The quadrature of lunes and circular sectors
Making an unsquarable lune known by comparing it with a squarable one.
A geometrical study in the quadrature of lunes (falcate), worked out through a single dense paragraph and small marginal figures. Leonardo doubles, halves and transposes triangular and lune-shaped pieces, taking care not to diminish the sector, which he keeps at one-eighth of the whole circle. By folding a triangle over its base and comparing lune a with the squarable lune b, he argues that the otherwise unsquarable lune a is made known, and with it the quantity of the sector portion g f.
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Making unsquarable lune a equal to squarable lune b
Leonardo doubles lune a by adding b, transposes the piece K to the opposite side outside h so as not to diminish the one-eighth sector, and removes the added triangle (two straight sides and one curved). Removing the like triangle from lune b leaves a squarable lune b equal to the unsquarable lune a, so that the quantity of the sector portion g f becomes known.
