Meno.
Socrates, Meno, Meno's Slave.
Soc. But since this side is also of two feet, there are twice two feet?
Boy. There are.
Soc. Then the square is of twice two feet?
Boy. Yes.
Soc. And how many are twice two feet? count and tell me.
Boy. Four, Socrates.
Soc. And might there not be another square twice as large as this, and having like this the lines equal?
Boy. Yes.
Soc. And of how many feet will that be?
Boy. Of eight feet.
Soc. 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.
He is partly guessing. Soc. 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?
Men. Yes.
Soc. And does he really know?
Men. Certainly not.
Soc. He only guesses that because the square is double, the line is double.
Men. True.
Soc. Observe him while he recalls the steps in regular order. (To the Boy.) Tell me, boy, do you assert that a 83 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 a double line?
Boy. Yes.
Soc. But does not this line become doubled if we add another such line here?
Boy. Certainly.
Soc. And four such lines will make a space containing eight feet?
Boy. Yes.
