The Divided Lever versus the Whole: Force and Lift
Diagrams arguing a divided lever gives more force while raising the load less high
The sheet examines how a lever divided into segments compares with an undivided one, claiming the divided lever exerts three-quarters more force while raising the load only half as high. Worked examples give the arms in braccia and the balancing loads in libbre: a 12-braccio lever with a one-braccio counter-arm balanced by 100 libbre, its divided version by 40, and a 40-braccio lever carrying 4000 libbre balanced by 100 libbre whole or 10 10/19 libbre divided. Two labelled diagrams (lever r c with counter-lever a r, and lever K g x m with counter-arms f K and h x) illustrate the geometry. Further faint writing occupies the upper part of the sheet.
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The divided lever gives three-quarters more force
The proof asserts that a lever divided into parts exerts three-quarters more force than the whole lever. In compensation, in its counter-lever it raises the weight only half as high as the whole one does.
Balancing lever r c and lever K g x m
For lever r c of 12 braccia with counter-lever a r of one braccio, when c falls four braccia to d the counter-arm a rises half a braccio to b; the lever K g x m, with two braccia of counter-arm f K and h x, raises f only a quarter of a braccio. A 12-braccio lever bearing 1200 libbre is balanced by 100 libbre, the divided lower lever by 40; a 40-braccio lever holding 4000 libbre balances against 100 libbre whole or 10 10/19 libbre divided.