E3P42D
Demonstration — Part III
Latin
Qui rem aliquam sibi similem amat, conatur quantum potest efficere ut ab ipsa contra ametur (per propositionem 33 hujus). Qui igitur præ amore in aliquem beneficium contulit, id facit desiderio quo tenetur ut contra ametur hoc est (per propositionem 34 hujus) spe gloriæ sive (per scholium propositionis 30 hujus) lætitiæ adeoque (per propositionem 12 hujus) hanc gloriæ causam quantum potest imaginari sive ut actu existentem contemplari conabitur. At (per hypothesin) aliud imaginatur quod ejusdem causæ existentiam secludit : ergo (per propositionem 19 hujus) eo ipso contristabitur. Q.E.D.
English (Elwes 1883)
When a man loves something similar to himself, he endeavours, as far as he can, to bring it about that he should be loved thereby in return (III. xxxiii.). Therefore he who has conferred a benefit confers it in obedience to the desire, which he feels of being loved in return; that is (III. xxxiv.) from the hope of honour or (III. xxx. note) pleasure; hence he will endeavour, as far as he can, to conceive this cause of honour, or to regard it as actually existing. But, by the hypothesis, he conceives something else, which excludes the existence of the said cause of honour: wherefore he will thereat feel pain (III. xix.). Q.E.D.
Modern English
He who loves something similar to himself strives as much as he can to have it love him in return (E3P33). He who therefore confers a benefit out of love does so out of the desire to be loved in return, that is, (E3P34), out of hope of glory, or (E3P30S) of joy. He will therefore strive as much as he can to imagine this cause of glory, or to contemplate it as actually existing. But by hypothesis he imagines something else that excludes the existence of that cause. He will therefore be affected with sadness (E3P19). Q.E.D.