Yi Shi Tong Bian (易筮通變)

經名：易筮通變。原題臨川道士雷思齊學。三卷。底本出處：《正統道藏》太玄部。參校版本：文淵閣四庫全書本經部易類（簡稱四庫本）

This book is titled "Comprehending Change in Yarrow Divination," originally attributed to "Lei Siqi, the Taoist from Linchuan." The entire work consists of three volumes. The edition used for collation is from the Taixuan Department of the Zhengtong Daozang, with the reference text being the version included in the Jingbu (Classics Section) of the Wenyuan Ge Siku Quanshu, hereafter referred to as the "Siku Ben."

臨川道士雷思齊學

This volume was written by the Daoist priest Lei Siqi of Linchuan (now Fuzhou, Jiangxi). The term "xue" in the title is a common modest expression used by authors in the Song and Yuan dynasties, meaning "what has been studied and gained," which is equivalent to saying that this is Lei Siqi's personal commentary on the Book of Changes.

《洪範》之《稽疑》曰：擇建立卜筮人，乃命卜筮。《詩》曰：爾卜爾筮，體無咎言。曰：卜筮偕止，會言近止。《記》之《月令》則曰：孟冬之月，命大史釁龜筮，占兆吉凶。宜若龜筮相須為用也。《易大傳》曰：探跡索隱，鉤深致遠，成天下之賽賽者，莫大乎曹龜。又曰：以卜筮者尚其占。則夫《易》宜兼卜筮之用者也。《大誥》曰：寧王遺我大寶龜，紹天明，即命。《金朦》曰：乃卜三龜，一習吉。於是莫見夫筮。《記》又曰：天子無筮，諸侯有守筮。天子道以筮。於是又莫見夫卜。

The "Kiyi" section of the "Shangshu · Hongfan" says that one should select and appoint specialists in divination with tortoise shells and yarrow stalks, and then have them perform both divination and augury. The "Shijing" says, "You divinate with tortoise shells and yarrow stalks, and the omens have no ominous words" — you divinate with both methods, and the signs from both are auspicious. It also says, "Divination with tortoise shells and yarrow stalks both speak, and they say the time of meeting is near." The "Liji · Yueling" says that in the first month of winter, the Grand Historian is ordered to use animal blood to smear and consecrate tortoise shells and yarrow stalks, to observe the omens for auspicious or inauspicious signs. According to these records, divination with tortoise shells and yarrow stalks seem to be meant to be used together. The "Xici Zhuan" says that seeking the profound and grasping the deep mysteries, nothing can accomplish the diligent endeavors of the world more than yarrow stalks and tortoise shells (the original text "sai sai" is actually "mei mei," and "cao" is a variant form of "zhi," meaning yarrow stalks). It also says, "Those who use divination should value its interpretation," implying that the "Zhouyi" should also use both tortoise shells and yarrow stalks. However, the "Shangshu · Dage" says that King Wen left me a great tortoise shell, using it to receive the mandate of heaven — the entire passage only discusses tortoise shell divination. The "Jinteng" says that Duke Zhou "divined with three tortoise shells, and all were auspicious" — three tortoise shells were used for divination, and all gave auspicious signs — here there is no mention of yarrow stalks. The "Liji" also says that the Son of Heaven does not use yarrow stalks in times of peace, but only the feudal lords have divination for their states, and the Son of Heaven uses yarrow stalks only when traveling — here there is no mention of tortoise shell divination.

而《說卦》則曰：昔者聖人之作《易》，幽贊於神明而生曹，參天兩地而倚數，觀變於陰陽而立卦，發揮於剛柔而生爻，以至和順於道德而理於義，窮理盡性以至於命。乃獨歸夫筮，而未始及夫卜也。由筮命曹，而曹筮之用著於大衍之數皇詳且備，而龜之卜則莫之一語及也。雖亦問見謂龜為卜，曹為筮之說於別出，而愚自童卯習見世之常占擲錢以畫卦爻，雲自京房始矣，且賈公彥亦以畫卦之單拆重交之爻謂以錢，復見有假於龜之剖中以布其錢者；又雜於傳記謂卜得某卦之某卦之大凡，且人有常言皇稱卜卦，故亦隨之等視曹龜卜筮為一盤，未嘗以為意也。

But the "Shuo Gua Zhuan" says that the ancient sages created the "Zhou Yi" with the help of divine spirits, and from this they obtained the yarrow stalks. They established the divination numbers by referring to the trinity of heaven and the duality of earth. They observed the waxing and waning of yin and yang to create the hexagrams, and through the shifting of firmness and softness, they generated the lines. Then they harmonized with morality and ordered things according to principles, explored the nature of things, and fully revealed human nature, all the way up to the mandate of heaven. All these discussions are centered around "shì" (divination with yarrow stalks), and there is no mention of "bǔ" (divination with turtle shells) throughout. The method of using yarrow stalks is explained in detail in the chapter "Da Yan Zhi Shu," while there is not a single mention of turtle shell divination. Although there are occasional references to the distinction between "gu jiao bǔ" (turtle shell divination) and "shi shi" (yarrow stalk divination), from my childhood I have seen that people usually use copper coins to draw the hexagrams and their lines. It is said that this method began with Jing Fang of the Han dynasty. Jia Gongyan of the Tang dynasty also mentioned that the four types of line patterns in hexagram drawing—single, split, double, and intersecting—were determined by tossing copper coins. I have also seen people using turtle shells, cutting them open and placing coins inside for divination. Moreover, historical records often vaguely refer to "bǔ de suoyi gua zhi suoyi gua," and people commonly refer to it as "bǔ gua." Therefore, I have always regarded yarrow stalks and turtle shells, as well as "bǔ" and "shi," as essentially the same thing, and I have never given it much thought.

蓋嘗見《周禮春官》之屬：大卜掌三兆之法，一日玉兆，二日瓦兆，三日原兆，其經兆之體皆百有二十，其頌皆千有二百，其下有卜師掌開龜兆，龜人掌六龜，以其方色，與體辨之；大卜又掌《三易》之法，一日《連山》，二日《歸藏》，三日《周易》，其經卦皆八，其別皆六十有四，其下有筮人掌《三易》之九筮，以辨吉凶。凡國之大事，先筮而後卜，上春相筮，凡國事共筮，然後知卜之用龜，則以兆其書，兆之體、頌至百有二十、千有二百之多，而《易》之筮用曹，固未始出於六十四卦之外，則卜自卜，筮自筮，未始相為用也。

Later I read about the officials under the Spring Officials in the "Zhou Li" who were responsible for divination. It said that the "Da Bu" (Great Diviner) was in charge of three methods of divination: one called Yu Zhaoguang (Jade Divination), another called Wa Zhaoguang (Tile Divination), and the third called Yuan Zhaoguang (Plain Divination). Each method had 120 "ti" (forms) and 1,200 "song" (interpretations). Under the Da Bu were the "Bu Shi" (Divination Master) who handled the preparation of the turtle shells and the reading of the omens, and the "Gui Ren" (Turtle Keeper) who managed six types of turtles, distinguishing them by their direction, color, and shape. The Da Bu also oversaw the methods of the "San Yi" (Three Changes)—one called "Lianshan" (Continuous Mountains), another called "Guicang" (Return to the Treasury), and the third called "Zhou Yi" (The Zhou Changes). All three had eight basic trigrams and sixty-four compound trigrams formed by combining them. Under the Da Bu were the "Shi Ren" (Divination Master) who handled the nine methods of divination used in the "San Yi" to discern fortune and misfortune. For all major state affairs, divination by the "Shi" (using yarrow stalks) was done first, followed by divination by the "Bu" (using turtle shells). In the first month of spring, the use of yarrow stalks and turtle shells was reviewed, and all state affairs were subject to divination. Reading this, I realized that divination by the "Bu" (turtle) relied on the turtle shells, producing omens that formed the basis of the divination texts, with 120 forms and 1,200 interpretations. In contrast, the divination of the "Yi" (I Ching) used yarrow stalks, which could not exceed the sixty-four hexagrams. This shows that divination by the "Bu" and divination by the "Shi" are distinct and have never been used interchangeably or mixed together.

況《洪範》固有龜從、筮從，龜從、筮逆、龜筮共違於人之別，則其卜筮之分校然，其辨白黑未始。若後世說卜筮者，樊然般亂，至若是之甚，心甚異之。由是於《左傳》之類究其成驗，乃判然識卜筮之道。卜者未嘗引《易》之筮，筮者未嘗引龜之卜也。今疏列為徵。

Moreover, the "Hong Fan" originally distinguishes between "turtle follows, divination follows" (both turtle divination and yarrow divination agree), "turtle follows, divination opposes" (turtle divination agrees while yarrow divination disagrees), and "both turtle and divination contradict the person" (both contradict the person's intention). This shows clearly that the boundaries between divination and yarrow divination are distinct, as clear as black and white, never ambiguous. However, later scholars who discuss divination and yarrow divination have become so confused and mixed up that I find it very strange. Therefore, I went to books like the "Zuo Zhuan" to examine actual instances of divination, and thus clearly discerned the distinct methods of divination and yarrow divination: those who use turtle divination never refer to the yarrow divination method from the "Yi Jing," and those who use yarrow divination never refer to the oracle signs from turtle divination. Now I will list these examples in order as evidence.

有專卜而不筮者。晉惠公之在梁，梁伯妻之。梁贏孕過期，卜招父與其子卜之。子曰：將生一男一女。招曰：然。男為人臣，女為人妾。名男日圉，女日妾。及圉西質於秦，妾為宦女焉。鄰文公卜遷於繹，史曰：利於民而不利於君。鄰子曰：苟利於民，遷也。天生民而樹之君，以利之也。民既利矣，孤必與焉。既遷，而鄰子卒。齊侯戒師期，將以伐魯，而有疾，醫曰：不及秋，將死。魯文公聞之，卜曰：尚無及期。叔仲惠伯令龜，卜楚丘占之，曰：齊侯不及期，非疾也。君亦不聞，今龜有咎。既而，齊懿公弒，文公先薨，惠伯亦卒。

First, consider the case where only turtle shells were used for divination without the use of yarrow stalks. When Duke Xi of Jin was in exile in the State of Liang, the Duke of Liang married his daughter to him. When Lady Liang became pregnant and her due date passed, Bo Zhao Fu and his son performed a divination for her. The son said: "A son and a daughter will be born." Zhao Fu said: "Yes, the son will become a minister, and the daughter will become a concubine." So they named the boy "Yu" and the girl "Jie." Later, Yu went west to Qin as a hostage, while Jie became a palace maid in Qin. When Duke Wen of Zhu planned to move the capital to Ye, the official historian said: "This will be beneficial for the people, but not for the ruler." Duke Zhu said: "If it is beneficial for the people, then I will move the capital." Heaven created the people and established a ruler for them, which is to benefit the people. Since the people have benefited, I will certainly also benefit. After the capital was moved, Duke Zhu died. When Duke Yi of Qi set a date for military action to attack Lu, he fell ill, and the physician said: "He will not live until autumn." When Duke Wen of Lu heard this, he performed a divination, and the oracle said: "May he not live until the time of the military action." Shu Zhong Hui Bo announced the oracle on the turtle shell, and Bo Chu Qu judged that Duke Yi of Qi would indeed not live until the time of the military action, but not because of illness. However, the king would not hear this news, and this divination would bring disaster upon me personally. Later, Duke Yi of Qi was assassinated, Duke Wen of Lu died first, and Shu Zhong Hui Bo was also killed.

楚王與葉公枚卜子良以為令尹，沈尹朱曰：吉，過於其志。葉公曰：王子而相國，過將何為？它日改卜子國以為令尹。若是四者，見卜之未嘗及於筮卦也。

King Chu and Ye Gong used the method of "enumerated divination" (divination without naming the subject) to consult the oracle on appointing Zi Liang as Minister of State. Shen Yin Zhu said: "It is auspicious, and it surpasses his original intention." Ye Gong replied: "To appoint a prince as Minister of State, what could 'surpassing his intention' mean? (Implied meaning: it suggests a desire to seize the throne.)" Later, they changed the appointment to Zi Guo as Minister of State. These four instances show that when using turtle-shell divination, it never involved the hexagrams obtained through yarrow stalks.

有筮而不卜者。畢萬筮仕於晉，遇《屯》之《比》。辛廖占之，曰：吉。《屯》固《比》入，吉孰大焉，其必蕃昌。震為土車從馬，足居之，兄長之，母覆之，眾歸之，六體不易，合而能固，安而能殺，公侯之卦也。公侯之子孫，必復其始。

Now consider the case where divination is done only with the yarrow stalks and not with the turtle shell. Bi Wan went to the state of Jin to seek an official position, and he divined with the yarrow stalks, obtaining the hexagram "Zun" changing to "Bi," meaning the first line of the hexagram "Zun" moved and transformed into the hexagram "Bi." Xin Liao interpreted this as auspicious. "Zun" represents stability, and "Bi" represents affinity. Is there a greater auspiciousness than this? He will certainly flourish and grow great. The movement of the trigram "Zhen" (Thunder) transforms into the trigram "Kun" (Earth). The chariot follows the horse, the feet are on the ground, the elder brother supports him, the mother covers him, and the people follow him. These six images remain unchanged. Combined, they form a firm and stable structure, capable of making decisive judgments within stability. This is the hexagram of a duke or marquis. The descendants of a duke or marquis will certainly restore their ancestors' original status.

泰伯伐晉，卜徒父筮之，曰：吉，涉河，侯車敗。詁之，對曰：乃大吉也，三敗必獲晉君。其卦遇《蠱》，其《縣》曰：千乘三去，三去之餘，獲其雄狐。夫狐蠱，必其君也。《蠱》之貞，風也；其悔，山也。歲云秋矣，我落其實而取其材，實落材亡，不敗何待？三敗及韓。晉侯逆秦師，戰於韓原，秦獲晉侯以歸。

Qin Mu Gong attacked the State of Jin (the original text refers to "Tai Bo," meaning Qin Bo), and Bo Tu Fu used the yarrow stalks for divination. He said it was auspicious; crossing the Yellow River, the war chariots of the feudal lords would be destroyed. Mu Gong questioned this, and he replied that this was indeed a great auspicious sign. After three defeats, the king of Jin would certainly be captured. The divination resulted in the hexagram "Gǔ." Its line statement says: "A thousand chariots retreat three times, after three retreats, capture the male fox." This refers to the "fox" in "Gǔ," which must be the king of Jin. The inner trigram (Zhen) of the hexagram "Gǔ" is Xun, representing wind; the outer trigram (Hui) is Gen, representing mountain. Now the season has entered autumn; we have shaken off its fruits and taken its timber. The fruits are all gone, the timber is all used up; when will it not fall? Later, the Jin army retreated three times, all the way to the area of Han. King Hui of Jin confronted the Qin army at Han Yuan, and the Qin army indeed captured the king of Jin and returned.

晉侯伐鄭，楚子救鄭，相遇於鄙陵。公筮之，史曰：士悶。卦遇《復》，曰：南國贓，射其無王，中厥目，國蹴王傷，不敗何待？及戰，呂錡射共王，中目。王曰：天敗楚也，吾不可待。乃宵遲。

King Jin Li Gong attacked the State of Zheng, and King Chu Gong Wang sent his army to rescue Zheng. The two armies met at Yancheng (the original text says "Biling," which is Yancheng). Li Gong ordered someone to divinate, and the historian said: auspicious (the original text says "Shi Men," which is a distorted form of "Ji," meaning auspicious). The hexagram obtained was Fu. The commentary said: "The southern state is distressed, shoot their king, hit his eye." The southern state is in distress, their king is wounded, when will they not be defeated? When the battle began, Lü Qi shot King Chu Gong Wang, and indeed hit his eye. King Chu said: this is heaven's will for Chu's defeat, I can no longer wait. So he withdrew his army at night.

晉獻公筮嫁伯姬於秦，遇《歸妹》之《睽》。史蘇占之，曰：不吉。其《縣》曰：士到羊，亦無血也；女承筐，亦無既也。西鄰責言，不可償也。《歸妹》之《睽》，猶無相也。震之離，亦離之震，為雷，為火，為贏敗姬。車說其轅，火焚其旗，不利行師，敗於宗丘。《歸妹》之《睽》，寇張之弧。侄其從姑，六年其通，逃歸其國，而棄其家。明年，其死於高梁之虛。

King Jin Xian Gong consulted the oracle to marry his daughter Bo Ji to the state of Qin, and obtained the hexagram "Gui Mei" changing to "Kui." The historian Su judged it as inauspicious. The hexagram's judgment says: "The man cuts the sheep, yet there is no blood; the woman carries the basket, yet there is nothing to carry." A western neighbor will demand reparation, and there will be no means to repay. The change from "Gui Mei" to "Kui" indicates that no one will help. The trigram Zhen changes to Li, which is fire, indicating that the state of Qin, of the Ying surname, will defeat the state of Jin, of the Ji surname. The chariot's yoke falls off, and the banner is burned by fire, which is unfavorable for military action, and a defeat will occur at the ancestral hill. The change from "Gui Mei" to "Kui" is exactly "the enemy stretches his bow," meaning the enemy will turn against them. The nephew of the bride, Yi Wu, who later went to Qin, will return to his homeland after six years, abandoning his family. The next year, he will die in the ruins of Gao Liang.

