THE COMPLETE WORKS OF PLATO. Plato

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      BOY: I do.

      SOCRATES: And you know that a square figure has these four lines equal?

      BOY: Certainly.

      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.

      SOCRATES: Such a space, then, will be made out of a line greater than this one, and less than that one?

      BOY: Yes; I think so.

      SOCRATES: Very good; I like to hear you say what you think. And now tell me, is not this a line of two feet and that of four?

      BOY: Yes.

      SOCRATES: Then the line which forms the side of eight feet ought to be more than this line of two feet, and less than the other of four feet?

      BOY: It ought.

      SOCRATES: Try and see if you can tell me how much it will be.

      BOY: Three feet.

      SOCRATES: Then if we add a half to this line of two, that will be the line of three. Here are two and there is one; and on the other side, here are two also and there is one: and that makes the figure of which you speak?

      BOY: Yes.

      SOCRATES: But if there are three feet this way and three feet that way, the whole space will be three times three feet?

      BOY: That is evident.

      SOCRATES: And how much are three times three feet?

      BOY: Nine.

      SOCRATES: And how much is the double of four?

      BOY: Eight.

      SOCRATES: Then the figure of eight is not made out of a line of three?

      BOY: No.

      SOCRATES: But from what line?—tell me exactly; and if you would rather not reckon, try and show me the line.

      BOY: Indeed, Socrates, I do not know.

      SOCRATES: Do you see, Meno, what advances he has made in his power of recollection? He did not know at first, and he does not know now, what is the side of a figure of eight feet: but then he thought that he knew, and answered confidently as if he knew, and had no difficulty; now he has a difficulty, and neither knows nor fancies that he knows.

      MENO: True.

      SOCRATES: Is he not better off in knowing СКАЧАТЬ