_Soc._ Is he not better off in knowing his ignorance? _Men._ I think that he is. _Soc._ If we have made him doubt, and given him the ‘torpedo’s shock,’ have we done him any harm? _Men._ I think not. _Soc._ We have certainly, as would seem, assisted him in some degree to the discovery of the truth; and now he will wish to remedy his ignorance, but then he would have been ready to tell all the world again and again that the double space should have a double side. _Men._ True. _Soc._ But do you suppose that he would ever have enquired into or learned what he fancied that he knew, though he was really ignorant of it, until he had fallen into perplexity under the idea that he did not know, and had desired to know? _Men._ I think not, Socrates. _Soc._ Then he was the better for the torpedo’s touch? _Men._ I think so. [Sidenote: _Construction of the figure of eight feet square._] [Sidenote: The boy arrives at another true conclusion: which is, that the square of the diagonal is double the square of the side.] _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? _Boy._ Yes. _Soc._ And now I add another square equal to the former one? _Boy._ Yes. _Soc._ And a third, which is equal to either of them? _Boy._ Yes. _Soc._ Suppose that we fill up the vacant corner? _Boy._ Very good. _Soc._ Here, then, there are four equal spaces? _Boy._ Yes. _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. _Boy._ True. _Soc._ And does not this line, reaching from corner to corner, bisect each of these spaces? 85 _Boy._ Yes. _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? _Boy._ Yes. _Soc._ And how many such spaces are there in this section? _Boy._ Four. _Soc._ And how many in this? _Boy._ Two. [Sidenote: _The doctrine of reminiscence._] _Soc._ And four is how many times two? _Boy._ Twice. _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? _Boy._ Yes.