Theaet. Yes, Socrates, there is no difficulty as you put the question. You mean, if I am not mistaken, something like what occurred to me and to my friend here, your namesake Socrates, in a recent discussion.
Soc. What was that, Theaetetus ?
Theaet. Theodorus was writing out for us something about roots, such as the roots of three or five, showing that they are incommensurable by the unit : he selected other examples up to seventeen — there he stopped. Now as there are innumerable roots, the notion occurred to us of attempting to include them all under one name or class.
Soc. And did you find such a class ?
Theaet. I think that we did ; but I should like to have your opinion.
Soc. Let me hear.
Theaet. We divided all numbers into two classes : those which are made up of equal factors multiplying into one another, which we compared to square figures and called square or equilateral numbers ; — that was one class.
Soc. Very good.
Theaet. The intermediate numbers, such as three and five, and every other number which is made up of unequal factors, either of a greater multiplied by a less, or of a less multiplied by a greater, and when regarded as a figure, is contained in unequal sides ; — all these we compared to oblong figures, and called them oblong numbers.
Soc. Capital ; and what followed ?
Theaet. The lines, or sides, which have for their squares the equilateral plane numbers, were called by us lengths or magnitudes ; and the lines which are the roots of (or whose squares are equal to) the oblong numbers, were called powers or roots ; the reason of this latter name being, that they are commensurable with the former (i.e., with the so-called lengths or magnitudes) not in linear measurement, but in the value of the superficial content of their squares ; and the same about solids.
Soc. Excellent, my boys ; I think that you fully justify the praises of Theodorus, and that he will not be found guilty of false witness.
Theaet. But I am unable, Socrates, to give you a similar answer about knowledge, which is what you appear to want ; and therefore Theodorus is a deceiver after all.
Soc. Well, but if some one were to praise you for running, and to say that he never met your equal among boys, and afterwards you were beaten in a race by a grown-up man, who was a great runner — would the praise be any the less true ?
Theaet. Certainly not.
Soc. And is the discovery of the nature of knowledge so small a matter, as just now said ? Is it not one which would task the powers of men perfect in every way ?
Theaet. By heaven, they should be the top of all perfection !
Soc. Well, then, be of good cheer ; do not say that Theodorus was mistaken about you, but do your best to ascertain the true nature of knowledge, as well as of other things.
Theaet. I am eager enough, Socrates, if that would bring to light the truth.