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. 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 other hand, he conceives that the object of hate loves him, he will to this extent (III. xxxviii.) regard himself with pleasure, and (III. xxix.) will endeavour to please the cause of his emotion. In other words, he will endeavour not to hate him (III. xli.), and not to affect him painfully; this endeavour (III. xxxvii.) will be greater or less in proportion to the emotion from which it arises. Therefore, if it be greater than that which arises from hatred, and through which the man endeavours to affect painfully the thing which he hates, it will get the better of it and banish the hatred from his mind. Q.E.D. XLIV. Hatred which is completely vanquished by love passes into love: and love is thereupon greater than if hatred had not preceded it. >>>>>Proof--The proof proceeds in the same way as Prop. xxxviii. of this Part: for he who begins to love a thing, which he was wont to hate or regard with pain, from the very fact of loving feels pleasure. To this pleasure involved in love is added the pleasure arising from aid given to the endeavour to remove the pain involved in hatred (III. xxxvii.), accompanied by the idea of the former object of hatred as cause.