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三統術詳說

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Text ID
KR3fb024
Date
1850–1882
Dynasty
清

Sāntǒngshù xiángshuō 三統術詳說

Detailed Explanation of the Santong System by 陳澧 (撰)

About the work

The Sāntǒngshù xiángshuō 三統術詳說, in five juàn, is the late-Qīng evidential-philological exegesis by Chén Lǐ 陳澧 (1810–1882) of Pānyú of Liú Xīn’s 劉歆 Sāntǒng 三統 system — the Hàn calendar transmitted in the Hàn shū “Lǜlì zhì” 律曆志. Composed at the Xuéhǎitáng 學海堂 in Canton during Chén’s mature scholarly period, the work sets out item by item the technical terms and constants of the Sāntǒng system and supplies clear arithmetic explanations, often in dialogue with Liú Bān’s 劉攽 Sòng-era commentary.

Abstract

The work has no separately signed preface; the front matter goes directly to the byline 「番禺陳澧撰」 (“composed by Chén Lǐ of Pānyú”) and into the technical exposition: 「黃鐘以其長自乘故八十一為日法」 (“the Yellow Bell, multiplied by its own length, accordingly gives 81 as the rìfǎ [day-divisor]…”). The body proceeds by quoting each technical term and constant of the Sāntǒng system in turn — rìfǎ 日法 = 81; yuèfǎ 月法 = 2,392; zhōutiān 周天 = 562,120; huì shù 會數 = 47; zhāng yuè 章月 = 235; rùnfǎ 閏法 = 19; etc. — and supplying detailed arithmetic explanations.

Chén’s distinctive contribution is to expose the Yìjīng-derived rationalisations of the Sāntǒng system (dàyǎn zhī shù 大衍之數, cāntiān liǎngdì 參天兩地) as post hoc numerological glosses on what are really empirical lunar-solar constants. Of the rìfǎ 81 he writes: “in reality this is not at all because the Yellow Bell is self-multiplied; it is rather because the moon overtakes the sun every 29 + 43/81 days, and so the day is divided into 81 parts. The Yellow-Bell explanation merely borrows the figure” (其實則因月行二十九日又八十一分日之四十三而與日會故命一日為八十一分也; 此借黃鐘為說耳). This is a characteristic Qīng kǎozhèng move — separating the technical-arithmetic content of an inherited tradition from its retrospective metaphysical justification — applied to the foundational document of Hàn mathematical astronomy.

The work belongs to Chén’s late mature period at the Xuéhǎitáng; notBefore is set at c. 1850, notAfter at 1882 (his death). CBDB confirms 1810–1882 (id 54955).

Translations and research

  • Cullen, Christopher. 2017. The Foundations of Celestial Reckoning: Three Ancient Chinese Astronomical Systems. London: Routledge. — The standard modern Western-language treatment of the Sān-tǒng lì; provides full English translation and analysis of the parent system that Chén here annotates.
  • Cullen, Christopher. 1993. “Motivations for Scientific Change in Ancient China: Emperor Wu and the Grand Inception Astronomical Reforms of 104 BC.” Journal for the History of Astronomy 24: 185–203.
  • Sivin, Nathan. 1969. Cosmos and Computation in Early Chinese Mathematical Astronomy. Leiden: Brill.
  • Elman, Benjamin A. 1984. From Philosophy to Philology: Intellectual and Social Aspects of Change in Late Imperial China. Cambridge, MA: Harvard University Press. — Treats Chén Lǐ’s Xué-hǎi-táng milieu and the Cantonese kǎozhèng tradition.
  • 蕭穆 Xiāo Mù et al. Late-Qīng appraisals of Chén Lǐ in the standard Qīng-rú xué-àn 清儒學案 tradition (Xú Shì-chāng 徐世昌 et al.).

Other points of interest

The companion work to this Xiángshuō is Chén Lǐ’s Hàn shū lǜlì zhì jiàoběn 漢書律曆志校本 (a critical text of the parent Hàn shū chapter), preserved in the Dōngshú yíshū 東塾遺書 collection. Together they constitute the most important Qīng-era treatment of the Hàn shū “Lǜlì zhì”; modern critical editions of the Hàn shū still cite Chén’s emendations.

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