tended substance is composed of parts, and such
a hypothesis I have shown (Prop. xii., and Coroll. Prop. xiii.)
to be absurd. Moreover, anyone who reflects will see that all
these absurdities (if absurdities they be, which I am not now
discussing), from which it is sought to extract the conclusion
that extended substance is finite, do not at all follow from the
notion of an infinite quantity, but merely from the notion that
an infinite quantity is measurable, and composed of finite parts
therefore, the only fair conclusion to be drawn is that:
infinite quantity is not measurable, and cannot be composed of
finite parts. This is exactly what we have already proved (in
Prop. xii.). Wherefore the weapon which they aimed at us has in
reality recoiled upon themselves. If, from this absurdity of
theirs, they persist in drawing the conclusion that extended
substance must be finite, they will in good sooth be acting like
a man who asserts that circles have the properties of squares,
and, finding himself thereby landed in absurdities, proceeds to
deny that circles have any center, from which all lines drawn to
the circumference are equal. For, taking extended substance,
which can only be conceived as infinite, one, and indivisible
(Props. viii., v., xii.) they assert, in order to prove that it
is finite, that it is composed of finite parts, and that it can
be multiplied and divided.

So, also, others, after asserting that a line is composed of
points, can produce many arguments to prove that a line cannot be
infinitely divided. Assuredly it is not less absurd to assert
that extended substance is made up of bodies or parts, than it
would be to assert that a solid is made up of surfaces, a surface
of lines, and a line of points. This must be admitted by all who
know clear reason to be infallible, and most of all by those who
deny the possibility of a vacuum. For if extended substance
could be so divided that its parts were really separate, why
should not one part admit of being destroyed, the others
remaining joined together as before? And why should all be so
fitted into one another as to leave no vacuum? Surely in the
case of things, which are really distinct one from the other, one
can exist without the other, and can remain in its original
condition. As, then, there does not exist a vacuum in nature
(of which anon), but all parts are bound to come together to
prevent it, it follows from this that the parts cannot