若是四者，筮則有卦，而無復卜兆辭也。且前之《屯》、《復》、《蠱》三卦，其縣固皆非《周易》之辭。後之《歸妹》之《睽》卦，辭近《周易》，而亦非也。盤可想見，《連山》、《歸藏》之《易》，其筮法同，而縣辭異也。

The four things mentioned above can be obtained as hexagrams through divination with yarrow stalks, but there is no oracle inscription from龟卜. Moreover, the line statements cited from the hexagrams of 《Zun》, 《Fu》, and 《Gu》 at the beginning are not actually the hexagram line statements of 《Zhou Yi》; and the line statement in 《Gui Mei》 related to 《Kui》, although its wording is similar to 《Zhou Yi》, is actually not from it. From this we can see that the two books of 《Lianshan》 and 《Guicang》 use the same divination method as 《Zhou Yi》, but differ only in the line statements attached.

有兼用卜、筮，而卜有辭，筮亦有辭者。魯成季之將生也，桓公使卜楚丘之父卜之。曰：男也，其名日友，在公之右；閒於兩社，為公室輔。季氏亡，則魯不昌。又筮之，遇《大有》之《乾》，曰：同復於父，敬如君所。及生，有文在其手日友，遂以命之。若是者，卜與筮各有辭，筮之卦辭亦非《周易》辭也。

Again, we see the use of both龟卜 and 蓍筮, and both methods have their own statements. When Duke Huan of Lu was about to have a son, he had his father, Bo Qu, perform a divination. The oracle said: it would be a boy, whose name would be "You," and he would be on the right side of the king. He would move between the亳社 and 周社, serving as an assistant to the royal house. If the Ji family were to perish, Lu would not flourish. Then, they also used 蓍筮 to inquire, and obtained the hexagram 大有 changing into 乾. Specifically, the line Six in the Fifth of 大有 moved to become 乾, and the statement said: "Returning to the father in harmony, showing respect as the king would have it." This means his status would be equal to his father, and he would be respected as the king would wish. When the child was born, there was a mark on his hand resembling the character "友," so they named him accordingly. In this case, both龟卜 and 蓍筮 had their own statements, and the statement from 蓍筮 was not from the Zhou Changes.

有先卜後筮者。晉獻公欲以驪姬為夫人，卜之，不吉；筮之，吉。公曰：從筮。卜人曰：筮短龜長，不如從長。且其《縣》曰：專之渝，攘公之褕。一熏一蓿，十年尚猶有臭。必不可。弗聽，立之。生奚齊。乃潛太子申生至於縊死，遂立奚齊。卒亂晉。

Now looking at the case where divination was first used and then augury. Duke Jin Xiangong wanted to make Li Ji his wife. He first used a turtle oracle, which was not auspicious; then he changed to using yarrow stalks for divination, which was auspicious. Duke Jin said: Then we will follow the divination. The oracle master said: Divination has short efficacy, while the turtle oracle has long efficacy; it is better to follow the one with long efficacy. Moreover, the oracle inscription of the turtle said: "Exclusive favor will bring about change, and will take away your virtue." "One fragrance, one stench, even after ten years, the stench remains." It is not advisable at all. Duke Jin did not listen, and still made Li Ji his wife, who gave birth to Xi Qi. Later, he finally forced Prince Shen Sheng to commit suicide, and made Xi Qi his heir, ultimately causing chaos in the state of Jin.

有先筮而後卜者。衛侯夢於北官，見人登昆吾之觀，被髮而噪曰：登此昆吾之虛，綿綿生之瓜。余為渾良夫，哄天無辜。公親筮之，胥彌赦占之，曰：不害。衛侯貞卜，《縣》曰：如魚窺尾，衡流而方羊。裔焉大國，滅之，將亡。闔門塞竇，乃自後瑜。冬十月，晉復伐衛，入其邪。衛出莊公而與晉平，晉立襄公之孫般師而還。若是二者，雖先卜後筮，先筮後卜，則殊筮無卦辭，卜乃有縣，然為卜為筮不比而同也。

Now looking at cases where divination comes first and then oracle bone divination follows. When Duke Zheng of Wei was staying in Beigong, he had a dream in which someone climbed up the terrace of Kunwu, with his hair loose and shouting loudly: "Climb this old site of Kunwu, and endless gourds will grow. I am Hun Liangfu, I call upon heaven to clear my innocence." Duke Zheng personally performed divination with yarrow stalks, and Xu Mishi judged that it would be harmless. Duke Zheng then used oracle bones for formal divination, and the oracle text said: "Like a fish tiredly flicking its tail, drifting in the current and hesitating; the state will be driven to the border, and will be destroyed; the gates will be closed and the passages blocked, but they will escape by climbing over the back wall." In the winter of the same year, the State of Jin attacked Wei again, entered the outer city of Wei's capital, and the people of Wei drove out Duke Zheng and made peace with Jin. Jin then established Ban Shi, the grandson of Duke Xiang of Wei, as the new ruler before withdrawing. In these two events, although one involved first divination and then oracle bone divination, and the other first oracle bone divination and then divination, when divination was performed there was no hexagram statement, but when oracle bone divination was used, there was an oracle text. This shows that divination and oracle bone divination are separate practices, and are not combined into one.

其若晉獻公卜伐驪戎，史蘇占之，曰：勝而不吉。公曰：何謂也？對曰：遇兆曰：挾以銜骨，齒牙為猾，戎夏交拌，是交勝也。臣故云。且懼有口，擁民國私心焉。公曰：何口之有？口在寡人，寡人弗受。誰其興之？對日；苟可以攜其入也，必甘受逞，而不知胡可壅也。公弗聽，遂伐驪戎，克之，獲驪姬以歸，卒以亂國。若是者，卜獨有縣辭，而不及筮，則《國語》猶然也，辭與《左傳》尚未相遠也。

For example, when Duke Jin Xiangong divined about attacking the Li Rong, Shi Su judged that they would win but it would not be auspicious. Duke Jin Xiangong asked, "Why is that?" Shi Su replied, "The omen said, 'Clasping with bones in the mouth, the teeth are disturbed by it.' This means that although they may seize the enemy, they will be troubled by it. 'The Huaxia and the Rong people contend,' meaning that the Huaxia and the Rong will fight each other, alternating in victory. That is why I said so. Moreover, we should fear the emergence of slander, stirring up the people's hearts and giving rise to private intentions. Duke Jin Xiangong said, "Where would such slander come from? The mouth is mine, and if I do not accept it, who else could incite it?" Shi Su replied, "As long as there is an opportunity to sow discord, people will willingly be tempted by it, and then we will not know how to stop it." Duke Jin Xiangong did not listen, and thus attacked the Li Rong, conquered them, captured Li Ji, and brought her back, ultimately causing chaos in the state. This case involves only the divination oracle of the turtle shell, and has nothing to do with the yarrow stalks. The account in the Guoyu is also like this, with the wording not differing greatly from that in the Zuo Zhuan.

若《家語》謂孔子嘗自筮得《賁》卦，愀然有不平之色。子張進曰：卜者得《賁》卦，吉也；而夫子之不平，何也？子曰：以其離邪。在《周易》，山下有火，賁；非正色之卦也。夫質也者，黑白宜正焉。今得《賁》，非吾兆也。吾聞丹漆不文，白玉不雕，何也？質有餘，不受飾也。

According to the "Sayings of the Master Kong," Master Kong once cast the "Zhen" hexagram and his face turned very unhappy. Zi Zhang approached and asked: The "Zhen" hexagram is considered auspicious, yet the Master is not happy. Why? Master Kong said: Because it is "Li." In the "Zhou Changes," fire beneath the mountain is called "Zhen," but it is not a hexagram of pure color. What is meant by "quality" is that black should be black and white should be white, only then is it proper. Now, having obtained "Zhen," it is not what I desire. I have heard that vermilion does not need patterns and white jade does not need carving, why? Because the essence is already sufficient, and no further decoration is needed.

由今觀之，是可疑者。且既謂孔子自筮，何子張乃謂之卜？況其辭與《易》不類？《賁》之《象》曰：賁，柔來而文剛。分剛上而文柔，故小利有攸往。天文也；文明以止，人文也。觀乎天文，以察時變；觀乎人文，以化成天下。何夫子於《象》取其文，於筮獨尚其質？自相抵悟，遽至於此，愚故不敢以《家語》為信。

Based on what is seen today, this account is very doubtful. If it is said that Confucius himself performed the divination, why does Zi Zhang refer to him as '卜' (divination by oracle bones)? Moreover, this passage is inconsistent with the statements in The Zhou Changes. The Commentary on the Judgment of the Qian hexagram says: 'Bian' is when a yao of yin comes to adorn a yao of yang, and when the yang yao ascends to adorn the yin yao, thus slightly favorable for going forward, which is the heavenly aspect; civilized and knowing moderation, which is the human aspect. Observing the heavenly aspect allows one to understand the changes of the four seasons; observing the human aspect allows one to educate the world. Confucius in the Commentary on the Judgment takes its 'wen' (civilization), so why, when performing divination, does he instead emphasize 'zhi' (substance)? This contradiction has reached such a degree that I dare not take the Analects of Master Kung as reliable evidence.

至皿左氏於專筮而不卜，列於《傳》者尚多有之，不克枚舉，悉以《周易》之辭推之。《周易》獨行至今，人莫不審悉。自《家語》一事之外，卜之用龜兆，筮之用曹卦，斷斷乎未嘗自為紛札也。抑亦見《連山》、《歸藏》之與《周易》而為三，其經卦皆八，其別皆六十有四者，於《禮》為不誣。《連山》、《歸藏》，今莫之見，例此迦求猶彷佛一二，曷嘗如後之俗誘，然同謐習稱曹筮為卜卦哉？

As for the many instances in the Zuo Zhuan where only divination by yarrow stalks was used without oracle bone divination, they are too numerous to list, and all of them can be interpreted using the hexagram and line statements of the Zhou Yi. The Zhou Yi has been passed down alone to the present day, and everyone is familiar with it. Except for that one incident mentioned in the Jia Yu, divination by oracle bones always used turtle shells, and divination by yarrow stalks always used the hexagrams, and there was never any mixing of the two. From this we can see that the Lian Shan, Gui Cang, and Zhou Yi were all regarded as three separate systems, with "their basic trigrams all being eight, and their differentiated trigrams all being sixty-four." The records in the Zhou Li did not lie. The Lian Shan and Gui Cang are no longer available today, but by following this example, we can still glimpse a little of their appearance. How different this is from later popular views, which indiscriminately refer to both yarrow stalk divination and oracle bone divination as "divination by hexagrams."

說者謂《易經》由混於卜筮、占兆得兔秦火，固亦或者，然其謂太卜所掌經兆之體皆百二十，其頌皆千二百，乃無得見者，豈所謂占兆可脫於火者亦不免邪？

Some people say that the Yi Jing was able to escape the burning of the Qin dynasty's books because it was mixed in with divination and oracle books. This has some truth to it. But according to the Zhou Li, the Grand Diviner was in charge of 120 forms of oracle signs and 1,200 oracle verses. Yet none of these are now to be found. So did those supposed oracle books that were said to have escaped the Qin fire ultimately not survive at all?

昔漢文自代來，卜得大橫，《縣》曰：大橫庚庚，余為天王，夏啟以光。釋者謂大橫，龜之正橫是其體也。文帝有土之象，則卜兆漢初似尚存，而後世不傳，唯北齊高洋欲篡東魏，卜於李密，亦謂大橫，曰：漢文之兆也。愚意：密特諂洋以成其篡耳。焉可盡信哉？後世卜兆之書，沒沒不聞，多中何哉？嗟乎，合其體既三百六十，分其頌乃三千六百之富，宜乎其不存也。誠使其存，誰其及之哉？

In the past, Emperor Wen of Han, when he was brought from the State of Dai to the capital, received an omen of "Da Heng." The oracle text said: "Da Heng Geng Geng, I shall be the heavenly king, like Xia Qi who expanded his father's achievements." The omen of "Da Heng" refers to a horizontal pattern in the tortoise shell divination, indicating that Emperor Wen would rule as a king by virtue of the land. This shows that in the early Han dynasty, the oracle texts of divination were still in existence, though they were later lost. Only when Gao Yang of the Northern Qi dynasty sought to usurp the Eastern Wei, he consulted Li Mi and was told again of the "Da Heng" omen, which was said to be the same as that of Emperor Wen. In my opinion, Li Mi was merely flattering Gao Yang to help him gain power, so how can we fully believe it? Later writings on divination omens have been lost, so how can we rely on them to be accurate? Alas, the total number of divination patterns is 360, and the accompanying oracle texts amount to 3,600. Such a vast amount is naturally hard to preserve. Even if they were preserved, who could truly understand them?

何以明之？《連山》、《歸藏》世固罔然，唯《周易》一書，卦之少唯六十有四，爻之多止於三百八十有四，更三古四聖之所作述，今未云至精至變至於至神之用，至若經卦與其別者，以辭而已，雜然註釋者皆是也。及問其著筮之唯變所適者，則茫乎，實莫知其為何事。若是者尚欲與之語《易》，不亦難矣哉？愚因論卜筮之不可盤同，尚浩嘆及之。

What can be used to demonstrate this? Although the books of "Lianshan" and "Guicang" have long been lost, only the "Zhouyi" remains. Its number of hexagrams is as few as sixty-four, and its lines no more than three hundred and eighty-four. Yet it has passed through three ages: the ancient, the middle, and the recent. It has been created and explained by four sages: Fuxi, King Wen, the Duke of Zhou, and Confucius. However, even up to today, we still cannot explain where its use lies, that it is "the most refined, the most changeable, and ultimately the most divine." As for the primary hexagrams and the derived ones, people talk only about the words, and all the commentaries are of this kind. If one asks how to actually perform the divination with yarrow stalks, "changing according to the situation," there is only confusion and no understanding of what it really is. How can one expect to discuss the "Zhouyi" with such people? It is indeed too difficult. I have spoken at length about the need to distinguish between divination and divination with yarrow stalks, and this is the result of my sigh.

聖人有以見天下之跡，而擬諸形容，象其物宜，是故謂之象。聖人有以見天下之動，而觀其會通，以行其典禮，擊辭焉以斷其吉凶，是故謂之爻。極天下之跡者存乎卦；鼓天下之動者存乎辭；化而裁之存乎變；推而行之存乎通。然則變而通所以盡利，通其變所以成文。八卦成列，而象在中；因而重之，而爻在中；剛柔相推，而變在中；繫辭命之，而動在中矣。八卦以象告，爻象以情言，變通以利言，吉凶以情遷。又曰：爻象動乎內，吉凶見乎外，功業見乎變，聖人之情見乎辭。

The sage has the ability to perceive the profound principles of the world and thus compares them to various forms and descriptions of what is appropriate, hence called "image" or "xiang." The sage also has the ability to observe the changes in the world and thus examines their convergence and interaction, using them to establish rituals and regulations, attaching words to judge fortune and misfortune, hence called "line" or "yao." The thorough understanding of the profound principles of the world lies in the hexagrams; the movement that drives the world's changes lies in the line statements. The transformation and adaptation of these principles lies in "change" or "bian," and their extension and application lies in "communication" or "tong." Thus, change leads to communication in order to fully realize benefits, and communication of change leads to the accomplishment of expression. The eight trigrams are arranged in sequence, and the images are contained within them; when they are combined in pairs, the six lines are contained within them; the interaction between strong and weak lines leads to change; attaching words to judge leads to the manifestation of intent. The eight trigrams use their images to reveal, and the line statements and line images express themselves according to actual circumstances. Change and communication are concerned with advantage and disadvantage, while fortune and misfortune shift according to actual circumstances. The "Great Treatise" also says: the line images are activated within the hexagram, while fortune and misfortune are revealed outside the hexagram, achievements are revealed through change, and the sage's intent is revealed through words.

