E3P22D
Demonstration — Part III
Latin
Qui rem quam amamus lætitia vel tristitia afficit, ille nos lætitia vel tristitia etiam afficit si nimirum rem amatam lætitia illa vel tristitia affectam imaginamur (per præcedentem propositionem). At hæc lætitia vel tristitia in nobis supponitur dari concomitante idea causæ externæ; ergo (per scholium propositionis 13 hujus) si aliquem imaginamur lætitia vel tristitia afficere rem quam amamus, erga eundem amore vel odio afficiemur. Q.E.D.
English (Elwes 1883)
He, who affects pleasurably or painfully the object of our love, affects us also pleasurably or painfully--that is, if we conceive the loved object as affected with the said pleasure or pain (III. xxi.). But this pleasure or pain is postulated to come to us accompanied by the idea of an external cause; therefore (III. xiii. note), if we conceive that anyone affects an object of our love pleasurably or painfully, we shall be affected with love or hatred towards him. Q.E.D.
Modern English
He who affects with joy or sadness a thing we love, affects us also with joy or sadness, provided we conceive the loved thing as affected with that joy or sadness (E3P21). But this joy or sadness in us is supposed to arise accompanied by the idea of an external cause. Therefore (E3P13S), if we conceive that someone affects with joy or sadness a thing we love, we will be affected with love or hatred toward that person. Q.E.D.