Xenophon's Cyropedia talks about Persians becoming centaurs when they get horses but Strauss has some esoteric reading about the centaur being some flawed creature, meant to symbolize a combination of the medes and persians i don't know.

Machiavelli (who strauss calls an evil teacher of evil) references Chiron who, unlike the most centaurs, was wise. Machiavelli says the prince should be like that or understand that Man himself is like that, part beast and part man.