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Title: Area and moment in De Analysi by Isaac Newton (Study of the History of Mathematics 2020)
Authors: Osada, Naoki
Author's alias: 長田, 直樹
Keywords: 01A45
Isaac Newton
antiderivative
area
moment
infinite series
Issue Date: Jul-2021
Publisher: Research Institute for Mathematical Sciences, Kyoto University
Journal title: 数理解析研究所講究録別冊
Volume: B85
Start page: 15
End page: 34
Abstract: In 1669, Isaac Newton wrote De Analysi to claim the priority of the analysis with infinite series. The method of infinite series requires the antiderivative of a simple curve ax^[m/n] and the derivative of an object to be sought. In the October 1666 tract and De Metodis (1671), Newton expressed the antiderivative using uxional equations, and the derivative by the ratio of the uxions. On the other hand, in De Analysi, Newton represented the antiderivative as the pair of the region described by the ordinate ax^[m/n] and its signed area, and he introduced the term momentum (moment) to represent the differential. In De Analysi, Newton replaced the terms and concepts of the uxional method with those of geometry.
Description: "Study of the History of Mathematics 2020". February 1-3, 2021. edited by Naoki Osada. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.
Rights: © 2021 by the Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University. All rights reserved.
URI: http://hdl.handle.net/2433/265135
Appears in Collections:B85 Study of the History of Mathematics 2020

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