Mouvement et origine du calcul infinit\'esimal : Th\'eorisation du mouvement et infinit\'esimaux

TL;DR

This paper explores how the mathematical formalization of movement influenced the development of infinitesimals, highlighting the philosophical and mathematical shifts from discrete to continuous concepts in physics and mathematics.

Contribution

It demonstrates the historical connection between the mathematization of movement and the emergence of infinitesimals in mathematics.

Findings

Mathematical formalization of movement changed the concept of motion.

Introduction of infinitesimals was driven by the need to describe continuous movement.

The work links philosophical ideas with mathematical developments in physics.

Abstract

In a previous article we gave the general foundations of the theory of movement considered from a philosophical and mathematical point of view. Philosophical it meant to understand the opposition of the one and the multiple, mathematically to consider the opposition between the discreet and the continuous. In this article we want to show how the widespread introduction of mathematics in physics by Galilei leas to a change in the very notion of movement. Conversely, this theorization of the movement is the origin of the elaboration of the infinitesimals, one of the major upheavals in mathematics.