Methods of weighing and bodies rolling down an incline
Two balance designs, and how a sphere's speed depends on where it touches a slope.
Leonardo sets out two methods of weighing: a triangular balance hung from its apex at r, carrying a plumb f and the weights m and n, and a balance staff swung before a graduated semicircle. He then analyzes a heavy sphere rolling down the incline a c, arguing that its speed grows as its point of contact p moves farther from the perpendicular of its central line m n. A closing note treats a conical (round-pyramid) body on a slope, which can move only in a circle about its point n.
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A triangular balance weighed against a plumb
An equilateral-triangle balance hangs from its apex at the pivot r, with a round plumb f and two spherical weights m and n on wires at the ends of the base. Graduated marks a, b, c, d run along one side. The diminished degrees a, b, c, d are found by experiment, and by as much as n outweighs m the degrees pass the wire r f.
Weighing with a graduated semicircle
A balance staff swings before a fixed semicircular frame marked a, b, c, d, e, f, the wire crossing at S and the ends of the staff at g and t. To see how much more g weighs than t, one counts how many times t s enters into S f; as many times will weight g enter into the weight d.
Speed of a sphere rolling down an incline
A spherical body gains a more rapid motion the farther its contact with the surface lies from the perpendicular of its central line. Because p is the pivot where the ball touches its plane, the mass m above p would fall faster but for the small counterweight o; the greater the distance from n to p, the swifter the ball's course.
A round-pyramid body on a slope
A weighty body shaped like a round pyramid (a cone), with tip and base n and m, rotates about its point n when it rolls on its oblique side. It can take no motion other than a circular one.