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112 THE FOTJEFOLD BOOT. [CHAP. IY.
limit each other, we mean, that both have their extreme
ends in common ; therefore only two extended things can
be conterminous, never two indivisible ones, for then they
would be one i.e. only lines, but not mere points, can be
conterminous. He then transfers this from Space to Time.
As there always remains a line between two points, so there
always remains a time between two nows ; this is the time
in which a change takes place i.e. when one state is in the
first, and another in the second, now. This time, like every
other, is divisible to infinity; consequently, whatever is
changing passes through an infinite number of degrees
within that time, through which the second state gradually
grows out of that first one. The process may perhaps be
made more intelligible by the following explanation. Be
tween two consecutive states the difference of which is
perceptible to our senses, there are always several inter
mediate states, the difference between which is not per
ceptible to us ; because, in order to be sensuously per
ceptible, the newly arising state must have reached a
certain degree of intensity or of magnitude : it is therefore
preceded by degrees of lesser intensity or extension, in
passing through which it gradually arises. Taken collec
tively, these are comprised under the name of change,
and the time occupied by them is called the time of change.
Now, if we apply this to a body being propelled, the first
effect is a certain vibration of its inner parts, which, after
communicating the impulse to other parts, breaks out into
external motion. Aristotle infers quite rightly from the
infinite divisibility of Time, that everything which fills it,
therefore every change, i.e. every passage from one state to
another, must likewise be susceptible of endless subdivision,
so that all that arises, does so in fact by the concourse of
an infinite multitude of parts ; accordingly its genesis is
always gradual, never sudden. From these principles and
the consequent gradual arising of each movement, he