Placing an 8-Pound Counterweight Against Three Loads
Finding where a single 8-lb weight balances loads of 1, 2 and 3 pounds
An upper and a lower balance diagram enclose the text, boxed weights labelled 1, 2, 3 and 8 hanging from one arm. Leonardo sets a statics problem: three weights of 1, 2 and 3 pounds hang at random distances on one arm, and he asks in what single place an 8-pound counterweight must be set on the opposite arm to make the beam equal.
On this page
Balancing three loads with one 8-pound weight
On one arm hang three weights of 1, 2 and 3 pounds at various random distances. The question is where a single 8-pound weight must be placed on the opposite arm to balance the three, the solution to be read from the accompanying diagram.
The site that equalises the opposing arms
Finding the position of the 8-pound weight is a proportional calculation, matching its distance from the pivot against the combined moments of the 1-, 2- and 3-pound loads. Leonardo directs the reader to the figure drawn below.
Two balance beams with hanging weights
Above the text a beam hung from a central post carries boxed weights labelled 8, 3, 2 and 1; the lower beam repeats the layout. The drawings illustrate the counterweight problem posed in the note.