Habash al-Hasib al-Marwazi (766 – d. after 869 in Samarra, modern Iraq[1]) was a Persian[2][3] astronomer,[4] geographer, and mathematician from Merv in Khorasan, who was the first to describe the trigonometric ratios tangent, and cotangent.
Habash flourished in Baghdad, and died a centenarian some time after 869. He worked under two Abbasid caliphs, al-Ma'mun and al-Mu'tasim.
Habash al-Hasib al-Marwazi | |
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Born | Habash al-Hasib al-Marwazi 766 AD Merv |
Died | 869 AD Samarra |
Nationality | Persian |
Ahmad ibn 'Abdallah Habash Hasib Marwazi 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.[5][6]
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:[7]
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