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Studies in the History of Natural Sciences  2020, Vol. 39 Issue (3): 269-287    DOI:
ARTICLES     
A Study of Proof and the Application of Gougu Identities during Qing Dynasty
LI Zhaohua
School of Mathematics, Tianjin Normal University, Tianjin 300387,China
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Abstract  The Gougu rule (Pythagorean theorem) and identities are an important part of the rudiments of ancient mathematics in China. Books by mathematicians during the Qing Dynasty (1644-1911) that were devoted to the amplification, proof and application of identities indicate a wealth of results that have not been specially studied. This paper lays emphasis on the investigation on examples for proof as well as the application of identities appearing in the above books. This paper points out that Gougu bili biao (Gougu Table of Proportion, 1863) by Wu Jiashan (1820-1885) provides a complete set with a total of 20 identities. All of the principles needed for identity proving can be found in Gougu yuanfang tuzhu (Illustrated Comments on Right Angled Triangle)by Zhao Shuang early in the 3rd century.Furthermore, the paper points out the relation between the application of the identities and Shuli jingyun (Essential Principles of mathematics,1723).Based on such historical mathematical materials,a better and more comprehensive understanding of Gougu identities can be gained.

Key words： Gougu identity      proof      Wu Jiashan      Gougu yuanfang tuzhu (Illustrated Comments on Right Triangle)      Shuli jingyun (Essential Principles of Mathematics)     
Received: 18 June 2018      Published: 22 June 2021
ZTFLH:  N092  
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LI Zhaohua. A Study of Proof and the Application of Gougu Identities during Qing Dynasty. Studies in the History of Natural Sciences, 2020, 39(3): 269-287.

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http://www.shns.ac.cn/     OR     http://www.shns.ac.cn/Y2020/V39/I3/269

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