Beams on two cords: equal angles, equal support
Statics of a beam hung by unequal cords; oblique versus perpendicular force
The sheet develops the statics of a beam hung from two cords: because equal angles are made at the beam, each cord bears an equal share, and cords of unequal length still sustain the same weight when set equally distant from the centre. A left-hand column adds that an oblique force acts upon the balance for the same office as a perpendicular one, tested with a drawn copper wire. A semicircular protractor ruled with radiating lines heads the page, and two rows of small figures show a rod raised from its cords through a graded series of angles.
On this page
A beam on two cords of unequal length
A beam lettered a, d, o, m, p, c, b, n hangs from two cords. Because it is held by equal angles, each cord bears an equal share, and though one cord is longer than the other, each sustains the same weight.
Why equal angles give equal support
The general statement explains that the equal angles made by the cords with the line of the beam are the reason unequal lengths of cord, placed equally distant from the beam's centre, sustain an equal weight.
Oblique force equals perpendicular
A left-hand column argues that an oblique force works upon the balance for the same office as a perpendicular one. Leonardo notes it was tested in the form below with a drawn copper wire.
A sequence of rods raised from cords
Two rows of small figures show a rod raised from its cords through a graded series of inclinations, with brief numbers (2 1 - 5 4 5; 2 4 2). They trace how the support changes as the rod is lifted.
A graduated protractor of angles
A semicircular protractor ruled with radiating lines heads the sheet, giving the angular framework used to reason about the cords and beams. It supplies the equal-angle constructions the notes depend on.