Dividing a circle and its double: lunes and inscribed square
Equating portions and triangles between a circle and one twice its size, each portion worth half a lune
On coarse brown paper Leonardo works through a problem of equal areas. At upper left are crescent-shaped lunes, and at upper right a large circle carrying an inscribed square and diagonals with its regions numbered. The first note explains how, by removing three portions a b c from a smaller circle and twice as much from a circle double its size, a triangle Q can be made equal to a triangle t so that the remainder o p r is double the remainder S t. A second short figure states that portions a b, b c and d c are equal to one another, each worth half a lune.
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A circle and its double, with inscribed square
Working with a smaller circle and one of double area, Leonardo removes three portions a b c from the smaller and twice as much from the larger, so that the remainders stay in the ratio two-to-one. He then removes a triangle Q equal to triangle t, leaving the remainder o p r double the piece S t, and further divides o p r into portions and triangles.
Portions each worth half a lune
A separate figure of portions labelled d b a c states that a b is worth b c and b c is worth d c, and that each of these is worth half a lune (mezza lunola) — relating the crescent lunes at upper left to the divided circle.