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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

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