besides God no substance can be granted, or, consequently, be
conceived. If it could be conceived, it would necessarily have
to be conceived as existent ; but this (by the first part of this
proof) is absurd. Therefore, besides God no substance can be
granted or conceived. Q.E.D.
Corollary I.-Clearly, therefore : 1. God is one, that is (by
Def. vi.) only one substance can be granted in the universe, and
that substance is absolutely infinite, as we have already
indicated (in the note to Prop. x.).
Corollary II.-It follows : 2. That extension and thought
are either attributes of God or (by Ax. i.) accidents
(affectiones) of the attributes of God.

PROP. XV. Whatsoever is, is in God, and without God nothing can
be, or be conceived.
Proof.-Besides God, no substance is granted or can be
conceived (by Prop. xiv.), that is (by Def. iii.) nothing which
is in itself and is conceived through itself. But modes (by Def.
v.) can neither be, nor be conceived without substance ;
wherefore they can only be in the divine nature, and can only
through it be conceived. But substances and modes form the sum
total of existence (by Ax. i.), therefore, without God nothing
can be, or be conceived. Q.E.D.
Note.-Some assert that God, like a man, consists of body and
mind, and is susceptible of passions. How far such persons have
strayed from the truth is sufficiently evident from what has been
said. But these I pass over. For all who have in anywise
reflected on the divine nature deny that God has a body. Of this
they find excellent proof in the fact that we understand by body
a definite quantity, so long, so broad, so deep, bounded by a