The Book of Changes: Venturing into the Changes

新安瞽目程良玉著，錢唐旅堂胡介定。

This book was written by Cheng Liangyu, a native of Xin'an (now Shexian, Anhui Province). He became blind at the age of five due to smallpox, so he signed his name as "Gumu" (meaning "blind"). It was edited and published by Hu Jie, a person from Qiantang (now Hangzhou, Zhejiang Province), who was known by the courtesy name Lutang. "Ding" refers to the act of deleting and proofreading.

餘在長安時，即聞程君元如賢，後十年而始得訪君於家，元如辭以疾，餘因鬍子旅堂為介紹，過從者再，元如始出。聆其言論，蓋君平公時之流也。自時厥後，餘數過其家，元如雖臥病，必強起為餘坐談弗倦。一日謂余曰：吾五歲而瞽於痘，不能習舉子業，學醫不成，始學易；初從星元先師遊，晚遇枯匏老人，互相質證，有所悟，命人筆記，歷年成書，而但慮辭多煩冗，意或重複，因托旅堂為餘商訂，書成公其為我序之。

When I was serving in the capital, I had heard of Mr. Cheng Yuanru's virtue. Ten years later, I was finally able to visit his home. At first, Mr. Cheng refused to see me because he was ill, but through the introduction of Mr. Hu Lutang, I visited him twice, and only then did he agree to meet me. After listening to his conversation, I realized he was a recluse of the same kind as Yan Junping of the Han dynasty. From then on, I visited him many times. Even though he was ill in bed, he would always make an effort to rise and talk with me at length without showing any fatigue. One day he said to me: I became blind in both eyes at the age of five due to smallpox, so I could not study for the imperial examinations like ordinary people. I also failed to become a physician, so I turned to studying the Book of Changes. At first I studied under Master Xing Yuan, and in his later years I met Master Kupao, and we questioned and verified each other's ideas, gaining some understanding. I then had someone write down my thoughts, and after years of accumulation, I completed this book. However, I am worried that the language is too verbose and the meaning may be repetitive, so I have asked Mr. Hu Lutang to help me decide what to include and exclude. After the book is completed, I wish to make it known to the world, so please write an introduction for me.

餘應諾。未幾旅堂歿，余竊慮無有贊助此書於成者矣。元如益傷悼痛哭，病日深，餘往問疾，不能出，然猶異其必起也。無何而元如亦下世矣，嗚呼痛哉！甫浹旬，有人衣縗絰衣，面深墨，持易冒一書，長跪而涕泣曰：吾父易簀時，執手叮嚀，謂所著書為我也，序者必楚中王先生，我是以恪遵遺命，來求先生，先生幸勿辭。餘聞其言而悲，又何忍辭。

I agreed. Soon after Hu Lutang died, I felt deeply worried that there would be no one left to help complete this book. Yuan Ru became even more sorrowful and wept bitterly, his illness worsening day by day. I went to visit him, but he was too weak to leave his room to meet me. I still hoped he would recover. Soon after, Yuan Ru also died, which was truly regrettable. Just ten days later, a man dressed in coarse hemp mourning clothes, with a dark complexion, came bowing and weeping, holding a copy of "Yi Mao" and kneeling for a long time. He said that his father, on his deathbed ("yi ze" is a reference to Zengzi's story of changing his bed at the end), held his hand and repeatedly instructed him, saying that this book was written for him, and that the person writing the preface must be Mr. Wang from Chu. I therefore strictly followed his last wish and came to beg the master, asking him not to refuse. Upon hearing these words, I felt extremely sorrowful and could not bear to refuse.

余竊嘆易學至今日，不絕於不學易，而絕於學易者，恆多矣。夫學易宜未絕也，絕於不易，其易而竊異端之術以為易，其為絕也，孰甚焉。程子傳易，本之王弼，弼則出之費直，朱子本義，本之呂伯恭，古易則本之田何，未嘗以非易言易也。

I privately lament: the development of the study of the I Ching has not been ruined by those who do not study the I Ching, but rather often by those who do study it. Studying the I Ching should not lead to its extinction; the problem lies in studying something that is not the I Ching itself—using heretical and occult practices to pretend to be the I Ching. Is there a more serious cause for its extinction than this? In the Song dynasty, Cheng Yi explained the I Ching by following the approach of Wang Bi of the Wei dynasty; Wang Bi's learning came from Fei Zhi of the Han dynasty; Zhu Xi's "The Original Meaning of the Zhou Changes" followed the approach of Lu Zuguang (whose courtesy name was Bo Gong), and Lu's version of the ancient I Ching was based on Tian He, who transmitted the I Ching in the early Han dynasty. Throughout history, great scholars have never used something that is not the I Ching to explain the I Ching.

元如之學易也，謂其辭有盡而其象無窮，每占一卦，觀其爻象貞悔陰陽動靜，而人之終身吉凶悔吝洞若觀火，以是聲名藉甚，甚有越千里以來求一言而去者。而元如益不敢自多也，日惟觀象玩占以自體驗。

Yuan Ru studied the Book of Changes, advocating that the statements of the lines are limited while the changes of the hexagrams are infinite. When he interpreted a hexagram, he only considered the "Zhen" (the inner trigram, the primary hexagram) and the "Hui" (the outer trigram, the resulting hexagram), examining their yin and yang and their motion and stillness. Thus, one's entire life of good fortune, misfortune, regret, and hardship became clear to him as clearly as seeing fire. Therefore his reputation became very great, and even people traveled thousands of miles just to obtain one sentence from him. Yet Yuan Ru became even more cautious and never satisfied with himself, each day observing the hexagrams and pondering the examples, using them to verify his own learning.

嗟乎，吾黨有人致身通顯，侈然以名士自居，人有舉其所治經大義以問，而尚不能默數其章句者，況能悉意義之精微乎？元如之所以不可及也。且今日之患，學士大夫以通經學古為迂，而好馳騖於詞章聲華，以鳴得意。即學易者不泥於數，則拘於理，未有得於意，言象數之外者。夫儒者不能傳其易，而使傳易者乃在一肓廢之人，是尤可悲也。

Alas, among our generation, some have attained high official positions and thus swagger about as scholars; when others ask them questions based on the fundamental principles of the classics, they cannot even recite the chapters, let alone grasp their subtle meanings. This is precisely where Yuan Ru surpasses others. The current problem is that scholars and officials regard studying the classics and ancient texts as old-fashioned, yet they are eager to chase literary style and fame to show off. Even those who study the Book of Changes do not go beyond examining its images and numbers, or get stuck in its meanings, and none can truly grasp its intent and express something beyond the images and numbers. Scholars themselves are unable to transmit the Book of Changes, yet they turn to a blind disabled person to do so, which is even more pitiful.

