Equal loading of three equidistant cords on a beam
a m in dupla-sesquialtera ratio to n a; the weight lies wholly in a, c, r
A horizontal beam n-c-a-r-m is suspended by three cords carrying three weights of 7 each (marked 7 7 7, with 15 and 6 along the beam). Leonardo argues from the ratios of the segments: because a m stands to n a in a dupla-sesquialtera ratio (five to two), the opposite weights of the span n m are in like proportion. Since the whole weight is found in a, c, r, and these are equally distant, by the seventh proposition of this book the cords are loaded with equal weight.
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Three equidistant cords carry equal loads
Because the weight of the beam n m is found entirely in the points a, c, r, and these points are equally distant from one another, Leonardo concludes, citing the seventh proposition of this book, that the three cords are each loaded with an equal weight.
The dupla-sesquialtera ratio of a m to n a
Leonardo notes that a m is a dupla sesquialtera of n a (a ratio of five to two), and infers that the opposite weights of the span n m stand to one another in the same proportion.