that he knows how long
a line is necessary in order to produce a figure of eight square feet;
does he not?

MENO: Yes.

SOCRATES: And does he really know?

MENO: Certainly not.

SOCRATES: He only guesses that because the square is double, the line is
double.

MENO: True.

SOCRATES: Observe him while he recalls the steps in regular order. (To
the Boy:) Tell me, boy, do you assert that a double space comes from
a double line? Remember that I am not speaking of an oblong, but of a
figure equal every way, and twice the size of this--that is to say
of eight feet; and I want to know whether you still say that a double
square comes from double line?

BOY: Yes.

SOCRATES: But does not this line become doubled if we add another such
line here?

BOY: Certainly.

SOCRATES: And four such lines will make a space containing eight feet?

BOY: Yes.

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

BOY: Yes.

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

BOY: True.

SOCRATES: And is not that four times four?

BOY: Certainly.

SOCRATES: And four times is not double?

BOY: No, indeed.

SOCRATES: But how much?

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 ar