The Second Story of Meno / A Continuation of Socrates' Dialogue with Meno in Which the Boy Proves Root 2 is Irrational

by Unknown

Socrates: And an even number is two times one whole number?

Boy: Of course.

Socrates: So if we use this even number twice in multiplication, as we have on top, we have two twos times two whole numbers?

Boy: Yes, Socrates.

Socrates: (nudges Meno) and therefore the top number is four times some whole number times that whole number again?

Boy: Yes, Socrates.

Socrates: And this number on top has to be twice the number on the bottom, if the even over odd number we began with is to give us two when multiplied by itself, or squared, as we call it?

Boy: Yes, Socrates.

Socrates: And if the top number is four times some whole number, then a number half as large would have to be two times that same whole number?

Boy: Of course, Socrates.