Les Éléments de géométrie de Clairaut : rupture ou héritage ?

Abstract

From the patrimonial point of view, the famous “Elements of geometry” published for the first time in 1741 par Alexis Clairaut is traditionally regarded as the starting point of a rich tradition, rather than the legacy of 17th and 18th geometry. This is due to the considerable success of the treatise from the time it was published onwards as well as to the brilliant way in which Clairaut opposed his project to the Euclidean model. Here we propose a slightly different view through the characterization of the highly particular nature of the flourishing production of geometrical treatises in the light of which the publication of Clairaut’s work must be understood. We shall first present the paradox inherent to Clairaut’s treatise, namely that the author claims both a high level of originality and a high level of conformity to the genre of “elements” in speculative geometry. We then indicate five major reasons why the text actually conformed to the contemporary expectation for new and “disruptive” geometries. Two original points of the treatise are thus highlighted : the fact that it blurred the traditional frontier between speculative and practical geometry ; and the fact that this work in geometry follows an “analytical order” but without algebra.