《易象圖說內篇》

This passage comes from the Inner Chapters on Diagrams of Yi Symbolism by Zhang Li of the Yuan dynasty, discussing the mysteries of the "Dragon Diagram" (i.e., the Hetu and Luoshu). It cites the views of the Song dynasty Daoist Chen Tuan (known as Master Xiyi) to explain the formation process of these cosmic diagrams.

Legend holds that during the era of Fuxi, a dragon-horse emerged from the Yellow River bearing a mystical pattern—this was the earliest "unintegrated numbers" version of the Dragon Diagram. At that time, the will of Heaven first revealed the design in a scattered form. Fuxi comprehended its profound principles through observation and synthesized its application, while Confucius later grasped its form through silent contemplation.

The original Dragon Diagram contained 55 numbers, divided into an upper section of 25 and a lower section of 30. The upper 25 represented heavenly numbers, encompassing the key digits 3, 5, and 9, with 15 numbers distributed around them. The lower 30 represented earthly numbers, arranged in five groups, each embodying the function of "five." These numbers later evolved into six configurations, symbolizing the manifestations of the earth.

When the numbers of Heaven and Earth merged, the heavenly number "1" (yi) occupied the upper position, representing the root of the Dao, while the earthly number "6" (liu) resided below, symbolizing the foundation of material forms (qi). The center was governed by "3," which coordinated the functions of "2" and "4" (note: this references the Yijing principle of "using nine" in the Qian hexagram and "using six" in the Kun hexagram). In forming the Bagua (Eight Trigrams), yang numbers avoided solitary yin, and yin numbers avoided isolated yang (note: this refers to the need for yin-yang balance in arrangement, where certain positions cannot form complete trigrams).

This passage reveals how ancient sages discerned the numerical patterns in natural phenomena to understand the workings of Heaven and Earth. The numerical arrangements and yin-yang avoidance principles discussed here are central to Daoist symbolic numerology (xiangshu), embodying the ancient mindset of "observing phenomena to derive laws."

This passage explains the transformation patterns of the ancient "Dragon Diagram" (a legendary mystical pattern said to have been carried from the Yellow River by a dragon-horse) and the nine moral principles revealed by Confucius (Zhongni) through the hexagrams of the Book of Changes (Yijing).

Confucius employed three sets totaling nine hexagrams to elucidate the essentials of moral cultivation: The first set comprises the Lü hexagram (symbolizing the foundation of virtue), Qian hexagram (representing the method to grasp virtue), and Fu hexagram (denoting the root of virtue). The second set includes Heng hexagram (symbolizing the stability of virtue), Sun hexagram (representing the cultivation of virtue), and Yi hexagram (indicating the abundance of virtue). The third set consists of Kun hexagram (symbolizing the discernment of virtue), Jing hexagram (representing the foundation of virtue), and Xun hexagram (denoting virtue that adapts to circumstances).

The text then explains the numerical patterns in the Dragon Diagram before the fusion of Heaven and Earth: The upper section represents the numbers of Heaven (Yang numbers), with five at the center, divided into five directions. The sum of one, three, five, seven, and nine is twenty-five, and these numbers exhibit specific patterns in their vertical and horizontal arrangements (for example, three numbers arranged vertically and horizontally always sum to five, while five numbers arranged this way always total fifteen). The lower section represents the numbers of Earth (Yin numbers), with six at the center, and the sum of two, four, six, eight, and ten is thirty, forming a hexagonal "Earth pattern" structure.

Finally, the passage describes the arrangement of the Dragon Diagram after the fusion of Heaven and Earth: The upper section symbolizes Heaven, where the odd numbers one, three, and five combine to form "Threefold Heaven" (representing Yang), while the even numbers two and four combine as "Twofold Earth" (representing Yin), totaling fifteen (the generative number of the Five Phases). Through specific calculations (such as subtracting four from five above to get one, or subtracting three from five below to get two), the central number ultimately remains unchanged. Quoting the Treatise on Harmonics and Calendrics, the text states that the beginning of Yang numbers is one, and the beginning of Yin numbers is two. In this diagram, the upper circle represents "one" (the beginning of Yang), the lower section represents the Earth pattern, while the center encompasses the Four Symbols and Five Phases.

This passage uses the numerical and directional symbolism from the study of changes (Yijing) to explain the patterns of cosmic operation. The "one" in the upper left represents the Great Yang (Fire), the "two" in the upper right represents Lesser Yin (Metal), the "three" in the lower left represents Lesser Yang (Wood), and the "four" in the lower right represents Great Yin (Water). Earth, as the harmonizing Qi (vital energy), resides at the center, balancing the four directions while embodying both Yin and Yang qualities.

The three dots on the right symbolize the Three Powers (Heaven, Earth, and Humanity), while the four dots on the left represent the cyclical changes of the four seasons. The upper numbers one, two, three, and four correspond to the counting stalks used in divination and the fundamental structure of trigrams. The lower numbers nine, eight, seven, and six represent the flourishing states of Metal, Wood, Fire, and Water respectively, with the central number ten symbolizing Earth's perfect completion.

Specifically: The central number six is distributed outward—adding one above yields seven, adding two to the left yields eight, adding three to the right yields nine, while the bottom remains six. Seven corresponds to the circular arrangement of divination stalks (7×7=49), eight matches the square arrangement of hexagrams (8×8=64), nine represents Yang lines (totaling 192), six signifies Yin lines (also 192), and ten embodies the Great Expansion number (where 5×10 or 10×5 both equal fifty).

The upper portion symbolizes celestial transformations (numbers one through four), while the lower represents terrestrial configurations (numbers six through nine). Heaven moves actively while Earth remains still—their interaction generates the Five Phases' (Wood, Fire, Earth, Metal, Water) directional relationships and the Bagua (Eight Trigrams) with nine palaces. This mirrors the Taiji Dunjia system where the celestial plate (above) rotates while the terrestrial plate (below) stays fixed, manifesting the principle of "Heaven moves while Earth rests." The number one initiates from the southern position, symbolizing the Dao of Heaven's rightward rotational movement.

(Note: Taiji Dunjia refers to an ancient cosmological system using rotating celestial and fixed terrestrial plates to model cosmic movement; the Great Expansion number denotes the fifty yarrow stalks used in Zhouyi divination.)

This passage explains the formation process of the Bagua (Eight Trigrams, fundamental Daoist symbols representing eight natural phenomena) and their relationship with the Hetu (River Chart) and Luoshu (Luo Writing, ancient mystical diagrams). The positional changes of the trigrams occur in several stages:

In the initial stage, Yang Qi gathers in the four directions of southeast, northwest, southwest, and northeast, while Yin Qi distributes below to the left. Thus Yin and Yang separate, and Heaven-Earth find their proper positions. After the first transformation, one resides in the northeast, two in the southwest, three in the southeast, and four in the northwest. The pairing of Yin and Yang generates the six derived trigrams (referring to all trigrams except Qian and Kun). Through two transformations, this forms the natural arrangement of the innate (Xiantian) Bagua.

Next comes numerical correspondence: one pairs with six, two with seven, three with eight, and four with nine. These numerically paired Yin-Yang relationships constitute what Shao Yong and Zhu Xi described as the Hetu arrangement. During the third transformation, one moves to the northwest, two to the southeast, three to the northeast, and four to the southwest. The interweaving of firm and yielding forms the four trigrams Kan, Li, Zhen, and Dui. In the fourth transformation, one shifts to the southwest, two to the northeast, three to the northwest, and four to the southeast, with Yang on the right and Yin on the left. The Qian and Kun trigrams take their proper positions, completing through these two transformations the artificial arrangement of the acquired (Houtian) Bagua.

Daoist scholar Jiang Shiwen explains: The completed numbers of the Hetu below symbolize the quiescent Earth, while the generative numbers above represent the moving Heavenly Dao. The innate Bagua manifests as a naturally formed image, whereas the acquired Bagua shows human-adjusted orientations. Observing these transformations: the first establishes the Yin-Yang duality, the second generates the six derived trigrams, the third positions Zhen-Dui opposite and Kan-Li interchanged, while the fourth fixes Qian-Kun and places Gen-Xun at the corners. The sages elevated Li to the south and lowered Kan to the north, thus rectifying the four directions; they positioned Qian in the northwest and withdrew Kun to the southwest, embodying the principle of the eldest daughter replacing the mother. The innate Bagua reveals natural laws, while the acquired Bagua demonstrates human-adjusted orientations.

Although this interpretation differs from previous Confucian explanations, the diagrams and numbers are clearly presented with coherent reasoning, forming a distinctive school of thought. Zhu Xi once remarked: "In leisure moments, one should frequently contemplate the Hetu and Luoshu, observing how the numbers flow naturally." Jiang Shiwen's explanation makes this all the more convincing.

Finally, this reveals the mystery of the generative numbers of Heaven and Earth within the Dragon Diagram (i.e., the Hetu).

This passage explains the mathematical structure of the ancient "Luoshu" (洛书) and its correspondence with cosmic patterns. The arrangement of numbers one through nine follows specific principles: numbers one, two, three, and four represent celestial movement (rotating clockwise), while six, seven, eight, and nine symbolize terrestrial forms (stationary positions). The number five occupies the central position as the pivotal axis connecting heaven and earth.

