P45: If someone imagines that someone like himself is affected with Hate toward a thing like himself which he loves, he will hate that {person}.

Dem.: For the thing he loves hates in return the one who hates it (by P40), and so the lover, who imagines that someone hates the thing he loves, thereby imagines the thing he loves to be affected with Hate, i.e. (by P13 S), with Sadness. And consequently (by P21), he is saddened, and his Sadness is accompanied by the idea of the one who hates the thing he loves—{this other being regarded} as the cause {of the Sadness}. I.e. (by P13 S), he will hate him, q.e.d.