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Introduction

  • Davide Crippa
Chapter
Part of the Frontiers in the History of Science book series (FRHIS)

Abstract

In this book, I will study several attempts to prove the impossibility of solving three fundamental problems in geometry by algebraic means: the squaring of the circle, the ellipse and the hyperbola within the mathematical context of Seventeenth Century. All of these problems involve measuring areas or, in modern parlance, evaluating certain integrals. The term “quadrature” reveals the geometrical tradition in which these problems were originally conceived. Within the tradition of Greek mathematics, and in Seventeenth Century geometry as well, to find the area of a figure meant to construct, by geometrical means (the ruler and the compass, in the easiest instances, or by higher curves), a square equivalent to it: “squaring” or “quadrature” are thus just synonyms for designating this geometrical operation. Since the circle, the hyperbola and the ellipse (but not the parabola) are conic sections that possess geometrical centres, I shall refer to them as “central conic sections,” and I use the synthetic expression “quadrature of the central conic sections” for the problem of determining their areas.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Davide Crippa
    • 1
  1. 1.Université Paris Diderot, SPHèreParisFrance

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