These numbers form particular paired relationships: one pairs with six in the northern quadrant, two with seven in the south, three with eight in the east, and four with nine in the west. This configuration is known as the "Numbers of Celestial-Terrestrial Intersection" (天地交午之数), representing the interaction of Yin-Yang forces. Han dynasty scholar Yang Xiong (style name Ziyun) and Song dynasty philosopher Zhu Xi both interpreted these numerical combinations as the mathematical foundation for the "four images" (四象 - Greater Yang [9], Lesser Yin [8], Lesser Yang [7], and Greater Yin [6]) used in Yijing divination with milfoil stalks.

The latter section references the "Nine Categories of the Great Plan" (洪范九章) from the Book of Documents (尚书), which Han scholars believed constituted the original 65-character Luoshu text. However, Song dynasty Daoist master Chen Tuan (known as Xiyi 希夷) transmitted an alternative tradition suggesting the Luoshu emerged through three transformations of the "Dragon Diagram" (龙图), ultimately forming the "Generative Diagram" (生成图). The passage concludes by quoting the Yijing: "The River brought forth the Diagram, the Luo produced the Writing, which the sages took as their model," emphasizing how these numerical diagrams served as sacred templates for ancient sages to emulate cosmic order.

Notes:

1. "Jiaowu" (交午): Refers to the interaction of Yin and Yang energies

2. "Dayan numbers" (大衍之数): The fifty milfoil stalks used in Yijing divination

3. "Four images": Greater Yang (9), Lesser Yin (8), Lesser Yang (7), Greater Yin (6)

4. "Great Plan" (洪范): A chapter in the Book of Documents detailing principles of governance

5. "Xiyi": Daoist name of Chen Tuan (陈抟), the renowned Song dynasty master

Kong Anguo (a Han dynasty Confucian scholar) explained: The River Chart (Hetu) appeared when Fuxi ruled the world—a dragon-horse emerged from the Yellow River bearing markings on its back, and Fuxi used these patterns to create the Eight Trigrams (Bagua). The Luo Writing (Luoshu) manifested during Yu the Great's flood control efforts, when a divine turtle surfaced carrying numerical arrangements up to nine, which Yu employed to establish the nine categories of governance. Liu Xin (a Western Han scholar) added that Fuxi received the River Chart as a heavenly mandate to rule and thereby derived the Eight Trigrams, while Yu was granted the Luo Writing during his flood taming, using it to formulate the ninefold administrative strategies. The River Chart and Luo Writing function as warp and weft to each other, with the Eight Trigrams and nine chapters mutually complementing one another.

Guan Ziming (a Northern Wei scholar of the Yi Jing) specified: The River Chart's numerical arrangement places seven in front, six behind, eight to the left, and nine to the right. The Luo Writing positions nine in front, one behind, three to the left, seven to the right, four front-left, two front-right, eight rear-left, and six rear-right.

Shao Yong (a Northern Song Neo-Confucian philosopher) proposed: Circular patterns represent celestial bodies, suggesting calendrical calculations likely originated from the River Chart (where yin-yang qi initiates firmness and softness, intermediate stages determine musical tones and calendar systems, culminating in intercalary month calculations). Square patterns symbolize terrestrial divisions, implying that the partitioning of nine provinces and the well-field system might have been modeled after the Luo Writing (with its nine provinces and nine-hundred-mu land division). Fuxi and King Wen of Zhou created the Book of Changes (Yijing) based on the River Chart, while Yu the Great and Jizi formulated the nine categories of the Hongfan according to the Luo Writing.

The numerical sequence of heaven and earth is: Heaven 1-Earth 2, Heaven 3-Earth 4, Heaven 5-Earth 6, Heaven 7-Earth 8, Heaven 9-Earth 10. Heavenly numbers comprise five odd digits (1,3,5,7,9), while earthly numbers contain five even digits (2,4,6,8,10). The heavenly numbers sum to twenty-five, the earthly numbers to thirty—combined they make fifty-five, a numerical system capable of deriving transformations and communicating with spiritual forces.

This passage primarily elucidates the numerical principles of the River Chart and Luo Writing: odd numbers represent yang (heaven) while even numbers signify yin (earth). The heavenly numbers (1+3+5+7+9) total twenty-five; the earthly numbers (2+4+6+8+10) sum to thirty—combined they form the foundational fifty-five. All yin-yang transformations and hexagram derivations stem from this numerical system. This framework can bifurcate to form the Two Modes (yin-yang), trifurcate into the Three Powers (heaven-earth-humanity), quintessentially correspond to the Five Phases (Wood, Fire, Earth, Metal, Water), octally constitute the Eight Trigrams, and nonally align with the nine palaces. Zhu Xi summarized: The universe originally existed as undifferentiated primordial qi; when differentiated into yin and yang qi, it formed numerical systems like the River Chart and Luo Writing.

The principles of Yin-Yang and the Five Phases (referring to Yin, Yang, and the five fundamental elements: Metal, Wood, Water, Fire, and Earth) constitute the fundamental laws governing the creation and transformation of all things, permeating every phenomenon from beginning to end. The Inner Canon states: The principles of Yin-Yang can be extrapolated to ten situations, expanded to a hundred variations, extended to a thousand forms, and generalized to ten thousand manifestations. Even when extended infinitely, as long as they are regulated by the laws of the Yijing (Book of Changes), there will be no omissions or deviations, enabling comprehension of all things.

Through the transformational patterns of "three and five" ("Sanwu" refers to the mutual coordination of the Three Powers [Heaven, Earth, and Humanity] with the Five Phases), by interweaving and synthesizing these numerical relationships, one can comprehend the Dao of transformation, thereby forming the patterns of Heaven and Earth. By exhausting these numerical principles, one can determine the phenomena of the world. If not for the most sublime transformational principles in the universe, how could such a state be achieved?

This further elucidates the transformational principles of the Hetu (River Chart) and Luoshu (Luo Writing), the legendary mystical diagrams said to have been carried by a dragon-horse and a divine turtle. "San" refers to mutual reference among the Three Powers (Heaven, Earth, and Humanity), similar to the "refrain from interfering in others' private affairs" mentioned in the Book of Rites. "Wu" denotes the Five Phases (Metal, Wood, Water, Fire, Earth) each occupying their proper positions, akin to the military organization of "squads and platoons." Specifically: the numbers one, two, three, and four interlace with six, seven, eight, and nine. "Cuo" (interlacing) refers to left-right cross arrangements, while "Zong" (synthesizing) indicates ascending-descending coordination. Through this method of Sanwu interlacing and Zong ascending-descending transformations, the patterns of Heaven and Earth are ultimately formed, establishing the images of all things. Thus, the Hetu and Luoshu are precisely the keys that unlock the most sublime transformations in the world.

When ancient sages created the Yijing, they invented milfoil divination (an ancient divination tool) through reverent rituals that resonated with divine spirits. They observed the numerical relationships of Heaven and Earth to establish hexagram numbers, created hexagram images through Yin-Yang transformations, and derived line statements based on firm and yielding qualities. They harmonized these principles with moral norms, systematically expounded their meanings, exhausted the inherent laws of phenomena, and ultimately comprehended the Mandate of Heaven.

This chapter reveals the fundamental purpose behind the sages' creation of the Yijing, as well as the origins of milfoil divination, numerical derivation, hexagram images, and line statements. "Resonating with divine spirits in stillness" describes how sages purified their minds through fasting and abstinence, silently perceiving divine assistance in tranquility. Using forty-nine milfoil stalks through procedures like "dividing, hanging, counting, and returning" (specific operations in ancient divination), they produced hexagram stalks symbolizing Yin-Yang and firm-yielding qualities. The numbers of Heaven and Earth combined to form the numerical principles of nine, eight, seven, and six in hexagram images. Therefore, by observing the transformations of Yin-Yang in Heaven they established hexagram images, and by examining the firm-yielding qualities on Earth they created line statements, harmonizing these principles with moral norms, systematically expounding their meanings, and ultimately exhausting the inherent nature of things to comprehend the Mandate of Heaven.

The patterns of Yin-Yang and hardness-softness between heaven and earth are comprehended by exhausting one's innate nature to understand the nature of all things. Those who achieve this can assist heaven and earth in nurturing all beings, completely merging with the operations of natural creation. This represents the highest attainment of the sage's state of utmost sincerity.

The ancient sages created the Book of Changes (Yijing) to conform with the principles of life's inherent nature. They established heaven's law as Yin-Yang, earth's law as hardness-softness, and humanity's law as benevolence-righteousness. Dividing the three powers (heaven, earth, and humanity) each into their Yin and Yang aspects, the Yijing thus uses six lines to form a hexagram. By distinguishing Yin and Yang and alternately applying hardness and softness across the six line positions, it creates a complete system.

The fundamental purpose of the sages in creating the Yijing was to help people understand the principles of life. Observing the transformations of Yin-Yang establishes the Dao of heaven (whose operation manifests as the alternation of cold and heat, day and night); examining the characteristics of hardness-softness establishes the Dao of earth (whose nature appears in flowing rivers, towering mountains, and growing things); while benevolence-righteousness establishes the Dao of humanity (whose foundation lies in filial piety, brotherly love, loyalty, and trustworthiness).

