Beam rotating in a quadrant: balancing a against b
A weighted beam swings from vertical toward horizontal within a quarter-circle
A quarter-circle frame at the top of the page contains a beam pivoted at the point a and swung down from the vertical toward the horizontal, with a plummet marking the true vertical. Three lines of mirror script beneath pose a balance problem: the end a is found to weigh twice as much as b, and Leonardo asks how much weight must be added at b to make the two ends equal.
On this page
How much weight to add at b to equal a
Leonardo states that end a has twice the weight of end b as the beam turns from vertical toward horizontal, and asks what weight must be added at b for the two to balance. The problem treats the changing effective weight of a beam's ends as it rotates about its pivot.
Quadrant frame with pivoted beam at a
The study is set inside a drawn quarter-circle: a vertical and horizontal edge meet, with the beam pivoting from the apex a and a hanging plumb line indicating the vertical. The arc measures the angular sweep of the beam.