既曰：鼓天下之動者存乎辭；繫辭而命之，動在其中。則又日繫辭焉以斷其吉凶，曰辨吉凶者存乎辭，則辭也者，《易》道之所必不得已也。是故《易》之為書，其道屢遷，變動不居，周流六虛，上下無常，剛柔相易，不可為典要，唯變所適。卦有小大，辭有險易；辭也者，各指其所之。

The Great Treatise says, "Those who stir up the movement of the world rely on words." It also says that the meaning of the previous text is connected through words to determine the outcome, and the motive lies within them. It further states, "Attach words to determine good and evil," and "The discernment of good and evil lies in words." This shows that "words" are an essential and unavoidable element in the Way of the Book of Changes. Therefore, the Book of Changes is a work whose principles constantly shift and change, moving endlessly through the six lines of each hexagram, fluctuating up and down without fixed position, with yin and yang alternating. It cannot be treated as a fixed doctrine, but must follow the movement of change. Hexagrams vary in size, and words vary in their danger or ease; the so-called "words" each point out the direction they are heading towards.

然則指其所之之之一字，特指其變動之所之適也；易，變易也，所以見天下之動，而鼓天下之動者，莫不於是乎觀。故《易》之筮，謂其爻變而動，而有所之適者，為某卦之某卦。今之謂辭指所之者，為之卦發也。韓康伯於此指所之之下無注。孔穎達疏曰：各指所之，謂爻卦之辭，各斥其爻卦之之適也。若之適於善，則其辭善；之適於惡，則其辭惡而已。夫以之之一字以訓適，非不然也。謂卦之變，爻之動，則未足以明其辭之所之也。

Therefore, the character "之" in the phrase "各指其所之" specifically refers to the destination toward which a line (yao) moves. "Easy" (易) means change, and it is used to reveal the changes in the world. The principle that moves the world to change is observed from this point. Therefore, the divination method of the Book of Changes (I Ching) states that whenever a particular line changes and moves, it is called "a certain hexagram changing into another hexagram." Today, when we say "辞各指其所之" (the statements refer to where they go), it is precisely referring to "the hexagram it goes to." Han Kangbo did not provide a commentary on the sentence "各指其所之." Kong Yingda, in his "Correct Meaning of the Zhou Changes," explains that "各指所之" means that the line statements and hexagram statements each point out the place to which the line or hexagram moves; if the destination is good, the statement is auspicious; if the destination is evil, the statement is inauspicious. Using the character "之" to mean "to go to" is not wrong; however, it only explains up to the point where the hexagram changes and the line moves, and it is insufficient to fully explain where the "statement" (辞) actually points to.

請亦以《左傳》明之。陳敬仲之少也，周史有以《周易》見陳侯，陳侯使筮之，遇《觀》之《否》，乃《觀》之四爻，之《否》之四爻也。故史指《觀》之四爻之辭曰：觀國之光，利用賓于王。因以知其代陳有國也。晉文公之納王也，筮之，遇《大有》之《睽》，乃《大有》之三，之《睽》之三也。故卜偃指《大有》之三爻曰：吉，公用享于天子之卦也。戰克而王享，吉孰大焉？《大有》九三，《易》以享為亨，然亨本墾曰為享。

Let me still use the "Zuo Zhuan" to illustrate. When Chen Jingzhong was young, a Zhou dynasty historian brought the "Zhou Yi" to visit Chen Hou. Chen Hou asked him to perform a divination, and he obtained the "Guan" hexagram transforming into the "Pǐ" hexagram, meaning the fourth line of the "Guan" hexagram was activated and transformed into the fourth line of the "Pǐ" hexagram. Therefore, the historian pointed to the line statement of the sixth line in the fourth position of the "Guan" hexagram and said, "Observing the brilliance of the state, it is suitable to serve as a guest of the king." Thus he concluded that his descendants would replace the state of Chen and establish their own state. When Duke Wen of Jin escorted King Xiang of Zhou back to his capital, he performed a divination and obtained the "Da You" hexagram transforming into the "Kui" hexagram, meaning the third line of the "Da You" hexagram was activated and transformed into the third line of the "Kui" hexagram. Therefore, Bo Yan pointed to the line statement of the ninth line in the third position of the "Da You" hexagram and said, "It is auspicious, this is the hexagram of 'the ruler uses the ceremony to honor the Son of Heaven.' After a victorious battle, the Son of Heaven holds a banquet to honor the ruler, is there a greater auspiciousness than this?" The third line of the "Da You" hexagram in the "Zhou Yi" writes "xiang" as "heng," and "heng" is originally read as "xiang."

齊崔杼欲取棠公之螫東郭姜，筮之，遇《困》之《大過》，乃《困》之三，之《大過》之三也。史皆曰：吉。以示陳文子，故文子指《困》之三爻曰：夫從風，風隕妻，不可取也。且其《縣》曰：困于石，據于羨華，入于其宮，不見其妻，凶。且釋之曰：困于石，往不濟也。據于羨華，所恃傷也？入于其宮，不見其妻，凶；無所歸也。崔杼必取棠姜，終以亂而家遂滅。

Qi State's Cui Zhu wanted to marry Tang Gong's widow, Dong Guo Jiang. He consulted a divination, obtaining the hexagram "Goon" changing to "Da Guo," meaning the third line of "Goon" was activated and transformed into the third line of "Da Guo." The court historians all said it was auspicious. Cui Zhu showed it to Chen Wenzi, who pointed to the third line of "Goon" called "Liuxi" and said: "Xun represents the elder daughter and wind; wind blows away the wife, so this marriage should not be made." Moreover, the "Yao Ci" says: "Confined by stone, leaning on thornbushes, entering his house but not seeing his wife, misfortune." This means being blocked by stone signifies failure in endeavor; leaning on thornbushes means relying on something that harms oneself; entering the house without seeing the wife and suffering misfortune means having nowhere to return. Cui Zhu insisted on marrying Tang Jiang, and eventually his family was destroyed by internal strife.

叔孫穆子之生，莊叔以《周易》筮之，遇《明夷》之《謙》，乃《明夷》之初，之《謙》之初也。以示卜楚丘，曰：明而未融，其當旦乎。之謙當烏，故曰明夷于飛；明而未融，故日垂其翼；象汨之動，故日君子攸行；當三在旦，故曰三日不食。離為火，火焚山敗；於人為言，言敗為讒，故曰有攸往，主人有言，言必讒也。蓋《明夷》初爻辭也。其卒以堅牛之亂。筮占無一不驗者。

When Shu Sun Mu Zi was born, his father Zhuang叔 used the Zhou Yi to divinate. He obtained the hexagram Ming Yi changing into Qian, meaning the first line of Ming Yi was activated and transformed into the first line of Qian. He showed it to Bo Chu Qiú. Chu Qiú said: "The light has not yet become strong, perhaps it is just at the time when the sky is just beginning to brighten." The transformation of Ming Yi into Qian takes the image of a bird, hence the phrase "Ming Yi yu fei" (the light of Ming Yi is flying). The light is not yet strong, hence "chui qi yi" (its wings are hanging down). There is an image of the sun rising and moving, hence "jun zi yu xing" (the gentleman is on the move). It is at the third position, corresponding to the morning, hence "san ri bu shi" (three days without food). Li represents fire, and fire burning a mountain causes the mountain to collapse; in human affairs, this corresponds to speech, and when speech is ruined, it becomes slander. Hence, "you you wang, zhu ren you yan" (there is a direction to go, the master has words), and this "yan" (word) must be slander. All of this refers to the line statement of the first line of Ming Yi. Later, Shu Sun Mu Zi indeed died in the turmoil caused by Shu Niu. This shows that the divination with the yarrow stalks never fails to be accurate.

衛襄夫人無子，璧人惆始生孟摯，孔成子夢康叔謂己：立無，余使羈之孫圉，與史苟相之。史朝亦夢康叔謂己：余命而子苟與孔需鈕之曾孫圉相無。史朝見成子，而告之。夢協。韓宣子為政，聘於諸侯之歲，惆始生子，名之日無。孟摯之足不良能行。

The wife of Duke Xiang of Wei did not have a son, but his favorite concubine, Zhuiyai, gave birth to Mengzhi. Kong Chengzi had a dream in which the first ancestor of Wei, Kangshu, told him: "Establish 'Yuan' as the ruler, and I will have Ji's grandson Yu and Shi Gong assist him." Shi Chao also had a dream in which Kangshu told him: "I appoint your son Gong to assist Yuan together with Yu, the great-grandson of Kong Zhengchu." Shi Chao went to see Kong Chengzi and told him his dream. The two dreams were exactly the same. In the year when Han Xuanzi was in charge of Jin and the feudal lords came to pay homage, Zhuiyai indeed gave birth to a son, whom they named Yuan. Meanwhile, Mengzhi had a leg ailment and could not walk properly.

成子以《周易》筮之，曰：無尚享衛國，主其社稷。遇《屯》之《比》。又曰：余尚立摯，尚克嘉之。遇《屯》，以示史朝。朝曰：元亨，又何極焉？成子曰：非長之謂也。曰：康叔命之，可謂長矣。是以《縣》曰：利建侯。嗣吉，何建？建非嗣也。二卦皆云子其建之，康叔命之，二卦告之。筮襲於夢，武王所用也。蓋再遇《屯》卦辭，皆曰：元亨。而《屯》變於初，故之《比》。《屯》之初爻辭曰：盤桓，利居貞，利建侯。於是立無。

Kong Chengzi used the Zhou Yi to divinate. The oracle said: "May the first son be able to inherit the state of Wei and preside over its ancestral sacrifices." He obtained the hexagram Zun (Obstruction) changing into Bi (Union). Then he divined again, saying: "I wish to make Meng Zhi king, and may the spirits approve." This time he obtained the hexagram Zun without any changing lines. He showed it to Shi Chao, who said: The hexagram statement says "original and prosperous," is there anything higher than that? Kong Chengzi said: This "original" does not mean "longevity," does it? Shi Chao said: Since Kang叔 personally designated him, he is certainly "long." Therefore the line statement says "favorable for establishing a feudal lord." If the legitimate eldest son inheriting the throne is already auspicious, why does it say "establishing a feudal lord"? "Establishing" is not the same as inheriting. Both hexagrams say "you should establish him," and Kang叔 personally designated him, so both hexagrams indicate this. The divination result coincides with the dream, which is exactly the method used by King Wu of Zhou. Originally, both times he encountered the hexagram Zun, and both hexagram statements said "original and prosperous." In the second instance, the first line of Zun moved, so it changed into Bi. The line statement of the first line of Zun says: "Hesitating, favorable for staying firm and upright, favorable for establishing a feudal lord." Therefore, he was appointed as king.

南蒯之將叛也，枚筮之，遇《坤》之《比》，曰：黃裳，元吉。以為大吉。示子服惠伯曰：即欲有事，何如？惠伯曰：吾嘗學此矣，忠信之事則可，不然必敗。黃，中之色也；裳，下之飾也；無，善之長也。中不中，不得其色；下不共，不得其飾；事不善，不得其極。非此三者，不當。且夫《易》不可以占險。蓋由《坤》之五，之《比》之五也，故釋以《坤》五之辭也。南劇卒以叛至於亡。

When Nan Kuan intended to rebel, he consulted the oracle using a method called "mei shi" (divination without specifying the matter), and received the hexagram "Kun" transforming into "Bi". The line statement said, "Yellow garment, original good fortune." He thought it was a great auspicious omen. He then showed it to Zi Fu Hui Bo and asked, "If I intend to take some action, how is it?" Hui Bo replied, "I have studied this before. If it is an act of loyalty and trustworthiness, it will be good; otherwise, it will certainly fail. 'Yellow' is the color of the center; 'garment' is the clothing of the lower part; 'original' is the beginning of all good things. If one's mind does not conform to the middle path, he is not worthy of the color 'yellow'; if one resides in the lower position but is not respectful and obedient, he is not worthy of the garment; if the matter he undertakes is not good, he is not worthy of the term 'original'. If none of these three are present, he is not worthy of this line statement. Moreover, the Book of Changes is not suitable for divining dangerous schemes. This line is the fifth line of the hexagram 'Kun' transforming into the fifth line of the hexagram 'Bi', so the line statement of the fifth line of 'Kun' is used to explain it. Nan Kuan eventually rebelled and fled.

故嘗例乎是數者，而夷考之《傳》，至皿尚多有之，皆以所之之卦、所動之爻言之。夫之卦也者，占變之事也。《易》有聖人之道，則謂以動者尚其變，以筮者尚其占，故通變之謂事，極數知來之謂占，占事則有之卦也。抑古之學《易》者，不惟占也。君子所居而安者，《易》之序也；所樂而玩者，爻之辭也。居則觀其象而玩其辭，動則觀其變而玩其占，不惟占則有之卦也。凡說諸心，研諸慮，事會所適，言意所致，引伸觸類，亦未始不用之卦也。

Therefore, I have taken these examples as a model and carefully examined them in the "Zuo Zhuan," finding that there are many such records. They all rely on the transformed hexagram and the activated line to make their statements. The so-called "zhi gua" refers to the act of divination through transformation. The "Yi" contains four principles of the sage's way, which include "those who act according to movement should value transformation, and those who use divination should value the interpretation." Thus, "to understand change is to understand the way of affairs, and to know the future through numbers is to be a diviner." Since divination is based on transformation, the concept of "zhi gua" arises. However, ancient scholars studied the "Yi" not merely for divination. The gentleman in peace and comfort follows the order of the hexagrams, and delights in the words of each line. In quietude, he observes the hexagram's image and contemplates its statement; when taking action, he observes the changing lines and contemplates the interpretation. Thus, even without being solely for divination, the concept of "zhi gua" is still useful. Whenever there is a mental satisfaction or a thoughtful inquiry, when events align and words and intentions reach their point, by analogy and extension, the concept of "zhi gua" is also applicable.

楚子圍鄭，克之。晉師救鄭，荀桓子聞鄭，及楚平欲還，曰：無及於鄭而剿民，焉用之？隨武子曰：善。贏季不可，以中軍佐濟。知莊子曰：此師殆哉。《周易》有之，在《師》之《臨》網，曰：師出以律；否臧，凶。指《師》之初，之《臨》之初也。鄭游吉至自楚，告子展曰：楚子將死矣。不修政德，而貪昧於諸侯，以逞其願，欲久得乎？在《復》之頤，曰：迷復，凶。其楚子之謂乎？指《復》之上，之《頤》之上也。

King Chu Zhuangwang besieged and captured the State of Zheng. The army of Jin came to rescue Zheng. The commander-in-chief, Xun Linfu, heard that Zheng had already made peace with Chu, and wanted to withdraw, saying: It is too late to save Zheng, and we would only weary the people, why should we do it? Su Wuzi said: Good. First Hu did not agree, and led the troops of the deputy commander of the middle army across the river. Zhi Zhuangzi said: This army is in danger. The Zhou Changes say: In the hexagram of "Military" changing into "Approaching", it says: "The army goes out in order, if it is disorderly, it will be ominous." This refers to the first line of the hexagram of "Military" moving to become the first line of the hexagram of "Approaching." Zheng Youji returned from Chu and told Zi Zhan: King Chu is about to die. He does not cultivate virtue and righteousness, but seeks the homage of the feudal lords to satisfy his own desires, how can he last long? This is what the hexagram of "Returning" changing into "Nourishing" says: "Returning in confusion, ominous." This is probably referring to King Chu. This refers to the top line of the hexagram of "Returning" moving to become the top line of the hexagram of "Nourishing."

鄭公子曼滿與王子伯廖語，欲為卿。伯廖告人曰：無德而貪，其在《周易》《豐》之《離》，弗過之矣。至皿指《豐》之上，之《離》之上也。其辭曰：豐其屋，部其家，閥其戶，板其無人，三歲不覬，凶也。閒一歲，鄭人果殺之。若是三者，尚不過舉其卦之一爻之所之之為然也。

Zheng's nobleman Man Man told Prince Bo Liao that he wished to become a minister. Bo Liao told others that without virtue yet seeking high position, this exactly matches the statement in the "Zhou Yi" "Feng" hexagram's "Li" line. He could not escape this fate. This refers to the top line of the "Feng" hexagram moving to become the top line of the "Li" hexagram. Its line statement says: "Make the house large, cover the family with mats, peer through the door, and find it empty and quiet, three years without seeing anyone, misfortune." A year later, the people of Zheng indeed killed him. These three points are merely examples of a single line changing within a hexagram.

