*Socrates:* It will be no easy matter, but I will try to please you to the utmost of my power. Suppose that you call one of your numerous attendants, that I may demonstrate on him.

*Meno:* Certainly. Come hither, boy.

*Socrates:* He is Greek, and speaks Greek, does he not?

*Meno:* Yes, indeed; he was born in the house.

*Socrates:* Attend now to the questions which I ask him, and observe whether he learns of me or only remembers.

*Meno:* I will.

*Socrates:* Tell me, boy, do you know that a figure like this is a square?

*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 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 right 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 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.

A concerned citizen#THIS ARTICLE IS OFFENSIVE TO MY RELIGIOUS BELIEFS I AM AN HONEST GODSFEARING PYTHAGOREAN AND I FIND THE MENTION OF A NUMBER SUCH THAT IT MULTIPLIED BY ITSELF WILL YIELD EIGHT EXTREMELY OFFENSIVE ESPECIALLY IN A CONTEXT WHERE CHILDREN MIGHT READ ABOUT IT

SUCH A NUMBER CAN BE SHOWN NOT TO BE A WHOLE NUMBER OR EVEN A FRACTION OF WHOLE NUMBERS AND IS THEREFORE AN ABOMINATION TO THE VERY FUNDAMENTAL PRINCIPLES OF THE UNIVERSE

SUCH A NUMBER SIMPLY HAS NO PLACE IN MATHEMATICS OR ANYWHERE ELSE AND ARE MERELY USED BY THE ATHENIAN LIBERAL CULTURAL ELITE IN THEIR DESTRUCTIVE WAR AGAINST THE TRADITIONAL DEFINITION OF NUMBERS

I DEMAND THAT THIS SOCRATES FELLOW IS PUT ON TRIAL AND JUDGED HARSHLY FOR FEEDING THIS AMORAL NONSENSE TO OUR CHILDREN

Amanda M#Hear hear!

*pickets*

GOD HATES SCALAWAGS!

An Inside Joke#Typical Pythagorean nonsense. Rational people proved non-Euclidean mathematics explains away any need to waste your time on Pythagoras’s make-believe (Yeah, I said it.) Wake up, Sheeple!

Stokes OTI Staff#Triangles: how the f___ do they work?