Boy: Larger, Socrates. For one squared gives only an area of one, and we need and area of two, which is larger.
Socrates: Good. And what of two?
Boy: Two gives a square of four, which is too large.
Socrates: Fine. So the square root of two is smaller than the side two which is the root of four, and larger than the side one which yields one?
Boy: Yes, Socrates.
Socrates: (Turning to Meno) So now he is as far as most of us get in determining the magnitude of the square root of two? And getting farther is largely a matter of guesswork, is it not?
Meno: Yes, Socrates, but I don't see how he will do it.
Socrates: Neither does he. But I do. Watch! (turning to the boy) Now I am going to tell you something you don't know, so Meno will listen very closely to make sure he agrees that I can tell you. You know multiplication, boy?
Boy: I thought I had demonstrated that, Socrates?
Socrates: So you have, my boy, has he not Meno?