Suànhǎi xiángshuō 算海詳說
Detailed Exposition of the Sea of Mathematics by 李長茂 (撰)
About the work
李長茂 Lǐ Chángmào’s early-Qīng practical-arithmetic compendium in 11 juàn, in the lineage of 程大位 Chéng Dàwèi’s KR3fc027 Suànfǎ tǒngzōng (1592). The work serves the early-Qīng merchant-apprentice and elementary-school audience, providing a comprehensive but accessible treatment of the standard arithmetic curriculum.
Abstract
The work belongs to the popular-mathematical genre of the late-Kāng-xī / early-Yōng-zhèng era, parallel to but more elementary than the imperially-sponsored Shùlǐ jīngyùn 數理精蘊 (1722) and the more theoretically-sophisticated productions of the Méngyǎng zhāi mathematicians. Lǐ Chángmào’s title Suànhǎi (Sea of Mathematics) emphasizes the encyclopedic-reference character of the work, xiángshuō (Detailed Exposition) emphasizes its pedagogical mission.
The eleven juàn cover the standard topical sequence inherited from the KR3fc027 Tǒngzōng tradition: (1–2) basic abacus arithmetic and the multiplication-division mnemonics; (3–6) the rules of three and false position, applied to commercial calculation; (7–9) area-and-volume calculations and the right-triangle; (10) root extraction; (11) a closing miscellany of “curious” problems including indeterminate-equation and recreational mathematics.
The work’s principal substantive innovation beyond the Tǒngzōng lineage is the integration of selected European-derived mathematical content from the post-1607 Jesuit-translation corpus. Lǐ Chángmào incorporates the proportional-divider (bǐlìguī) procedures from the Aleni 1630 translation, the basic Euclidean-geometric foundations from Ricci/Xú Guāngqǐ’s Jǐhé yuánběn, and some elements of the jiègēnfāng (borrowed-root algebraic) method newly introduced under the Kāngxī court. The integration is at the elementary-pedagogical level rather than the theoretical level; Lǐ Chángmào’s intended audience is the working merchant rather than the imperial mathematician.
The work was repeatedly reprinted in the eighteenth century and served as the principal practical-arithmetic textbook in many provincial schools through the mid-Qīng. It is one of the better documentary records of the level of elementary-mathematical instruction in the early-Qīng provincial-merchant environment.
Dating: NotBefore set conservatively at 1690 (late-Kāng-xī productive period for Lǐ Chángmào); notAfter at 1730 (mid-Yōng-zhèng), the outer-bound for the work’s plausible composition.
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 Kāng-xī-imperial mathematical-cultural context in which Lǐ Chángmào’s popular-mathematical work appeared.
- 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. 7. Beijing: Běi-jīng shī-fàn dà-xué chū-bǎn-shè.
Links
- Predecessor: KR3fc027 Suànfǎ tǒngzōng (Chéng Dàwèi)
- Contemporary high-level counterpart: Shùlǐ jīngyùn (imperial commission, 1722)