Midpoint of the cords divides a beam by its opposite weights
14 pounds balanced at the midpoint a divide equally, 7 to each cord
A horizontal beam m-n-a-o-p is suspended by cords carrying weight-boxes marked 7 and 7 (totalling 14). Leonardo gives a general rule: take the midpoint of the two suspending cords and use it to divide the beam, and the resulting parts stand in the same proportion to one another as the sums of the opposite weights hung at the ends. In the worked case, a is the midpoint, m a stands to a p in a subdupla-sesquialtera ratio, and because the point of equalization of the 14 pounds falls midway between the cords n and o, the 14 divides equally, giving 7 to each cord; this holds for the simple weights taken without the rods.
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Dividing a beam by the midpoint of its cords
Take the midpoint of the two cords that suspend the rods and use it to divide the rods; the parts so found stand in the same proportion to one another as the sums of the opposite weights hung at the ends. With a as the midpoint, the equalization of the 14 pounds falls midway between the cords n and o, so the 14 splits into equal parts of 7 for each cord.
The subdupla-sesquialtera ratio of m a to a p
Leonardo observes that m a has to a p a subdupla-sesquialtera ratio, and likewise the weight of p is a subdupla sesquialtera of that of m. He adds that this equal division of the 14 into two sevens is to be understood of the simple weights taken without the rods.