Loads in the Three Cords of a Suspended Beam
Resolving a 10-pound beam's weight into forces by base, axis, and hypotenuse
The page analyzes a beam S g weighing 10 pounds hung from three cords (a d, d n, n b), resolving its load into cord-forces by comparing each cord to a right triangle of base (basa), axis (assis), and hypotenuse (ipotenissa). Leonardo works the arithmetic step by step, turning 5 pounds into 6, splitting 40 pounds as 2/5 and 3/5, and adding halves, to conclude that the cords bear 56 pounds in all and so gain 46 pounds of 'force' over the true weight. A separate note states that the weight a set of cords supports relates to the force generated as the axis a c relates to the hypotenuse b c.
On this page
Supported weight to generated force as axis to hypotenuse
The cords that support the weight 8 of c make the weight they carry stand to the force generated in the same proportion as the axis a c has to the hypotenuse b c.
The base, axis, and hypotenuse triangle of forces
The right-hand figure is labelled with base (basa), axis (assis) set vertical, and hypotenuse (ipotenissa) set oblique, the geometric frame by which each cord's share of the load is measured.
Step-by-step load totalling 56 pounds on the cords
Because cord d b exceeds axis f d by a third, the 5 pounds of S become 6; because axis c n is exceeded by cord b n eightfold, the 5 pounds of g become 40, split 2/5 (16) to b and 3/5 (24) to d, with halves of the 6 added. In sum the 10-pound beam loads its cords by 56 pounds, gaining 46 pounds of force over the weight.