Comprehending Change in Yarrow Divination: Preface to the Book

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.