear. From the hexagram Guai to Kun, all are generated from Qian; from the hexagram Po to Qian, all are generated from Kun. The inner trigram "Zhen" governs it, while the outer trigram "Hui" initiates it: the outer trigram completes a full cycle before the inner trigram moves once; when both inner and outer trigrams complete a full cycle, Qian and Kun move once—thus the sixty-four hexagrams fully express the functions of Qian and Kun.

貞悔六陽為乾，其變也自悔始。上九變則得夬，九五變得大有，五與上變得大壯，九四變則得小畜，四與上變則得需，四與五變得大畜，以及乎泰，則悔卦之變一周矣。悔卦之變一周，則貞卦九三變而得履，乃乾艮而兌進矣。兌之變一周而離退，離之變一周而震進，震之變一周而坤進，然後貞悔之變一周而消息視之。

The entire six lines of the inner and outer trigrams being all yang is the hexagram Qian. Its transformation begins with the outer trigram (the hexagram of regret): the line at the top (nine at the top) changes to the hexagram Guai, the line at the fifth position (nine in the fifth) changes to Da You, the lines at the fifth and top positions change to Da Zhuang, the line at the fourth position (nine in the fourth) changes to Xiao Xu, the lines at the fourth and top positions change to Xu, the lines at the fourth and fifth positions change to Da Xu, and so on until reaching Tai. When the outer trigram has completed one full cycle of transformation, the inner trigram (the hexagram of sincerity) then changes at the third line (nine in the third) to the hexagram Liu. Thus, Qian retreats and Dui advances (the original text says 'Qian Gen' but should be 'Qian retreats', as shown by the following text 'Kun retreats and Gen advances'). When Dui completes one full cycle, Li retreats; when Li completes one full cycle, Zhen advances; when Zhen completes one full cycle, Kun advances; then both the inner and outer trigrams complete one full cycle each, and the waxing and waning of yin and yang can be seen clearly in the diagram.

貞悔六陰為坤，其變也亦自悔始。上六變則得剝，六五變得比，五與上變得觀，六四變則得豫，四與上變得晉，四與五變得萃，以及否，則悔卦之變一周矣。悔卦之變一周，則貞卦六三變而得謙，乃坤退而艮進矣。艮之變一周而坎退，坎之變一周而巽進，巽之變一周而乾進，然後貞悔之變又一周而消息亦視之。陰陽相易，貞悔相濟。六爻感應，若日月之往來而靡間也。若五緯之各得其道而不紊也。此其包括宇宙而無遺也。

The inner and outer trigrams with all six lines yin are the hexagram of Kūn. Its transformation begins with the outer trigram: the line at the top changes to Bō, the line at the fifth changes to Bǐ, the lines at the fifth and top together change to Guān, the line at the fourth changes to Yù, the lines at the fourth and top together change to Jìn, the lines at the fourth and fifth together change to Cuì, continuing until Pǐ. When the outer trigram has completed a full cycle of transformation, the line at the third of the inner trigram changes to Qiān, and thus Kūn retreats while Gèn advances. When Gèn completes a full cycle, Kǎn retreats, and when Kǎn completes a full cycle, Xùn advances, and when Xùn completes a full cycle, Qián advances. Then both the inner and outer trigrams complete a full cycle of transformation. The waxing and waning of yin and yang are clearly visible in the diagram. Yin and yang alternate with each other, the inner and outer trigrams support each other, and the six lines respond to each other, just as the sun and moon move without interruption, and the five elements of metal, wood, water, fire, and earth follow their respective orbits without disorder. This is why the circular diagram can encompass the universe without omission.

一陰一陽之謂道。陰無陽不成其為陰，陽無陰不成其為陽。陰陽相須，故圜圖有對待之象焉。乾生兌離震為陽卦。凡乾兌離震之所生，皆陽卦也。乾至復三十二卦，是以居左。坤生艮坎巽為陰卦。凡坤艮坎巽之所生，皆陰卦也。坤至姤三十二卦，是以居右。陽左陰右，兩儀對待也。

The *Great Treatise* says, "One yin and one yang is called the Way." Yin cannot become yin without yang, and yang cannot become yang without yin. Yin and yang depend on each other and seek each other, which is why the circular diagram has pairs of opposing images. The trigrams generated by Qian (Heaven) — Dui (Lake), Li (Fire), and Zhen (Thunder) — are all yang trigrams. Any trigrams generated by Qian, Dui, Li, or Zhen are also yang trigrams. From *Qian* to *Fu* there are thirty-two trigrams, so they are arranged on the left side of the diagram. The trigrams generated by Kun (Earth) — Gen (Mountain), Kan (Water), and Xun (Wind) — are all yin trigrams. Any trigrams generated by Kun, Gen, Kan, or Xun are also yin trigrams. From *Kun* to *Gou* there are thirty-two trigrams, so they are arranged on the right side of the diagram. Yang is on the left, yin on the right, forming the pattern of two principles facing each other.

