Two loaded beams: testing the sag of an arch under a hung weight
Comparing the deflection of two spans to see how differing weights give equal sag
Two curved beams, treated as arches, are drawn resting on uprights, each carrying a weight hung from its centre on a cord and shown as a small labelled disc. The note poses a test: whether the weight n produces the same sagitta (the 'arrow', or downward deflection) in its arch, which acts as its support, as does the arch a b. It then asks to note how the variety of the weights causes the two deflections to come out equal in length.
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Does weight n give the same sag as arch a b?
Leonardo sets a comparison between two loaded spans, asking to prove whether the weight n makes the 'saetta' (the sagitta, or deflection) of its arch, which is its own support, equal to that of the arch a b. He notes that the variety, or difference, of the weights is the cause of the equal length of the two deflections.
Two beams weighted at the centre
The drawing pairs two curved beams carried on posts; from the middle of each hangs a cord ending in a small round weight within a circle. The setup illustrates the loaded spans the note compares.