and cannot possibly appertain thereto.  (27) However, I think an attentive
reader will see that I have already answered their propositions; for all
their arguments are founded on the hypothesis that extended substance is
composed of parts, and such a hypothesis I have shown ([xii] , and Coroll. 
[xiii] ) to be absurd.  (15:28) Moreover, anyone who reflects will see
that all these absurdities (if absurdities they be, which I am not now
discussing), from which it is sought to extract the conclusion that
extended substance is finite, do not at all follow from the notion of an
infinite quantity, but merely from the notion that an infinite quantity is
measurable, and composed of finite parts; therefore, the only fair
conclusion to be drawn is that infinite quantity is not measureable, and
cannot be composed of finite parts.  (29) This is exactly what we have
already proved (in [xii] ).  (15:30) Wherefore the weapon which they aimed
at us has in reality recoiled upon themselves.  (31) If, from this
absurdity of theirs, they persist in drawing the conclusion that extended
substance must be finite, they will in good sooth be acting like a man who
asserts that circles have the properties of squares, and, finding himself
thereby landed in absurdities, proceeds to deny that circles have any
centre, from which all lines drawn to the circumference are equal.
(15:32) For, taking extended substance, which can only be conceived
as infinite, one, and indivisible ([viii] , [v] , [xii] ) they assert,
in order to prove that it is finite, that it is composed of finite parts,
and that it can be multiplied and divided.

(15:33) So, also, others, after asserting that a line is composed of
points, can produce many arguments to prove that a line cannot be
infinitely divided.  (34) Assuredly it is not less absurd to assert that
extended substance is made up of bodies or parts, than it would be to
assert that a solid is made up of surfaces, a surface of lines, and a
line of points.  (35) This must be admitted by all who know clear reason
to be infallible, and most of all by those who deny the possibility of a
vacuum.  (36) For if extended substance could be so divided that its parts
were really separate, why should not one part admit of being destroyed,
the others remaining joined together as before?  (37) And why should all
be so fitted into one another as to leave no vacuum?  (15:38) Surely in
the case of things, which are really distinct one from the other, one can
exist without the other, and can remain in its original condition.
(15:39) As then, there does not exist a vacuum in nature (of which anon),
but all parts are bound to come together to prevent it, it follows from
this also that the parts cannot be really distinguished, and that extended
substance in so far as it is substance cannot be divided.
 
(15:40) If anyone asks me the further question, Why are we naturally so
prone to divide quantity?  (41) I answer, that quantity is conceived by
us in two ways; in the abstract and superficially, as we imagine it; or
as substance, as we conceive it solely by the intellect.  (42) If, then,
we regard quantity as it is represented in our imagination, which we often
and more easily do, we shall find that it is finite, divisible, and
compounded of parts; but if we regard it as it is represented in our
intellect, and conceive it as substance, which it is very difficult to do,
we shall then, as I have sufficiently proved, find that it is infinite,
one, and indivisible.  (43) This will be plain enough to all, who make a
distinction between the intellect and the imagination, especially if it be
remembered, that matter is everywhere the same, that its parts are not
distinguishable, except in so far as we conceive matter as diversely
modified, whence its parts are distinguished, not really, but modally.
(15:44) For instance, water, in so far as it is water, we conceive to be 
divided, and its parts to be separated one from the other; but not in so
far as it is extended substance; from this point of view it is neither
separated nor divisible.  (45) Further, water, in so far as it is water,
is produced and corrupted; but, in so far as it is substance, it is neither
produced nor corrupted.

(15:46) I think I have now answered the second argument; it is, in fact,
founded on the same assumption as the first, namely, that matter, in so
far as it is substance, is divisible, and composed of parts.  (47) Even
if it were so, I do not know why it should be considered unworthy of the
divine nature, inasmuch as besides God (by [xiv] ) no substance can be
granted, wherefrom it could receive its modifications.  (48) All things,
I repeat, are in God, and all things which come to pass, come to pass
solely through the laws of the infinite nature of God, and follow (as I
will shortly show) from the necessity of his essence.  (49) Wherefore it
can in nowise be said, that God is passive in respect to anything other
than himself, or that extended substance is unworthy of the Divine nature,
even if it be supposed divisible, so long as it is granted to be infinite
and eternal.  (15:50) But enough of this for the present. 

PROP. [XVI]  From the necessity of the divine nature must follow 
             an infinite number of things in infinite ways, that is,
             all things which can fall within the sphere of infinite
             intellect.

Proof.- (16:1) This proposition will be clear to everyone, who remembers
that from the given definition of any thing the intellect infers several
properties, which really necessarily follow therefrom (that is, from the
actual essence of the thing defined); and it infers more properties in
proportion as the definition of the thing expresses more reality, that is,
in proportion as the essence of the thing defined involves more reality.
(16:2) Now, as the divine nature has absolutely infinite attributes (by
[D.vi] ), of which each expresses infinite essence after its kind, it
follows that from the necessity of its nature an infinite number of things
(that is, everything which can fall within the sphere of an infinite
intellect) must necessarily follow.  Q.E.D.

Corollary I.- (16:3) Hence it follows, that God is the efficient cause of
all that can fall within the sphere of an infinite intellect.

Corollary II.- (16:4) It also follows that God is a cause in himself
and not through an accident of his nature.