E2P38D
Demonstration — Part II
Latin
Sit A aliquid quod omnibus corporibus commune quodque æque in parte cujuscunque corporis ac in toto est. Dico A non posse concipi nisi adæquate. Nam ejus idea (per corollarium propositionis 7 hujus) erit necessario in Deo adæquata tam quatenus ideam corporis humani quam quatenus ideas habet ejusdem affectionum quæ (per propositiones 16, 25 et 27 hujus) tam corporis humani quam corporum externorum naturam ex parte involvunt hoc est (per propositiones 12 et 13 hujus) hæc idea erit necessario in Deo adæquata quatenus mentem humanam constituit sive quatenus ideas habet quæ in mente humana sunt; mens igitur (per corollarium propositionis 11 hujus) A necessario adæquate percipit idque tam quatenus se quam quatenus suum vel quodcunque externum corpus percipit nec A alio modo potest concipi. Q.E.D.
English (Elwes 1883)
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.
Modern English
Let A be something common to all bodies, and equally present in the part and in the whole of each body. I say A cannot be conceived except adequately. The idea of A in God will necessarily be adequate (E2P7C), both insofar as God has the idea of the human body and insofar as God has the ideas of its affections, which involve in part the nature of the human body and the nature of external bodies (E2P16). That is (E2P12)(E2P13), this idea will be adequate in God insofar as he constitutes the human mind, that is, insofar as he has the ideas that are in the human mind. The mind therefore (E2P11C) perceives A adequately, both when it perceives itself and when it perceives its own body or any external body, and A cannot be conceived in any other way. Q.E.D.