On the squaring of the surface of a sphere by rectilinear motion.

first - a - b - c. Knowledge of the aliquot part gives knowledge of its whole. From this it follows that the squaring of the eighth part of the surface of a sphere gives knowledge of what the squaring of the whole sphere would be. And let this knowledge be the eighth of the sphere a b c.

Second figure.

second - c - d e. In the second figure c d e the eighth of the spherical surface is divided into parallels equal in width, and the curvature of the two sides c d and e d e is straightened, and this is done by motion over a flat surface.

Third figure.

third - f - g h. In this third figure is what was promised in the second, and the straightened sides f g and g h are all the parallels of that second figure, which by their motion are widened and lengthened, because the same number of parallels made upon the grown lines f g and g h (which are equal to one another) have also, as the whole grows, grown their parts.

Fourth figure.

fourth - i - K L. In the fourth figure equal pyramidal (triangular) divisions are made, as f g h shows.

Fifth figure.

fifth - m o - n p. In the fifth figure the points of the pyramids (triangles) are opened and spread apart, and as many more pyramids are lent, and the square n m o p is made; but first, by motion, the line i l is straightened, and we have the fourth part of the spherical surface.

The junction of the curves c d e, straightened into f g h, should be at a right angle.