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.  (14:2) 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.  (3) Therefore, besides God no substance can be
granted or conceived.  Q.E.D.

Corollary I.- (14:4) Clearly, therefore: 1. God is one, that is (by [D.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 [x] ).

Corollary II.- (14:5) It follows: 2. That extension and thought are either
attributes of God or (by [A.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.- (15:1) Besides God, no substance is granted or can be conceived
(by [xiv] ), that is (by [D.iii] ) nothing which is in itself and is
conceived through itself.  (2) But modes (by [D.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.  (3) But substances
and modes form the sum total of existence (by [A.i] ), therefore, without
God nothing can be, or be conceived.  Q.E.D.

Note.- (15:4) Some assert that God, like a man, consists of body and mind,
and is susceptible of passions.  (5) How far such persons have strayed from
the truth is sufficiently evident from what has been said.  (6) But these
I pass over.  (7) For all who have in anywise reflected on the divine
nature deny that God has a body.  (8) 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 certain shape, and it is the height of absurdity to
predicate such a thing of God, a being absolutely infinite.  (15:9) But
meanwhile by the other reasons with which they try to prove their point,
they show that they think corporeal or extended substance wholly apart
from the divine nature, and say it was created by God.  (10) Wherefrom
the divine nature can have been created, they are wholly ignorant; thus
they clearly show, that they do not know the meaning of their own words. 
(15:11) I myself have proved sufficiently clearly, at any rate in my own 
judgment (Coroll. [vi] , and Note 2, [viii] ), that no substance can be
produced or created by anything other than itself.  (12) Further, I showed
(in [xiv] ), that besides God no substance can be granted or conceived.
(15:13) Hence we drew the conclusion that extended substance is one of the
infinite attributes of God. (14) However, in order to explain more fully,
I will refute the arguments of my adversaries, which all start from the
following points:-- 

(15:15) Extended substance, in so far as it is substance, consists, as
they think, in parts, wherefore they deny that it can be infinite, or,
consequently, that it can appertain to God.  (16) This they illustrate
with many examples, of which I will take one or two.  (17) If extended
substance, they say, is infinite, let it be conceived to be divided into
two parts each part will then be either finite or infinite.  (18) If the
former, then infinite substance is composed of two finite parts, which
is absurd.  (19) If the latter, then one infinite will be twice as large
as another infinite, which is also absurd. 

(15:20) Further, if an infinite line be measured out in foot lengths, it
will consist of an infinite number of such parts; it would equally consist
of an infinite number of parts, if each part measured only an inch:
therefore, one infinity would be twelve times as great as the other. 

(15:21) Lastly, if from a single point there be conceived to be drawn two
diverging lines which at first are at a definite distance apart, but are
produced to infinity, it is certain that the distance between the two lines
will be continually increased, until at length it changes from definite to
indefinable.  (22) As these absurdities follow, it is said, from considering
quantity as infinite, the conclusion is drawn, that extended substance must
necessarily be finite, and, consequently, cannot appertain to the nature of
God.

(15:23) The second argument is also drawn from God's supreme perfection.
(24) God, it is said, inasmuch as he is a supremely perfect being, cannot
be passive; but extended substance, in so far as it is divisible, is
passive.  (25) It follows, therefore, that extended substance does not
appertain to the essence of God.

(15:26) Such are the arguments I find on the subject in writers, who by
them try to prove that extended substance is unworthy of the divine nature,