Balance beam with weights in double proportion
Loads hung at a, b, f, c, d prove that distances and weights stand in a 2:1 ratio
A horizontal rod carries weights suspended at points labelled a, b, f, c and d, with fractional values (1/2, 1/4) and whole numbers marked along it. Leonardo argues that the space b-f relates to f-c as a-f relates to f-d, each being a 'double,' and that the opposed weights follow the same rule. Measuring from the midpoint of the weights a-b and c-d to the fulcrum f confirms a 2:1 proportion between the two arms.
On this page
Weights balanced in double proportion about the fulcrum f
Measuring from the mid-space of the weights a b and c d to the pole f, the middle of a b lies 6 half-braccia from f while c d lies 3 half-braccia from it, a 2:1 ratio. The loads balance because distance and weight are inversely paired about the fulcrum.
The 'dupla' (double) proportion of the spaces
The space b f stands to f c as a f stands to f d, each pair being a 'dupla' (2:1). The marked fractions 1/2 and 1/4 and the whole numbers record the proportional division of distances along the arm.