已書將成，旅堂與元如相繼殂謝，人以為奧義密理，不能為天地秘藏，或其洩機已甚。余謂學易寡過，思慮所及，通於鬼神，未聞天道禁人之覺酣於義理也。書將成而溘然長逝，亦朝聞夕可之義也哉，不然元如之終也，語不及私，拳拳以此書為念，豈好名哉？其平日心力之所至，竊恐後世不得其傳，故不自為慮，而為人慮也。然則元如諄切屬餘之意於是乎，慰矣。康熙三年仲秋楚江安史氏王澤弘撰。

When the book was about to be completed, both Lu Tang and Yuan Ru died consecutively. Some people thought this was because the profound and intricate principles in the book were not meant to be concealed by heaven and earth, perhaps revealing too much heavenly secrets. However, I believe that studying the Yi Jing is to reduce mistakes, and thoughts that reach the extent of thinking about ghosts and spirits are not forbidden by the heavenly way. The sudden death of the book's completion coincides with Confucius' saying, "If one hears the Way in the morning, he may die in the evening." Otherwise, when Yuan Ru was dying, he did not mention anything about personal matters, but kept thinking about this book. Could it be for the sake of reputation? He was afraid that his lifelong efforts would not be passed down to future generations, so he did not think of himself but of others. In this way, Yuan Ru's earnest request for me to write an introduction can be comforted. In the autumn of the third year of Kangxi (1664 AD), written by Wang Zehong of Chu Jiang An Shi.

嘗閱史至管公明善易者，不論易之說，謂是答何鄧之邙訑言耳，今觀程子著書而始信。夫程子垂簾虎林市上，辨吉凶論悔吝無非易也，而易冒一書，則不盡論易，無非易者理從易出，易之外無理。不盡論易者，易從數顯，數之用非易，然則何云易冒哉？悉是書者，可以善易，書蓋為易而說也。

I once read historical texts about Guan Lu (whose name was Gongming), who was skilled in the Yi Jing but did not discuss its interpretations directly. People said that his answers to He Yan and Deng Yang were merely extravagant words. But now, after reading Cheng Yuanru's writings, I believe Guan Lu was indeed such a person. Mr. Cheng set up his shop in Hangzhou (Hulín), hanging a curtain and offering consultations on auspicious and inauspicious signs, as well as on regret and hardship, and none of these were unrelated to the Yi Jing. However, the book "Yi Mai" is not entirely about the Yi Jing: it says that everything in it is derived from the Yi Jing, because its principles come from the Yi Jing and there are no other principles outside of it; yet it is not entirely about the Yi Jing, because the Yi Jing needs "numbers" to be revealed, and the use of numbers is not the same as the Yi Jing itself. So why is the book called "Yi Mai"? If one thoroughly understands this book, one will be good at using the Yi Jing. This shows that the book was originally written for the Yi Jing.

若夫生生之謂，易通變無方，而引伸觸類以窮神達化。聖人原不使人枯槁於彖辭爻象間，而遂謂之易也，故繫辭曰：冒，天下之道，冒，覆也。天覆乎上，而七曜五行春秋寒暑人物化育散見於中，皆不謂之天，而莫非天之事。易統其綱，而甲子六神變互反伏與諸星世應九十一之旨，皆未始耑言易，而莫非易之事。是程子之書不論易，而精於言易者也。

What is meant by "the continuous generation is called the Book of Changes" is that the Book of Changes has no fixed form or place, and one must rely on extension and inference, and by analogy, to fully grasp its profound mysteries and understand the workings of nature. The sages did not intend for people to be confined dryly within the interpretations of the hexagrams and the lines, so they called it the Book of Changes. Therefore, the Great Treatise says, "The Book of Changes encompasses all the principles of the world," where "encompass" means to cover. Heaven is above, and the sun, moon, five stars (seven luminaries), the Five Phases, the seasons, cold and heat, and the transformation of all beings are spread beneath Heaven. These are not called "Heaven," yet none of them is not an affair of Heaven. The Book of Changes governs these in general. The themes discussed in these ninety-one chapters, namely "Jiazi," "Six Spirits," "change and mutual transformation," "reversal and concealment," "various stars," and "World and Response Lines," do not specifically discuss the Book of Changes, yet none of them is not an affair of the Book of Changes. Therefore, it is said that Mr. Cheng's book does not explicitly discuss the Book of Changes on the surface, but it is most skillful in explaining the Book of Changes.

今人不察，每得焦氏諸人之書，秘諸帳中，遂謂道在是矣，烏知此中奧衍有若是哉。程子為當今管郭，有勿占，占則應，如鄉戶外趾相錯，日既昳，有不及叩而返者，如是二十餘年以為嘗。至四十時抱痾鍵戶，忽忽機動於中，遂得數見兆，因而發憤著書，窮極要妙，自謂能補前聖之所未備，極深研幾，蓋三年而書始成。書成，程子即謝世去。

Nowadays people do not distinguish carefully; once they obtain the books of Jiao Yanshou's "Yi Lin," they secretly keep them in their tents, believing that all the Dao is contained within them. But they do not realize how profound and extensive the study of the Yi is. Mr. Cheng is today's Guan Lu and Guo Pu: he does not divinate unless he must, and once he does, it surely comes true. Those seeking divination crowd his gate, their toes touching each other. By the time the sun sets, some are still unable to knock on the door and have to return. This has continued for more than twenty years, becoming routine. At the age of forty, he fell ill and closed his door, but suddenly felt a stirring in his heart, thus being able to foresee signs in advance. He became determined to write a book, thoroughly exploring its essential principles, believing he could supplement what the sages of previous generations had not completed. He delved deeply into the most subtle aspects, spending three years writing the book. As soon as the book was completed, Mr. Cheng passed away.

然則占墨視拆，程子雖欲秘之，有所不能秘。昔郭參軍有青囊書九卷，門人趙載竊去，未及讀而火焚之。似乎獨得之秘，為造物所忌，程子不死於未著書之前，適死於方成書之日，苟非天以此道絕續之，會令程子繼往哲，開來學，惡觀其有傳書乎？餘友文翎高子於程最稱服膺，餘因得盡讀其所著書，且以嘆程子之善易，而又天縱之以論易也，則視易冒一編，雖謂程子未嘗死亦可矣。康熙甲辰秋七月既望錢塘且巷顧豹文撰。

Thus, it seems that skills such as "Zhan Mo" and "Shi Che," which are methods of divination and interpreting omens, are difficult for Master Cheng to keep secret. In the past, Guo Pu of the Jin dynasty, who once served as a military advisor, wrote a book called "Qing Nang Shu" in nine volumes. His disciple Zhao Zai stole it, but before he could read it, it was burned. It seems that secret knowledge is destined to be despised by the forces of nature. Master Cheng died not before he had written his books, but precisely on the day when his writings were completed; if it were not for heaven's will to allow this discipline to be interrupted and then revived, enabling Master Cheng to continue the legacy of past sages and to open the way for future scholars, how could his writings have been passed down? My friend Gao Wenling most admires Master Cheng, so I have been able to read all his writings, and thus I feel that Master Cheng was not only skilled in using the Book of Changes, but was also specially chosen by heaven to explain the Book of Changes. In this view, the section "Yi Mao" of his work implies that Master Cheng did not die, and perhaps did not even die. On the sixteenth day of the seventh lunar month in the autumn of the year Jiachen (1664 AD), Gu Bo wen from Qiantang wrote this.

