154 ARISTOTLE
demonstrated that this independent thing can have no magnitude, but is without parts
and indivisible (for it causes motion for an infinite time, while no finite thing has an
infinite power, and since every magnitude must be either infinite or finite, it cannot have
magnitude, either finite, for the reason given, or infinite, because there is no infinite
magnitude at all). But surely it has also been demonstrated that it cannot be affected or
altered, since all other motions are derivative from change of place. So it is clear why
these things are this way.- But whether one must set down one or more than one such independent thing,
and how many, must not go unnoticed; but one has to mention, as far as the pronounce-
ments of others are concerned, that about the number of them they have said nothing
which can even be stated clearly. For the assumption about the forms contains no particu-
lar speculation about it (for those who speak of the forms say the forms are numbers, and
about the numbers, sometimes they speak as though about infinitely many, but sometimes
as though they had a limit at the number ten, but why the multitude of the numbers is just
so much, nothing is said with a serious effort at demonstrative reasoning). But it is neces-
sary for us to argue from the things that have been laid down and distinguished. For the
source and the first of beings is not movable either in its own right or incidentally, but sets
in motion the primary motion, that is one and everlasting. But since what is in motion
must be moved by something, and the first mover must be itself motionless, and an ever-
lasting motion must be caused by an everlasting source of motion and one motion by one
mover, while we see in addition to the simple motion of the whole heaven, which we
claim the first motionless independent thing causes, other everlasting motions which
belong to the planets (for the body that goes in a circle does so everlastingly and without
stopping, which is demonstrated in the writings on nature), it is necessary that each of
these motions also be caused by something that is itself motionless and an everlasting
independent thing. For the nature of the stars is for each to be an everlasting independent
thing, while the mover is everlasting and takes precedence over the thing moved, and what
takes precedence over an independent thing must be an independent thing. Accordingly, it
is clear that there must be that many independent things and that they must have a nature
such that they are everlasting and motionless in virtue of themselves, and, for the reason
stated above, without magnitude.
That, then, there are independent things, and of these a first one and a second, fol-
lowing the same order as the motions of the stars, is evident; but the number of motions is
already something one must examine from that kind of mathematical knowledge that is the
nearest kin to philosophy, namely from astronomy. For this kind makes its study about per-
ceptible, everlasting thinghood, while the others, such as those concerned with numbers
and with geometry, are not about thinghood at all. Now the fact that the motions are greater
in number than the things moved is clear to those who have touched on the subject even
moderately (since each of the wandering stars is carried along more than one motion); but
as for how many these happen to be, we now state what some of the mathematicians say,
for the sake of a conception of it, in order that some definite number be grasped in our
thinking, and as for what remains, it is necessary to inquire into some things ourselves,
while listening to what other inquirers say about others. If something should seem to those
who busy themselves with these matters to be contrary to what has just now been said, it is
necessary to welcome both accounts, but trust the more precise one.
Eudoxus, then, set it down that the motion of both the sun and the moon is in three
spheres, of which the first is that of the fixed stars, the second rotates along a path
through the midst of the zodiac, and the third along a path inclined along the width of
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