 Cavalieri’s applications of the theory of indivisibles were limited to finite figures and thus did not go beyond the geometrical boundaries typical of Greek mathematics. However, Torricelli broke new ground with the determination of the volume of an infinitely long (infinite longum) solid (Torricelli 1644). Up to then, all the results concerning finite figures obtained through indivisibles could easily be proved by finitary Archimedean techniques and by avoiding any mention of infinity—just as in the case of the quadrature of the circle presented in the