Studies of lunes, circle sectors and quadrature
Crescent lunes and circular sectors compared with rectilinear figures
The sheet is covered with crescent-shaped lunes (falcate), cones with inscribed figures, and portions and sectors of circles, in a sustained study of squaring curved areas. The notes reason about when the quantity of overlapping surfaces can be known and set out equalities between the lettered parts. In one case a rectilinear figure is declared equal and thrown away, leaving a circular portion equal to a sector.
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Measuring overlapping surfaces
The upper-left note argues that where surfaces are laid one over another, the quantity of the overlapping part can never be known except by approximations. It frames the mensuration problem the diagrams explore.
Group of lunes, a b c equal
A cluster of crescent lunes is labelled and declared equal: b, c, a, with the statement that a b c are equal. The forms are the curved slivers left between two arcs.
Double lune figure of equal nature
A double figure built from lunes is annotated as being of equal nature, i.e. the paired crescents share the same measure. It sits among the rows of lunes across the sheet.
Quadrant and sectors of a circle
A double figure combines a quadrant with sectors of a circle, marked with the letters a and n. It belongs to the series of cone-and-sector constructions in the lower band.
Rectilinear figure discarded; portion equals sector
Working with portions and sectors of circles labelled c, a, b, d, the note states that the rectilinear figure a b is equal and is thrown away. What remains, the c portion, is equal to the d sector.