E3P43D
Demonstration — Part III
Latin
Qui eum quem odit, odio contra erga se affectum esse imaginatur, eo ipso (per propositionem 40 hujus) novum odium oritur durante (per hypothesin) adhuc primo. Sed si contra eundem amore erga se affectum esse imaginetur, quatenus hoc imaginatur eatenus (per propositionem 30 hujus) se ipsum cum lætitia contemplatur et eatenus (per propositionem 29 hujus) eidem placere conabitur hoc est (per propositionem 41 hujus) eatenus conatur ipsum odio non habere nullaque tristitia afficere; qui quidem conatus (per propositionem 37 hujus) major vel minor erit pro ratione affectus ex quo oritur atque adeo si major fuerit illo qui ex odio oritur et quo rem quam odit (per propositionem 26 hujus) tristitia afficere conatur, ei prævalebit et odium ex animo delebit. Q.E.D.
English (Elwes 1883)
He who conceives, that an object of his hatred hates him in return, will thereupon feel a new hatred, while the former hatred (by hypothesis) still remains (III. xl.). But if, on the other hand, he conceives that the object of hate loves him, he will to this extent (III. xxxviii.) regard himself with pleasure, and (III. xxix.) will endeavour to please the cause of his emotion. In other words, he will endeavour not to hate him (III. xli.), and not to affect him painfully; this endeavour (III. xxxvii.) will be greater or less in proportion to the emotion from which it arises. Therefore, if it be greater than that which arises from hatred, and through which the man endeavours to affect painfully the thing which he hates, it will get the better of it and banish the hatred from his mind. Q.E.D.
Modern English
He who imagines that the one he hates is affected with hatred toward him will thereby feel a new hatred (E3P40) while the first hatred (by hypothesis) still persists. But if instead he imagines that the one he hates is affected with love toward him, then insofar as he imagines this he contemplates himself with joy (E3P30) and strives to please that person (E3P29), that is, (E3P41), he strives not to hate him and not to affect him with sadness. This striving (E3P37) will be greater or less in proportion to the affect from which it arises. If therefore it is greater than the striving that arises from hatred, by which he strives to affect the hated thing with sadness (E3P26), it will prevail over it and destroy the hatred. Q.E.D.