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Ahmad ibn 'Abdallah al-Marwazi, known as Habash al-Hasib (Persian: حبش الحاسب, lit. 'Abyssinian calculator', died c. 869) was a Persian astronomer, geographer, and mathematician from Merv in Khorasan, who was the first to describe the trigonometric ratios tangent, and cotangent. Al-Biruni who cited Habash in his work, expanded his astronomical tables.

Habash al-Hasib flourished in Baghdad, and died a centenarian some time between 864–874 possibly in Abbasid Samarra. The title "Habash" (Abbyssian) may refer to dark skin coulor. He worked under two Abbasid caliphs, al-Ma'mun and al-Mu'tasim.

Habash al-Hasib developed a trigonometric algorithm to solve problems related to parallax, which was later rediscovered by Johannes Kepler in 1609 and it is now known as Kepler's equation.

Habash is the father of the astronomer Abu Ja'far ibn Habash.

Work

Habash Hasib made astronomical observations from 825 to 835, and compiled three zijes (astronomical tables): the first were still in the Hindu manner; the second, called the 'tested" tables, were the most important; they are likely identical with the "Ma'munic" or "Arabic" tables and may be a collective work of al-Ma'mun's astronomers; the third, called tables of the Shah, were smaller.

Apropos of the solar eclipse of 829, Habash gives us the first instance of a determination of time by an altitude (in this case, of the sun); a method which was generally adopted by Muslim astronomers.

In 830, he seems to have introduced the notion of "shadow", umbra (versa), equivalent to our tangent in trigonometry, and he compiled a table of such shadows which seems to be the earliest of its kind. He also introduced the cotangent, and produced the first tables of for it.

The Book of Bodies and Distances

Habash al-Hasib conducted various observations at the Al-Shammisiyyah observatory in Baghdad and estimated a number of geographic and astronomical values. He compiled his results in The Book of Bodies and Distances (Kitāb al-ajrām wa-l-ab 'ād), in which some of his results included the following:

Earth

• Earth's circumference: 20,160 miles (32,444 km)
• Earth's diameter: 6414.54 miles (10323.201 km)
• Earth radius: 3207.275 miles (5161.609 km)

Moon

• Moon's diameter: 1886.8 miles (3036.5 km)
• Moon's circumference: 5927.025 miles (9538.622 km)
• Radius of closest distance of Moon: 215,208;9,9 (sexagesimal) miles
• Half-circumference of closest distance of Moon: 676,368;28,45,25,43 (sexagesimal) miles
• Radius of furthest distance of Moon: 205,800;8,45 (sexagesimal) miles
• Diameter of furthest distance of Moon: 411,600.216 miles (662,406.338 km)
• Circumference of furthest distance of Moon: 1,293,600.916 miles (2,081,848.873 km)

Sun

• Sun's diameter: 35,280;1,30 miles (56,777.6966 km)
• Sun's circumference: 110,880;4,43 miles (178,444.189 km)
• Diameter of orbit of Sun: 7,761,605.5 miles (12,491,093.2 km)
• Circumference of orbit of Sun: 24,392,571.38 miles (39,256,038 km)
• One degree along orbit of Sun: 67,700.05 miles (108,952.67 km)
• One minute along orbit of Sun: 1129.283 miles (1817.405 km)

See also

• List of Muslim scientists
• List of pre-modern Iranian scientists and scholars

Notes

1. ^ Kennedy, Edward Stewart (1956). A Survey of Islamic Astronomical Tables. American Philosophical Society. ISBN 978-0-87169-462-1.
2. ^ "Archived copy" (PDF). Archived from the original (PDF) on 2013-10-07. Retrieved 2013-09-04.{{cite web}}: CS1 maint: archived copy as title (link)
3. ^ Hartner, W (2012). "Ḥabas̲h̲ al-Ḥāsib al-Marwazī". referenceworks. doi:10.1163/1573-3912_islam_sim_2572. Retrieved 2024-11-07.
4. ^ Charette 2007.
5. General Cartography Archived 2017-12-09 at the Wayback Machine : "The Iranian geographers Abū Muhammad al-Hasan al-Hamdānī and Habash al-Hasib al-Marwazi set the Prime Meridian of their maps at Ujjain, a center of Indian astronomy"
6. Islamic Desk Reference, ed. E. J. Van Donzel, (Brill, 1994), 121.
7. ^ Selin, Helaine (2013-11-11). Encyclopaedia of the History of Science, Technology, and Medicine in Non-Westen Cultures. Springer Science & Business Media. ISBN 978-94-017-1416-7.
8. Livingston, John W. (2017-12-14). The Rise of Science in Islam and the West: From Shared Heritage to Parting of The Ways, 8th to 19th Centuries. Routledge. ISBN 978-1-351-58926-0.
9. North, John (2008-07-15). Cosmos: An Illustrated History of Astronomy and Cosmology. University of Chicago Press. ISBN 978-0-226-59441-5.
10. "trigonometry". Encyclopædia Britannica. Retrieved 2008-07-21.
11. Jacques Sesiano, "Islamic mathematics", p. 157, in Selin, Helaine; D'Ambrosio, Ubiratàn, eds. (2000), Mathematics Across Cultures: The History of Non-western Mathematics, Springer, ISBN 1-4020-0260-2
12. Langermann, Y. Tzvi (1985), "The Book of Bodies and Distances of Habash al-Hasib", Centaurus, 28 (2): 108–128 , Bibcode:1985Cent...28..108T, doi:10.1111/j.1600-0498.1985.tb00831.x

References

• Charette, François (2007). "Ḥabash al-Ḥāsib: Abū Jaʿfar Aḥmad ibn ʿAbd Allāh al-Marwazī". In Thomas Hockey; et al. (eds.). The Biographical Encyclopedia of Astronomers. New York: Springer. pp. 455–7. ISBN 978-0-387-31022-0. (PDF version)

External links

• Handbuch der Geschichte : aus den Handschriften der k.k. Hofbibliothek zu Wien, der herzoglichen Bibliothek zu Gotha und der Universitäts-Bibliothek zu Leyden (1850), ed.: Ferdinand Wüstenfeld
• An extract from Ibn Kutaiba's 'Adab al-Kâtib; or, The writer's guide (1877), ed.: William Oliver Sproull
• Ibn Kutaiba's Adab-al-kâtib. Nach mehreren Handschriften hrsg. von Max Grünert (1900), ed.: Max Grünert
• Liber poesis et poetarum (1904), ed.: Michael Jan de Goeje

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

• People from Merv
• 9th-century Iranian mathematicians
• Scientists who worked on qibla determination
• 9th-century Iranian astronomers
• Iranian men centenarians
• Mathematicians from the Abbasid Caliphate
• Astronomers from the Abbasid Caliphate