The quarrel between Brutus and Cassius arises when Brutus accuses Lucius Pella of taking bribes while Cassius seeks to protect Pella. Brutus believed that they killed Caesar because they were seeking justice and the good of Rome. But upon seeing Cassius's willingness to protect Pella, Brutus believes that Cassius has betrayed the agenda behind Caesar’s death. Apart from the accusation against Pella, Brutus also brings up the issue of Cassius's refusal to pay his soldiers, which Cassius denies. Although Cassius does not explicitly defend himself against these allegations, he appeals to Brutus’s honorable nature to end the quarrel. Cassius offers Brutus his sword and his bare chest suggesting that Brutus should kill him since he did the same to Caesar (but out of love).
Cassius and Brutus are fighting over Brutus' accusations against Lucius Pella, who Brutus believes to have taken bribes. Cassius defended the man, a friend of his, and is angry that Brutus punished Pella anyway, despite the fact that Cassius wrote letters in his defence. Brutus then goes on to accuse Cassius himself of accepting bribes, and is also angry because he had requested money from Cassius for the troops, which Cassius refused to send:
"I did send to you for gold to pay my legions, which you denied me."
Cassius denies this, and finally the argument is ended when Cassius offers Brutus his sword, telling him to go ahead and kill him if Brutus truly believes such things of him.
Cassius doesn't seem to really have much defense. It is difficult to tell if he has really done the things Brutus accused him of, and his method of ending the argument is to appeal to Brutus' honor...Of course Brutus isn't going to stab Cassius, and Cassius' offer takes the wind out of Brutus' angry sails.
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