On Gravity and Its Supports
A cord bent over a pulley bears twice the load of a straight one, strongest at its bend
Under the heading 'On gravity and its supports,' Leonardo states that a suspended weight acts wholly through the whole of its support and wholly in every part of it. He then argues that a cord bent over a pulley sustains more in its hanging ends than when stretched straight: a bent cord d c e f able to resist 10 would, drawn straight as a b, resist only 5, since (by the seventh proposition of the book) each cord gains as much in force as it loses in length. A further note finds that the bent cord is strongest at the middle of its bend, where it condenses over the pulley. The right margin shows weights on lettered cords and a pulley, with graduated scales numbered 1 through 8.
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A suspended weight acts wholly through the whole support
The gravity suspended or sustained is entire throughout the whole of its support, and entire in each part of it. Marginal figures show weights carried on lettered cords a b c d and e f g h i and on a fixed support, with graduated scales.
A cord bent over a pulley bears twice a straight one
A cord bent over its pulley sustains more in its hanging ends than when stretched straight: if the bent cord d c e f resists 10, the same cord drawn straight as a b will resist only five. This follows because the halves c d and e f, each half the length of a b, must have double its power, since each cord gains as much in force as it loses in length.
The bent cord is strongest at the middle of its bend
The greatest power of a bent cord lies at the middle of its bend, for (by the eighth proposition) the denser cord is the stronger. Condensing where it bends over the pulley, the cord there spreads and sinks a little, which forces the condensation.