E3P21D
Demonstration — Part III
Latin
Rerum imagines (ut in propositione 19 hujus demonstravimus) quæ rei amatæ existentiam ponunt, mentis conatum quo ipsam rem amatam imaginari conatur, juvant. Sed lætitia existentiam rei lætæ ponit et eo magis quo lætitiæ affectus major est : est enim (per scholium propositionis 11 hujus) transitio ad majorem perfectionem : ergo imago lætitiæ rei amatæ in amante ipsius mentis conatum juvat hoc est (per scholium propositionis 11 hujus) amantem lætitia afficit et eo majore quo major hic affectus in re amata fuerit. Quod erat primum. Deinde quatenus res aliqua tristitia afficitur eatenus destruitur et eo magis quo majore afficitur tristitia (per idem scholium propositionis 11 hujus) adeoque (per propositionem 19 hujus) qui id quod amat tristitia affici imaginatur, tristitia etiam afficietur et eo majore quo major hic affectus in re amata fuerit. Q.E.D.
English (Elwes 1883)
The images of things (as we showed in III. xix.) which postulate the existence of the object of love, help the mind's endeavour to conceive the said object. But pleasure postulates the existence of something feeling pleasure, so much the more in proportion as the emotion of pleasure is greater; for it is (III. xi. note) a transition to a greater perfection; therefore the image of pleasure in the object of love helps the mental endeavour of the lover; that is, it affects the lover pleasurably, and so much the more, in proportion as this emotion may have been greater in the object of love. This was our first point. Further, in so far as a thing is affected with pain, it is to that extent destroyed, the extent being in proportion to the amount of pain (III. xi. note); therefore (III. xix.) he who conceives, that the object of his love is affected painfully, will himself be affected painfully, in proportion as the said emotion is greater or less in the object of love. Q.E.D.
Modern English
Images of things that posit the existence of the loved thing support the mind's striving to imagine that loved thing (E3P19). Joy posits the existence of a joyful thing, and does so the more the affect of joy is greater, for joy is a transition to greater perfection (E3P11S). Therefore the image of joy in the loved thing supports the lover's mental striving, and thereby affects the lover with joy, the greater in proportion as this affect was greater in the loved thing. That was the first point.
As for sadness: insofar as a thing is affected with sadness, it is to that extent destroyed, and the more so the greater the sadness (E3P11S). Therefore (E3P19) whoever imagines that the thing he loves is affected with sadness will also be affected with sadness, greater in proportion as the affect is greater in the loved thing. Q.E.D.