
On The Heavens
defined, we mean a thing outside which no part of itself can be found,
and if addition is always possible to the straight line but never to
the circular, clearly the line which embraces the circle is
complete. If then the complete is prior to the incomplete, it
follows on this ground also that the circle is primary among
figures. And the sphere holds the same position among solids. For it
alone is embraced by a single surface, while rectilinear solids have
several. The sphere is among solids what the circle is among plane
figures. Further, those who divide bodies into planes and generate
them out of planes seem to bear witness to the truth of this. Alone
among solids they leave the sphere undivided, as not possessing more
than one surface: for the division into surfaces is not just
dividing a whole by cutting it into its parts, but division of another
fashion into parts different in form. It is clear, then, that the
sphere is first of solid figures.
If, again, one orders figures according to their numbers, it is most
natural to arrange them in this way. The circle corresponds to the
number one, the triangle, being the sum of two right angles, to the
number two. But if one is assigned to the triangle, the circle will
not be a figure at all.
Now the first figure belongs to the first body, and the first body
is that at the farthest circumference. It follows that the body
which revolves with a circular movement must be spherical. The same
then will be true of the body continuous with it: for that which is
continuous with the spherical is spherical. The same again holds of
the bodies between these and the centre. Bodies which are bounded by
the spherical and in contact with it must be, as wholes, spherical;
and the bodies below the sphere of the planets are contiguous with the
sphere above them. The sphere then will be spherical throughout; for
every body within it is contiguous and continuous with spheres.
Again, since the whole revolves, palpably and by assumption, in a
circle, and since it has been shown that outside the farthest
