Jabir b. Aflah on lunar eclipses

Abstract

In his most important work, the Islāh al-Majistī or Improvement of the Almagest, the Andalusian mathematician and theoretical astronomer, Jābir b. Aflah, presents a list of criticisms of Ptolemy's Almagest, mainly of a mathematical nature. One of these is devoted to the computation of the magnitude and phases of lunar eclipses. Ptolemy uses plane trigonometry and some approximations that Jābir b. Aflah contests. Ptolemy obtains the magnitude and phases for two particular cases - when the Moon is at its apogee and when it is at its perigee - and computes a table of interpolation for any other lunar anomaly. Jābir b. Aflah avoids the need for tables of interpolation providing a slightly different method for computing the magnitude and phases of a lunar eclipse. In addition, he claims to have found an error in Ptolemy's method of interpolation. However, thanks to aquotation of the Almagest appearing in the Islāh al-Majistī, we conclude that Jābir b. Aflah's criticism is due to the fact that there is a section missing in his manuscript of the Almagest, and not to an error committed by Ptolemy, nor to a deficient translation of the Almagest.