Sìyuán yùjiàn xìcǎo 四元玉鑑細草
Detailed Procedural Exposition of the Jade Mirror of the Four Origins by 沈欽裴 (細草)
About the work
沈欽裴 Shěn Qīnpéi’s parallel detailed-procedure exposition of 朱世傑 Zhū Shìjié’s Sìyuán yùjiàn (KR3fc017), produced independently of 羅士琳 Luó Shìlín’s parallel project (KR3fc018) in the same Dàoguāng decade. The catalog records the extent as 2 juàn, reflecting that the work survives only in partial form — Shěn Qīnpéi worked through only the first three chapters of the Sìyuán yùjiàn before Luó Shìlín’s complete xìcǎo appeared in 1839, after which Shěn’s project was effectively superseded.
Abstract
沈欽裴 Shěn Qīnpéi (the student of 李潢 Lǐ Huáng; also responsible for putting Lǐ’s KR3fc002 Jiǔzhāng and KR3fc003 Hǎidǎo expositions through final editing) began work on the Sìyuán yùjiàn in the 1820s, when a Korean recension of the work first became available to the Yángzhōu mathematical circle. Working in parallel with 羅士琳 Luó Shìlín, Shěn Qīnpéi independently developed a xìcǎo on the principal early chapters of the Sìyuán yùjiàn — Gǔfǎ qīchéngfāng tú (the binomial-coefficient triangle), the tiānyuányī introductory problems, and the first cluster of èryuán (two-unknown) problems.
The relationship between Shěn Qīnpéi’s and Luó Shìlín’s parallel projects is one of the most interesting collaborative scholarly relationships in the late-Qīng mathematical record. The two scholars exchanged drafts and discussed methodological points; some of Luó Shìlín’s published expositions incorporate corrections or refinements suggested by Shěn Qīnpéi (and vice versa). But the two scholars produced distinct published works: Luó Shìlín’s complete Xīnbiān sìyuán yùjiàn (KR3fc018, 1839) covers all 288 problems in 8 juàn; Shěn Qīnpéi’s Sìyuán yùjiàn xìcǎo covers only the initial chapters in 2 juàn.
The partial coverage of Shěn’s work means that for the sìyuán shù (four-unknown method) proper — the most mathematically advanced material of the Sìyuán yùjiàn, beginning only in the work’s later chapters — the standard scholarly reference is Luó Shìlín’s exposition rather than Shěn’s. But for the foundational early material (the binomial triangle, the one- and two-unknown methods) Shěn Qīnpéi’s exposition is preferred by some modern scholars (e.g. Hé Bǐngyù 1977) for its closer adherence to Zhū Shìjié’s original notational style.
Dating: notBefore set at 1820 (the earliest plausible start of Shěn’s work, given Lǐ Huáng died in 1811 and Shěn’s Jiǔzhāng / Hǎidǎo / Jígǔ editing was complete by c. 1820); notAfter at 1839 when Luó Shìlín’s complete xìcǎo appeared.
Translations and research
- Hé Bǐngyù 何丙郁 (John Hoe). 1977. Les systèmes d’équations polynomes dans le Siyuan yujian (1303). Paris: Collège de France. — Discusses both Shěn Qīnpéi’s and Luó Shìlín’s recovery commentaries.
- Wú Wénjùn 吳文俊, ed. 1985. Zhōng-guó shù-xué shǐ dà-xì 中國數學史大系, vol. 6. Beijing: Běi-jīng shī-fàn dà-xué chū-bǎn-shè.
- Bréard, Andrea. 1999. Re-Kreation eines mathematischen Konzepts im chinesischen Diskurs. Stuttgart: Steiner.