Socrates: And of how many feet will that be?
Boy: Of eight feet.
Socrates: And now try and tell me the length of the line which forms the side of that double square: this is two feet—what will that be?
Boy: Clearly, Socrates, it will be double.
Socrates: Do you observe, Meno, that I am not teaching the boy anything, but only asking him questions; and now he fancies 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?