Six Cord-and-Beam Cases in the Science of Weights
Equal vs unequal cords, parallel cords on a tilted beam, and loads proportional to obliquity
This page gathers six cases of weights and beams hung from cords. Equal cords from equal height keep equal obliquity and share the load equally, while of two unequal cords the longer is the more oblique; two parallel cords carry a tilted beam equally. Leonardo then states that cords of different obliquity carry loads in proportion to that obliquity, likening the arrangement to the arms of a balance (b c double b a), and that a beam hung by cords of contrary obliquity has its centre of gravity on the intercentric line. The right margin holds the matching series of small diagrams.
On this page
Equal cords from equal height share the load equally
Two equal cords converging from equal height to the same heavy body are always of equal obliquity and equally loaded with the weight they sustain. Labels: a, b, c, d.
Of two unequal cords the longer is more oblique
Of two unequal cords converging from equal height to the same heavy body, the longer cord is always the more oblique. Labels: a, c, b.
Parallel cords carry a tilted beam equally
If two parallel cords suspend a beam by its ends, then even when the beam is oblique it gives an equal weight to each of the two cords. Labels: a, f, m, n.
Load proportional to obliquity, shown by a balance
For two cords of different obliquity to the same body, the loads are as their obliquities. With obliquities in ratio 2:1, shown by the balance arms b c double b a, the cord c d feels half the weight the cord a d feels. Labels: a, b, c, d, e.
Contrary obliquities: centre of gravity on the intercentric line
If two cords of different and contrary obliquity descend from one place to the opposite ends of a beam at any obliquity, the beam's centre of gravity always lies on the intercentric line, together with the centre of the supplementary heights of the cords. Labels: a, f, c, e, g, b, d.