What Did They Mean by "Calculation Principles"?: Revisiting Argumentative Styles in Late Ming to Mid- Qing Chinese Mathematics

This article discusses the influence that two versions of the Elements had in Ming and Qing China as well as Chinese scholars’ efforts to “integrate” (huitong 會通) Western and Chinese mathematics into a unified system in terms of argumentative styles in mathematics. Although much high praise was given to the axiomatic-deductive system of Euclid’s Elements, numerical arguments and problem-solving re-main important traits in the works of Chinese scholars. The compilation of the Shuli jingyun 數理精蘊 and the inclusion of another version of the Elements in it again prompted East Asian mathematicians to reflect more upon their methods of argu-mentation, and later scholars began to write texts whose arguments are more abstract than numerical. This paper presents examples taken from the works of several rep-resentative scholars from the late Ming to the mid-Qing periods to argue that their efforts of huitong produced argumentative styles that are a combination of both Chi-nese and Western approaches, and that there was a trend of moving from concrete calculations to general arguments in mathematical texts throughout the course of history. Finally, the authors conclude that what 17th and 18th century Chinese math-ematicians meant by “calculation principles” (suanli 算理) was never the kind of pure deduction in the Euclidean manner, but a combination of induction and deduction, with the help of intuition, for the purpose of problem-solving.