act 3, scene 12
CAESAR'S camp in Egypt.

[Enter CAESAR, DOLABELLA, THYREUS, with others.]

CAESAR.
Let him appear that's come from Antony.--
Know you him?

DOLABELLA.
Caesar, 'tis his schoolmaster:
An argument that he is pluck'd, when hither
He sends so poor a pinion of his wing,
Which had superfluous kings for messengers
Not many moons gone by.

[Enter EUPHRONIUS.]

CAESAR.
Approach, and speak.

EUPHRONIUS.
Such as I am, I come from Antony:
I was of late as petty to his ends
As is the morn-dew on the myrtle leaf
To his grand sea.

CAESAR.
Be't so: declare thine office.

EUPHRONIUS.
Lord of his fortunes he salutes thee, and
Requires to live in Egypt: which not granted,
He lessens his requests; and to thee sues
To let him breathe between the heavens and earth,
A private man in Athens: this for him.
Next, Cleopatra does confess thy greatness;
Submits her to thy might, and of thee craves
The circle of the Ptolemies for her heirs,
Now hazarded to thy grace.

CAESAR.
For Antony,
I have no ears to his request. The queen
Of audience nor desire shall fail; so she
From Egypt drive her all-disgraced friend,
Or take his life there: this if she perform,
She shall not sue unheard. So to them both.

EUPHRONIUS.
Fortune pursue thee!

CAESAR.
Bring him through the bands.

[Exit EUPHRONIUS.]

[To THYREUS.] To try thy eloquence, now 'tis time. Despatch;
From Antony win Cleopatra. Promise,
And in our name, what she requires; add more,
From thine invention, offers: women are not
In their best fortunes strong; but want will perjure
The ne'er-touch'd vestal: try thy cunning, Thyreus;
Make thine own edict for thy pains, which we
Will answer as a law.

THYREUS.
Caesar, I go.

CAESAR.
Observe how Antony becomes his flaw,
And what thou think'st his very action speaks
In every power that moves.

THYREUS.
Caesar, I shall.

[Exeunt.]

gradesaver
Egypt. Caesar's camp. Antony's ambassador is brought to Caesar. The requests are humble, and the use of a tutor as ambassador says something about how short Antony is on personnel. Antony asks to be allowed to live in Egypt, or, if not, as a private man in Athens. Cleopatra asks that the crown of Egypt be preserved for her heirs. Caesar says that Antony's requests are in vain, but Cleopatra can have her wish on condition that she either exile or execute Antony. Caesar sends Thidias, ordering him to try to drive Cleopatra from Antony. He authorizes Thidias to offer the queen whatever she wants
cliffnotes
In his camp in Egypt, Caesar is meeting with some of his officers and also with Antony's ambassador, Euphronius. Euphronius presents Antony's requests to Caesar: Antony requests to be allowed to remain in Egypt, but if that is impossible, he asks that he at least be allowed to live as a private citizen in Athens. Euphronius also tells Caesar that Cleopatra acknowledges that Caesar is the victor and the supreme ruler of them all, but she requests that she be permitted to remain as queen of Egypt and to retain the crown of the Ptolemies, the Egyptian royal family, for her heirs. Caesar ignores Antony's request and makes an offer to Cleopatra: if she will betray Antony and drive him from Egypt, or kill him there, then he might consider her requests. Caesar then orders his servant Thyreus to return to Cleopatra with Caesar's answer. He comments that women are no stronger than their own interests, and that, being a woman, Cleopatra can probably be bribed with the promise of her own safety in exchange for Antony's life.
Caesar's own insecurity is revealed here by the harshness of his settlement. Certainly he has the right to demand Antony's life, but most Romans were known for being relatively generous to those whom they conquered. In this case, however, Caesar may be a more accurate judge of Antony's character than Antony was of Caesar's. Caesar knows, and rightly so, that he can never really feel safe as long as Antony is alive or free. Note, however, that Caesar is a very poor judge of Cleopatra's character. Since he can't see beyond the popular stereotype of her as being little more than a prostitute, he believes that she can easily be bought. This is not an unusual mistake for someone like Caesar to make; as far as we know, he does not really know what it is like to fall in love. Here, Caesar shows himself to be the complete soldier or strategist, not only in his ignorance about aspects of life not connected with war or politics, but also in the care he takes in his negotiations. He instructs Thyreus to be "cunning." Interestingly, Caesar is at his most "cunning" here, for he makes no firm promises to do anything at all for Cleopatra.
sparknotes
Caesar is with Dolabella and Thidias, two of his supporters, when Antony's ambassador arrives with his master's request: Antony asks to be allowed to live in Egypt or, barring that, to "breathe between the heavens and earth, / A private man in Athens". The ambassador further delivers Cleopatra's request that Egypt be passed on to her heirs. Caesar dismisses Antony's requests but declares that Cleopatra will have a fair hearing so long as she expels Antony from Egypt or executes him. He sends Thidias to lure Cleopatra to accept these terms, hoping that she will betray her lover
Act III, scenes viii-xiii Act III, scenes viii-x show that narrative time and chronological time occur at much different paces in Antony and Cleopatra. In the space of three scenes, we witness the full battle of Actium. We see Caesar, then Antony, prepare for battle and know the outcome of their meeting within the first four lines of Act III, scene x. In other sections of the play, the same number of scenes conveys less information and covers much less time. The rapid progression of these scenes attests to the ease with which time can be compressed onstage: in a matter of minutes, an entire naval battle is waged and won. What Enobarbus witnesses certainly complicates our perception of Antony, demonstrating that his failures take place not just in his private affiliations but in his public life as well. Although by Caesar's and even by his own account he has neglected his duties to Rome, Antony has remained a fierce and respected soldier: his quietly threatening presence, as much as any offer of Sicily and Sardinia, persuades young Pompey to accept the triumvir's offer of peace. Indeed, until this point, the blemishes on Antony's character have been of a more personal nature: although he is twice an adulterer, although he has risked the security of the empire in order to partake in the pleasures of Egypt, his military prowess has never been in question. His retreat, however, conflicts with his values, as he is a man whose honor rests almost exclusively in his performance as a soldier. A number of critics have attacked this moment in the play, asserting that such a retreat by an experienced general is unbelievable. To condemn or dismiss this scene for its lack of realism, however, misses the point for several reasons. First, by failing to allow Antony to be both the famed soldier and the distracted lover, to be both noble and irresponsible, one simplifies and diminishes his character. Second, the lost navy battle is more crucial on a symbolic than a literal level, for Antony's decision to flee encapsulates the climactic neglect of duty that haunts him throughout the play. The aftermath of the battle shows that Antony is struggling with divided, competing identities. His lament that he has fled from himself shows that his character has developed beyond his own understanding. The self he believes he has fled is the military hero; the self he now confronts is a man whose heart can lead him into defeat as surely as his reason has led him into victory. The play, however, refuses to side with Antony in his argument against himself. We may share in Enobarbus's disapproval of his commander's performance, but surely we still view Antony as a worthy and sympathetic character. Indeed, the fallen general's plea to Cleopatra makes it impossible to respond to him with simple contempt: Egypt, thou knew'st too wellMy heart was to thy rudder tied by th'strings,And thou shouldst tow me after. O'er my spiritThy full supremacy thou knew'st, and thatThy beck might from the bidding of the godsCommand me.           Antony's willingness to accept defeat out of his great love for Cleopatra does not make him a two-dimensional character, nor does it make him reprehensible to us. In fact, his flaws may be exactly what we respond to, since they highlight that he is human, riddled with weaknesses despite his famous strengths.