⚠Significant ink bleed-through from the reverse side of the leaf makes some lines difficult to read. Institutional library stamp at the bottom center.

ARCHIMEDES ON THE SPHERE

AND CYLINDER, BOOK I.

Archimedes to Dositheus, greeting.

On a former occasion I sent to you the things investigated by us, having written with a proof that every segment contained by a straight line and a section of a right-angled cone is four-thirds of the triangle having the same base as the segment and an equal height. But since then, certain theorems worthy of mention have occurred to me, and I have worked out the proofs of them. They are as follows: first, that the surface of any sphere is four times the greatest circle of those in the sphere. Next, that for any segment of a sphere, there is a circle equal to its surface whose radius is equal to the straight line drawn from the vertex of the segment to the circumference of the circle which is the base of the segment. In addition to these, that for any sphere, the cylinder having a base equal to the greatest circle of those in the sphere and a height equal to the diameter of the sphere is itself one-and-a-half times the sphere, and its surface is likewise one-and-a-half times the surface of the sphere. Now, these properties were by nature inherent in the aforementioned figures, but they were unknown by those who were occupied with geometry before us. None of...

NATIONAL LIBRARY OF ROME
VITTORIO EMANUELE