E2P26D
Demonstration — Part II
Latin
Si a corpore aliquo externo corpus humanum nullo modo affectum est, ergo (per propositionem 7 hujus) nec idea corporis humani hoc est (per propositionem 13 hujus) nec mens humana idea existentiæ illius corporis ullo etiam modo affecta est sive existentiam illius corporis externi ullo modo percipit. At quatenus corpus humanum a corpore aliquo externo aliquo modo afficitur eatenus (per propositionem 16 hujus cum corollario I ejusdem) corpus externum percipit. Q.E.D.
English (Elwes 1883)
If the human body is in no way affected by a given external body, then (II. vii.) neither is the idea of the human body, in other words, the human mind, affected in any way by the idea of the existence of the said external body, nor does it in any manner perceive its existence. But, in so far as the human body is affected in any way by a given external body, thus far (II. xvi. and Coroll.) it perceives that external body. Q.E.D.
Modern English
If the human body is in no way affected by a given external body, then (E2P7) neither the idea of the human body, that is (E2P13), the human mind, is in any way affected by the idea of the existence of that external body, nor does it perceive the existence of that external body in any way. But insofar as the human body is in some way affected by a given external body, to that extent (E2P16) it perceives that external body. Q.E.D.