刘岳云《测圆海镜通释》补证与解读

Supplementary Proofs and Interpretations of Liu Yueyun’s Ceyuan Haijing Tongshi

《测圆海镜》(1248)记载的勾股测圆术是中国古代数学的一项重要成果。晚清数学家又将这一成果予以发展和完善。其中,刘岳云(1849~1917)《测圆海镜通释》(1896)具有独到的见解。因传本缺少必要的解说,兼有文字脱误,故准确理解该书的内容存在困难。本文在校正原文的基础上,依据计算结果,就其难点予以分析,试图阐明其理论与方法,从而说明在晚清勾股测圆术的研究中刘岳云的理论建树。

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.