Odium reciproco odio augetur et amore contra deleri potest.
Hatred is increased by reciprocal hatred and in return may be destroyed by love.
DEMONSTRATIO: Qui eum quem odit, odio contra erga se affectum esse imaginatur, eo ipso (per propositionem 40 hujus) novum odium oritur durante (per hypothesin) adhuc primo. Sed si contra eundem amore erga se affectum esse imaginetur, quatenus hoc imaginatur eatenus (per propositionem 30 hujus) se ipsum cum lætitia contemplatur et eatenus (per propositionem 29 hujus) eidem placere conabitur hoc est (per propositionem 41 hujus) eatenus conatur ipsum odio non habere nullaque tristitia afficere; qui quidem conatus (per propositionem 37 hujus) major vel minor erit pro ratione affectus ex quo oritur atque adeo si major fuerit illo qui ex odio oritur et quo rem quam odit (per propositionem 26 hujus) tristitia afficere conatur, ei prævalebit et odium ex animo delebit. Q.E.D.
Whoever hates a person who imagines to be affected with hatred towards oneself, from that itself (by IIIP40 [Reciprocity of Hatred]) arises a new hatred enduring (by hypothesis) to the highest. But if, on the other hand, one imagines that the same one one is affected with love towards oneself, insofar as one imagines this to such an extent (by IIIP30 [Looking at Others Looking at Us]) does one view oneself with joy and to such an extent (by IIIP29 [Influence of Opinion of Others]) will try to please the same one, that is (by IIIP41 [Power of Love]) to such an extent tries to not have hatred to the person and affect with no sadness; indeed, whatever persisting (by IIIP37 [Feedback Loop of Desire]) will be more or less an emotion by reason from which arises and to such an extent if more will have been by that which arose from hatred and from which one tried to affect with sadness that one whom one hated, to that one it will prevail and destroy hatred from the heart.
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