Weights on a Beam Held by Two Cords
A horizontal beam hung from inclined cords, with a rule relating the weights to triangle faces and line segments
The sheet studies a horizontal beam suspended by two inclined cords, one drawn from S and one from m, meeting the beam at a marked point. Leonardo states that the ratio of the greater weight carried by cord m t to the lesser weight carried by cord c S equals the ratio of the face of triangle e n to the face of triangle a b, and equally the ratio of segment t x to x c matches that of m o to o S. Semicircular arcs at the base measure the angles the cords make with the beam. Below, small sketches show rods hung from cords over pulleys, with a note to test the principle by experiment.
On this page
Proportion of the weights carried by the two cords
The greater weight of the beam borne by cord m t stands to the lesser weight borne by cord c S as the face of triangle e n stands to the face of triangle a b. Likewise the line t x stands to the line x c as the line m o stands to the line o S. Semicircular arcs at the beam mark the angles the cords make where they meet it.
Rods hung from cords over pulleys, to be tested by experiment
At the foot of the sheet are small sketches of rods suspended from cords that run over pulleys, arranged to weigh the balance of loads. Leonardo adds only the instruction to test the matter by this means. The drawings translate the cord-and-angle rule above into a device that could be built and tried.