Prop. [XLV] If a man conceives, that anyone similar to himself
hates anything also similar to himself, which he
loves, he will hate that person.
Proof.- (45:1) The beloved object feels reciprocal hatred twards him who
hates it ([xl] ); therefore the lover, in conceiving that anyone hates
the beloved object, conceives the beloved thing as affected by hatred, in
other words ([xiii] ), by pain; consequently he is himself affected by
pain accompanied by the idea of the hater of the beloved thing as cause;
that is, he will hate him who hates anything which he himself loves
([xiii] note). Q.E.D.
Prop. [XLVI] If a man has been affected pleasurably or painfully
by anyone, of a class or nation different front 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.- (46:1) This is evident from [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.- (47:1) This is evident from [xxvii] .
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