SOCRATES: And if one side of the figure be of SOCRATES: And now try and tell me the length two feet, and the other side be of two feet, how of the line which forms the side of that double much will the whole be? Let me explain: if in one square: this is two feet—what will that be?
direction the space was of two feet, and in the BOY: Clearly, Socrates, it will be double.
other direction of one foot, the whole would be SOCRATES: Do you observe, Meno, that I am not of two feet taken once?
teaching the boy anything, but only asking him BOY: Yes.
questions; and now he fancies that he knows how SOCRATES: But since this side is also of two feet, long a line is necessary in order to produce a there are twice two feet?
figure of eight square feet; does he not?
BOY: There are.
MENO: Yes.
SOCRATES: Then the square is of twice two feet?
SOCRATES: And does he really know?
BOY: Yes.
MENO: Certainly not.
SOCRATES: And how many are twice two feet?
SOCRATES: He only guesses that because the count and tell me.
square is double, the line is double.
BOY: Four, Socrates.
MENO: True.
SOCRATES: And might there not be another SOCRATES: Observe him while he recalls the square twice as large as this, and having like this steps in regular order. (To the Boy:) Tell me, boy, the lines equal?
do you assert that a double space comes from a BOY: Yes.
double line? Remember that I am not speaking SOCRATES: And of how many feet will that be?
of an oblong, but of a figure equal every way, BOY: Of eight feet.
and twice the size of this—that is to say of eight 47
Meno
feet; and I want to know whether you still say BOY: Four times as much.
that a double square comes from double line?
SOCRATES: Therefore the double line, boy, has BOY: Yes.
given a space, not twice, but four times as much.
SOCRATES: But does not this line become doubled BOY: True.
if we add another such line here?
SOCRATES: Four times four are sixteen—are they BOY: Certainly.
not?
SOCRATES: And four such lines will make a space BOY: Yes.
containing eight feet?
SOCRATES: What line would give you a space of BOY: Yes.
eight feet, as this gives one of sixteen feet;—do SOCRATES: Let us describe such a figure: Would you see?
you not say that this is the figure of eight feet?
BOY: Yes.
BOY: Yes.
SOCRATES: And the space of four feet is made SOCRATES: And are there not these four divisions from this half line?
in the figure, each of which is equal to the figure BOY: Yes.
of four feet?
SOCRATES: Good; and is not a space of eight feet BOY: True.
twice the size of this, and half the size of the SOCRATES: And is not that four times four?
other?
BOY: Certainly.
BOY: Certainly.
SOCRATES: And four times is not double?
SOCRATES: Such a space, then, will be made out BOY: No, indeed.
of a line greater than this one, and less than that SOCRATES: But how much?
one?