 In conclusion, the “infinitistic revolution” in the 17th and the early 18th century left an important legacy for philosophy and mathematics. The theory of indivisibles introduced new magnitudes characterized infinitarily (the collection of all the indivisibles of a figure), and new infinitary geometrical objects extended the classical geometrical universe. Moreover, the debates on the calculus were focused on the nature of the infinitely small and the infinitely large. Finally, the issues emerging from Galileo’s paradox were a prelude to the problem of extending counting from finite to infinite collections.