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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

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