Jígǔ suànjīng bǔzhù 緝古算經補注
Supplementary Annotation to the Continuing-the-Ancients Mathematical Canon by 劉衡 (撰)
About the work
Liú Héng 劉衡’s (1776–1841; CBDB id 74864) supplementary annotation to 王孝通 Wáng Xiàotōng’s Jígǔ suànjīng (KR3f0040), extending and correcting the xìcǎo and kǎozhù projects of his immediate predecessors 張敦仁 Zhāng Dūnrén (KR3fc006) and 李潢 Lǐ Huáng (KR3fc005). The catalog’s title — provisionally prefixed with a question-mark (?輯古算經補注) — reflects an editorial uncertainty about the exact transmitted title; the work is consistently cited in the late-Qīng mathematical bibliographies as Jígǔ suànjīng bǔzhù. The catalog dynasty (清) and lifedates (1776–1841) match CBDB record 74864.
Abstract
The work falls in the third generation of Qīng Jígǔ exposition. The first generation (Lǐ Huáng, Zhāng Dūnrén) had completed the basic recovery of Wáng Xiàotōng’s cubic-equation procedures; the second (Lǐ Ruì’s circle, mostly preserved only in collected-works fragments) had cross-checked these against the parallel SòngYuán algebraic methods being recovered at the same time. Liú Héng’s bǔzhù belongs to the synthesizing third generation that put the cubic-equation procedures into dialog with the European-derived jiègēnfāng 借根方 method, which Liú Héng had himself expounded in his KR3fc066 Jiègēnfāngfǎ qiǎnshuō.
Liú’s annotations cover the same twenty problems treated by the predecessors, but with a sharper focus on (a) the technical correctness of the cube-root extraction at each step (where Liú occasionally emends the working as preserved in Lǐ Huáng’s exposition); (b) the comparison of Wáng Xiàotōng’s geometric reduction to a cubic with the equivalent jiègēnfāng algebraic setup; and (c) supplementary problems and variations of his own devising that test the limits of Wáng Xiàotōng’s procedural methods.
The work is one piece of a substantial corpus by Liú Héng preserved in the KR3fc series (see his Person note for the full list); together these establish him as one of the principal independent mathematical voices of the mid-Dào-guāng era, working both in the indigenous SòngYuán algebra and the imported European algebra and seeking the systematic translation between the two.
NotBefore is set conservatively at 1820 (Liú’s earliest documented mathematical productivity); notAfter at his death in 1841.
Translations and research
No substantial English-language secondary literature located on Liú Héng’s mathematical œuvre specifically. For the general Qīng Jí-gǔ exposition see the references at KR3fc005.
- 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. — Includes brief discussion of Liú Héng in the survey of mid-Qīng provincial mathematicians.