The Complete Aristotle (eng.)
process of passing through, the motion must be divisible:
for at the time when O was passing through, it neither was at rest
nor had completed its passage but was in an intermediate state:
while if it is passing through and has completed its passage at the
same moment, then that which is walking will at the moment when it
is walking have completed its walk and will be in the place to
which it is walking; that is to say, it will have completed its
motion at the place to which it is in motion. And if a thing is in
motion over the whole KBG and its motion is the three D, E, and Z,
and if it is not in motion at all over the partless section A but
has completed its motion over it, then the motion will consist not
of motions but of starts, and will take place by a thing’s having
completed a motion without being in motion: for on this assumption
it has completed its passage through A without passing through it.
So it will be possible for a thing to have completed a walk without
ever walking: for on this assumption it has completed a walk over a
particular distance without walking over that distance. Since,
then, everything must be either at rest or in motion, and O is
therefore at rest in each of the sections A, B, and G, it follows
that a thing can be continuously at rest and at the same time in
motion: for, as we saw, O is in motion over the whole ABG and at
rest in any part (and consequently in the whole) of it. Moreover,
if the indivisibles composing DEZ are motions, it would be possible
for a thing in spite of the presence in it of motion to be not in
motion but at rest, while if they are not motions, it would be
possible for motion to be composed of something other than
motions.
And if length and motion are thus indivisible, it is neither
more nor less necessary that time also be similarly indivisible,
that is to say be composed of indivisible moments: for if the whole
distance is divisible and an equal velocity will cause a thing to
pass through less of it in less time, the time must also be
divisible, and conversely, if the time in which a thing is carried
over the section A is divisible, this section A must also be
divisible.
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2
And since every magnitude is divisible into magnitudes-for we
have shown that it is impossible for anything continuous to be
composed of indivisible parts, and every magnitude is continuous-it
necessarily follows that the quicker of two things traverses a
greater magnitude in an equal time, an equal magnitude in less
time, and a greater magnitude in less time, in conformity with the
definition sometimes given of ‘the quicker’. Suppose that A is
quicker than B. Now since of two things that which changes sooner
is quicker, in the time ZH, in which A has changed from G to D, B
will not yet have arrived at D but will be short of it: so that in
an equal time the quicker will pass over a greater magnitude. More
than this, it will pass over a greater magnitude in less time: for
in the time in which A has arrived at D, B being the slower has
arrived, let us say, at E. Then since A has occupied the whole time
ZH in arriving at D, will have arrived at O in less time than this,
say ZK. Now the magnitude GO that A has passed over is greater than
the magnitude GE, and the time ZK is less than the whole time ZH:
so that the quicker will pass over a greater magnitude in less
time. And from this it is also clear that the quicker will pass
over an equal magnitude in less time than the slower. For since it
passes over the greater magnitude in less time than the slower, and
(regarded by itself) passes over LM the greater in more time than
LX the lesser, the time PRh in which it passes over LM will be more
than the time PS, which it passes over LX: so that, the time PRh
being less than the time PCh in which the slower passes over LX,
the time PS will also be less than the time PX: for it is less than
the time PRh, and that which is less than something else that is
less than a thing is also itself less than that thing. Hence it
follows that the quicker will traverse an equal magnitude in less
time than the slower. Again, since the motion of anything must
always occupy either an equal time or less or more time in
comparison with that of another thing, and since, whereas a thing
is slower if its motion occupies more time and of equal velocity if
its motion occupies an equal time, the quicker is neither of equal
velocity nor slower, it follows that the motion
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