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.g. to body, but to fire and earth,
whether there is something common to them, viz. body, or not. But in
fact the Platonists speak as if the One were homogeneous like fire
or water; and if this is so, the numbers will not be substances.
Evidently, if there is a One itself and this is a first principle,
'one' is being used in more than one sense; for otherwise the theory
is impossible.
When we wish to reduce substances to their principles, we state
that lines come from the short and long (i.e. from a kind of small and
great), and the plane from the broad and narrow, and body from the
deep and shallow. Yet how then can either the plane contain a line, or
the solid a line or a plane? For the broad and narrow is a different
class from the deep and shallow. Therefore, just as number is not
present in these, because the many and few are different from these,
evidently no other of the higher classes will be present in the lower.
But again the broad is not a genus which includes the deep, for then
the solid would have been a species of plane. Further, from what
principle will the presence of the points in the line be derived?
Plato even used to object to this class of things as being a
geometrical fiction. He gave the name of principle of the line-and
this he often posited-to the indivisible lines. Yet these must have
a limit; therefore the argument from which the existence of the line
follows proves also the existence of the point
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