The balance and the resistance of weights
Weights ranged along a balance arm, and questions on beams and ropes
Opening with the aphorism that flight is caused by motion, motion by force, and force by weight and motion, the page turns to the statics of the balance. Diagrams show pounds set at graduated points a, b, c, d, e resisting fifteen pounds at f, and a long weight m n treated as acting at its midpoint. Further sketches pose questions about the center of an oddly shaped weight, whether four stacked beams bear four times as much as one, and whether a hundred-braccia rope bears as much as a short one.
On this page
Flight, motion, force, and weight
A single chain of causes opens the page: flight is caused by motion, motion is born from force, and force from weight and motion. It frames the mechanical inquiries that follow.
Weights along a balance arm resist fifteen at f
With one pound at each of the equal divisions a, b, c, d, e, Leonardo asks how many pounds they resist at f. Point a resists one, b two, c three, d four, e five, so the whole resists fifteen pounds placed at f.
A weight as long as the arm acts at its midpoint
A six-pound weight m n as long as one balance arm can be treated as concentrated at the arm's middle, point a. Carried out to the arm's end at S, only three pounds at f are needed to resist it.
The center of an irregular weight hangs under its attachment
Even when a weight on the balance has unequal outward projection, its center falls beneath the center of its attachment. If it hangs out with unequal projection beyond the balance, the weight is 'not justified'.
Do four stacked beams bear four times as much?
A pair of drawings sets a small weight on one beam against a larger weight on four beams stacked together. Leonardo asks: if one beam bears one thousand pounds, how much will four beams laid one on another bear?
Does a long rope bear as much as a short one?
Two weights hang from ropes of different lengths. If a rope one braccio long bears one hundred pounds, how many pounds will a rope of the same thickness but a hundred braccia long bear?