Power and Resistance on a Cord-Drawn Balance
Two balance staffs whose loads hang from a cord over a pulley; the effort is unchanged along the cord
Two diagrams show a balance staff on a central pivot whose loads are carried by a cord running over a pulley, with a semicircle marking the counterlever radius about the pivot. In the upper figure the cord passes over a pulley at the upper right and the points above the staff's ends and pivot are labelled a, b and c; in the lower figure the pulley sits slightly lower and the points above the two ends are n and m, with perpendicular complements drawn to the staff. The note concludes that the power and resistance remain the same for whatever point the cord is attached along line abc, and likewise along line nm. The sheet continues Leonardo's study of balances, levers and the counterlever.
On this page
Balance loaded through a pulley (points a, b, c)
A balance staff on a central pivot has a cord, weighted at either end, led over a pulley at the upper right. The points lying directly above the staff's ends and pivot are labelled a, b and c, and a semicircle about the pivot marks the radius of the counterlever; an analytical line rises from the staff to point a.
Second balance with a lower pulley (points n, m)
In a companion figure the cord runs over a pulley set slightly below and to the right of the staff, with the points above the two ends labelled n and m. Perpendicular complements descend from n and rise from m, and again a semicircle about the pivot marks the counterlever.
The effort is the same wherever the cord attaches
Leonardo states that it is always the same power and resistance, at whatever place the cord is attached along line abc, and the same below along line nm. The demonstration turns on the fixed geometry of the counterlever rather than on the point of attachment.