Loading five arcs to one and the same deflection
Doubling weight to match doubling stiffness: 2, 4, 12 and 24 pounds, equal sag in each
The page pursues Leonardo's study of elastic deflection across a row of loaded bows. He wants to load five arcs of equal length and resistance so that an equal deflection (saetta) can be measured in each: two weights on arc c d do as much as one weight on arc a b, one weight on arc e f (12) equals the two on c d, and one counterweight on arc g h (24) equals each set before it. A related note claims the deflection of three arcs will bear the same proportion to their arcs as some further ratio, left unfinished.
On this page
Loading five arcs for equal deflection
Leonardo aims to give five arcs, all of equal length and resistance, such weights that an equal deflection can be measured in each one by itself.
Two weights on c d equal one on a b
The two weights placed on arc c d do just as much as the single weight does on arc a b, the loads doubling as the arcs are matched.
One weight on e f equals two on c d
The single weight on arc e f exerts as much power as the two weights on arc c d; likewise the single counterweight on arc g h matches each set of the earlier counterweights on their arcs.