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. And the motion of the planets involves, in each case,
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
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