Corollary I.—He who conceives, that one whom he loves hates him, will be a prey to conflicting hatred and love. For, in so far as he conceives that he is an object of hatred, he is determined to hate his enemy in return. But, by the hypothesis, he nevertheless loves him : wherefore he will be a prey to conflicting hatred and love.

Corollary II.—If a man conceives that one, whom he has hitherto regarded without emotion, has done him any injury from motives of hatred, he will forthwith seek to repay the injury in kind.

Proof.—He who conceives, that another hates him, will (by the last proposition) hate his enemy in return, and (III. xxvi.) will endeavour to recall everything which can affect him painfully ; he will moreover endeavour to do him an injury (III. xxxix.). Now the first thing of this sort which he conceives is the injury done to himself ; he will, therefore, forthwith endeavour to repay it in kind. Q.E.D.

Note.—The endeavour to injure one whom we hate is called Anger ; 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.