E3P16D
Demonstration — Part III
Latin
Id quod simile est objecto, in ipso objecto (per hypothesin) cum affectu lætitiæ vel tristitiæ contemplati sumus atque adeo (per propositionem 14 hujus) cum mens ejus imagine afficietur, statim etiam hoc vel illo afficietur affectu et consequenter res quam hoc idem habere percipimus, erit (per propositionem 15 hujus) per accidens lætitiæ vel tristitiæ causa adeoque (per præcedens corollarium) quamvis id in quo objecto est similis, non sit horum affectuum causa efficiens, eam tamen amabimus vel odio habebimus. Q.E.D.
English (Elwes 1883)
The point of resemblance was in the object (by hypothesis), when we regarded it with pleasure or pain, thus (III. xiv.), when the mind is affected by the image thereof, it will straightway be affected by one or the other emotion, and consequently the thing, which we perceive to have the same point of resemblance, will be accidentally (III. xv.) a cause of pleasure or pain. Thus (by the foregoing Corollary), although the point in which the two objects resemble one another be not the efficient cause of the emotion, we shall still regard the first--named object with love or hate. Q.E.D.
Modern English
The point of resemblance was in the object when we regarded it with an affect of joy or sadness (by hypothesis), and so (E3P14) when the mind is affected by its image it will immediately be affected by one or the other affect as well. Consequently, a thing we perceive to have that same point of resemblance will be (E3P15) the accidental cause of joy or sadness, and therefore (E3P15C), even though the point in which it resembles the object is not the efficient cause of those affects, we will still love or hate it. Q.E.D.