Shìlún 釋輪
Exposition of Wheels (Orbital Cycles) by 焦循 (撰)
About the work
焦循 Jiāo Xún’s monograph on the epicyclic / orbital-cycle methodology of pre-Keplerian astronomical theory, in 3 juàn. Part of the collected Lǐtáng xuésuàn jì (KR3fc042).
Abstract
The Shìlún treats the lún 輪 (“wheels”) — i.e., the epicycles and deferent-circles of the Ptolemaic-Tychonic geo-centric planetary theory that the Jesuits had transmitted to China through the late-Míng / early-Qīng Lìxiàng kǎochéng (KR3f0018) project. Although the Keplerian elliptical-orbit theory had been transmitted to China in fragmentary form in the eighteenth century (and would receive systematic treatment in Jiāo Xún’s companion KR3fc047 Shìtuǒ), the working framework of Qīng-era astronomical practice was still the Ptolemaic-Tychonic epicyclic system.
The work’s three juàn:
(1) The foundational geometry of epicycles: the jūnlún 均輪 (uniform-motion wheel), the zhènglún 正輪 (deferent), the cìlún 次輪 (epicycle), and the fǔlún 副輪 (auxiliary circle). The systematic procedure for combining these to produce the apparent motion of a planet.
(2) The application to specific planetary motions: the sun (with its xīnchā 心差 eccentric-deferent), the moon (with its more complex secondary epicycles), and the five visible planets (with their direct and retrograde motions explained by the epicycle-deferent combination).
(3) Computational procedures: the systematic computation of planetary positions for any date, with worked examples drawn from the imperial astronomical procedures.
The work is one of the principal Qián-Jiā-era systematic Chinese-language expositions of pre-Keplerian planetary theory. Although by Jiāo Xún’s lifetime the European astronomical mainstream had moved decisively beyond the epicyclic framework, the framework was still the working system of the Chinese Bureau of Astronomy and remained intellectually live in Qīng astronomical practice. Jiāo Xún’s exposition is therefore both a working reference for contemporary practice and a critical-historical treatment of the imported astronomical theory.
For Jiāo Xún’s broader project see KR3fc042.
Dating: bracketed by Jiāo Xún’s productive period 1797–1820.
Translations and research
- Hashimoto Keizō 橋本敬造. 1988. Hsü Kuang-ch’i and Astronomical Reform. Osaka: Kansai University Press. — Provides the context of the Tychonic-epicyclic transmission.
- Jami, Catherine. 2011. The Emperor’s New Mathematics. Oxford: Oxford University Press.
- Sivin, Nathan. 2009. Granting the Seasons. New York: Springer. — Treats the planetary-motion problem in the broader pre-modern Chinese astronomical tradition.
- Wú Wénjùn 吳文俊, ed. 1985. Zhōng-guó shù-xué shǐ dà-xì 中國數學史大系, vol. 7.