De Ponderibus: Suspended Weights, Levers, and an Arch
How a hanging load distributes among its supports, with lever, pulley, and arch-thrust rules
Under the heading 'De ponderibus,' a dense array of small diagrams treats how a suspended weight loads its supports. A ball of 28 hung by six cords, and an inverted version resting on six beams, show that a support nearer the weight's vertical center bears more; a load of 120 split between beams one and five spaces from center divides as 110 to 20. Further sketches give a lever rule — a counterlever lifts as many times more weight as it divides into the lever — and a note that an arch tending to break with 200 pounds of thrust is steadied by an equal opposing force. A bent staff shows that the part farthest from its supports declines most from straightness.
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A support nearer the weight's center bears more (labels 8, 4, 2)
A body suspended by ropes, or supported from below by beams whose ends are fixed at different places, weighs more on one support than the other in proportion as that support's point of attachment is closer to the perpendicular of the weight's center. The cords labeled 2, 4, 8 on each side of point a carry the ball of 28 accordingly.
A load of 120 divides 110 to 20 between two beams
A rectangular weight of 120 rests on two thin beams whose feet lie asymmetrically about the point b beneath its center. One beam, one space from center, bears 110; the other, five spaces away, bears 20. The nearer the beam to the center's perpendicular, the greater its share of the load.
Lever and counterlever rule (a, b, c; 200, 600, 600)
A weight at the end of a lever lifts, at the end of the counterlever, as many times more weight than itself as the counterlever enters into the lever. The drawing runs a wire through pulleys on poles a, b, c: two weights of 600 balance a central ball of 200.
Balancing the thrust of an arch (60; bases 50 and 10)
An acute arch carries a round weight of 60 on one spandrel, its perpendicular to the ground indicated, with its bases marked 50 and 10. If an arch exerts a force of two hundred pounds in tending to break, give it a contrasting two hundred pounds of weight or force and it will stand well.