The Complete Aristotle (eng.)

in
the case of a revolving sphere, in which the velocities of the
parts near the centre and of those on the surface are different
from one another and from that of the whole; this implies that
there is not one motion but many). As we have said, then, that
which is without parts can be in motion in the sense in which a man
sitting in a boat is in motion when the boat is travelling, but it
cannot be in motion of itself. For suppose that it is changing from
AB to BG-either from one magnitude to another, or from one form to
another, or from some state to its contradictory-and let D be the
primary time in which it undergoes the change. Then in the time in
which it is changing it must be either in AB or in BG or partly in
one and partly in the other: for this, as we saw, is true of
everything that is changing. Now it cannot be partly in each of the
two: for then it would be divisible into parts. Nor again can it be
in BG: for then it will have completed the change, whereas the
assumption is that the change is in process. It remains, then, that
in the time in which it is changing, it is in AB. That being so, it
will be at rest: for, as we saw, to be in the same condition for a
period of time is to be at rest. So it is not possible for that
which has no parts to be in motion or to change in any way: for
only one condition could have made it possible for it to have
motion, viz. that time should be composed of moments, in which case
at any moment it would have completed a motion or a change, so that
it would never be in motion, but would always have been in motion.
But this we have already shown above to be impossible: time is not
composed of moments, just as a line is not composed of points, and
motion is not composed of starts: for this theory simply makes
motion consist of indivisibles in exactly the same way as time is
made to consist of moments or a length of points.
    Again, it may be shown in the following way that there can be no
motion of a point or of any other indivisible. That which is in
motion can never traverse a space greater than itself without first
traversing a space equal to or less than itself. That being so, it
is evident that the point also must first traverse a space equal to
or less than itself. But since it is indivisible, there can be no
space less than itself for it to traverse first: so it will have to
traverse a distance equal to itself. Thus the line will be composed
of points, for the point, as it continually traverses a distance
equal to itself, will be a measure of the whole line. But since
this is impossible, it is likewise impossible for the indivisible
to be in motion.
    Again, since motion is always in a period of time and never in a
moment, and all time is divisible, for everything that is in motion
there must be a time less than that in which it traverses a
distance as great as itself. For that in which it is in motion will
be a time, because all motion is in a period of time; and all time
has been shown above to be divisible. Therefore, if a point is in
motion, there must be a time less than that in which it has itself
traversed any distance. But this is impossible, for in less time it
must traverse less distance, and thus the indivisible will be
divisible into something less than itself, just as the time is so
divisible: the fact being that the only condition under which that
which is without parts and indivisible could be in motion would
have been the possibility of the infinitely small being in motion
in a moment: for in the two questions-that of motion in a moment
and that of motion of something indivisible-the same principle is
involved.
    Our next point is that no process of change is infinite: for
every change, whether between contradictories or between
contraries, is a change from something to something. Thus in
contradictory changes the positive or the negative, as the case may
be, is the limit, e.g. being is the limit of coming to be and
not-being is the limit of ceasing to be: and in contrary changes
the particular contraries are the limits, since these are the
extreme points of any such process of change, and consequently of
every process of alteration: for alteration is always dependent
upon some contraries. Similarly contraries are the extreme points
of processes of increase and decrease: the limit of increase is to
be found in the complete magnitude proper to the peculiar nature of
the thing that is increasing, while the limit of decrease is the
complete loss of such