餘總角時聞新安有元如程先生者善卜，隱居吾杭城西今，車馬闐駢如市，日既晡，不得下簾休息。餘友旅堂鬍子亟稱其人，嘗從而竊窺之，其狀貌魁梧，言談若河注，心知其非日者卜筮之流矣。此元如徙郭外與餘比閭居，交益密，時時過從聞其緒論，雖老生宿儒不能及，私念京焦管郭精易數，有聲著述，元如以瞽目博洽若此，非夙有神解，何以至是？

I was still a young boy with my hair tied in a total angle when I first heard that there was a man named Cheng Yuanru in Xin'an who was skilled in divination. He lived in the western part of Hangzhou, and his house was always crowded with carriages and horses, like a market, and even at sunset he would not lower his curtain to rest. My friend Hu Lutang highly praised this man, and I once followed him to secretly visit. He had a robust appearance and spoke with the flow of a river, and I realized he was not an ordinary person who relied on divination for a living. Later, Yuanru moved to the outskirts of the city, becoming my neighbor, and our relationship became closer. I often visited him to listen to his opinions, and even the most experienced scholars could not match him. I thought to myself: Jing Fang, Jiao Yanshou, Guan Lu, and Guo Pu were all masters of the Yi and numbers, and they left behind writings for posterity. Yuanru, a blind man, had such profound knowledge. If he did not have innate wisdom, how could he achieve this?

餘攻舉子業，所習僅易書訓詁，每觀元如卜，其稱引繇詞與本義無殊旨，靡不奇中。人曰：元如精於數，秘而不洩，特廋其辭於常談耳。元如笑應曰：聖人窮理數，為理用，後賢極數理，以數彰，理數豈有二哉？考亭謂孔子以義理說易，是象數已明，不須要說，今人不知象數而妄言易理，亦復何當？

I am studying for the imperial examinations, and my learning is confined to the textual explanations of the Book of Changes. Every time I see Yuanru engage in divination, the oracle verses he cites are no different from the meaning conveyed in The Original Meaning of the Zhou Changes, yet they never fail to be accurate. Some people say that Yuanru is skilled in the numerical calculations of the Book of Changes, but keeps his secrets hidden, revealing only the key points through ordinary conversation. Yuanru laughed and replied: The sages explored the principles and the numerical patterns, so that the "numbers" could serve the "principles"; later scholars pushed the numerical patterns and principles to their extremes, so that the "principles" could be made evident through the "numbers." Are principles and numbers really two separate things? Zhu Xi (from the Kaiting school) said that Confucius used principles to explain the Book of Changes, because the numerical patterns were already clear and did not need to be mentioned again. Now, people who do not understand the numerical patterns yet talk about the principles of the Book of Changes, where can they possibly be accurate?

然人知理之示人者顯，數之告人者微，不知數之微者，其變有定，而理之顯者，其應無窮；吾幼遭廢疾，不獲探索聖人窮理之原，以極數之委，幸遇星元師及枯匏老人，深究聖賢書數而尋諸理，庶幾幽明，死生進退存亡之道，其亦可坐而照也。餘知元如殆得道之士，雖季主君平未必能過。

People only know that "li" gives clear revelations and "shu" conveys subtle messages, but they do not realize that the subtle "shu" has definite rules of change, while the clear "li" has infinite responses. When I was young, I suffered from a disability and could not explore the original principles of the sages in understanding "li" or thoroughly investigate the intricate aspects of "xiang" and "shu". Fortunately, I met the Star Origin Master and the Elder of the Dried Gourd, who deeply studied the "xiang" and "shu" in the writings of sages and then returned to seek the meaning of "li". In this way, perhaps the principles of the interplay between the subtle and the manifest, and the transitions of life and death, can all be understood clearly while sitting still. From this, I realized that Yuanru is probably a sage, and even the Han dynasty figures Sima Jizhu and Yan Junping might not have surpassed him.

辛丑夏元如夢青衣吏二人，以樶召之去，元如曰：去無難，第卜筮之道，沿習糟粕，而未窮其奧，餘得師傳，欲立言以問世，操是心幾二十年，而卒未就，奈何？吏人曰：吾為君請之，足了君事。比覺，遂發憤著書，越三年而書成，屬旅堂點次，點次甫定而旅堂逝，以其書授之梓，梓成而元如亦逝。

In the Xinchou year (1661), during the summer, Yuan Ru had a dream in which two officials dressed in green held a warrant to take him away. Yuan Ru said: It is not difficult to go with you, but the study of divination is followed by people as mere superficialities, and no one has yet explored its profound meaning. I have received the teachings of a master, and I wish to write a book to make it known to the world. This thought has been in my mind for nearly twenty years, yet I have never completed it. What should I do? The officials said: I will ask for an extension for you, giving you enough time to finish your work. After he woke up, he became determined to write his book. Three years later, the book was completed, and he entrusted it to Hu Lutang for proofreading and editing. Just as Lutang had finished proofreading, he died. Then the book was sent for printing, and as the printing was completed, Yuan Ru also died.

嗚呼，立言傳世，其功在人，元如抱斯志垂二十年，蓋成之，若斯之難也。朝聞夕死，不可謂非天為之，其書傳，其人不死矣？餘因是益嘆數之有定，而聖人作易以前民用者，不可誣也。若元如者，其為得道之士，而非日者卜筮之流，讀易冒者，自有會心知，非餘一人交深而私許之矣。康熙甲辰仲秋西冷陸進藎思父拜撰。

Alas, to write and transmit knowledge to future generations is a meritorious act that benefits people; Yuanru had held this aspiration for nearly twenty years before completing it, showing how difficult it is. The saying "If one hears the Way in the morning, he may die in the evening" cannot be said not to be heaven's arrangement; once the book is passed down, the person is not really dead. Therefore, I am even more moved by the idea that "numbers" have fixed rules, and that the sage composed the Book of Changes to guide the people in their daily lives; this cannot be falsely attributed. A person like Yuanru is a one who has attained the Way, not merely a common practitioner of divination. Those who read "Yi Mao" will understand it intuitively, and it is not just I, because of our close friendship, who privately praise him. In the mid-autumn of the Jiachen year of the Kangxi era (1664 AD), West Ling Lu Jin, style name Jinsi, composed this.

予世家新安之蟾谿，父映源公，業賈吳興；母謝氏，生予多蹇，五歲而瞽於痘，先君謂予母曰：是兒早慧，今得廢疾，不能受書學舉子業，莫若令習醫。遂授醫書，耳聽心受，手訓點畫，到十歲，予告父母曰：為醫之要在望聞問切，既不能望，術能神乎？乃棄而學卜，從日者家五六人，粗得其概。

My family has lived in Chanchi, Xianan for generations. My father, Yingyuan Gong, did business in Wuxing, and my mother was surnamed Xie. I was born with a difficult fate; at the age of five, I became blind in both eyes due to smallpox. My father once told my mother: "This child was intelligent from a young age, but now he has become disabled and cannot study for the imperial examinations. It would be better for him to learn medicine." So he taught me medical texts. I learned by listening with my ears, memorizing with my mind, and having someone guide my hand in writing. At the age of ten, I told my parents: "The essentials of medicine are 'observation, listening and inquiry, and palpation.' Since I cannot 'observe,' how can my medical skills be excellent?" Therefore, I gave up medicine and turned to divination. I studied under five or six diviners in succession, gaining a general understanding.

