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Studies in the History of Natural Sciences  2019, Vol. 38 Issue (1): 1-25    DOI:
ARTICLES     
Supplementary Proofs and Interpretations of Liu Yueyun's Ceyuan Haijing Tongshi
LI Zhaohua
School of Mathematics, Tianjin Normal University, Tianjin 300387, China
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Abstract  Gougu Ceyuanshu (Method for finding the diameter of a circle in contact with nine right triangles) recorded in Ceyuan Haijing (Sea Mirror of Circle Measurements, 1248) is one of the most important accomplishments of mathematics in pre-modern China. Furthermore, the method was improved and systematized by mathematicians in the late Qing Dynasty. Among them was Liu Yueyun (1849-1917), who gained a better understanding of Ceyuan Haijing and completed his book Ceyuan Haijing Tongshi (A Concise Explanation of Ceyuan Haijing,1896). However, owing to the lack of explanations and some textual errors in the transmitted text, his book is difficult to understand. Based on textual collation and calculations, this paper analyzes some of the knotty problems, and explains both Liu's theory and methods. The paper considers that, devoted to development of the theory of Gougu Ceyuan Shu, Liu's book is an example of research of considerable significance during the late Qing dynasty.

Key words： Ceyuan Haijing (Sea Mirror of circle measurements)      Gougu Ceyuanshu (Method for finding the diameter of a circle in contact with nine right triangles)      collation      proportional segments      equal quantities in thirteen right triangles     
Received: 31 August 2017      Published: 20 June 2021
ZTFLH:  O112  
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LI Zhaohua. Supplementary Proofs and Interpretations of Liu Yueyun's Ceyuan Haijing Tongshi. Studies in the History of Natural Sciences, 2019, 38(1): 1-25.

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http://www.shns.ac.cn/     OR     http://www.shns.ac.cn/Y2019/V38/I1/1

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