be included in its
definition; and from its definition alone existence must be
deducible. But from its definition (as we have shown, notes ii.,
iii.), we cannot infer the existence of several substances;
therefore it follows that there is only one substance of the same
nature. Q.E.D.

PROP. IX. The more reality or being a thing has, the greater the
number of its attributes (Def. iv.).

PROP. X. Each particular attribute of the one substance must be
conceived through itself.

Proof.--An attribute is that which the intellect perceives of
substance, as constituting its essence (Def. iv.), and,
therefore, must be conceived through itself (Def. iii.). Q.E.D.

Note--It is thus evident that, though two attributes are, in
fact, conceived as distinct--that is, one without the help of the
other--yet we cannot, therefore, conclude that they constitute two
entities, or two different substances. For it is the nature of
substance that each of its attributes is conceived through
itself, inasmuch as all the attributes it has have always existed
simultaneously in it, and none could be produced by any other;
but each expresses the reality or being of substance. It is,
then, far from an absurdity to ascribe several attributes to one
substance: for nothing in nature is more clear than that each
and every entity must be conceived under some attribute, and that
its reality or being is in proportion to the number of its
attributes expressing necessity or eternity and infinity.
Consequently it is abundantly clear, that an absolutely infinite
being must necessarily be defined as consisting in infinite
attributes, each of which expresses a certain eternal and
infinite essence.

If anyone now ask, by what sign shall he be able to
distinguish different substances, let him read the following
propositions, which show that there is but one substance in the
universe, and that it is absolutely infinite, wherefore such a
sign would be sought in vain.

PROP. XI. God, or substance, consisting of infinite attributes,
of which each expresses eternal and infinite essentiality,
necessarily exists.

Proof.--If this be denied, conceive, if possible, that God
does not exist: then his essence does not involve existence.
But this (Prop. vii.) is absurd. Therefore God necessarily
exists.

Another proof.--Of everything whatsoever a cause or reason
must be assigned, either for its existence, or for its
non--existence--e.g. if a triangle exist,