Jígǔ suànjīng xìcǎo 緝古算經細草
Detailed Procedural Exposition of the Continuing-the-Ancients Mathematical Canon by 張敦仁 (細草)
About the work
Zhāng Dūnrén 張敦仁’s xìcǎo (detailed-procedure exposition) of 王孝通 Wáng Xiàotōng’s Táng Jígǔ suànjīng 緝古算經 (KR3f0040), the principal cubic-equation classic of pre-modern Chinese mathematics. Composed in the closing years of the eighteenth century or early Jiāqìng, parallel to but independent of 李潢 Lǐ Huáng’s KR3fc005 Jígǔ suànjīng kǎozhù. The catalog records the entry under the title Jígǔ suànjīng (the parent-text title); the KX edition reproduces the parent text with Zhāng’s interlinear and appended xìcǎo working.
Abstract
Zhāng Dūnrén 張敦仁 (1754–1834; CBDB id 80926) was among the principal mathematical philologists of the Jiā-Dào-period scholarly circle at Yángzhōu, working alongside 焦循 Jiāo Xún (1763–1820) and 李銳 Lǐ Ruì (1768–1817). His Qiúyī suànshù (KR3fc041) had recovered the procedural specifics of 秦九韶 Qín Jiǔsháo’s Dàyǎn qiúyī shù (the Chinese Remainder Theorem); the present xìcǎo extended the same recovery method to Wáng Xiàotōng’s cubic algorithms.
Zhāng’s exposition differs methodologically from Lǐ Huáng’s parallel project in two respects. First, Zhāng’s xìcǎo is more compact: rather than reconstructing every implicit geometric reduction and supplying full túshuō (figure-and-explanation), Zhāng concentrates on the numerical computation, presenting the cube-root extraction step-by-step in counting-rod or column-form notation. Second, where Lǐ Huáng tends to defer to the received text and emend only where the procedure-logic forces it, Zhāng more readily proposes textual corrections based on his own computational reconstruction.
The two Qīng Jígǔ expositions are conventionally read together: Lǐ Huáng for the geometric reduction and Zhāng Dūnrén for the computational xìcǎo. Together they made Wáng Xiàotōng’s cubic methods fully accessible to mid-Qīng working mathematicians for the first time since the late Sòng. The work is also cited under the variant title Jígǔ suànjīng xìcǎo 緝古算經細草 in the bibliographies. Liú Héng 劉衡 (KR3fc007) subsequently added a bǔzhù 補注 to the work, extending Zhāng’s reconstructions.
The catalog records the work without specified juàn count; the KX-imprint preserves it as 1 juàn. NotBefore is set conservatively at 1800 (allowing for the work to have been completed in the same decade as the Qiúyī suànshù); notAfter at Zhāng’s death-year 1834.
Translations and research
- Wú Wénjùn 吳文俊, ed. 1985. Zhōng-guó shù-xué shǐ dà-xì 中國數學史大系, vol. 7. Beijing: Běijīng shī-fàn dà-xué chū-bǎn-shè. — Standard reference; treats Zhāng’s xì-cǎo in the context of late-Qīng Sòng-Yuán mathematical recovery.
- Martzloff, Jean-Claude. 1997. A History of Chinese Mathematics. Berlin: Springer. — Notes Zhāng’s role in the Yáng-zhōu mathematical circle.
Links
- Parent text: KR3f0040 Jígǔ suànjīng
- Companion exposition: KR3fc005 Jígǔ suànjīng kǎozhù (Lǐ Huáng)
- Subsequent extension: KR3fc007 Jígǔ suànjīng bǔzhù (Liú Héng)
- CBDB: https://cbdb.fas.harvard.edu/cbdbapi/person.php?id=80926