ample, when asked about the clay, he might have
said simply, that clay is moistened earth--what sort of clay is not to
the point.

THEAETETUS: 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.

SOCRATES: What was that, Theaetetus?

THEAETETUS: 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.

SOCRATES: And did you find such a class?

THEAETETUS: I think that we did; but I should like to have your opinion.

SOCRATES: Let me hear.

THEAETETUS: 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.

SOCRATES: Very good.

THEAETETUS: 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.

SOCRATES: Capital; and what followed?

THEAETETUS: 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.

SOCRATES: Excellent, my boys; I think that you fully justify the praises
of Theodorus, and that he will not be found guilty of false witness.

THEAETETUS: 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.

SOCRATES: 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