Dàtǒng lìzhì 大統歷志
Treatise on the Great-Comprehensive Calendar (the late-Míng Dàtǒng lì) by 梅文鼎 (Méi Wéndǐng, 1633–1721, 清, zhuàn 撰)
About the work
Méi Wéndǐng’s 8-juan systematic exposition of the late-Míng Dàtǒng lì 大統曆 — the calendrical system inherited from the Yuán Shòushí lì of Guō Shǒujìng (1281) and used continuously throughout the Míng dynasty (1368–1644). Composed at the request of the Míng-history compilation bureau (Míngshǐ guǎn 明史館) chartered Kāngxī bǐngwǔ (1666); the work supplied the technical-mathematical foundation for the Míngshǐ Lìzhì 明史曆志 (preserved in the present Míngshǐ of 1739). The work’s substantive purpose is to assess fairly — neither apologetically nor dismissively — the late-Míng calendrical methodology that the Chóngzhēn-period reforms had eventually superseded, and to clarify the genuine technical achievements of Guō Shǒujìng’s underlying Shòushí system.
The structure follows Guō Shǒujìng’s three-fold Shòushí lìjīng arrangement, with a fourth supplementary section:
(I) Fǎyuán 法原 (Method-Origins), in 7 sections: Gōugǔ cèliáng 勾股測量 (right-triangle measurement); Húshǐ gēyuán 弧矢割圓 (arc-and-sagitta circle-section); Huángchìdào chā 黄赤道差 (ecliptic-equatorial difference); Huángchìdào nèiwài 黄赤道内外 (ecliptic-equatorial inside-and-outside); Báidào jiāozhōu 白道交周 (white-path nodal-revolution); Rìyuè wǔxīng pínglìdìng sānchā 日月五星平立定三差 (sun-moon-five-planets first-second-third differences); Lǐchā lòukè 里差漏刻 (longitudinal-difference and clepsydra-divisions).
(II) Lìchéng 立成 (Ready-Reckoner Tables), in 4 sections: Tàiyáng yíngsuō 太陽盈縮 (solar variable-velocity); Tàiyīn chíjí 太陰遲疾 (lunar variable-velocity); Zhòuyè kèfēn 晝夜刻分 (day-night divisions); Wǔxīng yíngsuō 五星盈縮 (planetary variable-velocity).
(III) Tuībù 推步 (Computational Procedures), in 6 sections: Qìshuò 氣朔 (seasonal-nodes-and-new-moons); Rìchán 日躔 (sun-position); Yuèlí 月離 (moon-path); Zhōngxīng 中星 (meridian-stars); Jiāoshí 交食 (eclipses); Wǔxīng 五星 (five planets).
The 提要 frames the work as an explicitly historical rather than working-astronomical treatise: “The calendrical-arithmetician must, in measuring the future, use the new method; in deriving the past, must each seek by the original method — knowing why it was loose, in order then to obtain the dense; knowing why it was wrong, in order then to obtain the true; knowing why it gradually drifted, in order then to exhaust [its] ultimate variation. Then this book — although clarifying Master Guō’s method — is also for the heaven-measurer’s prior-affairs’ teacher.”
Tiyao
[Sub-classification: 子部, Tiānwén suànfǎ class 2, tuībù sub-category. Edition: WYG.]
Respectfully examined: Dàtǒng lìzhì, 8 juàn, by Méi Wéndǐng of Our Dynasty.
In the beginning of the Yuán, Guō Shǒujìng made the Shòushí lì; its method [was] denser than the ancient. The early Míng promulgated Dàtǒng lì used its old method. After many years it gradually drifted; those who knew the calendar always had differing opinions. Reaching the Chóngzhēn period, Xú Guāngqǐ extended-and-elaborated the Western method; dividing into bureaus measurement-and-verification, the looseness-and-error became increasingly clear. The Qīntiānjiān Director Gē Fēngnián 戈豐年 had nothing further to dispute, [so] passed-the-blame to Shǒujìng. Sūn Chéngzé composed the Chūnmíng mèngyú lù and again strongly defended Shǒujìng as the sage of the calendar, regretting [only] that [the Míng] could not fully use his method. The disputing-litigation reached no fixed conclusion.
In Kāngxī bǐngwǔ [1666] [the imperial bureau] opened to compile the Míngshǐ. The history-officials, [knowing that] Wéndǐng [was] refined in arithmetic, asked him about the source-flow of the Míng calendrical gains-and-losses. Wéndǐng accordingly took the Dàtǒng old method, in detail extending-and-elaborating, annotating-and-explaining; gathered [it] into this compilation, in order to maintain its impartiality. Divided into Fǎyuán, Lìchéng, Tuībù three sections.
[Detailed sub-section list — see above.]
The Method-Origins are by which to take the numbers; the Tables by which to make the numbers; the Computation by which to record the method — all are analyzed-and-divided clearly, having organization. For Wéndǐng, regarding the asterisms-and-coordinates’ motion, [he] truly was able to exhaust their why-they-are-so — and with the calendrical-officer-disciples who continue-the-hereditary-occupation and guard the established method, [their] viewpoints are [naturally] not the same.
