Jabir b. Aflah's on the four-eclipse method for finding the lunar anomaly period

Abstract

The four-eclipse method was used by pre-Ptolemaic astronomers, especially Hipparchus, for finding the lunar period in anomaly. It is described by Ptolemy in Almagest IV.2 where he adds new considerations to be fulfilled in order to obtain a correct period in anomaly. Jabir b. Aflab, who lived in early twelfth-century al-Andalus, considers this method in his Islāh al-Majistī. In his opinion, Ptolemy did not understand the conditions stated by the ancients. Jābir b. Aflah provides a complete set of conditions that makes Ptolemy's additions to the method unnecessary. In any case, the method presented by Jābir b. Aflah is more coherent and elegant from a mathematical point of view that Ptolemy's.