Brutus's soliloquy occurs in his orchard in the first scene of Act 2.
It must be by his death: and for my part,
I know no personal cause to spurn at him,
But for the general. He would be crown'd:
How that might change his nature, there's the question.
It is the bright day that brings forth the adder;
And that craves wary walking. Crown him?--that;--
And then, I grant, we put a sting in him,
That at his will he may do danger with.
The abuse of greatness is, when it disjoins
Remorse from power: and, to speak truth of Caesar,
I have not known when his affections sway'd
More than his reason. But 'tis a common proof,
That lowliness is young ambition's ladder,
Whereto the climber-upward turns his face;
But when he once attains the upmost round.
He then unto the ladder turns his back,
Looks in the clouds, scorning the base degrees
By which he did ascend. So Caesar may.
Then, lest he may, prevent. And, since the quarrel
Will bear no colour for the thing he is,
Fashion it thus; that what he is, augmented,
Would run to these and these extremities:
And therefore think him as a serpent's egg
Which, hatch'd, would, as his kind, grow mischievous,
And kill him in the shell.
He is being pressured to join in the plot to assassinate Julius Caesar, mainly by Cassius but also by other Roman aristocrats who fear that Caesar would seriously weaken their powers and privileges if he became king. Brutus is an extremely intellectual man. He will not act impulsively based on feelings but, very much like Hamlet, has to think thoroughly and carefully before undertaking any serious action. He has a strong sense of responsibility. He knows that if he agrees to join Cassius and the others in their plot, then they will move forward because he will have given them the justification they need for their violence. On the other hand, if he decides not to involve himself, the plot may come to nothing. Cassius knows this. That is why he is trying so urgently to persuade Brutus to join him, both by direct personal persuasion and by trickery.
In his soliloquy Brutus tells himself that Caesar intends to be crowned king. He says "He would be crown'd." Brutus is a good friend of Caesar's and knows him better than most people. He is concerned about how Caesar might change if he became the absolute ruler of Rome. Caesar has behaved modestly up to now--almost too much so. But Brutus knows that "lowliness is young ambition's ladder." That is a wise observation. Brutus is thinking that Caesar is only pretending to be humble and modest in order to make an impression on the masses. Brutus strongly suspects that Caesar is wildly ambitious and would become a tyrant if he obtained a monopoly on political, economic and military power.
Brutus decides that Caesar must be stopped because of what he could become if he were made king. Brutus is actually coming to the same conclusion as Cassius, who is much more practical, cunning, and worldly wise than Brutus. The key words in the soliloquy are:
So Caesar may.
Then, lest he may, prevent.
In other words, Caesar may become a tyrant, and he should be killed, not for anything he has done, but to prevent him from doing what he might do if he had the power. If they waited until he actually had that power, it would be too late.
Of course, no one will ever know what Julius Caesar actually would have done if he had lived.