Tuībù fǎ jiě 推步法解
Explanation of the Methods of Step-by-Step Astronomical Computation by 江永 (撰)
About the work
The Tuībù fǎ jiě is a six-juǎn mid-Qīng astronomical-computational treatise by 江永 Jiāng Yǒng (1681–1762), a founding figure of the Wǎnpài 皖派 (“Anhui school”) of kǎozhèng 考證. The title tuībù 推步 (“pushing forward and stepping through”) is the canonical term for the chain of calculations by which a calendar-maker derives ephemeris-data (solar / lunar / planetary positions, eclipse predictions, equation-of-time) from observational parameters; the fǎjiě 法解 (“methods explained”) signals a pedagogical treatise that takes each tuībù procedure of the Lǐxiàng kǎochéng 曆象考成 (1724) — the canonical Qīng calendrical textbook compiled by 何國宗, 梅瑴成 and others under 康熙 — and explains it step by step, with derivation and worked example.
Abstract
Composition window: Jiāng’s mature scholarly years, c. 1730–1762. He was the principal mid-eighteenth-century critical extender of Méi Wéndǐng 梅文鼎’s earlier synthesis of Chinese and Western (Jesuit-Tychonic) astronomical mathematics. The Tuībù fǎ jiě belongs to the same scholarly project as his more famous Shùxué 數學 (KR3f0031) — both work systematically through the apparatus of the imperial Lǐxiàng kǎochéng (1724) and the supplementary Lǐxiàng kǎochéng hòubiān (1742), reducing the imperial textbook to a teachable derivation.
The six-juǎn structure covers: (a) jièshǔ 解術 — geometric foundations including the spherical-triangle apparatus newly imported with Jesuit trigonometria; (b) solar-motion theory and the equation-of-centre; (c) lunar-motion theory including the evection and variation terms imported through the Lǐxiàng kǎochéng hòubiān (which Jiāng describes as the most important imperial addition to astronomical theory in the Qiánlóng reign); (d) eclipse-prediction calculation; (e) planetary theory in the Tychonic-Keplerian frame as transmitted in the Hòubiān; (f) the qīzhèng / èrshíbāxiù coordinate-conversion procedures. The work was studied in the Anhui school by Jiāng’s student Dài Zhèn 戴震 and by 梅瑴成 in Beijing, and via Dài entered the QiánJiā 乾嘉 mathematical mainstream.
The Tuībù fǎ jiě is preserved in Jiāng’s collected works (Jǐnshuǐ jí 近水集 supplementary fascicles), in the Sìkù wèishōu shū jíkān, and in the Zhōngguó kēxué jìshù diǎnjí tōnghuì (refid KX03-07-021).
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. — sets out the Lǐ-xiàng kǎochéng and Hòu-biān apparatus that Jiāng explicates.
- Han Qi 韓琦 1999. “Astronomy, Chinese and Western: The Influence of Xu Guangqi’s Views in the Early and Mid-Qing Period.” Statecraft and Intellectual Renewal in Late Ming China.
- 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.
- Martzloff, Jean-Claude. 1997. A History of Chinese Mathematics. Berlin: Springer. §3 on Qīng mathematics treats Jiāng among the Wǎn-pài.