SOCRATES: And these lines which I have drawn through the middle of the square are also equal? BOY: Yes. SOCRATES: A square may be of any size? BOY: Certainly. SOCRATES: And if one side of the figure be of two feet, and the other side be of two feet, how much will the whole be? Let me explain: if in one direction the space was of two feet, and in the other direction of one foot, the whole would be of two feet taken once? BOY: Yes. SOCRATES: But since this side is also of two feet, there are twice two feet? BOY: There are. SOCRATES: Then the square is of twice two feet? BOY: Yes. SOCRATES: And how many are twice two feet? count and tell me. BOY: Four, Socrates. SOCRATES: And might there not be another square twice as large as this, and having like this the lines equal? BOY: Yes. 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? 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.