The Impossibility of Squaring the Circle in the 17th Century

A Debate Among Gregory, Huygens and Leibniz

  • Davide Crippa

Part of the Frontiers in the History of Science book series (FRHIS)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Davide Crippa
    Pages 1-33
  3. Davide Crippa
    Pages 157-174
  4. Back Matter
    Pages 175-184

About this book


This book is about James Gregory’s attempt to prove that the quadrature of the circle, the ellipse and the hyperbola cannot be found algebraically. Additonally, the subsequent debates that ensued between Gregory, Christiaan Huygens and G.W. Leibniz are presented and analyzed. These debates eventually culminated with the impossibility result that Leibniz appended to his unpublished treatise De quadratura arithmetica.

The author shows how the controversy around the possibility of solving the quadrature of the circle by certain means (algebraic curves) pointed to metamathematical issues, particularly to the completeness of algebra with respect to geometry. In other words, the question underlying the debate on the solvability of the circle-squaring problem may be thus phrased: can finite polynomial equations describe any geometrical quantity? As the study reveals, this question was central in the early days of calculus, when transcendental quantities and operations entered the stage.

Undergraduate and graduate students in the history of science, in philosophy and in mathematics will find this book appealing as well as mathematicians and historians with broad interests in the history of mathematics.


transcendental functions transcendental numbers (π) Gregory Leibniz Huygens

Authors and affiliations

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

Bibliographic information