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漢三統術

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Text ID
KR3fc051
Date
1795–1817
Dynasty
清

Hàn Sāntǒng shù 漢三統術

The Hàn-Dynasty Sān-tǒng Calendrical System by 李銳 (述并注)

About the work

李銳 Lǐ Ruì’s (1768–1817) evidential-philological reconstruction in 3 juàn of the Sāntǒng lì 三統曆, the calendar designed by 劉歆 Liú Xīn (c. 50 BCE – 23 CE) in the closing years of the Former Hàn and adopted as the official calendar of Wáng Mǎng’s 王莽 Xīn 新 dynasty (9–23 CE). The original system is preserved only as the calendrical chapter (Lǜlì zhì 律曆志) of the Hànshū 漢書; Lǐ Ruì’s reconstruction recovers its procedural algorithms in a single consolidated treatise with technical commentary.

Abstract

The Sāntǒng lì is the earliest fully-preserved Chinese calendrical system. Its core innovation was the integration of the Tàichū 太初 calendar of 104 BCE (designed under Hàn Wǔdì’s 漢武帝 reform by Dèng Píng 鄧平 and others) with 劉歆 Liú Xīn’s enlarged numerological-cosmological framework relating the lunar-solar cycle, the jǐntiān 進天 day-numbering, and the cyclical “three-unities” (sāntǒng — heaven, earth, humanity) that gave the system its name. The system is preserved in the Hànshū Lǜlì zhì (treatise on pitch-pipes and the calendar), but its compilation there is fragmentary, with the procedural prescriptions interleaved with cosmological-philosophical discussion in a way that obscures the underlying algorithm.

Lǐ Ruì’s reconstruction extracts and systematizes the procedural content. The work presents the Sāntǒng algorithms in the standard format of a Chinese calendar treatise — fundamental constants, then derived constants, then the procedures for new-moon (shuò 朔) calculation, solar-term (qì 氣) calculation, eclipse prediction, and planetary mean-motion. Lǐ’s own zhù 注 commentary supplies derivations and reconstructions of corrupted figures, working systematically from the algorithmic logic to identify and emend errors in the received text. The prefatory note (preserved in the source as KR3fc051_002.txt onwards) makes Lǐ’s editorial principle explicit: where the textual evidence allows, corrupted figures are emended and the emendation explained in the zhù; where the evidence does not allow emendation, the corrupted text is retained and flagged in the zhù — “of suspect [readings] the old text is retained; in the zhù it is brought out and discussed (證據者改而注之，疑者仍其舊文，於注甄發之).”

The work is part of Lǐ Ruì’s larger sequence of Hàn and Sòng calendrical reconstructions (KR3fc051–KR3fc055). Read together, these constitute the principal QiánJiā 乾嘉 evidential-mathematical recovery of the historical Chinese calendrical tradition — paralleling the recovery of the Jiǔzhāng 九章 and other ancient mathematical texts under Dài Zhèn 戴震 and the Sìkù 四庫 project.

Dating: composed during Lǐ Ruì’s mature productive period in 阮元 Ruǎn Yuán’s patronage circle. notBefore 1795 (early post-formation); notAfter 1817 (death year). Plausibly contemporaneous with the Chóurén zhuàn 疇人傳 work of 1797–1799 in which Lǐ supplied the technical-mathematical biographies; the calendrical reconstructions are the natural extension of that biographical project.

Translations and research

  • Cullen, Christopher. 2017. The Foundations of Celestial Reckoning: Three Ancient Chinese Astronomical Systems. London: Routledge. — Critical edition and English translation of the Sān-tǒng, Sì-fēn and Qián-xiàng systems; cites Lǐ Ruì throughout.
  • Sivin, Nathan. 1969. Cosmos and Computation in Early Chinese Mathematical Astronomy. Leiden: Brill.
  • Sivin, Nathan. 2009. Granting the Seasons: The Chinese Astronomical Reform of 1280. New York: Springer.
  • Wú Wénjùn 吳文俊, ed. 1985. Zhōng-guó shù-xué shǐ dà-xì 中國數學史大系, vol. 7 (covers Qīng calendrical reconstruction).

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