I have before promised to describe in a separate chapter the strong objections which must occur to him who thinks that human wisdom comprehends fully the nature of the spheres and their motions; that these are subject to fixed laws, and capable of being comprehended as regards order and relation. I will now explain this. CHAPTER XXIV You know of Astronomy as much as you have studied with me, and learnt from the book Almagest; we had not sufficient time to go beyond this. The theory that [the spheres] move regularly, and that the assumed courses of the stars are in harmony with observation, depends, as you are aware, on two hypotheses: we must assume either epicycles, or excentric spheres, or a combination of both. Now I will show that each of these two hypotheses is irregular, and totally contrary to the results of Natural Science. Let us first consider an epicycle, such as has been assumed in the spheres of the moon and the five planets, rotating on a sphere, but not round the centre of the sphere that carries it. This arrangement would necessarily produce a revolving motion; the epicycle would then revolve, and entirely change its place; but that anything in the spheres should change its place is exactly what Aristotle considers impossible. For that reason Abu-bekr ibn-Alzaig, in an astronomical treatise which he wrote, rejects the existence of epicycles. Besides this impossibility, he mentions others, showing that the theory of epicycles implies other absurd notions. I will here explain them:—(1) It is absurd to assume that the revolution of a cycle has not the centre of the Universe for its centre; for it is a fundamental principle in the order of the Universe that there are only three kinds of motion—from the centre, towards the centre, and round the centre; but an epicycle does not move away from the centre, nor towards it, nor round it. (2) Again, according to what Aristotle explains in Natural Science, there must be something fixed round which the motion takes place; this is the reason why the earth remains stationary. But the epicycle would move round a centre which is not stationary. I have heard that Abu-bekr discovered a system in which no epicycles occur; but excentric spheres are not excluded by him. I have not heard it from his pupils; and even if it be correct that he discovered such a system, he has not gained much by it; for excentricity is likewise as contrary as possible to the principles laid down by Aristotle. For it seems to me that an excentric sphere does not move round the centre of the Universe, but round an imaginary point distant from the centre, and therefore round a point which is not fixed. A person ignorant of astronomy might think that the motion of the excentric spheres may still be considered as taking place round something fixed, since their centre is apparently within the sphere of the moon. I would admit this if the centre were situated in the region