Meno.
Socrates, Meno's Slave.
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 eight 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.
He has now learned to realize his own ignorance, and therefore will endeavour to remedy it. 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