Hobbes on the Ratios of Motions and Magnitudes

Abstract

Hobbes intended and expected De Corpore to secure his place among the foremost mathematicians of his era. This is evident from the content of Part iii of the work, which contains putative solutions to the most eagerly sought mathematical results of the seventeenth century. It is well known that Hobbes failed abysmally in his attempts to solve problems of this sort, but it is not generally understood that the mathematics of De Corpore is closely connected with the work of some of seventeenth-century Europe’s most important mathematicians. This paper investigates the connection between the main mathematical chapters of De Corpore and the work of Galileo Galilei, Bonaventura Cavalieri, and Gilles Personne de Roberval. I show that Hobbes’s approach in Chapter 16 borrows heavily from Galileo’s Two New Sciences, while his treatment of “deficient figures’ in Chapter 17 is nearly identical in method to Cavalieri’s Exercitationes Geometricae Sex. Further, I argue that Hobbes’s attempt to determine the arc length of the parabola in Chapter 18 is intended to use Roberval’s methods to generate a more general result than one that Roberval himself had achieved in the 1640s (when he and Hobbes were both active in the circle of mathematicians around Marin Mersenne). I claim Hobbes was convinced that his first principles had led him to discover a “method of motion” that he mistakenly thought could solve any geometric problem with elementary constructions.