Lìtǐ lüè 歷體畧
Brief Treatise on the Calendrical-Body (the celestial-mechanical foundations of calendrical computation) by 王英明 (Wáng Yīngmíng, fl. 1606–1612, 明, zhuàn 撰); diagrams supplied by Wēng Hànlín 翁漢麐 in the 1646 edition
About the work
Wáng Yīngmíng’s 3-juan introduction to the cosmological-astronomical foundations underlying calendrical computation, completed Wànlì rénzǐ (1612) and printed posthumously by his son Wáng Yǎng 王懩 in Shùnzhì bǐngxū (1646) with diagrams supplied by Wēng Hànlín 翁漢麐. The work consists of:
Upper juàn (6 chapters): Tiāntǐ dìxíng 天體地形 (heaven-body and earth-form), Èryào 二曜 (the two luminaries — sun and moon), Wǔwěi 五緯 (the five planets), Chéncì 辰次 (the lunar-stations and zodiacal sequence), Kèlòu jídù 刻漏極度 (clepsydra-divisions and polar elevation), Záshuō 雜説 (miscellany).
Middle juàn (3 chapters): Jígōng 極宫 (the polar palaces — the asterisms around the celestial pole), Xiàngwèi 象位 (the asterism positions), Tiānhàn 天漢 (the Heavenly River — the Milky Way).
Lower juàn (8 chapters): a separate section subtitled “successively derived from the European books, summarizing their essentials” (xù jiàn Ōuluóbā shū, cuō qí tǐyào 續見歐羅巴書，撮其體要): Tiāntǐ dìdù 天體地度 (heavenly-body and earthly-degrees), Dùlǐ zhī chā 度理之差 (degree-and-principle differences), Wěiyào 緯曜 (the planets), Jīngxiù 經宿 (the longitude-stations), Huángdào gōngjiè 黄道宫界 (ecliptic palace-boundaries), Chìdào wěichán 赤道緯纒 (equatorial latitude-and-position), Qìhòu kèlòu 氣候刻漏 (seasonal-nodes and clepsydra), and an appended Lùn rìyuè jiāoshí 論日月交食 (discussion of solar-and-lunar eclipses).
The work is unusual in the late-Wànlì astronomical literature for two reasons. First, it is among the earliest Chinese-authored works (not Jesuit-collaborated) that demonstrably integrate the European nine-spheres cosmology and the European geometric account of eclipses, despite Wáng Yīngmíng’s not being a Catholic convert and not being a direct member of the Beijing residence circle — documenting the indirect spread of Ricci-period European astronomy into the broader Wànlì literati culture by 1612, two decades before the Chóngzhēn lìshū would formalize the synthesis. Second, the work’s deliberate absence of diagrams in its original form reflects Wáng Yīngmíng’s principled cosmological position — that two-dimensional representation of the spherical heavens is necessarily misleading on four specific geometric grounds (set out in Wēng Hànlín’s 1646 preface).
Tiyao
[Sub-classification: 子部, Tiānwén suànfǎ class 1, tuībù sub-category. Edition: WYG.]
Respectfully examined: Lìtǐ lüè, 3 juàn, by Wáng Yīngmíng of the Míng. Yīngmíng’s zì was Zǐhuì 子晦, [a man] of Kāizhōu, jǔrén of the Wànlì bǐngwǔ year [1606]. This compilation was completed in the Wànlì rénzǐ year [1612].
[Detailed table-of-contents in three juàn — see the section above.]
However, what its upper-and-middle two juàn expound of Chinese methods is also in every case in agreement with the Western methods. For at this time, although Xú Guāngqǐ’s Xīnfǎ suànshū had not yet emerged, Lì Mǎdòu had previously arrived in China and his teachings had been transmitted; therefore Yīngmíng tacitly used them (Yīngmíng yīn yòng zhī ěr 英明陰用之耳). What he discusses are all the broad outlines of astronomy; he does not match the comprehensiveness of measurement-and-computation methods later developed by Méi Wéndǐng and Xuē Fèngzuò 薛鳳祚.
