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.