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 idea which produces this particular kind of motion; but as ideas are only possible in intellectual beings, the heavenly sphere is an intellectual being. But even a being that is endowed with the faculty of forming an idea, and possesses a soul with the faculty of moving, does not change its place on each occasion that it forms an idea: for an idea alone does not produce motion, as has been explained in [Aristotle's] Metaphysics. We can easily understand this, when we consider how often we form ideas of certain things, yet do not move towards them, though we are able to do so; it is only when a desire arises for the thing imagined, that we move in order to obtain it. We have thus shown that both the soul, the principle of motion, and the intellect, the source of the ideas, would not produce motion without the existence of a desire for the object of which an idea has been formed. It follows that the heavenly sphere must have a desire for the ideal which it has comprehended, and that ideal, for which it has a desire, is God, exalted be His name! When we say that God moves the spheres, we mean it in the following sense: the spheres have a desire to become similar to the ideal comprehended by them. This ideal, however, is simple in the strictest sense of the word, and not subject to any change or alteration, but constant in producing everything good, whilst the spheres are corporeal: the latter can therefore not be like this ideal in any other way, except in the production of circular motion: for this is the only action of corporeal beings that can be perpetual; it is the most simple motion of a body; there is no change in the essence of the sphere, nor in the beneficial results of its motion.

When Aristotle had arrived at this result, he further investigated the subject, and found, by proof, that there were many spheres, and that all moved in circles, but each with its peculiar motion as regards velocity and direction. He naturally argued that the ideal comprehended by the one sphere, which completes its circuit in one day, is different from that of another sphere which completes its circuit in thirty years: he thus arrived at the conclusion that there were as many ideals as there were spheres: each sphere has a desire for that ideal which is the source of its existence, and that desire is the cause of its individual motion, so that in fact the ideal sets the sphere in motion. Aristotle does not say, nor does any other authority, that there are ten or a hundred ideals: he simply states that their number agrees with that of the spheres. When, therefore, some of his contemporaries held that the number of spheres was fifty, he said, if that was true, the number of ideals must likewise be fifty. For the scholars in his time were few and possessed but imperfect learning; they thought that there must be a separate sphere for each movement, because they did not know that what appear to be several distinct movements can be explained as resulting from the inclination of one sphere as is, e.g., the case with the change in the longitude of a star, its declination and the places of its rising and setting noticed in the circle of the horizon. This point, however, does not concern us at present: let us therefore return to our subject.

The later philosophers assumed ten Intelligences, because they counted the spheres containing stars and the all-encompassing sphere, although some of the spheres included several distinct orbits. There are altogether nine spheres, viz., the all-encompassing sphere, that of the fixed stars, and those of the seven planets: nine Intelligences correspond to the nine spheres: the