Levers, balances and the angled cord bearing weights

A weight held up by two powers along an angled cord

The weight n hangs from an angled cord and is sustained by two different powers, m f and m b. Leonardo resolves the case into a lever f e and counter-lever f a, and finds f e to be 21/22 of f a, so that the mover b feels 22 when n weighs 21.

Second arrangement: counter-lever a third of the lever

In the second layout the lever b c and counter-lever b a are joined by the pendants c f and a n. The counter-lever is a third of the lever, so one pound of power at f resists 3 of weight at b a. Leonardo marks this the end of the rule for calculating the unequal arms of the angled cord.

The load an arched cord throws onto its ends

To learn what weight a cord stretched into an arc places on its two ends, inscribe within it a triangle of equal sides and compare its axis with its hypotenuse. The ratio of axis to hypotenuse equals the ratio of the cord's weight to the weight its ends feel.

A weight set to descend along a given incline

Leonardo poses the inclined-plane problems of finding where a weight 4 dragged by a weight 2 will come to rest, and the slope along which a weight 4 descends of itself.

Equal-armed balance with unequal weights

The concluding rule: a balance of equal arms carrying unequal weights never loads its pole (fulcrum) with more than twice the quantity of the smaller weight.

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On this page

A weight held up by two powers along an angled cord

Second arrangement: counter-lever a third of the lever

The load an arched cord throws onto its ends

A weight set to descend along a given incline

Equal-armed balance with unequal weights