Al-Khāzinī’s Complex Tables for Determining Lunar Crescent Visibility

Lunar crescent visibility is a multidisciplinary branch of astronomy from the Islamic period, which reflects the interrelationship between astronomy and Islam. Its importance endures today, since the Hijra Lunar Calendar is still organized according to the rules or criteria for lunar crescent visibility in different Muslim countries. In recent decades, several criteria for lunar crescent visibility from medieval Islamic astronomy have been studied by historians of astronomy, although many of these methods have not yet been investigated. Among the unstudied materials are two interesting tables in a valuable work entitled al-Zīj al-mu‘tabar al-sanjarī by the celebrated astronomer and author of treatises on mechanics Abū al-Fat¬ ‘Abd al- Ra¬mān al-Khāzinī (fl. 474-525 A.H./ 1081-1131 A.D.). In this article, I will analyze these two tables for determining lunar crescent visibility, included in al-Khāzinī’s Sanjarī Zīj. The first one is simpler and is based on straightforward limits and computations. The second
table, briefly introduced by Prof. Kennedy in 1956, allows the examination of lunar crescent visibility or invisibility on three levels. This more complex table is based on several astronomical and non-astronomical parameters, without any explanation of the rules by which the array of numerical values were computed. Undoubtedly al-Khāzinī presented this criterion under the influence of Thābit ibn Qurra, but he endeavored to construct a new criterion which also showed the effect of human and atmospheric conditions on lunar crescent visibility. Al-Khāzinī distinguishes three levels of crescent visibility (general, moderate and acute), thus introducing a concept of frequency.