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致曲術/致曲圖解

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Text ID
KR3fc076
Date
1850–1864
Dynasty
清

Zhìqū shù / Zhìqū tújiě 致曲術 / 致曲圖解

Procedures for Curves / Geometric-Illustrative Exposition of Curves by 夏鸞翔 (撰)

About the work

夏鸞翔 Xià Luánxiáng’s (1823–1864) paired treatises on the geometry and computation of qū 曲 (“curves”) — specifically, the higher-order curves (conic sections, cycloids, and the like) that go beyond the classical Chinese mathematical problem-domain of straight lines, right triangles, and circles. The two titles (Zhìqū shù “procedural” and Zhìqū tújiě “illustrative”) are typically transmitted together as a 2-juàn unit; the catalog records them under the slash-combined title.

Abstract

The classical Chinese mathematical tradition treated the circle (in the húshǐ 弧矢 / arc-and-sagitta problem-domain) and the straight line systematically, but had no developed apparatus for the higher-order curves — the conic sections (ellipse, parabola, hyperbola), the cycloid, and the various special curves that arise in European seventeenth- and eighteenth-century mathematics. These curves entered Chinese mathematical literature through the Jesuit translations and the imperially-commissioned Lǜlì yuānyuán 律曆淵源 of 1722–1723, but received no systematic indigenous-tradition treatment until the mid-nineteenth century.

Xià Luánxiáng’s Zhìqū shù / Zhìqū tújiě is one of the first systematic indigenous-style treatments of the higher-order-curve problem-domain. The Zhìqū shù presents procedural-algebraic methods for the curves — equations of the curves expressed in indigenous tiānyuán 天元 (celestial-element) notation, and procedures for solving the standard problem-types (tangent at a point, area of a segment, arc-length, and so on). The Zhìqū tújiě presents the geometric-illustrative side, with diagrams and geometric-synthetic derivations.

The work shows the partial absorption of European-derived methods (in particular, the calculus-of-differences techniques and the conic-section properties from the Lǜlì yuānyuán tradition) into a framework that remains recognisably continuous with the indigenous Chinese mathematical tradition. Xià Luánxiáng’s contemporary correspondent 李善蘭 Lǐ Shànlán was at the same time engaged in directly translating European mathematical texts (Loomis’s Analytical Geometry, De Morgan’s Elements of Algebra) on the same general subject matter; the contrast between Xià’s indigenous-style treatment and Lǐ Shànlán’s translation-style treatment illustrates the two roads available to mid-nineteenth-century Chinese mathematics.

Dating: Xià Luánxiáng lived 1823–1864. notBefore 1850 (mature productive period); notAfter 1864 (death year).

Translations and research

  • Tián Miǎo 田淼. 2003. Zhōng-guó shù-xué de xī-huà lì-chéng 中國數學的西化歷程.
  • Horng, Wann-Sheng [洪萬生]. 1991. “Li Shanlan, the Impact of Western Mathematics in China during the Late 19th Century.” Ph.D. diss., City University of New York.
  • Wú Wénjùn 吳文俊, ed. 1985. Zhōng-guó shù-xué shǐ dà-xì 中國數學史大系, vol. 8.

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