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Overview of Leibniz’ Notes to Arnauld’s Nouveaux elemens de geometrie

The Nouveaux Éléments de Géométrie were published by Arnauld in 1667, and in a second edition in 1683. It is a work that made school in the study of the foundations of geometry, and had a vast influence on French and European geometry in general. Arnauld’s approach to the foundations of geometry was, however, very different from Leibniz’, and was based on the assumption of a large number of principles and axioms that Arnauld considered “self-evident” and therefore impossible to prove. Leibniz discussed this work many times during his lifetime, and noted often that Arnauld had assumed propositions that instead needed to be proven in order to establish the foundations of geometry. These reading notes testify to the attention with which Leibniz read this fundamental text, and they are the origin of a great quantity of essays and subsequent observations on the foundations of geometry.

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