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Muḥyī al‐Milla wa al‐Dīn Yaḥyā Abū ʿAbdallāh ibn Muḥammad ibn Abī al‐Shukr al‐Maghribī al‐Andalusī (Arabic: محيي الدين المغربي; c. 1220 – June 1283), referred to in sources as Muhyi l'din, was an astronomer, astrologer and mathematician of the Islamic Golden Age. He belonged to the group of astronomers associated with the Maragheh observatory in the Ilkhanate, most notably Nasir al-Din al-Tusi. In astronomy, Muhyi l'din carried out a large‐scale project of systematic planetary observations, which led to the development of several new astronomical parameters.

Muhyi l'din died in Maragheh in modern-day Iran in June 1283.

Early career

Muhyi al-Dīn al-Maghribī was born in c. 1220 in al-Andalus. He worked for the Ayyubid sultan An-Nasir Yusuf in Damascus. This relationship was ultimately cut short when the sultan was killed by the Mongols in the Siege of Aleppo in 1257. He was then sent to the observatory at Maragheh.

Work at the Maragheh observatory

The Maragheh observatory was founded in the Ilkhanate, a part of the Mongol Empire, Muhyi l'din went to Maragheh in 1258 as a guest of the Mongol ruler Hulagu Khan, where from 1259 he was involved, along with Nasir al-Din al-Tusi, in its construction. The observatory was completed in 1262.

At Maragheh, Muhyi l'din observed up to a total of eight of the brightest stars, of which he used the latitudes collected to compare with the values within ancient computations. He concluded that the difference between his latitudes and ancients were not substantial, and any inconsistences were in fact due to the observations and not the subject itself. In his Talkhīṣ al‐Majisṭī, he commentated on Ptolemy's Almagest, presenting his own observations and hypothesizes in addition with it. For instance, Muhyi l'din supposed that the precession would only occur in a motion that was uniform and continuous at a rate that was 1° for ever 66 years from his systematic stellar observations.

An extant manuscript by Muhyi l'din details of observations made from 1262 to 1274. He continued to work on his observations at Maragheh until his death in 1283.

Other work

Muhyi l'din considered the problem of doubling the cube, which he approached means of a method devised by the Greek mathematician Hippocrates of Chios.

Commentaries and treatises

Astronomy

Muhyi l'din's known works on astronomy include:

• Tasṭīḥ al‐asṭurlāb, a description of the construction and use of the astrolabe;
• Maqāla fī istikhrāj taʿdīl al‐nahār wa saʿat al‐mashriq wa‐ʾl‐dāʾir min al‐falak bi‐ṭarīq al‐handasa, a description of the geometrical methods used to determine the meridian line, the rising amplitude, and the revolution of the sphere;
• Risālat al‐Khaṭā wa‐ʾl‐īghūr, a chronological work on the Chinese calendar, which was later translated from Arabic and Persian into Chinese.
• Three zījes:
  • Tāj al‐azyāj wa‐ghunyat al‐muḥtāj (The Crown of Astronomical Handbooks), also known as al‐muṣaḥḥaḥ bi‐adwār al‐anwār maʿa al‐raṣad wa‐ʾl‐iʿtibār;
  • Adwār al‐anwār madā al‐duhūr wa‐ʾl‐akwār, which contains astronomical observations carried out by Muhyi l'dinin Marāgha;
  • ʿUmdat al‐ḥāsib wa‐ghunyat al‐ṭālib;
• Three commentaries on Ptolemy's Almagest:
  • Talkhīṣ al‐Majisṭī (Compendium of the Almagest), based on his observations carried out between 1264 and 1275;
  • Khulāṣat al‐Majisṭī (Summary of the Almagest);
  • Muqaddimāt tataʿallaq bi‐ḥarakāt al‐kawākib (Prolegomena on the Motion of the Stars), which contains five geometric premises on the planetary motions in the Almagest.

