>>>>>Proof--To hate a man is (III. xiii. note) to conceive him as a cause of pain; therefore he who hates a man will endeavour to remove or destroy him. But if anything more painful, or, in other words, a greater evil, should accrue to the hater thereby --and if the hater thinks he can avoid such evil by not carrying out the injury, which he planned against the object of his hatred --he will desire to abstain from inflicting that injury (III. xxviii.), and the strength of his endeavour (III. xxxvii.) will be greater than his former endeavour to do injury, and will therefore prevail over it, as we asserted. The second part of this proof proceeds in the same manner. Wherefore he who hates another, etc. Q.E.D. *****Note--By "good" I here mean every kind of pleasure, and all that conduces thereto, especially that which satisfies our longings, whatsoever they may be. By "evil," I mean every kind of pain, especially that which frustrates our longings. For I have shown (III. ix. note) that we in no case desire a thing because we deem it good, but, contrariwise, we deem a thing good because we desire it: consequently we deem evil that which we shrink from; everyone, therefore, according to his particular emotions, judges or estimates what is good, what is bad, what is better, what is worse, lastly, what is best, and what is worst. Thus a miser thinks that abundance of money is the best, and want of money the worst; an ambitious man desires nothing so much as glory, and fears nothing so much as shame. To an envious man nothing is more delightful than another's misfortune, and nothing more painful than another's success. So every man, according to his emotions, judges a thing to be good or bad, useful or useless. The emotion, which induces a man to turn from that which he wishes, or to wish for that which he turns from, is called "timidity," which may accordingly be defined as "the fear whereby a man is induced to avoid an evil which he regards as future by encountering a lesser evil" (III. xxviii.). But if the evil which he fears be shame, timidity becomes "bashfulness." Lastly, if the desire to avoid a future evil be checked by the fear of another evil, so that the man knows not which to choose, fear becomes "consternation," especially if both the evils feared be very great. XL. He, who conceives himself to be hated by another, and believes that he has given him no cause for hatred, will hate that other in return. >>>>>Proof--He who conceives another as affected with hatred, will thereupon be affected himself with hatred (III. xxvii.), that is, with pain, accompanied by the idea of an external cause. But, by the hypothesis, he conceives no cause for this pain except him who is his enemy; therefore, from conceiving that he is hated by some one, he will be affected with pain, accompanied by the idea of his enemy; in other words, he will hate his enemy in return. Q.E.D.