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Al-Khalili
شمس الدين عبد الله محمد بن محمد الخليلي
A table compiled by al-Khalili showing the direction of the qibla from various longitudes and latitudes
Born	1320
Died	1380
Academic work
Era	Islamic Golden Age
Main interests	Astronomer; muwaqqit

Shams al-Dīn Abū ʿAbd Allāh Muḥammad ibn Muḥammad al-Khalīlī (Arabic: شمس الدين عبد الله محمد بن محمد الخليلي; 1320–1380) was a Mamluk-era Syrian astronomer who compiled astronomical tables. He worked for most of his life as a muwaqqit (a religious timekeeper) at the Umayyad Mosque in Damascus.

Little is known about his life.

Work

Al-Khalili is known for two sets of mathematical tables he constructed, both totalling 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 qibla (the direction of the city of Mecca) for all latitudes and longitudes for all the Muslim countries of the 14th century. The values present in al-Khalili’s tables have been determined to be accurate up to three or four significant figures. It is not known how exactly al-Khalili went about calculating each of his entries.

Notes

1. Knowledge of the direction of the qibla is essential in Islam because Muslims pray in the direction of Mecca.

References

1. King 1975.
2. King 1973, p. 99.
3. Van Brummelen 1991.

Sources

• Van Brummelen, G. (1991). "The numerical structure of al-Khalili's auxiliary tables" (thesis). Rivista Internazionale di Storia della Scienza. 28 (3): 667–697. ISSN 0031-9414.
• King, David A. (1973). "Al-Khalili's Auxiliary Tables for Solving Problems of Spherical Astronomy". Journal for the History of Astronomy. 4 (2): 99–110. Bibcode:1973JHA.....4...99K. doi:10.1177/002182867300400202. ISSN 0021-8286. S2CID 116031361.
• King, David A. (1975). "Al-Khalīlī's Qibla Table". Journal of Near Eastern Studies. 34 (2): 81–122. doi:10.1086/372399. ISSN 0022-2968. JSTOR 545208. S2CID 162253735.

Further reading

• King, David A. (2007). "Wābkanawī: Shams al-Munajjim [Shams al-Dīn] Muḥammad ibn ҁAlī Khwāja al-Wābkanawī [Wābkanawī]". In Hockey, Thomas; et al. (eds.). The Biographical Encyclopedia of Astronomers. Springer. pp. 625–626. doi:10.1007/978-0-387-30400-7_1433. ISBN 978-1-4419-9918-4.(PDF version)
• O'Connor, John J.; Robertson, Edmund F. "Shams al-Din Abu Abdallah Al-Khalili". MacTutor. University of St Andrews. Retrieved 26 February 2023.
• King, David A. (1981). "Khalīlī, Shams al-Dīn Abū ʿAbdallāh Muḥammad Ibn Muḥammad al-". In Gillispie, Charles Coulston; Holmes, Frederic Lawrence (eds.). Dictionary of Scientific Biography. New York: Scribner. OCLC 755137603 – via encyclopaedia.com.
• Roegel, Denis (2008). "An Extension of Al-Khalīlī's Qibla Table to the Entire World". Hal-Inria. HAL. Retrieved 26 February 2023.

v t e Mathematics in the medieval Islamic world
Mathematicians	9th century 'Abd al-Hamīd ibn Turk Sanad ibn Ali al-Jawharī Al-Ḥajjāj ibn Yūsuf Al-Kindi Qusta ibn Luqa Al-Mahani al-Dinawari Banū Mūsā brothers Hunayn ibn Ishaq Al-Khwarizmi Yusuf al-Khuri Ishaq ibn Hunayn Na'im ibn Musa Thābit ibn Qurra al-Marwazi Abu Said Gorgani 10th century Abu al-Wafa al-Khazin Al-Qabisi Abu Kamil Ahmad ibn Yusuf Aṣ-Ṣaidanānī Sinān ibn al-Fatḥ al-Khojandi Al-Nayrizi Al-Saghani Brethren of Purity Ibn Sahl Ibn Yunus al-Uqlidisi Al-Battani Sinan ibn Thabit Ibrahim ibn Sinan Al-Isfahani Nazif ibn Yumn al-Qūhī Abu al-Jud Al-Sijzi Al-Karaji al-Majriti al-Jabali 11th century Abu Nasr Mansur Alhazen Kushyar Gilani Al-Biruni Ibn al-Samh Abu Mansur al-Baghdadi Avicenna al-Jayyānī al-Nasawī al-Zarqālī ibn Hud Al-Isfizari Omar Khayyam Muhammad al-Baghdadi 12th century Jabir ibn Aflah Al-Kharaqī Al-Khazini Al-Samawal al-Maghribi al-Hassar Sharaf al-Din al-Tusi Ibn al-Yasamin 13th century Ibn al‐Ha'im al‐Ishbili Ahmad al-Buni Ibn Munim Alam al-Din al-Hanafi Ibn Adlan al-Urdi Nasir al-Din al-Tusi al-Abhari Muhyi al-Din al-Maghribi al-Hasan al-Marrakushi Qutb al-Din al-Shirazi Shams al-Din al-Samarqandi Ibn al-Banna' Kamāl al-Dīn al-Fārisī 14th century Nizam al-Din al-Nisapuri Ibn al-Shatir Ibn al-Durayhim Al-Khalili al-Umawi 15th century Ibn al-Majdi al-Rūmī al-Kāshī Ulugh Beg Ali Qushji al-Wafa'i al-Qalaṣādī Sibt al-Maridini Ibn Ghazi al-Miknasi 16th century Al-Birjandi Muhammad Baqir Yazdi Taqi ad-Din Ibn Hamza al-Maghribi
Mathematical works	The Compendious Book on Calculation by Completion and Balancing De Gradibus Principles of Hindu Reckoning Book of Optics The Book of Healing Book on the Measurement of Plane and Spherical Figures Encyclopedia of the Brethren of Purity Toledan Tables Tabula Rogeriana Zij
Concepts	Alhazen's problem Islamic geometric patterns
Centers	Al-Azhar University Al-Mustansiriya University House of Knowledge House of Wisdom Constantinople observatory of Taqi ad-Din Madrasa Maragheh observatory University of al-Qarawiyyin
Influences	Babylonian mathematics Greek mathematics Indian mathematics
Influenced	Byzantine mathematics European mathematics Indian mathematics
Related	Hindu–Arabic numeral system Arabic numerals (Eastern Arabic numerals, Western Arabic numerals) Trigonometric functions History of trigonometry History of algebra

• 1320 births
• 1380 deaths
• People from Damascus
• Medieval Syrian astronomers
• Medieval Syrian mathematicians
• Scientists who worked on qibla determination
• 14th-century astronomers
• 14th-century astrologers
• Scholars from the Mamluk Sultanate
• 14th-century Arab people
• 14th-century Syrian people