Humans receive the two energies (Qi) of Yin-Yang to obtain life, embody hardness-softness to form physical bodies, and contain benevolence-righteousness to fulfill their nature. When Qi, form, and nature are complete, they fully manifest the Dao of the three powers (heaven, earth, and humanity). In terms of the eight trigrams: the bottom line represents earth, the middle line represents humanity, and the top line represents heaven, each having their odd-even Yin-Yang distinctions. Dividing the three powers each into their Yin-Yang aspects forms the six-line hexagram: the first and second lines belong to earth, the third and fourth to humanity, and the fifth and sixth to heaven.

Specifically analyzed: the first, third, and fifth lines are Yang positions; the second, fourth, and sixth are Yin positions. Yang represents strength and firmness, Yin represents gentleness and yielding. The alternating application of Yin-Yang and hardness-softness across the six lines, with their mutual coordination, creates the infinitely variable system of hexagram imagery.

This classic (Jing) encompasses all phenomena, covering the Dao of heaven, humanity, and earth. The three powers each divided into Yin-Yang aspects are represented by six lines—these six lines are nothing other than the manifestation of the three powers' Dao. When the Dao undergoes change it's called a "line" (Yao); when lines have hierarchy they're called "things"; when things interweave they're called "patterns"; and when patterns become improper, fortune and misfortune arise.

What we call the Dao is precisely the Dao of the three powers (heaven, earth, and humanity). Heaven forms transformations through the interaction of Yin-Yang; earth forms textures ("乂" refers to interwoven patterns) through the interaction of hardness-softness; and ten fundamental changes combine to form line transformations. The lines are symbols that emulate these transformations, and their changes simulate the movement patterns of heaven, earth, and all things.

This passage explains the principles of Yao (the basic symbols constituting a hexagram) transformation in the Book of Changes (Yijing). The dynamic and static changes of Yao lines are divided into six positions: initial, second, third, fourth, fifth, and top, distinguished by the numbers seven, eight, nine, and six to represent different states.

Among them, seven and nine represent odd numbers, symbolizing Yang attributes, embodying strength and vigor, both belonging to the Qian hexagram (representing Heaven). Six and eight represent even numbers, symbolizing Yin attributes, embodying softness and receptivity, both belonging to the Kun hexagram (representing Earth). Nine represents a Yang Yao, six represents a Yin Yao, seven represents a firm Yao, and eight represents a yielding Yao. Yin-Yang are the intrinsic attributes of things, while firmness and softness are their external manifestations. Nine and six represent changing Yao lines, while seven and eight represent unchanging Yao lines.

When Yin and Yang interact and firmness and softness each take form, their interweaving creates patterns (the original meaning of the character "文" is a pictograph of Yin and Yang intersecting). If these patterns are harmonious, they bring auspiciousness (ji), as they align with the Dao (the Way). Actions that are balanced accord with the natural order, spontaneously producing good fortune (the character "吉" itself embodies the transformation of Yin and Yang).

Conversely, if the patterns are disharmonious, they bring misfortune (xiong), as they deviate from the Middle Way. Improper actions lead to predicaments (the character "凶" symbolizes change descending into a pit). Thus, the Yijing states that outcomes such as auspiciousness (ji), misfortune (xiong), regret (hui), and distress (lin) all arise from transformation.

Note: The Jin scholar Wang Luzhai mentioned in the text was a Yuan Dynasty expert on the Yijing. He interpreted the character "吉" (ji) as symbolizing Yang Qi emerging from the earth and the character "凶" (xiong) as symbolizing Yin Qi descending into the earth.

This passage primarily elucidates the Daoist cosmogony of "Taiji (Supreme Ultimate) generates the Two Modes (Liangyi), and the Two Modes generate the Four Symbols (Sixiang)," along with their correspondences to natural phenomena including the Five Phases (Wuxing), directions, and seasons.

The text first explains Taiji's differentiation: When Taiji divides, the light and pure Yang Qi ascends to form Heaven, while the heavy and turbid Yin Qi descends to form Earth. The sages, observing the operational patterns of Heaven and Earth and referencing the Hetu (an ancient mystical diagram), created the trigrams—using odd numbers to represent Yang and even numbers for Yin—thus establishing Heaven's position above and Earth's below. The intersecting symbols in the center signify the interaction of celestial and terrestrial Qi, from which emerge the Four Symbols and Eight Trigrams (Bagua), constituting the foundation of all creation. Zhou Dunyi (a Song Dynasty philosopher) states that Taiji's movement generates Yang; when movement reaches its limit, stillness produces Yin. Through this dynamic interplay of movement and stillness, Yin-Yang becomes established.

Next, it details how the Two Modes generate the Four Symbols: Zhu Xi explains that the Yang mode gives rise to Greater Yang (Taiyang) and Lesser Yin (Shaoyin), while the Yin mode produces Lesser Yang (Shaoyang) and Greater Yin (Taiyin). Traditional diagrams depict the Four Symbols arranged horizontally, whereas newer representations show the Yang mode below generating Yin-Yang and the Yin mode above producing hardness-softness, with the Four Symbols circulating continuously. The mutual interaction of hardness-softness and Yin-Yang, intersecting vertically and horizontally, gives birth to all things. Zhou Dunyi further describes how the transformations of Yin-Yang combine to generate the Qi of the Five Phases—Water, Fire, Wood, Metal, and Earth—which distribute sequentially to form the cyclical progression of the four seasons.

Finally, it specifically describes Lesser Yang among the Four Symbols: Lesser Yang represents Yang within Yin, corresponding to the east and spring. In spring, all things begin to stir—manifesting as wind in the heavens, Wood in the earthly realm, and the Wood Star (Jupiter) in celestial phenomena. In the Five Virtues (Wude), it embodies "Yuan" (the origin of goodness). Within the human body, it corresponds to tendons, the liver, and eyes; emotionally to anger; sonically to the exhalation sound; chromatically to green; gustatorily to sourness; musically to the Jue note (one of the pentatonic tones); and zoologically to. These correspondences exemplify the Daoist worldview of "the unity of Heaven and humanity."

This scripture employs the theory of the Five Phases (Wuxing) to establish correspondences between natural phenomena and human organs, emotions, etc., constructing a holistic worldview of cosmic-human unity.

The South corresponds to Fire and summer. Fire's characteristic is to make all things flourish ("things expand greatly"), manifesting as hot weather, corresponding to the heart and blood vessels in the human body, and expressing joy in emotions. The essence of Fire's Virtue (De) is smooth progress ("'Heng' signifies the gathering of excellence"), symbolizing the unimpeded development of things. Its specific manifestations include: the color red, bitter taste, the 'zhi' musical note, sheep among livestock, millet among grains, and the number seven (Fire's completion number).

The West corresponds to Metal and autumn. Metal's characteristic is contraction ("things gather and withdraw"), manifesting as dry weather, corresponding to the lungs and skin in the human body, and expressing sorrow in emotions. The essence of Metal's Virtue is appropriateness ("'Li' signifies the harmony of righteousness"), symbolizing everything finding its proper place. Its specific manifestations include: the color white, pungent taste, the 'shang' musical note, horses among livestock, rice among grains, and the number four (Metal's generation number).

The North corresponds to Water and winter. Water's characteristic is storage ("things culminate in concealment"), manifesting as cold weather, corresponding to the kidneys and bones in the human body, and expressing fear in emotions. The essence of Water's Virtue is steadfastness ("'Zhen' signifies the trunk of affairs"), symbolizing stability and endurance. Its specific manifestations include: the color black, salty taste, the 'yu' musical note, pigs among livestock, beans among grains, and the number six (Water's completion number).

The Center corresponds to Earth, harmonizing all directions, aligning with seasonal transitions. Earth's characteristic is nourishment ("warp and woof interweaving"), manifesting as humid weather, corresponding to the spleen and muscles in the human body, and expressing contemplation in emotions. The essence of Earth's Virtue is sincerity, symbolizing the foundation of all things. Its specific manifestations include: the color yellow, sweet taste, the 'gong' musical note, oxen among livestock, broomcorn millet among grains, and the number five (Earth's generation number).

These correspondences reflect the ancient mode of thought that connected natural laws with human physiology, unifying phenomena across different levels—seasons, celestial patterns, morality, physiology, and psychology—into one coherent system through the Five Phases (Wood, Fire, Earth, Metal, Water).

This passage primarily discusses the origin and evolution of the Bagua (Eight Trigrams). In ancient times, the legendary sage Fu Xi created the Bagua symbolic system by observing the patterns of heaven, earth, and all things, using it to comprehend the Dao of divine intelligence and the principles underlying all phenomena.

The formation process of the Bagua proceeds as follows: from the fundamental Taiji (Supreme Ultimate) emerges the two polarities of Yin and Yang; these two polarities then generate the four images (lesser Yang, greater Yang, lesser Yin, greater Yin); and from these four images derive the eight trigrams. The Bagua consists of these basic symbols: Qian (Heaven), Kun (Earth), Gen (Mountain), Dui (Lake), Zhen (Thunder), Xun (Wind), Kan (Water), and Li (Fire).

The Bagua has two primary arrangements: the Earlier Heaven sequence and the Later Heaven sequence. The Earlier Heaven arrangement forms a circular pattern with Qian in the south, Kun in the north, Li in the east, and Kan in the west. The Later Heaven arrangement forms a square pattern with Qian, Kun, Gen, and Xun at the four corners, and Kan, Li, Zhen, and Dui in the center. These two complementary arrangements manifest the operational laws of heaven and earth.