最後從星元先師遊，獨盡其傳，朝夕問訊，記憶控討，相隨五載，猶若茫然。乃漸遷心音律奕棋之戲，將墮厥，業師戒予曰：夫學易之道，專則純，純則業，精乃入神，分則雜亂，雜亂則疏，疏乃不入；今汝學，分而不專，其能達耶？

Finally, I followed Master Xingyuan on his travels for study, and received his entire teachings. I asked questions day and night, relying on memory to explore and discuss, accompanying him for five years, yet my mind remained still confused. Thus, I gradually shifted my focus to things like music and chess, and my studies seemed on the verge of being neglected. Master warned me: the way of studying the Book of Changes lies in concentration, for concentration leads to purity, and purity allows one to complete their studies; mastery leads to the divine and subtle. But if one's mind is scattered, it becomes chaotic, and chaos leads to superficiality, and superficiality prevents one from entering the gate. Now, you study with a scattered mind and not with concentration—how can you attain understanding?

於是益發憤研求，屏絕外嗜，竭思廢寢，以為天下之事億兆紛紜，何以得一理貫通其吉凶，而後不惑？年登十八，始悟用爻是此是彼，隨大隨細，惟一用爻而求，諸吉凶乃得其柄。如所謂老奴占幼主，必用父母，少君占衰僕，必用妻財，此以分不以年也；詞訟憑官而後世應，以勝負決於聽訟也；壽命憑用而後父母，以其享年也；科目先文而後官，廷試先官而後文，各有所重。由此引申，則左之右之，無不宜之矣。

So I became even more determined to study diligently, cutting off all other indulgences, exhausting my mind and body, neglecting sleep and food. I thought to myself: the affairs of the world are countless and complex; how can one find a single principle that connects all good and bad fortune, so that one would no longer be confused? At the age of eighteen, I finally realized that the "used line" (用爻) is determined by the matter being divined: one may take this line or that line, regardless of whether the matter is big or small. One should focus solely on this "used line" to seek the outcome, and thus all good and bad fortune can be understood. For example, if an old servant divines about his young master, he must use the "parents" line; if a young master divines about his old servant, he must use the "wealth" line. This is taking according to status, not age. When divining about lawsuits, one first looks at the "official ghost" (官鬼) line and then at the "world and response" (世应) lines, because the outcome depends on the court's judgment. When divining about lifespan, one first looks at the "used god" (用神) and then at the "parents" line, because the parents' lifespan determines the master's. For imperial examinations, one first looks at the "parents" line (representing documents) and then at the "official" line; for the palace examination, one first looks at the "official" line and then at the "parents" line. Each has its own emphasis. By applying this principle, one can navigate all situations without difficulty.

於是集舊聞，秉師說，本以心得，參以占驗，纂述成書，為筮類五十篇，而內詳三百七十有七問；復考聖人立法之所由，參研三載未得。己卯之冬，偶遇楚來枯匏老人，聚首三月，請益焉，乃曰：聖人不妄立法以教人，皆必有本，而具陳於百家之書，汝未能遍考，我一一授之子，子其秘之。

Therefore, I collected my past observations and experiences, followed my teacher's teachings, based on my own insights, and referred to actual divination practices to compile this book, dividing it into fifty chapters under the category of "Divination." Among them, three hundred seventy-seven questions are detailed. Later, I wanted to investigate the origin of the laws established by the sages, but after three years of study, I could not obtain the answer. In the winter of the Ji Mao year (1639 AD), I偶然 met an old man named Ku Paogao who came from the Chu region. We stayed together for three months and I asked him questions. He said: The sages do not arbitrarily establish laws to teach people. Each law must have its origin, and they are all stated in the writings of the various schools of thought. It is just that you have not thoroughly examined them. I will now explain them one by one to you, and you must keep them secret.

予曰：聖人立法，將以開後世之蒙，受而復秘，獨得之亦何益耶？枯匏曰：是心可以為人師矣！前言探子爾；立言傳世，功孰大焉。於是復究先賢闡易之書數十種，立法四十一篇，計九十一章，卷分有十，列成卦成爻之由，立世立應之法，諸星何事而名，六神何事而司；隨墓助傷，本凶而有弗凶也，絕生本吉，而亦有弗吉也；空破絕散，有真偽之分，飛伏互變，有輕重之取，豈執一義而盡之與？

I said: The sages established principles in order to enlighten the ignorance of future generations; I have accepted them yet kept them secret, possessing them alone, what benefit is there? The withered gourd elder said: With such intentions, one can become a teacher of people! That previous statement was merely a test; to write books and pass them on to future generations, what greater merit is there than this? Thus I again studied dozens of books by previous sages explaining the principles of the Book of Changes, establishing forty-one principles, totaling ninety-one chapters, divided into ten volumes: listing the origins of forming hexagrams and lines, establishing the methods of 'world' and 'response', explaining why the 'various stars' are named as such, and what each of the 'Six Spirits' is responsible for; 'following the grave' and 'assisting injury' originally indicate misfortune, yet there are times when they do not; 'desperation meeting salvation' originally indicates good fortune, yet there are times when it does not; 'empty, broken, cut off, scattered' have true and false distinctions, 'flying and hidden' and 'interchangeable transformation' have light and heavy considerations—can one fully explain everything by rigidly adhering to a single principle?

故黃金策言用化用則有用無用，其云化去是神忒也，伏吟之故爾，若化進神，安得無用乎？復曰太過者損之斯成，非雲吉凶，斷事之成合時也。若曰用爻太過為不吉，則生扶拱合之語非矣。卜易闡幽雲伏藏不論旬空，可以言輕重，豈言不空耶？亦長於彼而短於此也。卜筮元龜晴雨以世為地，應為天，京房以父母為天地，亦是於此而非於彼也。

Therefore, the "Golden Strategies" says, "When the useful god transforms into another useful god, some are useful and some are not." What it refers to as "transformation" is actually the loss of divine power, caused by "hidden chant." If the transformed god is an "advancing god," how could it be useless? It also says, "Excess must be reduced to achieve success," which is not about discussing fortune or misfortune, but rather about the completion of divination depending on the right timing. If a useful line is considered inauspicious simply because it is excessive, then the concepts of "birth, support, mutual assistance, and union" would not make sense. The "Explaining the Hidden Mysteries of Divination" says, "Hidden gods are not considered empty in the context of a旬空," which can only be interpreted as differences in emphasis; could it really mean that hidden gods are not considered empty? This is also a strength in one area and a weakness in another. The "Original Oracle of Divination" uses the "world" line for earth and the "response" line for heaven, while Jing Fang uses the "parents" line as heaven and earth. Similarly, they are correct in one place and incorrect in another.

