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. 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
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