The text references the perspective of Shao Yong (Master Shao): the Qian and Kun trigrams represent the great parental symbols, while the Fu and Gou trigrams represent lesser parental symbols. Among the eight trigrams, four (Qian, Kun, Kan, Li) remain constant, while two others (Zhen and Gen, or Xun and Dui) can transform into each other. The entire system of Yijing (Classic of Changes) philosophy is built upon these intertransformations of trigrams.

This passage primarily explains the generative principles of the Eight Trigrams (Bagua - Qian/Kun/Zhen/Xun/Kan/Li/Gen/Dui) and the operational laws of the cosmos. It illustrates the formation process of the trigrams through the transformations of Yin and Yang.

The text first describes how the Zhen trigram (representing thunder) inverts to become the Gen trigram (representing mountain), while the Dui trigram (representing marsh) inverts to form the Xun trigram (representing wind). Through six such transformations, the complete set of Eight Trigrams emerges. In the diagram, the Yang principle (Yang energy) moves leftward in the upper region while the Yin principle (Yin energy) moves rightward below, together constituting this trigram arrangement. Master Shao Yong (Northern Song Neo-Confucian scholar) observed: Kun (Earth) resides in the north, Qian (Heaven) in the south, Li (Fire) in the east, Kan (Water) in the west, Zhen (Thunder) in the northeast, Dui (Marsh) in the southeast, Xun (Wind) in the southwest, and Gen (Mountain) in the northwest - with Taiji (the Supreme Ultimate, cosmic origin) at the center.

The text cites multiple ancient sages to elucidate the concept of "innate nature": The Book of Documents states Heaven endows people with their nature; Master Liu claims humans receive the harmonized Qi of Heaven and Earth at birth; Confucius held that among Heaven-Earth's natures, human nature is most precious; Zisi taught that Heavenly Mandate constitutes our nature. Observing the trigram generation diagram, we see all things of creation contained within it - as Cheng Yi described "the inherent completeness within nature" or Mencius' assertion that "all things are complete within me."

The generative sequence of the Primordial Eight Trigrams (Fuxi's arrangement) progresses from One to Two, Two to Four, and Four to Eight, theoretically extending infinitely. Early Confucians regarded the heart-mind as Taiji, containing all principles while responding to myriad affairs. Mencius emphasized the altruistic principle of "extending from self to others," Zengzi's "loyalty and reciprocity," and Confucius' "single thread binding all" - all find expression here. Scholars must quietly contemplate and personally practice these truths to attain genuine understanding.

Finally, the trigram positions are explained: Kan (Water), Li (Fire), Zhen (Thunder), and Dui (Marsh) occupy the cardinal directions, while Qian (Heaven), Kun (Earth), Gen (Mountain), and Xun (Wind) reside in the four corners. This corresponds with the He Tu (River Chart) pattern where one-six belongs to Water in the north. The entire passage reveals the correspondences between the trigrams and cosmic phenomena, unveiling the universal laws embedded within them.

This passage explains the directional arrangement and symbolic meanings of the Post-Heaven Bagua (also known as King Wen's Eight Trigrams). In this system: the Kan trigram representing water is positioned in the north; the Li trigram representing fire resides in the south; the Zhen trigram symbolizing thunder (associated with Wood) occupies the east; the Dui trigram representing marshlands (associated with Metal) is placed in the west. The Qian trigram, embodying cold and ice, sits in the northwest and shares Metal's attribute with Dui; while the Xun trigram, denoting wind and ascension, is located in the southeast and shares Wood's nature with Zhen. The numbers five and ten represent the central earth element, jointly governed by Kun (earth) and Gen (mountain) - with yin-associated Kun retreating to the southwest and yang-associated Gen anchoring the northeast. This forms the foundational logic of Post-Heaven Bagua's orientation.

By correlating seasonal cycles, geographical features, and human affairs, we discern the sequence of the four seasons. The Shuogua Commentary notes that Gen symbolizes both the end and rebirth of all things. Since all creation requires governance, the Heavenly Emperor manifests first through Zhen (east, the sunrise position). Nothing governs material affairs better than the eldest son (Zhen), matched by the eldest daughter (Xun), representing familial continuity. Only with household harmony can states be well-ruled, hence follows Li (illumination), depicting sages facing south to govern like the noonday sun. Next comes Kun (docility), signifying rest after labor; Dui (west, sunset position) denotes evening repose; Qian (yang vigor) positioned in the yin-dominated northwest creates the dynamic tension described as "battle at Qian"; Kan (water) in due north corresponds to midnight obscurity - through toil comes achievement, ultimately returning to Gen to complete the cycle.

The accompanying diagram (sixth illustration) rearranges trigrams according to the "Four Symbols generating Eight Trigrams" principle: Qian, Li, Kan and Kun occupy central positions representing human head, eyes, heart and abdomen; while Zhen, Gen, Xun and Dui flank the sides symbolizing limbs. Northern Song Daoist Chen Tuan (Master Xiyi) affirmed this configuration mirrors human anatomy, as humans embody the fusion of heaven's and earth's essential Qi (Jing-Qi), endowed with the harmonizing nature bestowed by celestial virtue.

This passage primarily explains the combinatorial principles and symbolic meanings of the Eight Trigrams (Bagua) from the Book of Changes (Yijing). The eight trigrams—Qian (Heaven), Kun (Earth), Li (Fire), Kan (Water), Dui (Lake), Xun (Wind), Zhen (Thunder), and Gen (Mountain)—interweave to form the cyclical system of sixty-four hexagrams.

The text first outlines the fundamental attributes of the trigrams: Qian represents strength and vigor, Kun embodies docility and receptivity, Li symbolizes upward movement, Kan signifies downward flow, Dui manifests outwardly, Xun remains concealed within, Zhen denotes initiation and arousal, while Gen stands for stillness and cessation. These eight basic configurations combine to form the patterns underlying all transformations in the natural world.

Particular attention is given to the circular arrangement of the primal sixty-four hexagrams: Heaven (Qian) is positioned in the south, Earth (Kun) in the north, reflecting the cosmic hierarchy where Heaven is honored and Earth humble. The Mountain (Gen) anchors the northwest, while the Lake (Dui) gathers in the southeast; Thunder (Zhen) erupts from the northeast, Wind (Xun) prevails in the southwest, Fire (Li) descends in the east, and Water (Kan) ascends in the west. This spatial distribution embodies the dynamic equilibrium of Yin-Yang movement and stillness in nature.

The trigrams combine through alternating left-right pairings: Qian pairs with Xun, Kan with Dui, Li with Gen, and Kun with Zhen. Originally Yang trigrams (Qian, Dui, Li, Zhen) intermingle with Yin trigrams (Kun, Gen, Kan, Xun), creating a pattern where strength and suppleness harmonize to produce infinite variations. This combinatorial process ultimately forms the cyclical system of sixty-four hexagrams, mirroring how the twenty-eight lunar mansions revolve through the twelve earthly branches.

The concluding section elucidates the principle "Counting the past proceeds with the flow, knowing the future requires reversal": To examine past events, one follows the hexagram sequence forward (like counting backward from the present day), while forecasting future developments demands inverse reasoning. This dual approach of sequential and reverse thinking constitutes the fundamental methodology of Yijing divination.

This passage discusses the operational principles and hexagram transformations of the Eight Trigrams (Bagua) from the Book of Changes (Yijing). It consists of two main sections:

The first section explains the calculation methods of the trigrams. Counting forward from the winter solstice through the beginning of winter to the autumn equinox, the trigrams follow the sequence of Kun (Earth), Gen (Mountain), Kan (Water), and Xun (Wind) before reaching Qian (Heaven). Conversely, counting backward from the winter solstice through the beginning of spring to the spring equinox follows the sequence Kun (Earth), Zhen (Thunder), Li (Fire), Dui (Lake), and Qian (Heaven). All calculations in the Yijing proceed inversely—the lines are counted from bottom to top, and the trigrams are derived from right to left.

The second section details the transformation patterns of the trigrams within each palace in the Early Heaven (Xiantian) Bagua arrangement. In this diagram, the lower trigrams remain in their original positions while the upper trigrams rotate rightward, with Yin and Yang interacting to produce the sixty-four hexagrams. It specifically enumerates the eight-trigram transformations within seven palaces (excluding the Kun palace): Zhen (Thunder), Li (Fire), Dui (Lake), Qian (Heaven), Xun (Wind), Kan (Water), and Gen (Mountain).

The Zhen palace begins with the Fu hexagram, progressing through Zhen, Shihe, Sui, Wuwang, Yi, and Tun until reaching the Yi hexagram, which forms an inverted trigram pattern (Zhen below and Gen above). The Li palace starts with the Bi hexagram, moving through Mingyi, Feng, Li, Ge, Tongren, and Jiaren to culminate in the Jiji hexagram, representing a balanced Yin-Yang configuration (Li below and Kan above). Each palace follows similar transformational patterns, with the Qian palace ultimately achieving the pure Yang Qian hexagram and the Kun palace reaching the pure Yin Kun hexagram.

These hexagram transformations embody the principles of waxing and waning Yin-Yang dynamics and the harmonious interplay of strength and gentleness. Through their systematic arrangements and combinations, they reveal the operational laws governing heaven, earth, and all phenomena.

