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


In the previous chapters, I have shown that the question about the solvability of the problem of the indefinite and definite quadratures of the circle, the ellipse, and the hyperbola was a source of studies and debates among geometers from the second half of the Seventeenth Century. More particularly, I have chosen to study one episode within precise temporal bounds (1667–1676). The example I chose to analyze revolves around the claim made by James Gregory, in his Vera circuli et hyperbolae quadratura, regarding the impossibility of solving the quadrature of the circle in an exact way, and the criticism to which this claim was later exposed.


  1. Blåsjö, Viktor. 2017. Transcendental curves in the Leibnizian calculus. Amsterdam: Elsevier.Google Scholar
  2. Cortese, João. 2016. When two points coincide, or are at an infinitely small distance: some aspects of the relation between the works of Leibniz, Pascal (and Desargues). In Für unser Glück oder das Glück anderer: Vorträge des X. Internationalen Leibniz-Kongresses, vol. 4. Ed. Wenchao Li, 165–178. Hildesheim: Olms.Google Scholar
  3. Crippa, Davide. 2014. Impossibility results: from geometry to analysis. Université Paris Diderot: Phd Dissertation.Google Scholar
  4. Dehn, Max and Hellinger, Ernst. 1939. On James Gregory’s “Vera quadratura”. In The James Gregory tercentenary memorial volume. Ed. Herbert W. Turnbull, 468–478. Edinburgh: Royal Society of Edinburgh.Google Scholar
  5. Dehn, Max and Hellinger Ernerst. 1943. Certain mathematical achievements of James Gregory. In The American Mathematical Monthly. 50(3): 149–163.MathSciNetCrossRefGoogle Scholar
  6. Debuiche, Valérie. 2013. L’expression Leibnizienne et ses modèles mathématiques. Journal of the History of Philosophy 51(3): 409–459.CrossRefGoogle Scholar
  7. Detlefsen, Michael. 2008. Interview with Michael Detlefsen. In Philosophy of Mathematics. 5 Questions. Eds. Vincent F. Hendricks and Hannes Leitgeb. Copenhagen: Automatic Press.Google Scholar
  8. Gavagna, Veronica. 2014. Radices Sophisticae, Racines Imaginaires: The Origins of Complex Numbers in the Late Renaissance. In The art of science. From perspective drawings to Quantum randomness. Eds. Rossella Lupacchini, Annarita Angelini, 165–190. Dordrecht Heidelberg New York London: Springer.Google Scholar
  9. Girard, Albert. 1629. Invention nouvelle en l’algebre. Amsterdam: Guillaume Iansson Blaeuw.Google Scholar
  10. Heeffer, Albrecht. 2008. The Emergence of Symbolic Algebra as a Shift in Predominant Models. Foundations of science, 13(2): 149–161.MathSciNetCrossRefGoogle Scholar
  11. Jesseph, Douglas. 1999. Squaring the Circle: the War between Hobbers and Wallis. Chicago and London: University of Chicago Press.zbMATHGoogle Scholar
  12. Leibniz, Gottfried Wilhelm. 1984. Philosophical essays. Eds. Roger Ariew, Daniel Garber. Indianapolis & Cambridge: Hackett Publishing Company.Google Scholar
  13. Leibniz, Gottfried Wilhelm. 2011. Gottfried Wilhelm Leibniz: Die mathematischen Zeitschriftenartikel. Eds. Hans-Jürgen Hess, and Malte-Ludof Babin. Hildesheim, Zürich, New York: Georg Olms Verlag.Google Scholar
  14. Leibniz, Gottfried Wilhelm. 2018. Ecrits sur la mathesis universalis. Ed. David Rabouin. Paris: Vrin.Google Scholar
  15. Lützen, Jesper. 2009. Why was Wantzel overlooked for a century? The changing importance of an impossibility result. Historia Mathematica. 36: 374–394.MathSciNetCrossRefGoogle Scholar
  16. Lützen, Jesper. 2014. 17th century arguments for the impossibility of the indefinite and the definite quadrature of the circle. Revue d’histoire des mathématiques. 20: 211–251.zbMATHGoogle Scholar
  17. Malet, Antoni. 1996. From Indivisibles to Infinitesimals: Studies on Seventeenth-Century Mathematizations of Infinitely Small Quantities. Barcelona: Universitat Autonoma de Barcelona.zbMATHGoogle Scholar
  18. Stevin, Simon. 1958. The principal works of Simon Stevin. Ed. D. J. Struik. Amsterdam: Swets & Zeitlinger.zbMATHGoogle Scholar
  19. Viète François. 1593. Variorum de rebus mathematicis responsorum Liber VIII. Tour: Mettayer.Google Scholar
  20. Vuillemin Jules. 1963. La philosophie de l’algèbre: t. I: Recherches sur quelques concepts et méthodes de l’algèbre moderne. Paris: Epimethée.Google Scholar
  21. Wallis, John. 1685. A treatise of algebra both historical and practical shewing the original, progress, and advancement thereof, from time to time; and by what steps it hath attained to the height at which now it is. London.Google Scholar
  22. Wallis, John. 2004. The arithmetic of infinitesimals. Ed., transl. Jacqueline Stedall. Dordrecht Heidelberg New York London: Springer.Google Scholar
  23. Wallis, John. 2014. The Correspondence of John Wallis (1616-1703). Volume IV. 1672-April 1675. Eds. Philip Beeley, Cristoph Scriba. Oxford: Oxford University Press.Google Scholar
  24. Zeuthen, H. Georg. 1903. Geschichte der Mathematik im XVI. and XVII. Jahrhundert. transl. R. Meyer. Leipzig: Teubner.zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

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

Personalised recommendations