We have distinguished, then, the different ways in which the term
"nature" is used.

    The next point to consider is how the mathematician differs from the
physicist. Obviously physical bodies contain surfaces and volumes,
lines and points, and these are the subject-matter of mathematics.

    Further, is astronomy different from physics or a department of
it? It seems absurd that the physicist should be supposed to know
the nature of sun or moon, but not to know any of their essential
attributes, particularly as the writers on physics obviously do
discuss their shape also and whether the earth and the world are
spherical or not.

    Now the mathematician, though he too treats of these things,
nevertheless does not treat of them as the limits of a physical
body; nor does he consider the attributes indicated as the
attributes of such bodies. That is why he separates them; for in
thought they are separable from motion, and it makes no difference,
nor does any falsity result, if they are separated. The holders of the
theory of Forms do the same, though they are not aware of it; for they
separate the objects of physics, which are less separable than those
of mathematics. This becomes plain if one tries to state in each of
the two cases the definitions of the things and of their attributes.
"Odd" and "even", "straight" and "curved", and likewise "number",
"line", and "figure", do not involve motion; not so "flesh" and "bone"
and "man"-these are defined like "snub nose", not like "curved".

    Similar evidence is supplied by the more physical of the branches of
mathematics, such as optics, harmonics, and astronomy. These are in
a way the converse of geometry. While geometry investigates physical
lines but not qua physical, optics investigates mathematical lines,
but qua physical, not qua mathematical.

    Since "nature" has two senses, the form and the matter, we must
investigate its objects as we would the essence of snubness. That
is, such things are neither independent of matter nor can be defined
in terms of matter only. Here too indeed one might raise a difficulty.
Since there are two natures, with which is the physicist concerned? Or
should he investigate the combination of the two? But if the
combination of the two, then also each severally. Does it belong
then to the same or to different sciences to know each severally?

    If we look at the ancients, physics would to be concerned with the
matter. (It was only very slightly that Empedocles and Democritus
touched on the forms and the essence.)

    But if on the other hand art imitates nature, and it is the part
of the same discipline to know the form and the matter up to a point
(e.g. the doctor has a knowledge of health and also of bile and
phlegm, in which health is realized, and the builder both of the
form of the house and of the matter, namely that it is bricks and
beams, and so forth): if this is so, it would be the part of physics
also to know nature in both its senses.

    Again, "that for the sake of which", or the end, belongs to the same
department of knowledge as the means. But the nature is the end or
"that for the sake of which". For if a thing undergoes a continuous
change and there is a stage which is last, this stage is the end or
"that for the sake of which". (That is why the poet was carried away
into making an absurd statement when he said "he has the end for the
sake of which he was born". For not every stage that is last claims to
be an end, but only that which is best.)

    For the arts make their material (some simply "make" it, others make
it serviceable), and we use everything as if it was there for our
sake. (We also are in a sense an end. "That for the sake of which" has
two senses: the distinction is made in our work On Philosophy.) The
arts, therefore, which govern the matter and have knowledge are two,
namely the art which uses the product and the art which directs the
production of it. That is why the using art also is in a sense
directive; but it differs in that it knows the form, whereas the art
which is directive as being concerned with production knows the
matter. For the helmsman knows and prescribes what sort of form a helm
should have, the other from what wood it should be made and by means
of what operations. In the products of art, however, we make the
material with a view to the function, whereas in the products of
nature the matter is there all along.

    Again, matter is a relative term: to each form there corresponds a
special matter. How far then must the physicist know the form or
essence? Up to a point, perhaps, as the doctor must know sinew or
the smith bronze (i.e. until he understands the purpose of each):
and the physicist is concerned only with things whose forms are
separable indeed, but do not exist apart from matter. Man is
begotten by man and by the sun as well. The mode of existence and
essence of the separable it is the business of the primary type of
philosophy to define.