This passage explains the correspondence between the transformations of the Eight Trigrams (Bagua) in the Book of Changes (Yijing) and the natural solar terms. The Eight Trigrams (Qian, Kun, Zhen, Xun, Kan, Li, Gen, Dui) follow a specific sequence of changes, like beads strung into an orderly network, systematically revealing the profound mysteries of heaven and earth.

Beginning with the Kun hexagram (pure Yin), the sequence progresses through the Yu, Jin, Cui, Pi, Guan, Bi, and Bo hexagrams, ultimately returning to Kun to complete a full cycle. This cycle mirrors the seasonal transitions throughout the year.

At the winter solstice, when Yang energy first emerges, the Fu hexagram's single Yang line (the initial nine) appears within Kun, symbolizing the stirring of Qian's Yang energy. At the summer solstice, when Yin energy first emerges, the Gou hexagram's single Yin line (the initial six) appears within Qian, symbolizing the stirring of Kun's Yin energy. The winter solstice marks the peak of Yin—the shortest day and longest night—while the summer solstice marks the peak of Yang—the longest day and shortest night.

During the spring and autumn equinoxes, Yin and Yang are balanced, with equal day and night lengths. In spring, the Kan (Water) hexagram begins transforming from the Jie hexagram's second nine line, while in autumn, the Li (Fire) hexagram begins transforming from the Lü hexagram's second six line.

Seasonal changes further illustrate these patterns: in spring, the Yi hexagram (two Yang lines outside, four Yin lines inside) transforms into the Bi hexagram; in summer, the Zhongfu hexagram (four Yang lines outside, two Yin lines inside) transforms into the Xiaochu hexagram. These shifts indicate that during spring and summer, Yang energy dominates externally while Yin energy resides internally—a time for nurturing Yang in cultivation. Conversely, in autumn, the Daguo hexagram (two Yin lines outside, four Yang lines inside) transforms into the Kun hexagram; in winter, the Xiaoguo hexagram (four Yin lines outside, two Yang lines inside) transforms into the Yu hexagram. This shows that during autumn and winter, Yang energy retreats inward while Yin energy prevails externally—a time for nurturing Yin in cultivation. These transformations follow natural laws beyond human alteration.

This passage explains how ancient scholars used the hexagrams of the Book of Changes (Yijing) to model celestial movements. Both Shao Yong (Master Shao) and Zhu Xi (Master Zhu) believed the Early Heaven (Xiantian) Bagua diagram perfectly corresponds to the cyclical patterns of heaven and earth.

The diagram maps seasonal variations in daylight, even down to monthly lunar phases. For instance: The moon begins its cycle at "Double Kun" (representing the dark new moon). On the third day, it appears at dusk in the western Geng position (aligned with the Zhen trigram of the Minor Over hexagram). By the eighth day, the waxing crescent reaches the southern Ding position (matching the Dui trigram of Major Over). The full moon (Qian trigram) culminates in the eastern Jia position on the fifteenth, then wanes—appearing at dawn in the western Xin position (Xun trigram of Inner Trust) on the eighteenth, and as a last-quarter moon in the Bing position (Gen trigram of Nourishment) by the twenty-third.

The Gen trigram, representing the northeast, symbolizes nature's cyclical renewal. The winter solstice aligns with the Mountain-Thunder Nourishment hexagram, while spring's onset initiates from Mountain-Fire Adornment—all reflecting natural laws. Thus, the Yijing's principles perfectly mirror cosmic operations.

Shao Yong noted that though this diagram contains no words, it encompasses all cosmic patterns. Zhu Xi elaborated that its cyclical framework applies universally—from grand 129,600-year cosmic cycles down to the twelve daily shichen (时辰), each beginning with the Return hexagram (symbolizing yang qi's initial resurgence).

The referenced Great Commentary (Xici Zhuan) opening outlines foundational cosmic principles: Heaven's loftiness and earth's lowliness establish Qian and Kun; movement and stillness define yin-yang; like attracts like, generating fortune/misfortune; celestial and terrestrial patterns manifest change. Through yin-yang interactions and trigram resonances, thunder stirs, rain nourishes, and the sun-moon cycle creates seasons—with Qian's way producing males and Kun's yielding females. This passage reveals the core meaning of the Early Heaven 64-hexagram circular diagram: the clear heavens above and turbid earth below form the universe's fundamental order.

This passage elucidates the natural classification and operation of all things in heaven and earth according to the characteristics of Yin and Yang, hardness and softness. Turbid and heavy elements naturally settle below, while light and pure elements rise above—just as Heaven (Qian) is noble and Earth (Kun) is humble, with this hierarchical order being fixed. Yang represents nobility and initiative, while Yin represents humility and stillness, akin to how the ruler is honored and the minister is modest, each occupying their distinct positions and ranks.

All things follow patterns in movement and stillness: external motion with internal stillness belongs to Yang, while internal motion with external stillness belongs to Yin. Just as Heaven (Qian) gravitates upward and Earth (Kun) downward, the Eight Trigrams (Bagua) also naturally cluster—the Yang trigrams of Qian (Heaven), Dui (Lake), Li (Fire), and Zhen (Thunder) gather in the southeast, while the Yin trigrams of Kun (Earth), Gen (Mountain), Kan (Water), and Xun (Wind) assemble in the northwest. Living creatures in the world also group by kind: horses, cattle, sheep, and pigs each form their own herds, illustrating the principle that "like attracts like."

Master Zheng Hesha further explains: Animals belong to Yang (capable of movement), while plants belong to Yin (fixed in growth). Yet only humans possess the dual nature of both Yin and Yang—able to move yet also remain still, thus becoming the most spiritual of all beings. Specifically: the Qian trigram represents pure Yang, corresponding to birds and beasts; the Gen, Kan, and Zhen trigrams, which are Yang with Yin aspects, correspond to insects and fish; the Kun trigram represents pure Yin, corresponding to earth and minerals; while the Xun, Li, and Dui trigrams, which are Yin with Yang aspects, correspond to flowers and trees.

The interweaving of Yin and Yang, hardness and softness, produces auspicious or ominous signs. For instance, the timely alternation of wind, rain, cold, and heat signifies good fortune, but an excess or deficiency of any climate becomes an ill omen. In heaven, there are the images of the sun, moon, and stars; on earth, there are the tangible forms of metal, wood, water, and fire—thus the patterns of transformation between heaven and earth are revealed. Hard and soft elements interact through friction (odd numbers 1, 3, 5, 7, 9 being hard, even numbers 2, 4, 6, 8 being soft), and through this friction and transformation, the Eight Trigrams are formed. The trigrams agitate one another (like shaking water to cleanse a vessel), as Qian, Kun, Kan, Li, Zhen, Gen, Xun, and Dui interact to generate the sixty-four hexagrams. The thunder's vibration (Zhen and Gen trigrams), the nourishing wind and rain (Xun and Dui trigrams), and the movement of the sun and moon—all these are concrete manifestations of the transformations of Yin and Yang.

This passage explains the operational principles of the Eight Trigrams (Bagua) from the Classic of Changes (Yijing). The alternation of cold and heat follows the sun's trajectory: when the sun moves southward away from its extreme point, the weather turns cold; when it moves northward toward its extreme, the weather becomes warm. This exemplifies the natural interplay of Yin and Yang. The Qian (Heaven) trigram symbolizes masculine Yang energy, while the Kun (Earth) trigram embodies feminine Yin virtue (De) — concrete manifestations of how all things are generated and transformed. By observing these trigram diagrams, one can grasp the greater principles at work.

The sixty-four hexagrams are formed by combining the eight trigrams. Specifically: Zhen (Thunder) represents vibration and activation, Xun (Wind) signifies diffusion and dissemination, Kan (Water) denotes nourishment and moistening, Li (Fire) embodies warmth and illumination, Gen (Mountain) stands for stillness and stability, Dui (Marsh) expresses joy and harmony, Qian (Heaven) governs and leads, while Kun (Earth) contains and stores. These trigrams radiate outward from a central axis, interconnected in all directions, thus establishing the spatial arrangement of the sixty-four hexagrams.

The directional correspondences are as follows: The southeast belongs to Yang, where the Qian trigram resides, corresponding to the fourth month; the northwest belongs to Yin, where the Kun trigram resides, corresponding to the tenth month. The Tai hexagram aligns with the first month in the Yin position, while the Pi hexagram corresponds to the seventh month in the Shen position, forming the four cardinal directions of Yin-Shen-Si-Hai. At the winter solstice, Yang energy first emerges with the Fu hexagram (eleventh month); at the summer solstice, Yin energy appears with the Gou hexagram (fifth month). The spring equinox aligns with the Dazhuang hexagram (second month), and the autumn equinox with the Guan hexagram (eighth month), establishing the four primary directions of Zi-Wu-Mao-You. The remaining months (Chen-Xu-Chou-Wei) attach to the four corners: the Lin hexagram (twelfth month) neighbors the Tai hexagram, hence in the Later Heaven arrangement, the Chou-Yin position belongs to Gen (Mountain) in the northeast; the Guai hexagram (third month) associates with Qian, so the Chen-Si position belongs to Xun (Wind) in the southeast; the Dun hexagram (sixth month) relates to Pi, placing the Wei-Shen position under Kun (Earth) in the southwest; the Bo hexagram....

