I Ching Numerology Hidden Diagrams

石門梁氏寅曰：「『天地定位』一節首乾坤，此一節則先六子者，蓋前乃先天八卦之體也，故先言不用者而後言用；此乃先天八卦之用也，故先言其用者而後言不用。如文王八卦専以用言之，亦始於震巽，而退乾於西北，退坤於西南。於此見八卦之體用固當不同也。」

Shi Men person Liang Yin said: The section "Heaven and Earth are positioned" in "Shuo Gua" begins with Qian and Kun, but this section starts with the six subordinate trigrams. The reason is that the previous section discusses the "body" of the Earlier Heaven Trigrams, so it first mentions Qian and Kun, which do not directly function, and then the six subordinate trigrams, which do function. This section discusses the "function" of the Earlier Heaven Trigrams, so it first mentions the six subordinate trigrams, which do function, and then Qian and Kun, which do not directly function. As for the King Wen Trigrams, which are based specifically on "function," they also begin with Zhen and Xun, and place Qian in the northwest and Kun in the southwest. This shows that the "body" and "function" of the Trigrams should inherently be different.

「神也者，妙萬物而為言者也。動萬物者莫疾乎雷，撓萬物者莫疾乎風，燥萬物者莫熯乎火，說萬物者莫說乎澤，潤萬物者莫潤乎水，終萬物始萬物者莫盛乎艮。故水火相逮，雷風不相悖，山澤通氣，然後能變化，既成萬物也。」

The "Commentary on the Hexagrams" continues by saying: The term "spirit" refers to its subtle ability to transform all things. Nothing is more swift in stirring up all things than thunder; nothing is more swift in gently moving all things than wind; nothing is more intense in drying out all things than fire; nothing is more capable of bringing joy to all things than the marsh; nothing is more effective in nourishing all things than water; and nothing is more powerful in ending and beginning all things than mountain. Therefore, water and fire influence each other, thunder and wind do not contradict each other, and the energies of mountain and marsh are interconnected, only then can transformation and movement take place, leading to the generation of all things.

平庵項氏曰：「動、撓、燥、說、潤、盛皆據後天分治之序，而相逮、不相悖、通氣、變化復據先天相合之位者，明五氣順布、四季分王之時，無極之真、二五之精所以妙合而凝者，未始有戾於先天之學也。苟無此章，則文王為無體，伏羲為無用矣。」

Ping'an Master Xiang Anshi said: "Motion, disturbance, dryness, speech, moisture, and prosperity" these phrases are all explaining the order of the Later Heaven Trigrams governing the four seasons; while "mutual assistance," "not conflicting," "communication," and "change" these phrases return to the position of the Earlier Heaven Trigrams where each pair combines with another. This is to show that when the five phases' energies proceed in order and each of the four seasons takes its turn, the "true essence of the boundless void" and the "essence of yin and yang and the five phases" can miraculously combine, never violating the teachings of the Earlier Heaven. If there were no this chapter, then the Later Heaven Trigrams of Wen Wang would have no origin, and the Earlier Heaven Trigrams of Fuxi would have no function.

又曰：「先天之首以天地、山澤、雷風、水火為序，後天之末乃自水火、雷風、山澤、天地倒而言之，彼言乾坤之用成於坎離，此推坎離之功歸於乾坤也。」

Xiang Anshi also said: In the beginning of the Earlier Heaven section, the order is arranged as Heaven and Earth, Mountains and Marshes, Thunder and Wind, Water and Fire; but at the end of the Later Heaven section, it starts from Water and Fire, Thunder and Wind, Mountains and Marshes, Heaven and Earth, and goes back in reverse order. The former explains that the functions of Heaven and Earth depend on Kan and Li, while the latter attributes the achievements of Kan and Li back to Heaven and Earth.

按：「天地定位」「雷以動之」二章皆以對待之體言，一首乾坤明六子所自出，一先六子而歸功於乾坤，未見其為先天之方位也。「帝出乎震」章以流行之用言，故順四時以為序而各著其方位。「神也者」章兼流行、對待言之：動、撓、燥、說、潤、盛，流行之用也；水火、雷風、山澤，對待之體也。雖不言乾坤，而六子之功用莫非乾坤之所為，「神」與「變化」正指乾坤而言，與「雷以動之」章略同，亦無以見上六句為後天之位而下三句為先天之位也。

Hu Wei remarked: "The chapters 'Heaven and Earth are positioned' and 'Thunder moves it' both discuss the two opposing 'bodies' in pairs. The first chapter begins with Qian and Kun, explaining from which six sub-trigrams arise. The second chapter first discusses the six sub-trigrams and attributes the credit to Qian and Kun. From these two chapters, one cannot see that they refer to the earlier heaven arrangement. The chapter 'The Emperor arises from Zhen' discusses the popular 'use' and thus arranges the order according to the four seasons, and each is marked with its own position. The chapter 'What is the spirit' discusses both the popular and the opposing aspects: the six phrases 'movement, disturbance, dryness, speech, moisture, and prosperity' belong to the popular use; the three phrases 'water and fire, thunder and wind, mountain and marsh' belong to the opposing body. Although the text does not explicitly mention Qian and Kun, the functions of the six sub-trigrams are all attributable to Qian and Kun. The term 'spirit' and the word 'change' refer precisely to Qian and Kun, similar to the chapter 'Thunder moves it'. Therefore, one cannot see that the six phrases above refer to the later heaven positions and the three phrases below refer to the earlier heaven positions.

橫圖、方圖從中起者為震、巽，人皆謂根柢於此。自余觀之，「三索」章先父母而後六子，此兩章先六子而後父母，要皆歸重於乾坤，豈有六子居母前之理？此天地之大經、古今之通義，而邵圖紊亂如此，尚可信乎？

The positions in the horizontal diagram and square diagram that are counted from the middle are Zhen and Xun. People often say that the root of the Earlier Heaven theory lies here. In my opinion, the chapter in "Shuo Gu" that talks about "one inquiry, two inquiries, three inquiries" first discusses the parents and then the six sons. However, these two chapters first discuss the six sons and then return to the parents. In the end, they all place emphasis on Qian and Kun. How can the six subsidiary trigrams come before the parents? This is a great principle in the universe and a principle that has been consistent throughout ancient and modern times. Yet Shao Yong's diagram has become so disordered, how can we still believe in it?

右論邵子伏羲八卦次序。

The above discussions concern Shao Yong's diagram of the "Fuxi Eight Trigrams Sequence."

