A lune made equal to a circular sector
The lune m p r S q, a tenth of the semicircle, equated with the sector a p n
A large semicircle carries a small triangle and a crescent-shaped lune (falcata) at its base. Leonardo argues that the lune m p r S q, being a tenth part of the semicircle, equals the sector a p n, itself a tenth of the same semicircle; removing the small common portion a p from each leaves both figures exactly squared. He adds that the ten lunes contained in the semicircle, whose sides have various curvatures, can all be squared in the same way.
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The lune m p r S q equal to the sector a p n
Because it is a tenth part of the semicircle, the lune m p r S q is set equal to the sector a p n, which is likewise a tenth of that semicircle. Taking the small portion a p away from each leaves the two exactly squared. The same method is said to square all ten lunes of varied curvature inside the semicircle.