Sìlǜ qiǎnshuō 四率淺說
An Elementary Exposition of the Four-Term Proportion by 劉衡 (撰)
About the work
劉衡 Liú Héng’s (1776–1841) introductory treatise in 2 juàn on the sìlǜ 四率 method — the four-term proportion (a : b :: c : d, given three of which, find the fourth) that constitutes the European-Greek rule of three, introduced to China alongside the jiègēnfāng (cf. KR3fc066) under the Jesuit mathematical-translation programme.
Abstract
The sì-lǜ (literally “four ratios” — i.e. a four-term proportion) is the indigenous Chinese terminological label for the Greek rule of three. The same problem-type is treated under different names across the world’s mathematical traditions: the jīn-yǒu shù 今有術 (“now-given method”) of the Jiǔ-zhāng suàn-shù Chapter 2 Sù-mǐ 粟米 is the indigenous Chinese formulation; the regola del tre of medieval Italian commercial arithmetic is the European; the trairāśika of Indian mathematics another. The Jesuits’ sì-lǜ presentation introduced the proportional formulation (with all four terms explicit, including the unknown) in place of the indigenous implicit-unknown formulation.
Liú Héng’s 2-juàn qiǎnshuō is an elementary primer on the sìlǜ, with extended worked examples drawn from commercial, agricultural, and practical-engineering contexts. The treatise serves as a companion to his Jiègēn fāngfǎ qiǎnshuō (KR3fc066): the sìlǜ and the jiègēnfāng together cover the two principal European-derived computational apparatuses needed for the practical and commercial mathematical work of mid-Qīng provincial life. The sìlǜ qiǎnshuō in particular reflects Liú Héng’s pedagogical mission: making the European-derived apparatus accessible to provincial mathematical learners.
Dating: Liú Héng lived 1776–1841. notBefore 1800; notAfter 1841.
Translations and research
- Jami, Catherine. 2012. The Emperor’s New Mathematics. Oxford: Oxford University Press.
- Tián Miǎo 田淼. 2003. Zhōng-guó shù-xué de xī-huà lì-chéng 中國數學的西化歷程. Jǐ-nán: Shān-dōng jiāo-yù chū-bǎn-shè.