《說卦傳》曰：「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。」（「數往」，色主反；「逆數」，色具反。）

The Sayings on the Trigrams states: Heaven and Earth established their positions above and below, the energies of Mountain and Marsh interconnect, Thunder and Wind interact with each other, and Water and Fire do not mutually dislike each other. Thus the Eight Trigrams are interrelated. Counting past events follows the order, while predicting future events involves reversing the order. Therefore, the Book of Changes is about reversing numbers. (The "数" in "数往" is pronounced "se3 zhu3 fan3" using reverse phonetic annotation; the "数" in "逆数" is pronounced "se3 ju4 fan3.")

韓氏康伯注曰：「《易》八卦相錯，變化理備，於往則順而知之，於來則逆而數之。」又曰：「作《易》以逆覩來事，以前民用。」

Han Kangbo explained that the Book of Changes uses the eight trigrams to interconnect and pair, thus encompassing all the principles of change; for past events, one can follow the sequence to understand them, and for future events, one can work backwards to calculate them. He also said that the sages composed the Book of Changes precisely to foresee future events, thereby guiding the people's actions.

孔氏穎達《正義》曰：「此一節就卦象明重卦之意。《易》以乾坤象天地，艮兌象山澤，震巽象雷風，坎離象水火。若使天地不交、水火異處，則庶類無生成之用，品物無變化之理，所以因而重之，令八卦相錯，則天地人事莫不備矣。故云天地定位而合徳，山澤異體而通氣，雷風各動而相薄，水火不相入而相資。」

Kong Yingda in The Correct Meaning of the Zhou Changes says: This section explains the purpose of the compound hexagrams by referring to the trigrams. The Zhou Changes use Qian and Kun to symbolize Heaven and Earth, Gen and Dui to symbolize Mountain and Lake, Zhen and Xun to symbolize Thunder and Wind, and Kan and Li to symbolize Water and Fire. If Heaven and Earth do not interact, and Water and Fire remain separate, then myriad things would not have the function of generation, and the principle of change would not exist. Therefore, the eight trigrams are overlapped to make compound hexagrams, so that the eight trigrams are intermingled and paired. Thus, the ways of Heaven, Earth, and human affairs are all complete. Therefore, Heaven and Earth each occupy their proper position yet their virtues are harmonized, Mountains and Lakes have different forms yet their energies are connected, Thunder and Wind each move independently yet they interact and generate movement, and Water and Fire which naturally do not mix yet they support each other.

「既八卦之用變化如此，故聖人重卦，令八卦相錯，乾坤震巽坎離艮兌莫不交互而相重，以象天地雷風水火山澤莫不交錯，則《易》之爻卦與天地等，成性命之理、吉凶之數，既往之事、將來之幾備在爻卦之中矣。故《易》之為用，人慾數知既往之事者，《易》則順後而知之；人慾數知將來之事者，《易》則逆前而數之。是故聖人用此《易》道以逆數知來事也。」

Since the functions and transformations of the Eight Trigrams have reached this level, the sage combined them to form hexagrams, making the Eight Trigrams intermingle and pair with each other. Thus, Qian (Heaven), Kun (Earth), Zhen (Thunder), Xun (Wind), Kan (Water), Li (Fire), Gen (Mountain), and Dui (Lake) all interact and overlap with one another, symbolizing the interconnection of heaven and earth, thunder and wind, water and fire, and mountains and marshes. In this way, the lines and hexagrams of the Book of Changes are equivalent to heaven and earth. The principles of life and death, the numbers of good fortune and misfortune, past events and the signs of future occurrences are all contained within the lines and hexagrams. Therefore, in terms of the function of the Book of Changes: when people wish to calculate and know past events, the Book of Changes follows the past to understand them; when people wish to calculate and know future events, the Book of Changes goes against the future to predict them. Thus, the sage used this system of the Book of Changes, relying on reverse calculation to foresee future events.

平庵項氏曰：「數往者順，即卦以藏往也；知來者逆，即蓍以知來也。」

Xiang Anshi said: "Knowing the past is following the trend," refers to using hexagrams to conceal past events; "Knowing the future is going against the trend," refers to using the yarrow stalks to foresee future events.

丘氏程曰：「《易》言『藏徃知來』『彰徃察來』，又言『數往知來』，則方來已往之事《易》皆有以知之。然往者已過而易知，來者未形而難見，《易》之占筮為知來設，故曰『《易》逆數也』。正如所謂『占事知來』、所謂『遂知來物』、所謂『前民用』，皆逆數之謂也。」

Qu Cheng said: The Yi Classic speaks of "concealing the past to know the future" and "making clear the past to observe the future," and also mentions "using numbers of the past to know the future." This shows that both what is about to come and what has already passed can be known through the Yi. However, past events have already occurred and are therefore easy to know, while future events have not yet taken shape and are therefore difficult to see. The divination of the Yi is specifically designed to foresee the future, hence it is said "the Yi is inverse in its numbers." As the Yi also states "divining matters to know the future" and "thus knowing the coming things," and "guiding the people's daily use," all of these refer to the inverse calculation of numbers.

亭林顧氏炎武《日知錄》曰：「數往者順，造化人事之跡有常而可驗，順以考之於前也；知來者逆，變化云為之動日新而無窮，逆以推之於後也。聖人神以知來，知以藏往，作為《易》書以前民用，所設者未然之占，所期者未至之事，是以謂之逆數。雖然，若不本於八卦已成之跡，亦安所觀其會通而繫之爻象乎？是以『天下之言性也，則故而已矣』。」

Gu Yanwu (Tinglin) in his "Rizhilu" says: "To understand the past is to follow the pattern," because the signs of nature and human affairs have regularities that can be verified, so one follows them to investigate the past; "To know the future is to reverse the process," because changes and human actions are constantly renewed day by day and have no end, so one reverses to predict the future. The sage, with his divine knowledge, foresees the future, and with his wise knowledge, retains the past, and composed the Book of Changes to guide the people's conduct. The Book of Changes deals with divination about things that have not yet occurred, and aims at events that have not yet arrived, hence it is called "reversing the count." Nevertheless, if one does not take the existing signs of the Eight Trigrams as the foundation, on what basis can one observe their interconnections and attach the line statements and hexagram images? Therefore, the "Mengzi" says: "The world discusses human nature, only based on the already manifested signs."

劉汝佳云：「天地間一理也。聖人因其理而畫為卦以象之，因其象而著為變以占之。象者體也，象其已然者也；占者用也，占其未然者也。已然者為往，往則有順之之義焉；未然者為來，來則有逆之之義焉。」

Liu Ruji says: Between heaven and earth there is only one principle. The sages based on this principle to draw the trigrams to symbolize it, and further based on these trigrams to deduce changes in order to predict them. "Xiang" (image) belongs to the body, it is a simulation of things that have already happened; "Zhan" (divination) belongs to the application, it is used to predict things that have not yet happened. Things that have already happened are called "Wang" (past), and "Wang" contains the meaning of counting in order; things that have not yet happened are called "Lai" (future), and "Lai" contains the meaning of reasoning backwards.

