knew, and answered confidently as if he knew, and had no difficulty;
now he has a difficulty, and neither knows nor fancies that he knows.

  Men. True.

  Soc. Is he not better off in knowing his ignorance?

  Men. I think that he is.

  Soc. If we have made him doubt, and given him the "torpedo's shock,"
have we done him any harm?

  Men. I think not.

  Soc. We have certainly, as would seem, assisted him in some degree
to the discovery of the truth; and now he will wish to remedy his
ignorance, but then he would have been ready to tell all the world
again and again that the double space should have a double side.

  Men. True.

  Soc. But do you suppose that he would ever have enquired into or
learned what he fancied that he knew, though he was really ignorant of
it, until he had fallen into perplexity under the idea that he did not
know, and had desired to know?

  Men. I think not, Socrates.

  Soc. Then he was the better for the torpedo's touch?

  Men. I think so.

  Soc. Mark now the farther development. I shall only ask him, and not
teach him, and he shall share the enquiry with me: and do you watch
and see if you find me telling or explaining anything to him,
instead of eliciting his opinion. Tell me, boy, is not this a square
of four feet which I have drawn?

  Boy. Yes.

  Soc. And now I add another square equal to the former one?

  Boy. Yes.

  Soc. And a third, which is equal to either of them?

  Boy. Yes.

  Soc. Suppose that we fill up the vacant corner?

  Boy. Very good.

  Soc. Here, then, there are four equal spaces?

  Boy. Yes.

  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.

  Boy. True.

  Soc. And does not this line, reaching from corner to corner,
bisect each of these spaces?

  Boy. Yes.

  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?

  Boy. Yes.

  Soc. And how many spaces are there in this section?

  Boy. Four.

  Soc. And how many in this?

  Boy. Two.

  Soc. And four is how many times two?

  Boy. Twice.

  Soc. And this space is of how many feet?

  Boy. Of eight feet.

  Soc. And from what line do you get this figure?