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