「如象天而畫為乾，象地而畫為坤，象雷風而畫為震巽，象水火而畫為坎離，象山澤而畫為艮兌，此皆觀變於陰陽而立卦、發揮於剛柔而生爻者也，不謂之數往者順乎？」

For example, taking the image of heaven to form the trigram Qian, taking the image of earth to form the trigram Kun, taking the images of thunder and wind to form the trigrams Zhen and Xun, taking the images of water and fire to form the trigrams Kan and Li, and taking the images of mountain and marsh to form the trigrams Gen and Dui. These all belong to what the "Sayings on the Trigrams" (Sayi) discusses, namely "observing the changes of yin and yang to establish the trigrams, and expressing the function of firmness and flexibility to generate the lines (yao)." This is not precisely "understanding the past in order to follow the trend" ("shu wang zhe shun")?

「如筮得乾而知『乾元亨利貞』，筮得坤而知『坤元亨，利牝馬之貞』，筮得震而知『震亨，震來虩虩，笑言啞啞』，筮得巽而知『巽小亨，利有攸往，利見大人』，筮得坎而知『習坎，有孚維心亨，行有尚』，筮得離而知『離利貞亨，畜牝牛吉』，筮得艮而知『艮其背，不獲其身，行其庭，不見其人』，筮得兌而知『兌亨利貞』，此皆通神明之徳、類萬物之情者也，不謂之知來者逆乎？」

For example, if one obtains the Qian hexagram through divination, one knows that its hexagram statement is "Yuan, Heng, Li, Zhen"; if one obtains the Kun hexagram, one knows its hexagram statement is "Yuan, Heng, beneficial to the virtuous mare's constancy"; if one obtains the Zhen hexagram, one knows "Zhen Heng, Zhen comes with fear, laughter and joy follow"; if one obtains the Xun hexagram, one knows "Xun small Heng, beneficial to go somewhere, beneficial to see a great person"; if one obtains the Kan hexagram, one knows "Practice Kan, with sincerity in the heart, the path is smooth, action is commendable"; if one obtains the Li hexagram, one knows "Li, beneficial to constancy and smoothness, keeping the virtuous bull is auspicious"; if one obtains the Gen hexagram, one knows "Gen its back, not obtaining its body, walking in the courtyard, not seeing the person"; if one obtains the Dui hexagram, one knows "Dui, smooth, beneficial to constancy." All these belong to what the Great Treatise says, "penetrating the virtue of the divine, comparing the forms of myriad things"; is this not exactly "knowing the future by reversing the present"?

「夫其順數已往，正所以逆推將來也。孔子曰『殷因於夏禮，所損益可知也；周因於殷禮，所損益可知也』，數往者順也；『其或繼周者，雖百世可知也』，知來者逆也。故曰『《易》逆數也』。」

Counting the past in order is done in order to reverse and predict the future. Confucius said, "The Shang dynasty followed the rites of the Xia dynasty; what was reduced and what was added can be known. The Zhou dynasty followed the rites of the Shang dynasty; what was reduced and what was added can also be known," which is called "numbering the past in sequence." He also said, "If there is a successor to the Zhou dynasty, even after a hundred generations, it can be foreknown," which is called "knowing the future in reverse." Therefore, it is said, "The Book of Changes is about reversing numbers."

「若如邵子之說，則是羲、文之《易》已判而為二，而又以震、離、兌、乾為數已生之卦，巽、坎、艮、坤為推未生之卦，殆不免強孔子之書以就已之說矣。」

If we follow Shao Yong's view, then Fuxi's Book of Changes and King Wen's Book of Changes would be split into two separate parts. Moreover, he treats Zhen, Li, Dui, and Qian as already formed trigrams, while Xun, Kan, Gen, and Kun are regarded as trigrams yet to be formed. This inevitably forces Confucius' writings to fit his own theory.

按：此章與八方之位無涉。「天地定位」，言乾坤自為匹也；「山澤通氣」，言艮兌自為匹也；「雷風相薄」，言震巽自為匹也；「水火不相射」，言坎離自為匹也。至於「八卦相錯」，則天或位乎下、地或位乎上，而且與六子之位同列矣；山澤之氣不但二者自相通，而且與天地、雷風、水火之氣互相通矣，雷風水火亦然。

Hu Wei remarked: The chapter "Say on the Trigrams" has nothing to do with the eight cardinal directions. "Heaven and earth are positioned" means that the trigrams Qian (Heaven) and Kun (Earth) form a pair by themselves; "Mountains and marshes communicate with each other" means that the trigrams Gen (Mountain) and Dui (Lake) form a pair by themselves; "Thunder and wind contend with each other" means that the trigrams Zhen (Thunder) and Xun (Wind) form a pair by themselves; "Water and fire do not oppose each other" means that the trigrams Kan (Water) and Li (Fire) form a pair by themselves. When it comes to "the eight trigrams interconnect," then heaven may be below and earth may be above, and they also need to be arranged together with the six subordinate trigrams; the qi of mountains and marshes is not only mutual communication between them, but also interconnected with the qi of heaven, earth, thunder, wind, water, and fire. The situation is similar for the trigrams of thunder, wind, water, and fire.

上四句即所謂「八卦成列，象在其中」，下一句即所謂「因而重之，爻在其中」也，意重下句。孔疏云「就卦象明重卦之意」，深得經旨。夫子《大象》皆以二體八物發明其義，此節正其註腳。八卦相錯是為六十四卦，而占筮之法生焉。

The four sentences above correspond to what is said in the "Great Treatise" that "When the eight trigrams are arranged in order, the images are already contained within them." The next sentence refers to "stacking them together, the lines are then included." The emphasis of the meaning lies in the latter sentence. Kong Yingda's commentary explains that this is "using the trigram images to explain the purpose of stacking trigrams," which thoroughly captures the original meaning of the text. The "Great Image Commentary" composed by Confucius all use the upper and lower parts and eight kinds of physical images to explain the meanings of the trigrams. This section serves as a commentary on the "Great Image Commentary." "The eight trigrams interacting with each other" becomes the sixty-four trigrams, and the method of divination is thus established.

