秦九韶对大衍术的筭图表达——基于《数书九章》赵琦美钞本(1616)的分析  

Qin Jiushao's Writing of the Dayan Algorithm:An Analysis Based on Zhao Qimei's Manuscript of the Mathematical Book in Nine Chapters (1616)

作　　者：朱一文[1] ZHU Yiwen(Department of Philosophy ＆ Institute of Logic and Cognition, Sun Yat-sen University, Guangzhou 510275, China)

机构地区：[1]中山大学哲学系暨逻辑与认知研究所,广州510275

出　　处：《自然科学史研究》2017年第2期244-257,共14页Studies in The History of Natural Sciences

基　　金：国家社会科学基金青年项目"儒家经典注疏中天算文献的整理与研究"(项目编号:16CZS012)

摘　　要：秦九韶的《数书九章》(1247)是中国数学史上的名篇,其所载的大衍总数术是一项世界级成就。然而,以往的数学史研究并未从文本表达形式的角度分析秦氏大衍术。从对最接近秦书足本的赵琦美钞本(1616)的分析看,秦氏对大衍术的表达运用了文字、筹码、筭图、连线等多种文本形式。一方面,秦氏著书的部分原因是为了参与宋廷改历。另一方面,秦氏认为数术分成内算与外算两部分,与历算、《周易》相关的大衍总数术属于内算,其核心算法大衍求一术则与传统方程术不同,应独立为一项数学内容。因此,依据"其用相通,不可歧二"的原则,秦氏有理由公开揭示大衍术。而且,由于筭图能够呈现算法的全部筹算过程,故而成为秦氏表达原先"算而不书"的大衍术的最佳工具。总之,通过分析秦九韶的著书动机、天文历算与传统数学的差异、筭图与连线的功能,我们可以全面理解秦氏记述大衍术的历史事实。The Dayan algorithm is one of the highlights of the Mathematical Book in Nine Chapters, completed by Qin Jiushao in 1247. Based on Zhao Qimei＇s manuscript of this book （1616）, which has not been fully studied before, this paper researches the process of Qin Jiushao＇s writing of the Dayan algorithm. Firstly, an introduction is provided concerning the writing system derived from counting rods used in Zhao Qimei＇s manuscript. Next, Qin Jiushao＇s use of various writing modes are analyzed. Moreover, the connections between Dayan, Fangcheng methods, and the Book of Changes established by Qin Jiushao are studied in order to reveal Qin＇s aim in writing the Dayan algorithm. In summary, this writing process can be understood in the context of Qin＇s aim in writing the book, and the tension between astronomy and mathematics at that time.

关 键 词：秦九韶 大衍术 《数书九章》 赵琦美 筭图 连线 

分 类 号：O11[理学—数学]