Again, by virtue of what, and when, will mathematical magnitudes
be one? For things in our perceptible world are one in virtue of soul,
or of a part of soul, or of something else that is reasonable
enough; when these are not present, the thing is a plurality, and
splits up into parts. But in the case of the subjects of
mathematics, which are divisible and are quantities, what is the cause
of their being one and holding together?
Again, the modes of generation of the objects of mathematics
show that we are right. For the dimension first generated is length,
then comes breadth, lastly depth, and the process is complete. If,
then, that which is posterior in the order of generation is prior in
the order of substantiality, the solid will be prior to the plane
and the line. And in this way also it is both more complete and more
whole, because it can become animate. How, on the other hand, could
a line or a plane be animate? The supposition passes the power of
our senses.
Again, the solid is a sort of substance; for it already has in a
sense completeness. But how can lines be substances? Neither as a form
or shape, as the soul perhaps is, nor as matter, like the solid; for
we have no experience of anything that can be put together out of
lines or planes or points, while if these had been a sort of
material substance, we should have observed things which could be
put together out of them.
Grant, then, that they are prior in definition. Still not all
things that are prior in definition are also prior in
substantiality.
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