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Report Montucla Prize 2013

Sébastien Maronne
For his article

The ovals in the Excerpta Mathematica and the origins of Descartes' method of normals

(Issue 37.3, 2010)

Montucla Prize 2013

In this article Maronne sheds light on the geometrical origins of Descartes’ method of normals through a close reading of two of Descartes’ texts from the Excerpta Mathematica together with the related parts of La Géométrie. The former, which were written prior to La Géométrie, deal with curves used in dioptrics (a branch of optics used in the construction of accurate lenses) which Descartes called ‘ovals’. The context for Descartes’ solution of the Pappus problem is relatively well documented, whereas the context within which the method of normals was invented and developed by Descartes needed clarification and this has now been provided by this paper. As a result of his detailed examination of the texts, Maronne provides strong evidence for a deep connection between dioptrics, ovals, and the method of normals. Maronne shows that in his study of normals Descartes remained anchored to the classical geometric tradition based on diagrammatic analysis. The article, which presents a new interpretation of the genesis of one of Descartes’ important ideas, is a substantial addition to the corpus of Cartesian scholarship.

Also highly commended were (in order of publication):

Jia-Ming Ying 
The Kujang sulhae 九章術解: Nam Pyoˇng-Gil's reinterpretation of the mathematical methods of the Jiuzhang suanshu
(Issue 38.1, 2011)

Victor Blåsjö 
The rectification of quadratures as a central foundational problem for the early Leibnizian calculus 
(Issue 39.4, 2012)