TEMI GENERALI NELL'OPERA DI LUCA VALERIO

In this paper I try to prove that the tendency of Luca Valerio to generalize definitions and results is not limited to the few rightly famous examples, but is one of the characteristic features of all his mathematical work. This is particularly evident for the limiting procedures widely used in De centro gravitatis solidorum that I compare with analogues procedures in the Subtilium indagationum liber, an early treatise by Valerio where he seems to approach infinitesimal mathematics concepts from a physical point of view. I also compare some passages of Valerio's treatises with analogous Archimedean passages, underlining where Valerio diverges in a significant way from the classical source. Moreover I draw reader's attention to a theorem where Valerio compares two different figures with the same height and with the bases on the same plane or straight line, by means of their sections with planes or straight lines parallel to the bases using the corpus of propositions which allow him to deal with abstract properties of a class of figures.