Gǔsuàn yǎnlüè 古算衍略
Brief Elaboration of the Ancient Mathematical Methods by 梅文鼎 (撰)
About the work
A historical-mathematical treatise by 梅文鼎 Méi Wéndǐng (1633–1721) on the ancient Chinese mathematical methods, in 1 juàn. The catalog records “extent: 1633-1721” — Méi Wéndǐng’s lifedates entered as the extent field. The work is part of the Méi Wéndǐng corpus and is included in his collected Lìsuàn quánshū 歷算全書 (KR3f0026).
Abstract
The Gǔsuàn yǎnlüè is Méi Wéndǐng’s brief historical-systematic survey of pre-Sòng Chinese mathematical methods, addressing in compact form the methods of the KR3f0032 Jiǔzhāng suànshù tradition and its early commentarial development (Liú Huī, Lǐ Chúnfēng). The work belongs to the same intellectual project as Méi Wéndǐng’s longer treatments of specific topics (his Píngsānjiǎo jǔyú on plane trigonometry, his Húsānjiǎo jǔyú on spherical trigonometry, etc.) but in compressed form: rather than developing an exhaustive treatment of any single topic, the Gǔsuàn yǎnlüè surveys the principal procedures of the ancient mathematical canon and provides condensed exposition.
Méi Wéndǐng’s general historiographical position — the Xīfǎ Zhōngyuán 西法中源 (“Western methods originate from the East”) thesis that would become the standard high-Qīng position — is operative throughout. The work systematically identifies parallels between the indigenous Chinese methods of the Suànjīng shíshū canon and the European-derived methods imported through the Jesuit translations, arguing in each case that the indigenous Chinese formulation has chronological priority and that the European versions are refinements rather than novelties. The argument runs parallel to Méi Wéndǐng’s better-known and more systematic argument about the Zhōubì suànjīng and Greek astronomy.
The work is one of the principal documents of Méi Wéndǐng’s historiographical project — the systematic placement of the indigenous Chinese mathematical tradition within the unified Sino-European mathematical synthesis that he was constructing. Together with his bibliographic catalog Wù’ān lìsuàn shūjì (KR3f0028), it shows the encyclopedic scope of his engagement with the indigenous mathematical heritage.
Dating: NotBefore set at 1680 (allowing for Méi Wéndǐng’s mature productive period from the 1670s onward); notAfter at his death-year 1721.
For Méi Wéndǐng’s broader intellectual context — his rejection of official examination, the 1702 imperial encounter at Dézhōu, the publication of his collected works in 1726 — see the Person note at 梅文鼎.
Translations and research
- Jami, Catherine. 2011. The Emperor’s New Mathematics: Western Learning and Imperial Authority during the Kangxi Reign (1662–1722). Oxford: Oxford University Press. — Provides the standard Western-language treatment of Méi Wéndǐng’s project and the Xī-fǎ Zhōng-yuán thesis.
- Hé Bǐngyù 何丙郁 (John Hoe). 1973. “Mei Wending and Western Mathematics.” Chinese Studies in History 7.3.
- Hashimoto Keizō 橋本敬造. 1988. Hsü Kuang-ch’i and Astronomical Reform. Osaka: Kansai University Press.
- Bréard, Andrea. 2019. Nine Chapters on Mathematical Modernity. Cham: Springer.
- Liú Dùn 劉鈍. 1986. Méi Wéndǐng yǔ Zhōng-Xī shù-xué 梅文鼎与中西数学. Beijing.