the deviation assumed in respect to the latitude of the paths of Venus and Mercury, I have already clearly shown you vivâ voce that it is impossible to imagine material beings under such conditions. You have seen that Ptolemy has already pointed out this difficulty. He says as follows: “Let no one think that these and similar principles are improbable. If any one considers what we have here expounded in the same light as he considers things produced by skill and subtle work, he will find it improbable; but it is not right to compare human things to divine things.” This is, as you know, what Ptolemy says, and I have already pointed out to you the passages by which you can verify all I said, except what I stated about the position of the centres of the excentric spheres; for I have not heard that any one has paid attention to this question. But you will understand it when you know the length of the diameter of each sphere, and the extent of its excentricity in terms of radii of the earth, according to the facts which Kabici has established in his treatise on the distances. When you notice these distances you will confirm my words. Consider, therefore, how many difficulties arise if we accept the theory which Aristotle expounds in Physics. For, according to that theory, there are no epicycles, and no excentric spheres, but all spheres rotate round the centre of the earth! How then can the different courses of the stars be explained? how is it possible to assume a uniform perfect rotation with the phenomena which we perceive, except by admitting one of the two hypotheses or both of them? The difficulty is still more apparent when we find that admitting what Ptolemy said as regards the epicycle of the moon, and its inclination towards a point different both from the centre of the Universe and from its own centre, the calculations according to these hypotheses are perfectly correct, within one minute; that their correctness is confirmed by the most accurate calculation of the time, duration, and extent of the eclipses, which is always based on these hypotheses. Furthermore, how can we reconcile, without assuming the existence of epicycles, the apparent retrogression of a star with its other motions? How can rotation or motion take place round a point which is not fixed? These are real difficulties.