Ahmad ibn 'Abdallah al-Marwazi, known as Habash al-Hasib (, 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, in which some of his results included the following: