Triangular balance and proportional distribution of weights
Distributing a weight about the pole r, with sixfold and half proportions between the arms
The sheet continues the study of balances from the recto. Beam and triangular-balance diagrams are lettered with weights (2 and 12) and a pole r about which a weight a is to be distributed to b and c. Leonardo divides the arms by proportion, saying that since 2 is one-sixth of 12 the length 7 must be split so one part is sixfold the other, giving 1 to the two and 6 to the twelve. A further diagram reasons that when c weighs half of a, the space between b and c is halved, because a and c together are half of b. Ink staining darkens the lower part of the sheet.
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Distributing a weight about the pole r
In a triangular balance lettered c, b, r with weights 2 and 12, Leonardo divides the weight a proportionally between b and c, remembering the centre or pole r. Because 2 is one-sixth of 12, he splits the length 7 so one part is sixfold the other, assigning 1 to the two and 6 to the twelve.
Halving the arm when one weight is half the other
If c weighed as much as a, the 6 at b would stand midway between a and c; but because c is half of a, the space between b and c is halved. This follows because a and c together are half of b.
