Area and moment in De Analysi by Isaac Newton (Study of the History of Mathematics 2020)

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.