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 for the first time described the trigonometric ratios: sine, cosine, tangent and cotangent.

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


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]


See also


  1. Charette 2007.
  2. http://www.usc.edu/schools/college/crcc/private/cmje/heritage/History_of_Islamic_Science.pdf
  3. Islamic Desk Reference, ed. E. J. Van Donzel, (Brill, 1994), 121.
  4. "trigonometry". Encyclopædia Britannica. Retrieved 2008-07-21.
  5. Jacques Sesiano, "Islamic mathematics", p. 157, in Selin, Helaine; D'Ambrosio, Ubiratan, eds. (2000), Mathematics Across Cultures: The History of Non-western Mathematics, Springer, ISBN 1-4020-0260-2
  6. Langermann, Y. Tzvi (1985), "The Book of Bodies and Distances of Habash al-Hasib", Centaurus, 28 (2): 108–128 [111], doi:10.1111/j.1600-0498.1985.tb00831.x


External links

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