Soc. And four such lines will make a space containing eight feet?

  Boy. Yes.

  Soc. Let us describe such a figure: Would you not say that this is
the figure of eight feet?

  Boy. Yes.

  Soc. And are there not these four divisions in the figure, each of
which is equal to the figure of four feet?

  Boy. True.

  Soc. And is not that four times four?

  Boy. Certainly.

  Soc. And four times is not double?

  Boy. No, indeed.

  Soc. But how much?

  Boy. Four times as much.

  Soc. Therefore the double line, boy, has given a space, not twice,
but four times as much.

  Boy. True.

  Soc. Four times four are sixteen-are they not?

  Boy. Yes.

  Soc. What line would give you a space of right feet, as this gives
one of sixteen feet;-do you see?

  Boy. Yes.

  Soc. And the space of four feet is made from this half line?

  Boy. Yes.

  Soc. Good; and is not a space of eight feet twice the size of
this, and half the size of the other?

  Boy. Certainly.

  Soc. Such a space, then, will be made out of a line greater than
this one, and less than that one?

  Boy. Yes; I think so.

  Soc. Very good; I like to hear you say what you think. And now
tell me, is not this a line of two feet and that of four?

  Boy. Yes.

  Soc. Then the line which forms the side of eight feet ought to be
more than this line of two feet, and less than the other of four feet?

  Boy. It ought.

  Soc. Try and see if you can tell me how much it will be.

  Boy. Three feet.

  Soc. Then if we add a half to this line of two, that will be the
line of three. Here are two and there is one; and on the other side,
here are two also and there is one: and that makes the figure of which
you speak?

  Boy. Yes.

  Soc. But if there are three feet this way and three feet that way,
the whole space will be three times three feet?

  Boy. That is evident.

  Soc. And how much are three times three feet?

  Boy. Nine.

  Soc. And how much is the double of four?

  Boy. Eight.

  Soc. Then the figure of eight is not made out of a of three?

  Boy. No.

  Soc. 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.

  Soc. 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