A solução cartesiana da quadratura do círculo
DOI:
https://doi.org/10.1590/S1678-31662010000400005Keywords:
Descartes, Quadrature of the circle, Quadratrix, Pappus, Clavius, Euler, Geometrical exactness, Acceptability, ArchimedesAbstract
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.Downloads
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2010-12-01
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A solução cartesiana da quadratura do círculo . (2010). Scientiae Studia, 8(4), 597-621. https://doi.org/10.1590/S1678-31662010000400005