How does the allusion to Cassius in Fahrenheit 451 add meaning to the plot?
After Montag's house is burned, Montag takes the hose and turns it toward Captain Beatty. With his life in imminent danger, Beatty taunts Montag with an illusion to Cassuis:
There is no terror, Cassius, in your threats, for I am arm'd so strong in honesty that they pass me by as the idle wind, which I respect not.
This reference comes from Act IV, Scene III of Shakespeare's Julius Caesar. By taking on the role of Brutus, Beatty is portraying himself as the tragic hero: he has tried to help Montag, tried to persuade him that books are pointless and cannot lead to happiness, and, in return for his advice, Montag now threatens his life.
The threat on his life, however, does not hold any "terror" for Beatty because he believes in the system. Even if Montag kills him, a replacement captain will soon follow. In other words, Beatty is not afraid of dying because he knows that his murder is not enough to overthrow the firemen and revolutionise society.
In this understanding, then, the allusion to Cassius represents Montag's powerlessness and his social isolation. This is, perhaps, why Montag fires the hose at Beatty and kills him: he is demonstrating his commitment to changing society and saying, in a most violent manner, that nothing will stand in his way. He is prepared to do whatever it takes to change society's attitude to books and to remove all traces of censorship.
(For more information on Cassius and Brutus, please see the second reference link provided.)
In Part Three, Captain Beatty is about to arrest Montag after he makes him burn his home. Before Beatty can arrest him, Montag aims the flamethrower in his direction and threatens to kill him. Captain Beatty responds by asking Montag if he is going to "belch" Shakespeare at him before quoting Brutus from Shakespeare's Julius Caesar. Captain Beatty tells Montag,
"There is no terror, Cassius, in your threats, for I am arm'd so strong in honesty that they pass by me as an idle wind, which I respect not!" (Bradbury, 55).
This quote takes place in Act Four, Scene 3 of Julius Caesar and is Brutus's response to Cassius's threats during their argument before the Battle of Phillippi. Captain Beatty compares himself to the honorable Brutus in this allusion and uses it to signify that he does not fear Montag's threats. Captain Beatty thoroughly believes in the firemen structure and thinks that he is in the right, similar to how Brutus believes he is honorable while Cassius is a greedy, corrupt politician. By quoting Brutus, Captain Beatty is telling Montag that he does not fear his threats because society will continue to destroy novels and suppress intellectual pursuits.