E2P17D2
Demonstration — Part II
Latin
Dum corpora externa corporis humani partes fluidas ita determinant ut in molliores sæpe impingant, earum plana (per postulatum 5) mutant, unde fit (vide axioma 2 post corollarium lemmatis 3) ut inde alio modo reflectantur quam antea solebant et ut etiam postea iisdem novis planis spontaneo suo motu occurrendo eodem modo reflectantur ac cum a corporibus externis versus illa plana impulsæ sunt et consequenter ut corpus humanum dum sic reflexæ moveri pergunt, eodem modo afficiant, de quo mens (per propositionem 12 hujus) iterum cogitabit hoc est (per propositionem 17 hujus) mens iterum corpus externum ut præsens contemplabitur et hoc toties quoties corporis humani partes fluidæ spontaneo suo motu iisdem planis occurrent. Quare quamvis corpora externa a quibus corpus humanum affectum semel fuit, non existant, mens tamen eadem toties ut præsentia contemplabitur quoties hæc corporis actio repetetur. Q.E.D.
English (Elwes 1883)
When external bodies determine the fluid parts of the human body, so that they often impinge on the softer parts, they change the surface of the last named (Post. v.); hence (Ax. ii., after the Coroll. of Lemma iii.) they are refracted therefrom in a different manner from that which they followed before such change; and, further, when afterwards they impinge on the new surfaces by their own spontaneous movement, they will be refracted in the same manner, as though they had been impelled towards those surfaces by external bodies; consequently, they will, while they continue to be thus refracted, affect the human body in the same manner, whereof the mind (II. xii.) will again take cognizance--that is (II. xvii.), the mind will again regard the external body as present, and will do so, as often as the fluid parts of the human body impinge on the aforesaid surfaces by their own spontaneous motion. Wherefore, although the external bodies, by which the human body has once been affected, be no longer in existence, the mind will nevertheless regard them as present, as often as this action of the body is repeated. Q.E.D.
Modern English
When external bodies determine the fluid parts of the human body such that they often impinge on the softer parts, they change the surfaces of those softer parts (E2Post5). From this it follows (E2AInt2) that the fluid parts are reflected from them in a different manner than before, and that afterward, when those fluid parts encounter those same new surfaces by their own spontaneous motion, they are reflected in the same manner as when they were driven toward those surfaces by external bodies. Consequently, while the fluid parts continue to move in this way, they affect the human body in the same manner, and the mind (E2P12) will again think of it, that is, (E2P17), the mind will again regard the external body as present. This occurs as often as the fluid parts of the human body encounter those surfaces by their own spontaneous motion. Therefore, even though the external bodies by which the human body was once affected no longer exist, the mind will nonetheless regard them as present as often as this action of the body is repeated. Q.E.D.