PREFACE.

In the notes added to the interpretation, I have striven above all to supply what had been omitted by Archimedes in the demonstration and to illustrate the more obscure passages. In the books On the Sphere and Cylinder and the short treatise On the Measurement of a Circle, I have indicated in the notes whatever one may suspect regarding the genuine writing of Archimedes. For these books have not only been stripped of their Doric dialect but have also been reconstructed in very many places, as the transcriber both added what seemed necessary to him and omitted what he thought could be absent, and altogether introduced the speech of his own age and the names of mathematical things that were in use at that time. Therefore, when I understood that the hand of Archimedes could not be restored in these books, I judged it better to follow the later recension and to correct only the most obvious scribal errors. But besides the fact that,

1) These passages were indicated to me by O. Siesbye, a most learned man.