A rod on two cords: shifting one cord toward the middle
Full demonstration that a 6-pound rod redistributes its load as one supporting cord is moved inward
A closely written demonstration analyses a rigid rod suspended by two cords. When the cords are tied at the rod's ends, the 6-pound rod is shared equally, each cord bearing 3 pounds; but as one cord is drawn toward the middle, the fixed end cord is unburdened by half, dropping to 1 1/2 pounds. Leonardo shows the motions are proportional: the overhang beyond a cord goes twice into the enclosed span, just as the transferred weight goes twice into the weight it meets. Three numbered propositions summarize the rule that the weight the movable cord gains stands to the stable cord's as the lost cord interval stands to its remainder.
On this page
Redistribution as a cord moves toward the middle
With both cords at the ends, the 6-pound rod gives 3 pounds to each. Move one cord toward the middle and the cord left at the end sheds half its load, now bearing only 1 1/2. The rod that juts beyond a cord goes twice into the span enclosed between the cords, and the transferred weight likewise goes twice into the weight it meets, so nature works by equal movements.
The rule of equal sharing and its proportion
First proposition: a rod hung by its ends from two cords shares its weight equally between them. Second: the more one cord moves toward the middle, the more of the rod's weight it takes on. Third: the weight the movable cord gains stands to the stable cord's as the loss of the first cord interval stands to its remainder.
Proportion of the overhang to the enclosed span
The weight divided off from the stable cord stands to the first weight of the moving cord where it is applied as the part of the rod jutting beyond one cord stands to its remainder enclosed between the two cords.