English Translation of the Sphaerica of Menelaus

The SPHAERICA (in English: Spherics) of Menelaus of Alexandria (dating to roughly 100 AD) is among the oldest known works on spherical geometry and trigonometry. Spherical geometry is the study of geometric objects on the surface of a sphere and spherical trigonometry is the study of relationships among sides and angles in triangles on a sphere, where the sides are arcs of “great circles.” The SPHAERICA was originally written in Koiné Greek, but editions in this language are no longer extant. One of the oldest complete editions still available is Abu Nasr Mansur’s “improved” edition in Arabic. Other editions exist in Arabic, Hebrew, Latin, and German, but none in English. In this thesis I give an English translation of Abu Nasr Mansur’s edition, and discuss certain aspects of the text from a modern point of view.