The load and motion of five pulley-block cords
Which cord bears most, which one breaks, and the proportion of their motions
A page of pulley-block mechanics, illustrated by marginal diagrams of a series of pulleys and their cords. Leonardo lays down numbered propositions: the motor is always more powerful than the load; the descending cord feels more weight and fatigue than its rising opposite; and the first cord is the one that breaks. He then proves that the last cord suffers least, ranks the fatigue of cords a b, c d, e f, g h, i K in order, and gives the rule of motion: with five cords, when the first moves one braccio the last moves one fifth, and so on to infinity.
On this page
The descending cord bears more weight and fatigue
Leonardo opens with two propositions: the motor is always more powerful than the thing moved, and the cord of the pulley-blocks that descends feels more weight, and hence more fatigue, than its opposite cord that rises. These set the terms for the analysis of a multi-cord tackle. The motor's surplus power, not the load itself, is what strains the cords.
The first cord is the one that breaks
A marginal note states that the first cord of the pulley-blocks is always the one that breaks. This happens in the last part of its height, at the end of its rest upon the wheel. It identifies the point of greatest stress in the tackle.
Five cords: the motor descends five braccia to raise one
The series-of-pulleys diagram is labelled K g f c b, 1 2 3 4 5, i h e d a, 4 1. Leonardo states that if the weight raised by pulley-blocks of five cords rises one braccio, the motor of the first cord descends five braccia. It fixes the trade of distance for force in the five-fold tackle.
The last cord suffers least; the ladder of fatigue
As a third proposition, the last cord feels less fatigue from the motor's power than any other. Leonardo ranks them: a b, the first mover, can do more than c d; c d more than e f; e f more than g h; and g h more than i K. This fatigue comes not from the load, which divides equally, but from the surplus by which the motor exceeds the thing moved, and the powers stand in proportion to the velocities of the cords' motions.
The proportion of motion of motor to load
The motion of the motor relates to the motion of the raised weight as the raised weight relates to the weight of its motor. It follows that as the weight rises one braccio the motor descends four, plus the one by which the weight first rose, so that the motor stands five braccia lower than the load. The motion of the last cord to the first is as the number of cords: with five cords the last moves one fifth, with six one sixth, and so on to infinity.