The Meno by Plato. - HTML preview

50

Meno

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.