A weight on a pulley finds the middle of a slack cord
Crank wheel, winding beam and pulley; where a loaded pulley rests on an arched cord
Folio 79r combines drawings of machine elements, a crank wheel with handle and pole, a winding beam (subbio) and a pulley (carrucola), with a statics demonstration of a weight hung from a pulley riding on a sagging cord. Leonardo states that such a weight always settles at the middle of the cord, loading both ends equally; if the ends are at unequal heights it settles proportionally nearer the lower one, yet the ends stay equally burdened. On the labelled cord a f p, where a is lower than p by half, the pulley rests so that n m is half of m S, and the same ratio would persist even if the cord ran to infinity along the same slope.
On this page
A pulley-borne weight rests at the middle of an arched cord
A weight supported by a pulley on an arched cord always comes to rest at the middle of the cord, giving equal loads to its two ends at the site of equality. If the ends are at unequal height it rests as much nearer the lower end as that end is lower, staying between equal angles, and the ends remain equally burdened.
The cord a f p worked as a proportion
Let the cord be a f p and f the pulley-borne weight. It rests as much nearer a than p as a is lower than p; since a is lower by half, n m is half of m S, yet a feels as much weight as p. The same would hold if f p ran to infinity along the same slope, n and n m each entering p S and m S four times.
Crank wheel, winding beam and pulley
The upper figures are labelled with the handle, pole and wheel of a crank, a winding beam (subbio) and a pulley (carrucola). They supply the built mechanisms whose behaviour the folio's statics measures.