卦之徳方以知，知以藏往，所謂數往者順也，君子居則觀其象而玩其辭，藏往之學也；蓍之徳圓而神，神以知來，所謂知來者逆也，君子動則觀其變而玩其占，知來之道也。雖往來並舉，卻重在知來。知來乃揲蓍求卦之事，《繫辭傳》云「極數知來之謂占」，又云「無有逺近幽深，遂知來物」，又云「占事知來」，有一不以蓍言者乎？於卦何與焉？

The virtue of the hexagram is upright and wise, and wisdom allows it to contain the past, which is called "knowing the past in order to follow the trend." A gentleman, when at ease, observes the hexagram and reflects on its line statements, which is the study of containing the past. The virtue of the yarrow stalks is round and profound, and their profundity allows them to foresee the future, which is called "knowing the future in reverse." A gentleman, when acting, observes the changing lines and reflects on the divination, which is the way of foreseeing the future. Although "past" and "future" are mentioned together, the emphasis is on "knowing the future." And "knowing the future" is precisely what the yarrow stalk divination entails. The "Great Treatise" says, "Exhausting the yarrow stalks' numbers to know the future is called divination," and also says, "No matter how distant or deep, one can know the future," and again says, "Divining a matter and foreseeing the future." Which of these is not speaking about the yarrow stalks? Then what is the connection with the hexagram?

卦主象，蓍主數，雖象中亦有數、數中亦有象，然其間有賓主之辨。韓康伯曰：「蓍極數以定象，卦備象以盡數。」賓主極其分明。希夷之圖，象學也，而康節則専精於數，故往往以蓍數為卦象，與經旨背。

Hexagrams are primarily based on "images" while the yarrow stalks are primarily based on "numbers"; although images contain numbers and numbers contain images, there is a distinction between the main and the auxiliary. Han Kangbo said, "The yarrow stalks exhaust numbers to determine the images, while the hexagrams possess images to exhaust numbers." The distinction between main and auxiliary is very clear. Chen Tuan's diagram belongs to the school of image studies, while Shao Kangjie specialized in the study of numbers, so he often took the numbers of the yarrow stalks as the images of the hexagrams, which goes against the original meaning of the classic.

至於據橫圖從中折取，以自震至乾為順數已生之卦、自巽至坤為逆推未生之卦，然則「《易》逆數也」，豈専用巽坎艮坤而不用乾兌離震乎？就其言解之，已有不可得通者矣。

As for the method of taking the diagram by splitting it in the middle, taking the section from Zhen to Qian as proceeding in order to indicate already formed hexagrams, and the section from Xun to Kun as proceeding in reverse to indicate hexagrams yet to be formed, then the statement "The Book of Changes is about reverse counting" — could this be referring only to the four hexagrams of Xun, Kan, Gen, and Kun, and not to the four of Qian, Dui, Li, and Zhen? Even if we follow his own words for explanation, there are already inconsistencies.

《本義》圖說：《說卦傳》曰「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」，邵子曰「乾南坤北，離東坎西，震東北，兌東南，巽西南，艮西北，自震至乾為順，自巽至坤為逆」。後六十四卦方位仿此。

The Original Meaning of the Zhou Changes includes a diagrammatic explanation which states: The Sayings on the Trigrams say, "Heaven and Earth are positioned, mountains and marshes communicate, thunder and wind interact, water and fire do not oppose each other, and the Eight Trigrams interconnect; to understand the past is to follow the sequence, to foresee the future is to reverse the sequence." Shao Yong based his theory on this, stating that Qian is located in the due south, Kun in the due north, Li in the due east, Kan in the due west, Zhen in the northeast, Dui in the southeast, Xun in the southwest, and Gen in the northwest; counting from Zhen to Qian is in the order of progression, while counting from Kun to Qun is in the order of regression. After this, the arrangement of the sixty-four hexagrams also follows this method.

《易學啟蒙》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，故曰數往也；知來者逆，若逆天而行是右行也，皆未生之卦也，故云知來也。夫《易》之數由逆而成矣。」此一節直解圖意，若逆知四時之謂也。

The "Yixue Qimeng" cites Shao Yong's words: this section explains the Eight Trigrams of Fuxi. The phrase "the eight trigrams are intermingled" means that the eight trigrams are combined in pairs to form the sixty-four hexagrams. The phrase "counting the past in the direction of movement" is like following the direction of the celestial movement, which is left rotation, and the counted are all the already existing hexagrams, hence called "counting the past"; the phrase "knowing the future in the opposite direction" is like going against the direction of the celestial movement, which is right rotation, and the deduced are all the hexagrams that have not yet been formed, hence called "knowing the future." The numbers of the "Yi" are indeed formed by reverse deduction. The "Qimeng" says: this section directly explains the meaning of the diagram, just like going against to foresee the four seasons.

（以橫圖觀之，有乾一而後有兌二，有兌二而後有離三，有離三而後有震四，有震四而巽五、坎六、艮七、坤八亦以次而生焉，此《易》之所以成也。而圓圖之左方，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，猶自今日而逆計來日也，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。）

Zhu Xi's own commentary: Looking at the horizontal diagram, there is first Qian one, then Dui two, then Li three, then Zhen four; after Zhen four, Xun five, Kan six, Gen seven, and Kun eight follow in sequence, which is the entire process by which the Book of Changes comes into being. Now looking at the circular diagram: its left half starts from Zhen as the winter solstice, passes through Li and Dui as the spring equinox, and reaches Qian's end as the summer solstice; the sequence along this path consists of already formed trigrams, like counting backwards from today to yesterday, which is called "knowing the past in a forward direction." Its right half starts from Xun as the summer solstice, passes through Kan and Gen as the autumn equinox, and reaches Kun's end as the winter solstice; the sequence along this path consists of trigrams yet to be formed, like calculating backwards from today to tomorrow, which is called "knowing the future in a reverse direction." However, tracing back to the origin, the formation of the Book of Changes follows the order of the horizontal diagram and the right half of the circular diagram. Therefore, it is said, "The Book of Changes is counted in reverse."

