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Ceyuan (測圓海鏡) and Jiuyong Yandai (九容演代)

  • Received : 2013.10.26
  • Accepted : 2014.02.09
  • Published : 2014.02.28

Abstract

The book ${\ll}$Ceyuan Haijing${\gg}$ studies inscribed and circumscribed circles in a right triangle and shows equations that give the diameters of the circles. We discuss the development of mathematical contents written by the scholar Yang Zhaoyun in Qing dynasty on the contents of ${\ll}$Ceyuan Haijing${\gg}$ in his book ${\ll}$Jiuyong Yandai${\gg}$. He derived equations to find the diameters of the circles based on algebraic knowledge known in the Qing dynasty. In this paper, we conclude that Yang's methods in devising the equations include the Gou-Gu Theorem, mathematical expressions derived from Gou-Gu ratio table, and the technique of interchanging triangles and events. We conclude that the Gou-Gu ratio table was a very important tool when Yang devised the equations in ${\ll}$Ceyuan Haijing${\gg}$.

Keywords

References

  1. CHEN Weiqi, Zhong Xi Suan Xue Da Cheng 41, 1889. 陳維祺, 中西算學大成 41卷, 1889.
  2. LI Shanlan, Jiuyong Tubiao (1876), in Guo Shuchun ed., Zhongguo Kexue Jishu Dianji Tonghui, Shuxuejuan Volume 5, Henan Jiaoyue Chuban She, 1993, 1035-1038. 李善蘭, 九容圖表 (1876), 郭書春 編輯, 中國科學技術典籍通彙 5卷 數學卷, 河南敎育出版社, 1993, 1035-1038.
  3. LI Yan, Ceyuan Haijing yanjiu licheng kao, in GUO Shuchun ed., Li Yan and Qian Baocong Kexueshi Quanji, Volume 8, Liaoning Jiaoyue Chuban She, 1998, 37-222. 李儼, 測圓海鏡硏究歷程考, 郭書春 編輯, 李儼錢寶琮科學史全集 8卷, 遼寧敎育出版社, 1998, 37-222.
  4. LI Zhi, Ceyuan Haijing Xicao, according to Baoshi Zhi Buzu Zhai Chongshu (1248), LI Rui (1798), in Xuxiu Siku Quanshu Volume 1042, p. 297-437, Shanghai Guji Chubanshe, 1995. 李治, 測圓海鏡細草, 鮑氏知不足齋叢書 (1248), 李銳 (1789), 續修四庫全書 1042卷, 297-437, 上海古籍出版社, 1995.
  5. LIU Yueyun, Ceyuan Haijing Tongshi, Zunjing Shuju, 1896. 劉嶽雲, 測圓海鏡通釋, 尊經書局, 1896.
  6. Qian Baocong, A few questions on Ceyuan Haijing (1996), in GUO Shuchun ed., Li Yan and Qian Baocong Kexueshi Quanji Volume 9, Liaoning Jiaoyue Chuban She, 1998, 701-711. 錢寶琮, 有關<<測圓海鏡>> 的幾個問題 (1996), 郭書春 編輯, 李儼錢寶琮科學史全集 9卷, 遼寧敎育出版社, 1998, 701-711.
  7. YANG Zhaoyun, Jiuyong Yandai, in Xuman Jinglu Suanxue Volume 13-17 (1898). 楊兆鋆, 九容演代, 須曼精盧算學 13-17卷 (1898).