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.