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數書九章

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Text ID
KR3fc008
Date
1247–1247
Dynasty
宋

Shùshū jiǔzhāng 數書九章

Mathematical Treatise in Nine Sections by 秦九韶 (撰)

About the work

A non-WYG recension of 秦九韶 Qín Jiǔsháo’s monumental 18-juàn mathematical treatise of 1247, preserving the work under its original title Shùshū jiǔzhāng 數書九章 (“Mathematical Treatise in Nine Sections”) rather than the corrupted Sìkù form Shùxué jiǔzhāng 數學九章 under which the work is catalogued at KR3f0041. The KX edition almost certainly descends from the Yíjiātáng 宜稼堂 cóngshū imprint of Yù Sōngnián 郁松年 (1842), based on the Wényuángé 文淵閣 manuscript collated against the Zhàojí 趙琦 transcription discovered in 1842 — the recension that established the now-standard title and modernized the textual presentation.

Abstract

The work, in 9 topical chapters of 9 problems each (81 problems total, in 18 juàn), is universally recognized as the supreme mathematical achievement of the SòngYuán period. The nine chapters: (i) Dàyǎn 大衍 (the Chinese Remainder Theorem in fully systematic algorithmic form — the Dàyǎn qiúyī shù 大衍求一術, generalizing the KR3f0033 Sūnzǐ suànjīng problem-26 procedure into a complete algorithm for any system of linear congruences); (ii) Tiānshí 天時 (astronomical-calendrical computation); (iii) Tiányù 田域 (area calculations); (iv) Cèwàng 測望 (depth-and-distance measurement); (v) Fùyì 賦役 (taxation and labor service); (vi) Qiángǔ 錢穀 (currency and grain); (vii) Yíngjiàn 營建 (civil engineering); (viii) Jūnlǚ 軍旅 (military formations and supply); (ix) Shìyì 市易 (commerce).

For the full mathematical-historical discussion — the Dàyǎn qiúyī shù algorithm; the Lì tiānyuányī shù 立天元一術 systematic algebraic-equation methodology; the Héyīn shù 和因術 (anticipating Horner’s method for polynomial evaluation); the systematic treatment of indeterminate equations — see the WYG companion entry KR3f0041.

The textual significance of the present KX recension is twofold. First, it preserves the correct original title Shùshū jiǔzhāng (which had been corrupted in the Wényuángé manuscript and Sìkù line to Shùxué jiǔzhāng); the Yíjiātáng editors restored it on the basis of the Zhàojí transcription. Second, it incorporates the 宋景昌 Sòng Jǐngchāng zhájì 札記 (see KR3fc012) as marginal notes, providing the running textual-critical apparatus that had been worked out in the 1830s and 1840s by the Yíjiātáng / Yángzhōu circle. The KX edition is therefore the modern scholarly base text on which most subsequent critical work (Qián Bǎocóng 1957, Lam Lay-Yong 1977, Libbrecht 1973) depends.

Composition: the entire work was composed in a single concentrated effort during Qín Jiǔsháo’s enforced retirement at Húzhōu 湖州 following his mother’s death in 1244–47, presented to the throne (without imperial response) in 1247. NotBefore and notAfter both fixed at 1247 per the preface.

Translations and research

  • Libbrecht, Ulrich. 1973. Chinese Mathematics in the Thirteenth Century: The Shu-shu chiu-chang of Ch’in Chiu-shao. Cambridge, Mass.: MIT Press. — Foundational and still-essential English-language monograph; full study of the Dà-yǎn qiú-yī shù and its place in the history of indeterminate analysis.
  • Lam Lay-Yong. 1977. “Chu Shih-Chieh’s Suan-hsüeh ch’i-meng 算學啟蒙 (Introduction to Mathematical Studies).” Archive for History of Exact Sciences 21: 1–31 (and other papers). — Treats Qín Jiǔsháo’s contributions in the broader Sòng-Yuán context.
  • Lam Lay-Yong and Ang Tian-Se. 2004. Fleeting Footsteps, rev. edn. Singapore: World Scientific.
  • Martzloff, Jean-Claude. 1997. A History of Chinese Mathematics. Berlin: Springer.
  • Qián Bǎocóng 錢寶琮. 1957. Zhōng-guó shù-xué shǐ 中國數學史. Beijing: Kē-xué chū-bǎn-shè.
  • Wú Wénjùn 吳文俊, ed. 1987. Qín Jiǔsháo yǔ Shù-shū jiǔ-zhāng 秦九韶與數書九章. Beijing: Běi-jīng shī-fàn dà-xué chū-bǎn-shè. — Major conference-volume collection on Qín Jiǔsháo and his work.

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