The measurement is to be made on the greater circle of the lune, with the line a b of the triangle.

n - m - c - e a d b

I wish to give a straight line equal to the curve of a semicircle.

We shall do it thus: we already have certainty that the tapering lune-figure d b n m e and the rectilinear figure b c a are of equal quantity between them, being, as has been said, each the tenth part of the same semicircle. Now we know, by the fifth [proposition] of this [book], that each of them is uniformly non-uniform, and that as much as the one is longer, so much the more slender it is, and as much as the other is thicker than its fellow, so much the shorter it is; and if I compress the short one to the length of the long one, that short rectilinear figure will become as long as the long curvilinear one.