E3P40D2
Demonstration — Part III
Latin
Qui aliquem odio erga se affectum esse imaginatur, eum contra (per præcedentem propositionem) odio habebit et (per propositionem 26 hujus) id omne comminisci conabitur quod eundem possit tristitia afficere atque id eidem (per propositionem 39 hujus) inferre studebit. At (per hypothesin) primum quod hujusmodi imaginatur, est malum sibi illatum; ergo idem statim eidem inferre conabitur. Q.E.D.
English (Elwes 1883)
He who conceives, that another hates him, will (by the last proposition) hate his enemy in return, and (III. xxvi.) will endeavour to recall everything which can affect him painfully; he will moreover endeavour to do him an injury (III. xxxix.). Now the first thing of this sort which he conceives is the injury done to himself; he will, therefore, forthwith endeavour to repay it in kind. Q.E.D.
Modern English
He who imagines another to be affected with hatred toward him will hate that other in return (E3P40), and will strive to think of everything that can affect him with sadness (E3P26), and will strive to inflict it on him (E3P39). Now by hypothesis the first thing of this kind he imagines is the harm done to himself. He will therefore immediately strive to repay that same harm. Q.E.D.