it out when you consider the known distances and magnitudes of each sphere and each star, all expressed in terms of the radii of the earth. There is a uniform measure for all, and the excentricity of each sphere is not determined by units proportionate to its own magnitude.
It is still more improbable and more objectionable to assume that there are two spheres, the one within the other; that these are closely joined from all sides, and have, nevertheless, different centres. For in this case the smaller sphere might move whilst the larger be at rest; but the smaller cannot be at rest when the larger moves, and must move with the larger when the latter rotates round any other axis than that which passes through the two centres. Now we have this proposition which can be proved; and, further, the established theory that there is no vacuum, and also the assumed excentricity of the spheres; from all this it follows that in every two spheres the motion of the upper one should cause the lower sphere to move in the same way, and round the same centre. But this is not the case: the outer and the inner spheres do not move in the same way, and not round the same centre or the same axis: each of them has its peculiar motion. For this reason it has been assumed that between every two spheres there are substances different from those of the spheres. It may be very much doubted whether this is the case: for where should the centres of these intermediate substances be placed? have these substances likewise their own peculiar motion? Thabith has explained the above-mentioned theory in one of his treatises, and proved that we must assume a substance of a spherical form intermediate between one sphere and the other. All this is part of that which I have not explained to you when you studied with me, for I was afraid you might become confused and would not understand even those things which I wished to show you. But as to the inclination and 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
