I.

Archimedes to Dositheus, greeting.

Before, I sent to you what I had perceived up to that time, written with the demonstrations attached: that any segment contained by a straight line and a parabola is one-third greater than a triangle having the same base as the segment, and equal height. 1) i.e. Quadrature of the Parabola 17, 24. But afterward, when I had happened upon certain theorems not yet demonstrated, I worked out their proofs. They are these: first, that the surface of any sphere is four times greater than the greatest circle; 2) i.e. On the Sphere and Cylinder I, 30. then, that the surface of any segment of a sphere is equal to a circle whose radius is equal to the line drawn from the vertex of the segment to the circumference of the circle which is the base of the segment. 3) ibid. I, 39–40. And besides, any cylinder base...

I provided the restoration of this letter in Quaest. Arch. p. 131, which I have followed here. The whole exists in FB alone (Quaest. Arch. p. 118–22). In VAD the first words: Archimedes — to you in line 2 exist; the remaining part of the first page is empty (Quaest. Arch. p. 117; I personally inspected the Venetian codex later); then at the top of page 2 follow well etc. p. 6, 6. Only these final words have C, Basil edition; the interpretation of I. Cremonensis offers only the first part (Quaest. Arch. p. 122).

perhaps of this kind. of every] of the F; "of all" Cr. 10. circle] circle of those in it B. then] after a gap then B. 11. circle] B; cone F; "that circle" Cr. 14. base B; of base F.