E4P15D
Demonstration — Part IV
Latin
Ex vera boni et mali cognitione quatenus hæc (per propositionem 8 hujus) affectus est, oritur necessario cupiditas (per 1 affectuum definitionem) quæ eo est major quo affectus ex quo oritur major est (per propositionem 37 partis III). Sed quia hæc cupiditas (per hypothesin) ex eo quod aliquid vere intelligimus, oritur, sequitur ergo ipsa in nobis quatenus agimus (per propositionem 3 partis III) atque adeo per solam nostram essentiam debet intelligi (per definitionem 2 partis III) et consequenter (per propositionem 7 partis III) ejus vis et incrementum sola humana potentia definiri debet. Porro cupiditates quæ ex affectibus quibus conflictamur oriuntur, eo etiam majores sunt quo hi affectus vehementiores erunt atque adeo earum vis et incrementum (per propositionem 5 hujus) potentia causarum externarum definiri debet quæ, si cum nostra comparetur, nostram potentiam indefinite superat (per propositionem 3 hujus) atque adeo cupiditates quæ ex similibus affectibus oriuntur, vehementiores esse possunt illa quæ ex vera boni et mali cognitione oritur ac proinde (per propositionem 7 hujus) eandem coercere vel restinguere poterunt. Q.E.D.
English (Elwes 1883)
From the true knowledge of good and evil, in so far as it is an emotion, necessarily arises desire (Def. of the Emotions, i.), the strength of which is proportioned to the strength of the emotion wherefrom it arises (III. xxxvii.). But, inasmuch as this desire arises (by hypothesis) from the fact of our truly understanding anything, it follows that it is also present with us, in so far as we are active (III. i.), and must therefore be understood through our essence only (III. Def. ii.); consequently (III. vii.) its force and increase can be defined solely by human power. Again, the desires arising from the emotions whereby we are assailed are stronger, in proportion as the said emotions are more vehement; wherefore their force and increase must be defined solely by the power of external causes, which, when compared with our own power, indefinitely surpass it (IV. iii.); hence the desires arising from like emotions may be more vehement, than the desire which arises from a true knowledge of good and evil, and may, consequently, control or quench it. Q.E.D.
Modern English
From true knowledge of good and bad, insofar as this knowledge is an affect (E4P8), desire necessarily arises (E3DA1), and this desire is greater in proportion as the affect from which it arises is greater (E3P37). But since this desire arises, by hypothesis, from our truly understanding something, it follows that it is present in us insofar as we are active (E3P3), and must therefore be understood through our essence alone (E3D2). Consequently (E3P7) its force and growth must be determined by human power alone. The desires arising from the affects that assail us, on the other hand, are greater in proportion as those affects are more vehement, and their force and growth must therefore (E4P5) be determined by the power of external causes, which, compared with our own power, surpasses it indefinitely (E4P3). The desires arising from such affects can therefore be more vehement than the desire arising from true knowledge of good and bad, and can accordingly check or quench it (E4P7). Q.E.D.