E3P17D
Demonstration — Part III
Latin
Est enim (per hypothesin) hæc res per se tristitiæ causa et (per scholium propositionis 13 hujus) quatenus eandem hoc affectu imaginamur, eandem odio habemus et quatenus præterea aliquid habere imaginamur simile alteri quæ nos æque magno lætitiæ affectu afficere solet, æque magno lætitiæ conamine amabimus (per propositionem præcedentem) atque adeo eandem odio habebimus et simul amabimus. Q.E.D.
English (Elwes 1883)
The given thing is (by hypothesis) in itself a cause of pain, and (III. xiii. note), in so far as we imagine it with this emotion, we shall hate it: further, inasmuch as we conceive that it has some point of resemblance to something else, which is wont to affect us with an equally strong emotion of pleasure, we shall with an equally strong impulse of pleasure love it (III. xvi.); thus we shall both hate and love the same thing. Q.E.D.
Modern English
The thing is by hypothesis a cause of sadness in itself, and (E3P13S) insofar as we imagine it with that affect we hate it. And insofar as we also conceive it to have some point of resemblance to something else that normally affects us with an equally strong affect of joy, we will love it with an equally strong striving toward joy (E3P16). We therefore hate it and at the same time love it. Q.E.D.