Isaac Newton e a origem do cálculo diferencial e integral

Abstract

This paper presents part of Isaac Newton's (1642-1727) contribution to the development of Differential and Integral Calculus. In order to build our analysis, we searched literature, and from our research we learned that the calculus of Newton, known as the Method of Fluxions, was developed within the context of his studies in Natural Philosophy, specifically those on issues related to the motion of bodies, not having the development of mathematics as its main objective. Therefore, we formulated the following research question: what was actually calculus in its origin? To answer this question, we tried to understand the context and the reasons why Newton developed his method, and thus established as a goal for this research to reflect on some aspects of the method of fluxions which appear in his treatise entitled "Mathematical Principles of Natural Philosophy", also known as "Principia", in which the laws of motion and the law of universal gravitation are presented. In order to do this, we present in our paper: a brief biography of Newton; an account on the changes that occurred in the natural philosophy of the seventeenth century, as well as the appreciation for mathematics in this period; the problem of the tangent to a curve and the problem of the quadrature of curves, which were the starting point for Newton to develop the method of fluxions; and the way in which Newton presented his method in the Principia in order to solve problems related to the motion of bodies