E2P16D
Demonstration — Part II
Latin
Omnes enim modi quibus corpus aliquod afficitur ex natura corporis affecti et simul ex natura corporis afficientis sequuntur (per axioma 1 post corollarium lemmatis 3) : quare eorum idea (per axioma 4 partis I) utriusque corporis naturam necessario involvet adeoque idea cujuscunque modi quo corpus humanum a corpore externo afficitur, corporis humani et corporis externi naturam involvit. Q.E.D.
English (Elwes 1883)
All the modes, in which any given body is affected, follow from the nature of the body affected, and also from the nature of the affecting body (by Ax. i., after the Coroll. of Lemma iii.), wherefore their idea also necessarily (by I. Ax. iv.) involves the nature of both bodies; therefore, the idea of every mode, in which the human body is affected by external bodies, involves the nature of the human body and of the external body. Q.E.D.
Modern English
All the modes by which any body is affected follow from the nature of the affected body together with the nature of the affecting body (by Axiom 1 after the Corollary of Lemma 3) (E2AInt3); therefore their idea (by Axiom 4 of Part 1) (E1A4) will necessarily involve the nature of both bodies. Hence the idea of any mode by which the human body is affected by external bodies involves the nature of the human body and the nature of the external body. Q.E.D.