The Strength of Loaded Staffs, Beams, and Twisted Cords
Why a shorter staff bears more, bound staves multiply their load, and twisted cords grow stronger
A folio of diagrams and proportional reasoning on how the load a staff, beam, or cord can bear depends on its length and arrangement. Leonardo argues that a short staff bears proportionally more than a long one of the same width, and that a single staff projecting one hundred of its widths from a wall bears far less than one projecting only five, so that a hundred such staves bound together at a b would bear twenty thousand pounds. He extends the rule to suspending cords, where the shorter is the stronger, and closes by observing that two cords twisted together grow stronger in proportion to how much the twisting shortens them.
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A short staff bears more than a long one of equal width
If a lance of two braccia bears ten pounds, a staff one braccio long of the same width will bear twenty. As many times as the short staff enters into the long one, so many times more weight will it support.
Staves bound and projecting from a wall (m n; a b)
A single staff projecting one hundred of its own widths from a wall bears ten pounds; one projecting only five widths bears ten times as much. So one hundred such staves, bound and united and projecting five widths at a b, would bear twenty thousand pounds.
Of two suspending cords the shorter is the stronger (10, 100)
Two cords of different length each suspend a weight, the longer bearing 10 and the shorter 100. As many times as the shorter cord enters into the longer one, so much stronger will it be than the longer one.
Twisted cords grow stronger as they shorten
Comparing a simple cord with two cords twisted together, Leonardo asks whether twisting adds strength. He finds that as much as the cords lose in length through the twisting, by so much are they stronger than before.