ept adequately.

Proof.--Let A be something, which is common to all bodies, and
which is equally present in the part of any given body and in the
whole. I say A cannot be conceived except adequately. For the
idea thereof in God will necessarily be adequate (II. vii.
Coroll.), both in so far as God has the idea of the human body,
and also in so far as he has the idea of the modifications of the
human body, which (II. xvi., xxv., xxvii.) involve in part the
nature of the human body and the nature of external bodies; that
is (II. xii., xiii.), the idea in God will necessarily be
adequate, both in so far as he constitutes the human mind, and in
so far as he has the ideas, which are in the human mind.
Therefore the mind (II. xi. Coroll.) necessarily perceives A
adequately, and has this adequate perception, both in so far as
it perceives itself, and in so far as it perceives its own or any
external body, nor can A be conceived in any other manner.
Q.E.D.

Corollary--Hence it follows that there are certain ideas or
notions common to all men; for (by Lemma ii.) all bodies agree
in certain respects, which (by the foregoing Prop.) must be
adequately or clearly and distinctly perceived by all.

PROP. XXXIX. That, which is common to and a property of the
human body and such other bodies as are wont to affect the human
body, and which is present equally in each part of either, or in
the whole, will be represented by an adequate idea in the mind.

Proof.--If A be that, which is common to and a property of the
human body and external bodies, and equally present in the human
body and in the said external bodies, in each part of each
external body and in the whole, there will be an adequate idea of
A in God (II. vii. Coroll.), both in so far as he has the idea of
the human body, and in so far as he has the ideas of the given
external bodies. Let it now be granted, that the human body is
affected by an external body through that, which it has in common
therewith, namely, A; the idea of this modification will involve
the property A (II. xvi.), and therefore (II. vii. Coroll.) the
idea of this modification, in so far as it involves the property
A, will be adequate in God, in so far as God is affected by the
idea of the human body; that is (II. xiii.), in so far as he
constitutes the nature of the human mind; therefore (II. xi.
Coroll.) this idea is also adequate in the human mind. Q.E.D.

Corollary.--Hence it follows that the