Shams al-Dīn Abū Abd Allāh al-Khalīlī

Shams al-Dīn Abū ʿAbd Allāh Muḥammad ibn Muḥammad al-Khalīlī (1320–1380) was a Mamluk-era astronomer who compiled extensive tables for astronomical use. He worked for most of his life as a religious timekeeper (muwaqqit) at the Umayyad Mosque in Damascus. Little else is known about his life.

Al-Khalili is known for two sets of mathematical tables he constructed, both totaling roughly 30,000 entries. He tabulated all the entries made by the celebrated Egyptian Muslim astronomer Ibn Yunus, except for the entries that al-Khalili made himself for the city of Damascus. He computed 13,000 entries into his 'Universal Tables' of different auxiliary functions which allowed him to generate the solutions of standard problems of spherical astronomy for any given latitude. In addition to this, he created a 3,000 entry table that gave the direction of the city of Mecca (the Qibla) for all latitudes and longitudes for all the Muslim countries of the 14th century. Knowledge of the direction of the Qibla is essential in Islam because Muslims pray in the direction of Mecca. The values present in al-Khalili’s tables have been determined to be accurate up to three or four significant decimal digits. Up to the present time, it is not known how exactly al-Khalili went about calculating each of his entries.