P39: If something is common to, and peculiar to, the human Body and certain external bodies by which the human Body is usually affected, and is equally in the part and in the whole of each of them, its idea will also be adequate in the Mind.

Dem.: Let A be that which is common to, and peculiar to, the human Body and certain external bodies, which is equally in the human Body and in the same external bodies, and finally, which is equally in the part of each external body and in the whole. There will be an adequate idea of A in God/Nature (by P7 C), both insofar as he has the idea of the human Body, and insofar as he has ideas of the posited external bodies. Let it be posited now that the human Body is affected by an external body through what it has in common with it, i.e., by A; the idea of this affection will involve property A (by P16), and so (by P7 C) the idea of this affection, insofar as it involves property A, will be adequate in God/Nature insofar as he is affected with the idea of the human Body, i.e. (by P13), insofar as he constitutes the nature of the human Mind. And so (by P11 C), this idea is also adequate in the human Mind, q.e.d.

Cor.: From this it follows that the Mind is the more capable of perceiving many things adequately as its Body has many things in common with other bodies.