Balance-beam experiments and a rule of division
How a shifting weight changes the loads on a beam's arms; dividing 3 by 4
Folio 83r is crowded with balance-beam experiments: horizontal arms carrying suspended weights, several of them running over little wheels, arranged to show how a weight's position redistributes the load to a beam's two arms. The notes argue that although the beam's support gains no fresh effort when a weight merely shifts, the proportions of weight on the arms change at every degree of motion. A passage down the left margin teaches a rule of arithmetic division, working the example of 3 divided by 4 as the fraction 3/4. Numeric labels annotate the many figures.
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A weight shifting beneath a beam changes the arm loads
Leonardo lets a weight c travel beneath the line a b at will. It seems to carry nothing, yet every degree of its motion varies the degrees of weight on its little wheels, and though the support gains no new effort, the proportions of weight on the two arms are constantly changed.
Effort at the foot of the support at every degree of motion
A short caption states that as the weight moves, at every degree of motion it varies the effort felt at the foot of the support of that arm at f.
Dividing a lesser number by a greater (3 by 4)
The rule: if you cannot divide the lesser by the greater, divide the greater by the lesser. To divide 3 by 4, since 4 is not contained in 3, place the 3 over the 4 to read 3/4; remaking the first number as 12/4 restores 3 whole.