E3P23D
Demonstration — Part III
Latin
Quatenus res odiosa tristitia afficitur eatenus destruitur et eo magis quo majore tristitia afficitur (per scholium propositionis 11 hujus). Qui igitur (per propositionem 20 hujus) rem quam odio habet, tristitia affici imaginatur, lætitia contra afficietur et eo majore quo majore tristitia rem odiosam affectam esse imaginatur; quod erat primum. Deinde lætitia existentiam rei lætæ ponit (per idem scholium propositionis 11 hujus) et eo magis quo major lætitia concipitur. Si quis eum quem odio habet, lætitia affectum imaginatur, hæc imaginatio (per propositionem 13 hujus) ejusdem conatum coercebit hoc est (per scholium propositionis 11 hujus) is qui odio habet, tristitia afficietur etc. Q.E.D.
English (Elwes 1883)
In so far as an object of hatred is painfully affected, it is destroyed, to an extent proportioned to the strength of the pain (III. xi. note). Therefore, he (III. xx.) who conceives, that some object of his hatred is painfully affected, will feel pleasure, to an extent proportioned to the amount of pain he conceives in the object of his hatred. This was our first point. Again, pleasure postulates the existence of the pleasurably affected thing (III. xi. note), in proportion as the pleasure is greater or less. If anyone imagines that an object of his hatred is pleasurably affected, this conception (III. xiii.) will hinder his own endeavour to persist; in other words (III. xi. note), he who hates will be painfully affected. Q.E.D.
Modern English
In so far as a hated thing is affected with sadness, it is destroyed, and the more so the greater the sadness (E3P11S). Therefore, he who conceives a thing he hates to be affected with sadness will be affected with joy in return (E3P20), and the more so the greater the sadness he conceives in the hated thing. This was the first part.Joy, for its part, posits the existence of the joyful thing (E3P11S), and the greater it is conceived to be, the more it does so. If someone conceives a hated thing to be affected with joy, this conception (E3P13) will restrain his own striving, that is, (E3P11S), he who hates will be affected with sadness. Q.E.D.