Abstract
The first four chapters of the Analyse followed the general outlines of the Lectiones de calculo differentialis, the notes on the differential calculus that Bernoulli had provided to l’Hôpital when he tutored him in 1691–92. Chapter 5 is the first of six chapters that l’Hôpital had a more independent role in composing. It concerns finding the evolute of a given curve, which may be defined as the locus of the centers of curvature of that given curve. The study of these curves originated with Huygens. L’Hôpital determines the formula for finding the center of curvature at any point on a curve, whether in rectangular coordinates or in the case where ordinates all emanate from a single point. He then finds the evolutes of many different curves, including the cycloid, which Huygens had shown is congruent to its evolute. The chapter concludes with l’Hôpital’s description of the cusp of the second kind. Chapter 5 is one of the two longest chapters in the Analyse.