 From a geometrical point of view, the calculus provides techniques for drawing tangents at an arbitrary point of a curve and for measuring the area under a portion of a curve. The differential calculus treats the first problem and the integral calculus the second. The fundamental theorem of the calculus states that these problems are inverses of each other. The calculus was developed independently by Newton and Leibniz, but its spread owed much to a significant number of mathematicians throughout Europe. The first textbook of the differential calculus was published in 1696 by the Marquis de l’Hôpital (1696; see Bradley et al. 2015 for a translation, which we follow below, with commentary). It is worthwhile to consider its axiomatized structure, for it will help us see immediately the infinitary foundations on which the new discipline presented itself to the international community. We first have two definitions: