But since there are three sorts of friendship, based on excellence, utility, and pleasantness respectively, and two varieties of each of these for each of them may imply either superiority or equality and the justice involved in these is clear from the debates that have been held on it, in a friendship between superior and inferior the claim for proportion takes different forms, the superior's claim being one for inverse proportion, ie as he is to the inferior, so should what he receives from the inferior be to what the inferior receives from him, he being in the position of ruler to subject; if he cannot get that, he demands at least numerical equality.