至於蔡墨對魏獻子之問龍見絳郊，則直曰：《周易》有之，在《乾》之《姤，曰：潛龍勿用。其《同人》，曰：見龍在田。其《大有》，曰：飛龍在天。其《夬》，曰：亢龍有悔。其《坤》，曰：見草龍無首，吉。《坤》之《剝》曰：龍戰于野。此雖於象龍、真龍之事，有不容於理討，然其所舉《乾》、《坤》之爻凡六，必皆互以《乾》、《坤》反覆相之爻辭，以相校而明其所之者，謂全《易》之卦六十有四，其爻三百八十有四，變之所之，率由是道也。是足以迦明《易大傳》之辭也者，各指其所之者，非為它設也，為之卦設也。

As for Cai Mo's answer to Wei Xianzi's question about "a dragon appearing outside the capital city of Jiangdu," he directly said that the Zhou Changes contain such statements: in the fourth line of the Qian hexagram, it says "the dragon remains hidden and should not be used"; in the fourth line of the Tongren hexagram, it says "the dragon appears in the fields"; in the fourth line of the Dayyou hexagram, it says "the dragon soars in the sky"; in the fourth line of the Guai hexagram, it says "the dragon reaches its peak and regrets it"; in the fourth line of the Kun hexagram, it says "a group of dragons appear without a leader, which is auspicious"; and in the fourth line of the Bao hexagram, it says "dragons fight in the fields." Here, he is talking about the symbolic dragon and the real dragon. Although there are some parts that are hard to understand, the six lines of the Qian and Kun hexagrams he cited all necessarily use the line statements of the Qian and Kun hexagrams changing back and forth to correspond with each other, in order to explain where each line changes to. This shows that all sixty-four hexagrams and 384 lines in the entire Zhou Changes follow this method of change. This is sufficient to prove that the statement in the Xici Zhuan, "the statements refer to where they go," is not for other matters, but specifically for "the changing hexagram."

是固所以見天下之動，而觀其會通，以行其典禮，斷其吉凶；化而裁之，推而行之，唯變所適也。變之所適，之卦之謂也。故曰：爻象動乎內，吉凶見乎外，功業見乎變，聖人之情見乎辭。卦有小大，辭有險易；辭也者，各指其所之。學者因之，以是審於觀變以立卦，倚數以生爻，極深乎至精，研幾乎至變，以至於至神，和順於道德而理於義，窮理盡性以至於命，胸中包有全《易》之體用，其斯至矣。

This is precisely how one discerns the changes in the world, observes their convergence and interconnection, and uses them to establish rituals and laws, and to judge auspiciousness and misfortune. By transforming and applying them, one follows the changes wherever they go. The movement of change is called "the moving hexagram." Therefore, the lines of a hexagram are activated within the hexagram, while auspiciousness and misfortune manifest outside of it. Achievements are revealed through change, and the mind of the sage is expressed through words. Hexagrams vary in size, and the words vary in difficulty and ease. The "words" each point out the direction they are heading towards. Those who study the I Ching follow this principle, using it to carefully "observe changes to establish hexagrams and rely on numbers to generate lines." They delve deeply into the most refined aspects, investigate subtle changes to the utmost, and ultimately reach the most divine. They harmonize with morality and organize according to principles, exhaust physical laws, fully reveal human nature, and thus reach the understanding of heavenly mandate. Having fully encompassed the essence and application of the Zhou Changes within their hearts, they have truly mastered it.

易筮通變卷上竟

The Comprehending Change in Yarrow Divination, Volume One, the chapters "Divination" and "The Hexagram" come to an end here.

『亦』，四庫本作『一』。『土』，四庫本誤作『主』。『車敗』，四庫本作『軍敗』。『弧』，原作『張』，據四庫本改。『禮』，四庫本作『體』。『俗誘』，四庫本作『俗群』。『尚』，四庫本作『嘗』。『立』，原作『玄』，據四庫本改。『之』，據其文義例補。

These are nine collation notes for this section, indicating variations between the original text of the "Zhengtong Daozang" and the Siku Quanshu edition. In the main text, the character "亦" is in the Siku Quanshu edition as "一"; the character "土" is mistakenly written as "主" in the Siku Quanshu edition; "车败" is written as "军败" in the Siku Quanshu edition; the character "弧" was originally "张" in the original text but is corrected to "弧" according to the Siku Quanshu edition; the character "礼" is written as "体" in the Siku Quanshu edition; "俗诱" is written as "俗群" in the Siku Quanshu edition; the character "尚" is written as "尝" in the Siku Quanshu edition; the character "立" was originally "玄" in the original text but is corrected to "立" according to the Siku Quanshu edition; the character "之" is added according to the meaning and style of the context.

臨川道士雷思齊學

This volume still bears the name of the Daoist priest Lei Siqi of Linchuan, indicating that the essay titled "Jiu Liu" within is also the personal interpretation of this Yuan dynasty Daoist from Fuzhou.

《易》始於陰陽之畫，而陽之畫而為奇，陰之畫而為耦。由乾之畫，分而為震、為坎、為艮卦之奇；坤之，分而為巽、為離、為兌三卦之耦，故曰：陽卦奇，陰卦耦；陽卦多陰，陰卦多陽。雖奇耦少多若可數計，而未始謂為九，為六也。聖人之作《易》，觀變於陰陽而立卦，則天之道曰陰與陽；發揮於剛柔而生爻，則地之道日柔與剛，故《易》六畫而成卦，分陰分陽，迭用柔剛，六位而成章。其日畫日位者，是所謂卦爻也。豈嘗有九、六之分哉？

The Zhou Changes begin with the two types of lines called yao, which are yin and yang. The yang line is called "qi," and the yin line is called "ou." From the Qian hexagram, which is entirely yang, three hexagrams—Zhen, Kan, and Gen—branch out, each containing one yang line. From the Kun hexagram, which is entirely yin, three hexagrams—Xun, Li, and Dui—branch out, each containing one yin line. Therefore, yang hexagrams are mainly composed of qi, and yin hexagrams are mainly composed of ou. Although the number of qi and ou can be counted, they have never been called "nine" and "six." The sage created the Zhou Changes, "observing changes in yin and yang to establish hexagrams," and the way of heaven is called yin and yang. "Expanding through strength and flexibility to produce yao," and the way of earth is called flexibility and strength. Therefore, the Zhou Changes use six lines to form a hexagram, distinguishing between yin and yang positions, alternating the use of flexible and strong lines, forming the structure of the six yao. Here, the term "line" and "position" refer to the usual hexagram and yao. How could there ever be a distinction between "nine" and "six"?

由重乾卦之畫之位，皆陽奇之爻，而爻辭上必係以九，且有用九之例；重坤卦之畫之位，皆陰耦之爻，而爻辭上必係以六，且有用六之例。而凡卦之爻，莫不各繫以九且六，學者積於所見所聞之成習，以此誠為九、六也。從而九、六之無復討其所以然者，竊自異之。

This is because the six lines of the Qian hexagram are all yang lines, so the line statements all begin with the character 'nine' (九), and there is also a general rule called 'use of nine' (用九). Similarly, the six lines of the Kun hexagram are all yin lines, so the line statements all begin with the character 'six' (六), and there is also a general rule called 'use of six' (用六). For the lines of all other hexagrams, they are also marked with either 'nine' or 'six' accordingly. Those who study the Book of Changes become accustomed to this over time and, after a long period, mistakenly believe that the lines themselves should be called 'nine' or 'six'. From then on, they no longer inquire into the origin of 'nine' and 'six'. I personally find this quite strange.

夫九、六，數也。《大傳》曰：極數知來之謂占，通變之謂事。蓋九‘、六也者，占變之事也。始乎參伍以變，錯綜其數。天數五，地數五，天數二十有五，地數三十，凡天地之數五十有五，所以成變化而行鬼神者，未嘗即謂其九、六也。由天數謂一、三、五、七、九，而後知其積為二十有五；地數謂二、四、六、八、十，而後知其積為三十。

In fact, both "nine" and "six" are numbers. The Great Treatise says: "To know the future by means of numbers is called divination; to understand change is called affairs." This shows that nine and six are the numbers used in the matter of "change" in divination. It begins with "three and five combined to produce change, and their numbers are interwoven." The numbers of Heaven are one, three, five, seven, and nine, totaling twenty-five. The numbers of Earth are two, four, six, eight, and ten, totaling thirty. The total of Heaven and Earth's numbers is fifty-five, which is the basis for producing change and acting upon spirits. However, they are not directly called nine and six here. First, one must know that the numbers of Heaven are one, three, five, seven, and nine, then one understands that they add up to twenty-five. First, one must know that the numbers of Earth are two, four, six, eight, and ten, then one understands that they add up to thirty.

由五位相得而各有合，乃以五已前為生數，五已後為成數，而一合六謂水，二合七謂金，三合八謂木，四合九謂火，五合十虛謂土，是九、六盤見其問，而未著所以用也。五位已前，其體數；五位已後，其用數也。體之生數，以天一、天三、天五參之而九，地二、地四兩之而六，參天兩地而倚數，參參而九，參兩而六，於是九、六特啟其用也。

The concept of "five positions interacting and each having its corresponding combination" divides the numbers before five as "birth numbers" and those after five as "formed numbers." One combines with six to represent water, two with seven for metal (though according to the usual sequence of the Five Phases, it should be fire), three with eight for wood, four with nine for fire (though according to the usual sequence, it should be metal), and five with ten for earth. Nine and six appear mixed within this sequence but have not yet shown their function. The numbers before the five positions are called "body numbers," and those after are called "function numbers." In terms of the fundamental birth numbers, taking the three heavenly numbers: Tian Yi (Heavenly One), Tian San (Heavenly Three), and Tian Wu (Heavenly Five), and combining them gives nine. Taking the two earthly numbers: Di Er (Earthly Two) and Di Si (Earthly Four), and combining them gives six. This is called "three from heaven and two from earth to form the numbers" — three threes add up to nine, and three twos add up to six. It is at this point that nine and six begin to show their function.

故以一四而伍，二三而五。五因兼而五，是參伍之始變；而以一伍五而六，二伍五而七，三伍五而八，四伍五而九，五虛伍而十，因以五兼十而十五，七兼八而十五，九兼六而十五，是所謂參伍以變，錯綜其數者也。凡九、六、七、八之數，均得以地數之成，而成其天數之生也者，是所謂成象也。是一五而六為老陰，二五而七為少陽，三五而八為少陰，四五而九為老陽，是九、六、七、八皇相變為用也。

Therefore, one combines with the four ministers to form five, two combines with three to form five, and five itself combines with itself to form five. This is the first transformation of "San Wu." Then take five to combine with each number: one combines with five to make six, two combines with five to make seven, three combines with five to make eight, four combines with five to make nine, and five (the empty position) combines with five to make ten. Thus five and ten combine to form fifteen, seven and eight combine to form fifteen, and nine and six also combine to form fifteen. This is called "San Wu yi bian, cuo zong qi shu." The numbers nine, six, seven, and eight are all achieved through the "cheng shu" of earth to complete the "sheng shu" of heaven, which is called "cheng xiang." Thus, one plus five makes six, which is old yin; two plus five makes seven, which is young yang; three plus five makes eight, which is young yin; and four plus five makes nine, which is old yang. The numbers nine, six, seven, and eight then transform and interact with each other.

世雖知陰陽之少者不變，老者則變。而習見於《易》全書之畫，凡卦之爻，奇之陽，其下分繫以九；耦之陰，其下分繫以六，而不知之畫寔七，之畫寔皇八也。

People know that among yin and yang, the "few" remains unchanged while the "old" changes. However, having become accustomed to the way the entire Zhou Changes is written—where all yang lines are marked with "nine" and all yin lines with "six"—they do not realize that the static yang line drawn actually represents seven, and the static yin line drawn actually represents eight.

何以明之？《易》，變易也；極數知來之謂占，通變之謂事。謂其占變之事，具蝶曹法，四營而成《易》，十有八變而成卦。每三變而積為一爻，以四與八為奇耦。而每三變各得一、四、二、八，則象震，象坎，象艮，則皆畫為之奇。每三變各得一、八、二、四，則象巽，象離，象兌，則皆畫為之耦。

What can prove that "Yi" means change? "Change is the essence of Yi; knowing the future through the extremes of numbers is called divination, and understanding change is called affairs." This refers precisely to the practice of divination through change, which is realized through the method of divining with yarrow stalks: "Four operations form Yi, and eighteen changes form a hexagram." Each set of three changes forms a line, using four and eight to distinguish odd and even. If the three changes result in one four and two eights, they are taken as the images of Zhen, Kan, and Gen, and are drawn as a yang line. If the three changes result in one eight and two fours, they are taken as the images of Xun, Li, and Dui, and are drawn as a yin line.

蓋寓陰陽相索為六子之意，以三變皆得四，始畫為，以象乾；三變皆得八，始畫為，以象坤。凡一、四、二、八之積為一之定畫，是謂七；一、八、二、四之積為之定畫，是謂八，此兩者其不變者也。惟三變純四，謂陽奇之極，為之動爻，是謂九；三變純八，謂陰耦之極，為之動爻，是謂六；此兩者皆其變者也。

This passage contains the meaning of the interaction between Heaven and Earth leading to the six sons' hexagrams. If all three transformations result in four, then a yang line is drawn to represent Heaven (Qian); if all three result in eight, then a yin line is drawn to represent Earth (Kun). Any fixed line formed by one four and two eights is called 'seven'; any fixed line formed by one eight and two fours is called 'eight'—these two remain unchanged. Only when all three transformations are four, it is called yang extreme, forming a moving line called 'nine'; and when all three are eight, it is called yin extreme, forming a moving line called 'six'—these two are subject to change.

凡奇耦之定畫，所以悉列於各卦之首者，不取其動，而專以標剛柔之體，不變而畫為定卦。至一九六之變爻，雜然交寓於各卦之內者，不列於畫，而專以寄陰陽之用，適變以動而為之卦，而乃所以著其用九、用六者也。

All fixed lines, whether odd or even, are listed on the hexagrams because their focus is not on movement but on indicating the fundamental nature of yin and yang, which remains unchanged and forms a fixed hexagram. However, the lines marked as nine and six, which are changing lines, are scattered within the hexagrams and are not included in the hexagram diagram. Instead, they are used specifically to express the function of yin and yang, which act in accordance with change and thus produce the changing hexagrams. This is why the hexagrams Qian and Kun specifically mention "use of nine" and "use of six."

《乾鑿度》曰：陽動而進，陰動而退。故陽以七，陰以八為象；陽變七之九，陰變八之六也。晁說之以道曰：古者畫卦之奇耦為陰陽，而卦爻但有六位，而未有七、八之名，因搽曹衍《易》，以老陽之變九、老陰之變六、少陽之變七、少陰之變八。《周易》之七、八，即古之奇耦也。《易》筮之九、六見於卦文則變焉如六位皆九，即《乾》之《坤》；六位皆六，即《坤》之《乾》也。此則用九用六之例，足以明與。今我所見，皇同然也。

The Yi Wei · Gan Zao Du says: When yang moves, it advances; when yin moves, it retreats. Therefore, yang is fixed with seven and yin with eight as their symbolic numbers. When yang changes once, seven becomes nine; when yin changes once, eight becomes six. Zhao Shuo Zhi (with the style name Yidao) says: Ancients drew the hexagrams by distinguishing yin and yang through odd and even numbers, and the hexagrams have only six lines, without the names seven or eight. Later, because of the method of divining with yarrow stalks, there came the idea that old yang becomes nine, old yin becomes six, young yang becomes seven, and young yin becomes eight. The numbers seven and eight in the Zhou Yi are the odd and even numbers mentioned by ancients. The numbers nine and six appearing on the hexagram lines are for change: if all six lines are nine, it becomes the hexagram Qian transforming into Kun; if all six lines are six, it becomes the hexagram Kun transforming into Qian. This is the general rule of 'using nine' and 'using six,' which clearly explains the principle. What I see today is exactly the same as his view.

今之《左傳》之所紀，復有可以相明，而且有不得不究其所注之失者。魯穆姜薨於東宮。始往而筮之，遇《艮》之八也。史曰：是謂《艮》之《隨》。隨其出君必速出。

The events recorded in the present version of the Zuo Zhuan have further corroboration, and some of the old annotations contain errors that must be examined. Duke Mu Jiang of Lu died in the Eastern Palace. When she was moved to the Eastern Palace, she had a divination and obtained the hexagram "Gen" changing to "Suí." The historian said: This is called "Gen" changing to "Suí"; "Suí" means to go away, so you will certainly leave quickly.

