"Galileo's access to Jesuit sources at the Collegio Romano is well documented. Galileo did not himself take up the calculus because he did not quite understand it, as is clear from the difficulties and the various paradoxes of the infinite that he raised in his letters to Cavalieri. Thus, this state of affairs is better explained by supposing that there was a common body of Indian work related to the calculus, known to both Galileo and Cavalieri, and that Galileo was not satisfied with Cavalieri's interpretation of it, and not willing to risk his reputation, while Cavalieri was. Nevertheless, out of deference for his teacher, he waited five years before staking his claim."