This passage primarily explains the correspondence between the Eight Trigrams (Bagua) and celestial/terrestrial patterns. The hexagram associated with the ninth month neighbors the Kun (Earth) trigram. In the Later Heaven Bagua arrangement, the Xu-Hai direction corresponds to the Qian (Heaven) trigram in the northwest, aligning with the earthly orientation. Viewed from the perspective of Qian above and Kun below, the Eight Trigrams resemble warp threads, while the remaining fifty-six hexagrams interweave like weft threads—this reflects the Yijing's (Book of Changes) statement that "after Heaven and Earth take their positions, the Dao of Change operates within."

When examined through the lens of Pi (Standstill) above and Tai (Peace) below, the Eight Trigrams arrange systematically while the fifty-six hexagrams intersect vertically, as described in the Yijing: "After Qian and Kun are positioned, the Dao of Change is established." The surrounding twenty-eight hexagrams correspond to the twenty-eight lunar mansions: the seven hexagrams from Qian to Daxu match the Azure Dragon constellations of the east, with the Horn constellation beginning at Qian; the seven from Tai to Qian correspond to the Black Tortoise of the north; the seven from Kun to Cui align with the White Tiger of the west; and the seven from Pi to Lü mirror the Vermilion Bird of the south.

The Zhouyi Cantongqi (The Kinship of the Three) further elaborates: The first day of each month corresponds to Fu (Return), when yang energy begins circulating. During this phase, Neidan (internal alchemy) practice should follow natural rhythms, akin to the Yellow Bell pitch pipe vibrating in the eleventh month (Zi) as yang energy gradually manifests. As months progress, yang energy grows: the twelfth month (Chou) aligns with the Dalu pitch, marking yin-yang equilibrium; the first month (Yin) sees all things gathering; the second month (Mao) reaches the vernal equinox's perfect balance; by the fourth month (Si), yang peaks; and the fifth month (Wu) corresponds to the Ruibin pitch, where yin dominates as yang recedes. These patterns describe the waxing and waning dynamics of yin-yang energies throughout the annual cycle.

This passage elucidates the operational principles and philosophical implications of the Prenatal Bagua (Eight Trigrams) directional diagram (known as the "Square Chart") from the Xiangshu (Image-Number) studies of the Yijing (Classic of Changes).

It begins by describing the natural rhythm of Yin-Yang fluctuation: When the proper time has not yet arrived, all things exist in a state of chaotic closure. As Yin qi expands, Yang qi retreats, observable in autumn's cycle from sprouting to withering. While physical forms eventually dissipate, the transformative process of qi never ceases, ultimately returning to Earth's origin (Kun Yuan), moving in accordance with natural law.

The text then cites Shao Yong's (Shaozi) "Dayi Yin" to explain the trigrams' spatial relationships: Heaven and Earth (Qian and Kun) establish cardinal directions, Mountain and Marsh (Gen and Dui) exchange vital breath, Thunder and Wind (Zhen and Xun) mutually stimulate, while Water and Fire (Kan and Li) reflect each other. These interactions generate sixteen transformations through the four images' intersections, with overlapping trigrams forming the sixty-four hexagrams. Zhu Xi (Zhuzi) clarifies this describes the Square Chart's structure—the Qian trigram at the southeast corner directly opposes Kun at the northwest, manifesting "Heaven and Earth's fixed positions"; the Pi hexagram at the southwest corresponds to Tai at the northeast, demonstrating "Pi and Tai's inverse correspondence."

Cheng Zhifang (of the Xin'an Cheng lineage) further elaborates: Shao Yong's Prenatal learning constitutes a heart-method, with all diagrams (including both circular and square charts) emanating from the center. The circular chart symbolizes Heaven with positioning as its root, while the square chart represents Earth with dynamic dispersion as its function. This interplay of movement and stillness embodies the essence of Prenatal heart-method.

Finally, the "Xici Zhuan" (Great Commentary) is quoted: When trigrams arrange to form images and overlap to create hexagram lines, the mutual pushing of firm and yielding generates transformation. The shifting of lines produces auspicious and inauspicious omens—precisely the profound truth the Prenatal sixty-four hexagram Square Chart reveals. The trigrams arrayed vertically and horizontally form a complete cosmological operational schema.

This passage explains the principles governing the arrangement and combination of the Eight Trigrams (Bagua) — Qian (Heaven), Kun (Earth), Zhen (Thunder), Xun (Wind), Kan (Water), Li (Fire), Gen (Mountain), and Dui (Lake). Calculated from the center outward, the trigrams Zhen, Li, Dui, Qian, Xun, Kan, Gen, and Kun form specific patterns. Whether viewed horizontally, diagonally, linearly, or in terms of spatial directions (front/back, left/right), these arrangements follow consistent laws that encompass the fundamental trigrams representing natural phenomena: Heaven-Earth, Water-Fire, Thunder-Wind, and Mountain-Lake.

The method of combining the trigrams involves superimposing the Eight Trigrams upon each trigram, distinguishing between Yin and Yang, and alternately applying the Dao of hardness and softness. This process contains the transformations of the six yao lines (initial, second, third, fourth, fifth, and top lines). The principle of mutual interaction between hardness and softness operates as follows: Yang Qi begins from the initial nine (Yang) line of the Fu hexagram (Earth over Thunder) and progresses upward through each line until reaching the six lines of the Qian hexagram; Yin Qi starts from the initial six (Yin) line of the Gou hexagram (Heaven over Wind) and descends through each line to the six lines of the Kun hexagram. Thus, the patterns governing changes in hexagrams and yao lines are fully contained within this system.

The ancient sages, observing these patterns of change in the hexagrams and lines, attached judgments of auspiciousness, inauspiciousness, regret, and difficulty. Through these trigrams, the laws governing the movement and transformation of all things in the universe could thereby be manifested.

This passage explains the transformational patterns of the sixty-four hexagrams in the Book of Changes (Yijing). Zhang Li (courtesy name Zhongchun) illustrates the fundamental principles of hexagram transformation through diagrammatic analysis.

The core concept states that firmness (Yang) and yielding (Yin) form the basis of hexagram transformation. The Qian hexagram (乾) represents pure Yang's vigorous strength, while the Kun hexagram (坤) embodies pure Yin's gentle compliance—these two serve as unchanging references. Beginning with the transformation of Kun's bottom Yin line into Yang, we progressively obtain the Fu (复), Lin (临), Tai (泰), Dazhuang (大壮), and Guai (夬) hexagrams, ultimately culminating in the pure Yang Qian hexagram. This process mirrors the growth of Yang energy from winter to summer. Conversely, when Qian's bottom Yang line transforms into Yin, it generates the Gou (姤), Dun (遯), Pi (否), Guan (观), and Bo (剥) hexagrams before returning to Kun, analogous to Yin energy's gradual expansion from summer to winter.

This transformational pattern manifests as follows: changes in the first line produce six hexagrams each with one Yin and one Yang; changes in the second line yield fifteen hexagrams each with two Yin and two Yang; changes in the third line create twenty hexagrams each with three Yin and three Yang, and so forth. These transformations interweave horizontally and vertically, mutually deriving from one another—the key lies in grasping the principle of flexible adaptation without rigid constraints.

The text particularly emphasizes: Yang energy governs upward movement (rising leftward from the Fu hexagram), while Yin energy dominates downward movement (descending rightward from the Gou hexagram). The Tai and Pi hexagrams represent states of Yin-Yang equilibrium. From the Yin hour (3-5 AM) to the Shen hour (3-5 PM)—daytime—the Qian hexagram dominates; from the You hour (5-7 PM) to the Chou hour (1-3 AM)—nighttime—the Kun hexagram prevails. Thus hexagram transformations embody the principles of Yin and Yang's advance and retreat, with firmness and yielding alternating as naturally as day and night.

(Note: Fu, Lin, Tai, etc. are hexagram names from the Yijing; Yin, Shen, etc. refer to earthly branch time periods; "lines" denote the Yin-Yang symbols within hexagrams)

This scripture elucidates the correspondence between the human body and the cosmic patterns of Yin-Yang, as well as the internal principles of cultivation. The hexagrams manifest both firmness and yielding, gain and loss, with the principles of fortune and misfortune transforming within their interplay. The Qian hexagram (representing Heaven) above and Kun hexagram (representing Earth) below form the unchanging foundation, mirroring the eternal operation of celestial and terrestrial laws.

The Li hexagram (symbolizing Fire) in the south and Kan hexagram (symbolizing Water) in the north resemble the sun and moon following their respective orbits, embodying the constant principles of celestial motion. The transformations of all phenomena are boundless—following these patterns brings auspiciousness while violating them invites calamity. That which maintains the unchanging Dao embodies perpetual truth.

Zhu Xi observed that the Zhouyi Cantongqi uses Qian and Kun hexagrams to represent the alchemical cauldron, Kan and Li as medicinal ingredients, with the remaining sixty hexagrams symbolizing firing times. Extending this principle, human anatomy corresponds to cosmic Yin-Yang: the head corresponds to Qian above, the abdomen to Kun below; the heart's fiery nature aligns with Li above, while the kidneys' watery essence resonates with Kan below. Yang energy begins its ascent from the Fu hexagram (Winter Solstice) along the left side, akin to the Governor Vessel (Yang meridian) rising from the coccyx up the spine to the crown. Yin energy descends from the Gou hexagram (Summer Solstice) along the right side, mirroring the Conception Vessel (Yin meridian) descending from the throat through the chest to the abdomen.

