METAPHYSICS(BOOKXII) 155
the zodiac (but with that along which the moon is carried inclined to a greater width
than that along which the sun is carried); but he set it down that the motion of each of
the wandering stars is in four spheres, of which the first and second are the same as the
former ones (for the sphere of the fixed stars is that which moves them all, and
the sphere assigned to the place under this and having its motion along a path through
the midst of the zodiac is common to them all), while the poles of the third sphere for all
of them are in the path through the midst of the zodiac, and the motion of the fourth is
along a path inclined to the equator of the third. And he set it down that the poles of the
third sphere are peculiar to the different planets, but those for Venus and Mercury are
the same. Callippus set down the same arrangement of spheres as did Eudoxus, and
gave the same number as he did for Jupiter and Saturn, but for the sun and the moon he
thought there were two spheres still to be added if one were going to account for the
appearances, and one for each of the remaining planets.
But it is necessary, in order to account for the appearances, if all the spheres are
going to be fit together, that there be for each of the planets (less one) other spheres, turn-
ing backwards and continuously restoring to the same position the first sphere of the star
situated next below; for only in that way is it possible for them all to produce the motion of
the planets. Since, then, the spheres in which they themselves are carried are eight [for
Jupiter and Saturn] and twenty-five [for the sun and moon, Mars, Venus, and Mercury], and
of these one, that in which the star situated lowest is carried, does not need to be counter-
turned, the spheres to counter-turn those of the first two planets will be six, while the ones
to counter-turn those of the four lower ones will be sixteen; so the number of all the carry-
ing spheres plus those that turn backward against them will be fifty-five. But if one were
not to add to the moon and the sun the motions which we mentioned, all the spheres will be
forty-seven. So let the number of the spheres be so many, so that it is reasonable to assume
that the number of independent things which are motionless sources is also that many (for
let the number that is necessary be left for more relentless people to say).
But if it is impossible for there to be any motion that is not directed into the
motion of a star, and if in addition every nature and every independent thing that is unaf-
fected and has, by virtue of itself, attained its best condition, must be regarded as an
end, there could be no other nature besides these, but this is necessarily the number of
independent things. For if there were others, they would be movers as final causes of
motion; but it is impossible for there to be other motions besides those mentioned. And
this is reasonable to assume from the things that are moved. For if what carries some-
thing is naturally for the sake of what is carried, and every motion belongs to something
that is carried, no motion could be for the sake of itself or for the sake of another
motion, but they are for the sake of the stars. For if there were to be a motion for the
sake of a motion, the latter too would have to be for the sake of another one; so since
this cannot go to infinity, there will be as an end for every motion one of the divine
bodies carried through the heaven. And it is clear that there is one heaven. For if there
were a plurality of heavens, as there is of human beings, there would be one kindof
source for each one, but many of them in number. But those things that are many in
number contain material (for one and the same articulation belongs to many things, as
does the articulation of a human being, but Socrates is one). But what it primarily is for
something to be does not contain material, for it is a being-at-work-staying-itself.*
*
completeness with that of continuity or persistence. Aristotle invents the word by combining
plete, full-grown) with
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