logical and emotional appeals in Act I
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Logical: Brutus hears a general shout from the people and says that he is afraid that the people will choose Caesar to be their king. Cassius then logically deduces that if Brutus fears this, then he must not want it to happen.
Emotional: Cassius appeals to Brutus loyalty to Rome "There was a Brutus once that would have brook'd the eternal devil to keep his state in Rome as easily as a king." (I.ii)
He uses logic again by giving examples of Caesar is an ordinary man. He tells how he (Cassius) saved him from drowning and how he saw him once fall with an epileptic fit. He concludes that Caesar is no better than himself or Brutus and does not deserve his lofty status.