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九章算術細草圖說

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Text ID
KR3fc002
Date
1800–1820
Dynasty
清

Jiǔzhāng suànshù xìcǎo túshuō 九章算術細草圖說

Detailed Procedure and Diagrammatic Exposition of the Nine Chapters on the Mathematical Art by 李潢 (撰), 沈欽裴 (校訂)

About the work

A complete Qīng-period detailed-procedure-and-diagrammatic exposition of the KR3f0032 Jiǔzhāng suànshù — the foundational pre-modern Chinese mathematical classic — by Lǐ Huáng 李潢 (d. 1811), worked through problem-by-problem and procedure-by-procedure in 11 juàn. The work was incomplete at Lǐ’s death and was put through final editing and publication around 1820 by his student Shěn Qīnpéi 沈欽裴 (沈欽裴). It is the principal Qián-Jiā-period scholarly exposition of the Jiǔzhāng and remained the standard reference work for working through the procedural details of the classic down to the modern critical editions.

Abstract

Lǐ Huáng’s project belongs to the high QiánJiā evidential-scholarship (kǎozhèng 考證) recovery of the Suànjīng shíshū 算經十書 (Ten Mathematical Classics). His twin convictions, exemplified across this work and its sister pieces KR3fc003 Hǎidǎo suànjīng xìcǎo túshuō and KR3fc005 Jígǔ suànjīng kǎozhù, were (a) that the surviving classical mathematical texts had been corrupted in transmission to the point that their procedural logic was no longer recoverable by surface-reading alone, and (b) that the only scholarly path of recovery was a full step-by-step reconstruction in which every implicit operation was made explicit and the geometric figures underlying every area-and-volume decomposition were re-drawn. The work therefore presents, for each of the 246 problems of the Jiǔzhāng, a xìcǎo 細草 (detailed working) of the procedure as Liú Huī had implicitly stated it, accompanied by túshuō 圖說 (figure-and-explanation) reconstructing the geometric demonstration.

The work’s principal scholarly contribution beyond exposition was Lǐ’s textual-emendation programme, which he applied conservatively but consistently: corruption was diagnosed only where the implicit procedural logic of Liú Huī’s commentary or the Hǎidǎo could not be reconciled with the received character-readings. Lǐ’s emendations to the Shānggōng 商功 (Construction-Computations) and Fāngchéng 方程 (Rectangular Arrays) chapters in particular were widely accepted by subsequent scholars, including the Sìkù editors who had earlier had to work without the benefit of his close procedural analysis. Lǐ Huáng’s jìnshì of Qiánlóng 36 (1771) and his ultimately reaching the office of Gōngbù shàngshū 工部尚書 (President of the Board of Works) before his death in 1811 (CBDB id 59341 confirms the death year; the birth year is not securely recorded) place the work’s composition in the closing decade of his life — notBefore 1800, notAfter his death year 1811, with the final published form (after Shěn Qīnpéi’s editing) appearing c. 1820.

The work was published together with the Hǎidǎo suànjīng xìcǎo túshuō and the Jígǔ suànjīng kǎozhù as a triad covering the three principal procedural classics of the Suànjīng shíshū. It was repeatedly reprinted in the late Qīng, including in the Gǔjīn suànxué cóngshū 古今算學叢書 (Liú Duó 劉鐸, 1898), through which it entered the standard reference shelf of modern Chinese mathematical historians.

Translations and research

  • Horng Wann-Sheng 洪萬生. 1991. “Lǐ Huáng Jiǔ-zhāng suàn-shù xì-cǎo tú-shuō shù-xué chéng-jiù chū-tàn” 李潢《九章算術細草圖說》數學成就初探. HPM Tōngxùn 通訊 (Taiwan). — Standard Chinese-language scholarly assessment of Lǐ’s mathematical contributions.
  • Martzloff, Jean-Claude. 1997. A History of Chinese Mathematics. Berlin: Springer. — Includes discussion of Lǐ Huáng’s Jiǔ-zhāng exposition in the context of Qián-Jiā mathematical philology.
  • Guo Shuchun 郭書春. 1990. Gǔ-dài shì-jiè shù-xué tài-dǒu Liú Huī 古代世界數學泰斗劉徽. Jǐ-nán: Shān-dōng kē-xué jì-shù chū-bǎn-shè. — Treats Lǐ Huáng’s emendations and procedural reconstructions in detail.

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