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九章筭經

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Text ID
KR3fc001
Date
-100–656
Dynasty
漢

Jiǔzhāng suànjīng 九章筭經

The Nine Chapters Mathematical Canon by 劉徽 (注), 李淳風 (等釋)

About the work

A non-WYG recension of the Jiǔzhāng 九章 — the foundational mathematical classic of the Chinese tradition — under its Táng-canonical title Jiǔzhāng suànjīng 九章筭經 (“Canon of the Nine Chapters” — note the older orthography 筭 for the later standard 算). The WYG edition of the same work is catalogued in nine juàn under its Hàn title Jiǔzhāng suànshù 九章算術 (KR3f0032); the present KX entry preserves a five-juàn division of the text under the Táng-canonized title, with the 劉徽 commentary (preface dated Jǐngyuán 4 = 263 CE, but the work itself begun before and continued after the WèiJìn transition of 265) and the 李淳風 zhùshì sub-commentary commissioned by Táng Gāozōng in 656 CE for the Suànjīng shíshū 算經十書 imperial mathematical curriculum.

The Jiǔzhāng contains 246 problems-with-solutions organized into nine topical chapters: (i) Fāngtián 方田 (Square Fields — plane-area calculation, fractions, π); (ii) Sùmǐ 粟米 (Grain-Rice — proportional exchange); (iii) Cuīfēn 衰分 (Distribution by Proportion); (iv) Shǎoguǎng 少廣 (Less-Width — square- and cube-root extraction); (v) Shānggōng 商功 (Construction — volume calculation); (vi) Jūnshū 均輸 (Equitable Transport — weighted distribution); (vii) Yíng bùzú 盈不足 (Surplus-and-Deficit — the Rule of False Position); (viii) Fāngchéng 方程 (Rectangular Arrays — Gaussian elimination of linear systems, with the first systematic mathematical use of negative numbers in any tradition); and (ix) Gōugǔ 勾股 (Right-Triangle — the Pythagorean theorem and its applications).

Abstract

The Jiǔzhāng is the single most influential pre-modern Chinese mathematical work. Internal evidence (the reference to the Shànglín 上林 imperial park at Chángān, established under Hàn Wǔdì in the 130s BCE) fixes a terminus post quem for the received compilation in the late Western Hàn, with traditional attribution of the basic redaction to Zhāng Cāng 張蒼 and Gěng Shòuchāng 耿壽昌 in the early Hàn — almost certainly an idealizing back-projection. The book entered its received Táng-canonical form in three stages: the base compilation (c. 100 BCE), the Liú Huī commentary (begun 263 CE, with later supplements after the WèiJìn transition), and the Lǐ Chúnfēng zhùshì of 656 — at which point the work was retitled Jiǔzhāng suànjīng to fit the Suànjīng shíshū canonical series, with which it was promulgated as the head text of the Imperial-Academy mathematics curriculum.

The KX edition’s five-juàn division most likely reflects an older recension line transmitted via the Yǒnglè dàdiǎn 永樂大典 fragments and the Bāo Tíngbó 鮑廷博 Zhībùzú zhāi 知不足齋 collated reprint of the Sòng Mǎ Yánjiā 馬延家 imprint; the WYG line gives the same content in nine juàn (one per chapter) plus the Lǐ Jí 李籍 Yīnyì 音義 supplementary juàn. The work’s mathematical content is identical across recensions; for the substantive discussion of method, transmission, and modern scholarship see the WYG companion KR3f0032. The chief later commentaries — Lǐ Huáng’s 李潢 detailed reading KR3fc002 Jiǔzhāng suànshù xìcǎo túshuō, Yáng Huī’s 楊輝 KR3fc011 Xiángjiě jiǔzhāng suànfǎ, and Wú Jìng’s 吳敬 KR3fc023 Jiǔzhāng xiángzhù bǐlèi suànfǎ dàquán — are all preserved in the present KR3fc series.

Translations and research

  • Chemla, Karine, and Guo Shuchun 郭書春. 2004. Les Neuf Chapitres: Le classique mathématique de la Chine ancienne et ses commentaires. Paris: Dunod. — The standard French critical edition with exhaustive philological apparatus.
  • Shen, Kangshen, John N. Crossley, and Anthony W.-C. Lun. 1999. The Nine Chapters on the Mathematical Art: Companion and Commentary. Oxford / Beijing: Oxford University Press / Science Press. — The standard English translation.
  • Guo Shuchun 郭書春. 2014. Jiǔ-zhāng suàn-shù xīn-jiào 九章算術新校. Héféi: Zhōngguó Kējì Dàxué Chū-bǎn-shè. — Principal modern Chinese critical edition.
  • Cullen, Christopher. 2004. “The Suàn shù shū 筭數書 ‘Writings on Reckoning’: A Translation of a Chinese Mathematical Collection of the Second Century BC, with Explanatory Commentary.” Needham Research Institute Working Papers 1. — Sets the Jiǔ-zhāng against the excavated Zhāngjiāshān bamboo-strip mathematical text.
  • Martzloff, Jean-Claude. 1997. A History of Chinese Mathematics. Berlin: Springer.

Other points of interest

The five-juàn division used in the present KX edition preserves the older medieval recension structure attested in the Suí shū Jīngjí zhì 隋書經籍志 (“Jiǔ zhāng suànjīng nine juàn, yīnyì one juàn”) only in the supplemental Yīnyì count; the body division into five rather than nine juàn reflects the Sòng Mǎshì imprint’s repagination. Comparison of this division with the WYG/SBCK nine-juàn division is a standard reference point for Jiǔzhāng textual scholarship.

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