After reading Plato's account of a dialog between Protagoras and Socrates, I've got to say I've lost a lot of respect for all concerned. The question under debate is whether wisdom and virtue can be learned, with Protagoras initially taking the affirmative. Socrates then chases him around the rhetorical map with what seem to me to be pointless word games, getting P to concede that this and that have similarities or similar opposites. A better Protagoras, I think, would just have said: "Socrates, Socrates, hang up your word games. Let's just say that different words have different meanings, and that even the same word can have different meanings in different contexts." P, in Plato's telling, never points out some of the ridiculous weaknesses in the argument of Socrates, like the absurd chain by which Socrates gets Protagoras to equate courage with knowledge.
Frankly, I consider it unlikely that the minds who created Greek geometry could have bought into this weakly argued stuff.