E4P21D
Demonstration of Proposition 21 — Part IV
Latin
Hujus propositionis demonstratio seu potius res ipsa per se patet et etiam ex cupiditatis definitione. Est enim cupiditas (per 1 affectuum definitionem) beate seu bene vivendi, agendi etc. ipsa hominis essentia hoc est (per propositionem 7 partis III) conatus quo unusquisque suum esse conservare conatur. Ergo nemo potest cupere etc. Q.E.D.
English (Elwes 1883)
The proof of this proposition, or rather the proposition itself, is self-evident, and is also plain from the definition of desire. For the desire of living, acting, &c., blessedly or rightly, is (Def. of the Emotions, i.) the essence of man—that is (III. vii.), the endeavour made by everyone to preserve his own being. Therefore, no one can desire, &c. Q.E.D.
Modern English
The demonstration of this proposition — or rather the thing itself — is self-evident, and also plain from the definition of desire. For desire (by the First Definition of the Affects (E3DA1)) is the very essence of a human being with respect to living well and acting well, that is (by P7 of Part III (E3P7)) the conatus by which each person strives to preserve their being. Therefore no one can desire, etc. Q.E.D.