E3P20D
Demonstration — Part III
Latin
Mens (per 13 propositionem hujus) ea imaginari conatur quæ rerum existentiam quibus corporis agendi potentia minuitur vel coercetur, secludunt hoc est (per scholium ejusdem propositionis) ea imaginari conatur quæ rerum quas odio habet, existentiam secludunt atque adeo rei imago quæ existentiam ejus quod mens odio habet, secludit, hunc mentis conatum juvat hoc est (per scholium propositionis 11 hujus) mentem lætitia afficit. Qui itaque id quod odio habet, destrui imaginatur, lætabitur. Q.E.D.
English (Elwes 1883)
The mind (III. xiii.) endeavours to conceive those things, which exclude the existence of things whereby the body's power of activity is diminished or constrained; that is (III. xiii. note), it endeavours to conceive such things as exclude the existence of what it hates; therefore the image of a thing, which excludes the existence of what the mind hates, helps the aforesaid mental effort, in other words (III. xi. note), affects the mind pleasurably. Thus he who conceives that the object of his hate is destroyed will feel pleasure. Q.E.D.
Modern English
The mind strives to imagine things that exclude the existence of those things by which the body's power of acting is diminished or constrained (E3P13), that is, it strives to imagine things that exclude the existence of what it hates (E3P13). So the image of a thing that excludes the existence of what the mind hates supports that striving, and thereby affects the mind with joy (E3P11S). Whoever imagines that the thing he hates is destroyed will therefore feel joy. Q.E.D.