Weighing a beam held by a slanting cord
Statics outside right angles: reducing a four-weight beam by the fifth proposition.
A single note on the statics of a beam suspended by a cord that meets it "outside of right angles." A semicircular graduated arc with an inscribed triangle and a small hanging weight sits above a long block of mirror-script working the problem. Leonardo reduces the slanting case to the perpendicular one by the fifth proposition: for a beam of 4 weights the near head carries 1 and the far head 3, and the cord a c is compared with m c (it goes in twice) so that 2 weights at r balance c. The tag marks it as mechanics.
On this page
Reducing a slanting cord to the perpendicular case
For a beam bound by a cord and weighing 4 weights, the fifth proposition gives head 2 as 1 weight (with a cord at a right angle to the beam) and the other head as 3 weights. Comparing cord a c with m c, into which it goes twice, 2 weights at r balance c; so the beam of 4 weights has its foot receiving them plus the 2 counterweights of r.
Graduated arc with inscribed triangle
The construction is set out on a semicircular graduated arc carrying an inscribed triangle and a small weight hung at the right, the geometric frame in which the cord's angle to the beam is measured. Letter labels for the working include a, c, m, n, r.