The limits of solar and lunar eclipses were computed by Ptolemy in Almagest VI.5 to establish the maximum interval in the argument of latitude in which it was possible for an eclipse to occur when the moon’s mean position in the argument of latitude at each mean syzygy falls within the limits of this interval. To determine these limits, Ptolemy first obtained the true nodal distance of the Moon in the lunar inclined orbit at the apparent syzygy for a minimum possible eclipse. He then added to this true position the maximum difference in the argument of latitude between the mean and true syzygies. The interval obtained, after taking into account the argument of latitude of the lunar nodes, was slightly wider than the maximum interval in the argument of latitude of lunar mean positions at mean syzygies for solar eclipses. This can be seen, either, as a suitable but rough estimate of the correct value or as an inaccurate procedure for deducing the lunar mean position in the argument of latitude at mean syzygies from apparent syzygies. Jābir b. Aflaḥ, the twelfth-century Andalusian astronomer, understood Ptolemy’s procedure in this second sense. He noticed this point and showed the accurate procedure for obtaining lunar mean positions in the argument of latitude at the mean syzygy from the apparent syzygy and thus provided more accurate estimations of the eclipse limits.

Ministerio de Educación y Ciencia (FFI2008-00234/FILO) FEDER

European Regional Development Fund

Ministerio de Educación y Ciencia

Peer reviewed