邵子《觀物外篇》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，尊卑之義也。乾坤定上下之位，離坎列左右之門，天地之所闔闢，日月之所出入，是以春夏秋冬、晦朔弦望、晝夜長短、行度盈縮莫不由乎此矣。」

Shao Yong said in "Guangwu Wai pian" that Zhen is when the yin energy begins to meet and yang energy arises, Xun is when yang energy begins to decline and yin energy arises; Dui is when yang energy gradually increases; Gen is when yin energy gradually increases. Zhen and Dui belong to the yin on the heavenly side, while Xun and Gen belong to the yang on the earthly side. Therefore, the top line of Zhen and Dui is yin while the bottom line is yang, and the top line of Xun and Gen is yang while the bottom line is yin. From the perspective of the beginning of heaven, yin is above and yang is below, which represents the meaning of "jiao tai" (mutual generation). From the perspective of the completion of earth, yang is above and yin is below, which represents the meaning of "zun bi" (respect and hierarchy). Qian and Kun determine the positions of above and below, Li and Kan arrange the positions of left and right, which are the places where heaven and earth open and close, and where the sun and moon rise and set. Therefore, the shifting of the four seasons, the changing of the new moon, full moon, and the waxing and waning of the moon, the changes in the length of day and night, and the expansion and contraction of celestial movements all originate from this.

朱子《語類》曰：「先天圖直是精微，不起於邵子。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》中所言亦有些意思。」

The Zhu Zi Yu Leiu records Zhu Xi's words saying: The Earlier Heaven diagram is indeed profound and subtle, and was not first created by Shao Yong. There was already such a diagram before Chen Tuan, but it was kept secret and not passed on, probably transmitted through generations of alchemists. What is discussed in the Threefold Concordance on the Zhou Changes also shares some similar meanings.

按：「震始交陰而陽生」，謂震與坤按而一陽生於下，三日夕月出庚，納震一陽之氣也，即《參同契》所謂「三日出為爽，震庚受西方」也；「巽始消陽而陰生」，謂巽與乾接而一陰生於下，十六日旦月退卒，納巽一陰之氣也，即《參同契》所謂「十六轉就緒，巽辛見平明」也。自震一陽進而納兌之二陽，至乾三陽而滿，此望前三候明生魄死之月象也；自巽一陰退而納艮之二陰，至坤三陰而滅，此望後三候魄生明死之月象也。

Hu Wei explains: The statement "Zhen begins to meet Yin and Yang is born" means that the Zhen trigram connects with Kun, and one Yang is generated at the lower trigram; on the third day of the month, the moon appears in the Geng direction in the evening, which is receiving the Yang energy of the Zhen trigram, as mentioned in the "Cantong Qi" as "on the third day, the moon appears as Shuang, Zhen receives Geng and is seen in the west." The statement "Xun begins to eliminate Yang and Yin is born" means that the Xun trigram connects with Qian, and one Yin is generated at the lower trigram; on the sixteenth day of the month, the moon gradually retreats in the morning, which is receiving the Yin energy of the Xun trigram, as mentioned in the "Cantong Qi" as "on the sixteenth day, the moon completes its cycle, Xun receives Xin and is seen at dawn." From the one Yang of Zhen advancing to receive the two Yang of Dui, reaching the three Yang of Qian and the full moon, this is the first three phases before the full moon "ming is born and魄 is dead" in the lunar cycle; from the one Yin of Xun retreating to receive the two Yin of Gen, reaching the three Yin of Kun and the moonlight fading away, this is the last three phases after the full moon "魄 is born and ming is dead" in the lunar cycle.

《禮運》曰「播五行於四時，和而後月生也，是以三五而盈，三五而闕」，正合此意。「播五行於四時」，以一歲中四氣之流行言之，「出震齊巽」之方位是也；「三五而盈，三五而闕」，以一月中月體之消長言之，「乾南坤北」之方位是也。

The Li Ji · Li Yun says, "Distributing the Five Phases among the four seasons, harmony is achieved and then the moon begins to shine; thus, after fifteen days it is full, and after another fifteen days it wanes," which precisely matches the meaning discussed above. "Distributing the Five Phases among the four seasons" refers to the flow of the four seasonal energies throughout the year, which corresponds to the Later Heaven arrangement of "The Emperor arises from Zhen, and harmonizes with Xun." "After fifteen days it is full, and after another fifteen days it wanes" refers to the waxing and waning of the moon's body within a month, which corresponds to the Earlier Heaven arrangement of "Qian in the south and Kun in the north."

熊氏朋來《五經說》曰：「《參同契》云『易謂坎離』，又云『日月為易』『乾坤門戶，坎離匡廓，牝牡四卦』。先天以乾坤坎離牝牡，兌震巽艮四卦。又云『坎離者乾坤二用，老陽變陰用九，老陰變陽用六』，其牝牡之體、九六之用皆坎離也。」

Xiong Penglai's "Commentary on the Five Classics" says: "The "Zhou Yi Cang Tong Qi" says 'the "Yi" is the Kan and Li,' and also says 'the sun and moon combined make the character "Yi." 'The Qian and Kun are the gateways, and the Kan and Li are the outer walls, with the male and female principles together forming four trigrams.' The Earlier Heaven diagram precisely pairs the Qian and Kun with the male and female principles, and the Dui, Zhen, Xun, and Gen as the other four trigrams. The "Zhou Yi Cang Tong Qi" also says 'the Kan and Li are the two functions of the Qian and Kun; the old yang transforms into yin and is called 'use nine,' and the old yin transforms into yang and is called 'use six.' ' It is evident that the substance of the male and female principles and the functions of nine and six ultimately all rest upon the Kan and Li.

「姑就《參同契》言之，則先後天圖已在其中。乾坤爐鼎，坎離水火，故後天坎離居先天乾坤之位，以坎中陽實離中陰虛仍為乾坤，故丹經謂之還元。乾専於陽，坤専於陰，曰爐鼎者，器之。惟夫離已日光，坎戊月精，互相根依，在納甲則主中宮戊巳之功，在先天則為日東月西之象，在後天則正火南水北之位。」

Taking the "Cantongqi" as an example, both the Earlier Heaven diagram and the Later Heaven diagram are already included within it. Qian and Kun are regarded as the furnace and cauldron, while Kan and Li represent water and fire. Therefore, in the Later Heaven diagram, Kan and Li occupy the positions of Qian and Kun in the Earlier Heaven diagram. Using the yang element of the middle line of the Zan卦 (Kan) to fill the yin vacancy of the middle line of the Li卦, it reverts back to Qian and Kun, hence the alchemical texts refer to this as "returning to the original state" (huan yuan). Qian is entirely yang and Kun is entirely yin, and they are called "furnace and cauldron" because they are regarded as vessels. As for Li paired with Ji to form the light of the sun and Kan paired with Wu to form the essence of the moon, they depend on each other. In the Najia method, they oversee the functions of the central palace (zhonggong) governed by Wu and Ji. In the Earlier Heaven diagram, they form the image of the sun in the east and the moon in the west. In the Later Heaven diagram, they are positioned at the south for fire and the north for water.

