In a letter of 23 May 1702, Varignon told Leibniz that his friend Fontenelle, captivated by the "Géométrie des infiniment petits", planned to write "des élemens Metaphysiques de votre calcul." Although the German philosopher considered Fontenelle to be an "esprit galant et beau", he judged the project vain. Élémens de la Géométrie de l'infini, published in 1727, is the fruit of this project, which was over twenty years in the making. Varignon with Guillaume de L'Hôpital was the main promoter of differential calculus within the Academy, in particular through the reading of memoirs using it. Most of these memoirs were commented on by Fontenelle in the "History" section, from which Élémens de la Géométrie de l'infini takes its inspiration. In this contribution, we focus on one of the fundamental concepts of differential calculus, that of a curve considered as a polygon with infinitely many sides. We examine how this concept functions within the early Leibnizian calculus, in particular the way Varignon appropriates it in his practice, and then examine the manner in which Fontenelle thematizes it in his writings.