Abstract
Abstract The celebrated inventor of the “Ocular Harpsichord” is less well known as the author of Mathématique universelle, published in 1728. In this work, the Jesuit teacher develops a cheerful method of instruction in inspired by his desire to popularize a discipline hitherto marked with the seal of austerity. In order to clear away the illusory superiority of professional geometers, Father Castel makes argumentative breaks from tradition, aiming to devalue the ethos of contemporary mathematicians. Through textual analysis of certain rhetorical professions such as candid directness (aretè), ostentatious goodwill (eunoia) and, in a more general sense, the dissociation of appearance from reality, the present study seeks to place in evidence certain ethical concerns which were shaking Jesuite learned world in its confrontation with the new epistemology of the century of the Enlightenment.