「八卦中乾兌二金，坤艮二土，震巽二木，皆陰陽和順；惟坎離水陰根陽、火陽根陰，不同他卦。天降而地升，陽倡而陰和，坎離者天地之交也。」

Among the Eight Trigrams, Qian and Dui belong to metal, Kun and Gen belong to earth, Zhen and Xun belong to wood, and all are harmonious within yin and yang. Only Kan and Li are different: Kan represents water, which is yin with yang as its root; Li represents fire, which is yang with yin as its root, differing from the other trigrams. When heavenly energy descends and earthly energy ascends, yang initiates and yin follows in response. Kan and Li are precisely where heaven and earth meet.

「故日為太陽精，離者日之象，何不三爻純陽而中有陰爻？才說太陽，其間便有少陰，所以日納月之烏，認得日中有月則可以知離卦。月為太陰精，坎者月之象，何不三爻純陰而中有陽爻？才說太陰，其間便有少陽，所以月納日之兔，認得月中有日可以知坎卦。」

Therefore, the sun is the essence of extreme yang, and the Li hexagram represents the image of the sun; yet why is it not composed of three yang lines with one yin line in the center? Because when we speak of the sun, it already contains a trace of yin, so the sun contains the black bird, which belongs to the moon. Understanding that the sun contains the moon allows one to understand the Li hexagram. The moon is the essence of extreme yin, and the Kan hexagram represents the image of the moon; yet why is it not composed of three yin lines with one yang line in the center? Because when we speak of the great yin, it already contains a trace of yang, so the moon contains the rabbit, which belongs to the sun. Understanding that the moon contains the sun allows one to understand the Kan hexagram.

「乾與離同受太極之陽，而離者中虛之乾；坤與坎同受太極之陰，而坎者中滿之坤。乾坤，太極之兩儀；坎離，太極之四象。是以坎離二卦常為陰陽造化之樞紐也。」

Qian and Li both receive the Taiji yang, but Li is merely Qian with a hollow center; Kun and Kan both receive the Taiji yin, but Kan is merely Kun with a filled center. Qian and Kun are the two yin and yang produced by Taiji, while Kan and Li are the four images produced by Taiji. Therefore, the two trigrams Kan and Li often serve as the pivot of yin and yang transformation.

「乾南坤北，離東坎西」之圖，朱子雖知其出於《參同契》而不欲盡言，至熊與可始發其隠。崑山吳先輩喬著《他石錄》，其外篇《儒辨》曰：「六經多被混亂，尤甚者《易》，《易》中尤甚者先天八卦。夫卦之方位，『帝出乎震』章八方有明文，『天地定位』章不言八方，蓋謂有天上地下之《否》而亦有地上天下之《泰》，八卦相蕩而成六十四卦也。逆數者，卜筮而前知吉凶也。先天之文見於乾卦，『先』讀去聲，非邵子之所謂也。」

The diagram "Qian in the south, Kun in the north, Li in the east, Kan in the west" was known by Zhu Xi to come from the "Zhou Yi Cang Tong Qi," but he did not fully explain it. It was not until Xiong Penglai (whose name was Yu Ke) that the hidden meaning was revealed. The elder scholar from Kunshan, Wu Qiao, wrote a book called "He Shi Lu," whose outer part, "Ru Bian," says: the Six Classics have been greatly confused, and the "Zhou Yi" is the most disturbed. Among the "Zhou Yi," the Earlier Heaven Trigrams are the most significant. Regarding the directions of the trigrams, the chapter "Di Chu Hu Zhen" in "Shuo Gua" clearly states the directions of the eight trigrams, but the chapter "Tian Di Ding Wei" does not mention directions. That passage merely refers to the "Pu" hexagram which has heaven below and earth above, and the "Tai" hexagram which has earth below and heaven above. The eight trigrams interact with each other to form the sixty-four hexagrams. The term "ni shu" refers to divination where the outcome is known in advance. As for the term "xiangan," its origin is found in the "Wenyan" of the Qian hexagram, "xiangan er tian fei wei," where the character "xian" is pronounced in the falling tone, and is not the "xiangan" as explained by Shao Yong.

「愚嘗得張平叔《悟真篇》之傳於方外士（宋天台張伯端，字平叔，一名用成，撰《通玄秘要悟真篇》一卷），其意與邵子之圖適合：離東者，移火於木位，東三南二同成五也；坎西者，移水於金位，北一西將四共之也；乾南坤北者，移坎之中實以填離之中虛，而成金丹三家相見結嬰兒也。」

I once received the transmission of Zhang Pingshu's "Wuzhen Pan" from a hermit (Zhang Bodaon, a person from Tiantai during the Song dynasty, also known as Zhang Yongcheng, who wrote a single volume called "Tongxuan Miya Wuzhen Pan"), and found that its meaning coincided exactly with Shao Yong's diagram. The statement that "Li is in the east" refers to moving fire to the position of wood, combining the number three of the east with the number two of the south to make five; the statement that "Kan is in the west" refers to moving water to the position of metal, combining the number one of the north with the number four of the west to be together; the statement that "Qian is in the south and Kun is in the north" refers to removing the yang element from the middle line of Kan hexagram to fill the yin vacancy in the middle line of Li hexagram, which is what the alchemists call "three families meeting" to form an infant.

「巽居西南坤位，以長女合老陰，黃婆也；艮居西北乾位，以少男合老陽，築基也；兌居東南巽位，以少女合長女，隠寓三七於其中，鼎器也；震居東北艮位，以長男合少男，隠寓二八於其中，藥物也。其於數往知來，遙寓順則成人、逆則仙也。」

The Trigram Xun occupies the Southwest, which originally belongs to Kun, thus combining the Elder Sister with the old yin, referring to the "Yellow Wife" mentioned by the alchemists. The Trigram Gen occupies the Northwest, which originally belongs to Qian, thus combining the Young Son with the old yang, referring to "building the foundation." The Trigram Dui occupies the Southeast, which originally belongs to Xun, thus combining the Young Girl with the Elder Sister, implicitly indicating the number "three and seven," referring to the "cauldron." The Trigram Zhen occupies the Northeast, which originally belongs to Gen, thus combining the Elder Son with the Young Son, implicitly indicating the number "two and eight," referring to the "medicine." As for the phrase "knowing the future from the past," it remotely embodies the alchemists' principle of achieving human longevity through progressive cultivation and immortality through reverse cultivation.

