On Weight Distributed Along a Sustaining Cord
Pulleys and tackles, bends over wheels, and the three natures of a heavy body
Under the heading 'On weight,' Leonardo studies how a load distributed along the whole length of a cord strains it less than the same load hung at its lowest point, invoking a proposition from his 'Elements' that among cords of equal thickness the longer is the weaker. He then treats multi-wheel tackles, stating that one cord bears more than another in proportion to the number of its bends over the wheels, and that the meeting of two cords hanging from one pulley points toward the centre of the world. A final note distinguishes three natures of the heavy body: its immutable natural gravity, an accidental gravity infinite in force, and a variable friction. The right margin carries diagrams of pulleys, a many-wheeled tackle, and balanced suspended rods, lettered a, b, c, t.
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A load spread along a cord strains it less than one hung at the foot
Weight distributed along the whole length of a cord harms it less than if suspended at its lowest part, since (by a proposition of the 'Elements') among cords of equal thickness the longer is the weaker. Thus a b, sustaining the weight spread over the rest of the cord b t, is stronger than the opposite part a c in proportion as it is shorter.
Counting a tackle's bends to find each cord's load
In a many-wheeled tackle, one cord sustains more weight than another by as many times as the number of their bends over the wheels, plus one. The division made by a cord over its pulley is never a right angle, as shown by two simple cords hanging from one pulley whose lines converge at the centre of the world.
Three natures of a heavy body: natural, accidental, friction
The heavy body has three natures: its simple natural gravity, its accidental gravity, and the friction it generates. The natural weight is unchangeable in itself, the accidental one joined to it is infinite in force, and the friction varies with the places where it acts, whether rough or smooth.