A solução cartesiana da quadratura do círculo

Abstract

Although the problem of squaring the circle, that is, the problem of constructing a square having the same area of a given circle, was considered an open problem among early XVIIth century mathematicians, René Descartes affirmed that it could not be solved. On the other hand, he himself provided a solution to the problem, that can be dated in the period, 1625-1628. In this article, I will examine this solution by comparing it to an analysis made a century later by Euler, and to a solution known to the ancients and discussed by Pappus. I will investigate, successively, the reasons that led Descartes to dismiss these two solutions as not acceptable in the light of the ideal of exactness deployed in the Geometry.