The upper twenty hexagrams symbolize Heaven (embodying light, pure Yang Qi), thus predominantly displaying four or five Yang lines. The lower twenty represent Earth (embodying heavy, turbid Yin Qi), hence predominantly showing four or five Yin lines. The middle twenty signify humanity—endowed with the virtues of Heaven and Earth, blending Yin and Yang—thus consistently displaying three Yin and three Yang lines, much like the human meridians with three Yin and three Yang channels in each limb. The human form follows Heaven above, humanity at the center, and Earth below, embodying this very principle.

The Heng hexagram (恒, Constancy) occupies the central position, echoing the Book of Documents' injunction to "preserve constancy of nature" and Mencius' teaching on "steadfastness." Its commentary states: "The sun and moon follow Heaven's Dao to shine perpetually; the four seasons alternate to complete all things; sages persist in the true Dao to transform the world." Contemplating Heng's principle reveals the essential nature of cosmic phenomena.

The final reference to the "Diagram of Sixty-Four Hexagrams' Practical Application" illustrates operational schemata of hexagram transformations. The Shuogua Zhuan explains: "All beings emerge from Zhen (East), become ordered in Xun (Southeast), manifest in Li (South), and are nourished in Kun (Southwest)"—demonstrating hexagrams' correspondence with natural patterns.

This passage explains the arrangement principles of the Post-Heaven (or King Wen) Bagua (Eight Trigrams). Zhu Xi (Master Zhu) once questioned the directional positions of the Post-Heaven Bagua, arguing that its arrangement need not be forcibly explained. However, the author deduces the logic behind its formation by analyzing the numerical transformations of the Hetu (River Chart, an ancient mystical diagram) in relation to the directional positions of the Pre-Heaven (or Fu Xi) Bagua.

The northwest belongs to the Qian (Heaven) trigram, as ancient people believed the heavens tilted toward the northwest. Correspondingly, the Kun (Earth) trigram should originally occupy the southeast, but legend says the earth sank in that direction, so it is replaced by the Xun (Eldest Daughter) trigram. Thus, Kun retreats to the southwest, forming a perfect opposition with Qian—their three lines (yao, the horizontal lines composing each trigram) are entirely inverted.

The south belongs to the Li (Fire) trigram (flames rise upward), while the north belongs to Kan (Water) trigram (water flows downward)—their three lines are also completely opposite. The Gen (Mountain) trigram in the northeast and the Xun (Wind) trigram in the southeast are similarly inverted: if all three lines of Gen are transformed, it becomes Dui (Lake), which, when reversed, appears as Xun; if all three lines of Xun are transformed, it becomes Zhen (Thunder), which, when reversed, appears as Gen.

The Zhen (Thunder) trigram in the due east and the Dui (Lake) trigram in the due west form a lateral symmetry, much like lightning sparking thunder. The Song dynasty Yijing (Classic of Changes) master Shao Yong stated, "Zhen and Dui are arranged horizontally, while the other six trigrams are arranged vertically—this is the applied Dao of the Yijing." Precisely because of this arrangement, in modern divination charts, Qian and Kun, Kan and Li, Zhen and Dui all appear in paired opposition.

This passage reveals that behind the seemingly arbitrary directional positions of the Post-Heaven Bagua lies a rigorous logic of Yin-Yang transformation. Through the interplay of line changes and mutual conversions among the trigrams, it constructs a dynamically balanced cosmic model.

This passage primarily discusses the transformational patterns of the Eight Trigrams (Bagua) and divination methods. It first explains the mutual transformations between the trigrams: the Gen (Mountain) and Xun (Wind) trigrams can transform into each other. From the perspective of the Kun (Earth) trigram, the Gou hexagram in the Qian (Heaven) palace transforms into the Guai hexagram. Similarly, the Dun hexagram in the Qian palace corresponds to the Dazhuang hexagram in the Kun palace, while the Pi hexagram in the Qian palace corresponds to the Tai hexagram in the Kun palace—this correspondence runs throughout the entire Bagua system.

In the Kan (Water) palace, the Jie hexagram transforms into the Huan hexagram when viewed from the Li (Fire) trigram's perspective. The Tun hexagram in the Kan palace corresponds to the Meng hexagram in the Li palace, and this same principle of correspondence applies to other hexagram transformations. In the Zhen (Thunder) palace, the Yu hexagram transforms into the Qian hexagram when viewed from the Dui (Lake) trigram's perspective. These mutual transformations between hexagrams reflect the waxing and waning patterns of Yin and Yang.

The text particularly mentions two special types of hexagram transformations: "Wandering Soul" (Youhun) and "Returning Soul" (Guihun). When the fifth line of the original palace changes while all three lines of the outer trigram transform, it's called "Wandering Soul," representing outward transformation. When the fifth line changes while the three lines of the inner trigram remain unchanged, it's called "Returning Soul," signifying inward return. These transformation patterns embody the operating principles of heaven and earth.

The second part explains divination methods. It mentions that the Yijing (Book of Changes) uses fifty yarrow stalks (called the "Great Expansion Number"), though only forty-nine are actually used. This number derives from multiplying the central five and ten in the Hetu (an ancient mystical diagram). During divination, the forty-nine stalks are bundled together, symbolizing the undivided Taiji (Supreme Ultimate). The Yang symbol has seven strokes, and the Yin symbol also has seven strokes—seven multiplied by seven equals forty-nine, a number that encompasses all principles of Yao line generation in the Eight Trigrams. This divination method is considered a manifestation of natural law, not something that can be arbitrarily altered by human will.

The yarrow stalks used for divination (an ancient divinatory tool) possess perfectly harmonious and spiritually wondrous qualities. Their circular form represents the odd number seven, as the stalks naturally cluster into circular formations when gathered together; while the hexagrams manifest the wisdom of square integrity, with their eight directions corresponding to the even number eight, their layered structures naturally revealing square patterns. Here, "spirit" (shen) refers to mysterious and unfathomable function, while "wisdom" denotes flexible adaptability. The yarrow stalks belong to Yang while the hexagrams pertain to Yin - the stalks govern movement while the hexagrams govern stillness, embodying the supreme state of the substance-function relationship in the "Book of Changes."

In actual practice, one first randomly divides forty-nine yarrow stalks into left and right bundles to symbolize the two polarities of Heaven and Earth, then removes one stalk to hang in the center representing humanity. This leaves twenty-four stalks in each hand, totaling forty-eight stalks corresponding to the line numbers of the eight trigrams (each trigram's three lines make twenty-four strokes total, doubling to forty-eight when forming hexagrams). The specific procedure is: holding the left bundle in the left hand, one takes a single stalk from the right bundle to hang motionless at the center, symbolizing how humanity resides between Heaven and Earth without interfering with Yin-Yang transformations. Though this suspended stalk doesn't participate in calculations, it combines with the forty-eight to form the triad of Heaven-Earth-Humanity.

Next, one counts the left-hand stalks in groups of four using the right hand, placing the remainder (one to four stalks) between the ring and little fingers to symbolize the three-year intercalary month cycle. Then taking a portion from the right bundle (possible combinations include taking three leaving three, or taking one leaving two), one places this between middle and ring fingers to represent the five-year two-intercalation cycle. Finally, all remainders are gathered near the initially suspended stalk, following the "fourfold union" method recorded in the Yunhui compendium. This "returning the remainders" technique not only follows the ancient "double grasping then hanging" procedure, but through concrete operations demonstrates the intercalary month principles of the calendar system.

This scripture details the ancient divination method using yarrow stalks (a traditional divination tool) for numerical calculations. The process consists of several key steps:

First comes the "four divisions" operation (splitting the yarrow stalks into four portions), yielding either the number four or eight. Obtaining four counts as an odd number (one four), while eight counts as even (two fours). This process repeats with the remaining stalks being divided into four portions again for a second calculation, followed by a third iteration.

After three calculations, the numerical combinations determine the hexagram lines:

• Three odd numbers (old yang)
• Three even numbers (old yin)
• Two even and one odd number (with odd as primary - young yang)
• Two odd and one even number (with even as primary - young yin)

Each set of three calculations forms one yao (the fundamental symbol of a hexagram). Eighteen calculations complete an entire hexagram. A single hexagram can transform into sixty-four possible configurations, generating a total of 4,096 possible variations.

The text cites ancient explanations that dividing into four symbolizes the four seasons, while remainders represent intercalary months. It further specifies the yin-yang attributes corresponding to different remainder combinations:

• Left remainder one with right remainder three, or left three with right one - both yang numbers
• Left remainder two with right remainder six, or four on both sides - both yin numbers

Zhu Xi explains that odd numbers symbolize the circle (with diameter one and circumference three), while even numbers symbolize the square (with side one and perimeter four). The text meticulously lists the numerical relationships corresponding to old yang, old yin, young yang, and young yin.

Finally, it discusses the transformation patterns of the Qian hexagram (pure yang) and Kun hexagram (pure yin), along with methods to determine hexagram changes through odd-even combinations in the three calculations. The entire divination process reveals the exquisite correspondence between numbers and hexagram imagery.

