Circles as squares of their diameters; dividing a lune
Doubled inscribed circles, a lune equated to a triangle, and a half-portion split into equal parts
A geometrical sheet of lunes, semicircles, triangles and circles, faded and worked over an earlier layer of writing. Leonardo states that circles stand to one another as the squares of their diameters, then reasons on a series of inscribed circles each double the next to reduce a lune to a triangle. A lower construction sets out to divide a half-portion into any required number of equal parts.
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Circles are as the squares of their diameters
The same proportion holds from one circle to another as from one square to another made from the multiplication of its diameter. It opens the reasoning of the sheet.
Doubled inscribed circles and a lune equal to a triangle
If the first circle is double the second and the second double the third, from the first to the third the proportion is quadruple, so half the first equals the whole second and a quarter of the second equals half the third. By laying equal parts one upon the other, the remainder is shown equal, giving a lune equal to the triangle.
Dividing a half-portion into equal parts
Working from the lettered figure r (m), a d, d e, h g, L K, c f i m, p n, Leonardo proposes to divide the half-portion n r p into as many equal parts as required. First it is halved, one part being a b c d e f and the other the remainder.