The rolling wheel, weight, and the causes of motion
Why a wheel rolls downhill about its point of contact, and why no motion lasts once its cause is spent
Leonardo analyzes a wheel descending an inclined plane: its point of contact with the ground acts as a pivot, and because the part S t beyond the pivot outweighs S r, that side falls and the wheel rolls furiously downhill-the higher the pivot (at n rather than c), the faster it rolls. He states that every heavy body tends toward the center of the earth and that the more oblique the resistance, the less it opposes the fall. A further discourse holds that no lifeless thing can push or pull without accompanying what it moves, and that once the moving force or weight is consumed the motion must stop, for without causes there are no effects. A last proposition maintains that a body on a perfectly smooth plane whose pivot does not lie between equal weights never comes to rest, as with those who slip on ice.
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A wheel's contact point is its pivot on the slope
Every heavy body tends to fall to the center of the earth, and the more oblique opposition resists it less. Wherever the wheel touches the earth is its pivot; since S x is the pivot, S t weighs more than S r, so S t falls, prevails over S r and raises it, and the ball rolls furiously downhill. With the pivot higher at n, the wheel rolls as much faster as n c enters into c b.
The wheel's load upon the ground
On weight: this wheel weighs twice as much upon the supporting ground as the part r S, and no more.
No motion outlasts the force or weight that causes it
No lifeless thing can push or pull without accompanying what it moves, and what pushes can only be force or weight. Weight moves a thing because it desires stability, and once at rest cannot restore itself; force is consumed as it moves the thing, and once spent cannot renew the motion. So nothing moved can have a long operation, for if the causes do not exist, neither do the effects.
A body on a smooth plane never stops until balanced
On a smooth, perfect plane, an object whose pivot does not lie between parts of equal weight will never stop, as seen in those who slip on the ice, who do not stop until their parts return equidistant about their center.
A weighted cord wound on an axle drives the wheel
A wheel mounted on an axle has a cord wrapped around it; a weight hung from the cord's end sets the wheel turning, but the motion is unrecoverable once the weight has descended.