ce of anything, than of the
existence of a being absolutely infinite or perfect--that is, of
God. For inasmuch as his essence excludes all imperfection, and
involves absolute perfection, all cause for doubt concerning his
existence is done away, and the utmost certainty on the question
is given. This, I think, will be evident to every moderately
attentive reader.

PROP. XII. No attribute of substance can be conceived from which
it would follow that substance can be divided.

Proof.--The parts into which substance as thus conceived would
be divided either will retain the nature of substance, or they
will not. If the former, then (by Prop. viii.) each part will
necessarily be infinite, and (by Prop. vi.) self--caused, and (by
Prop. v.) will perforce consist of a different attribute, so
that, in that case, several substances could be formed out of one
substance, which (by Prop. vi.) is absurd. Moreover, the parts
(by Prop. ii.) would have nothing in common with their whole, and
the whole (by Def. iv. and Prop. x.) could both exist and be
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 neces