The Lantern

Meno15

SE

Boy: Very good.

Socrates: Here, then, there are four equal spaces?

Boy: Yes.

Socrates: And how many times larger is this space than this other?

Boy: Four times.

Socrates: But it ought to have been twice only, as you will remember.

Boy: True.

Socrates: And does not this line, reaching from corner to corner, bisect each of these spaces?

Boy: Yes.

Socrates: And are there not here four equal lines which contain this space?

Boy: There are.

Socrates: Look and see how much this space is.

Boy: I do not understand.

Socrates: Has not each interior line cut off half of the four spaces?

Boy: Yes.

Socrates: And how many spaces are there in this section?

Boy: Four.

Socrates: And how many in this?

Boy: Two.

Socrates: And four is how many times two?

Boy: Twice.

Socrates: And this space is of how many feet?

Boy: Of eight feet.

Socrates: And from what line do you get this figure?

Boy: From this.