[Sidenote: _Socrates and the boy._] _Soc._ Let us describe such a figure: Would you not say that this is the figure of eight feet? [Illustration] _Boy._ Yes. _Soc._ And are there not these four divisions in the figure, each of which is equal to the figure of four feet? _Boy._ True. _Soc._ And is not that four times four? _Boy._ Certainly. _Soc._ And four times is not double? _Boy._ No, indeed. _Soc._ But how much? _Boy._ Four times as much. _Soc._ Therefore the double line, boy, has given a space, not twice, but four times as much. _Boy._ True. _Soc._ Four times four are sixteen—are they not? _Boy._ Yes. _Soc._ What line would give you a space of eight feet, as this gives one of sixteen feet;—do you see? _Boy._ Yes. _Soc._ And the space of four feet is made from this half line? _Boy._ Yes. _Soc._ Good; and is not a space of eight feet twice the size of this, and half the size of the other? _Boy._ Certainly. _Soc._ 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. _Soc._ 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. [Sidenote: He has now learned to realize his own ignorance, and therefore will endeavour to remedy it.] _Soc._ 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. _Soc._ Try and see if you can tell me how much it will be. _Boy._ Three feet. [Sidenote: _The progress of the boy’s education._] _Soc._ 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. _Soc._ 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. _Soc._ And how much are three times three feet? _Boy._ Nine. _Soc._ And how much is the double of four? _Boy._ Eight. _Soc._ Then the figure of eight is not made out of a line of three? _Boy._ No. _Soc._ But from what line?—tell me exactly; and if you 84 would rather not reckon, try and show me the line. _Boy._ Indeed, Socrates, I do not know. _Soc._ 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. _Men._ True.