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four spheres, and of these also the first and second are the same as
the first two mentioned above (for the sphere of the fixed stars is
that which moves all the other spheres, and that which is placed
beneath this and has its movement in the circle which bisects the
zodiac is common to all), but the poles of the third sphere of each
planet are in the circle which bisects the zodiac, and the motion of
the fourth sphere is in the circle which is inclined at an angle to
the equator of the third sphere; and the poles of the third sphere are
different for each of the other planets, but those of Venus and
Mercury are the same.
Callippus made the position of the spheres the same as Eudoxus
did, but while he assigned the same number as Eudoxus did to Jupiter
and to Saturn, he thought two more spheres should be added to the
sun and two to the moon, if one is to explain the observed facts;
and one more to each of the other planets.
But it is necessary, if all the spheres combined are to explain
the observed facts, that for each of the planets there should be other
spheres (one fewer than those hitherto assigned) which counteract
those already mentioned and bring back to the same position the
outermost sphere of the star which in each case is situated below
the star in question; for only thus can all the forces at work produce
the observed motion of the planets. Since, then, the spheres
involved in the movement of the planets themselves are--eight for
Saturn and Jupiter and twenty-five for the others, and of these only
those involved in the movement of the lowest-situated planet need
not be counteracted the spheres which counteract those of the
outermost two planets will be six in number, and the spheres which
counteract those of the next four planets will be sixteen; therefore
the number of all the spheres--both those which move the planets and
those which counteract these--will be fifty-five. And if one were
not to add to the moon and to the sun the movements we mentioned,
the whole set of spheres will be forty-seven in number.
Let this, then, be taken as the number of the spheres, so that the
unmovable substances and principles also may probably be taken as just
so many; the assertion of necessity must be left to more powerful
thinkers. But if there can be no spatial movement which does not
conduce to the moving of a star, and if further every being and
every substance which is immune from change and in virtue of itself
has attained to the best must be considered an end, there can be no
other being apart from these we have named, but this must be the
number of the substances. For if there are others, they will cause
change as being a final cause of movement; but there cannot he other
movements besides those mentioned. And it is reasonable to infer
this from a consideration of the bodies that are moved; for if
everything that moves is for the sake of that which is moved, and
every movement belongs to something that is moved, no movement can
be for the sake of itself or of another movement, but all the
movements must be for the sake of the stars. For if there is to be a
movement for the sake of a movement, this latter also will have to
be for the sake of something else; so that since there cannot be an
infinite regress, the end of every movement will be one of the
divine bodies which move through the heaven.
(Evidently there is but one heaven. For if there are many
heavens as there are many men, the moving principles, of which each
heaven will have one, will be one in form but in number many. But
all things that are many in number have matter; for one and the same
definition, e.g. that of man, applies to many things, while Socrates
is one. But the primary essence has not matter; for it is complete
reality. So the unmovable first mover is one both in definition and in
number; so too, therefore, is that which is moved always and
continuously; therefore there is one heaven alone.) Our forefathers in
the most remote ages have handed down to their posterity a
tradition, in the form of a myth, that these bodies are gods, and that
the divine encloses the whole of nature. The rest of the tradition has

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