Levers, screws and counterweights: force cannot be increased
Balance of weights 3 to 1, screw and nut, and a beam breaking at c
The verso continues the 'Motion' theorems on the conservation of force in machines. Leonardo asserts that no variety of instruments can increase a fixed sum of force applied to raising weights, illustrating a balance in which counterweights b d f h descend as a c e g rise, each pan resisting three to one. He adds that levers and screws of equal length and equal number of turns cost the same labour whatever their thickness, and that a nut girding a screw changes nothing for its mover. A closing rule notes that the shorter the motion of the load compared with the driving motion, the less force is needed, and a small diagram shows a beam a b that will break at c.
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No instrument can increase a fixed sum of force
It is impossible, with any variety of instruments, to give increase to a determined sum of forces and motion applied to raising weights. This holds in equal motion of cord and counterweight, between equal elevation and weight on the opposite side, for every variety of motions and instruments.
Counterweights b d f h descend as a c e g rise, three to one
As the counterweights b d f h descend to the line i K, the weights a c e g rise from the line n p to the line m o. In each balance one weight stands equal to and resists three.
Levers and screws: thickness costs no extra labour
Levers and screws of equal length with a like number of turns will not increase labour for their mover, however varied their thickness. The proposition separates mechanical advantage from the mere bulk of the parts.
The nut girding the screw changes no force
The nut (female screw) that girds the twisted threads of the screw, whether with many or few turns, neither increases nor takes away force from its mover. The screw-and-nut figure marked 74, labelled 'nut', illustrates the case.
The shorter the load's motion, the less force is needed
The shorter the motion of the thing moved compared with the motion that moves it, the less force suffices for its mover. This states the trade of distance for force at the heart of the preceding theorems.
The beam a b will break at c
A short caption beside a loaded beam declares that the wood a b will break at c. It applies the mechanics of load and support to the failure point of a timber.