he same attributes (per prop, five)--that
is (per prop. two,) that hare anything in common with each other; and,
therefore (per prop, three,) one cannot be the cause of the other.

Corollary 1. Hence it follows that substance cannot be created by
anything else. For there is nothing in nature except substance and its
modes (per axiom one, and def. three and five.) Now, this substance, not
being produced by another, is self-caused.

Corollary 2. This proposition is more easily to be demonstrated by the
absurdity of its contradiction; for if substance can be produced by
anything else, the conception of it would depend on the conception of
the cause (per axiom four,) and hence (per def. three,) it would not be
substance.

VII. It pertains to the nature of substance to exist. Dem. Substance
cannot be produced by anything else (per coroli. prop, six,) and is
therefore the cause of itself--that is (per def. one,) its essence
necessarily involves existence; or it pertains to the nature of
substance to exist.--Q. E. D.

VIII. All substance is necessarily infinite. Dem. There exists but one
substance of the same attribute; and it must either exist as infinite or
finite. But not finite, for (per def. two) as finite it must be limited
by another substance of the same nature, and in that case there would be
two substances of the same attributes, which (per prop, five) is absurd.
Substance therefore is infinite.--Q. E. D.

"Scholium I.--I do not doubt but that to all who judge confusedly
of things, and are not wont to inquire into first causes, it will be
difficult to admit the demonstration of prop. 7, because they do not
sufficiently distinguish between the modifications of substances, and
substances themselves, and are ignorant of the manner in which things
are produced. Hence it follows, that the commencement which they see
natural things have, they attribute to substances; for he who knows not
the true cause of things, confounds all things, and feigns that trees
talk like men; that men are formed from stones as well as from seeds,
and that all forms can be changed into all other forms. So, also, those
who confound the divine nature with the human, naturally attribute
human affections to God, especially as they are ignorant of how these
affections are produced in the mind. If men attended to the nature of
substance, they would not, in the least, doubt proposition seven; nay,
this proposition would be an axiom to all, and wou