Weights on a Curve, a Windlass, and a Clamping Machine
Force of a weight along arc versus chord, a bucket hoist, and a note on birds flying into the wind
Two mounted sheets (105a and 105b recto) work through problems of weight and mechanical advantage. The main study finds how much force a weight retains when it travels along a curved path rather than a straight chord: an arc of 11 braccia exceeds its 7-braccio chord by 4/7, so a 5-lb weight is left with about 7 ounces of effective force. A geared windlass with a bucket lets a 200-lb man, stepping into a stirrup, raise a 33 1/3-lb load 18 braccia while descending 3, and a large lettered circle argues that every moving body pushes along the line of its motion. A marginal note observes that a bird gaining ground against the wind beats its wings and rows backwards, while the second sheet shows a barrel-like device "to clamp a thing in an arc."
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Force of a weight descending along an arc
The weight m goes to n along the obliquity m n, which gives it weight equal to a fifth of its natural gravity. Because the arc n f m (11 braccia) exceeds its chord n m (7 braccia) by 4/7, a 5-lb weight is left with the force of about one pound; so with roughly 7 ounces of force the pound falls by way of the arc.
Motion begins at right angles (mn, a, b, p)
If b is fixed and a is free, a begins its motion, which is produced within right angles; the same b does when free upon the loosened fixed point a. Therefore every moving body pushes along the line of its motion, and nm ab leans on p.
Windlass and bucket: a man's weight as the motor
With the axle one braccio and the wheel 6 braccia in diameter (radius 3), a man weighing 200 pounds, placing his foot in the stirrup a, raises a bucket weighing 33 1/3 pounds, moving it 18 braccia while he himself descends 3 braccia.
A bird gaining ground against the wind
A marginal note on the flight of birds: if the bird wishes to gain ground against the wind, it beats its wings and rows backwards.
Barrel device to clamp a thing in an arc
The second sheet (105b) shows a large barrel wound with a band and driven by a toothed crank-wheel; the note above it states that the mechanism serves to tighten or clamp a thing in an arc.