However, those who study astronomy must necessarily first know the [character of] the asterisms-and-stars and the [reasons] of [their] motion, and only afterward can they investigate their precision through the degree-numbers. This book’s exposition, although shallow, is indeed the doorway by which beginners enter the field.
The book opens with five diagrams. According to Wēng Hànlín’s preface, Yīngmíng originally composed the book without diagrams; the present recension is from Wáng Yīngmíng’s son Wáng Yǎng’s reprint, in the Shùnzhì bǐngxū year [1646], when Wáng Yǎng was serving as Jiāngnán Grain-Transport Intendant — Hànlín then supplied [the diagrams]. Now examining within the book: under Bùtiān gē 步天歌 chapter 1, there is an interlinear note saying “the Bùtiān gē has no good editions; this is corrected from the master, so as to be free of fish-and-tortoise [scribal] errors” and so on. Verifying the textual style, this too is Hànlín’s wording. So this book was reorganized by Hànlín — it is not the original recension.
Respectfully collated, Qiánlóng 46, tenth month [November 1781].
Chief Compilers: (subject) Jì Yún 紀昀, (subject) Lù Xíxióng 陸錫熊, (subject) Sūn Shìyì 孫士毅. Chief Collator: (subject) Lù Fèichí 陸費墀.
Original preface (Wáng Yīngmíng, 1612)
In antiquity, Jīzǐ taught the Way of the Five Cardinal Relations (which the Holy Yǔ had set in order) to King Wǔ of Zhōu — and the Five Categories ultimately end with the calendrical numbers. The calendar is the Imperial-Royal HóngFàn (Great Plan) for governing-the-age; for our Confucians of practical use, [it is] our great enterprise.
What is meant by body (tǐ)? Just the tiāntǐ (heaven-body): the two-pole-and-twenty-eight-mansions are the heaven-body; the seven-luminaries-and-twelve-stations are the heaven-body. As “for things [Heaven] is not two” — the earth-body is also the heaven-body. Of the calendar, the imaging-and-the-imparting-of-seasons is most urgent. Why have the divination-and-omen schools made [calendrics] their fúyìng (lucky-correspondence) ranking? It is as though the qīnruò shòushí (reverent-regulation impartment-of-seasons) classic of Yáo and Shùn had been borrowed-from to support the schools of [astrologers like] Zǐ Shèn 梓慎 and Bēi Zào 禆竈! The lower-current’s defects: the Day-Officials take the state-prohibition [against amateur calendrics] as their authority. The foolish-self [I, Yīngmíng] received the Shàngshū [tradition] for generations; calendrical imaging is my hereditary occupation. I always lament that the unfamiliar avoid-and-cover [the subject] as unknowable, while the bureau-officials excuse themselves [by saying] it is not their pressing business; even those styled great Confucians of name-and-principle here often speak in dream-language. Therefore I have taken actually-measured fixed-degrees and ancient-and-modern aphorisms, abridged-them and made-a-volume, as a help to my son’s classical study. All passages touching on the bùjīng (uncanonical, irregular) I have one-and-all rejected. The longitude-and-latitude both raised, the broad outline is plainly visible. As for [the calendar’s] applications — these are the methods of the jīhéng (armillary sphere) and Língxiàn, the numbers of multiplication-division-step-computation, the alternation-and-illumination — there is nothing not [governed by] ultimate-principle. [These methods] are all set out in other writings; here [I do] not detail [them].
As for those numerous-stars whose names are dependent-imitations from Qín-and-Hàn onward, all retain their old usage: why? Names of heaven — even the twenty-eight mansions are also borrowings. The book having been completed, [I have] in toto kept it secret in the curtain-tent, not daring to show it to others. Wànlì rénzǐ [1612], ancient-Chán [Chánzhōu = Kāizhōu] Wáng Yīngmíng, shū (writes).
Postface preface (Wēng Hànlín 翁漢麐, 1646, on supplying diagrams)
Master Wáng of Chányuān came to inspect Jiāngnán: humane, intelligent, incorruptible, decisive, what he did to make-fortune for the people cannot be counted on the fingers. Within a thousand-lǐ square, the joyful sound was on the road; only [Wáng] gōng covered-and-sheltered [the people] virtuously, and they did not know that gōng’s benefiting-the-people with substantial benefit was [the fruit of] his late father’s bequeathing instruction with substantial learning.
