左潜“释”《割圆密率捷法》的相关问题探微  

A Study of Issues Related to Zuo Qian’s Reform of the Geyuan Milü Jiefa

作　　者：王鑫义[1] 郭世荣[1] WANG Xinyi;GUO Shirong(Institute for the History of Science and Technology,Inner Mongolia Normal University,Hohhot 010022,China)

机构地区：[1]内蒙古师范大学科学技术史研究院,呼和浩特010022

出　　处：《中国科技史杂志》2021年第1期123-135,共13页The Chinese Journal for the History of Science and Technology

基　　金：全国高等院校古籍整理研究工作委员会直接资助项目(项目编号:2040);内蒙古自治区研究生教育创新计划资助项目(项目编号:B20191160Z);内蒙古师范大学研究生科研创新基金资助项目(项目编号:CXJJB19001)。

摘　　要：左潜的《缀术释明》是在徐有壬的《割圆八线缀术》影响下完成的,该书不仅以徐氏"缀术"来"释"明安图的《割圆密率捷法》,校正了其中的多处舛误,而且推广了"缀术"的应用范围,也使明氏的工作更为清晰、规范。通过解读《缀术释明》,并与《割圆密率捷法》《割圆八线缀术》进行比较,分析了左潜运用"缀术"予以改造和简化明安图的无穷级数表达方式及其推演的动机和方法。《缀术释明》完成于微积分传入中国之后,以往的研究对此书关注不多。本文阐明了《缀术释明》的内容要点和左潜的方法新意,以期全面了解清代算家理解、吸收和探索无穷级数的历史进程。Zuo Qian’s Zhuishu Shiming, a mathematical treatise under the influence of Xu Youren’s Geyuan Baxian Zhuishu, not only uses the latter’s method to transform Ming Antu’s Geyuan Milü Jiefa, correcting many errors in Ming’s book, but also promotes the application scope of the method of Zhuishu, making Ming’s work clearer and more standardized. Through interpreting Zuo’sZhuishu and comparing it with the works of Ming and Xu, this paper analyzes Zuo’s motivation and method of transforming and simplifying Ming’s expression of infinite series and its deduction. Zuo’s work was completed after calculus was introduced into China;yet the work had not received much attention in the past from historians of mathematics. This paper expounds the main points of the content and the new ideas of Zuo’s method, with a view to comprehensively understand, absorb and explore the historical process of infinite series by the mathematicians in the Qing dynasty.

关 键 词：左潜 《缀术释明》 《割圆密率捷法》 《割圆八线缀术》 天元术 

分 类 号：N092[自然科学总论—科学技术哲学] O112[理学—数学]