Balance rod: proving the equality of suspended weights
Two suspended-rod diagrams on how opposite weights balance in proportion
Two diagrams show a horizontal rod hung from above, with weights carried by cords at its ends. Leonardo sets out to prove the equality of the weights, and in the second scheme notes that the point h, the centre of the segment n m, divides the rod so that the greater part stands to the lesser as four to three (sesquitertian), the opposing weights at the ends keeping the same ratio. Numeric labels along each rod record the balancing quantities.
On this page
Proof of the equality of the weights
A rod suspended by two cords carries opposing weights hung at its ends. The exercise is framed as a proof that these weights stand in equality on the balancing rod.
Sesquitertian division at the centre h
The point h, taken as the centre of segment n m, divides the rod into two parts whose greater is to the lesser as four to three. Leonardo states that the opposing weights hung at the ends keep this same ratio among themselves.