補遺飛伏其七世皆伏本宮，而京房獨以游魂飛伏不相侔合，如晉外伏艮而內伏乾，己酉世爻以丙戌為飛伏；如需外伏兌而內伏坤，戊申世爻以丁亥為飛伏，占之屢驗。然先師成書時，未得此學也。即搜決鬼神多載，湖下之聖，六合之內，有土風名俗之相異，百世而下再成之神，但能以義理相揆，豈可實指其姓字乎？先師每謂予曰：生平之學，補遺缺是二端甚矣，著書之難也。

The Complete Book of Divination, Supplemental Section, discusses flying and hidden lines, stating that within one palace there are seven hexagram positions, each concealing the line of the same palace. Only Jing Fang disagreed with this view regarding the flying and hidden lines of the wandering soul hexagram. For example, in the hexagram Jin, the outer trigram conceals Gen and the inner trigram conceals Qian, with Jiyou as the world line and Bingxu as the flying and hidden line. In the hexagram Xu, the outer trigram conceals Dui and the inner trigram conceals Kun, with Wushen as the world line and Dinghai as the flying and hidden line. Using this method for divination has repeatedly proven accurate. However, when my predecessors wrote their books, they had not yet encountered this discipline. Another example is divining about ghosts and deities. I have sought and judged for many years: the deities worshipped in the countryside and among the people, throughout the world, have different local names and titles, and new deities are constantly established over generations. We can only infer based on principles, how can we specify their names? My master often told me: the difficulty of my entire life's study lies in filling gaps and raising doubts—writing a book is truly very difficult.

予荒陋管窺，敢言能備與惟所知者載之，不知者以待高賢之教我也。予常終日凝思，久而不悟，春秋相繼而未得。逍遙子謂予曰：致虛守靜，以觀其復，靈明生焉。密雲禪師謂予曰：但會取本有。吾於二師有默契，雲古之人有以風占鳥占諺占，言語卜威儀卜政事卜是無卜，筮而知吉凶也，況著草金錢木丸之占，而必執同異相非乎？愚以為易者，象也，象也者，像也，其辭則異，其象則符，但告於著則以著占，告於五行則以五行占，告於焦氏則以焦氏占可也，其成卦成爻一也。

I have limited knowledge and my understanding is like seeing a leopard through a tube; how dare I claim to be complete? I merely record what I know and leave the unknown for those more enlightened to teach me. I often spend whole days in deep thought, unable to gain insight, and year after year I have made no progress. Xiao Yaozi told me: "Achieve utmost emptiness and hold fast to profound stillness, and observe the return of all things." Then clarity will naturally arise. Mingyun Chan master told me: "Just grasp what is originally present." I have a deep resonance with the words of these two teachers. To know that ancients used wind divination, bird divination, and proverb divination, and also divined through speech, demeanor, and political affairs, without using yarrow stalks, yet could discern good and bad fortune; how much more so should we not be attached to differences or criticize one another when using yarrow stalks, coins, or wooden balls for divination? I believe: "Yi" is "Xiang," and "Xiang" is "Xiang." Although the words differ, the hexagrams correspond to each other. If the divine signs appear on yarrow stalks, use yarrow divination; if they appear on the Five Phases, use Five Phases divination; if they appear on Jiao Yanshou's "Yi Lin," use Jiao's method of divination. All of them have the same principles for forming hexagrams and lines.

久思著書問世，以造門之問，日晐不遑。年四十而疽發於背，始得杜門謝客，而草創之，歷三年之久而撰藁粗成，就正於故人旅堂先生，先生與其同學見而亟稱之，乃下榻草堂，重加刪定為梓以行世。嗟乎，苟有小補於世，則安敢逃於妄述之罪哉。康熙甲辰歲仲夏朔旦新安瞽目程良玉敘。

I have long wanted to write a book and make it known to the world, but because so many people came to me for divination, I was constantly busy with their requests and had no time to spare. At the age of forty, I developed a malignant abscess on my back, which allowed me to close my door, refuse visitors, and begin drafting the work. It took me three years to complete the draft. I took it to my old friend Cheng Liangyu for his comments. He and his classmates praised it highly, and they stayed in my thatched cottage to revise and finalize it, then sent it to the printer for publication. Alas, as long as my work can benefit the world a little, how could I dare to avoid it out of fear of being accused of "fabrication"? Written on the first day of the sixth month in the year Jiachen of the Kangxi era (1664), by Cheng Liangyu, a blind man from Xin'an.

天干有十，地支有十二。（幹猶本也，象天生物，故曰天干；支猶枝也，象地成物，故曰地支。干有十：甲乙丙丁戊己庚辛壬癸；支有十二：子丑寅卯辰巳午未申酉戌亥。）用甲乘子，取乙駕丑，干支終始而循環，天地之數六十而盡矣。（甲子之法，以天干順佈於地支之上，始自甲子至癸酉，幹終而始甲戌，支終而始丙子，若枝本之不離，並盡於癸亥，計有六十也。）

There are ten heavenly stems and twelve earthly branches. (Note: "Stems" are like the trunk of a tree, symbolizing the heavens' ability to generate things, hence called "heavenly stems"; "branches" are like the branches of a tree, symbolizing the earth's ability to form things, hence called "earthly branches." The ten heavenly stems are Jia, Yi, Bing, Ding, Wu, Ji, Geng, Xin, Ren, and Gui; the twelve earthly branches are Zi, Chou, Yin, Mao, Chen, Si, Wu, Wei, Shen, You, Xu, and Hai.) Using Jia with Zi, Yi with Chou, the stems and branches cycle continuously, connecting head to tail. The numbers of heaven and earth are exhausted after sixty combinations. (Note: The method of arranging Jiazi involves placing the heavenly stems sequentially over the earthly branches: from Jiazi to Guiyou, the ten stems are used up and then start again from Jiaxu; when the twelve branches are used up, they start again from Bingzi—the heavenly stems and earthly branches are like the trunk and branches of a tree, inseparable, and finally end together at Guihai, making a total of sixty combinations.)

天分五運，地分六氣，以造化萬物於其中，乃作甲子以記歲時，使日月四時之有經也。（五運謂東南西北中，十干動運乎上；六氣，謂十二支六陰六陽之氣，司寒暑春秋升消長之權，靜成乎下，而吉凶禍福，由是以兆。）自漢武從寅，則無復四同之甲子，迨婁景補韻，則始傳分象之五行。（周正建子，則以甲子年起甲子月，甲子日起甲子時；夏正建寅，漢武帝述之，退三位而取丙寅，所以無復有四甲子也。古納音但有甲子乙丑屬金，丙寅丁卯屬火之法，及婁景先生推五行之理作歌，始有海中金爐中火之說。）

Heaven is divided into the Five Movements, and Earth into the Six Qi. All things are generated and transformed within them. Thus, sages created the Jiazi (甲子) to record years, months, days, and hours, giving the movement of the sun and moon and the succession of the four seasons a regular pattern. (Note: The Five Movements refer to the five directions—east, south, west, north, and center—with the ten heavenly stems continuously moving above. The Six Qi refer to the six yin and six yang energies of the twelve earthly branches, which govern the cold and heat of the seasons, spring and autumn, and the rising and falling, growth and decline of things. These energies operate below quietly to form all things, and thus omens of good fortune, misfortune, calamity, and blessing are revealed.) Since Emperor Wu of the Han dynasty adopted the Xia calendar with the rat (子) month as the beginning of the year, there have been no instances where the year, month, day, and hour all coincide with Jiazi. It was not until the Lousheng (娄景) Master composed rhymed verses that the system of the Five Phases (五行) associated with the Nayin (纳音) elements began to spread. (Note: The Zhou calendar took the rat (子) month as the beginning of the year, so the Jiazi year started with the Jiazi month, and the Jiazi day started with the Jiazi hour. The Xia calendar took the tiger (寅) month as the beginning of the year. Emperor Wu adopted it and moved the month builder back by three positions to take the Bingyin (丙寅) as the starting point, so there were no cases where all four pillars (year, month, day, hour) were Jiazi. In ancient times, the Nayin only had statements such as 'Jiazi and Yichou belong to metal, Bingyin and Dingmao belong to fire.' It was not until the Lousheng Master studied the principles of the Five Phases and composed rhymes that names like 'Sea of Metal' and 'Furnace of Fire' appeared.)

