SOCRATES: But from what line?--tell me exactly; and if you would rather not reckon, try and show me the line.

BOY: Indeed, Socrates, I do not know.

SOCRATES: Do you see, Meno, what advances he has made in his power of recollection? He did not know at first, and he does not know now, what is the side of a figure of eight feet: but then he thought that he 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.

MENO: True.

SOCRATES: Is he not better off in knowing his ignorance?

MENO: I think that he is.

SOCRATES: If we have made him doubt, and given him the 'torpedo's shock,' have we done him any harm?

MENO: I think not.

SOCRATES: We have certainly, as would seem, a.s.sisted 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 s.p.a.ce should have a double side.

MENO: True.

SOCRATES: 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?

MENO: I think not, Socrates.

SOCRATES: Then he was the better for the torpedo's touch?

MENO: I think so.

SOCRATES: 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.

SOCRATES: And now I add another square equal to the former one?

BOY: Yes.

SOCRATES: And a third, which is equal to either of them?

BOY: Yes.

SOCRATES: Suppose that we fill up the vacant corner?

BOY: Very good.

SOCRATES: Here, then, there are four equal s.p.a.ces?

BOY: Yes.

SOCRATES: And how many times larger is this s.p.a.ce than this other?

BOY: Four times.

SOCRATES: But it ought to have been twice only, as you will remember.

BOY: True.

SOCRATES: And does not this line, reaching from corner to corner, bisect each of these s.p.a.ces?

BOY: Yes.

SOCRATES: And are there not here four equal lines which contain this s.p.a.ce?

BOY: There are.

SOCRATES: Look and see how much this s.p.a.ce is.

BOY: I do not understand.

SOCRATES: Has not each interior line cut off half of the four s.p.a.ces?

BOY: Yes.

SOCRATES: And how many s.p.a.ces are there in this section?

BOY: Four.

SOCRATES: And how many in this?

BOY: Two.

SOCRATES: And four is how many times two?

BOY: Twice.

SOCRATES: And this s.p.a.ce is of how many feet?

BOY: Of eight feet.

SOCRATES: And from what line do you get this figure?

BOY: From this.

SOCRATES: That is, from the line which extends from corner to corner of the figure of four feet?

BOY: Yes.

SOCRATES: 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 s.p.a.ce is the square of the diagonal?