Although it is a little bit confusing to discern the various options, the best summary of this monologue is Antony shakes the hands of all the conspirators and says he knows that his love for Caesar puts him in an unstable position. Then he imagines that it would break Caesar’s heart to see Antony making peace with his assassins.
This scene takes place right before Antony's praising oration over Caesar's corpse, and right after Brutus's speech in defense of their actions. Antony sincerely shakes the hands of the perpetrators, but, by doing so, he acknowledges that they might judge him as a coward or a flatterer, who is afraid of sharing Caesar's fate, and that Caesar's spirit might suffer from seeing him doing that.
(Mark) Antony was a supporter of Julius Caesar and had served as his general, and when, as part of a conspiracy, he was assassinated at the hands of various Roman senators on the Ides of March of 44 BC, he eventually became his successor. He, nevertheless, spared the assassins a punishment, but eventually fought against two of them, Brutus and Cassius, in a civil war.
The 7th president was Andrew Jackson :)