納音之法，以干支之數，合大衍之用四十有九，去其本數復考其零，以五行相生而納諸屬也。（納音所屬之法，大衍之數五十，其用四十有九，考其干支所屬之數幾何，於四十九數內，去其干支本數，而所零者以五除之，其餘復以水一、火二、木三、金四、土五，數至四十有九，得水則納音是木，得土則納音是金也。）

The method of determining the Nayin sound element involves taking the fixed numbers of each Heavenly Stem and Earthly Branch, combining them with the number used in the Great Derivation, which is forty-nine. Subtract the number of the specific Heavenly Stem and Earthly Branch from forty-nine, then examine the remaining number. Divide this remainder by five and match the remainder with the Five Phases according to the order "water one, fire two, wood three, metal four, earth five," continuing until the total reaches forty-nine. If the result is water, the Nayin belongs to wood; if the result is earth, the Nayin belongs to metal—always following the principle of mutual generation among the Five Phases.

（法曰，六旬甲子妙尤元，七七中除地與天，五減零求生數立，納音得此幾人傳。夫干支之數，謂甲己子午九、乙庚丑未八、丙辛寅申七、丁壬卯酉六、戊癸辰戌五、巳亥四為則，此干支定數也，以萬物闢子而合申，故甲己子午，自子至申得九，乙庚丑未，自丑至申得八，如甲乃九數，子亦九數，乙乃八數，丑亦八數，計三十有國，於四十九內除之，其餘十五，復減其十，所零五數，五為土，土生金是也，餘仿此。）

The mnemonic says: "The sixty Jiazi cycles are profound and fundamental, subtract seven times from the heavens and earth, reduce five to find the number of life, and the Nayin sound element is passed on to a few." The numbers of the heavenly stems and earthly branches are as follows: Jia and Ji, Zi and Wu are nine; Yi and Geng, Chou and Wei are eight; Bing and Xin, Yin and Shen are seven; Ding and Ren, Mao and You are six; Wu and Gui, Chen and Xu are five; Si and Hai are four. This is the fixed number of the heavenly stems and earthly branches. The origin of these numbers is that all things begin with Zi and converge at Shen. Therefore, Jia and Ji, Zi and Wu start from Zi and count to Shen, resulting in nine; Yi and Geng, Chou and Wei start from Chou and count to Shen, resulting in eight. For example, Jia is nine, Zi is nine, Yi is eight, Chou is eight, totaling thirty-four (the original text says "thirty and guo," where "guo" is likely a mistake for "four"). Subtract this from forty-nine, leaving fifteen; then subtract ten, leaving five. Five belongs to earth, and earth produces metal, so the Nayin sound element of Jiazi and Yichou is metal. The rest follow the same pattern.

復引申其用，渾甲同此而作，三式由此而成。（渾甲，以六十甲子納八卦之下也，三式，謂太乙統宗，天之數也，奇門遁甲，地之數也，大六壬神，人之數也。）幹乃天，虛而無形，故不專禍福，支乃地，實而有象，則有旺衰生死進退消長破沖刑害，以曲成萬物之能。（天無形，故干神之用，專於五化，謂甲己化土，乙庚化金之類；地有象，則成能萬物，吉凶以昭，故支神之用，有當生者旺，所生者相，四生四死，進神退神，升降消長，三刑六害之類。）

Further extending its application, the method of "Hun Jia" is based on this principle, and the "Three Systems" are formed from it. (Note: "Hun Jia" refers to the arrangement of the sixty Jiazi within the Eight Trigrams. The "Three Systems" refer to "Taiyi Tongzong," which deals with the numbers of Heaven; "Qimen Dunjia," which deals with the numbers of Earth; and "Daliu Ren Shenke," which deals with the numbers of Humanity.) The Heavenly Stems belong to Heaven, being empty and without form, so they do not solely determine fortune or misfortune. The Earthly Branches belong to Earth, being substantial and having form, thus they have changes such as prosperity and decline, birth and death, advancement and retreat, increase and decrease, as well as destruction, conflict, punishment, and harm, which are used to fully explain the abilities of all things. (Note: Heaven has no form, so the function of the Heavenly Stems is mainly "Five Harmonies," such as Jia and Ji harmonizing into Earth, Yi and Geng harmonizing into Metal, etc. Earth has form and can create all things and indicate auspiciousness and inauspiciousness, so the function of the Earthly Branches includes: those in season are "Prosperous," those that I generate are "Prosperous," there are four places of birth and four places of death, there are "Advancing Gods" and "Retreating Gods," there is rising and falling, increase and decrease, as well as the Three Punishments and Six Harmful Relationships.)

是以位之四方，納之八卦，立星煞之神，生生不已，新新不停，咸備五行之用，通書所謂三大三小，諺語所謂無水無金、上古天皇地皇人皇，皆資是始，萬化之用，豈能外此哉。（以干支列於四方，謂壬子癸、丑艮寅、甲卯乙、辰巽巳、丙午丁、未坤申、庚酉辛、戌乾亥是也；以干支納於八卦之下，義見後篇。立吉星凶煞之神，吉凶咸備。他如通書所謂六甲下納大金小金大火小火大水小水之法，諺語謂甲子甲午旬中全無水，甲申甲寅旬中不見金之說，即上古天王君起甲子，地王君起甲申，人王君起甲寅，莫不造端於此，故曰甲子不立，則五行不神，五行不神，則吉凶不著矣，是以著易，必首明甲子。）

Therefore, the heavenly stems and earthly branches are arranged in the four directions, and assigned to the eight trigrams, thereby establishing various auspicious stars and malevolent influences. This process is continuous and ever-renewing, encompassing all the functions of the Five Phases. For example, the "three greats and three smalls" mentioned in the Tongshu, the saying "without water and without metal," and the dating systems of the ancient heavenly emperor, earthly emperor, and human emperor all originate from this. How could the operations of heaven and earth and all transformations be separated from it? (Note: Arranging the heavenly stems and earthly branches in the four directions refers to the sequence: Renzi, Kui, Chou, Genyin, Jia, Maoyi, Chen, Xunsi, Bingwu, Ding, Wei, Kunsen, Gengyou, Xin, Xu, Qianhai. Assigning the heavenly stems and earthly branches to the eight trigrams is explained in the following "Najia Chapter." Establishing auspicious and malevolent influences completes the distinction between good and bad. Other examples include the method in the Tongshu of assigning "great gold, small gold, great fire, small fire, great water, small water" under the six jia, the saying that in the two decades of Jiazi and Jiawu there is no water, and in the two decades of Jiashen and Jiayin there is no metal. Also, the ancient heavenly emperor began his reign in Jiazi, the earthly emperor in Jiashen, and the human emperor in Jiayin—all originating from this. Therefore, without Jiazi, the Five Phases would not be effective; without effective Five Phases, good and bad would not be clear. Hence, the book of Changes must first explain Jiazi.)

