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籌算

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Text ID
KR3fc036
Date
1678–1721
Dynasty
清

Chóusuàn 籌算

Counting-Rod Calculation (Napier’s Bones) by 梅文鼎 (撰)

About the work

梅文鼎 Méi Wéndǐng’s monograph on the Napier’s-bones type of calculating-rods, in the catalog without explicit juàn-count (the parent Lìsuàn quánshū edition is 2 juàn). The title Chóusuàn — literally “counting-rod calculation” — refers specifically to the John Napier (1614) lattice-multiplication rods (virgulae numericae, “Napier’s bones”), translated into Chinese as chóu 籌 (counting-rods) by analogy to the indigenous counting-rod tradition but referring substantively to the European-style multiplication-and-division aid.

Abstract

The work is one of Méi Wéndǐng’s principal contributions to the early-Qīng introduction of European calculating instruments to the Chinese mathematical curriculum. Napier’s bones — invented by John Napier in 1617 as a mechanical aid for multiplication, division, and root-extraction — had been introduced to China through the Jesuit channel in the early-to-mid seventeenth century; the Chóusuàn is the principal Chinese-language exposition.

The work systematizes:

(1) The construction of the rods: each rod is a strip displaying the multiplication table for one digit (1 × 1, 1 × 2, …, 1 × 9 along the rod for the digit 1; 2 × 1, 2 × 2, …, 2 × 9 along the rod for the digit 2; etc.), with each multiplication-result split into “tens” and “units” digits separated by a diagonal line within each cell of the rod. The rods are arranged with the digits of one factor displayed across the tops, the digits of the other factor down the side, and the result read off by following the diagonal-summation pattern.

(2) The arrangement and reading procedures for multiplication and division.

(3) The extension to root extraction, using the special “square-root” and “cube-root” rods that combine the basic multiplication-rod content with the appropriate squaring or cubing operations.

(4) The relation of the rod-procedures to the indigenous Chinese counting-rod (chóu 籌) and abacus (suànpán) computations — Méi Wéndǐng systematically shows that the same arithmetical operations can be performed by all three instruments, with the rod-procedures providing in some cases (notably root-extraction) computational shortcuts.

Méi Wéndǐng’s typical historiographical move is operative: although Napier’s bones are recognized as a European invention, Méi Wéndǐng identifies parallels with the indigenous counting-rod tradition and argues that the underlying procedure has classical Chinese roots in the Jiǔzhāng Shǎoguǎng and Shānggōng chapters.

The work was widely cited in the early-Qīng mathematical literature and helped establish the rods as a standard calculating instrument in the Méngyǎng zhāi curriculum. Through the 1726 Lìsuàn quánshū publication, the Chóusuàn shaped the Qián-Jiā-era understanding of Napier’s bones in particular and European calculating-aids in general.

Dating: the work is plausibly placed in Méi Wéndǐng’s middle productive period; notBefore 1678 (allowing for the work to have been substantially complete by the time of Méi Wéndǐng’s first significant publications); notAfter his death year 1721. The work is included in the 1726 Lìsuàn quánshū.

Translations and research

  • Jami, Catherine. 2011. The Emperor’s New Mathematics. Oxford: Oxford University Press. — Treats Méi Wéndǐng’s introduction of European calculating instruments in detail.
  • Hé Bǐngyù 何丙郁 (John Hoe). 1973. “Mei Wending and Western Mathematics.” Chinese Studies in History 7.3.
  • Liú Dùn 劉鈍. 1986. Méi Wéndǐng yǔ Zhōng-Xī shù-xué 梅文鼎与中西数学. Beijing.
  • Wú Wénjùn 吳文俊, ed. 1985. Zhōng-guó shù-xué shǐ dà-xì 中國數學史大系, vol. 7.

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