Screw versus wheel: equal work by two men in one hour
Two hoisting machines proven to raise the same weight to the same height with equal force
Leonardo compares two men raising loads with different machines: one uses an endless (worm) screw m, the other a wheel n, each applying equal force and equal speed. He works the case numerically — if together they must lift 100,000 pounds to a height of 100 braccia, 50,000 pounds falls to each; the screw m brings its share up in one turn, the wheel n in ten, and at the tenth turn n stands at 100 braccia alongside m. The two are found to be equal, demonstrating that gain in force is paid for in distance or turns. The drawings show a rack driven by a toothed wheel with a hanging weight, and a worm-and-wheel hoist with counterpoised buckets and a great winch.
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Two men, two machines, equal work
Two men employ equal force (25 pounds) and equal speed for one hour, one drawing his weight with the endless screw m, the other with the wheel n. If together they must raise 100,000 pounds to 100 braccia, 50,000 falls to each; m lifts its share in one turn, n in ten, so that n's tenth turn reaches 100 braccia together with m — and the two prove equal.
The endless screw m and the wheel n
The machine at m is an endless (worm) screw turning a toothed wheel, its share raised in a single turn; the machine n is a wheel-and-winch with pulleys that raises the same load over ten turns. Counterpoised buckets and a rack with a hanging weight illustrate the mechanisms.