以錢代蓍，但求奇偶。（上古以蓍揲而成爻，後因揲蓍之煩，故以錢代蓍，不必分二掛一，揲四歸奇，但求奇偶，所謂舍四營而減為一擲者也。）奇者陽也，像天之覆，偶者陰也，像地之載，觀覆載而奇偶得矣。（錢分奇偶，以形測之，錢覆者如天之覆懸於上，故屬陽而為奇，錢仰者如地之仰載於下，故屬陰而為偶。）

Using copper coins instead of the yarrow stalks, one simply determines whether the result is odd or even. (Note: In ancient times, the yarrow stalks were used to divide and count the lines, but later, due to the complexity of the process, copper coins were used instead. There was no need for the steps of "dividing into two, hanging one, dividing four, and returning the remainder," and instead, only the determination of odd or even was required. This is called simplifying the four operations into a single toss.) Odd represents yang, symbolizing the heavens covering above; even represents yin, symbolizing the earth bearing below. By observing the covering and the bearing, the odd and even are determined. (Note: The determination of odd or even with copper coins is based on their shape: when the back side is up (covering), it resembles the heavens covering above, thus belonging to yang and being odd; when the side with characters is up (upward), it resembles the earth bearing below, thus belonging to yin and being even.)

得‥奇則曰單，謂之少陽，得－偶則曰拆，謂之少陰，三覆曰重，謂之老陽，三仰曰交，謂之老陰，重乃三奇，交乃三偶，陰陽老少既成，而八卦由此生也。（奇圓圖三，偶方圖四，三用其全，四用其半，故得一奇二偶是七，而為少陽，得一偶二奇是八，而為少陰，三覆是三奇而為九，乃老陽也，三仰是三偶而為六，乃老陰也，九名重，六名交，七為單，八為拆。）

When one odd (marked as ``‥``) is obtained, it is called ``single`` and represents the young yang; when one even (marked as ``－``) is obtained, it is called ``split`` and represents the young yin; when all three coins are covered, it is called ``heavy`` and represents the old yang; when all three coins are upright, it is called ``crossing`` and represents the old yin. ``Heavy`` corresponds to three odds, and ``crossing`` corresponds to three evens. Once the old and young yin and yang are determined, the eight trigrams are thus generated. (Note: Odd numbers are associated with roundness, and the numerical value of a circle is three; even numbers are associated with squareness, and the numerical value of a square is four. For three, we take its full number three; for four, we take half of it, which is two. Therefore, one odd and two evens add up to three plus two plus two, totaling seven, which represents the young yang; one even and two odds add up to two plus three plus three, totaling eight, which represents the young yin; all three coins being covered, which is three odds, add up to nine, representing the old yang; all three coins being upright, which is three evens, add up to six, representing the old yin. Nine is called ``heavy``, six is called ``crossing``, seven is called ``single``, and eight is called ``split``.)

法云：向上言眉，向下言背，亦謂如乾坤之形耳。（法曰：兩背由來拆，雙眉本是單，渾眉交定位，總背是重看，謂乾形覆背在上，坤形仰眉在上是也。近俗有以笤辯陰陽者則異是，以竹中剖，其心向上為陽，向下為陰，錢以體成，其形覆為陽，仰為陰，各有取義也。）

In divination methods, "upward" refers to the eyebrows facing upward, and "downward" refers to the back facing upward. This refers to the images of the Qian and Kun trigrams. (Note: The mnemonic says, "Two backs have always been split, two eyebrows are originally single, the whole eyebrows intersect to determine position, the total back is viewed as double." This means: one eyebrow and two backs is "split," two eyebrows and one back is "single," three eyebrows all facing upward is "intersecting," and three backs all facing upward is "double." The form of Qian is the back covering the top, while the form of Kun is the eyebrows facing upward. Recently, some people in the folk use bamboo brushes to distinguish yin and yang, which is different: when the bamboo is split in the middle, the split surface facing upward is yang and facing downward is yin; for copper coins, the whole coin is considered, with the coin covering the top as yang and facing upward as yin—each method has its own meaning.)

既成三象，始有二老。（一畫而分陰陽，二畫而分太少，三畫而備三才，三才備而二老交，二老交而六子立矣。）純陽曰乾，純陰曰坤，剛柔交而得一陽曰震，乾坤蕩而得一陰曰巽，再磨而成坎，復媾而為離，三索奇偶而生艮兌，六子備而八卦立矣。（八卦從二老而生六子，三單純陽為乾父，三拆純陰為坤母，二老始交，陰獲陽為震，陽得陰為巽，再索之坤中爻獲陽為坎，乾中爻得陰為離，三索之坤上爻獲陰為艮，乾上爻得陰為兌，於是乾兌離震之順，巽坎艮坤之逆，首尾交接而成圓圈，先天八卦備矣。）

Once the trigrams of three lines are established, the two fundamental trigrams, Qian (Heaven) and Kun (Earth), are formed. (Note: When drawing one line, yin and yang are distinguished; when drawing two lines, the four types of yin and yang are differentiated: Taiyin, Taoyang, Xiaoyin, and Xiaoyang; when drawing three lines, the three elements of heaven, earth, and humanity are complete. When the three elements are complete, the two fundamental trigrams interact, and through their interaction, the six subsidiary trigrams, Zhen (Thunder), Xun (Wind), Kan (Water), Li (Fire), Gen (Mountain), and Dui (Lake), are established.) A trigram with all three lines yang is called Qian, and one with all three lines yin is called Kun. When yang and yin interact to produce one yang line, it is called Zhen; when Qian and Kun interact to produce one yin line, it is called Xun. Through further interaction, Kan is formed, and through further union, Li is formed. Through a third search for odd and even, Gen and Dui are produced. When all six subsidiary trigrams are complete, the eight trigrams are established. (Note: The eight trigrams arise from the interaction of Qian and Kun to produce the six subsidiary trigrams. A trigram with all three lines single and yang is called Qian, the father; a trigram with all three lines split and yin is called Kun, the mother. In the first interaction, Kun receives yang from Qian to form Zhen, and Qian receives yin from Kun to form Xun. In the second search, the middle line of Kun receives yang to form Kan, and the middle line of Qian receives yin to form Li. In the third search, the upper line of Kun receives yang to form Gen (the original text says 'obtain yin,' which should be 'obtain yang'), and the upper line of Qian receives yin to form Dui. Thus, Qian, Dui, Li, and Zhen proceed in order, while Xun, Kan, Gen, and Kun proceed in reverse order, connecting head and tail to form a circle, completing the Earlier Heaven Trigrams.)

