E4P47D
Demonstration — Part IV
Latin
Spei et metus affectus sine tristitia non dantur. Nam metus est (per 13 affectuum definitionem) tristitia et spes (vide explicationem 12 et 13 affectuum definitionum) non datur sine metu ac proinde (per propositionem 41 hujus) hi affectus non possunt esse per se boni sed tantum quatenus lætitiæ excessum coercere possunt (per propositionem 43 hujus) Q.E.D.
English (Elwes 1883)
Emotions of hope and fear cannot exist without pain. For fear is pain (Def. of the Emotions, xiii.), and hope (Def. of the Emotions, Explanation xii. and xiii.) cannot exist without fear; therefore (IV. xli.) these emotions cannot be good in themselves, but only in so far as they can restrain excessive pleasure (IV. xliii.). Q.E.D.