; the endeavour to repay in kind injury done to ourselves
is called Revenge.

PROP. XLI. If anyone conceives that he is loved by another, and
believes that he has given no cause for such love, he will love
that other in return. (Cf. III. xv. Coroll., and III. xvi.)

Proof.--This proposition is proved in the same way as the
preceding one. See also the note appended thereto.

Note.--If he believes that he has given just cause for the
love, he will take pride therein (III. xxx. and note); this is
what most often happens (III. xxv.), and we said that its
contrary took place whenever a man conceives himself to be hated
by another. (See note to preceding proposition.) This
reciprocal love, and consequently the desire of benefiting him
who loves us (III. xxxix.), and who endeavours to benefit us, is
called gratitude or thankfulness. It thus appears that men are
much more prone to take vengeance than to return benefits.

Corollary.--He who imagines that he is loved by one whom he
hates, will be a prey to conflicting hatred and love. This is
proved in the same way as the first corollary of the preceding
proposition.

Note.--If hatred be the prevailing emotion, he will endeavour
to injure him who loves him; this emotion is called cruelty,
especially if the victim be believed to have given no ordinary
cause for hatred.

PROP. XLII. He who has conferred a benefit on anyone from
motives of love or honour will feel pain, if he sees that the
benefit is received without gratitude.

Proof.--When a man loves something similar to himself, he
endeavours, as far as he can, to bring it about that he should be
loved thereby in return (III. xxxiii.). Therefore he who has
conferred a benefit confers it in obedience to the desire, which
he feels of being loved in return; that is (III. xxxiv.) from
the hope of honour or (III. xxx. note) pleasure; hence he will
endeavour, as far as he can, to conceive this cause of honour, or
to regard it as actually existing. But, by the hypothesis, he
conceives something else, which excludes the existence of the
said cause of honour: wherefore he will thereat feel pain (III.
xix.). Q.E.D.

PROP. XLIII. Hatred is increased by being reciprocated, and can
on the other hand be destroyed by love.

Proof.--He who conceives, that an object of his hatred hates
him in return, will thereupon feel a new hatred, while the former
hatred (by hypothesis) still remains (III. xl.). But if, on the
othe