Boy: Four times as much.
Socrates: Therefore the double line, boy, has given a space, not twice, but four times as much.
Boy: True.
Socrates: Four times four are sixteen—are they not?
Boy: Yes.
Socrates: What line would give you a space of eight feet, as this gives one of sixteen feet;—do you see?
Boy: Yes.
Socrates: And the space of four feet is made from this half line?
Boy: Yes.
Socrates: Good; and is not a space of eight feet twice the size of this, and half the size of the other?
Boy: Certainly.
Socrates: 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.
Socrates: 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.
Socrates: 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.
Socrates: Try and see if you can tell me how much it will be.
Boy: Three feet.
Socrates: 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.
Socrates: 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.
Socrates: And how much are three times three feet?
Boy: Nine.