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 mind is fitted to perceive adequately more things, in proportion as its body has more in common with other bodies.
PROP. XL. Whatsoever ideas in the mind follow from ideas which are therein adequate, are also themselves adequate.
Proof.—This proposition is self—evident. For when we say that an idea in the human mind follows from ideas which are therein adequate, we say, in other words (II. xi. Coroll.), that an idea is in the divine intellect, whereof God is the cause, not in so far as he is infinite, nor in so far as he is affected by the ideas of very many particular things, but only in so far as he constitutes the essence of the human mind.
Note I.—I have thus set forth the cause of those notions, which are common to all men, and which form the basis of our ratiocination. But there are other causes of certain axioms or notions, which it would be to the purpose to set forth by this method of ours; for it would thus appear what notions are more useful than others, and what notions have scarcely any use at all. Furthermore, we