Tiānyuán lìlǐ quánshū 天元歷理全書
Complete Book of the Algebra and Theory of the Calendar by 徐發 (撰)
About the work
The Tiānyuán lìlǐ quánshū is a fifteen-juǎn early-Qīng monograph by 徐發 Xú Fā (hào Nánhú Pǔrén 南湖圃人), of Jiāxīng 嘉興 in Zhèjiāng, on the theoretical foundations and computational techniques of calendar-making. The title combines tiānyuán 天元 — the standard term for “celestial element” algebra developed by 李冶 Lǐ Yě (1248) and 朱世傑 Zhū Shìjié (1303) — with lìlǐ 歷理 (“theory of the calendar”) and quánshū 全書 (“complete book”). The combination signals that this is a synthesis treatise: it puts the Yuán-tradition algebraic techniques to work on the calendrical apparatus of the Schall-Verbiest Xīyáng xīnfǎ lìshū and the Shòushí lì substratum.
Abstract
Xú Fā is best known to the Buddhist canon as the lay-Buddhist author of the Jīngāng jīng yǐngshuō 金剛經郢說 (KR6c0076, dated Kāngxī 12 = 1673). The combination of Vajracchedikā exegesis with calendrical mathematics is characteristic of the kǎozhèng-inflected early-Qīng Jiāxīng intellectual milieu, in which laymen pursued Buddhist text-critical work alongside Western-influenced suànxué in the same career. The composition window of the Tiānyuán adopted here (1673 — the dated Jīngāng preface — to 1700) corresponds to Xú’s mature scholarly period.
The work is in fifteen juǎn. From its size and the (partial) modern descriptions it covers: (a) the cosmological and theoretical frame, including the tàijí and qì tradition reinterpreted in the light of Jesuit astronomy; (b) the geometry of the celestial sphere and the ecliptic / equator reduction; (c) the standard chain of calendar-making calculations — solar and lunar mean motion, the equation of centre, the lunar nodes, eclipse prediction; (d) planetary theory in the Tychonic frame; (e) the algebra-and-tabulation of intermediate quantities using tiānyuán notation; (f) extensive worked examples. It is comparable in scope to Méi Wéndǐng 梅文鼎’s Lìsuàn quánshū 曆算全書 (the great Anhui Qing-Confucian synthesis of Western and Chinese astronomical mathematics), with which it is roughly contemporary; Méi’s work however reached imperial publication and Xú’s did not.
The work is preserved in private Qīng libraries, in the Sìkù wèishōu shū jíkān, and is reprinted in the Zhōngguó kēxué jìshù diǎnjí tōnghuì (refid KX03-07-020). It is consulted by modern historians (Catherine Jami, Han Qi) as an important regional witness to the early-Qīng synthesis of Yuán-Chinese algebra with Jesuit-Tychonic astronomy.
Translations and research
No substantial Western-language translation located.
- Jami, Catherine. 2012. The Emperor’s New Mathematics: Western Learning and Imperial Authority during the Kangxi Reign (1662–1722). Oxford: OUP. — the standard recent treatment of Kāng-xī-era mathematical-astronomical synthesis.
- Martzloff, Jean-Claude. 1997. A History of Chinese Mathematics. Berlin: Springer. — chapter on early-Qīng synthesis treats tiān-yuán technique and its Jesuit-era revival.
- Mei Rongzhao 梅榮照 (ed.). 1991. Méi Wéndǐng yǔ Zhōngguó zǎoqī shùxué shǐ 梅文鼎與中國早期數學史. Beijing: Kēxué chūbǎnshè.