In Shakespeare's Julius Caesar, what does "Thus did Mark Anthony bid me fall down" signify?

Directly after the assassination of Julius
Caesar in Act 3, Scene 1, Mark Antony flees to his house to save his own
life. But he realizes that he is not safe anywhere if the conspirators have decided to
kill him too. He has no idea how many people they intend to slaughter, but he believes
that all close friends of Caesar must be in extreme jeopardy, and he is the closest
friend of all. It was he who offered Caesar the symbolic crown, showing that he intended
to help his friend become the supreme monarch of the Roman
Empire.

Antony decides that he must present himself before
the triumphant conspirators and try to convince them that he is no threat to their
proposed new political order. But he thinks it prudent to send a messenger first, and he
instructs the Servant exactly how to act and what to say. He also tells the Servant to
appeal directly to Brutus because he believes that Brutus is an honorable man, that he
is the de facto leader of the conspiracy, and that he can be
trusted to keep his word if he gives the Servant assurance of Antony's safety. Perhaps
Antony senses that the co-leader of the conspirators, Cassius, wants to have him killed.
At least he understands that Cassius would be much harder to fool than the idealistic,
scholarly, unworldly Brutus.

The Servant approaches and,
acting on Antony's instructions, kneels before Brutus and then falls prostrate--i.e.
face down--while he delivers Antony's message. This is dramatically effective. What is
happening is that Antony himself is symbolically falling prostrate, although he could
not bring himself to do such a thing in person regardless of the danger he was
in.

Thus,
Brutus, did my master bid me kneel:
Thus did Mark Antony bid me fall
down;
And, being prostrate, thus he bade me say:
Brutus is noble,
wise, valiant, and honest;
Caesar was mighty, bold, royal, and
loving:
Say I love Brutus, and I honour him;
Say I fear'd Caesar,
honour'd him and loved him.
If Brutus will vouchsafe that Antony
May
safely come to him, and be resolved
How Caesar hath deserved to lie in
death,
Mark Antony shall not love Caesar dead
So well as Brutus
living; but will follow
The fortunes and affairs of noble
Brutus
Through the hazards of this untrod state
With all true faith.
So says my master
Antony.

Brutus has many noble
qualities, but he repeatedly shows himself to be as much of an egotist as Julius Caesar.
When Brutus addresses the mob he speaks mainly about himself and his honorable motives.
He is flattered to have this messenger groveling before him, as Antony fully expected he
would be, and also flattered to be addressed as the sole leader and sole decision-maker
of his faction. Brutus is easily persuaded to guarantee Antony's safety. His response
is:

Thy
master is a wise and valiant Roman;
I never thought him worse.
Tell
him, so please him come unto this place,
He shall be satisfied; and, by my
honour,
Depart
untouch'd.

Antony does not
ask to be allowed to speak at Caesar's funeral until he appears in person and shakes
hands with all the conspirators. He fully intends to try to turn the Roman people
against the men who murdered his friend, but he has to proceed with extreme caution.
Cassius wanted to have him killed, but Brutus overruled him. Cassius advises Brutus that
it could be disastrous to let Antony address the assembled mob, but once again Brutus
overrules him. Cassius wanted Brutus to be a figurehead, but he is learning that Brutus
is impossible to control now that he has tasted political power.