Rolling ball: motion on the ground versus through air
Why a ball rolling on a flat, dense surface travels farther than one thrown through the air
The main leaf carries a dense argument on the motion of a ball (ballotta): rolling over a flat, hard floor it travels farther than when hurled freely through the air. Leonardo separates the compound motion of the rolling ball into a revolving motion about its own centre and a straight motion, and relates them by the ratio 3 and one-seventh, the same ratio the circumference bears to the diameter. A small adjoining leaf bears geometric figures with letter-labels keyed to the argument, plus a fragmentary line beginning 'God can make you...'.
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Compound motion of a rolling ball
Leonardo argues that a ball drawn over a flat, dense floor moves with a compound motion made of two parts: a revolving (circumvolving) motion of the surface about the ball's own centre, and a straight motion. On the ground the revolving motion equals the motion of the centre; through the air the rolling motion is lost, so the ball travels less far.
Ratio of diameter to circumference (3 and 1/7)
The revolving motion is said to be three times and one seventh longer than the straight motion measured by the ball's diameters. Leonardo states that the proportion from motion to motion is the same as the proportion of the diameter to the circumference of the rolling sphere, i.e. the value 3 1/7.
