Jiāo Xún 焦循
Style name Lǐtáng 理堂 (also written 里堂 Lǐtáng — the form used in the title of his collected mathematical works). Native of Gānquán 甘泉 (Yángzhōu prefecture, Jiāngsū). Born Qiánlóng 28 (1763); died Jiāqìng 25 (1820). CBDB id 29794 confirms the lifedates.
Jǔrén of Jiāqìng 6 (1801); did not advance to jìnshì. Spent his life in Yángzhōu, devoted to classical and mathematical scholarship; never held substantial official post. Studied with 阮元 Ruǎn Yuán in his youth and remained part of Ruǎn Yuán’s intellectual circle through Ruǎn Yuán’s official career. The defining intellectual figure of the Yángzhōu school of kǎozhèng evidential scholarship.
Polymath. His scholarly output spans:
(1) Classical philology: his Mèngzǐ zhèngyì 孟子正義 (the standard Qīng critical edition of the Mèngzǐ) and Yìxué sānshū 易學三書 (the Yì tōngshì, Yì zhāngjù, and Yìtú lüè — his three Book-of-Changes works) place him among the leading classical philologists of the QiánJiā era.
(2) Mathematical scholarship: the central focus of the present catalog. His mathematical works are collected as the Lǐtáng xuésuàn jì 里堂學算記 (KR3fc042), comprising:
- Jiājiǎn chéngchú shì 加減乘除釋 (KR3fc043) — Exposition of the four basic operations.
- Tiānyuányī shì 天元一釋 (KR3fc044) — Exposition of the tiānyuányī algebraic-equation method.
- Shìhú 釋弧 (KR3fc045) — Exposition of spherical-trigonometric arcs.
- Shìlún 釋輪 (KR3fc046) — Exposition of orbital cycles (planetary theory).
- Shìtuǒ 釋橢 (KR3fc047) — Exposition of ellipses.
- Kāifāng tōngshì 開方通釋 (KR3fc048) — General exposition of root extraction and equation-solving.
(3) Theatrical history: he is one of the principal pre-modern Chinese historiographers of zájù (Yuán theater) and kūnqǔ — his Jùshuō 劇說 is a fundamental source.
His mathematical project belongs to the Yáng-zhōu-circle SòngYuán recovery movement: alongside 張敦仁 Zhāng Dūnrén on the qiúyī method and 李銳 Lǐ Ruì on equation-theory, Jiāo Xún undertook the systematic exposition of the tiānyuányī algebraic-equation method. His exposition is methodologically distinctive: where Zhāng Dūnrén and Lǐ Ruì work primarily within the indigenous mathematical idiom, Jiāo Xún consistently brings the imported European jiègēnfāng (borrowed-root) method into the discussion, working out the precise correspondence between the two notational systems. The result is the most theoretically-developed Qīng-period treatment of the tiānyuányī method.
Jiāo Xún’s Shìhú / Shìlún / Shìtuǒ trio extends the program to spherical trigonometry and to ellipses (the latter newly relevant in the post-Kepler astronomy that the Jesuits had transmitted to China through the Lǐsuàn quánshū (KR3f0026) and the Lìxiàng kǎochéng (KR3f0018)). These works are among the earliest substantive Chinese-language treatments of conic sections.