Jiǔzhāng xiángzhù bǐlèi suànfǎ dàquán 九章詳註比類算法大全
Comprehensive Compendium of Detailed Annotation and Categorical-Comparative Mathematical Methods on the Nine Chapters by 吳敬 (撰)
About the work
吳敬 Wú Jìng’s 1450 mid-Míng practical-mathematical compendium in 12 juàn, organized under the nine-chapter framework of the KR3f0032 Jiǔzhāng suànshù but with substantial expansion. The work also carries a sub-title Chéngchú kāifāng qǐlì 乘除開方起例 (Introductory Examples for Multiplication-Division-and-Root-Extraction) referring to the introductory juàn. The work is one of the principal mid-Míng abacus-arithmetic textbooks.
Abstract
Wú Jìng’s Dàquán contains some 1300 problems-with-solutions, expanding the Jiǔzhāng’s 246 by absorbing substantial YuánMíng practical material on commercial calculation, taxation, surveying, currency exchange, and the standard abacus-arithmetic mnemonics. The organizational principle is the bǐlèi 比類 method: problems are grouped by analogical pattern within each of the nine traditional chapters, with the simplest cases first and progressively more elaborate cases working out the same pattern. This pedagogical approach was Wú Jìng’s principal contribution and would become the standard organizational principle of late-Míng / early-Qīng practical-mathematical writing.
The work also includes a substantial introductory juàn (the Chéngchú kāifāng qǐlì) covering the basic arithmetic operations on the abacus: the jiǔjiǔ multiplication-table, the multiplication-division shortcut mnemonics, the addition-and-subtraction methods, and the square-and-cube-root extraction procedures adapted to the abacus from the SòngYuán counting-rod tradition. This introductory material is among the most systematic pre-Chéng Dàwèi accounts of the abacus operations and was a principal source for 程大位 Chéng Dàwèi’s KR3fc027 Suànfǎ tǒngzōng (1592).
The work’s substantive significance beyond pedagogy lies in its preservation of significant amounts of SòngYuán mathematical material. Wú Jìng’s source-citations include problem-types from the lost 楊輝 Rìyòng suànfǎ, the Yǎnggǔ jí 養古集 of Lǐ Sī 李思 (otherwise lost), and citations of 朱世傑 Zhū Shìjié’s Suànxué qǐméng by problem-type if not by direct quotation. The SòngYuán tiānyuányī algebraic method is, however, absent from Wú Jìng’s Dàquán — the early-Míng forgetting of SòngYuán algebra is essentially complete in his work, foreshadowing the full late-Míng forgetting documented in 顧應祥’s KR3f0043.
Dating: 1450 per Wú Jìng’s own preface (preserved in the work’s opening).
Translations and research
- Lam Lay-Yong. 1977. A Critical Study of the Yang Hui Suan Fa. Singapore: Singapore University Press. — Treats Wú Jìng’s preservation of Yáng Huī’s Rì-yòng problem-types.
- 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.
- 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.