聞分館君 Ask BunKanKun

筆算說略

3 min read

Text ID
KR3fc074
Date
1810–1853
Dynasty
清

Bǐsuàn shuōlüè 筆算說略

An Outline Exposition of Brush-and-Pen [Western Notational] Arithmetic by 鄭復光 (撰)

About the work

鄭復光 Zhèng Fùguāng’s (1780–1853) primer in 2 juàn on bǐsuàn 筆算 — written-notation arithmetic, performed by writing successive intermediate results on paper, as opposed to the indigenous Chinese arithmetic traditions of chóusuàn 籌算 (counting-rod manipulation) and zhūsuàn 珠算 (abacus computation). The work is one of the principal nineteenth-century Chinese pedagogical treatments of the European arithmetic-notation method.

Abstract

The standard indigenous Chinese arithmetic methods through the seventeenth century were the counting-rod (chóusuàn) tradition — manipulation of bamboo rods on a board — and from the late Sòng onwards the abacus (zhūsuàn) tradition. Both methods operate by manipulation of physical tokens; the intermediate results are not written down and only the final result is recorded.

The European notational arithmetic — in which the operands are written down and the intermediate results successively built up on paper — was introduced to China by the Jesuit mathematicians in the early seventeenth century (notably in Matteo Ricci 利瑪竇 Lì Mǎdòu and Lǐ Zhīzǎo 李之藻’s Tóngwén suànzhǐ 同文算指 of 1614). The method spread slowly in eighteenth-century Chinese mathematical practice and became increasingly important in the nineteenth century as the volume and complexity of computational work grew (especially in the late-Qīng astronomical, surveying, and translation projects).

Zhèng Fùguāng’s Bǐsuàn shuōlüè is an elementary 2-juàn presentation of bǐsuàn for the educated Chinese reader unfamiliar with the European method. The first juàn presents the four basic operations (addition, subtraction, multiplication, division) in the written-notation form, with extensive worked examples. The second juàn extends to more complex operations: long multiplication and long division of large numbers, calculation with fractions, and the jiègēnfāng 借根方 algebraic procedure performed in bǐsuàn notation. The pedagogical emphasis is on showing the educated Chinese reader, accustomed to the indigenous chóusuàn or abacus methods, exactly how the same problems are performed in the European notation — and on demonstrating the practical advantages of the written method for large-number and multi-step computations.

The work is one of the foundational documents of nineteenth-century Chinese arithmetic pedagogy. By the late-Qīng period the bǐsuàn method had become the dominant Chinese arithmetic tradition for advanced mathematical work, and the abacus had been displaced to commercial-clerical use. Zhèng Fùguāng’s primer played a significant role in this transition, particularly through its use as a school textbook in the late-Tóng-zhì period when European-style mathematics curricula began to be introduced in Chinese schools.

Dating: Zhèng Fùguāng lived 1780–1853. notBefore 1810; notAfter 1853.

Translations and research

  • Jami, Catherine. 2012. The Emperor’s New Mathematics. Oxford: Oxford University Press. — Covers the Jesuit-era introduction of bǐ-suàn.
  • Engelfriet, Peter M. 1998. Euclid in China. Leiden: Brill.
  • Tián Miǎo 田淼. 2003. Zhōng-guó shù-xué de xī-huà lì-chéng 中國數學的西化歷程.

Other points of interest

Zhèng Fùguāng is unusual among Qīng mathematicians for his parallel work on optics and instrument-making (cf. his Jìngjìng língchī 鏡鏡詅癡, not preserved in the present KR3fc series). The combination of mathematical-pedagogical and optical-experimental work places him as a precursor of the late-Qīng gézhì 格致 (“natural philosophy”) movement.

Graph View

Backlinks