【作者】 董杰；

【导师】 郭世荣；

【作者基本信息】 内蒙古师范大学 ， 科学技术史， 2008， 硕士

【摘要】 本文以明末《大测》的传入以及前清中算家对它的研究工作为线索,分析和探讨了《大测》介绍的西方三角学内容以及中算家在理解、完善和重构这些知识方面的一系列会通工作。在此基础上,进一步指出中算家使用了自己熟悉的方式对《大测》介绍的西方三角学知识进行会通,取得了丰硕的成果。论文主要分为三章。第一章详细分析了《大测》中的三角学内容,纠正了前人的一些误解,介绍了《测量全义》对《大测》的进一步补充工作。由此得出:传教士在引进西方数学时,已经考虑到中算家接受这些知识的可能性。第二章着重研究李子金、王锡阐、薛凤祚为代表的清初中算家在完善《大测》中缺失的数学证明方面的工作。认为早期中算家开辟了以勾股术会通西方三角学的途径,为后来中算家指明了会通的方向。第三章以梅文鼎对平面三角学、杨作枚对三角函数造表法的研究为重点,展示中算家对《大测》的重构工作。他们的成果标志着中算家已圆满完成了对《大测》的会通工作。在会通的过程中,他们使用了适合自身习惯的数学方法和说理方式,受西方逻辑推理的影响有限。本文以中算家会通《大测》的过程为线索,探究了前清中算家在维护中算传统基础上做出的创新工作,据此认为明末清初中西数学交流中,中算家在维护中算传统价值观的基础上,全面会通了《大测》中的数学内容。更多还原

【Abstract】 Based on a study of the first Chinese trigomometrical treatise dace (Great Measurement)which was compiled by Jesuit missionary Jean Terrenz (1576-1630,Chinese name Deng Yuhan邓玉函)and of Chinese mathematicians’ researches on the treatise in the early Qing dynasty,this dissertation analyses detailedly the trigonometrical knowledge in the dace and studies the Chinese mathematicians’ works on comprehend,refinement, reconstruction of the western mathematical knowledge.It comes to the conclusion that Chinese mathematicians took their own familiar terms and methodology in their studies of the trigonometrical knowledge and obtained many results.This paper is composed of three parts.Chapter one deals with the contents of trigonometrical knowledge in the dace,and corrects some historians’ misunderstanding about some formulae introduced in the dace.In addition,the content of celiang quanyi(Complete Meaning of Measurement,《测量全义》,1631)which provided some supplements to the trigonometry contents in the dace.Based on the study,the present author concludes that the missionaries had considered the mathematical tradition and research custom of Chinese mathematicians when they introduces western mathematical knowledge.Chapter two analyzes the research works of Chinese mathematicians of the early Qing dynasty,such as Li Zijin(李子金,1622～1701)and Wang Xichan(王锡阐,1628～1682),and Xue Fengzuo(薛凤祚,1599～1680), in refining and supplying mathematical proofs to formulae appeared in the dace,and comes to the conclusion that their works open a way of establishing a communication between Chinese and western mathematics by using the their familiar method of gougu(Pythagorean,theorem),and,therefore, formularized the direction of their study of the trigonometry.Chapter three studies Chinese mathematicians’ reconstruction researches on trigonometry,especially those in Mei Weiding’s(梅文鼎,1633-1721)ping sanjiao juyao(The Outline of Trigonometry in Plane,《平三角举要》)and in Yang Zuomei’s(杨作枚)fie geyuan baxian zhigen(The Fundament of Establishing the Trigonometrical Function Tables,《解割圆八线之根》).Their works implied that the Chinese mathematicians had realized their task of establishing communication between Chinese and western trigonomitry. During the whole process,the Chinese mathematicians used their own familiar terms and reasoning methods,adopting comparatively limited western logic idea.Summarily,in the present paper we traces the studies of Chinese mathematicians of the early Qing dynasty on the trigonometry introduced in dace to show how Chinese mathematicians obtained new research results and how they established communication between traditional mathematical knowledge and western one in the frame of the Chinese mathematics tradition.更多还原