A balance instrument and beams resting on beams
A device with varying lever and counter-lever, and how one beam burdens another
At the top right a curved balancing instrument is drawn over a block with a hanging counterweight, and below it a semicircular balance carries two weights on cords. Leonardo says this instrument gives, at every degree of its motion, a varying lever and counter-lever both in length and in weight, and labels one arrangement a balance that is 'quite good'. Lower on the sheet, lettered beams laid across one another are used to show how the load of an overhanging beam is carried, working out for example that a projecting eighth needs a counterbalancing eighth so its support feels two eighths. An arithmetical division of 8 by 3 apportions a beam's weight as 2 2/3 and 5 1/3.
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An instrument of varying lever and counter-lever
This instrument, Leonardo writes, will give in every degree of its motion a variety of lever and counter-lever, both by length and by weight. It is drawn as a curved balancing arm poised over a block, with a counterweight hanging at one side.
A balance that is quite good
A short caption names the semicircular figure below as 'a form of balance which is quite good'. Two weights hang from cords at its rim, poised about a central pivot.
An overhang burdens its support by two eighths
Where the upper beam projects beyond the pole n by one eighth of its length (the part o that juts out), Leonardo argues that another eighth must be added as counterweight beyond the pole. The head of the lower beam is therefore burdened by two eighths of the beam laid upon it.
Dividing a beam's load, 8 into 2 2/3 and 5 1/3
Because b c is a third of the space a c that rests on the lower beam, and a load of 8 parts bears there, Leonardo divides 8 by 3 to get 24 thirds. He assigns 16 thirds (5 and 1/3) to c and 8 thirds (2 and 2/3) to a.