On the argument of simplicity in Elements and schoolbooks of Geometry

Abstract

Simplicity arguments are to be found in most geometrical works, from those of Proclus in his Commentaries on the First Book of Euclid’s Elements, up to those of contemporary manuals. Our goal is to read these arguments in their historical contexts to analyze agreements, disagreements and the multiplicity of points of view. For a better apprehension and a better understanding of the different conceptions, we will focus on the notion of angles and their measurements. We will study the notion of ≪ simplicity ≫ in various Elements of Geometry, in particular those of Euclid, Peletier du Mans (1628), Arnauld (1667), Lacroix (1803) and Houel (1867). From there, we will examine French schoolbooks of geometry, beginning from the 1960s up to the 1990s, including those of the so-called period of ≪la reforme des mathematiques modernes≫ in France.