Cassius's letters to Brutus are all aimed to manipulate him into joining the conspiracy to kill Caesar. Note, first of all, that they are all forgeries. At the end of act 1, scene 2, Cassius describes his plan to write multiple letters, pretending that they have been written by different Roman citizens. (Note also that Cassius even goes so far as to alter his handwriting to further the illusion.)
One of the critical passages, as Cassius outlines his plan in act 1, scene 2, can be found when Cassius states, in reference to Brutus himself:
Writings, all tending to the great opinion
That Rome holds of his name
Historically, Rome began as a monarchy before transitioning into a Republic. As legend had it, one of the critical leaders in driving out the last of these kings and instituting the Republic was Brutus's ancestor, Lucius Junius Brutus. In this respect, Brutus's entire family legacy is closely intertwined with the Republic itself, a factor which Cassius exploits in the letters.
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