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On The Heavens   


weight to it, a thing which has weight. But the difference between

weight and weight must be a weight, as the difference between white

and whiter is white. Here the difference which makes the superior

weight heavier is the single point which remains when the common

number, four, is subtracted. A single point, therefore, has weight.

Further, to assume, on the one hand, that the planes can only be put

in linear contact would be ridiculous. For just as there are two

ways of putting lines together, namely, end to and side by side, so

there must be two ways of putting planes together. Lines can be put

together so that contact is linear by laying one along the other,

though not by putting them end to end. But if, similarly, in putting

the lanes together, superficial contact is allowed as an alternative

to linear, that method will give them bodies which are not any element

nor composed of elements. Again, if it is the number of planes in a

body that makes one heavier than another, as the Timaeus explains,

clearly the line and the point will have weight. For the three cases

are, as we said before, analogous. But if the reason of differences of

weight is not this, but rather the heaviness of earth and the

lightness of fire, then some of the planes will be light and others

heavy (which involves a similar distinction in the lines and the

points); the earthplane, I mean, will be heavier than the

fire-plane. In general, the result is either that there is no

magnitude at all, or that all magnitude could be done away with. For a

point is to a line as a line is to a plane and as a plane is to a

body. Now the various forms in passing into one another will each be

resolved into its ultimate constituents. It might happen therefore

that nothing existed except points, and that there was no body at all.

A further consideration is that if time is similarly constituted,

there would be, or might be, a time at which it was done away with.

For the indivisible now is like a point in a line. The same

consequences follow from composing the heaven of numbers, as some of

the Pythagoreans do who make all nature out of numbers. For natural

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