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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 of fire or air, although the spheres would not move round a stable point. But 1 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 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.

I have explained to you already vivâ voce, that these difficulties do not concern the astronomer: for he does not profess to tell us the existing properties of the spheres, but to suggest, whether correctly or not, a theory in which the motion of the stars is circular and uniform, and yet in agreement with our observation. You know that Abu-bekr al-Zaig, in his treatise on Physics, expresses a doubt whether Aristotle knew the excentricity of the sun but ignored it, and only discussed the effect of the inclination, because he saw that the effect of the excentricity was identical with that of the inclination; or whether he did not perceive it. The truth is that he did not notice it or hear of it: the science was not perfect in his age. If he had heard of it, he would have strongly opposed it; if he had been convinced of its correctness, he would have been greatly embarrassed as regards all that he said on the question. What I said before (ch. xxii.) I will repeat now, namely, that the theory of Aristotle, in explaining the phenomena in the sublunary world, is in accordance with logical inference; here we know the causal relation between one phenomenon and another; we see how far science can investigate them, and the management of nature is clear and intelligible. But of the things in the heavens man knows nothing except a few mathematical calculations, and you see how far these go. I say in the words of the poet,” The heavens are the Lord’s, but the earth He hath given to the sons of man” (Ps. cxv. 16); that is to say, God alone has a perfect and true knowledge of the heavens, their nature, their essence, their form, their motions, and their causes; but He gave man power to know the things which are under the heavens; here is man’s world, here is his home, into which he has been placed, and of which he is himself a portion. This is in reality the truth. For the facts which we require in proving the existence of heavenly beings are withheld from us; the heavens are too far from us, and too exalted in place and rank. Man’s faculties are too deficient to comprehend even the general proof the heavens contain for the existence of Him who sets them in motion. It is in fact ignorance or a kind of madness to weary our minds with finding out things which are beyond our reach. without having the means of approaching them. We must content ourselves with that which is within our reach, and that which cannot be approached by logical inference let us leave to him who has been endowed with that great and divine influence, expressed in the words: “Mouth to mouth do I speak with Him” (Num. xii. 8).

This is all I can say on this question; another person may perhaps be able to establish by proof what appears doubtful to me. It is on account of my great love of truth that I have shown my embarrassment in these matters and I have not heard, nor do I know that any of these theories have been established by proof.

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