Determination of the Longitude of Earth positions Based on Moon Eclipse in Bīrūnī’s Taḥdīd Nihāyāt al-Amākin

All geographical works in Islamic period, both descriptive and mathematical, agree to choose the equator as the source of latitude, but following the Indians, the source of the longitude was sometimes considered the “cupola of the Earth” (Qubba al-ʾArḍ) and following the Greeks sometimes the “Eternal Island” (Jazāʾir Khālidāt). Moreover, division of the inhabited part of the Earth into seven Climes is based on the length of the longest day and it also depends to geographical latitude. Hence, the authors of the astronomical works bring the computations of the latitude in their works but they do not usually mention to the computations of the longitude. Bīrūnī, in his Taḥdīd Nihāyāt al-Amākin -that we can consider it as a mathematical geography work- brings two kind of computations. This article studies the methods of computation of the longitude deference between two places based on moon eclipse in Bīrūnī’s Taḥdīd.