The calendrical-arithmetic family: in measuring the future, must use the new method; in deriving the past, must each seek by the original method — knowing why it was loose, in order then to obtain the dense; knowing why it was wrong, in order then to obtain the true; knowing why it gradually drifted, in order then to exhaust [its] ultimate variation. Then this book — although clarifying Master Guō’s method — is also for the heaven-measurer’s prior-affairs’ teacher.
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.
Abstract
Composition window: c. 1666 (when the Míngshǐ compilation began and Méi Wéndǐng was approached for technical input on the calendrical-history section) – 1721 (Méi Wéndǐng’s death; the work may have been substantially complete much earlier). The work was produced for institutional purposes — to support the Míngshǐ Lìzhì compilation — but Méi Wéndǐng’s interest in the Dàtǒng lì / Shòushí lì substrate was substantive and lifelong, and the work circulated independently of the Míngshǐ publication.
The work’s significance:
(a) Restoration of Guō Shǒujìng’s reputation: by the early Kāngxī period, the late-Míng calendrical-reform debate (in which Xú Guāngqǐ’s reformist party had eventually triumphed against the Wèi Wénkuí 魏文魁 traditionalist party) had created an intellectual climate hostile to the Shòushí lì tradition. Sūn Chéngzé’s Chūnmíng mèngyú lù, by attempting to defend the Shòushí exclusively on philosophical-principial grounds (crediting the philosophical Xǔ Héng over the technical Guō Shǒujìng), had inadvertently weakened the case. Méi Wéndǐng’s Dàtǒng lìzhì restores the Shòushí methodology to its proper technical context — neither defending it as final nor dismissing it as inadequate, but understanding why it gradually drifted from observed reality and what its genuine technical innovations were.
(b) The historical-rather-than-working framing: the 提要’s articulation of the principle that astronomical-historical work requires understanding each system in its own terms — rather than judging all by the latest method — is one of the most sophisticated late-imperial Chinese statements of historical-scientific method. The principle would shape later Chinese astronomical historiography (notably the Lǜlì yuānyuán’s historical sections and the various Qing dynastic-history Lǜlì zhì).
(c) Foundation for the Míngshǐ Lìzhì: through the Dàtǒng lìzhì, Méi Wéndǐng’s understanding of the late-Míng calendar entered the official Qīng-period historiographical record. The Míngshǐ Lìzhì (in the Míngshǐ finalized 1739) draws extensively on Méi’s work, and through the Míngshǐ the Qīng-period understanding of late-Míng calendrical history was substantially shaped by Méi’s interpretation.
(d) The genealogy from Guō Shǒujìng: the 提要’s earlier judgment in KR3f0026 Lìsuàn quánshū’s 提要 — zì Guō Shǒujìng yǐlái hǎn jiàn qí bǐ “from Guō Shǒujìng onward, [his] equal has rarely been seen” — is here given technical foundation: Méi Wéndǐng was the early-Qīng successor to the Yuán-period mathematical-astronomical tradition that Guō Shǒujìng had founded, with the late-Míng intervening period treated as a long stagnation under the inadequate care of the Dàtǒng establishment.
For Méi Wéndǐng’s biography, see 梅文鼎. For the broader Méi-anthology, see KR3f0026 Lìsuàn quánshū. For the Shòushí lì whose Míng-period inheritance the Dàtǒng represents, see external scholarship (the Shòushí lì itself is not in the Sìkù-included list but is referenced throughout the Tiānwén suànfǎ category).
Translations and research
- Sivin, Nathan. Granting the Seasons: The Chinese Astronomical Reform of 1280, New York: Springer, 2009 (the Shòu-shí lì; essential context).
- Hashimoto Keizō 橋本敬造. Joju-reki no kenkyū 授時暦の研究, Kōbe: Tōhō Shoten, 1979 (essential context on the Shòu-shí).
- Han Qi 韓琦, Tōng-tiān zhī xué 通天之學, Beijing: Sānlián, 2018.
- Cullen, Christopher. Heavenly Numbers: Astronomy and Authority in Early Imperial China, Oxford: Oxford University Press, 2017.
- Liu Dun 劉鈍, Méi Wéndǐng tā de shù-xué shǐ chéng-jiù 梅文鼎和他的數學史成就, in various journal articles, Beijing: Kē-xué Chū-bǎn-shè.
Other points of interest
The 提要’s careful articulation of why a Dàtǒng work is needed even after the Shíxiàn / Lǐxiàng kǎochéng reforms — for the historical-comparative purpose of understanding past calendrical practice in its own terms rather than judging it by present standards — represents one of the most explicit late-imperial Chinese statements of the principle of historical understanding in the history of science. The verdict that the work serves as the prior-affairs’ teacher (qiánshì zhī shī 前事之師) for “the heaven-measurer” frames mathematical-astronomical history as an indispensable preparation for working astronomy.