Final answer:
The quoted passages utilize different rhetorical appeals: the first uses ethos based on authority, the second uses logos based on logic and facts, and the third uses pathos based on emotional hope for the future.
Step-by-step explanation:
The first quote, "At this second appearing to take the oath of the Presidential office, there is less occasion for an extended address than there was at the first," primarily uses the appeal of ethos. The speaker refers to the act of taking the presidential oath, which draws on their authority and credibility.
The second quote, "The progress of our arms, upon which all else chiefly depends, is as well known to the public as to myself, and it is, I trust, reasonably satisfactory and encouraging to all," is an example of logos. This is because it refers to the logical reasoning and facts about the progress of their arms known to the public and the speaker.
The third quote, "With high hope for the future, no prediction in regard to it is ventured," appeals to pathos. It evokes emotions connected with hope and the uncertainty of the future.