Two Cords of Unequal Thickness Sharing One Weight
The nearer-to-center cord bears more; the "double proportion" of thicknesses
On folio 165r Leonardo pursues how two cords of unequal thickness share a suspended weight, holding that the part nearer the center of gravity of the load carries the more, and that unequal cords can never be equally loaded at the ends of one and the same weight. A "proof" keyed to cords n a and m b and the center of gravity c reasons from the ratio of the intervening spaces, and a marginal heading names the "double proportion" of cord thicknesses. Several cases are drawn as balance-beams with cords and weights, one of them marked "bona" (good).
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Two cords: the part nearer the load's center bears more
Those parts of the thicknesses of two cords that sustain one and the same weight are the more burdened which lie nearer to the center of the gravity they support. A companion rule restates this for a single cord's thickness.
Proof by the ratio of spaces to center c
Let n a and m b be the thickness of the two cords, 4 the weight they sustain, and c the center of gravity. As many times as the space from cord-part a to center c goes into the space from the center to the extremity of the opposite cord, so many more times does a feel of the weight than b.
Double proportion of cord thicknesses
A heading labels the case "weight of cords in their thicknesses" and names it a "double proportion," expressing the load ratio as a proportion between the cords' thicknesses.
Unequal cords can never be equally loaded
It is impossible for cords of unequal thickness, fixed at the ends of an equal weight, to be equally loaded by it. The parts enclosed between the centers gain exactly as much load as the opposite parts outside the centers lose.