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includes that of the right angle; for he who defines the acute uses
the right angle; for the acute is 'less than a right angle'. The
circle and the semicircle also are in a like relation; for the
semicircle is defined by the circle; and so is the finger by the whole
body, for a finger is 'such and such a part of a man'. Therefore the
parts which are of the nature of matter, and into which as its
matter a thing is divided, are posterior; but those which are of the
nature of parts of the formula, and of the substance according to
its formula, are prior, either all or some of them. And since the soul
of animals (for this is the substance of a living being) is their
substance according to the formula, i.e. the form and the essence of a
body of a certain kind (at least we shall define each part, if we
define it well, not without reference to its function, and this cannot
belong to it without perception), so that the parts of soul are prior,
either all or some of them, to the concrete 'animal', and so too
with each individual animal; and the body and parts are posterior to
this, the essential substance, and it is not the substance but the
concrete thing that is divided into these parts as its matter:-this
being so, to the concrete thing these are in a sense prior, but in a
sense they are not. For they cannot even exist if severed from the
whole; for it is not a finger in any and every state that is the
finger of a living thing, but a dead finger is a finger only in
name. Some parts are neither prior nor posterior to the whole, i.e.
those which are dominant and in which the formula, i.e. the
essential substance, is immediately present, e.g. perhaps the heart or
the brain; for it does not matter in the least which of the two has
this quality. But man and horse and terms which are thus applied to
individuals, but universally, are not substance but something composed
of this particular formula and this particular matter treated as
universal; and as regards the individual, Socrates already includes in
him ultimate individual matter; and similarly in all other cases. 'A
part' may be a part either of the form (i.e. of the essence), or of
the compound of the form and the matter, or of the matter itself.
But only the parts of the form are parts of the formula, and the
formula is of the universal; for 'being a circle' is the same as the
circle, and 'being a soul' the same as the soul. But when we come to
the concrete thing, e.g. this circle, i.e. one of the individual
circles, whether perceptible or intelligible (I mean by intelligible
circles the mathematical, and by perceptible circles those of bronze
and of wood),-of these there is no definition, but they are known by
the aid of intuitive thinking or of perception; and when they pass out
of this complete realization it is not clear whether they exist or
not; but they are always stated and recognized by means of the
universal formula. But matter is unknowable in itself. And some matter
is perceptible and some intelligible, perceptible matter being for
instance bronze and wood and all matter that is changeable, and
intelligible matter being that which is present in perceptible
things not qua perceptible, i.e. the objects of mathematics.
We have stated, then, how matters stand with regard to whole and
part, and their priority and posteriority. But when any one asks
whether the right angle and the circle and the animal are prior, or
the things into which they are divided and of which they consist, i.e.
the parts, we must meet the inquiry by saying that the question cannot
be answered simply. For if even bare soul is the animal or the
living thing, or the soul of each individual is the individual itself,
and 'being a circle' is the circle, and 'being a right angle' and
the essence of the right angle is the right angle, then the whole in
one sense must be called posterior to the art in one sense, i.e. to
the parts included in the formula and to the parts of the individual
right angle (for both the material right angle which is made of
bronze, and that which is formed by individual lines, are posterior to
their parts); while the immaterial right angle is posterior to the
parts included in the formula, but prior to those included in the
particular instance, and the question must not be answered simply. If,

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