Q.E.D.
PROP.XLVI.

If a man has been affected pleasurably or painfully by anyone, of a class or nation different from his own, and if the pleasure or pain has been accompanied by the idea of the said stranger as cause, under the general category of the class or nation: the man will feel love or hatred, not only to the individual stranger, but also to the whole class or nation whereto he belongs.
Proof .-- This is evident from III.

xvi.
PROP.XLVII.

Joy arising from the fact, that anything we hate is destroyed, or suffers other injury, is never unaccompanied by a certain pain in us.
Proof .-- This is evident from III.xxvii.

For in so far as we conceive a thing similar to ourselves to be affected with pain, we ourselves feel pain.
Note .-- This proposition can also be proved from the Corollary to II.xvii.