E4P46D
Demonstration — Part IV
Latin
Omnes odii affectus mali sunt (per corollarium I præcedentis propositionis) adeoque qui ex ductu rationis vivit, quantum potest conabitur efficere ne odii affectibus conflictetur (per propositionem 19 hujus) et consequenter (per propositionem 37 hujus) conabitur ne etiam alius eosdem patiatur affectus. At odium odio reciproco augetur et amore contra extingui potest (per propositionem 43 partis III) ita ut odium in amorem transeat (per propositionem 44 partis III). Ergo qui ex ductu rationis vivit, alterius odium etc. amore contra compensare conabitur hoc est generositate (cujus definitionem vide in scholio propositionis 59 partis III). Q.E.D.
English (Elwes 1883)
All emotions of hatred are bad (IV. xlv. Coroll. i.); therefore he who lives under the guidance of reason will endeavour, as far as possible, to avoid being assailed by such emotions (IV. xix.); consequently, he will also endeavour to prevent others being so assailed (IV. xxxvii.). But hatred is increased by being reciprocated, and can be quenched by love (III. xliii.), so that hatred may pass into love (III. xliv.); therefore he who lives under the guidance of reason will endeavour to repay hatred with love, that is, with kindness. Q.E.D.
Modern English
All affects of hatred are bad (E4P45C1). One who lives under the guidance of reason will therefore try, as far as possible, to avoid being assailed by such affects (E4P19), and consequently (E4P37) will try to prevent others from being so assailed as well. But hatred grows when it is returned, and can be extinguished by love (E3P43) so that hatred passes into love (E3P44). One who lives under the guidance of reason will therefore try to repay another's hatred and the like with love, that is, with high-mindedness (for its definition see the Scholium of E3P59). Q.E.D.