Theodosius Sphaerica: Arabic and Medieval Latin Translations. Edited by PAUL KUNITZSCH and RICHARD LORCH. Boethius. vol. 62. Stuttgart: FRANZ STENER, 2010. Pp. vii + 431. [euro]64.
Paul Kunitzsch and Richard Lorch have provided the first critical editions of one of the Arabic versions of Theodosius's Spherics and of Gerhard of Cremona's Latin translation made on the basis of this. These are accompanied by a "mathematical summary" that does not attempt to translate the full literal meaning of the source texts, but conveys the mathematical argument.
Theodosius's Spherics was written around the end of the second century B.C.E as a compilation and reorganization of basic material in spherical geometry and spherical astronomy. By late antiquity it had secured a place in the curriculum of teachers of the exact sciences as a treatise of the so-called Little Astronomy used as a preparatory course to reading Ptolemy's Almagest for students who had mastered elementary geometry. In the Islamic middle ages it continued to serve in this role in the compendium of mathematical and astronomical treatises known as the "Middle Books," or "Intermediaries." Spherics is in three books, of which the first is purely geometrical and the second two deal with topics applicable to spherical geometry but still expressed in an almost purely geometrical idiom. The first book treats the properties of lesser circles and great circles on a sphere that are analogous with the properties of the chords and diameters on a circle in Elements 111: the second book explores those properties of lesser circles and great circles of a sphere that are analogous with those of circles and lines in Elements III. which leads to a theory of tangency and theorems dealing with the relationships between great circles and sets of parallel lesser circles. This book ends with a number of theorems of purely astronomical interest having to do with the horizon, the equator, and the always visible, and always invisible, circles. The third book deals with what we would call the transformation of coordinates, or the projection of points of one great circle onto another, and concludes with theorems that can be interpreted as concerning the rising and setting times of arcs of the ecliptic.
The publication of an Arabic text of Spherics allows us to make some comparisons with the Greek version, which may, in turn, shed some light on each. The most obvious difference is in the numbering of propositions. The...