conceived without its parts, which everyone will admit to be
absurd. If we adopt the second alternative-namely, that the
parts will not retain the nature of substance-then, if the whole
substance were divided into equal parts, it would lose the nature
of substance, and would cease to exist, which (by Prop. vii.) is
absurd.

PROP. XIII. Substance absolutely infinite is indivisible.
Proof.-If it could be divided, the parts into which it was
divided would either retain the nature of absolutely infinite
substance, or they would not. If the former, we should have
several substances of the same nature, which (by Prop. v.) is
absurd. If the latter, then (by Prop. vii.) substance absolutely
infinite could cease to exist, which (by Prop. xi.) is also
absurd.
Corollary.-It follows, that no substance, and consequently no
extended substance, in so far as it is substance, is divisible.
Note.-The indivisibility of substance may be more easily
understood as follows. The nature of substance can only be
conceived as infinite, and by a part of substance, nothing else
can be understood than finite substance, which (by Prop. viii)
involves a manifest contradiction.

PROP. XIV. Besides God no substance can be granted or conceived.
Proof.-As God is a being absolutely infinite, of whom no
attribute that expresses the essence of substance can be denied
(by Def. vi.), and he necessarily exists (by Prop. xi.) ; if any
substance besides God were granted, it would have to be explained
by some attribute of God, and thus two substances with the same
attribute would exist, which (by Prop. v.) is absurd ; therefore,