E3P55D2
Demonstration — Part III
Latin
Invidia est ipsum odium (vide scholium propositionis 24 hujus) sive (per scholium propositionis 13 hujus) tristitia hoc est (per scholium propositionis 11 hujus) affectio qua hominis agendi potentia seu conatus coercetur. At homo (per scholium propositionis 9 hujus) nihil agere conatur neque cupit nisi quod ex data sua natura sequi potest; ergo homo nullam de se agendi potentiam seu (quod idem est) virtutem prædicari cupiet quæ naturæ alterius est propria et suæ aliena adeoque ejus cupiditas coerceri hoc est (per scholium propositionis 11 hujus) ipse contristari nequit ex eo quod aliquam virtutem in aliquo ipsi dissimili contemplatur et consequenter neque ei invidere poterit. At quidem suo æquali qui cum ipso ejusdem naturæ supponitur. Q.E.D.
English (Elwes 1883)
Envy is a species of hatred (III. xxiv. note) or (III. xiii. note) pain, that is (III. xi. note), a modification whereby a man's power of activity, or endeavour towards activity, is checked. But a man does not endeavour or desire to do anything, which cannot follow from his nature as it is given; therefore a man will not desire any power of activity or virtue (which is the same thing) to be attributed to him, that is appropriate to another's nature and foreign to his own; hence his desire cannot be checked, nor he himself pained by the contemplation of virtue in some one unlike himself, consequently he cannot envy such an one. But he can envy his equal, who is assumed to have the same nature as himself. Q.E.D.
Modern English
Envy is hatred itself (E3P24S), or (E3P13S) sadness, that is (E3P11S), an affection whereby a person's power of acting or *conatus* is checked. A person strives for and desires nothing but what can follow from his given nature (E3P9S). Therefore a person will not desire that any power of acting, or, what is the same thing, virtue, be attributed to him that is proper to another's nature and foreign to his own. His desire cannot be checked, and so he himself cannot be saddened, by contemplating some virtue in someone unlike himself. He cannot, therefore, envy such a person. But he can envy his equal, who is assumed to share the same nature. Q.E.D.