The excerpt represents the core issue or deciding factor on which you must meditate, and is drawn from Theaetetus by Plato:|
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