Weights Hung from Unequal Cords on a Balance
Studies showing a suspended weight rests beneath its cord's central line
This leaf, headed by the later note 'Experimented,' collects related mechanics studies of weights hung from a balance staff by cords of unequal length. Leonardo first states the governing principle, that any suspended weight rests directly beneath the central line of the cord that holds it, then tests it with a spherical weight (labeled 6, on arm-ends 4 and 2) drawn by two converging cords, arguing that the longer cord bears proportionally more load. A further diagram carries the analysis to a load c slung between two pulleys, where the line a b must always be cut by the line of equality.
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Governing rule: a weight hangs beneath its cord's central line
An upper balance staff, hung out of equilibrium, suspends a second balance staff by two unequal cords, with a dotted line marking the central line of the sustaining cord. Leonardo states the principle that the center of any suspended heavy object stands directly under the central line of the cord that sustains it.
Unequal cords share a weight in proportion to their length
A balance staff (ends 4 and 2) suspends a spherical weight labeled 6 by two cords that part from equal arms but differ in length, converging to the same place. He argues that if one cord is twice the other, it feels as much more of the weight as it is longer than the other.
A load c between two pulleys and the line of equality
A long cord passes over two pulleys set at different heights, hanging weights 4 and 2 at its ends and a weight c between them. Within the angle where the cords converge, an analytical line a b marks the line of equilibrium, which Leonardo says must always be cut by the line of equality.