Lǐtáng xuésuàn jì 里堂學算記
Record of Mathematical Studies from the Lǐ-táng Studio by 焦循 (撰)
About the work
焦循 Jiāo Xún’s collected mathematical works, transmitted under the studio-name Lǐtáng 里堂. The collection comprises six independent monographs (the catalog records this entry at 1 juàn — apparently the introductory or programmatic piece for the collection):
- Jiājiǎn chéngchú shì 加減乘除釋 (KR3fc043) in 9 juàn — the four basic operations
- Tiānyuányī shì 天元一釋 (KR3fc044) in 3 juàn — the tiānyuányī algebraic-equation method
- Shìhú 釋弧 (KR3fc045) in 4 juàn — spherical trigonometry (arcs)
- Shìlún 釋輪 (KR3fc046) in 3 juàn — orbital cycles (planetary theory)
- Shìtuǒ 釋橢 (KR3fc047) in 2 juàn — ellipses
- Kāifāng tōngshì 開方通釋 (KR3fc048) in 2 juàn — root extraction and equation-solving
The collection — the Lǐtáng xuésuàn jì proper — provides Jiāo Xún’s programmatic statement of his mathematical project, with prefaces, table of contents, and the broader methodological framing of the six constituent works.
Abstract
The Lǐtáng xuésuàn jì is the principal Yáng-zhōu-circle mathematical production of the Jiāqìng era, alongside 張敦仁 Zhāng Dūnrén’s KR3fc041 Qiúyī suànshù and 李銳 Lǐ Ruì’s equation-theory works. Where Zhāng Dūnrén focused on the Dàyǎn qiúyī shù (Chinese Remainder Theorem) and Lǐ Ruì on equation-theory specifically, Jiāo Xún’s project covers the broadest substantive range: from the elementary arithmetic operations (Jiājiǎn chéngchú shì) through the indigenous tiānyuányī algebraic-equation method (Tiānyuányī shì) to the imported Euclidean-spherical-trigonometric content (Shìhú, Shìlún, Shìtuǒ) and the general theory of equation-solving (Kāifāng tōngshì).
The methodological signature of Jiāo Xún’s project is its programmatic integration of indigenous and imported mathematics. His treatment of the tiānyuányī method consistently brings the imported European jiègēnfāng (borrowed-root) algebraic notation into the discussion, working out the precise correspondence between the two notational systems. His treatment of spherical trigonometry (in Shìhú) similarly brings the indigenous Chinese gēyuán circle-cutting methodology into dialogue with the imported Jesuit-translated trigonometric methods. The result is the most theoretically-developed Qīng-period treatment of these topics in any single integrated corpus.
For Jiāo Xún’s biographical and intellectual context — his jǔrén of 1801, his Yángzhōu intellectual circle, his classical-philological and theatrical-historical productions — see the Person note at 焦循.
Dating: the collected Lǐtáng xuésuàn jì was assembled in the closing decade of Jiāo Xún’s life; the individual works composed across his entire productive period from c. 1797 onward. NotBefore 1797 (the earliest documented work of the collection); notAfter his death year 1820.
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. — Treats Jiāo Xún’s tiān-yuán-yī exposition.
- Elman, Benjamin A. 1984. From Philosophy to Philology. Cambridge, Mass.: Council on East Asian Studies, Harvard University. — Treats Jiāo Xún’s intellectual context.
- Wú Wénjùn 吳文俊, ed. 1985. Zhōng-guó shù-xué shǐ dà-xì 中國數學史大系, vol. 7.
- Bréard, Andrea. 1999. Re-Kreation eines mathematischen Konzepts im chinesischen Diskurs. Stuttgart: Steiner.
- Lǐ Zhàohuá 李兆華. 2001. “Jiāo Xún de shù-xué chéngjiù” 焦循的数学成就. Zhōng-guó shǐ yán-jiū 中国史研究.