「《易》道無所不包，何獨丹法？凡醫藥、相地、三命等無不倚之以立言，而離於文王處憂患、孔子無大過，即非吾儒之《易》。希夷，仙也，不妨以外道說《易》；邵子交於二程，何可出此？考亭于丹道有所見，是以手注魏伯陽之《參同契》，見邵子之圖欣然會心，入之《本義》，而不計丹道可以倚《易》、《易》不為丹道作也。《本義》之混濫者多矣，以『天地定位』章為第一。」

The principles of the I Ching encompass everything, not merely the art of alchemy. All fields such as medicine, geomancy, and the three destinies rely on the I Ching to establish their theories. However, if one departs from the fundamental idea that King Wen composed the I Ching in times of distress and Confucius studied it to avoid great mistakes, then it is no longer the Confucian I Ching. Chen Tuan was originally a person of the Daoist tradition, so it is acceptable for him to use external doctrines to explain the I Ching. Shao Yong, having interacted with the two Cheng brothers, how could he produce such things? Zhu Xi (from the Kao Ting school) had some understanding of alchemy, so he personally annotated Wei Boyang's Treatise on the Concordance of the Three. When he saw Shao Yong's diagrams, he was delighted and included them in his The Original Meaning of the Zhou Changes, without realizing that while alchemy can be related to the I Ching, the I Ching was not created for alchemy. There are many mixed and confused parts in The Original Meaning of the Zhou Changes, with the chapter on "Heaven and Earth Positioned" being the first.

渭按：「丹道可以倚《易》，《易》不為丹道作」，又云「《易》道無所不包，而離於文王處憂患、孔子無大過，即非吾儒之《易》」，此真千古格言。方技家既借「天地定位」四句撰為此圖，下文順逆亦自有其說，邵子「已生未生」之解大非。「順則成人，逆則仙」，修齡義亦有所未盡，說在《參同契》「坎離之為易」也。

Hu Wei remarked: Wu Qiao said, "The Dao of alchemy can be based on the Book of Changes, but the Book of Changes was not written for alchemy." He also said, "The Dao of the Book of Changes encompasses everything, but once it departs from King Wen's concern with calamities and Confucius' pursuit of avoiding great mistakes, it is no longer the Book of Changes of the Confucian school." This is indeed a timeless and unchanging saying. Since the practitioners of techniques have used the four lines "Heaven and Earth are positioned" to fabricate this diagram, the subsequent terms "ascending" and "descending" must have their own interpretations in their view. Shao Yong's explanation using "already born" and "not yet born" is entirely wrong. As for the statement that "ascending leads to human life and descending leads to immortality," in terms of the meaning of cultivating longevity and health, there are still aspects not fully explained. This point will be discussed again when we talk about the "Kan and Li as the Book of Changes" in the "Cantongqi."

《周易參同契》曰：「天地設位，而易行乎其中矣。天地乾坤也，易謂坎離。坎離者，乾坤二用；二用無爻位，周流行六虛，往來既不定，上下亦無常。」又曰：「坎戊月精，離己日光，日月為易，剛柔相當。」又曰：「人所稟軀，體本一元，元精雲布，因氣托初。陰陽為度，魂魄所居。陽神日魂，陰神月魄，魂之與魄，互為室宅。」

The "Zhou Yi San Tong Qi" says: Heaven and Earth have established positions of above and below, and "Yi" operates within them. By "Heaven and Earth" it refers to Qian and Kun; by "Yi" it refers to Kan and Li. Kan and Li are the two functions of Qian and Kun; these two functions have no fixed lines, but pervade the six voids in all directions. Their movement has no fixed place, and their up and down have no regular pattern. It also says: Kan belongs to Wu and is the essence of the moon, while Li belongs to Ji and is the light of the sun. The sun and moon together form the character "Yi," with the firm and the yielding precisely matching each other. It also says: the body humans receive is originally derived from the single source. The original essence spreads like clouds, and takes form by relying on the original qi. Yin and Yang serve as the standards, being the dwelling places of the soul and spirit. The yang spirit is the sun's soul, and the yin spirit is the moon's body, with the soul and spirit mutually serving as each other's dwelling.

朱子《語類》曰：「《參同契》所言坎離水火龍虎鉛汞之屬，只是互換其名，其實則精氣二者而已。精，水也，坎也，龍也，汞也；氣，火也，離也，虎也，鉛也。其法以神運精氣，結而為丹。陽氣在下初成水，以火煉之則凝，神丹內外異色，如鴨子卵。」又曰：「水一也，火二也，以魂載魄，以二守一，則水火相濟而不相離，所以能永年也。養生家千言萬語，說龍說虎，說鉛說汞，說坎說離，其術只如此而已。」

The *Zhu Zi Yu Le* records Zhu Xi's words: The *Cantongqi* speaks of Kan and Li, water and fire, dragon and tiger, lead and mercury, but these are merely different names for the same things. In reality, they are only "essence" and "vital energy." Essence is water, Kan, dragon, and mercury; vital energy is fire, Li, tiger, and lead. Its method is to use the "useful god" to transform essence and energy, and to condense them into the elixir. When yang energy is at the bottom, it first becomes water. By using fire to refine it, it can condense. The inner and outer colors of the elixir are different, like a duck egg. He also said: The number of water is one, and the number of fire is two. Using the soul to carry the body, and using two to guard one, water and fire can assist each other without separation, thus achieving longevity. The words of the alchemists, speaking of dragon and tiger, lead and mercury, Kan and Li, are all just this.

先天八卦方位，丹家用之最親切而有味。其所謂「易」者，坎離也，與儒學不同，故解此章之順逆亦自有其義。孔子之意在蓍卦，丹家之意在水火。

The directional arrangement of the Earlier Heaven Trigrams is most fitting and meaningful for the Daoist alchemists. They refer to "Yi" as meaning Kan and Li, which differs from the Confucian approach. Therefore, their interpretation of the terms "shun" and "ni" in this chapter has their own set of principles. Confucius focused on the use of the yarrow stalks and the hexagrams, while the Daoist alchemists focused on water and fire.

人之一身，乾為首，坤為腹。自首以下有心，心屬火而為氣之總會；自腹以下有腎，腎屬水而為精之所藏。火炎上，水潤下，自有生而已然，所謂數往者順也。及加以修煉之功，以乾坤為爐鼎，坎離為鉛汞，務使火降而下、水升而上，所謂知來者逆也。

In the human body, Qian corresponds to the head and Kun corresponds to the abdomen. From the head downward is the heart, which belongs to fire and is the gathering place of qi; from the abdomen downward is the kidney, which belongs to water and is the storage of essence. Fire tends to rise upward, while water tends to descend and moisten, and this is the way it is from the moment a person is born, which is what the Daoist alchemists refer to as "knowing the past in a natural way." When cultivation is added, one uses Qian and Kun as the furnace and cauldron, and Kan and Li as lead and mercury. One must necessarily make the fire descend and the water ascend, which is what they call "knowing the future in a reverse way."

