Suànfǎ quánnéng jí 算法全能集
Comprehensive Collection of Mathematical Methods by 賈亨 (撰)
About the work
An early-Míng practical-mathematical compendium in 3 juàn by Jiǎ Hēng 賈亨, fl. c. 1373–1402. Drawn together from a wide range of YuánMíng practical-arithmetic primers, oriented toward abacus computation. The work belongs to the same intellectual lineage as the KR3fc013 Dīng Jù suànfǎ and KR3fc014 Xiángmíng suànfǎ.
Abstract
The Suànfǎ quánnéng jí is one of the key transitional documents between the Yuán practical-arithmetic primers (Dīng Jù, Ān Zhǐzhāi) and the mature Míng abacus-arithmetic tradition that would culminate in 程大位 Chéng Dàwèi’s KR3fc027 Suànfǎ tǒngzōng (1592). Its three juàn cover (1) the jiǔjiǔ multiplication-table system and the basic abacus-shortcut mnemonics; (2) the standard rules of three and false position, applied to commercial and taxation problems; (3) area-and-volume calculations, the right-triangle, and a small number of root-extraction problems.
Jiǎ Hēng’s work shows the suànpán (abacus) as the assumed computing instrument throughout: where the KR3f0032 Jiǔzhāng tradition had presented calculations in counting-rod terms, Jiǎ Hēng presents them in abacus-mnemonic terms, with the kǒujué (oral-formula) shortcut-mnemonics integrated into the body of each procedure. The shift in presentational style — from counting-rod to abacus — that had begun with the Dīng Jù suànfǎ (1355) and the Xiángmíng suànfǎ (1373) is in Jiǎ Hēng essentially complete.
The work is also a key documentary record of late-Yuán / early-Míng mathematical bibliography: Jiǎ Hēng’s source-citations preserve titles and partial contents of a number of Yuán mathematical primers that are otherwise lost. NotBefore and notAfter are bracketed by the catalog dynasty placement (early Míng) — between the 1373 Xiángmíng date and the end of the Jiànwén reign (1402), the latter being the conventional outer-bound for Jiǎ Hēng’s productive period.
Translations and research
- Lam Lay-Yong. 1986. “Linkages: Exploring the Similarities between the Chinese Rod Numeral System and Our Numeral System.” Archive for History of Exact Sciences 37: 365–392. — Discusses the rod-to-abacus transition.
- Wú Wénjùn 吳文俊, ed. 1985. Zhōng-guó shù-xué shǐ dà-xì 中國數學史大系, vol. 6. Beijing: Běi-jīng shī-fàn dà-xué chū-bǎn-shè.
- Martzloff, Jean-Claude. 1997. A History of Chinese Mathematics. Berlin: Springer.