Quote 4
POPE ADRIAN
Go forthwith to our holy consistory
And read amongst the statutes decretal
What, by the holy council held at Trent,
The sacred synod hath decreed for him
That doth assume the papal government
Without election and a true consent. (3.1.105-109)
The Pope relies upon book-learning… sort of. Really, he's counting on the law books to help him in his case against Bruno. This is quite a different kind of knowledge than the one Faustus has come to rely on—the experience and exploration of the world, all thanks to Mephistopheles.
Quote 5
POPE
Cast down our footstool.
RAYMOND
Saxon Bruno, stoop.
Whilst on thy back his Holiness ascends
Saint Peter's chair and state pontifical.
BRUNO
Proud Lucifer, that state belongs to me.
But thus I fall to Peter, not to thee.
POPE
To me and Peter shalt thou grovelling lie
And crouch before the papal dignity. (3.1.88-95)
The Pope demands a display of submission from schismatic pope Bruno, forcing him to get down on his hands and knees so he can use his back as a step-stool. Talk about humiliating. Bruno only submits, he says, because he respects St. Peter, implying that he recognizes the power of the office of Pope (which Peter represents), but not the power of the man who now fills it.
Quote 6
BRUNO
Pope Adrian, let me have some right of law;
I was elected by the Emperor.
POPE
[…]
He grows too proud in his authority
Lifting his lofty head above the clouds
And, like a steeple, overpeers the Church.
But we'll put down his haughty insolence. (3.1.125-126, 132-135)
The dispute between Adrian and Bruno is over who has the power to appoint the pope. Pope Adrian believes that this power belongs only to members of the Church, but Bruno argues that a former pope gave the Holy Roman Emperor this same power. This belief is why Bruno claims "right of law," i.e., that he's the lawfully chosen Pope.