Differential Geometry

It is commonly believed that the invention of calculus was motivated by the desire to formulate and solve differential equations, especially the equations of motion of Newtonian dynamics. In fact, purely geometrical problems, such as the determination of tangents and curvatures, feature prominently among its earliest applications. The first calculus textbook, the Analyse des infiniment petits, pour l'intelligence des lignes courbes (see Fig. 8.1), published in 1696 by the French aristocrat Guillaume Francois Antoine de l'Hôpital (1661–1704), is an exposition on the elementary differential geometry of plane curves.¹