Abstract
In Chapter 4 of the Analyse, l’Hôpital defines higher order differentials and describes how second order differentials may be used to locate inflection points and cusps on a curve. In addition to the usual rectangular coordinates, l’Hôpital also considers the case where ordinates all emanate from a single point. Although these are not the polar coordinates that came into use in later centuries, because there is no accompanying angular coordinate, they are nevertheless useful in this and subsequent chapters for describing certain curves. L’Hôpital finds the inflection points of the prolate cycloid, the Conchoid of Nicomedes and of a curve that is essentially the same as the “Witch of Agnesi.”