姜曰：亡。是於《周易》曰：《隨》，元、亨、利、貞，無咎。元，體之長也；亨，嘉之會也；利，義貞，事之乾也。體仁足以長人，嘉會足以合禮，利物足以和義，固足以乾事。然固不可誣也，是以雖《隨》無咎。今我婦人而與於亂，不可謂無；不靖國家，不可謂亨；作為害身，不可謂利；棄位而姣，不可謂貞。有四德者，《隨》而無咎。我皆無之，豈《隨》也哉？我則取惡，不可作而害，能無咎乎？必死是宮，不得出矣。

Mu Jiang said: No, that is not the case. This passage is from the "Zhou Changes": "The hexagram of Following, has the virtues of originality, prosperity, benefit, and constancy, without blame." Originality refers to the head of the body; prosperity refers to the gathering of beauty; benefit refers to the harmony of righteousness; constancy refers to the backbone of doing things. To take benevolence as the foundation, is sufficient to be the leader of the people; the gathering of beauty is sufficient to conform to propriety; to allow all things to obtain their benefits, is sufficient to harmonize with righteousness; to maintain firm constancy, is sufficient to accomplish things. These four virtues cannot be falsely claimed, so possessing them allows one to "follow without blame" — even though one follows the times, there will be no fault. Now, I, a woman, have participated in the turmoil, occupying a low position without benevolence, so I cannot be called "originality"; I have failed to bring peace to the country, so I cannot be called "prosperity"; my actions have harmed myself, so I cannot be called "benefit"; abandoning the position I should hold and engaging in licentiousness, I cannot be called "constancy." Only those who possess these four virtues are worthy of "following without blame." Since I lack all four, how can I be worthy of the hexagram of Following? I have brought upon myself evil, causing harm to both others and myself, how can I have no fault? I must surely die in this palace and will not be able to leave.

故嘗因是《艮》之八之筮，尤有以審七、八之定畫，不為九、六之動爻，而注則誤矣。《周禮》大卜掌三《易》以行九筮，則日《連山》、《歸藏》、《周易》，謂其經卦皆八，其別皆六十有四。是《易》雖三名，筮則同一法也。其以七、八為卦畫之體，以九六為卦爻之用，是以謂《艮》之八也。

Therefore, I once used this example of divination with the hexagram 「Gèn (Mountain) No. 8」 to clearly see that the lines seven and eight are fixed and do not move, and cannot be treated as the moving lines nine and six. The old annotations were entirely wrong. The Classic of Rites says that the Grand Diviner is in charge of three books of the I Ching to perform nine kinds of divination methods, namely the Lianshan, Guicang, and Zhouyi. It says that all three have eight primary trigrams and sixty-four compound hexagrams. This shows that although the I Ching has three names, the method of divination is the same. It uses the lines seven and eight as the 「body」 of the hexagram, and the lines nine and six as the 「use」 of the hexagram. Hence, there is a saying like 「Gèn (Mountain) No. 8」.

《艮》之變其初之《賁》三之《剝》四之《旅》，五之《漸》，上則之《謙》，趨明其筮是《艮》之一卦，凡六爻而爻之變者已。凡五卦之之者，亦五矣。史雜而視之，無所適從於斷也。惟二爻之陰耦無所變，無所之爾，故覆而斷之以《艮》之《隨》也。且即稽其筮而曰：《隨》其出也，君必速出。姜則自審，無以當此卦之德也。因謂是於《周易》曰：《隨》，元、亨、利、貞，無咎。就申其釋之者，如上云耳。曷嘗引《連山》、《歸藏》二《易》，而且有所更筮哉？

This hexagram's transformation is: The first line of the hexagram "Gen" (Mountain) changes to "Ben" (Beauty), the third line changes to "Bo" (Splitting), the fourth line changes to "Lv" (Travel), the fifth line changes to "Jian" (Gradual Progress), and the top line changes to "Qian" (Humility). This indicates that the original hexagram was "Gen," and among its six lines, five have moved and transformed, resulting in five transformed hexagrams. The historian mixed these five hexagrams together and found himself at a loss, unable to make a decision. Only the second line remained as a yin line without transformation, and thus he returned to the original hexagram "Gen" and used "Gen" changing to "Sui" (Following) to make his judgment. Furthermore, based on this divination, "Sui" signifies going out, so he concluded that the person would certainly go out soon. Mu Jiang herself considered whether she was worthy of the four virtues of the hexagram "Sui," and then she explained the meaning of the text in the "Zhou Yi" which says, "Sui: Yuan, Heng, Li, Zhen, Wu Jiu." She then elaborated on the previous reasoning. How could she have quoted the "Lianshan" and "Guicang," the other two "Yi" systems, or have divined again?

杜氏不明《周易》之筮，耦之畫本只謂八，乃妄指二《易》以七、八為占，且又謂史疑占《易》遇八為不利，更以《周易》占變爻而論之，何其誤也。由今竅之，則七、八之為卦體之成畫，而不名九、六，不亦明矣哉？

Du Yu did not understand the method of divination in the Zhou Yi, and did not know that the fixed lines of yin and yang are originally called "eight," yet he mistakenly claimed that the use of the Lianshan and Guicang Yi was involved in divination with numbers seven and eight. He also said that the officials doubted that encountering the number "eight" in divination with the Yi was inauspicious, and tried to explain it using the method of changing lines from the Zhou Yi, how wrong he was! From today's perspective, the numbers seven and eight are fixed lines of the hexagram, originally not called nine or six, isn't this very clear?

《國語》晉公子重耳筮尚有晉國。得貞《屯》悔《豫》，皆八。韋昭注：震在《屯》之內卦，兩陰爻不動；震在《豫》之外卦，兩陰爻亦不動，故曰皆八。是其征也。董因又筮之，得《泰》之八，昭又注：《泰》，無動爻，陰爻不動，其數皆八，則為耦畫之不動者皆為八。又其征也。

The Guoyu records that Jin公子 Chong'er consulted a divination to inquire whether he could obtain the state of Jin. The result was "Zhen 'Zun' Hui 'Yu', all eight"—the primary hexagram was 'Zun', the following hexagram was 'Yu', and all were eight. Wei Zhao made a commentary saying: the Zhen trigram is the inner trigram of 'Zun', and its two yin lines are unmoving; the Zhen trigram is the outer trigram of 'Yu', and its two yin lines are also unmoving. Therefore, it is said "all eight." This is a clear evidence. Later, Dong Yin also consulted a divination for him, obtaining "Tai 'eight'". Wei Zhao again commented saying: the Tai hexagram has no moving lines, the yin lines are unmoving, and their numbers are all eight. This shows clearly that any yin lines that are unmoving are universally referred to as eight. This is another clear evidence.

由耦之畫不動者皆為八，則奇之畫不動者皆為七，校然明甚矣。今《易》之全書，不見七、八，而唯見九、六，學者冥視其用九、用六之文承誤於九、六之分，而未明九、六之例所以用者，其盤如前所論為之卦設也。合《左傳》凡云某卦之某卦者，皆以爻之動，而變者指其所之云爾。所謂唯變所適也，以筮者尚其占，以動者尚其變；爻也者，言乎其變者也。聖人有以見天下之動，而觀其會通，以行其典禮，繫辭焉以斷其吉凶，是故謂之爻。言天下之動而不可亂，故曰：六爻之義易以貢也。

Since the fixed lines of the yin couples are all eight when they do not move, the fixed lines of the yang odd numbers are all seven when they do not move. The reasoning is clear. Now, in the entire text of The Zhou Changes, one does not see the numbers seven and eight, but only nine and six. Scholars have been confused about the words "use nine" and "use six," continuing the mistake of "yao divided into nine and six," without understanding where exactly the general rule of nine and six is applied. In fact, as discussed earlier, this rule is specifically for the "resulting hexagram." Looking at the Zuo Zhuan, whenever it mentions "a hexagram changing into another hexagram," it refers to the movement and change of the yao, indicating where it is going. This is called "changing to adapt": "those who use divination focus on the divination, and those who use movement focus on the change." The term "yao" refers precisely to change. The sage has the ability to observe the changes in the world, examine their convergence and connection, and use them to implement rituals and regulations, attaching words to determine fortune and misfortune. Therefore, it is called "yao." Discussing the changes in the world without confusion, this is why it is said, "the meaning of the six yao is easily presented through change." The meaning of the six yao lies in using change to inform people.

以是研之，定爻之，固自七、八。而於其動，則七乃進為九，而含陰；八乃退而六，而含陽也。《傳》於占之變卦之爻，固悉如前之卦之說，而於蔡墨之答魏獻子之問龍，尤曉然著白也。曰：《周易》有之，在《乾》之《姤》，曰：潛龍勿用。其《同人》曰；見龍在田。其《大有》曰：飛龍在天。其《夬》曰：亢龍有悔。其《坤》曰：見覃龍無首，吉。《坤》之《剝》曰：龍戰于野。

Following this principle to study the hexagrams, the fixed lines are originally seven and eight; once they move, seven becomes nine and contains yin, while eight becomes six and contains yang. The "Zuo Zhuan" explains the changing lines of hexagrams, which are entirely consistent with the previous "original hexagram" statements. In particular, Cai Mo's answer to Wei Xianzi's question about dragons is especially clear and explicit. He said that the "Zhou Yi" contains such statements: in the hexagram "Qian" changing to "Gou," it says "the dragon remains hidden and should not be used"; in the hexagram "Qian" changing to "Tong Ren," it says "the dragon appears in the field"; in the hexagram "Qian" changing to "Da You," it says "the dragon soars in the sky"; in the hexagram "Qian" changing to "Gua," it says "the dragon reaches its peak and incurs regret"; in the hexagram "Qian" changing to "Kun," it says "a group of dragons appears without a leader, which is auspicious"; and in the hexagram "Kun" changing to "Po," it says "dragons fight in the fields."

則足以見七八之動而變，始得謂九且六也。不然，則《乾》之諸爻謂九者，其辭分配固如潛龍勿用等雲；而《坤》之上六，其辭固雲龍戰于野。又何必枚舉《乾》之《姤》、《坤》之《剝》等卦，然後始稱其本爻九、六之下文以為所之之辭，而申見其例也哉？

From this we can see that only when the seventh and eighth lines are activated and transformed can they be called the ninth and sixth. Otherwise, since all the lines of the Qian hexagram are called 'nine,' their line statements are originally different ones such as 'the dragon remains hidden and should not be used,' and the line statement of the sixth line of the Kun hexagram is originally 'the dragon fights in the fields.' Then why would Cai Mo list one by one the hexagrams transformed from Qian's Gou and Kun's Po, and then quote the statements under the ninth and sixth lines as the statements of the transformed hexagrams, in order to explain this general rule?

況《乾》卦於用九之下文曰：見旱龍無首，吉。而墨乃特謂之《坤》，然後釋之方如所云。則凡用九為爻之變畫，例此不約而合，尤未深切著明，可以不言而信矣。其所以每爻先引之卦，而始徵以其辭者，以見七之變，進而始為九、八之變，退而始為六也。由是以夷考於《傳》，凡所舉之卦之辭，則見每爻之為九為六者，必待七、八之動，而變乃然也。

Moreover, the text under "Use of Nine" in the Qian hexagram clearly states "Seeing a group of dragons without a leader, it is auspicious." However, Cai Mo insists on interpreting it as Qian combined with Kun. Then he proceeds to explain it in the manner mentioned above. This shows that all instances of "Use of Nine" refer to the changing lines of the hexagram. Following this example, there is no need for prior agreement; the meaning naturally aligns, making the reasoning even more profound and clear. It is unnecessary to elaborate further to convince people. The reason why he first mentions the changing hexagram for each line and then cites its text as evidence is to demonstrate that seven changes make it nine, and eight changes make it six. Based on this, if we carefully examine the examples in the Zuo Zhuan, we can see that whenever a hexagram is cited, the reason why a line is called nine or six is because it must wait for seven or eight changes to occur before it becomes so.

故有用九用六之例，是九、六之用。如《乾》之初至上，皆必待陽奇之七動而變，始謂九；《坤》之初至上，皆必待陰耦之八動而變，始謂六。如晁氏云、九、六見於卦爻，則變六位皆九，即《乾》之《坤》；六位皆六，即《坤》之《乾》也。

Therefore there is the general rule of "use of nine" and "use of six," which precisely demonstrates the function of nine and six. For instance, in the hexagram Qian, from the first line to the top line, all lines must wait for the movement of the yang odd number seven before they change, and this is called nine. In the hexagram Kun, from the first line to the top line, all lines must wait for the movement of the yin even number eight before they change, and this is called six. As Chao Shuozi explained, when nine or six appears on a hexagram line, it signifies a change: if all six lines are nine, it becomes the hexagram Kun from Qian; if all six lines are six, it becomes the hexagram Qian from Kun.

《乾鑿度》重見其說：陽動而進，變七之九，象其氣之息；陰動而退，變八之六，象其氣之消也。又謂《乾》三十二世消，《坤》三十二世息也。故《易大傳》曰：乾、坤，其《易》之門邪？生皿由乾、坤之門以入，則凡諸卦必仿此以通，每卦之變而始名九、六也，故用九、用六不見於它卦，而特見於《乾》、《坤》者。生皿不止為《乾》、《坤》設，皇並它卦例以用之也。

The "Qian Zao Du" again restates this idea: Yang moves and advances, with seven changing to nine, symbolizing its energy growing; Yin moves and retreats, with eight changing to six, symbolizing its energy retreating. It also says that the hexagram Qian lasts through thirty-two generations before it ceases, and the hexagram Kun lasts through thirty-two generations before it stops. Therefore, the "Great Treatise" says: "Qian and Kun, are they the gate of the Book of Changes?" This probably means that by entering through the gate of Qian and Kun, the other hexagrams should follow this method: only when a hexagram changes does it become nine or six. Hence, "use nine" and "use six" do not appear in other hexagrams, but only in Qian and Kun. This was not originally set up only for Qian and Kun, but also serves as an example for the other hexagrams to follow.

故占法謂六爻皆不變者，則斷以本卦之《象》辭；五爻皆變，一爻獨不變者，則斷以之卦爻之不動者之《象》辭，而不用爻辭者，是其爻不動，不得以名九、六故也。

Therefore, the method of divination stipulates: if none of the six lines change, use the "Image" (Xiang) from the primary hexagram for interpretation. If all five lines change except one, then use the "Image" (Xiang) associated with the unchanging line from the "changed hexagram" (zhi gua), and not the line statement (yao ci). This is because that line, being unchanging, cannot be referred to as a "nine" or "six."

歐陽永叔曰：《乾》曰用九，《坤》日用六，何謂也？曰：釋七、八不用也。《乾》爻七、九，九則變；《坤》爻八、六，六則變；《易》用變為占，故以名其爻也。

Ouyang Xiu said: The "Qian" hexagram discusses "All Nines," and the "Kun" hexagram discusses "All Sixes." What does this mean? The answer is: To indicate that the numbers seven and eight are not used. The lines of the "Qian" hexagram consist only of seven and nine, and only nine changes. The lines of the "Kun" hexagram consist only of eight and six, and only six changes. The "Book of Changes" uses change to predict, so it names the lines according to the changing number.

朱元晦甚稱其說，則又曰：《乾》、《坤》之用九、用六，何謂也？曰：《乾》爻七、九，《坤》爻六、八，九、六變而七、八元為，《易》道占其變，故以占者為爻，不謂六爻皆九、六也。及其筮也，七、八常多，而九、六常少，有元九、六者焉，不可不釋也。六十四卦皆然，特於《乾》、《坤》見之，則餘可知爾。且謂其按此說發明先儒所未到，最為有功。論七、八多，而九、六少，又見當時占法三變皆卦，如一行說。今愚又以是觀之朱之所說，惟見歐說若晁說，朱蓋所未見也。

Zhu Xi highly valued this view and also said: What does "use of all nines" and "use of all sixes" mean in the trigrams Qian and Kun? The answer is: The lines of Qian consist of seven and nine, and the lines of Kun consist of six and eight; nine and six are changing, while seven and eight are unchanging. The Way of the Book of Changes is about change, so the changing numbers obtained in divination are taken as lines, not meaning that all six lines are nines or all six lines are sixes. In actual divination, seven and eight are often more frequent, while nine and six are less frequent, and sometimes even a single nine or six may not appear, which must be explained. All sixty-four trigrams are like this, but only the trigrams Qian and Kun are explicitly mentioned, and the rest can be inferred accordingly. He also said that Ouyang Xiu's view revealed something that previous Confucian scholars had not discussed, and thus made the greatest contribution. As for the observation that seven and eight are more frequent than nine and six, it can also be seen that the divination method of the time was "three changes produce a trigram," which is the same as the method described by Yixing of the Tang dynasty. Now, looking at Zhu Xi's discussion, he only saw Ouyang Xiu's view; Chao Shuozi's view, Zhu Xi probably did not see.

