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Habash al-Hasib al-Marwazi

Ahmad ibn 'Abdallah Habash Hasib Marwazi (796 - d. after 869 in Samarra, Iraq[1] ) was a Persian[2] astronomer,[3] geographer, and mathematician from Merv in Khorasan who described first time Trigonometric ratios: SIN, COS, TAN & COT.

He flourished in Baghdad, and died a centenarian after 869. He worked under the Abbasid caliphs al-Ma'mun and al-Mu'tasim.


  • Work 1
    • The Book of Bodies and Distances 1.1
  • See also 2
  • Notes 3
  • References 4
  • External links 5


He made observations from 825 to 835, and compiled three 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.[4][5]

The Book of Bodies and Distances

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, in which some of his results included the following:[6]

  • 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'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


  1. ^ Charette 2007.
  2. ^
  3. ^ Islamic Desk Reference, ed. E. J. Van Donzel, (Brill, 1994), 121.
  4. ^ "trigonometry".  
  5. ^ Jacques Sesiano, "Islamic mathematics", p. 157, in  
  6. ^ Langermann, Y. Tzvi (1985), "The Book of Bodies and Distances of Habash al-Hasib",  


  • Charette, François (2007). "Ḥabash al‐Ḥāsib: Abū Jaʿfar Aḥmad ibn ʿAbd Allāh al‐Marwazī". In Thomas Hockey; et al. The Biographical Encyclopedia of Astronomers. New York: Springer. pp. 455–7. (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
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