Cassius is using the logic that a king should be someone that is more worthy than all others. He says that Caesar is the same as us and that he doesn't deserve the role because they all had the same privileges and rights.
“I was born free as Caesar; so were you; We both have fed well as Caesar, and we can both endure the winter’s cold as well as he.”(I:2:104-106.)
Cassius' argument represents ethos because he is saying how he would never change sides and fully support the protestors. This shows Brutus that Cassius is a loyal person and that he is dedicated to assassinating Caesar.
“We’re I a common laughter, or did use to stale with ordinary oaths my love to every new protestor; if you know that I do fawn on men and hug them hard and after scandal them, or if you know that I profess myself in banqueting to all the rout, then hold me dangerous”(I:2:78-84)
Cassius is appealing to Brutus' emotions by reminding him of his ancestor who led a rebellion against the oppressive Roman monarchy and how his ancestor would rather have a Devil ruling Rome rather than a king. This helps Brutus see how much suffering a king would cause to the point that it would be worse than the chaos a Devil can cause.
"There was a Brutus once that would have brooked th' eternal devil to keep his state in Rome as easily as king."(I:2:168-170)