Final answer:
The rhetoric used in the statement is antithesis, highlighting a contrast between love for Caesar and love for Rome to persuasively address one's patriotic duty.
Step-by-step explanation:
The type of rhetoric being used in the statement, "Not that I lov'd Caesar less, but that I lov'd Rome more. Had you rather Caesar were living and die all slaves, than that Caesar were dead, to live all free men?" is an example of antithesis as it juxtaposes two contrasting ideas - love for Caesar and love for Rome - to highlight a deeper meaning. This rhetorical device is often used to persuade or convince an audience by presenting a stark choice between two opposites and appealing to the audience's values and emotions.
The choice of sacrificing Caesar for Rome versus living in slavery portrays the speaker as a patriot and forces the listener to consider what they value more - the life of a leader or the freedom of the people.