Levers, Pulleys, and Why a Long Rope Cannot Be Pulled Straight
The blow that lifts a weight, a rope that breaks before straightening, and how to weigh a lever's counterweight
The folio turns from arches to weights, levers, and pulleys. A small drawing shows how a hammer-blow on a band around two ropes lifts a block, and Leonardo argues at length that a hundred-braccia rope slung between two pulleys, each end loaded with a thousand pounds, will break before a hundred-pound weight hung at its middle can be lifted to the line a—the middle weight acts as a counterweight on a fifty-braccia lever, so the pull needed runs to tens of thousands of pounds. He then gives a method for measuring the counterweight of a lever of equal thickness, dividing an eight-braccio arm into marked spaces and summing the pounds until the seven spaces balance thirty-five pounds against one on the counterlever, and refines it by noting that each half-braccio farther from the fulcrum weighs more than the nearer. The margins carry diagrams of the pulleys, the counterlever, and a graduated balance.
On this page
A hammer-blow that lifts a weight
A rope over a support is tied to the two ends of a large block; a metal band around the ropes is struck simultaneously by two hammers, tightening the ropes together and raising the block. The caption demonstrates how the blow lifts the weight.
Why a long loaded rope breaks before it straightens (o r a)
It is impossible to straighten a hundred-braccia rope between two pulleys a hundred braccia apart, each end bearing a thousand pounds: a hundred-pound weight at the middle will break the rope before it lifts to a. That middle weight counterweights the thousand pounds as if on a fifty-braccia lever; measuring how many times half the pulley's diameter (o r) enters into r a reveals the true pull—running to tens of thousands of pounds—so a very long rope will not straighten without breaking.
Measuring the counterweight of a lever (1–8; 10 each)
To find the counterweight of a lever of equal thickness, mark it off with the counterlever's length: for an eight-braccia arm against one, reckon the pounds space by space up to seven braccia, so that all seven weigh thirty-five pounds together, and one pound on the counterlever brings it to balance.
The half farther from the fulcrum weighs more
For the complete truth, note that in each arm of the lever the half farther from the attachment weighs more than the nearer half. To see it exactly, take half of the last braccio, attach it to the end of the other half-braccio, and use whatever weight you find.
A graduated balance with unequal arms
A schematic balance has arms of different lengths, the longer arm marked at regular intervals, with a round weight hung from the shorter arm and a removed piece of the arm shown at the end of the longer one.