因而重之，坤始震而至純乾，左旋之三十二象也，乾配巽而至純坤，右轉之三十二象也，是故聖人以象義而名卦，以變次而成章焉。（八卦之上，重加八卦，以坤獲一陽之初，而坤加於震，從此始左逆行，以坤艮坎巽震離兌乾配於震上，次而離，次而兌，次而乾，此左旋三十二卦也；以乾得一陰之初，而乾加於巽，從此始右順行，以乾兌離震巽坎艮坤配於巽上，次而坎，次而艮，次而坤，此右轉三十二卦也。）

The eight trigrams are combined two by two to form the sixty-four hexagrams. Starting from Zhen, which is formed by adding one yang line to Kūn, and proceeding through all the hexagrams up to Qian, which is entirely yang, this sequence represents the left rotation of thirty-two hexagrams. Starting from Xun, which is formed by adding one yin line to Qian, and proceeding through all the hexagrams up to Kūn, which is entirely yin, this sequence represents the right rotation of thirty-two hexagrams. Therefore, the sages named the hexagrams according to their images and meanings, and arranged them in order according to the sequence of change. (Note: On top of the eight trigrams, another set of eight trigrams is superimposed. Since Zhen is formed by adding one yang line to Kūn, Kūn is placed above Zhen, and from then on, the sequence proceeds in a leftward direction, pairing Kūn, Gen, Kan, Xun, Zhen, Li, Dui, and Qian successively above Zhen; after completing the Zhen group, the Li group is arranged, then the Dui group, then the Qian group, forming the left-rotating thirty-two hexagrams. Since Xun is formed by adding one yin line to Qian, Qian is placed above Xun, and from then on, the sequence proceeds in a rightward direction, pairing Qian, Dui, Li, Zhen, Xun, Kan, Gen, and Kūn successively above Xun; after completing the Xun group, the Kan group is arranged, then the Gen group, then the Kūn group, forming the right-rotating thirty-two hexagrams.)

（易卦次由十六變而成，謂乾一變姤，二變遁，三變否，四變觀，五變剝，上爻天也，故不變，而復下變四爻為晉，易章成有七焉，三變旅，遊入離宮，故聖人以火地晉為游魂，二變鼎，一變大有，不序他卦，還入本宮，易章始成八卦，故聖人以大有為歸魂也。蓋凡九變，萬物歸還，理數以極，自然之象，復二變為離，三變噬嗑，四變頤，五變益，復四變無妄，三變同人，二變仍乾，乃十六變也。後天八宮易章之成如此，此卦變非動爻變也。）

The order of the eight trigrams in the eight palaces is arranged according to the "sixteen transformations." Taking the Qian palace as an example: the first line of Qian transforms into Gou, the second into Dun, the third into Poi, the fourth into Guan, the fifth into Bo; the top line belongs to Heaven and remains unchanged, so it returns to transform the fourth line into Jin, completing seven trigrams in the first palace. If the third line is then transformed into Li, it moves into the Li palace, so the sage designated Fire Earth Jin as the "wandering soul" trigram. Afterwards, the second transformation becomes Ding, and the first becomes Da You, which does not enter other palaces but returns to its original palace, completing the eight trigrams of the first palace, so the sage designated Da You as the "returning soul" trigram. In total, there are nine transformations, and all things return to their original positions, the principles and numbers reach their ultimate, which is the natural image. Continuing on: the second transformation becomes Li, the third becomes Shi He, the fourth becomes Yi, the fifth becomes Yi; then transforming the fourth line becomes Wu Wang, transforming the third line becomes Tong Ren, and transforming the second line returns to Qian—combined, this makes sixteen transformations. The sequence of the eight palaces in the Later Heaven is thus arranged. Note that the "trigram transformation" mentioned here refers to the change in the order of the palaces, not the transformation of the moving lines when divining.

夫大衍之數，成一為奇，成二為偶，周奇而後周偶，四營為一，三扐為爻，老少乃得，然則經文卦序，不由象而由義也。（此言爻與卦殊也，如大衍之數，單奇雙偶，先有奇而後有偶，四營為一變，一變為一扐，三扐為一爻，始見老少皆從奇偶而成，若經之名卦序卦，皆以義起也。）

Now looking at the method of divination with the yarrow stalks: forming a single "one" is considered odd, forming a single "two" is considered even. First, all odd numbers are counted, then all even numbers. The "four operations" count as one change; three "tapping" actions make one line (yao). Thus, the old yang, old yin, young yang, and young yin are derived. From this perspective, the names and order of the hexagrams in the Classic of Changes are not based on the hexagram images, but on their meanings. (Note: This refers to the different ways in which the lines (yao) and the hexagrams (gua) are formed. For example, in the method of yarrow stalk divination, single units are odd, pairs are even; first odd numbers are counted, then even numbers. The "four operations" refer to dividing into two, hanging one, counting four, and returning the remainder, which counts as one change. One change produces one tapping, and three tapplings form one line. Thus, the four basic images (old yang, old yin, young yang, young yin) are derived from odd and even. As for the naming and ordering of the hexagrams in the Classic, these are based on their meanings.)

若一生二，二生四，四生八，八生十六，十六生易，此易之窮於象也。（象與義雖異而不相離，故一畫陰陽為二儀，則生二畫之四象，二畫老少為四象，則生三畫之八卦，八卦再重而十六，十六四重而成天地雷風水火山澤之易，則易之道，從象而終也。）

As for the process of one giving rise to two, two giving rise to four, four giving rise to eight, eight giving rise to sixteen, and sixteen giving rise to all the sixty-four hexagrams of the Book of Changes, this is the complete expression of the Book of Changes in terms of "xiang" (images). (Note: Although "xiang" and "yi" (meaning) are different, they are not separate. One line of yin and yang forms the "two yi" (two principles), the two principles give rise to two lines forming the "four xiang" (four images); the old and young of two lines form the four xiang, which in turn give rise to three lines forming the "eight trigrams"; the eight trigrams are then overlapped to form sixteen, and sixteen are overlapped four times to form the complete set of hexagrams representing heaven, earth, thunder, wind, water, fire, mountain, and marsh. This shows that the way of the Book of Changes concludes in terms of "xiang.")

一與九，二與八，三與七，四與六，五與十，此圖之終於數也。（此言單拆交重之數，盡於河圖中也。）蓋以數以象以義而成易，則數象義相乘，而吉凶出矣。（此言象不離數，義不離象，以成卦斷吉凶也。）

One and nine, two and eight, three and seven, four and six, five and ten are paired in pairs, which is the conclusion of the Yellow River Chart in terms of numbers. (Note: This refers to the numbers of the four categories of single, split, intersecting, and overlapping, all of which are contained within the Yellow River Chart.) In summary, the Book of Changes is achieved through numbers, images, and meaning. The three elements of number, image, and meaning interact and complement each other, and thus the fortune and misfortune become evident. (Note: This refers to the fact that images cannot be separated from numbers, and meaning cannot be separated from images; based on this, hexagrams are formed to judge fortune and misfortune.)