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Rewriting Euclid in the Early Modern Era

Why were mathematicians and philosophers in the seventeenth century re-examining and publishing new editions of Euclid’s Elements? Why, long after the appearance of Zamberti’s translation of Euclid in 1505 - the first published translation from Greek sources - did mathematicians and philosophers continue in the project of rewriting Euclid? Who in the Renaissance and early modern era was engaged in the continued examination of Euclid and to what end? Translation disputes and arguments about the worthiness of the Greek sources account for some of these interventions. What were there other, less widely acknowledged, motivations for engaging in the task of rewriting Euclid?

To answer this question, I have focussed on the Nouveaux éléments de géométrie produced by Antoine Arnauld. In my research, I examine the ends for which Antoine Arnauld, a prominent theologian and philosopher of the 17th century, published a work of elementary geometry. Why, in a century of such staggering intellectual achievements as the development of analytic geometry by Fermat and Descartes, and the invention of the versions of the differential and integral calculus elaborated by Newton and Leibniz, did Arnauld believe it was necessary to rewrite the Elements of Euclid? 

For Antoine Arnauld, the answer to this question has little to do with the mathematical insights that inhere in the Elements. Arnauld and his collaborator Pierre Nicole exhort the extra-mathematical lessons that accrued to practitioners of Euclid’s Elements, to the exclusion of the more instrumental, theoretical aims of mathematical study. The value of mathematics, for Arnauld and Nicole, as it was described in their Nouveaux éléments de géométrie, lay in the moral, spiritual and intellectual virtues it cultivated in practitioners.

This research draws on work completed during my PhD, supervised by Emeritus Professor Stephen Gaukroger and Professor Dan Garber.

I have presented this research at Oxford University, Princeton University, The University of Nottingham, and Macquarie University, among others. Journal articles in progress issuing from these talks (under provisional titles) here:

  • The Mathematical Ambitions of Antoine Arnauld and Pierre Nicole

  • Moral Mathematics at Port-Royal

  • Rethinking Epistemology at Port-Royal: Mathematics and the Visual Arts

  • Reason and its Virtues: Arnauld’s Epistemological Commitments in the Nouveaux éléments de géométrie

  • Definitions and a Theory of Principles in Port-Royalist Works