The Complete Aristotle (eng.)

will have taken place in half the time
and in fact in any part of it: for as soon as any division is made
there is always a time defined by moments. If, then, all time is
divisible, and that which is intermediate between moments is time,
everything that is changing must have completed an infinite number
of changes.
    Again, since a thing that changes continuously and has not
perished or ceased from its change must either be changing or have
changed in any part of the time of its change, and since it cannot
be changing in a moment, it follows that it must have changed at
every moment in the time: consequently, since the moments are
infinite in number, everything that is changing must have completed
an infinite number of changes.
    And not only must that which is changing have changed, but that
which has changed must also previously have been changing, since
everything that has changed from something to something has changed
in a period of time. For suppose that a thing has changed from A to
B in a moment. Now the moment in which it has changed cannot be the
same as that in which it is at A (since in that case it would be in
A and B at once): for we have shown above that that that which has
changed, when it has changed, is not in that from which it has
changed. If, on the other hand, it is a different moment, there
will be a period of time intermediate between the two: for, as we
saw, moments are not consecutive. Since, then, it has changed in a
period of time, and all time is divisible, in half the time it will
have completed another change, in a quarter another, and so on to
infinity: consequently when it has changed, it must have previously
been changing.
    Moreover, the truth of what has been said is more evident in the
case of magnitude, because the magnitude over which what is
changing changes is continuous. For suppose that a thing has
changed from G to D. Then if GD is indivisible, two things without
parts will be consecutive. But since this is impossible, that which
is intermediate between them must be a magnitude and divisible into
an infinite number of segments: consequently, before the change is
completed, the thing changes to those segments. Everything that has
changed, therefore, must previously have been changing: for the
same proof also holds good of change with respect to what is not
continuous, changes, that is to say, between contraries and between
contradictories. In such cases we have only to take the time in
which a thing has changed and again apply the same reasoning. So
that which has changed must have been changing and that which is
changing must have changed, and a process of change is preceded by
a completion of change and a completion by a process: and we can
never take any stage and say that it is absolutely the first. The
reason of this is that no two things without parts can be
contiguous, and therefore in change the process of division is
infinite, just as lines may be infinitely divided so that one part
is continually increasing and the other continually decreasing.
    So it is evident also that that that which has become must
previously have been in process of becoming, and that which is in
process of becoming must previously have become, everything (that
is) that is divisible and continuous: though it is not always the
actual thing that is in process of becoming of which this is true:
sometimes it is something else, that is to say, some part of the
thing in question, e.g. the foundation-stone of a house. So, too,
in the case of that which is perishing and that which has perished:
for that which becomes and that which perishes must contain an
element of infiniteness as an immediate consequence of the fact
that they are continuous things: and so a thing cannot be in
process of becoming without having become or have become without
having been in process of becoming. So, too, in the case of
perishing and having perished: perishing must be preceded by having
perished, and having perished must be preceded by perishing. It is
evident, then, that that which has become must previously have been
in process of becoming, and that which is in process of becoming
must previously have become: for all magnitudes and all periods of
time are infinitely divisible.
    Consequently no absolutely first stage of change can be
represented by any particular part of space or time which the
changing thing may occupy.
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7
    Now since the motion of everything that is in