And will not palter? And what other oath / Than honesty to honesty engaged / That this shall be or we will fall for it? (2.1.135-139)

Brutus appeals to their status and credibility as honorable Romans. This is why they shouldn't have to swear an oath because they're Romans, and as Romans they have credibility and honor of doing what's right.

Be hung with Caesar’s trophies. I’ll about the streets; / So do you too, where you perceive them thick.

And keep us all in servile fearfulness. (1.1) 

If we thin out the crowd of Caesar supporters, then we help lower Rome's enthusiasm for Caesar and his return.

Be hung with Caesar’s trophies. I’ll about the streets; / So do you too, where you perceive them thick.

These growing feathers plucked from Caesar’s wing / Will make him fly an ordinary pitch, / Who else would soar above the view of men

And keep us all in servile fearfulness. (1.1)

Fear - Flavius uses fear to motivate Marullus to help him thin out the crowd and remove the decorations from Caesar's statues. If they don't lessen people's love for Caesar, then they will live in fear of Caesar's growing power over all of Rome.

Whose ransoms filled the government treasury.

Did this seem ambitious in Caesar?

Whenever the poor have cried, Caesar has wept;

Ambition should be made of sterner stuff.

But Brutus says he was ambitious;

And Brutus is an honorable man.

You all saw that on the Lupercal

I offered him a kingly crown three times,

Which he refused three times. Was this ambition?"(3.2)

Antony is using logos, by giving off reasons as to why Caesar was not ambitious. He helped bring home captives, he wept with the poor, he even refused the crown three times.

I grant I am a woman, but withal

A woman well reputed, Cato's daughter.

Think you I am no stronger than my sex,

Being so father'd and so husbanded? (2.1)

Portia uses ethos when talking to Brutus as she is establishing her credibility as Cato's daughter and Brutu's wife, she is also a well reputed and honorable woman. This shows that Brutus should share his secret with Portia because he can trust her. 

A woman well reputed, Cato's daughter” (Act 2. Scene  ) 

Portia shows her credibility as she explains how she is the daughter of a very well known roman, Cato, and the husband of Lord Brutus

Whose ransoms filled the government treasury.

Did this seem ambitious in Caesar?

Whenever the poor have cried, Caesar has wept;

Ambition should be made of sterner stuff.

But Brutus says he was ambitious;

And Brutus is an honorable man.

You all saw that on the Lupercal

I offered him a kingly crown three times,

Which he refused three times. Was this ambition?" (3.2).

Mark Antony uses logos to give reason to the Roman Citizens on why Caesar was not ambitious. He uses examples including; help bring captives home, wept with the poor, and refused the crown three times.