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, 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.