Weights on an Angled Cord: Four Demonstrations
How widening the cord's angle changes the potential lever and counter-lever
This page steps through four numbered demonstrations (Prima, Seconda, Terza, Quarta) of a weight held at the bend of a cord treated as an angular balance about a pole. Leonardo sets out which lines are the real supports and which the potential lever and counter-lever, noting that the potential angle inside the real one never has the lever smaller than the counter-lever. He shows that as the cord's angle grows wider the potential lever diminishes while the potential counter-lever grows, and that the counter-lever a b cannot change with the angle a t n while the lever a c shrinks as that angle increases. The fourth, 'real' figure is a balance beam with a pulley and weights, to which he adds an arm m n as counterweight so the weighted real figure can stand for the weightless potential one.
On this page
Widening the cord's angle shrinks the potential lever
The more the angle of the cord that supports the weight n at the middle of its length grows wider, the more the potential lever diminishes and the more the potential counter-lever that supports the weight grows. The potential angle inside the real one never has the lever smaller than the counter-lever.
Real supports versus the potential lever and counter-lever
a t n m are the real supports of the weight o, while lines a c and a b are its potential lever and counter-lever, and c n and b m are the semi-real pendants joining them. The counter-lever a b never changes with the angle a t n, but the lever a c becomes smaller the greater that angle grows.
A real balance-beam figure with an added counterweight arm
This fourth real figure m p o, a balance beam with pulley and weights, represents the second potential figure a c b. Because the real one has weight and the potential one does not, Leonardo adds the arm m n as a counterweight to the arm m o.