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新編四元玉鑒

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Text ID
KR3fc018
Date
1830–1839
Dynasty
清

Xīnbiān sìyuán yùjiàn 新編四元玉鑒

Newly-Edited Jade Mirror of the Four Origins by 朱世傑 (撰) — original; with detailed-procedure exposition (細草) by 羅士琳 (撰)

About the work

羅士琳 Luó Shìlín’s Xīnbiān sìyuán yùjiàn in 8 juàn is the principal Dào-guāng-era recovery commentary on 朱世傑 Zhū Shìjié’s KR3fc017 Sìyuán yùjiàn — the foundational SòngYuán four-unknown algebra. The work belongs to the Yíjiātáng 宜稼堂 cóngshū compilation of 1839. The catalog records the entry under the title Xīnbiān sìyuán yùjiàn (Newly-Edited Jade Mirror) — Luó Shìlín’s preferred title for his annotated re-edition.

Abstract

The recovery of the Sìyuán yùjiàn in the early Dàoguāng decades is one of the major late-Qīng mathematical-philological achievements. The sìyuán shù (four-unknown method) had been forgotten in China from the early Míng — 顧應祥 Gù Yìngxiáng’s mid-16th-century commentary on the simpler 李冶 Lǐ Yě Cèyuán hǎijìng had already had to remove the tiānyuányī (one-unknown) sections because he could not understand them (KR3f0043) — and the entire SòngYuán algebraic tradition had been replaced by the European-derived jiègēnfāng 借根方 method imported under the Kāngxī court. The first stirrings of recovery had come with Méi Juéchéng’s 梅㲄成 identification of tiānyuányī with European jiègēnfāng in the early 18th century (the foundational statement of the Xīfǎ Zhōngyuán “Western Method, Chinese Origin” thesis applied to algebra); but the sìyuán method specifically remained inaccessible until Luó Shìlín and 沈欽裴 Shěn Qīnpéi independently took up the recovery in the 1820s.

Luó Shìlín’s xìcǎo (detailed procedural exposition) supplies, problem by problem, the implicit computational working of Zhū Shìjié’s sìyuán operations — which Zhū Shìjié had presented in his original schematic counting-rod-grid form, accessible to his immediate students but opaque to later readers. Luó systematically reconstructs (a) the polynomial-expression notation in the tiān / dì / rén / wù grid; (b) the multiplication and addition operations on grid-arrangements; (c) the elimination procedure (xiāofǎ 消法) for reducing a four-variable system to a single-variable equation; (d) the cube-root and higher-root extractions required by the reduced equations. The result is a complete restored procedural-mathematical text of the Sìyuán yùjiàn, intelligible to a mid-Qīng working mathematician trained in the jiègēnfāng tradition.

A second methodological contribution: Luó systematically compares the sìyuán method to its European algebraic equivalent. Where Zhū Shìjié’s elimination procedure reduces a four-variable system, Luó shows by parallel computation that the jiègēnfāng method reaches the identical reduced equation through different notational manipulations. The comparison is the principal mid-Qīng demonstration of the substantive equivalence of indigenous and imported algebra, and is the foundational source for the late-19th-century synthesis that 李善蘭 Lǐ Shànlán would consolidate.

The catalog records Luó Shìlín’s Xīnbiān sìyuán yùjiàn in 8 juàn, the standard division for the published Yíjiātáng cóngshū edition. NotBefore is set at 1830 (allowing for the work’s preparation in the late 1820s); notAfter at the 1839 published date.

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. — The standard Western-language treatment; uses Luó Shìlín’s xì-cǎo throughout.
  • Hé Bǐngyù 何丙郁 (John Hoe). 2008. The Jade Mirror of the Four Unknowns by Zhu Shijie. New Zealand: Mingming Bookroom.
  • 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. — Treats the Luó Shìlín / Shěn Qīnpéi recovery in detail.
  • Martzloff, Jean-Claude. 1997. A History of Chinese Mathematics. Berlin: Springer.

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