至若《乾鑿度》等書，儒者又鄙之，以為《易緯》，不惟不取，至有不觀，有不見者，而不知其有可參考也。自今校之，古今所見，固有不求同而同，不期然而然者，然皆未及於九、六之所以然。如《左傳》之卦之徵驗，以為《易》道欠事，故得兼載其詳。然余復審晁氏謂卦爻見九、六，不見七、八，特其致疑，而然非真有見於九、六者也。

As for works like the "Qian Zao Du," Confucian scholars also look down upon them, considering them part of the "Yi Wei." Not only do they not adopt them, but some have never even seen them. Yet they do not realize that there are elements within them that may be of reference. When we compare today's findings with those of ancient scholars, there are naturally coinciding points without seeking them, and things that happen without intention. However, none have touched upon the fundamental reason why nine and six are considered nine and six. I believe the verification of the "zhi gua" in the "Zuo Zhuan" is an essential part of the Yi doctrine, so I have also recorded its details. However, upon further examination of Zhao Shuo's statement that "the hexagrams and lines only show nine and six, not seven and eight," this is merely his own doubt, not a true understanding of the principles behind nine and six.

謹按《說卦》昔者聖人之作《易》，幽贊於神明而生曹者，是已明著用筮之法矣。其謂參天兩地而倚數者，生皿參其三三而九為參天，已見乾元用九；兩其三二而六為兩地，已見坤元用六，是九、六之用所由始也。觀變於陰陽而立卦者，是所謂立天之道日陰與陽，立地之道日柔與剛，立人之道日仁與義，兼三才而兩之，故《易》六畫而成卦，足以見標奇耦二於卦首，不動為定畫，乃寄其七、八也。

Carefully following the "Commentary on the Hexagrams" which says, "In ancient times, the sage composed the Book of Changes, secretly praising the divine and thus created the yarrow stalks," this clearly points out the method of divination using the yarrow stalks. The phrase "three heavens and two earths, relying on numbers" probably means: using three multiplied by three to get nine, which is called "three heavens," already showing why the trigram Qian (Heaven) uses nine; using three multiplied by two to get six, which is called "two earths," already showing why the trigram Kun (Earth) uses six—thus the use of nine and six originates here. The phrase "observing changes in yin and yang to establish the hexagrams" refers to "establishing the principle of heaven as yin and yang, the principle of earth as soft and hard, and the principle of humanity as benevolence and righteousness; combining the three elements and dividing them into two, hence the Book of Changes forms a hexagram with six lines." From this, it is evident that the odd lines and even lines at the beginning of each hexagram, which remain fixed without change, are based on the numbers seven and eight.

至於發揮於剛柔而生爻者，爻與畫異，爻之未變而動名畫，畫之既動而變為爻，故《易》六位而成章。

As for "developing through the interaction of firm and yielding to produce the trigrams," the term "yao" and "hua" are distinct: when there has been no change yet, it is called "hua," and when it has already changed and become active, it is called "yao." Therefore, the Book of Changes is formed by the six positions to create its symbolic expressions.

此卦畫六位，自初至上，分陰陽定位，而以剛柔迭用於其中，變動不居，周流六虛，上下元常，剛柔相易，唯變所適。或參天而九，或兩地而六，用九用六，九、六所以變動於各爻，因以生之卦者也。九之與六，何疑之有？聖人有以見天下之跡，見天下之動，擬諸形容，觀其會通，擊辭焉以斷其吉凶，故謂其成章也。其立言《易》簡而理得，所以示天下後世者，至昭昭也。學者既其名，未既其實，終身由之，而不知因疑生解，乃以為獨有所見，自著其說，益可悲已。故為之特發揮於是。

The six positions of the hexagram, from the first line to the top line, are divided into yin and yang positions, with strong and weak lines alternating in them. They change constantly, flowing through the six empty positions, rising and falling without fixed places. Strong and weak lines alternate, following the movement wherever it goes. Some reach the height to form nine, others form six in pairs, which is called "use of nine" and "use of six." These nine and six lines change in each position, thus producing the "changed hexagram." What is there to doubt about nine and six? The sage has the ability to perceive the hidden and subtle aspects of the world and its changes, comparing them to various forms, observing their convergence and connection, attaching words to them to judge fortune and misfortune. Therefore, it is said that it "forms a chapter." His words are simple yet the principles and numbers are naturally understood, used to enlighten the world and future generations, which is already very clear. Those who study the Book of Changes only remember the names without understanding the essence, use them all their lives without knowing why, thus doubts arise and they try to explain it, mistakenly believing they have unique insights and start writing books, which is even more pitiful. Therefore, I specially elaborate on this here.

易筮通變卷中竟

The "Nine and Six" section of Volume Two of Comprehending Change in Yarrow Divination ends here.

『進』，原作『確』，據四庫本改。『卦文』，四庫本作『卦爻』。『焉』，原作『為』，據四庫本改。『穆姜』原作『穆華』，據四庫本改。

Here are the four collation notes for this section. The character '进' in the original text was '确', and it has been corrected according to the Siku Quanshu edition; '卦文' in the Siku Quanshu edition is '卦爻'; the character '焉' in the original text was '为', and it has been corrected according to the Siku Quanshu edition; '穆姜' in the original text was '穆华', and it has been corrected according to the Siku Quanshu edition.

臨川道士雷思齊學

This volume also begins with the same signature — the Daoist Lei Siqi of Linchuan's research findings. The two chapters below, "Yanshu" and "Mingashi," are still written by his hand.

天地之數五十有五，以天數之一、三、五、七、九而二十有五，地數之二、四、六、八、十而三十。宜乎？斷斷乎不得有所損益，而大衍之數遽損其五，而特謂之五十，是以求其理而不得，稽其數而不合，卒莫之要其宿；人莫不有說，說莫不有其理之似，而卒未有會其真是者，古猶今也。

The total number of the Heavenly and Earthly numbers is fifty-five: the Heavenly numbers one, three, five, seven, and nine add up to twenty-five, while the Earthly numbers two, four, six, eight, and ten add up to thirty. This seems to be a fixed total that cannot be increased or decreased. Yet the "Great Derivation Number" subtracts five and simply states fifty. Therefore, people cannot grasp its meaning, and when they check the numbers, they do not match. Thus, its origin remains unclear. Everyone has their own explanation, and each explanation seems to have some merit, but no one has ever hit upon the true explanation, whether ancient or modern.

《列子》之書，儒者桔於傳習，蓋所不取，所不觀，殊不察。其首篇謂：聖人因陰陽以統天地。夫有形生於元形，則天地安從生，故日：有太易，有太初，有太始，有太素。太易者，未見氣者也；太初者，氣之始也；太始者，形之始也；太素者，質之始也。氣、形、質具而未相離，故日渾淪。渾淪者，言萬物相渾淪而未相離，故曰易也。易變而為一，一者形變之始也。是說也，重見於《易緯》之《乾鑿度》，亦固謂然也。

The book of Liezi is not taken seriously by Confucian scholars who are bound by traditional teachings, and they have never read or believed in it, which is truly due to their failure to examine it carefully. Its first chapter says: the sage governs heaven and earth according to yin and yang. All things with form arise from the formless, so where do heaven and earth come from? Therefore, it says there is "Taiyi," "Taichu," "Taishi," and "Taisu." Taiyi is the stage before even qi appears. Taichu is the beginning of qi. Taishi is the beginning of form. Taisu is the beginning of substance. When qi, form, and substance are all present but not yet separated, it is called "hunlun." Hunlun refers to all things being mixed together without separation, so it is also called "yi." When yi changes, it becomes "one," and this "one" is the beginning of form transformation. This theory is also found in the "Yi Wei · Qian Zao Du," which discusses exactly the same ideas.

由是而觀，則《易》之有太極，而太極也者，特渾淪之寄稱爾。渾淪而上，既有謂易，謂初，謂始，謂素，凡四其稱，而至於渾淪而五，故以渾淪為太極，是之謂五太也。是則太極也者，既先含其五於中矣，故天地之數五十有五，而大衍之數乃五十者，既虛其太極己上之五，而取用於五十之妙也。《大傳》日：生生之謂易，成象之謂乾，效法之謂坤，極數知來之謂占，通變之謂事，陰陽不測之謂神。蓋謂是也。

Looking at it this way, the "Taiji" mentioned in the "Zhou Yi" is merely a name given to "Hunlun." Above Hunlun there are already four names: Taiyi, Taichu, Taishi, and Taisu. Adding Hunlun itself makes five, so calling Hunlun Taiji is referred to as the "Wu Tai." Thus, the concept of Taiji already contains the number "five" within it. Therefore, the number of the heavens and earth is fifty-five, yet the Great Derivation takes only fifty. This is precisely leaving the "five" above Taiji unused, and only employing the fifty for its subtlety. The "Xici Zhuan" says: "To produce constantly is called the Change; to form images is called Qian; to emulate and follow is called Kun; to reach the number and know the future is called divination; to understand change is called affairs; and the mystery of yin and yang is called the divine." This is precisely what is being explained.

由是知《易》有太極之為一，而一所以為形變之始矣。既謂《易》有太極，而又謂為生生之謂易，而遂繼以成象之謂乾，而不及太極，何也？是未識夫《易》者，至皿陰陽之總；而太極者，特陰陽變化之宗會焉爾。故曰：易變而為一，一者形變之始也。《易》由太極以標其一，所以為成象之謂乾，即所謂形變之始，而乃所以為一也。

From this we can see that the "Taiji" mentioned in the Zhouyi refers to "one," and this "one" is the beginning of transformation. Since it says "The Zhouyi has Taiji," and also says "The easy is called the continuous generation," yet it then says "The formation of images is called Qian" and no longer mentions Taiji, why is this so? This is because people have not recognized that "Yi" is the general term for yin and yang, and "Taiji" is merely the central point where the transformation of yin and yang occurs. Therefore, it says "Yi changes into one, and one is the beginning of transformation." The Zhouyi uses Taiji to indicate this "one," and this "one" becomes "the formation of images is called Qian," which is referred to as the beginning of transformation, hence it is called "one."

由乾分其一以為二，而始謂之坤，是大衍五十不用之一，象之為《易》有太極之。而之分為，所以象兩。夫兩不謂二，而謂之象兩，正以一之分也。故大衍之五十，先尊其太極不用之一，以為生生之本。而謂其用四十有九者，蓋由一之二，其一以生兩儀，是分而為二以象兩，又參其一以為三才之道，是掛一以象三，一復其一為四象，則北、南、束、西之判，冬、夏、春、秋之序，水、火、木、金之位，莫不由是以著，則所以揲之以四以象四時者也。而河圖之數，所以四十者也。

Heavenly Stem Jia splits the "one" into "two," and only then is Kun introduced. This is the unused stalk of yarrow used in the Great Derivation of fifty, symbolizing "The Book of Changes has the Taiji." Then this "two" is divided again to represent "two principles." Here it is not called "two" but "resembling two," because it comes from the division of "one." Therefore, the number of the Great Derivation is fifty, first honoring the unused one as the Taiji, regarded as the source of generation; and it says "its use is forty-nine," because from one comes two, using one to generate the two principles, which is "dividing into two to resemble two principles." Then adding one more to correspond to the three elements, which is "hanging one to resemble three." Then restoring this one to form the four images, thus the distinctions of the four directions—north, south, east, west—the four seasons—winter, summer, spring, autumn—the four elements—water, fire, wood, metal—are all revealed. This is the meaning of "dividing by four to resemble the four seasons," and the reason why the number of the Yellow River Chart is only forty.

然天地之數五十有五，大衍之數則五十。天五既無位於四象，地十又元位於八卦，何其不合若是之甚也。天五之有數而元位者，五之文，古之體為，象交午以為五，今之體為，見陰陽之交變於二之中以為五，而十之體亦兆見於此。五固為土，而土之文為，為十為一，其始於一，而中於五，而終於十，而復歸於一乎。土亦元正位，故四象無五，八卦元十也。

But the number of heaven and earth is fifty-five, while the number of the Great Derivation is only fifty. The number "five" of heaven is not found among the four images, and the number "ten" of earth is not found among the eight trigrams. How can they be so mismatched? The number five of heaven has a number but no position, because in ancient writing, the character for "five" was written in a cross shape resembling the intersection of two lines, using the intersecting lines to represent five. In modern writing, the character for "five" is written with two horizontal strokes and the presence of yin and yang transformation between them to represent five, and the shape of "ten" already reveals a hint of this. Five originally corresponds to earth, and the character for "earth" is written as a "ten" with an additional "one" on top. It begins with one, reaches the center at five, ends at ten, and then returns to one. Earth also has no fixed position, so five is not included in the four images, and ten is not included in the eight trigrams.

蓋嘗探索於天地之數五十有五之元矣。四象之一、二、三、四所以為八卦者，不過再用一、二、三、四，而各以五參之為六、七、八、九爾。其數止四十八。卦之一九而二八，三七而四六相交，而十之其數，亦止此四十，未嘗有天五地十之定位者，正以天五與地十以五乘十而為此大衍之五十也。何以明之？

I have carefully explored the origin of the number fifty-five of heaven and earth. The reason why the numbers one, two, three, and four of the four images can become the eight trigrams is that they merely repeat the numbers one, two, three, and four, each combined with five to form six, seven, eight, and nine. These numbers together total only forty-eight. The numbers of the opposing trigrams— one and nine, two and eight, three and seven, four and six—when paired together, each form a ten, and altogether they make up only forty. There has never been a fixed position for heaven five and earth ten; precisely because heaven five and earth ten are multiplied by five and ten respectively, they form the great derivation of fifty. What can be used to explain this?

五之妙用，伍北坎之一以五而合六為西北之乾，伍束震之三以五而合八為束北之艮者，先其方之正，後其維之偏；伍西南坤之二以五而合七於西方之兌，伍束南巽之四以五而合九於正南面之離者，先其維之偏，後其方之正。故陽奇得五而為陰耦，陰耦得五而為陽奇，所以分陰分陽，八卦以之成列。

First, the use of the number five: The one from the north (Kan) combined with five becomes six, forming the trigram Qian in the northwest; the three from the east (Zhen) combined with five becomes eight, forming the trigram Gen in the northeast — this is first taking the main direction and then reaching the secondary direction. The two from the southwest (Kun) combined with five becomes seven, falling to the west (Dui); the four from the southeast (Xun) combined with five becomes nine, falling to the south (Li) — this is first taking the secondary direction and then reaching the main direction. Thus, the yang odd numbers become yin even numbers when they receive five, and the yin even numbers become yang odd numbers when they receive five; through this division of yin and yang, the eight trigrams are arranged in sequence.

至於十之用，則什離南之九以相對，而交十於坎北之一；什兌西之七相對，而交十於震束之三，是陽數自交於陽，而各立其方之正。什艮束北之八以相對，而交十於坤西南之二；什乾西北之六相對，而交十於巽束南之四，是陰數自交於陰，而均就其維之偏。因而各虛五於中，則又皆十五之變。所以剛柔相摩，八卦相蕩相錯，變而通之，推而行之者，見天五、地十獨專五、十之用也。故衍之於碟，必以四以象四時。五、十之用，正在於是。

The use of the number ten is as follows: the nine of the south trigram Li (Fire) corresponds with the one of the north trigram Kan (Water), and their numbers combine to make ten; the seven of the west trigram Dui (Lake) corresponds with the three of the east trigram Zhen (Thunder), and their numbers also combine to make ten—this is where the yang numbers intersect with each other, each standing in the central position. The eight of the northeast trigram Gen (Mountain) corresponds with the two of the southwest trigram Kun (Earth), and their numbers combine to make ten; the six of the northwest trigram Qian (Heaven) corresponds with the four of the southeast trigram Xun (Wind), and their numbers also combine to make ten—this is where the yin numbers intersect with each other, each falling in the lateral positions. Thus, each leaves out the number five in the center, and thus they all become fifteen. Therefore, the interaction between yin and yang, and the interplay of the eight trigrams, lead to transformation and communication. The use of five and ten is specifically embodied here. Therefore, when applying this to the process of divination with yarrow stalks, it is necessary to use four to symbolize the four seasons. The function of five and ten is precisely here.

其搽之以四者，蓋由五其一、二、三、四於上，而十其六、七、八、九於下，足以明之五與天一合而成六，則四其六而二十有四，為老陰坤之策；五與地二合而成七，則四其七而二十有八，為少陽震、坎、艮之策；五與天三合而成八，則四其八而三十有二，為少陰巽、離、兌之策；五與地四合而成九，則四其九而三十有六，為老陽乾之策。故少陰、陽之七、八不變，合之而十五，以為重卦之成畫；老陰、陽之九、六所以變者，合之而亦十五，以為重卦之動爻。《易》之變通配四時，故四四而碟以象之。其四營成《易》，莫不由此。

The phrase "揲之以四" refers to the method of counting by fours. This is because one, two, three, and four, each multiplied by five, are placed above, while six, seven, eight, and nine, each multiplied by ten, are placed below. This demonstrates that five combined with heaven one forms six; four sixes make twenty-four, which is the count for old yin, the earth. Five combined with earth two forms seven; four sevens make twenty-eight, which is the count for young yang, zhen, kan, and gen. Five combined with heaven three forms eight; four eights make thirty-two, which is the count for young yin, xun, li, and dui. Five combined with earth four forms nine; four nines make thirty-six, which is the count for old yang, qian. Therefore, the eight of young yin and the seven of young yang remain unchanged, adding up to fifteen, which is used as the fixed image for the completed hexagram. The six of old yin and the nine of old yang are the ones that change, also adding up to fifteen, which is used as the moving line for the hexagram. The "Book of Changes" adapts to the four seasons, so it counts in groups of four each time, symbolizing the four seasons. The phrase "four operations form the Book of Changes" originates from this method.

