Dùcè 度測
Surveying-and-Measurement by 陳藎謨 (撰)
About the work
陳藎謨 Chén Jìnmó’s principal late-Míng surveying treatise in 6 juàn, integrating imported European instrument-based methods with the indigenous gōugǔ (right-triangle) survey tradition. Composed in the closing decades of the Míng (Tiānqǐ / Chóngzhēn era), in the immediate aftermath of the Jesuit-translation period.
Abstract
The Dùcè belongs to the lower-Yangzi independent tradition of late-Míng mathematical scholarship — distinct from the Beijing-based Jesuit-collaborator circle of 徐光啟 Xú Guāngqǐ and 李之藻 Lǐ Zhīzǎo, but engaging substantively with the same imported European mathematical-instrumental content. Chén Jìnmó’s principal interest is in the proportional-divider (the bǐlìguī 比例規 — the Galilean compasso proporzionale translated into Chinese by Giulio Aleni in the Bǐlìguī jiě 比例規解 of 1630), a survey-and-engineering instrument that allowed proportional scaling of distances and angles by a graduated pair of jointed legs.
The work’s six juàn cover:
(1) Basic gōugǔ relations and their applications to surveying — the indigenous Chinese remote-sensing tradition deriving from 劉徽 Liú Huī’s Hǎidǎo and KR3f0032 Jiǔzhāng chapter 9.
(2) The proportional-divider instrument: its construction, its graduation system, and the procedures for using it to scale measurements.
(3) Combined indigenous + European procedures: surveying problems solved by both the traditional chóngchā (double-difference) sighting method and the European proportional-divider method, with comparison of results.
(4–5) Applied surveying problems: heights and distances, areas of irregular figures, depth of wells and ravines, position of distant objects.
(6) Astronomical applications: solar altitude, latitude determination, and the related practical instruments.
The work is one of the principal late-Míng integrative treatments of indigenous and European surveying mathematics, providing a working synthesis distinct from but parallel to Xú Guāngqǐ’s more theoretically-oriented Gōugǔ yì (KR3fc026). The Dùcè was widely cited in early-Qīng practical-mathematical writing (notably by 梅文鼎 Méi Wéndǐng).
Dating: NotBefore set at 1620 (allowing for early productive period after the 1607 Euclid translation and the 1630 Bǐlìguī jiě — though Chén Jìnmó’s specific source for the proportional-divider may pre-date the published Aleni translation); notAfter at 1650, allowing for late-Chóng-zhēn / early-Shùn-zhì productivity.
Translations and research
- Engelfriet, Peter M. 1998. Euclid in China. Leiden: Brill.
- Jami, Catherine. 2011. The Emperor’s New Mathematics. Oxford: Oxford University Press. — Treats the proportional-divider in the imperial mathematical curriculum.
- 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.
- Wú Wénjùn 吳文俊, ed. 1985. Zhōng-guó shù-xué shǐ dà-xì 中國數學史大系, vol. 6.