The persuasive appeal used in the lines given above is REASON.
According to Aristotle, there are three types of persuasive appeal, these are: appeal to reason, appeal to one's character and appeal to emotions. Appeal to reason is a form of rhetorical approach, in which a speaker made an argument by giving or presenting facts that lead the audience to reach the kind of conclusion that the speaker desire. In the question given above, the speaker was appealing to the reason of his audience, leading them to reach the conclusion that the refusal of the kingly crown does not signify a reasonable and ambitious attitude.