On The Heavens
attributes which are simple are nevertheless divisible. Attributes
of this kind will serve, therefore, to illustrate the impossibility of
the view. It is impossible, if two parts of a thing have no weight,
that the two together should have weight. But either all perceptible
bodies or some, such as earth and water, have weight, as these
thinkers would themselves admit. Now if the point has no weight,
clearly the lines have not either, and, if they have not, neither have
the planes. Therefore no body has weight. It is, further, manifest
that their point cannot have weight. For while a heavy thing may
always be heavier than something and a light thing lighter than
something, a thing which is heavier or lighter than something need not
be itself heavy or light, just as a large thing is larger than others,
but what is larger is not always large. A thing which, judged
absolutely, is small may none the less be larger than other things.
Whatever, then, is heavy and also heavier than something else, must
exceed this by something which is heavy. A heavy thing therefore is
always divisible. But it is common ground that a point is indivisible.
Again, suppose that what is heavy or weight is a dense body, and
what is light rare. Dense differs from rare in containing more
matter in the same cubic area. A point, then, if it may be heavy or
light, may be dense or rare. But the dense is divisible while a
point is indivisible. And if what is heavy must be either hard or
soft, an impossible consequence is easy to draw. For a thing is soft
if its surface can be pressed in, hard if it cannot; and if it can
be pressed in it is divisible.
Moreover, no weight can consist of parts not possessing weight.
For how, except by the merest fiction, can they specify the number and
character of the parts which will produce weight? And, further, when
one weight is greater than another, the difference is a third
weight; from which it will follow that every indivisible part
possesses weight. For suppose that a body of four points possesses
weight. A body composed of more than four points will superior in