The aim of this paper is twofold: (1) to show the principal aspects of the way in which
Newton conceived his mathematical concepts and methods and applied them to rational
mechanics in his Principia; (2) to explain how the editors of the Geneva Edition interpreted,
clarified, and made accessible to a broader public Newton’s perfect but often elliptic
proofs. Following this line of inquiry, we will explain the successes of Newton’s mechanics,
but also the problematic aspects of his perfect geometrical methods, more elegant, but
less malleable than analytical procedures, of which Newton himself was one of the inventors.
Furthermore, we will also consider the way in which Newtonianism was spread before
in England and afterwards on continental Europe. In this respect the Geneva Edition plays
a fundamental role because of its complete apparatus of notes, and because it appeared
only thirteen years after the publication of the third edition of the Principia (1726). Finally,
we will also confront some problems connected to the metaphysics of calculus. Therefore,
the case of Newton is one of those in which, starting from mathematics applied to physics,
it is possible to connect an impressive series of fundamental arguments such as the role of
mathematics in science; the comparison between Newton’s geometrical methods and analytical
methods; the way in which Newtonianism was spread as well as the philosophical
implications of Newton’s mathematical concepts.
