E3P39D
Demonstration — Part III
Latin
Aliquem odio habere est (per scholium propositionis 13 hujus) aliquem ut tristitiæ causam imaginari adeoque (per propositionem 28 hujus) is qui aliquem odio habet, eundem amovere vel destruere conabitur. Sed si inde aliquid tristius sive (quod idem est) majus malum sibi timeat idque se vitare posse credit non inferendo ei quem odit malum quod meditabatur, a malo inferendo (per eandem propositionem 28 hujus) abstinere cupiet idque (per propositionem 37 hujus) majore conatu quam quo tenebatur inferendi malum, qui propterea prævalebit, ut volebamus. Secundæ partis demonstratio eodem modo procedit. Ergo qui aliquem odio habet etc. Q.E.D.
English (Elwes 1883)
To hate a man is (III. xiii. note) to conceive him as a cause of pain; therefore he who hates a man will endeavour to remove or destroy him. But if anything more painful, or, in other words, a greater evil, should accrue to the hater thereby--and if the hater thinks he can avoid such evil by not carrying out the injury, which he planned against the object of his hate--he will desire to abstain from inflicting that injury (III. xxviii.), and the strength of his endeavour (III. xxxvii.) will be greater than his former endeavour to do injury, and will therefore prevail over it, as we asserted. The second part of this proof proceeds in the same manner. Wherefore he who hates another, etc. Q.E.D.
Modern English
To hate someone is to imagine him as a cause of sadness (E3P13S), and therefore whoever hates someone will strive to remove or destroy him (E3P28). But if he fears something more distressing, that is, a greater harm, will come to him as a result, and believes he can avoid it by not inflicting the harm he had planned on the one he hates, he will want to refrain from inflicting it (E3P28), and this desire (E3P37) will be stronger than the desire to do harm and will prevail over it, as we asserted. The demonstration of the second part proceeds in the same way. Therefore whoever hates someone, etc. Q.E.D.