Squaring lunes: converting curved surfaces into squares
Compass figures of lunes and semicircles with lettered constructions
Small compass figures of lunes and triangles set within semicircles accompany lettered demonstrations of turning curved-sided surfaces into equivalent rectilinear ones. Leonardo works through operations of removing and exchanging portions ('I remove b and render a of equal value'; 'I remove o from n and n remains'), concluding that two equal quantities bounded by unequal curves are always quadrable into a single rational, aliquot portion of a circle. The fragment also carries further blocks of mirror-writing not included in this transcription.
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Removing and exchanging portions to square a figure
Working with points n, o, t, m, b, Leonardo removes o from n, then removes t from m to leave m b equal to n, and swaps the half-portion ti for the whole portion b. What remains, m t with one curved side, equals the rectilinear surface n.
Two equal curved quantities are always quadrable
He concludes that if you are given two equal quantities bounded by two curves of unequal value, they are without doubt always quadrable into a single portion of a rational and aliquot circle. It is the general claim toward which the lettered manipulations build.
Equating lettered figures by subtracting portions
For figures L, omnXS and others, SnoX is said to equal abcph and adre. Removing from the first its whole portion n m o and from the last its half portion dKr of equal value leaves the triangle abc equal to the remainder.