The Divided Lever Exerts Greater Force
Proof that a divided lever gives three-quarters more force, with two diagrams and weight calculations
Below several lines of text and numerical working, two lever diagrams with lettered points run across the lower half of the sheet. The text argues that a divided lever exerts three-quarters more force than a whole one while raising the weight in its counter-lever only half as high, and it works this through a lever r c of 12 braccia against a one-braccio counter-lever, and a doubly divided lever K g x m. Concrete balances follow: a counter-lever load of 1200 pounds held by 100 on the lever, or by 40 when divided, and 4000 pounds held by 100 pounds versus only 10 and 10/19 pounds. Additional numerical notes appear at the head of the sheet beyond the transcribed passages.
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The divided lever: more force, less lift
A proof that a divided lever exerts three-quarters more force than the whole one. In compensation, it raises the weight in its counter-lever only half as high, trading height of lift for gain in force.
Motion of the lever arms (r, c, a, b, K, g, x, m, f, h, e)
If the lever r c is 12 braccia and the counter-lever a r one braccio, then when c descends four braccia to d, a rises to b by half a braccio. The lever K g x m has two braccia of counter-lever (f K, h x); when m reaches the point n, h moves to g and g to h, and f rises to e by a quarter of a braccio, half as much as the lever above.
Weights balanced by whole and divided levers
The lever r c, with 1200 pounds on its counter-lever, is balanced by 100 pounds on the lever c, while the divided lever below does the same with 40. For levers of 40 braccia with one braccio of counter-lever bearing 4000 pounds, the whole lever holds the weight in balance with 100 pounds, and the divided lever with 10 and 10/19 pounds.