"Believe me on my honor, and respect that honor so that you will believe me."
Brutus's Speech- Pathos
"...just as i killed my best friend for the good of Rome."
Brutus's Speech- Logos
"His death has been recorded in the capital."
Brutus is speaking to the people of Rome using ethos to persuade them that his honor should be powerful enough for them to have his word. He uses the credibility that now that he is ruler of Rome after completing a "difficult yet necessary" task that he should be honored. Brutus relates to the people to get them on his side.
Antony's Speech- Ethos
"He brought many captives home to Rome whose ransoms enriched us all."
Brutus is speaking to the people using pathos to appeal to their emotions. He wants people to feel for him after having to kill his "best friend" for the better of Rome. Brutus wants others to think about what they would do if they had to kill their best friend so that everyone can see how Brutus wants to do what's best for Rome.
Antony's Speech- Pathos
"My heart is in the coffin with Caesar,"
Brutus uses Logos to show how he is not afraid to declare Caesar's death and that he did what he thought was best. Declaring that the  death in the capital is proof to the people. Using this logic to back himself up makes him for reliable to the crowd.
Antony's Speech- Logos
"The bad things men do live on after their deaths, but the good things are often buried with their bones."
Antony uses Ethos to gain the trust of the crowd during Caesar's funeral. Talking about all the good Caesar has done allows people to see the good side of Caesars ruling and overlook the bad. Antony makes sure that all the people remember how much they used to love and honor Caesar and how now just because he's dead, he should lose that honor.
Antony uses Pathos to get the audience emotionally on his side. Saying his heart is with Caesar shows that he is mourning him and that he doesnt think Caesar deserved this. This hinting of his pain got the crowd to go against Brutus and the conspirators without them knowing.
Antony used Logos to honor Caesar. Showing how much good Caesar did for the people under his rule helps convince them he was a good man for Rome. Without talking about the good Caesar did, the people would continue to think that he was too ambitious. 
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