《鼎器歌》云「陰在上，陽下奔」，陰謂水，陽謂火。丹家以坎離為易，水下而反上，火上而反下，故曰「易逆數也」。《說卦》離南而坎北，丹家抽坎之中實以填離之中虛，故乾南而坤北。《參同契》云「子南午北，互為綱紀，一九之數，終而復始」，亦此義也。

The "Ding Qi Ge" from the "Cantong Qi" says, "Yin is above, Yang rushes downward," where "Yin" refers to water and "Yang" refers to fire. Alchemists associate Kan and Li with the "Yi" (Change). Water naturally resides below but rises upward, while fire naturally resides above but descends downward, hence the saying "the Yi reverses the order." The Later Heaven directions in "Shu Gua" place Li in the south and Kan in the north. Alchemists extract the Yang element from the middle line of Kan and use it to fill the Yin deficiency in the middle line of Li, resulting in Qian in the south and Kun in the north. The "Cantong Qi" states, "The position of Zi is in the south, the position of Wu is in the north, they mutually form the framework; the numbers one and nine, cycle and repeat," which explains the same principle.

人之生也，火在水上，未濟之象也；神丹既成，則水在火上為既濟。以魂守魄，使陰陽不相離，可以長生而久視。仙訣云「五行順行，法界火坑；五行顛倒，大地七寳」，是為順則成人、逆則仙也。

When a person is born, fire is on water, which corresponds to the image of the hexagram "Not Yet Completed." Once the divine elixir is successfully prepared, it becomes water on fire, forming the hexagram "Already Completed." By using the soul to control the body, and keeping yin and yang from separating, one can achieve long life and prolonged vision. The secret words of the immortal masters say, "If the Five Phases proceed in order, the entire realm becomes a fire pit; if the Five Phases reverse, the whole world is filled with treasures." This is what is meant by following the natural order to be a human being, and reversing the order to become an immortal.

邵子小橫圖用加一倍法以為伏羲八卦之次序，誤矣；而又推之於方位，以自震至乾為順、自巽至坤為逆，且喻之以左旋右行。夫天之與日月五星也，左則俱左，右則俱右，豈有左右各半之理乎？既失丹家之旨，又非孔子之義，無一而可者也。

Shao Yong's small horizontal diagram arranges the trigrams by doubling, treating them as the order of Fuxi's eight trigrams, which is already incorrect. He further applied this method to directions, claiming that from Zhen to Qian is clockwise and from Xun to Kun is counterclockwise, using left rotation and right movement as metaphors. However, the movement of heaven and the sun, moon, and five planets either all move left or all move right; there is no logic to having half moving left and half moving right. In this way, it loses the essence of the Daoist alchemists' teachings and contradicts Confucius's original meaning, and there is nothing that stands up to scrutiny.

或問：「子以希夷先天圖為康節之學所自出，其詳可得聞乎？」曰：「康節受《易》於李之才，以先天古《易》衍其旨，蓍書十餘萬言（謂《皇極經世》《觀物內外篇》《漁樵問對》）以發希夷之蘊。史稱『探賾索隠，妙悟神契，洞徹蘊奧，汪洋浩博，德其所自得者』，此實録也。」

Someone asked, "Do you think Chen Tuan's Earlier Heaven Diagram is the source of Shao Kangjie's learning? Could you explain in detail?" The answer was: Shao Yong learned the study of the Book of Changes from Li Zhicai, using the ancient Earlier Heaven version of the Book of Changes to explore its meaning, and wrote more than ten thousand words of works, including The Huangji Jingshi, The Guanwu Neiwaipian, and The Yuqiao Wen Dui, to elaborate on the profound insights of Chen Tuan's school. Historical records say he "explored the profound, searched for the hidden, had a wonderful insight that harmonized with the divine principles, thoroughly understood its depth, and his vast and profound knowledge was all his own," and these words are accurately recorded.

今以八卦次序、方位圖考之：太極即希夷先天圖之環中也；初畫為兩儀，即圈之白黒各半左右回互者；中畫為四象，即白中之黒、黒中之白與半白半黒而為四也；終畫為八卦，即一圈界分為八，而八卦竒偶之畫與白黒之質相應者也。從中折取，則乾南坤北、離東坎西、震東北、兌東南、巽西南、艮西北，八卦有方位而九宮具焉也。

Now examining the sequence diagram of the Eight Trigrams and the directional diagram of the Eight Trigrams: the so-called "Taiji" is the central circle in Chen Tuan's Earlier Heaven diagram. The two principles at the lowest line are represented by the black and white each occupying half of the circle, interlocking and embracing left and right. The four images at the middle line are formed by the black within white, the white within black, and the half-black and half-white, making a total of four. The Eight Trigrams at the top line are formed by dividing the circle into eight parts, and the odd and even lines of the Eight Trigrams correspond exactly with the black and white qualities. By folding the diagram from the center, the directions of the Eight Trigrams are determined: Qian in the South, Kun in the North, Li in the East, Kan in the West, Zhen in the Northeast, Dui in the Southeast, Xun in the Southwest, and Gen in the Northwest. The Eight Trigrams now have directions, and the nine-square grid numbers are included within this structure.

圓者引之使長，合者攡之使分，而圖遂化為畫矣。然兩儀、四象、八卦皆子在母外，既失希夷之本意；而又以白代單、以黒代拆，則乾之三連變為三白□，坤之六斷變為三黒□，六子皆然（坎離即水火匡廓之形）。表畫以色，有竒無偶，大非三代以來相傳之卦象，瀆經侮聖與劉牧無異，何為其從之也？

To stretch the circle into a straight line to make it longer, and to separate what was joined to make it dispersed, thus the circular diagram became the hexagram diagram. However, in this way, the two principles, four images, and eight trigrams all became like "a child outside the mother's body," having lost Chen Tuan's original meaning. Moreover, using white to represent the odd lines and black to represent the even lines, the three continuous lines of Qian became three white squares, and the three broken lines of Kun became three black squares, and all six sub-trigrams were treated in the same way (the trigrams Kan and Li are the shape described in the "Compendium of the Three" as water and fire encircling each other). Using colors to indicate the trigrams results in only odd lines and no even lines, which greatly contradicts the trigrams' forms passed down since the Three Dynasties. This disrespectful treatment of the classics and contempt for the sages is no different from Liu Mu's approach, so why follow him?

右論邵子伏羲八卦方位。

The above points discuss the "Fuxi Eight Trigrams Diagram" as determined by Shao Yong.