SOCRATES: Here, then, there are four equal SOCRATES: And how many spaces are there in spaces?
this section?
BOY: Yes.
BOY: Four.
SOCRATES: And how many times larger is this SOCRATES: And how many in this?
space than this other?
BOY: Two.
BOY: Four times.
SOCRATES: And four is how many times two?
SOCRATES: But it ought to have been twice only, BOY: Twice.
as you will remember.
SOCRATES: And this space is of how many feet?
BOY: True.
BOY: Of eight feet.
SOCRATES: And does not this line, reaching from SOCRATES: And from what line do you get this corner to corner, bisect each of these spaces?
figure?
BOY: Yes.
BOY: From this.
SOCRATES: And are there not here four equal SOCRATES: That is, from the line which extends lines which contain this space?
from corner to corner of the figure of four feet?
BOY: There are.
BOY: Yes.
SOCRATES: Look and see how much this space SOCRATES: And that is the line which the learned is.
call the diagonal. And if this is the proper name, BOY: I do not understand.
then you, Meno’s slave, are prepared to affirm SOCRATES: Has not each interior line cut off half that the double space is the square of the diago-of the four spaces?
nal?
BOY: Yes.
BOY: Certainly, Socrates.