Here are the lines from Julius Caesar that I paraphrased. It seems probable that Shakespeare was alluding to Tusculan Disputations in this dialogue.
QuoteDisplay MoreCas. Tell me, good Brutus, can you see your face?
Bru. No, Cassius; for the eye sees not itself
But by reflection, by some other things.
Cas. ‘Tis just,
And it is very much lamented, Brutus,
That you have no such mirrors as will turn
Your hidden worthiness into your eye,
That you might see your shadow. I have heard
Where many of the best respect in Rome
(Except immortal Caesar), speaking of Brutus
And groaning underneath this age's yoke,
Have wish'd that noble Brutus had his eyes.
Bru. Into what dangers would you lead me, Cassius,
That you would have me seek into myself
For that which is not in me?
Cas. Therefore, good Brutus, be prepar'd to hear;
And since you know you cannot see yourself
So well as by reflection, I, your glass,
Will modestly discover to yourself
That of yourself which you yet know not of.
And be not jealous on me, gentle Brutus:
Were I a common laughter, or did use
To stale with ordinary oaths my love
To every new protester; if you know
That I do fawn on men and hug them hard,
And after scandal them; or if you know
That I profess myself in banqueting
To all the rout, then hold me dangerous.
Is Cassius Longinus exploiting his knowledge of Platonism to persuade Brutus to rise against Caesar?
QuoteThe soul has not sufficient capacity to comprehend itself; yet, the soul, like the eye, though it has no distinct view of itself, sees other things: it does not see (which is of least consequence) its own shape; perhaps not, though it possibly may; but we will pass that by: but it certainly sees that it has vigour, sagacity, memory, motion, and velocity; these are all great, divine, eternal properties. What its appearance is, or where it dwells, it is not necessary even to inquire.