然陽卦之中亦有陰，陰卦之中亦有陽，又莫不自相對待。如一陽五陰之復、剝、比、豫、謙、師，則對一陰五陽之姤、夬、大有、小畜、履、同人也。二陰四陽之無妄、家人、離、革、中孚、睽、兌、大畜、需、大壯、大過、鼎、巽、訟、遯。則對二陽四陰之升、解、坎、蒙、小過、蹇、艮、萃、晉、觀、頤、屯、震、明夷、臨也。若泰、歸妹、節、損、豐、既濟、賁、隨、噬嗑、益之對否、漸、旅、咸、渙、未濟、困、蠱、井、恆，則陰陽半焉者也。乾之與坤，則以純陽而對純陽也。多寡相配，上下相求。東西成列一陰一陽，而開物成務之事畢矣。

However, the yin elements are contained within the yang trigrams, and the yang elements are contained within the yin trigrams. They are interdependent and complementary. For example, the trigrams with one yang and five yin, such as Fu, Bo, Bi, Yu, Qian, and Shi, correspond to those with one yin and five yang, such as Guo, Guai, Da You, Xiao Xu, Lu, and Tong Ren. The trigrams with two yin and four yang, such as Wu Wang, Jia Ren, Li, Ge, Zhong Fu, Kui, Dui, Da Xu, Xu, Da Zhuang, Da Guo, Ding, Xun, Song, and Duan, correspond to those with two yang and four yin, such as Sheng, Jie, Kan, Meng, Xiao Guo, Jian, Gen, Cui, Jin, Guan, Yi, Tun, Zhen, Ming Yi, and Lin. As for Tai, Gui Mei, Jie, Shen, Feng, Ji Ji, Ben, Sui, Shi He, and Yi, which correspond to Po, Zhen, Lu, Shan, Huan, Wei Ji, Kun, Gu, Jing, Heng, these are of the type where yin and yang are equally divided. Qian and Kun are opposite to each other, representing pure yang and pure yin respectively (the character 'yang' in the original text should be 'yin'). The quantity of yin and yang is balanced, and the two lines above and below are interdependent. The lines on the east and west sides are arranged in pairs, with one yin and one yang corresponding exactly. The principles of opening up all things and achieving success are fully contained within this.

孔子之說卦也，則曰八卦成列，因而重之。邵子之說卦也，則曰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。二說蓋不類云，及詳夫圜圖，而知邵子固已摻孔子左券也。卦次運行以中為界。乾姤為首，坤復為尾，六十四卦若翼之垂。左右分行，起首而止乎尾。故貞卦兌二次乾一，繼而離三，繼而震四，左行及尾止焉。

Confucius discussed the arrangement of hexagrams, stating in the Great Treatise that "the eight trigrams are arranged in order, and then each is repeated." Shao Yong, on the other hand, described the process as dividing one into two, two into four, four into eight, eight into sixteen, sixteen into thirty-two, and thirty-two into sixty-four. At first glance, these two approaches seem different, but upon closely examining the circular diagram, it becomes clear that Shao Yong actually held evidence consistent with Confucius's view (ancient people split a symbol into two halves, each holding one half, and the "left voucher" refers to the matching half). The order of the hexagrams is arranged on the diagram with the center as the boundary. The hexagrams "Qian" and "Gou" are at the beginning, while "Kun" and "Fu" are at the end. The sixty-four hexagrams spread out like the wings of a bird, extending to the left and right from the beginning to the end. Therefore, considering the inner trigram (the confirming hexagram), "Dui" follows "Qian," then "Li," then "Zhen," proceeding to the left until reaching the end.

巽五亦次乾一，繼而坎六，繼而艮七，繼而坤八，右行極尾止焉。悔則八卦一周，當貞之一卦，亦起首而止乎尾。左起乾一次二三，向左疊行，終而復始，乾至復是也。右亦起乾一次二三，向右疊行，終而復始。姤至坤是也。孔子所謂因而重之者此卦，邵子所謂遽而者即此卦也。邵子則言其相生之漸，孔子則言其已成之象。非邵子則孔子之言不明，非孔子則邵子之言不全，後之人執一而失之，亦重可慨夫。

The fifth trigram Xun follows the first trigram Qian, then comes the sixth trigram Kan, followed by the seventh trigram Gen and the eighth trigram Kun, proceeding to the right until reaching the end. As for the outer trigram (the trigram of regret), it must go through all eight trigrams in one full cycle before arriving at one trigram of the inner trigram, starting again from the beginning and proceeding to the end. On the left side, starting from Qian, it proceeds in order to the second, third, and so on, layer by layer to the left, and after completing one cycle, it starts again, which corresponds to the section from Qian to Fu. On the right side, it also starts from Qian, proceeding in order to the second, third, and so on, layer by layer to the right, and after completing one cycle, it starts again, which corresponds to the section from Guo to Kun. Confucius' statement "thereby stacking them again" refers precisely to these trigrams. Shao Yong's description of layer by layer generation (the words "ju er" are suspected to be a mistake or omission) also refers to these trigrams. Shao Yong discusses the gradual process of mutual generation, while Confucius discusses the already formed trigrams. Without Shao Yong, Confucius' words would be unclear; without Confucius, Shao Yong's words would be incomplete. Later scholars each hold only one side and lose the other, which is truly regrettable.