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 in