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| Paragraph 1 |
It is clear, then, why these things are as they are. |
| Paragraph 2 |
Eudoxus supposed that the motion of the sun or of the moon involves,
in either case, three spheres, of which the first is the sphere of
the fixed stars, and the second moves in the circle which runs along
the middle of the zodiac, and the third in the circle which is inclined
across the breadth of the zodiac; |
| Paragraph 3 |
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; |
| Paragraph 4 |
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; |
| Paragraph 5 |
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; |
| Paragraph 6 |
(Evidently there is but one heaven. |
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created 1996/11/25 modified 2009/04/26