Astrology

Muhyi l'din's astrological works were mainly devoted to horoscopes and planetary conjunctions, used to tell the future.

Mathematics

Muhyi l'din's notable works in trigonometry were The Book on the Theorem of Menelaus and Treatise on the Calculation of Sines. He is known for his commentaries on ancient Greek mathematical works, in particular, his commentary on Book XV of Euclid's Elements, which discussed measurements of the regular polyhedra. Muhyi l'din's writings on trigonometry contain some elements that are original.

In his treatise on the calculation of sines, Muhyi l'din interpolated a value for the sine of one degree; a more accurate value was not obtained until the 15th century, when the mathematicians Qāḍī Zāda al-Rūmī and Jamshid al-Kashi tackled the problem. Whilst working on the sines, Muhyi l'din used the methods devised by Archimedes to find an approximate value for pi.

References

1. ^ Comes 2007.
2. ^ O'Connor & Robertson 1999.
3. ^ Mozaffari 2014.
4. Roberts 1966.
5. ^ Mozaffari 2016.
6. Tekeli 1981, pp. 555–557.

Sources

• Comes, Mercè (2007). "Ibn Abī al‐Shukr: Muḥyī al‐Milla wa‐ʾl‐Dīn Yaḥyā Abū ʿAbdallāh ibn Muḥammad ibn Abī al‐Shukr al‐Maghribī al‐Andalusī [al‐Qurṭubī]". In Hockey, Thomas; et al. (eds.). Biographical Encyclopedia of Astronomers. New York: Springer Publishers. pp. 548–549. doi:10.1007/978-0-387-30400-7_1433. ISBN 978-1-4419-9918-4. (PDF version)
• Mozaffari, S. Mohammad (2014). "Muḥyī al-Dīn al-Maghribī's lunar measurements at the Maragha observatory". Archive for History of Exact Sciences. 68 (1): 67–120. doi:10.1007/s00407-013-0130-4. ISSN 0003-9519. JSTOR 24569613.
• Roberts, Victor (1966). "The Planetary Theory of Ibn al-Shatir: Latitudes of the Planets". Isis. 50 (3). Chicago: The University of Chicago Press: 208–219. JSTOR 227960.
• Mozaffari, S. Mohammad (2016). "A forgotten solar model". Archive for History of Exact Sciences. 70 (3). Springer Nature: 267–291. doi:10.1007/s00407-015-0167-7. ISSN 0003-9519. JSTOR 24913461.
• O'Connor, J.J.; Robertson, E.F. (1999). "Muhyi l'din al-Maghribi". MacTutor. University of St Andrews. Retrieved 28 February 2023.
• Tekeli, Sevim (1981). "Muḥyi 'L-Dīn Al-Maghribī (Muḥyi 'I-Milla Wa 'L-Dīn Yaḥyā Ibn Muḥammad Ibn Abi 'I-Shukr Al-Maghribī' Al-Andalusī)". In Gillispie, Charles Coulston; Holmes, Frederic Lawrence (eds.). Dictionary of Scientific Biography. Vol. 9. New York: Scribner. OCLC 755137603.

Further reading

• Dorce, Carlos (2003). "The Taj al-azyāj of Muḥyī al-Din al-Maghribī (d. 1283): methods of computation". Suhayl. International Journal for the History of the Exact and Natural Sciences in Islamic Civilisation. 3. University of Barcelona: 193–212. ISSN 1576-9372 – via RACO (Catalan Journals with Open Access).

External links

• Digitized manuscript (Tasṭīḥ al-asṭurlāb) - Folios 1A-7B, Sprenger 1876 (Berlin State Library)

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

• 1283 deaths
• Astronomers from al-Andalus
• Astrologers of the medieval Islamic world
• Mathematicians from al-Andalus
• 13th-century astronomers
• 13th-century astrologers
• 13th-century mathematicians
• 13th-century people from al-Andalus
• People from Córdoba, Spain
• 13th-century Iranian astronomers