Shakespeare and Machiavelli

Here' a good quiz question!
Which Shakespeare character refers to the Renaissance political philosopher Niccolo Machiavelli?
Answer: Richard III.

This happens in Act 3 Scene 2 of "Henry VI, part 3", a very early Shakespeare play. Richard, then Duke of Gloucester, announces his future career of wickedness and deception with these words:-

"I'll play the orator as well as Nestor,
Deceive more slyly than Ulysses could,
And, like a Sinon, take another Troy.
I can add colours to the chameleon,
Change shapes with Proteus for advantages,
And set the murderous Machiavel to school.
Can I do this, and cannot get a crown?
Tut, were it farther off, I'll pluck it down."

This scene is set in the year 1470. The historical Richard would then have been eighteen years old, and, one might think, possessing an oratorical fluency and depth of knowledge unusual in a teenager. But the real problem with the passage is that in 1470 Machiavelli would only have been a child. There seems to be uncertainty as to the precise year of Niccolo Machiavelli's birth (1459? 1467? 1469?), but he was certainly active in the government of Florence between 1498 and 1512, and wrote his most famous book "The Prince", to which Shakespeare is referring, in 1513-14, following his enforced retirement (accompanied by arrest and torture) and exile. Richard was, of course, killed at the Battle of Bosworth in 1485, several years before Machiavelli had even started his political career.

We can deduce from this that Shakespeare knew something of Machiavelli's writings, or at least of his reputation, but was distinctly hazy on the biographical details!