Suànfǎ 算法
Mathematical Methods by 楊輝 (編)
About the work
A brief mathematical compendium in 1 juàn attributed in the catalog to 楊輝 Yáng Huī. The work’s bibliographic identification is uncertain: under the bare title Suànfǎ 算法 it could plausibly refer to (a) Yáng Huī’s Rìyòng suànfǎ 日用算法 of 1262 — a daily-use computational primer cited by later YuánMíng mathematical works but otherwise transmitted only in fragments — or (b) an abridged or alternative title for one of the constituent works of KR3fc010 Yáng Huī suànfǎ. The single-juàn extent and the Sòng-dynasty placement match the Rìyòng suànfǎ most closely.
Abstract
The Rìyòng suànfǎ 日用算法 (1262), as cited in the YuánMíng bibliographic literature, was the second of Yáng Huī’s mathematical works — a daily-use computational primer occupying a middle position between his more substantive Xiángjiě jiǔzhāng (KR3fc011, 1261) and the later compendium Yáng Huī suànfǎ (KR3fc010, 1274–75). It systematized elementary arithmetic for practical commercial, taxation, and labor-distribution applications, providing the kǒujué 口訣 (oral-formula) mnemonics for multiplication and division shortcuts and a small selection of worked problems on each standard topic.
The work was largely lost in China by the late Míng; the KX recension presumably preserves a partial reconstruction from Korean and Japanese citations and from internal cross-references in the surviving Yáng Huī works. The work’s significance is primarily transmissional: it represents the practical-arithmetic counterpoint to Yáng Huī’s high-mathematical Xiángjiě commentary, and the pattern of one mathematician producing both high-theoretical and practical-pedagogical work in close succession is characteristic of the Southern-Sòng mathematical scene.
Dating: the Rìyòng suànfǎ preface (preserved in citation) gives Xiánchún 8 (1262); the Xùgǔ zhāiqí of 1275 references the Rìyòng explicitly. NotBefore set at 1262 if the present work is the Rìyòng; notAfter at 1275 to bracket the alternative interpretation that the present work is an extracted portion of the Yáng Huī suànfǎ compendium.
For 楊輝 Yáng Huī’s biographical context see his Person note.
Translations and research
- Lam Lay-Yong. 1977. A Critical Study of the Yang Hui Suan Fa. Singapore: Singapore University Press. — Treats the Rì-yòng suàn-fǎ in the context of Yáng Huī’s complete corpus.
- Wú Wénjùn 吳文俊, ed. 1985. Zhōng-guó shù-xué shǐ dà-xì 中國數學史大系, vol. 5. Beijing: Běi-jīng shī-fàn dà-xué chū-bǎn-shè.