Raising a beam: lever, counter-lever, and center of weight
As the beam rises the counter-lever m grows and the lever f shrinks; lengths in proportion to weight
These diagrams analyze the forces as a hinged beam (trave) is raised upright about the fixed pole n. The line a n is the perpendicular of the pole; m is the counter-lever and f the lever, and at every degree of rising the counter-lever grows while the lever shrinks. A concluding rule states that the length of the beam's central line a b stands to b c as the weight left on the cord n a stands to half the weight of the beam. Fractional graduations (1½, 3, 4¼, 5½, 6, 12) mark the stages of the lift.
On this page
Counter-lever m grows, lever f shrinks as the beam rises
The line a n is the perpendicular of the fixed pole n; m is the counter-lever and f the lever. As the beam rises through each degree, m increases and f diminishes, so the counter-lever must be reckoned anew at each stage. m is one third of v f, with v as counterweight and only f bearing the load.
Lengths in proportion to the supported weight
The proportion that the central line a b of the rising beam has to the line b c is the same that the weight remaining on the cord n a has to half the weight of the beam.