Archimedis Opera Omnia cum Commentariis Eutocii, Vol. I (Heiberg 1880)

having a base equal to the greatest circle of the sphere, and a height equal to the diameter of the sphere, is itself one and a half times larger than the sphere, and its surface is one and a half times larger than the surface of the sphere. 1) i.e. I, 31 lemma. These properties, however, existed from the beginning by the very nature of the figures I have mentioned, but they were ignored by those who studied geometry before me. But when I understood that they were proper to these figures, I did not hesitate to place them in the same location as those things I previously perceived, and those things which are considered to be demonstrated by the most solid documents of those theorems which Eudoxus proposed concerning solid figures: although a pyramid is a third part of a prism having the same base as the pyramid, and an equal height, and any cone is a third part of a cylinder having the same base as the cone, and an equal height. For since these properties also existed from the beginning by the very nature of these figures, it happened that by every...

The whole letter up to well p. 6, 6 in F was written by a later hand, of the 15th century, as it seems. Rivaltus followed cod. B, while supplementing its gaps partly by conjectures and partly by the interpretation of I. Cremonensis translated into Greek. Torellius provides the writing of Rivaltus with the accepted conjectures of Barrow (Archimedes' works. London 1675. 4 p. 1–2); but in the beginning he received I sent to you from the Venetian codex.

gap left. at that time] the F; and B. theorized B. and to] although Rivaltus; as Barrow. 11. to be demonstrated most securely] many gap left F; many gap left B. of those by Eudoxus] om. F gap left; xus after gap B; of those by the Eudoxus Rivaltus. 12. theorized F; theorized B; corr. Rivaltus. 13. part is B. pyramid F. 15. base indeed Torellius. 16. of these] B; where of the F; om. Torellius. 17. Between before and Eudoxus B has a gap, but in the margin in these final places nothing is missing. 18. by] the Rivaltus; from Barrow.