This passage explains the combinatorial principles of yarrow stalk arrangements (an ancient divination tool) in the I Ching (Book of Changes). There are four main scenarios:

The first represents the "Lesser Yang" hexagram images (Gen, Kan, Zhen), characterized by two even and one odd numbers with odd numbers dominant. Through three transformations, 24 combinations emerge—8 for Gen, 8 for Kan, and 8 for Zhen. In calculations, the remaining stalks (guile) yield 20 counts, while the actually used stalks (guosui) give 28 counts. Dividing both by 4 results in 5 and 7, symbolizing the stable, unchanging state of a Yang line.

The second is the "Lesser Yin" hexagram images (Xun, Li, Dui), marked by two odd and one even numbers with even numbers dominant. Similarly, there are 24 combinations—8 for Xun, 8 for Li, and 8 for Dui. The remaining stalks yield 16 counts, the used stalks 32 counts, and dividing by 4 gives 4 and 8, representing the stable, unchanging state of a Yin line.

The third is "Greater Yang" (Qian hexagram), where all three transformations are odd numbers. The remaining stalks yield 12 counts, the used stalks 36 counts, and dividing by 4 results in 3 and 9. Here, 9 represents the extreme of Yang, which transforms into Yin. In the I Ching, this is taken as an omen of change—all transforming Yang lines are denoted as "nine."

The fourth is "Greater Yin" (Kun hexagram), where all three transformations are even numbers. Both the remaining and used stalks yield 24 counts, and dividing by 4 gives 6. Six represents the extreme of Yin, which transforms into Yang—all transforming Yin lines are denoted as "six."

These patterns embody the philosophy of Yin-Yang transformation: Lesser Yang and Lesser Yin remain stable, while Greater Yang and Greater Yin, upon reaching their extremes, undergo change. This reflects the I Ching's core principle that "things reverse upon reaching their limits." Divination uses these numerical shifts to predict auspicious or inauspicious outcomes.

The Eight Trigrams (Bagua), the eight fundamental symbols used in ancient divination, each originally had eight variations, which when combined form the sixty-four hexagrams. Regarding the method of counting yarrow stalks during divination, Masters Cheng and Zhang proposed that in the second and third transformations, there is no need to set aside stalks. Specifically: during the first transformation, one stalk is set aside to symbolize the human element, after which it is no longer used; the subsequent two transformations proceed without setting aside additional stalks.

When counting the stalks, only the left portion is tallied while the right is disregarded, following the theories of Tang dynasty scholars Zhang Yuan and Zhuang Chuo. They held that heaven (yang) is active while earth (yin) is still, with yang energy transforming and yin energy consolidating—earth carries out the movement of heaven’s Dao. If one stalk remains on the left, it is paired with three on the right; if three remain on the left, they are paired with one on the right, forming an odd (yang) number. If two remain on the left, they are paired with six on the right; if four remain, they are paired with four, forming an even (yin) number. This ensures balance between the dynamic and static, old and young aspects of yin and yang.

The common practice today involves setting aside stalks in all three transformations and counting both left and right portions, yielding twelve instances of old yang, twenty-eight of young yin, twenty of young yang, and four of old yin—resulting in uneven distributions. However, following the ancient method—setting aside stalks only in the first transformation and counting both sides—produces twenty-seven instances of great yang, twenty-seven of young yin, nine of young yang, and one of great yin. Though the total remains sixty-four, the purely yin great yin hexagram is exceedingly rare; some diviners may go an entire year without encountering a pure Kun (earth, symbolizing total yin) transforming into Qian (heaven, symbolizing total yang). Those studying the Dao of transformation should contemplate the subtleties here with care.

Regarding hexagram calculations: the total stalk count for Qian is 216 (36 × 6 lines), while Kun totals 144 (24 × 6 lines), summing to 360—symbolizing the days of a year. The two sections of the Book of Changes (Yijing) employ 11,520 stalks in total, corresponding to the number of all things in creation. Four operations complete one transformation; eighteen transformations form one hexagram. The Eight Trigrams serve as the foundational framework, and through their expansion and deduction, one may exhaustively explore the patterns of change governing all phenomena under heaven.

Note that the 360 days mentioned here refer to the lunar calendar’s twelve-month cycle. When calculated by synodic months (lunations), the count is 354 days.

This passage elucidates the numerical calculations and divination principles from the Zhouyi (Book of Changes).

It first explains the origin of the 360-day year: while the sun's complete cycle actually takes 365 and a quarter days, ancient scholars adopted 360 days as the standard for calculation. The text then details the numerical relationships between Yin and Yang lines: each young Yang line (initial Yang state) counts as 28 stalks (calculation units), making 168 stalks for the six lines of the Qian hexagram; each young Yin line (initial Yin state) counts as 32 stalks, totaling 192 stalks for the Kun hexagram. Combined, these equal exactly 360 stalks.

The Yijing primarily employs old Yang (36 stalks) and old Yin (24 stalks) for calculations. Multiplying 192 Yang lines by 36 yields 6,912, while 192 Yin lines multiplied by 24 gives 4,608, summing to 11,520 stalks—symbolizing the number of all things. Interestingly, using young Yang (28) multiplied by Yang lines results in 5,376, and young Yin (32) multiplied by Yin lines produces 6,144, which also adds up to 11,520. This demonstrates that the numerical values of young Yin and Yang are inherently contained within old Yin and Yang.

Regarding divination methods: if none of the six lines change, one interprets the hexagram statement. For example, the Zuozhuan records how Kong Chengzi divined about establishing Prince Yuan of Wei and obtained the Zhun hexagram (Zhen below, Kan above), whose statement reads "favorable to establish a lord." Similarly, when Duke Qin attacked Jin and obtained the Gu hexagram (Xun below, Gen above), the interpretation "steadfast wind over regretful mountain" was based on the unchanging hexagram's imagery.

If one line changes, the changing line's statement is consulted. For instance, when Bi Wan of Jin obtained Zhun transforming into Bi (Kun below, Kan above), the ninth line had changed, so the ninth line statement of Zhun was referenced. Cai Mo's example also illustrates this method.

These represent the fundamental rules for applying the numbers nine and six in the transformations of the sixty-four hexagrams. As Zhu Xi summarized: when no lines change, consult the original hexagram statement; when lines change, examine the statements of the changing lines.

This passage explains the method of determining auspicious or inauspicious outcomes in ancient divination based on line transformations (changes between yin and yang lines in the hexagrams).

When the Qian hexagram (composed of two identical Qian trigrams) transforms into the Tongren hexagram (Li below, Qian above), one examines the change in the second line's yang (nine) position. When Duke Wen of Jin divined and encountered the Dayou hexagram transforming into the Kui hexagram (Dui below, Li above), he observed the change in the third line's yang (nine) position.

When Chen Jingzhong performed divination and saw the Guan hexagram (Kun below, Xun above) transform into the Pi hexagram (Kun below, Qian above), he examined the change in the fourth line's yin (six) position. Nan Kuai encountered the Kun hexagram (pure yin) changing to the Bi hexagram (Kun below, Kan above) and observed the fifth line's yin (six) transformation. When Duke Xian of Jin divined using the Guimei hexagram (Dui below, Zhen above) transforming into the Kui hexagram (Dui below, Li above), he analyzed the top line's yin (six) change. These are all examples of single-line transformations where judgments are made based on the changing line's statement in the original hexagram.

For two-line transformations, one consults both changing lines' statements in the original hexagram but gives priority to the upper line. With three-line changes, both the original and transformed hexagrams' judgments (tuanci) are considered, using the original hexagram as primary (zhen) for determining auspiciousness and the transformed hexagram (hui) as supplementary. For instance, when Prince Chong'er divined about gaining rulership, his original hexagram was Zhun (Zhen below, Kan above) transforming into Yu (Kun below, Zhen above), with the first and fifth lines changing to yang and the fourth to yin—three transformations total. Minister Sikong Jizi concluded "all favorable for establishing feudal lords," demonstrating the three-line transformation method.

With four-line changes, focus shifts to the two unchanged lines in the transformed hexagram, prioritizing the lower line. Five-line transformations require examining the single unchanged line in the transformed hexagram—as when Mu Jiang encountered the Gen hexagram (Gen below, Gen above) with five transformed lines, where only the second line remained unchanged. Though the judgment should have followed the Sui hexagram's (Zhen below, Dui above) second yin line statement "tying the youth but losing the husband," the court diviner mistakenly quoted Sui's hexagram statement instead.

For complete six-line transformations, only the Qian and Kun hexagrams require special "using nine" or "using six" line statements—all others use the transformed hexagram's judgment. For example, Cai Mo noted "when Qian transforms into Kun, the 'headless dragons' omen indicates good fortune." Through these transformation rules, each hexagram can evolve into sixty-four possibilities, creating 4,096 potential variations in total.

This passage explains the application principles of the Bagua (Eight Trigrams), the eight fundamental symbols used in ancient divination. The six trigrams (referring to all except the Qian and Kun trigrams) are inherently contained within the Bagua system. By extending and elaborating upon these trigram images through deductive reasoning, and expanding their application through analogical thinking, one can exhaustively comprehend the patterns of change governing all phenomena under heaven.

This excerpt comes from the second volume of Yixiang Tushuo Neipian (Inner Chapters on Diagrams and Explanations of the Yi), primarily expounding how to understand the world through the deductive application of the Bagua. The phrase "extending and elaborating" refers to the logical derivation from basic trigram images, while "expanding through analogical thinking" means continuing to broaden applications when encountering similar phenomena. The author maintains that mastering this method enables thorough comprehension of the operational laws governing all things in the world.