If we had to pick one rhetorical device to describe this speech, it would be the rhetorical question.

This happens when a speaker asks a question he's not expecting an answer to…kind of like when your mom asks "Are you trying to drive me insane?" but with higher stakes.

When someone like Henry asks a rhetorical question, he just wants to get you thinking about it. Typically, these questions are asked in such a way as to lead the listener to the same conclusion as the speaker.

Check out this ginormous lump of questions:

And what have we to oppose them? Shall we try argument? Sir, we have been trying that for the last ten years. Have we anything new to offer upon the subject? Nothing. We have held the subject up in every light of which it is capable; but it has all been in vain. Shall we resort to treaty and humble supplication? What terms shall we find which have not been already exhausted? (30-37)

By the numbers: twenty-one of seventy-five sentences are questions. That's almost thirty percent of the speech. Henry appears to have been pretty confident that his listeners would answer the questions the same way he would.