The Force Needed to Move a Cart
Wheel-and-axle leverage of 24 to one, friction, and the rule of three
Folio 46r works out the power required to move a cart, illustrated by a pen drawing of a cross-shaped axle and a small wheel diagram marked 6000, 3000 and 'to the mover'. Leonardo takes an iron axle 1/8 thick and a wheel 3 braccia in diameter, giving a leverage of 24 to one, and combines it with the friction at the hub (a quarter of the load) to conclude that one pound of power draws 96. He then applies the rule of three to find that on level ground 6000 pounds is balanced by 62 and a half, with the columns of arithmetic set out at the right. An untranscribed red-chalk sketch at the upper right shows a large curved, wing-like membrane with radiating ribs above a small operating mechanism.
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Leverage and friction reduce the force to move a load
With an iron axle 1/8 thick and a wheel 3 braccia across, the wheel gives a leverage of 24 to one; the friction at the hub is a quarter of the load, so 96 pounds come to 24. Combining the two, one pound of power draws 96 pounds, taken as the foundation of a general rule.
The rule of three applied to a 6000-pound load
If 96 stands equal with one, the rule of three is used to ask what balances 6000. The worked answer is that on a flat surface 6000 pounds stands equal with 62 and a half, and columns of figures at the right carry out the division.
The cart axle and wheel
A pen drawing shows the cross-shaped iron axle at the left and, at center, a small circle diagram of the wheel marked 6000 and 3000 with the note directed 'to the mover'. Together they illustrate the wheel-and-axle mechanism analysed in the text.
Untranscribed winged-apparatus sketch
At the upper right a faint red-chalk sketch shows a large curved membrane spread with radiating ribs, above a smaller mechanism and figure. It is not covered by the transcription and is described here only from what is drawn.