Plato's Meno dialogue between Socrates and slaveboy
is not this a square of four feet which I have drawn?
Soc. And now I add another square equal to the former one?
Soc. And a third, which is equal to either of them?
Soc. Suppose that we fill up the vacant corner?
Boy. Very good.
Soc. Here, then, there are four equal spaces?
Soc. And how many times larger is this space than this other?
Boy. Four times.
Soc. But it ought to have been twice only, as you will remember.
Soc. And does not this line, reaching from corner to corner, bisect each of these spaces?
Soc. And are there not here four equal lines which contain this space?
Boy. There are.
Soc. Look and see how much this space is.
Boy. I do not understand.
Soc. Has not each interior line cut off half of the four spaces?
Soc. And how many spaces are there in this section?
Soc. And how many in this?
Soc. And four is how many times two?
Soc. And this space is of how many feet?
Boy. Of eight feet.
Soc. And from what line do you get this figure?
Boy. From this.
Soc. That is, from the line which extends from corner to corner of the figure of four feet?
Soc. And that is the line which the learned call the diagonal. And if this is the proper name, then you, Meno's slave, are prepared to affirm that the double space is the square of the diagonal?
Boy. Certainly, Socrates.