Statics of balance beams and loaded inclined bars
Diagrams and proofs dividing a weight between the ends of a beam or the base of a triangle.
A sheet of statics: balance beams marked with weights (30-60-30, 10-60-50 and 60) run across the top, and below them geometric proofs show how a load is shared between the ends of a bar or the corners of a triangle. In one problem, if a b weighs 3, Leonardo finds by dropping a perpendicular h m at the midpoint of a f that a carries two parts of the weight and b one. Another asks how a weight of 30 hung at the apex m of a triangle divides between corners a and b, resolved by dropping a perpendicular to the base a c. A steelyard sketch below notes a weight of 10 that 'weighs nothing'. The drawings are in faint pen and pencil in mirror script.
On this page
Dividing the weight of an inclined bar a b
For a bar a b weighing 3, the true division of the load is found where a perpendicular h m raised at the midpoint of a f meets the line a b, at point m. Since a m is two-thirds of a b, a carries two parts of the weight and b one.
A weight of 30 hung at a triangle's apex m
If the corner m bears a weight of 30, a line dropped from m perpendicular to the base a c divides the load: as much as b c enters by measure into c a, so much a b enters by weight into b c, so b c is the divider of c a.
A weight that reads nothing on the steelyard
Below, a balance with an oblique appendage carries a weight marked 10; the note remarks that this weight of 10 weighs nothing on the steelyard.
