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.[9][10]
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 860, 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.[11][12]
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),[8] in which some of his results included the following:[13]
^General CartographyArchived 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"
^Islamic Desk Reference, ed. E. J. Van Donzel, (Brill, 1994), 121.
^"Trigonometry - India, Islamic World | Britannica". www.britannica.com. 2025-02-07. Retrieved 2025-02-14. The first table of tangents and cotangents was constructed around 860 by Ḥabash al-Ḥāsib ("the Calculator"), who wrote on astronomy and astronomical instruments.
