“Um estudo sobre o cálculo de fluxões de Isaac Newton” - Zeferino Junior, Jorge Luiz de Almeida (2021)
In this paper we present a brief study of Isaac Newton's calculus of fluxions that was used to solve curvature and quadrature problems in 17th century England. To this end, we analyze the main parts of two of his works that deal with his calculus with more propriety. They are De Analysi per Aequationes Numero Terminorum Infinitas of 1669 and The Method of Fluxions and Infinite Series; with its Application to the Geometry of Curve-Lines of 1736, the latter being translated and published by John Colson (1680 - 1760). Our analysis focused on the study of curves presented by Newton in these two treatises and in Colson's commentaries, specifically in sections VI and VII of the second work. For this, we performed a contextual and epistemological analysis of the work The Method of Fluxions and Infinite Series; with its Application to the Geometry of Curve-Lines of 1736, directing the study to a more updated historiographical proposal. In view of this, we discuss the context of the treatise's elaboration, bringing out the fundamental principles mobilized by Isaac Newton in his method of fluxions, presenting the different approaches between his works. We conclude that the different approaches to the calculus of fluxions do not correspond only to a new mathematical notation established, but, above all, they announce that Newton is making the transition from the synthetic method to the analytical method