The late father was broad in talent and learning; in calendrics, pitch-pipes, military affairs, agricultural-and-frontier defense, river-and-water control — there was nothing he did not deeply investigate. Outstanding [among] the great Confucians of the age. Young, he ascended the high-rank examinations; court and county both regarded him as one expected for the rank of gōngfǔ (Three-Highest). But he absolutely repudiated the official career, closed his gate and cultivated the Way; the four directions’ famous-and-eminent lined his door — sandals and shoes always full. He always urged: “Today’s pen-wielding houses are like the Jìn-period pure-conversers; the scholar must work for what is of use”. Therefore he developed and clarified the classics’ purport, parsing-and-deciding the nature-and-fate; outside that, he simply gathered prior-dynasties’ precedents and the era’s pressing essentials, [in] question-and-answer.
After his hand had elaborated [the work] into a finished book, [the work] nearly filled-the-rafters. Although [it] suffered war-fires, there are still [things] preserved. Now [Wáng] gōng cannot bear to keep his family-treasure private; gradually [he] is bringing them to the engraving-blocks. First the Lìtǐ one book — and supplying-diagrams [for it] [he] entrusted to me, [his] junior. I [though] — what should I [know of] calendrics, that I should presume? But still: in matters there is the [practice of] continuing-the-tail [adding to existing work]; in feeling, [I am] tied [to the senior]. And being honored with [Wáng] gōng’s command, what would I dare to refuse?
Strenuously exhausting my dullness, weighing past-and-present, measuring inches-and-tenths, comparing the round-and-square — for all the high-and-low, sparse-and-dense placements, the broad-and-narrow, longitude-and-latitude of degree-numbers — only afraid of the slightest deviation from the qiánxiàng (heavenly imagery), to disgrace this book.
But in my private heart there is what is unsatisfied: (1) The North Pole’s elevation is 35 or 36 degrees; its position is in the north, but the diagram [necessarily] cannot but place it in the center — first non-conformity. (2) The heaven-body’s half is below the earth, rotating-and-revolving without fixity, but the diagram cannot but lay-it-out as a static layout — second non-conformity. (3) The heavenly-degrees are all obliquely-divided, but the diagram [represents them] as straight rows — third non-conformity. (4) From the north-pole what is divided meets at the south-pole; therefore beyond the equator the degrees gradually narrow, but the diagram on the contrary spreads out at the four edges — fourth non-conformity.
This [is no other reason than that] the heaven-body is [a] full-round [sphere]; the four directions, up-and-down, revolve-and-return without limit; today using the limited extent of the paper to convert it to a flat circle — this is the Gàitiān [cosmology] but not the Húntiān (Sphere-Heaven). The body has ten-thousand-thousand non-resemblances. I now realize that Master Wáng’s composing the book without composing diagrams is not negligence; rather, the diagrams [simply] cannot be composed, so by means of not-composing he composed [them]. Now if [we] only enable the reader of this book to know why the yuán (constellation-walls) are three, why the yě (territories) are nine, why the xiù (lunar-mansions) are twenty-eight — that is graspable at one glance, [and] sufficient to be free of vague-vagueness in upward-glancing.
How should I claim that this diagram is truly sufficient to supplement this book? Only that [Wáng] gōng extends his family-learning to graciously instruct me, your junior, allowing me to participate in the guǎnkuī (tube-peep, meaning narrow view-of-the-whole) — for this I bow my head in reverence; would [I] dare to say only one matter of submitting-and-transporting [merit, but rather to add] my voice to the multitude singing of his sheltering kindness? — Eastern Wú [Sūzhōu] Wēng Hànlín respectfully records.
Abstract
Composition: 1612 (Wànlì rénzǐ — the date both the 提要 and Wáng Yīngmíng’s own preface affirm). Recension preserved: 1646 (Shùnzhì bǐngxū — Wáng Yǎng’s reprint with Wēng Hànlín’s diagrams), reorganized in some details from Wáng Yīngmíng’s original. The Sìkù-preserved text reflects this 1646 recension.