河圖之實數四十，虛天五之二五，而以地十衍之而五十也。夫四營成《易》，四四而揲，每爻之揲凡三，每碟其蓍以合左右之奇，或一三而四，或三一而四，或二二而四。其或左奇既先四，則右奇後亦必四。因二其四耦之成八，以紀其數者，奇必有耦也。奇四而耦八，亦見數之四十增八者，河圖四十而成八卦也。

The numerical total of the Yellow River Chart is forty. The number five from the Heaven's Five is left blank, and then the Earth's Ten is used to derive the rest, resulting in fifty. The phrase "four operations form the Book of Changes" refers to counting the yarrow stalks in groups of four. To form one trigram, the stalks are counted three times (three transformations). Each time the stalks are counted, the remaining numbers in both hands are combined: either one on the left and three on the right make four, or three on the left and one on the right make four, or two on each side make four. If four remains on the left first, then four must also remain on the right afterwards, making eight in total. This eight is used to record the number for that transformation, because if there is an odd number, there must be an even one. The remaining number is four, and the even number is eight. This shows the logic of adding eight to forty, which is how the Yellow River Chart of forty leads to the formation of the Eight Trigrams.

然其所碟之四，未嘗五與九也。今碟蓍者，必謂初搽不五則九，始由《易疏》謂：第一變之奇，不五則九；第二揲、第三搽之奇，始皆不四則八。原其第一搽，誤以未揲之先，所謂掛一之蓍同在數中以自亂其四而然也。蓋所揲之奇，四之上加一則五，八之上加一則九，所以見也。

However, the remaining numbers obtained through divination are only four and eight, never five or nine. Now, those who perform the divination with yarrow stalks always say that the remaining number of the first change is either five or nine. This idea originates from Kong Yingda's commentary in The Correct Meaning of the Zhou Changes, which states that the remaining number of the first change is either five or nine, while the remaining numbers of the second and third changes are always four or eight. Investigating why the first change is like this, the error lies in including the single stalk that is "hung" before the divination begins in the count, thereby confusing the remaining number that should originally be four. The remaining numbers obtained through divination, when one stalk is added to four, become five, and when one stalk is added to eight, become nine. Thus, five and nine arise in this way.

殊不識此一之加為五為九，元成虧於所碟之四，而徒為擾擾耳。且夫掛一，自當四營之一營，在分而象兩之後、碟之以四之先，元未以之與於搽也。若非以掛一之一誤於自亂，則安得謂第二揲、第三搽而不四則八也？

They had no idea: this additional stick, whether it made five or nine, made no difference to the original "four" that was obtained, only adding unnecessary confusion. Moreover, "hang one" was originally meant to be one of the four groups in the four camps, coming after "divide into two to represent the two" and before "divining by four," and thus did not take part in the divining process. If it were not for mistakenly including that stick and disrupting the count, how could it be said that only the second and third changes are not four but eight?

夫每更左右兩揲四，始為一變，《傳》謂十有八變而成卦，則凡碟之變固不容有所異也，安得每三搽之中，第一揲為不五則九也？如是，則十有八變中獨六變。若是之異，若於中六變獨異，則又安得總謂十有八變也哉？

Each time, both hands are used to count four times, making one change; the "Great Treatise" says "eighteen changes are needed to form a hexagram," indicating that all changes in the divination process should be the same, so why is the first change among every three changes different, being either five or nine? According to this, there are six changes (the first change of each line) that are different among the eighteen changes. If these six changes are uniquely special, how can they still be generally called "eighteen changes"?

此孔《疏》始為此誤，而後之來者既不加察，而傳信傳疑，愈說愈紛，卒未能有以正其誤者，千載良一既也。若謂掛一者，合置於奇數中之用以為數，則至於功而後掛者，又當何以哉？

This error was first introduced by Kong Yingda's commentary, and later people did not examine it carefully, passing on both credible and doubtful interpretations together. As a result, the explanation became more and more confused, and ultimately no one corrected it. For a thousand years, this has been a great regret. If the single strand used in the "gua yi" should be counted among the zero strands as part of the count, then what should be done with the strands hung in the second and third changes, which are hung after the "gui la" is completed?

載原其誤者，蓋泥於衍數五十，其用四十有九，謂掛一之一實在四十有九所用之中，而不識夫掛一者，所以標每變四十有八之用，而計其□有八變之數，則乃所以為用也。豈以夫一而自亂於四十有八所搽之眾哉？故所搽之蓍，皇行其變者四十有八標、夫掛一者以紀其變之十有八，固所以為四十有九之用，並與其始太極所不用之一通為大衍之五十也。

To trace the origin of this error, it is probably due to a rigid interpretation of the phrase "衍数五十，其用四十有九," which assumes that the single stalk used in the "挂一" step is actually counted among the forty-nine used. However, one fails to understand that "挂一" is actually used to mark that in each change, only forty-eight stalks are actually used, and it is also used to count the number of eighteen changes. This is its true purpose. How could that single stalk disturb the forty-eight stalks used in the divination? Therefore, the actual number of stalks used in the divination process is forty-eight, while the one hung aside is used to keep track of the eighteen changes. Although it is counted within the forty-nine, when combined with the initial one left aside as the Taiji, they make up the total of fifty, as in the Great Derivation.

所以謂夫五十者，蓄之德員而神者，其員以七，七七而四十有九；卦之德方以知者，其方以八，八八而六十有四。是以七合八之十五，既合而見於蓍卦之數矣。六爻之義易以貢者，乃散而分見於《戲》之用九、《坤》之用六，以九合六之十五之甩，而由五以下七、八、九、六元有不著於用者焉。故以五乘十，而所以謂為大衍五十也。

Therefore, the number 'fifty' refers to the virtue of the yarrow stalks, which is round and divine. The roundness is measured by seven, and seven times seven equals forty-nine. The virtue of the hexagrams is square and based on knowledge, measured by eight, and eight times eight equals sixty-four. Thus, the combination of seven and eight, which totals fifteen, is already embodied in the numbers of the yarrow stalks and the hexagrams. As for the meaning of the six lines, it is expressed in the 'use of nine' in the Hexagram Qian and the 'use of six' in the Hexagram Kun (the original text's 'xi' is a variant form of 'Qian'). The combination of nine and six, which also totals fifteen, is included in these. From five downwards, seven, eight, nine, and six are all applied in practical terms. Hence, multiplying five by ten gives the number fifty, which is called the great derivation number.

若是，則由天之與地，自一而至十，五十有五之數，莫不真見其著落，而大衍之五十與其用四十有九者，亦莫不悉究其詣實。其謂生生之易，成象之乾，效法之坤，極數知來之占，通變之事，於此瞭然可盡，至於陰陽不測之謂神，神而明之存乎其人哉。

In this way, from the heavenly numbers to the earthly numbers, from one to ten, the total of fifty-five numbers are all truly and clearly accounted for; and the fifty used in the Great Derivation as well as the forty-nine actually used are all clearly explained in terms of their actual meanings. As for the saying "the continuous generation is called the Book of Changes, the forming of images is called Qian, the following of patterns is called Kun, the knowing of future from the extremes of numbers is called divination, and the understanding of change is called affairs," all of these can now be clearly understood and fully explained. As for the phrase "the indescribable movement of yin and yang is called the divine," that requires each person to personally grasp and understand it in a divine and clear manner.

《說卦》曰：昔者聖人之作《易》也，幽贊於神明而生蓍，參天兩地而倚數，觀變於陰陽而立卦，發揮於剛柔而生爻。若是，則蓍豈徒生？數豈虛倚？卦豈苟立？而爻豈饅為哉？因爻畫卦，因卦兆數，因子用蓍，以極天下之跡，以鼓天下之動，由此其選也。

The Shuogua Transmission says: In the past, the sage created the Zhou Changes, secretly receiving assistance from the divine to produce the yarrow stalks. By taking the heavens as three and the earth as two, the sage established the divination numbers. Observing the changes of yin and yang, the sage established the hexagrams. By expressing the movement of firmness and flexibility, the sage produced the lines. So, how could the yarrow stalks have appeared without purpose? How could the numbers have arisen without foundation? How could the hexagrams have been established at random? How could the lines have been placed without meaning? From the lines came the hexagrams, from the hexagrams came the manifestation of numbers, from the numbers came the use of the yarrow stalks. Using them to exhaust the hidden and profound aspects of the world and to stir up the changes in the world, this is the reason why the yarrow stalks, numbers, hexagrams, and lines were chosen.

《大傳》曰：蓍之德員而神，卦之德方以知，六爻之義易以貢。此大衍之數之蓍所由著也。大衍之數，至皿五十其蓍，而其用乃四十有九者，蓋已尊其一於不用，以為太極之全體，是所謂《易》有太極者也。乃分其四十有九之蓍，列左右，為二以象兩，是所謂太極生兩儀也。兩儀者陰陽，陰陽相儀匹而有老少，則兩儀已含四象矣。

The Great Treatise says: "The virtue of the divining stalk is round and divine, the virtue of the hexagram is square and knowing, and the meaning of the six lines is easy and contributes." This is precisely where the method of the Great Derivation becomes clear. The Great Derivation originally used fifty stalks of the divining herb, but in practice only forty-nine were used. The reason is that one stalk was set aside and respected, not used, representing the whole Taiji. This is called "The Book of Changes contains Taiji." Then the forty-nine stalks were randomly divided and placed on both sides, forming two to symbolize the two principles, which is called "Taiji produces the two principles." The two principles are yin and yang. When yin and yang are paired, they have old and young, so the two principles already contain the four images.

乃左取蓍而掛其一以象三，八卦之畫以三而成，則三才之道也。益以元五十不用之一，與分兩之二兼之而成此三也，是於分兩之二，推其一以掛於兩之際，所以象人極之立位乎兩問也。是則參天兩地而倚數，特寓於此，不用之一，象兩之二，掛一之三，參天也。分而象兩，固所以兩地者也。於是觀變於陰陽而立卦矣。所謂太極不用之一，雖不以為用，而乾陽之始一，皇兆乎此，則其用未始不由此以出也。

Then take one from the pile on the left and hang it up to represent the number three; the trigrams are composed of three lines, which embody the principle of the three elements. Adding the one that was not used from the original fifty, together with the two formed by dividing into two piles, it becomes the number three. In practice, one stick is drawn from the two piles and hung between the left and right piles to symbolize the human principle standing between heaven and earth. Thus, the phrase "参天两地而倚数" is embodied here: the unused one represents the number one, the two formed by dividing represents the number two, and the hung one represents the number three. Together they form "参天" (reaching the heavens). Dividing to represent two is naturally "两地" (two lands). At this point, we have "观变于阴阳而立卦" (observing changes in yin and yang to establish the trigrams). The stick not used by the Taiji, although not used, already reveals the initial "one" of Qian (Heavenly Yang). Its use is not without origin here.

因此，乾用之一以分而為坤體之二，則所謂象兩而為兩儀，以兩儀而一陰一陽以老、少於其位，是兩儀已含四象矣。是以繼之以象三之一，而分陰分陽，迭柔剛而用之，而象三以畫，則四象遂生八卦，而八卦者已成列矣。八卦各三位，八卦而小成，三極之道於是乎見矣。

Thus, the "one" used by Qian is divided to become the "two" of Kun's body, which is called "resembling two" to form the two principles; among the two principles, one yin and one yang each occupy their respective positions according to old and young, showing that the two principles already contain the four images. Then using the "three" represented by the yarrow stalks, the yin and yang are further divided, alternating between soft and strong, to resemble three and form the lines, thus the four images give rise to the eight trigrams, and the eight trigrams are arranged in order. Each of the eight trigrams has three lines, and with the eight trigrams comes a smaller completion; the three fundamental principles are thus revealed.

合而言之，是《易》有太極，是生兩儀，兩儀生四象，四象生八卦，已著於用而成於體矣。然而大衍之數之用，雖略見於分兩掛一之始，而未大成也。

Putting it all together, this is "The Book of Changes has the Taiji, from which the two principles arise, the two principles give rise to the four images, and the four images give rise to the eight trigrams," which already shows the emergence and establishment in terms of form. However, the full function of the Great Derivation number, although slightly indicated at the beginning of dividing into two and hanging one, has not yet been fully realized.

且太極不用之一，象兩之二，掛一之三，雖等列而三位，而其正用之蓍特不用之一，與掛一之一，其實數特二爾。且以五十而始用其二，則未用之蓍正存四十有八，是用河圖之數四十以行八卦也。且八卦各六位，以八卦而其位各六而八之，非四十有八者乎？八卦雖八八而六十四，而其為游魂、歸魂者凡十有六，不列於正八卦之六位，故其數止於四十有八也。

Moreover, the Taiji does not use the first, the two of the image, and the three of hanging one, although they are listed as three positions. However, the actual stalks of yarrow used are only the one not used and the one hung up, which amounts to just two stalks. If two stalks are first used out of fifty, then the remaining un-used stalks are exactly forty-eight. This is how the number forty from the Yellow River Chart is used to generate the Eight Trigrams. Moreover, each of the Eight Trigrams has six lines, so six lines per trigram multiplied by eight trigrams gives forty-eight. Although the Eight Trigrams can be combined in pairs to form the sixty-four Trigrams, the sixteen Trigrams belonging to the wandering souls and returning souls are not included within the six positions of the original Eight Trigrams, so the number stops at forty-eight.

由四十有八，而上虛此十六卦為四四以揲之用，乃所以成六十有四也。於是乎觀變於陰陽而立卦，則遂發揮於剛柔而生爻。爻也者，效天下之動者也。立天之道日陰與陽，立地之道日柔與剛，立人之道曰仁與義，兼三才而兩之，故《易》六畫而成卦也。

From these forty-eight, we now leave the sixteen trigrams empty, using them as groups of four for divination. This completes the sixty-four trigrams. At this point, it is said, "Observing changes in yin and yang to establish the trigrams." Then follows, "Expressing these changes through the principles of firmness and flexibility to produce the lines." The lines are modeled after the changing nature of the world. Establishing the principle of heaven is yin and yang, the principle of earth is flexibility and firmness, and the principle of humanity is benevolence and righteousness. By combining the three elements and pairing them, the Book of Changes forms a trigram with six lines.

前既以不用之一、象兩之二、掛一之三等而三之，由三而四，故先以分左之蓍，揲之以四以象四時，四時而八節猶四象生八卦也。故以四行八，足以見十六卦之四四，皇用六十四卦之八八也。四四之奇，所以寄乾；八八之奇，所以寄坤。八八之奇，雖謂之耦，然亦奇。四所協以配，故兼謂之歸奇也。

Before arranging the unused stalks, the single stalk, and the two stalks in three positions in order, moving from three to four, we first take the pile of stalks on the left and count them in groups of four (揲之以四), symbolizing the four seasons. The four seasons are divided into eight solar terms, just as the four trigrams give rise to the eight trigrams. Therefore, using the number four to generate the eight trigrams shows how the sixteen trigrams are formed by "four times four" and the sixty-four trigrams by "eight times eight." The remaining numbers from "four times four" are used to represent the trigram Qian (Heaven), and those from "eight times eight" represent the trigram Kun (Earth). Although the remainder from "eight times eight" is called "couple," it is still odd, since it is formed by pairing "four." Thus, both are referred to as "returning the odd."

所揲之奇，不一則二，不三則四，則歸之功於是謂之歸奇於功以象閏。閏乃餘數之所歸，故以奇象之奇亦餘也。然後以分右之蓍，四四而揲，所揲之奇四且八之，其得一則先左之奇必三合之而四，得三則其先左之奇必一合之而四。得二則其先左之奇亦必二通合之為四，得四則其先左之奇亦必四特合之為八，蓋左先一而後右三，與左先三而後右一，固皆合四以為奇，而其左先二而後右二，雖亦合之為四，而理乃倍四而耦八也。

The remaining number after counting is either one or two, or three or four. This number is then placed between the fingers, which is called "returning the remainder to the space between the fingers to symbolize the leap month." The leap month is the destination of the remainder, so the remainder is used to symbolize it. "Qi" originally means "remainder." Then, the bundle of chrysanthemum grass on the right is counted in groups of four as well. The remainder on the right combined with the remainder on the left is either four or eight: if the right has a remainder of one, the left must have had a remainder of three, making a total of four; if the right has a remainder of three, the left must have had a remainder of one, also totaling four; if the right has a remainder of two, the left must have had a remainder of two, still totaling four; if the right has a remainder of four, the left must have had a remainder of four, totaling eight. Thus, when the left has a remainder of one and the right has a remainder of three, or the left has a remainder of three and the right has a remainder of one, they both total four and are considered odd. However, when both the left and the right have a remainder of two, although they also total four, according to Lei's explanation, this is considered double four, and should be classified under the category of even eight.

