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On The Heavens   

circumference there is neither void nor place, from these grounds also

it will follow necessarily that the heaven is spherical. For if it

is to be rectilinear in shape, it will follow that there is place

and body and void without it. For a rectilinear figure as it

revolves never continues in the same room, but where formerly was

body, is now none, and where now is none, body will be in a moment

because of the projection at the corners. Similarly, if the world

had some other figure with unequal radii, if, for instance, it were

lentiform, or oviform, in every case we should have to admit space and

void outside the moving body, because the whole body would not

always occupy the same room.

Again, if the motion of the heaven is the measure of all movements

whatever in virtue of being alone continuous and regular and

eternal, and if, in each kind, the measure is the minimum, and the

minimum movement is the swiftest, then, clearly, the movement of the

heaven must be the swiftest of all movements. Now of lines which

return upon themselves the line which bounds the circle is the

shortest; and that movement is the swiftest which follows the shortest

line. Therefore, if the heaven moves in a circle and moves more

swiftly than anything else, it must necessarily be spherical.

Corroborative evidence may be drawn from the bodies whose position

is about the centre. If earth is enclosed by water, water by air,

air by fire, and these similarly by the upper bodies-which while not

continuous are yet contiguous with them-and if the surface of water is

spherical, and that which is continuous with or embraces the spherical

must itself be spherical, then on these grounds also it is clear

that the heavens are spherical. But the surface of water is seen to be

spherical if we take as our starting-point the fact that water

naturally tends to collect in a hollow place-'hollow' meaning

'nearer the centre'. Draw from the centre the lines AB, AC, and let

their extremities be joined by the straight line BC. The line AD,

drawn to the base of the triangle, will be shorter than either of

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