This article analyzes the evolution of Mersenne's views concerning the validity of Galileo's theory of acceleration. After publishing, in 1634, a treatise designed to present empirical evidence in favor of Galileo's odd-number law, Mersenne developed over the years the feeling that only the elaboration of a physical proof could provide sufficient confirmation of its validity. In the present article, I try to show that at the center of Mersenne's worries stood Galileo's assumption that a falling body had to pass in its acceleration through infinite degrees of speed. His extensive discussions with, or his reading of, Descartes, Gassendi, Baliani, Fabri, Cazre, Deschamps, Le Tenneur, Huygens, and Torricelli led Mersenne to believe that the hypothesis of a passage through infinite degrees of speed was incompatible with any mechanistic explanation of free fall.

No abstract

Thought experiments play an important epistemic, rhetorical, and didactic function in Galileo's dialogues. In some cases, Salviati, Sagredo, and Simplicio agree about what would happen in an imaginary scenario and try to understand whether the predicted outcome is compatible with their respective theoretical assumptions. There are, however, also situations in which the predictions of the three interlocutors turn out to be theory laden. Salviati, Sagredo, and Simplicio not only disagree about what would happen, but they reject one another's solutions as question begging and sometimes even dismiss one another's thought experiments as misleading or nonsensical.

is article analyzes Galileo's mathematization of motion, focusing in particular on his use of geometrical diagrams. It argues that Galileo regarded his diagrams of acceleration not just as a complement to his mathematical demonstrations, but as a powerful heuristic tool. Galileo probably abandoned the wrong assumption of the proportionality between the degree of velocity and the space traversed in accelerated motion when he realized that it was impossible, on the basis of that hypothesis, to build a diagram of the law of fall. e article also shows how Galileo's discussion of the paradoxes of infinity in the First Day of the Two New Sciences is meant to provide a visual solution to problems linked to the theory of acceleration presented in Day ree of the work. Finally, it explores the reasons why Cavalieri and Gassendi, although endorsing Galileo's law of free fall, replaced Galileo's diagrams of acceleration with alternative ones.

In everyday language, the use of such words as "chance," "coincidence,"