Beginning of the book: support strength and lever balance
The part of a support farthest from its fixing is weakest; balancing 2- and 4-pound arms by converse proportion
Folio 171r opens a new section headed 'Beginning of the book,' stating that a part of a support (sostentaculo) is weaker and resists less the farther it lies from its fixed point. A worked balance follows: the arm a b exerts a force of 2 pounds at its middle q, while the arm b c exerts 4 pounds at b. By the 'converse proportion' arising from position, q lightens the load by one pound, so b's 4 pounds act as 3, which are then met at a by 3 further pounds, restoring the equal proportionality. Diagrams of a wheel and of divided balance beams loaded with weights fill the right of the page.
On this page
The weaker part of a support lies farther from its fixing
Under the heading 'Beginning of the book,' Leonardo states that the part of a support will be weaker, and resist less, the more remote it is from the fastening of its whole.
Balancing arms of 2 and 4 pounds
The arm a b exerts a force of 2 pounds at its middle q; the arm b c exerts 4 pounds at b. The problem is to restore equilibrium between these unequal arms and weights.
Equilibrium by the converse proportion of position
By the converse proportion of position, q lightens one pound at b, so b's 4 pounds do the office of 3, met at a by another 3 pounds equidistant from the pole with b; thus the equal proportionality remains.