On the quadrature of the spherical surface.

first - n m - a b c d e - f g h

second - r L h c S - i z y x - v t. By the motion of the quarter of the sphere's greater circle, the straight line r S is made on a flat surface, and the true rectilinear extension is set, without doubt, in r t, similar to r S, in right-angled conjunction at the point r, and the curve S x t is made. Then divide the line r S into as many equal parts as you please, and mark all the circumferential portions c y, h z, L i indefinitely, carrying the line r t. Then go back and cut the paper, and move the circumference of the cut circle over the marked circumference c y, and carry the line r t indefinitely, as far as the contact of the moving circumference over the fixed circumference, and note that boundary. Do the same with the following circumference h z, and likewise with all the other circumferences, noting the boundaries of the motion of each circumference, over which boundaries you will draw the curve r v t.

third - a h f d b - i g c c

fourth - a h f d b - i g c c. And if you wished to make such parallel motions over the straight lines of the third or fourth figure, it would be a better expedient, because the part of the wheel (made of paper) moves better over straight lines than over curved lines, provided the straight parallels are of width equal to the curved parallels. Then, by the motion, you will square the portion of the circle by the said motion, that is, the portion a c i taken from the triangle a b c; and once you have squared it, add it to the triangle a b c, and the sum will be 1/8 of the surface of the sphere, etc.