若左奇既四，右奇亦四，因合而八以為耦。耦雖謂八，亦奇四之分配以成之也。猶坤之，乃乾一之所分，故統謂之奇。乃隨後右所合之奇、所奇之蓍，再功於左，而兼取左右所奇者，掛之以待第二、第三變，是謂再劫而後掛也。然而前掛一之掛，則謂於四十有九中，先取一蓍以獨掛此劫，而後掛之掛，則特謂掛其所奇之蓍也。

If there are four remaining on the left and four on the right, together they make eight, which is called "cou." Although "cou" is called eight, it is actually formed by the combination of two "four" odd numbers; just as the yin lines of the坤 (Earth) trigram are derived from the single line of the乾 (Heaven) trigram, they are collectively referred to as odd. Then, the leftover number from the right side is again placed between the fingers (a second "tou" action), and the leftovers from both sides are combined and hung up, to be used in the second and third changes. This is called "tou and then hang." However, the "hang" in the earlier "hang one" refers to taking one stalk from the forty-nine and hanging it separately. The "hang" here, in "after hanging," specifically refers to hanging up the leftover stalks.

乃又總前已分二，已掛一，與所已過揲之蓍，悉合之以還於大衍之初，是之謂四營而成《易》，而通為第一爻也。所謂四營者，分二者，其一也；掛一者，其二也；揲四，其三也；歸奇終營，之四也。其營既畢，所奇既掛，是為第一變之周也。

Then take the bundle that has already been divided into two groups, the one that has already been hung up, and the stalks that have already been counted (over揲), and bring them all together again, restoring them to the original whole bundle of large yarrow stalks. This is called "four operations to form the Book of Changes," and this is the first step in seeking the first yao. The so-called "four operations" are: dividing into two is the first operation, hanging one is the second operation, counting by four is the third operation, and gathering the remaining stalks (by holding them between the fingers) to conclude is the fourth operation. After completing the four operations, the remaining stalks are also hung up, which constitutes one complete cycle for the first change.

一變之後，存其前所奇之外，以所合前衍過搽之蓍，如第一變之分二之掛一之揲四之歸奇再功。而後掛其所奇，以合前變之奇，以待第三變也。

After the first change, leave the remaining number of stalks aside, take the rest that were gathered together, and use them along with the leftover stalks from the previous change. Perform the same process of dividing into two, hanging one, shaking four, returning the remainder, and separating again as in the first change. Then, hang up the leftover stalks from this change and combine them with the leftover stalks from the previous change, keeping them ready for the third change.

其第三變則又如第一、第二變之分二掛一、搽四歸奇再功。而合此三變所奇之蓍以數之，以四為少，八為多。三變皆少，則所奇者十二，則其過搽之所存總四九三十有六，為乾之策；三變皆多，則所奇者二十四，則其過揲之所存四六亦二十有四，為坤之策；兩多而一少，則所奇者二十，則其過揲之所存總四七二十有八，是為震，為坎，為艮之策；兩少而一多，則所奇者十六，則其過揲之所存總四八三十有二，是為巽，為離，為兌之策。

The third change is carried out in the same way as the first and second changes, dividing into two, hanging one, shaking four, returning the odd, and then handling again. After this, the remaining numbers from the three changes are combined for calculation. Using four as 'few' and eight as 'many', if all three changes result in 'few' (each being four), the total remaining is twelve, and after subtracting the remainder from the shaking, it leaves thirty-six, which is the count for Qian (old yang); if all three changes result in 'many' (each being eight), the total remaining is twenty-four, and after subtracting the remainder from the shaking, it leaves twenty-four, which is the count for Kun (old yin); if two are 'many' and one is 'few', the total remaining is twenty, and after subtracting the remainder from the shaking, it leaves twenty-eight, which is the count for Zhen, Kan, and Gen (young yang); if two are 'few' and one is 'many', the total remaining is sixteen, and after subtracting the remainder from the shaking, it leaves thirty-two, which is the count for Xun, Li, and Dui (young yin).

凡如是三變竟始得為一爻之成晝，亦必以所奇之策，由初以終，自下而上，層積而紀之，如畫卦之三爻。然其奇之四為陽，八為陰，效八卦以取之。

After three changes, one line of the hexagram is completed. It is also necessary to record the remaining number of counting sticks for each change, starting from the first change to the last, layer by layer from the bottom up, just like the three lines of the hexagram. As for the remaining number being four, it is considered yang; and the remaining number being eight, it is considered yin. This method is imitating the eight trigrams to take their symbolic forms.

兩多而一少者，其先四、中八、後八為得陽之初，象少陽七之震；先八、中四、後八為得陽之中，象少陽七之坎；先八、中八、後四為得陽之上，象少陽七之艮。兩少而一多，其先八、中四、後四為得陰之初，象少陰八之巽；先四、中八、後四為得陰之中，象少陰八之離；先四、中四、後八為得陰之上，象少陰八之兌。

The situation of two yin and one yang: if the first is four, the middle eight, and the last eight, the yang is in the initial position, symbolizing the trigram Zhen (Thunder) of the lesser yang seven; if the first is eight, the middle four, and the last eight, the yang is in the middle position, symbolizing the trigram Kan (Water) of the lesser yang seven; if the first is eight, the middle eight, and the last four, the yang is in the upper position, symbolizing the trigram Gen (Mountain) of the lesser yang seven. The situation of two yin and one yang: if the first is eight, the middle four, and the last four, the yin is in the initial position, symbolizing the trigram Xun (Wind) of the lesser yin eight; if the first is four, the middle eight, and the last four, the yin is in the middle position, symbolizing the trigram Li (Fire) of the lesser yin eight; if the first is four, the middle four, and the last eight, the yin is in the upper position, symbolizing the trigram Dui (Lake) of the lesser yin eight.

凡遇震、坎、艮，則皆畫為陽爻也；遇巽、離、兌，則皆畫為陰爻也。者皆謂之少者，象少者未遽變也。獨其三變通得四，四四者特謂為陽之純，象老陽九之乾，乃畫為今俗謂重，為老陽九之爻。其三變通得八，八八者特謂為陰之純，象老陰六之坤，乃畫為今俗謂交，為老陰六之爻。

Whenever the trigrams Zhen, Kan, or Gen appear, they are all drawn as yang lines; whenever the trigrams Xun, Li, or Dui appear, they are all drawn as yin lines. These are collectively referred to as 'minor' (少), symbolizing something that has not yet changed immediately. Only when all three lines are four (四), forming a pure four (四四相纯), is it specially called pure yang (阳之纯), symbolizing the old yang nine (老阳九) of Qian, and is drawn as the commonly known 'heavy' line (重), which represents the old yang nine line. Similarly, only when all three lines are eight (八), forming a pure eight (八八相纯), is it specially called pure yin (阴之纯), symbolizing the old yin six (老阴六) of Kun, and is drawn as the commonly known 'cross' line (交), which represents the old yin six line.

乾為老陽者，本九奇而變含六耦之陰。坤為老陰者，本六耦而變含九奇之陽。乾、坤之畫兼謂老者，以老故變也。其必三變始成一畫者，寓陰陽變化擬議以定之也。於三變所奇之策，第其四與八之互者，寓乾坤相索生六子意也。

The reason Qian is called Old Yang is because it originally represents the yang odd number nine, but when it changes once, it contains the yin even number six. The reason Kun is called Old Yin is because it originally represents the yin even number six, but when it changes once, it contains the yang odd number nine. The trigrams Qian and Kun are both called "old" because they are old and thus require change. The reason why it must take three changes to form one line is to indicate that the transformation of yin and yang must be deliberated repeatedly before being determined. The sequence of the remaining numbers arranged with four and eight alternating represents the idea of Qian and Kun seeking each other and giving rise to the six subsidiary trigrams.

凡如是而分而掛而搽，且初積其奇而合過搽之蓄者，三謂之三變，始謂一爻之成。又如是而三變，則謂二爻之成。又如是而三變，乃通謂三爻之成。是謂九變。九變備，三爻具，始可當為卦之八者，止三畫，三其畫而八之，則為八卦成列。謂內卦，謂下卦，謂三微，謂內貞，是謂八卦而小成，是三《易》所謂經卦皆八也。

Thus, the process is repeated, dividing into two, hanging one, and drawing four, accumulating the remaining numbers each time, and combining them with the stalks used in the divination. This process is repeated three times, known as "three changes," to form one line of the hexagram. Repeating this process three times forms the second line; repeating it a third time forms the third line. This is called "nine changes." After completing the nine changes, the three lines are complete, and it is considered as one of the eight trigrams, though it only has three lines. By developing this group of three lines into eight, the eight trigrams are formed. These three-line trigrams are called the inner trigram, the lower trigram, the three subtle lines, and the inner purity, which is referred to as "eight trigrams and a small completion," corresponding to the "eight trigrams" mentioned in the "Three Classics."

蓋必又如是以營以分，以掛以揲，以初以計其所奇之積。三而三之，以為九變；再成三畫，以為外卦，為上卦，為三蓍，為外悔；合前九變之三畫，是謂六畫而成卦，是三《易》所謂其別皆六十有四，始全其十有八變而成卦，以備六位成章也。

Next, one must proceed in the same manner to count, divide, and set aside the stalks, and again tally the remaining numbers from the beginning: three changes repeated three times, making nine changes in total. These are then recombined into three lines, forming the outer trigram, also called the upper trigram, three stalks, or outer regret. Combining this with the three lines formed from the first nine changes, this constitutes the "six lines forming the hexagram," which is what the "Three Classics" refer to as "each variation has sixty-four." Only at this point does the process of "eighteen changes forming the hexagram" complete, fully establishing the six lines of the hexagram.

其所以變必十有八者，震、坎、艮各五畫，得十五，用乾之三，為十八。而二乾之一、三、五，固十八也。巽、離、兌各四畫得十二，用坤之六為十八。而三坤之一不四，亦十八也。

As for why the number of changes must be eighteen, it can be calculated as follows: the trigrams Zhen, Kan, and Gen each have five lines (a single yang line counts as one, and two yin lines each count as two), totaling fifteen, plus the three lines of Qian, making a total of eighteen; and the sum of the first, third, and fifth lines of two Qian trigrams (each group totaling nine) is also eighteen. The trigrams Xun, Li, and Dui each have four lines, totaling twelve, plus the six lines of Kun, making eighteen; and the sum of the second and fourth lines of three Kun trigrams (each group totaling six, with the original text's "一不四" being a miswriting of "二、四") is also eighteen.

合兩十八，則為《乾》之策四九三十六，是前九變每爻四營，積九變之營，固三十六也。倍之，則龜之策七十二。五行之土，分王四時，各十八日，四其十八，亦七十二日。各九十日，分土王之十八日，亦各七十二，故積十有八變，每變四營，通十八變，計其營之數亦七十二。五其七十二，則三百有六十，當期之日。故有取於十八變、七十二營，以用四十有九曹也。

Adding these two eighties together gives thirty-six, which is exactly the number of lines in one trigram of the Qian hexagram, calculated as four times nine, which equals thirty-six. This is also the total number of lines in the first nine transformations, where each line consists of four operations, and nine transformations amount to thirty-six. Doubling this gives seventy-two, which is referred to as the "turtle's measure" in the text. In the Five Phases, the element earth rules over the four seasons, each season having eighteen days, and four times eighteen equals seventy-two days; each season is ninety days, and from these, the eighteen days ruled by earth are subtracted, leaving seventy-two days for each season. Therefore, accumulating eighteen transformations, each with four operations, the total number of operations is again seventy-two. Five times seventy-two equals three hundred and sixty, which matches the number of days in a year. Thus, using eighteen transformations and seventy-two operations, the fifty-one stalks of yarrow are employed.

蓋前九變，三畫分陰陽而列之，不過八卦成列而象在中；後九變，三畫迭柔剛而用之，乃因而重之而爻在中，因其十八變，而爻之迭柔剛也。用此柔剛以相摩相蕩，相推相易，而通其變；引而伸之於六十四卦，唯變所適，是所謂變在其中。由六十四卦觸類長之於三百八十四爻之外，則天下之能事誠可畢矣。

The first nine transformations involve dividing the three lines into yin and yang arrangements, but this is simply "the eight trigrams are arranged in order and the images are contained within them." The latter nine transformations involve alternating the use of soft and strong lines in the three lines and applying them in practice, thus "thereby being repeated and the lines are contained within them." It is precisely because of these eighteen transformations that the lines have the alternation of soft and strong. By using the mutual friction and collision between soft and strong, and their mutual shifting and succession, we can connect and understand its changes. Then, extending this to the sixty-four trigrams, following the changes wherever they occur, this is called "the changes are contained within them." By extending from the sixty-four trigrams to the 384 lines beyond, then all the possible things under heaven can truly be accomplished.

曹之德可不謂員而神於其常用，卦之德可不謂方以知於其常體，而六爻之義可不謂易以貢於受命，如響之變化者乎？又可不謂寂然不動，感而遂通天下之故者乎？故以之通天下之志，成天下之務，定天下之業，而斷天下之疑，其於幽贊於神明而生曹，參天兩地而倚數，觀變於陰陽而立卦，發揮於剛柔而生爻者，著豈徒生？數豈虛倚？卦豈苟立？而爻豈饅為哉？果能此道以神明其德，誠可以顯道神德行，而酬醉佑神矣。大衍之數五十，其用四十有九，其以是夫。

Thus, the virtue of the yarrow stalks in their daily use can truly be said to be "round and divine." The virtue of the hexagrams, fixed in form, can truly be said to be "square and knowing." The meaning of the six lines lies in their ability to receive the mandate and respond as if echoing, which can truly be said to be "easy and offering." Is it not also precisely "silent and unmoving, yet responsive to all things and thus comprehending the workings of the world"? Therefore, it can be used to communicate the hearts of people across the land, accomplish the affairs of the world, establish great achievements, and resolve doubts of the world. Looking back at the words "the yarrow stalks arise from the divine and the holy, the number is based on the heavens and earth, the hexagrams are observed through the changes of yin and yang, and the lines are developed through the interplay of strength and flexibility": could the yarrow stalks have arisen without purpose? Could the numbers have been established without foundation? Could the hexagrams have been created at random? Could the lines have been placed without meaning? Truly following this path to manifest one's own virtue, one can indeed illuminate the Way of the Book of Changes, transform virtue, and respond to the assistance of the divine. The principle "the great derivation consists of fifty numbers, but only forty-nine are used" is probably based on this very idea.

易筮通變卷下竟

The two chapters "Deriving Numbers" and "Using the Yarrow Stalks" in Volume Three of "Comprehending Change in Yarrow Divination" conclude here, and the entire book of three volumes is completed.

『不』，原作『無』，據四庫本改。『為』，原作『朱』，據四庫本改。『數』，原作『五』，據四庫本改。『巽』，原作『其』，據四庫本改。『畫』，原作『書』，據四庫本改。『夫』，原作『天』，據四庫本改。『以』，據四庫本補。『標』，四庫本作『碟』。『所碟之眾』，原作『所搽者之眾』，據四庫本刪『者』字。『標』，四庫本作『標』。『曹』，原作『著』，據四庫本改。

Here are eleven collation notes for this section. The character '不' in the original text was '无', corrected according to the Siku Quanshu edition; the character '为' was originally '朱', corrected according to the Siku Quanshu edition; the character '数' was originally '五', corrected according to the Siku Quanshu edition; the character '巽' was originally '其', corrected according to the Siku Quanshu edition; the character '画' was originally '书', corrected according to the Siku Quanshu edition; the character '夫' was originally '天', corrected according to the Siku Quanshu edition; the character '以' was added according to the Siku Quanshu edition; the character '标' in the Siku Quanshu edition is '碟' (a variant form of '揲'); '所碟之众' was originally '所搽者之众' in the base text, with the character '者' deleted according to the Siku Quanshu edition; another occurrence of '标' remains as '标' in the Siku Quanshu edition; the character '蓍' was originally '着', corrected according to the Siku Quanshu edition.