of fire or air, although the spheres would not move round a stable point. But I will show that the amount of excentricity has, in a certain way, been described in the Almagest; and later scholars have calculated the exact amount of excentricity in terms of radii of the earth, and have proved the result. The same measure has been used in astronomy in describing all distances and magnitudes. It has thus been shown that the point round which the sun moves lies undoubtedly beyond the sphere of the moon, and below the superficies of the sphere of Mercury. The centre for the circuit of Mars, that is, the centre of the excentric sphere of Mars, is beyond the sphere of Mercury, and below the sphere of Venus. The centre of Jupiter has the same distance; it lies between the sphere of Venus and that of Mercury, whilst the centre of Saturn lies between the spheres of Mars and Jupiter. Now, consider how improbable all this appears according to the laws of Natural Science. You will find 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