Medieval Hebrew texts on the quadrature of the lune

Abstract

Hippocrates' successful quadrature of the lune was one of the earliest achievements of Greek geometry. Our only source for the nature of Hippocrates' work is Simplicius, who comments on Artistotle's remark that the inference from the quadrature of the lune to the quadrature of the circle is an example of faulty reasoning. In this article two groups of Hebrew texts are translated and analyzed. The first come from mathematical treatises, and their contents show that materials similar to those cited by Simplicius were translated and read in the later medieval period. The second group comprises constructions found as comments to the Averroean corpus, and they attest to the existence of a more limited tradition preserving simple constructions that were necessary to the understanding of Averroes' commentaries on Aristotle. Levi ben Gerson's reconstruction of the quadrature is wholly original. © 1996 Academic Press, Inc.