明安图对交错级数的表述及处理  

Ming An-tu’s representation and treatment of alternative series

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

出　　处：《西北大学学报（自然科学版）》2019年第5期819-824,共6页Journal of Northwest University（Natural Science Edition）

基　　金：国家社会科学基金资助项目(17CZS052);内蒙古自治区研究生教育创新计划;内蒙古师范大学研究生科研创新基金资助项目(CXJJB19001);中国博士后科学基金资助项目(2017M621115)

摘　　要：清代数学家明安图所著的《割圆密率捷法》是中算史上第一部将三角弦矢函数展开为无穷级数的著作,文中根据他的思路与方法,分析了《割圆密率捷法》中其对交错级数正负项的左右书写形式及其对交错级数的恰当处理方式。文中认为:其一,明安图对交错级数的表述及处理源于西法,又缘于梅瑴成在《赤水遗珍》中所使用的分类处理方法;其二,明安图将交错级数视为形式级数来处理,以多项式运演无穷级数,在级数收敛的前提下,运算是可行的,结果是正确的。这对现今分析学中处理交错级数的方法可加深历史认识。Ge Yuan Mi LüJie Fa(Quick methods for trigonometry and for determining the precise ratio of the circle)was the first book in the history of Chinese mathematics to expand the trigonometric string vector function into infinite series.Following the author′s thinking and method,this paper analyses the author′s right and left writing form of positive and negative terms of alternative series and the proper treatment of alternative series in the Ge Yuan Mi LüJie Fa.This paper holds that:firstly,the author′s expression and treatment of alternative series had its origin from western method and the classification method used by Mei Jue-cheng in Chi Shui Yi Zhen.Secondly,the author treated alternative series as a formal series,and performed infinite series with polynomials.On the premise of convergence of series,the operation is feasible and the result is correct.This enhances the historical understanding of the methods dealing with alternative series in modern analytics.

关 键 词：《割圆密率捷法》 交错级数 《赤水遗珍》 形式级数 

分 类 号：N09[自然科学总论—科学技术哲学]