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Studies in the History of Natural Sciences  2020, Vol. 39 Issue (2): 135-151    DOI:
ARTICLES     
A Probe into the Problems of Gougu Hejiao in Zhongxi Shuxue Tushuo
GAO Feng
Institute for the History of National Science, CAS, Beijing 100190, China
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Abstract  Zhongxi shuxue tushuo中西数学图说(Illustration of Chinese and Western Mathematics)is a mathematical work written by Li Dupei, a scholar of the late Ming Dynasty, against the background of the introduction of western mathematics into China. The book's research on gougu hejiao勾股和较(sum and difference of three sides of right-angled triangles) was unique for the period and ground-breaking. Through an analysis of the issues tackled in the book, this paper points out that although the works Tongwen suanzhi 同文算指 and Gougu yi 勾股义 were the direct sources of knowledge on gougu hejiao in Li's work, he did not adopt the form of proof given by them that was from the Jihe yuanben 几何原本 (Chinese translation of Euclid's Elements), but instead uses the principle of churu xiangbu 出入相补(out-in complementary) from Chinese traditional mathematics. Geometric figures, which are consistent with Zhao Shuang's 赵爽 Gougu yuanfang tuzhu勾股圆方图注, are the basis for the proof of gougu hejiao problems in Zhongxi shuxue tushuo. On the basis of the existing problems of gougu hejiao, Li makes a systematic summary of all the situations in which it is used, and lays out and proves one by one the situations that need to be demonstrated. The achievements of the work have many overlaps and similarities with the work done by mathematicians in the early and middle Qing dynasty on gougu hejiao. The geometric proof and systematic summarization of gougu hejiao reflect the efforts of Zhongxi shuxue tushuo to interpret the contents of traditional mathematics under the influence of western mathematics.

Key words： gougu hejiao      Zhongxi shuxue tushuo      Li Dupei      interaction between Chinese and Western mathematics     
Received: 12 February 2020      Published: 22 June 2021
ZTFLH:  N092  
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GAO Feng
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GAO Feng. A Probe into the Problems of Gougu Hejiao in Zhongxi Shuxue Tushuo. Studies in the History of Natural Sciences, 2020, 39(2): 135-151.

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http://www.shns.ac.cn/     OR     http://www.shns.ac.cn/Y2020/V39/I2/135

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