PROP. [XIII] Substance absolutely infinite is indivisible.
Proof.- (13:1) 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. (2) If the former, we should have several substances of the
same nature, which (by [v] ) is absurd. (3) If the latter, then (by
[vii] ) substance absolutely infinite could cease to exist, which ([xi] )
is also absurd.
Corollary.- (13:4) It follows that no substance, and consequently no
extended substance, in so far as it is substance, is divisible.
Note.- (13:5) The indivisibility of substance may be more easily understood
as follows. (6) 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 [viii] ) involves a manifest contradiction.
PROP. [XIV] Besides God no substance can be granted or conceived.
Proof.- (14:1) As God is a being absolutely infinite, of whom no attribute
that expresses the essence of substance can be denied (by [D.vi] ), and he
necessarily exists (by [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 [v] ) is
absurd; therefore, besides God no substance can be granted, or
consequently, be conceived.
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