Meno Proof with diagrams
Soc. I know, Meno, what you mean; but just see what a tiresome dispute you are introducing. You argue that man cannot enquire either about that which he knows, or about that which he does not know; for if he knows, he has no need to enquire; and if not, he cannot; for he does not know the, very subject about which he is to enquire.
Soc. Tell me, boy, do you know that a figure like this is a square?
Boy. I do.
Soc. And you know that a square figure has these four lines equal?
Here is a figure to go with this part of the dialogue.
Soc. 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?
Soc. But does not this line become doubled if we add another such line here? [Add BJ to AB]
Soc. And four such lines will make a space containing eight feet?
Soc. Let us describe such a figure: Would you not say that this is the figure of eight feet? [add JK, KL, and LA]
Soc. And are there not these four divisions in the figure, each of which is equal to the figure of four feet?
Here is a second figure to go with this part of the dialogue.
Soc. Mark now the farther development. I shall only ask him, and not teach him, and he shall share the enquiry with me: and do you watch and see if you find me telling or explaining anything to him, instead of eliciting his opinion. Tell me, boy, is not this a square of four feet which I have drawn? [Draws ABCD]
Here is the third figure to go with this part of the dialogue.
Soc. And now I add another square equal to the former one?
Soc. And a third, which is equal to either of them?
Soc. Suppose that we fill up the vacant corner?
Boy. Very good.
Soc. Here, then, there are four equal spaces?
Soc. And how many times larger is this space than this other?
Boy. Four times.
Soc. But it ought to have been twice only, as you will remember.
Soc. And does not this line, reaching from corner to corner, bisect each of these spaces?
Soc. And are there not here four equal lines which contain this space?
Boy. There are.
Soc. Look and see how much this space is.
Boy. I do not understand.
Soc. Has not each interior line cut off half of the four spaces?
Soc. And how many spaces are there in this section?
Soc. And how many in this?
Soc. And four is how many times two?
Soc. And this space is of how many feet?
Boy. Of eight feet.
Soc. And from what line do you get this figure?
Boy. From this.
Soc. That is, from the line which extends from corner to corner of the figure of four feet?