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defines 'straight' and 'round'; for a hoop touches a straight edge not
at a point, but as Protagoras used to say it did, in his refutation of
the geometers), nor are the movements and spiral orbits in the heavens
like those of which astronomy treats, nor have geometrical points
the same nature as the actual stars.-Now there are some who say that
these so-called intermediates between the Forms and the perceptible
things exist, not apart from the perceptible things, however, but in
these; the impossible results of this view would take too long to
enumerate, but it is enough to consider even such points as the
following:-It is not reasonable that this should be so only in the
case of these intermediates, but clearly the Forms also might be in
the perceptible things; for both statements are parts of the same
theory. Further, it follows from this theory that there are two solids
in the same place, and that the intermediates are not immovable, since
they are in the moving perceptible things. And in general to what
purpose would one suppose them to exist indeed, but to exist in
perceptible things? For the same paradoxical results will follow which
we have already mentioned; there will be a heaven besides the
heaven, only it will be not apart but in the same place; which is
still more impossible.

(6) Apart from the great difficulty of stating the case truly with
regard to these matters, it is very hard to say, with regard to the
first principles, whether it is the genera that should be taken as
elements and principles, or rather the primary constituents of a
thing; e.g. it is the primary parts of which articulate sounds consist
that are thought to be elements and principles of articulate sound,
not the common genus-articulate sound; and we give the name of
'elements' to those geometrical propositions, the proofs of which
are implied in the proofs of the others, either of all or of most.
Further, both those who say there are several elements of corporeal
things and those who say there is one, say the parts of which bodies
are compounded and consist are principles; e.g. Empedocles says fire
and water and the rest are the constituent elements of things, but
does not describe these as genera of existing things. Besides this, if
we want to examine the nature of anything else, we examine the parts
of which, e.g. a bed consists and how they are put together, and
then we know its nature.
To judge from these arguments, then, the principles of things
would not be the genera; but if we know each thing by its
definition, and the genera are the principles or starting-points of
definitions, the genera must also be the principles of definable
things. And if to get the knowledge of the species according to
which things are named is to get the knowledge of things, the genera
are at least starting-points of the species. And some also of those
who say unity or being, or the great and the small, are elements of
things, seem to treat them as genera.
But, again, it is not possible to describe the principles in
both ways. For the formula of the essence is one; but definition by
genera will be different from that which states the constituent
parts of a thing.
(7) Besides this, even if the genera are in the highest degree
principles, should one regard the first of the genera as principles,
or those which are predicated directly of the individuals? This also
admits of dispute. For if the universals are always more of the nature
of principles, evidently the uppermost of the genera are the
principles; for these are predicated of all things. There will,
then, be as many principles of things as there are primary genera,
so that both being and unity will be principles and substances; for
these are most of all predicated of all existing things. But it is not
possible that either unity or being should be a single genus of
things; for the differentiae of any genus must each of them both
have being and be one, but it is not possible for the genus taken

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