Rod Hung by Two Cords: Lightening of a Load
How the projecting half of a beam relieves the cord that carries its end
Below a diagram of a horizontal beam carried by two vertical cords, Leonardo states two proportional rules of statics. He argues that the ratio of the half of the plain rod to the whole greater part governs how much the load is lightened where it is lifted. A second rule relates the half of the overhanging beam to the span sustained between the two cords, describing how the projection shifts weight off the cord that holds the beam's end.
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Proportional lightening of a beam supported on two cords
The proportion that the lesser part (the half of the plain rod) bears to the whole greater part determines the lightening of the load at the point where it is raised. Likewise, the ratio of the half of the projecting beam to the whole span held between the two cords fixes how much weight the overhang removes from the cord that carries the beam's end, compared with what that cord bore before.