Loads on a balance beam carried by a support pole
Lever and counter-lever reckoning: cord feels 96, foot 17, pole 192 pounds
A beam balanced on a support pole is drawn at the upper right, labelled with weights (32, 64, 96, 192, 8, 16) and letters a m h c n f g b, with a smaller detail at the side. Leonardo computes what each part feels: the cord a n feels 96 pounds, the foot g feels 17 pounds beyond its own weight, and the tip of the pole m feels 192 pounds. The main column works this out through repeated lever-against-counter-lever ratios (8 at 4 spaces makes 32, doubled to 64; another 64 from the load at c makes 128; 128 plus 64 is 192), and a marginal note treats a separate case where weight n is 9 and pole b feels 16.
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The support g m stays straight under equal load
Leonardo notes that the support g m will not bend, because it is loaded with equal weight on each side.
What the pole, cord and foot each feel
Written into the figure: the foot of the pole feels 17 pounds, the cord a n feels 96 pounds, and the pole m feels 192 pounds. The 17 at the foot g is besides its own natural weight, being 9 of the rod a c and 8 of the weight hung at c.
Lever and counter-lever reckoning to 192 pounds
The 8 pounds distant from the pole by 4 spaces (shown in m h) act on a counter-lever of one space, making 32, and 32 more of force is needed to balance, giving 64. The 8 pounds at c, acting 8 against one on pole m, become 64 and require 64 more, giving 128; added to 64 this makes 192, the load on pole m, of which the cord feels 96, its half.
Beam balanced on a support pole
The apparatus is a horizontal beam resting on an upright support pole with a cord and hanging weights, numbers marking the forces at each station. A smaller detail beside it repeats part of the arrangement.
Marginal case: weight n is 9, pole b feels 16
In the margin, the weight n is 9 and the balance arm p is 8; therefore the pole b feels 16, since the weight n being 9 is counterweighed by 8 on the opposite arm. The note breaks off before completing the reasoning.