Corollary I.- (40:6) He who conceives, that one whom he loves hates him,
will be a prey to conflicting hatred and love. (7) For, in so far as he
conceives that he is an object of hatred, he is determined to hate his
enemy in return. (8) But, by the hypothesis, he nevertheless loves him:
wherefore he will be a prey to conflicting hatred and love.
Corollary II.- (40:9) 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.- (40:10) He who conceives, that another hates him, will (by the
last proposition) hate his enemy in return, and ([xxvi] ) will
endeavour to recall everything which can affect him painfully; he will
moreover endeavour to do him an injury ([xxxix] ). (11) 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.- (40:12) 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. [xv] Coroll., and [xvi] )
Proof.- (41:1) This proposition is proved in the same way as the
preceding one.
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