"He was my friend, faithful, and just to me... (3.2.64)"
"When that the poor have cried, Caesar hath wept. (3.2.64)"
"I thrice presented him a kingly crown. Which he did thrice refuse: was this ambition? Yet Brutus says he was ambitious. (3.2.64)"
Antony is showing that him and Caesar were good friends and that they were close. He was very loyal to Caesar and is now showing that. He is trying to make other citizens feel the same way about Caesar.
This was showing that Caesar cared for his people and felt the pain that they felt as well. This is appealing to the emotions of the people.
Antony is showing that Caesar refused to accept the crown in an effort to gain the peoples trust. This is showing logic by needing the peoples trust.