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The rolling motion made by a ball drawn over a flat and dense site is longer than the free motion it makes through the air. The ball, conditioned as here proposed, moves with a compound motion, and this compound motion has no place through the air. It is proved by saying thus: if the compound motion is in contact with the said floor, it ordinarily has two motions, of which one is made by the surface of the moving body about its centre — and this is called revolving (circumvolving) motion — and the other is straight motion. The revolving motion is longer and faster than the straight motion would be by itself through the air; but rolling upon the floor, the straight motion becomes equal to the revolving motion, which is three times and one seventh longer than the straight motion measured by the diameters of that sphere; and such proportion of motion to motion is as the proportion of the diameter to the circumference of the sphere rolling upon the floor, or thrown through the air without revolution of that sphere. Therefore we conclude that the revolving motion of uniform revolution, being made along the flat floor, is three times and one seventh longer than being made freely through the air; but on the ground the revolving motion is equal to the motion of the centre, and through the air it is less by two times and 1/7. Why does the rolling motion of the ball drawn over a flat, dense place make more distance than when drawn through the air? Read above.

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