Squaring an annular band against a triangle
Two concentric circles: the ring-band r S o p shown equal to the triangle a n m
Within two concentric circles Leonardo draws a 45-degree sector and an inscribed triangle, then argues that the triangle a n m equals the circular band (annular strip) r S o p. Each figure is reckoned as a ninth part of the whole circle less an equal small portion, so that both come out as the same fraction of one quantity and are therefore declared equal. The demonstration belongs to his study of the quadrature of lunes and sectors.
On this page
Triangle a n m equal to the circular band r S o p
The triangle a n m is asserted to equal the annular strip r S o p, and is said to be proved. Each is the ninth part of the whole circle less an equal cut-away portion, so both amount to the same tenth part of one quantity. On this basis the two figures are called equal.