 We see in the above the explicit infinitary characterization of some of the basic entities appealed to in the new calculus. Both postulates require something that the Greeks had studiously avoided, namely the consideration of infinitely small quantities and the reduction of curves to infinilateral polygons. While l’Hôpital and a number of French mathematicians were enthusiastic about going “infinitary”, Leibniz himself developed a fictionalist account of the appeal to infinitely small quantities (foreshadowed already in his early De Quadratura which did not see the light of day until 1993; see Leibniz (1993)). Also note the use of geometrical and kinematic (i.e. based on movement, as implied by the notions of continual increase or decrease) concepts. Much of the 19th century work on the calculus was devoted to removing geometrical and kinematic notions from the foundations of the discipline.