Infinitesimals in the foundations of Newton's mechanics

This paper discusses two concepts of “moment” (infinitesimal) used successively by Newton in his calculus and relates these two concepts to the two concepts of force that Newton presented in Law II and Def. VIII of the Principia, to which the approximations to the action of a centripetal force known as the polygonal and parabolic models are considered to be related. It is shown that in the context of the application of the calculus to mechanics, the transition in the use of these concepts of “moment” took place in 1684, between the writing of De Motu and its first revision.