Habash al-Hasib
Ahmad ibn 'Abdallah al-Marwazi, known as Habash al-Hasib was a Persian astronomer, geographer, and mathematician from Merv in Khorasan, who discovered 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 and 874 possibly in Abbasid Samarra. The title "Habash" may refer to dark skin color. 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 : 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 ; a method which was generally adopted by Muslim astronomers.
In 860, he seems to have introduced the notion of "shadow", umbra, 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:;Earth
- Earth's circumference: 20,160 miles
- Earth's diameter: 6414.54 miles
- Earth radius: 3207.275 miles
- Moon's diameter: 1886.8 miles
- Moon's circumference: 5927.025 miles
- Radius of closest distance of Moon: 215,208;9,9 miles
- Half-circumference of closest distance of Moon: 676,368;28,45,25,43 miles
- Radius of furthest distance of Moon: 205,800;8,45 miles
- Diameter of furthest distance of Moon: 411,600.216 miles
- Circumference of furthest distance of Moon: 1,293,600.916 miles