Distributing a hung weight to the ends of a cord
A fan of cords from a fixed weight, worked through every angle
A large fan of cords radiates from a hub at n up to lettered points b, c, d, e, f, g on a semicircular arc, with a weight box hanging below. Leonardo sets the weight n in place and imagines swinging the cord g n through every degree up to a, tracking how the load shifts onto its support m. He grounds the analysis on two cited propositions: that a body's center of gravity falls perpendicularly beneath the sole cord holding it, and that when the weight's perpendicular bisects the angle between two cords, both cords are loaded equally.
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The end-load follows the ratio g n to g f
Whatever proportion g n has with g f, such will the weight sustained by f have with that sustained by m. Leonardo keeps the weight n fixed and shifts the cord g n through all degrees up to a, seeking every variation the weight gives to its mover and to the support m.
Two cited rules of gravity and the bisected angle
By the first proposition of the second book, the center of every gravity falls perpendicularly beneath the sole cord that sustains it, so a bears the whole weight n. By the second proposition, if the weight's perpendicular divides the angle of the two cords into equal parts, both cords are equally burdened by that weight.