The work’s significance:
(a) Indirect Jesuit influence by 1612: the 提要’s careful observation that Wáng Yīngmíng “tacitly used” Ricci’s transmitted teachings provides precious documentation of the diffusion of Jesuit astronomical doctrine into the broader Wànlì literati community within a decade-and-a-half of Ricci’s settlement in Beijing (1601). Wáng Yīngmíng was not a Catholic convert and was not a member of the inner Beijing residence circle; his absorption of the European nine-spheres cosmology and the geometric account of eclipses by 1612 demonstrates that the technical content of the new astronomy — separated from its Christian theological apparatus — was already in indirect circulation among non-Catholic Chinese astronomical specialists by the late Wànlì period.
(b) The deliberate refusal of diagrams: Wáng Yīngmíng’s principled position that two-dimensional planar diagrams of three-dimensional celestial geometry are necessarily misleading is one of the most sophisticated late-Wànlì meditations on the limits of geometric representation. Wēng Hànlín’s preface preserves the four specific geometric objections — placement of the north pole, layout of the lower hemisphere, oblique-vs-straight degree-divisions, and false outward-spreading at the southern edge — and acknowledges that any 2D diagram is merely Gàitiān and not Húntiān. This is, in effect, an early-modern Chinese articulation of what would later be called the cartographic projection problem: any planar projection of a sphere necessarily distorts.
(c) Authorial humility and pedagogical purpose: Wáng Yīngmíng’s own preface is characteristically modest — he describes the work as composed for his son’s classical study, “kept secret in the curtain-tent, not daring to show it to others”. The decision to print only came posthumously through his son. This locates the work in the late-Wànlì tradition of family-pedagogical scholarship — not unrelated to but distinct from the more formal scholar-bureaucrat publications.
The 提要’s comparison of Wáng Yīngmíng to the early-Qīng mathematicians Méi Wéndǐng and Xuē Fèngzuò 薛鳳祚 — “[Wáng’s exposition] does not match the comprehensiveness of measurement-and-computation methods later developed by [these]” — frames the work as preparatory rather than mature: a doorway (ménjìng 門徑) for beginners but not the complete mathematical system. This is the standard late-imperial Chinese assessment of the late-Wànlì transitional astronomical literature.
For the broader Wànlì astronomical context, see KR3f0008 Gǔjīn lǜlì kǎo (the contemporary calendar-reform agitation), KR3f0009 Qiánkūn tǐyì (Ricci’s foundational cosmographic primer), and KR3f0013 Xīnfǎ suànshū (the eventual systematic synthesis). For Wáng Yīngmíng’s biography, see 王英明.
Translations and research
- No substantial secondary literature located on the Lì-tǐ lüè in any European language. The work has received occasional treatment in Chinese-language history-of-Chinese-science scholarship.
- Cullen, Christopher. Heavenly Numbers: Astronomy and Authority in Early Imperial China, Oxford: Oxford University Press, 2017 (background on the late-Wànlì astronomical milieu).
- Hashimoto Keizō 橋本敬造. Hō Yū-ran: Christian Mission and Calendrical Reform in Late Ming China, Kyoto: Kansai University Press, 1988 (essential context on the indirect Jesuit influence).
Other points of interest
The 提要’s observation that Wáng Yīngmíng’s lower juàn explicitly cites European books (the chapter being subtitled “successively derived from the European books, summarizing their essentials”) is documentation of an important transitional moment: by 1612, an independent Chinese scholar in a provincial location can openly reference “European books” as a recognized source-category. The phrase Ōuluóbā shū 歐羅巴書 (“books from Europe”) was still novel in Chinese writing of the period; Wáng’s casual deployment of it suggests it had already become acceptable terminology for the educated provincial reader.
Wáng Yīngmíng’s preface includes an early-modern critique of Chinese state-astronomy’s institutional secrecy (“the lower-current’s defects: the Day-Officials take the state-prohibition [against amateur calendrics] as their authority”) — a striking late-Wànlì call for the democratization of astronomical knowledge that aligns Wáng with the broader contemporary critique of the Qīntiānjiān’s institutional inadequacies that motivated the 1611 calendar-reform memorial.