This paper offers a study of J.L.Lagrange's research on history of mathematics,aiming to clarify Lagrange's intention in carrying out historical work.To this end,I first document how Lagrange worked with and e...This paper offers a study of J.L.Lagrange's research on history of mathematics,aiming to clarify Lagrange's intention in carrying out historical work.To this end,I first document how Lagrange worked with and exerted his influence on other scholars in the translation and diffusion of ancient Greek texts.Second,investigating Lagrange's style in doing and writing history of mathematics,this paper takes a new perspective and elucidates his motivation in these activities.In particular,it focuses on Lagrange's presentation of the history of calculus while he was teaching analysis at the Ecole Polytechnique(1795-1799)so as to clarify the function of history in Lagrange's mathematical works.My thesis is that Lagrange's intention in examining the different methods employed by his predecessors was to find inspiration and useful contents in his search for the proper approach to mathematical problems.I thus argue in this paper that history served as a guide or methodology for Lagrange's mathematics.Meanwhile,through an analysis of his historical writing,this paper points to four epistemological values according to which Lagrange judged various historical methods of differential calculus:generality,simplicity,clarity,and rigor.Lagrange's move to rigorize analysis was connected to his interest in and research of Greek texts;he was attempting to introduce the rigor of the ancient Greeks'demonstration in his works of analysis.展开更多
文摘封面巴黎综合理工学院旧址正门
巴黎综合理工学院(Ecole Polytechnique,以下简称EP)诞生于法国大革命的电闪雷鸣之中:当时外敌压境、内争纷起、叛乱频仍,共和国的道路桥梁遭到严重的破坏,为了迅速调遣军队保卫祖国,国民公会接受学者们的建议,决定以最快的速度在巴黎兴办一所培养道桥技术人才和工兵及炮兵军官的学校.发起建议的科学家包括时任国民公会主席的数学家老卡诺(Lazare Carnot,1753-1823)、画法几何的奠基人蒙日(Gaspard Menge,1746-1818)、化学家贝托莱(Claude-Louis Berthollet,1748-1822)、天文学家拉普拉斯(Pierre Simon de Laplace,1749-1827)等.国民公会于1794年3月11日通过建校法案,12月正式开课,校址设在塞纳河边的波旁宫,学生多为贫家子弟,分散居住到附近的公民家庭而由国家给予补贴.
文摘This paper offers a study of J.L.Lagrange's research on history of mathematics,aiming to clarify Lagrange's intention in carrying out historical work.To this end,I first document how Lagrange worked with and exerted his influence on other scholars in the translation and diffusion of ancient Greek texts.Second,investigating Lagrange's style in doing and writing history of mathematics,this paper takes a new perspective and elucidates his motivation in these activities.In particular,it focuses on Lagrange's presentation of the history of calculus while he was teaching analysis at the Ecole Polytechnique(1795-1799)so as to clarify the function of history in Lagrange's mathematical works.My thesis is that Lagrange's intention in examining the different methods employed by his predecessors was to find inspiration and useful contents in his search for the proper approach to mathematical problems.I thus argue in this paper that history served as a guide or methodology for Lagrange's mathematics.Meanwhile,through an analysis of his historical writing,this paper points to four epistemological values according to which Lagrange judged various historical methods of differential calculus:generality,simplicity,clarity,and rigor.Lagrange's move to rigorize analysis was connected to his interest in and research of Greek texts;he was attempting to introduce the rigor of the ancient Greeks'demonstration in his works of analysis.
