The Complete Aristotle (eng.)

identify the odd with 1; for if the odd implied 3 how
would 5 be odd? Again, spatial magnitudes and all such things are
explained without going beyond a definite number; e.g. the first,
the indivisible, line, then the 2 &c.; these entities also
extend only up to 10.
    Again, if number can exist separately, one might ask which is
prior—1, or 3 or 2? Inasmuch as the number is composite, 1 is
prior, but inasmuch as the universal and the form is prior, the
number is prior; for each of the units is part of the number as its
matter, and the number acts as form. And in a sense the right angle
is prior to the acute, because it is determinate and in virtue of
its definition; but in a sense the acute is prior, because it is a
part and the right angle is divided into acute angles. As matter,
then, the acute angle and the element and the unit are prior, but
in respect of the form and of the substance as expressed in the
definition, the right angle, and the whole consisting of the matter
and the form, are prior; for the concrete thing is nearer to the
form and to what is expressed in the definition, though in
generation it is later. How then is 1 the starting-point? Because
it is not divisiable, they say; but both the universal, and the
particular or the element, are indivisible. But they are
starting-points in different ways, one in definition and the other
in time. In which way, then, is 1 the starting-point? As has been
said, the right angle is thought to be prior to the acute, and the
acute to the right, and each is one. Accordingly they make 1 the
starting-point in both ways. But this is impossible. For the
universal is one as form or substance, while the element is one as
a part or as matter. For each of the two is in a sense one-in truth
each of the two units exists potentially (at least if the number is
a unity and not like a heap, i.e. if different numbers consist of
differentiated units, as they say), but not in complete reality;
and the cause of the error they fell into is that they were
conducting their inquiry at the same time from the standpoint of
mathematics and from that of universal definitions, so that (1)
from the former standpoint they treated unity, their first
principle, as a point; for the unit is a point without position.
They put things together out of the smallest parts, as some others
also have done. Therefore the unit becomes the matter of numbers
and at the same time prior to 2; and again posterior, 2 being
treated as a whole, a unity, and a form. But (2) because they were
seeking the universal they treated the unity which can be
predicated of a number, as in this sense also a part of the number.
But these characteristics cannot belong at the same time to the
same thing.
    If the 1-itself must be unitary (for it differs in nothing from
other 1’s except that it is the starting-point), and the 2 is
divisible but the unit is not, the unit must be liker the 1-itself
than the 2 is. But if the unit is liker it, it must be liker to the
unit than to the 2; therefore each of the units in 2 must be prior
to the 2. But they deny this; at least they generate the 2 first.
Again, if the 2-itself is a unity and the 3-itself is one also,
both form a 2. From what, then, is this 2 produced?
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9
    Since there is not contact in numbers, but succession, viz.
between the units between which there is nothing, e.g. between
those in 2 or in 3 one might ask whether these succeed the 1-itself
or not, and whether, of the terms that succeed it, 2 or either of
the units in 2 is prior.
    Similar difficulties occur with regard to the classes of things
posterior to number,-the line, the plane, and the solid. For some
construct these out of the species of the ‘great and small’; e.g.
lines from the ‘long and short’, planes from the ‘broad and
narrow’, masses from the ‘deep and shallow’; which are species of
the ‘great and small’. And the originative principle of such things
which answers to the 1 different thinkers describe in different
ways, And in these also the impossibilities, the fictions, and the
contradictions of all probability are seen to be innumerable. For
(i) geometrical classes are severed from one another, unless the
principles of these are implied in one another in such a way that
the ‘broad and narrow’ is also ‘long and short’ (but if this is so,
the plane will be line and the solid a plane; again, how will
angles and figures and such things be