Ahmad ibn 'Abdallah Habash Hasib Marwazi (766 - d. after 869 in Samarra,

Iraq Iraq,; ku, عێراق, translit=Êraq officially the Republic of Iraq, '; ku, کۆماری عێراق, translit=Komarî Êraq is a country in Western Asia. It is bordered by Turkey to the north, Iran to the east, the Persian Gulf and K ...

) was a north-eastern

Iranian Iranian may refer to: * Iran, a sovereign state * Iranian peoples, the speakers of the Iranian languages. The term Iranic peoples is also used for this term to distinguish the pan ethnic term from Iranian, used for the people of Iran * Iranian lan ...

astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, moons, comets and galaxies – in either ...

geographer A geographer is a physical scientist, social scientist or humanist whose area of study is geography, the study of Earth's natural environment and human society, including how society and nature interacts. The Greek prefix "geo" means "earth" a ...

, and

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

from

Merv Merv ( tk, Merw, ', مرو; fa, مرو, ''Marv''), also known as the Merve Oasis, formerly known as Alexandria ( grc-gre, Ἀλεξάνδρεια), Antiochia in Margiana ( grc-gre, Ἀντιόχεια ἡ ἐν τῇ Μαργιανῇ) and ...

in Khorasan who for the first time described the trigonometric ratios: sine, cosine,

tangent In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. Mo ...

and cotangent. He flourished in

Baghdad Baghdad (; ar, بَغْدَاد , ) is the capital of Iraq and the second-largest city in the Arab world after Cairo. It is located on the Tigris near the ruins of the ancient city of Babylon and the Sassanid Persian capital of Ctesiphon. I ...

, and died a centenarian after 869. He worked under the

Abbasid caliphs The Abbasid caliphs were the holders of the Islamic title of caliph who were members of the Abbasid dynasty, a branch of the Quraysh tribe descended from the uncle of the Islamic prophet Muhammad, Al-Abbas ibn Abd al-Muttalib. The family came to ...

al-Ma'mun and

al-Mu'tasim Abū Isḥāq Muḥammad ibn Hārūn al-Rashīd ( ar, أبو إسحاق محمد بن هارون الرشيد; October 796 – 5 January 842), better known by his regnal name al-Muʿtaṣim biʾllāh (, ), was the eighth Abbasid caliph, ruling ...

Work

He made observations from 100 to 2035, 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

trigonometry Trigonometry () is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies ...

, 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.Jacques Sesiano, "Islamic mathematics", p. 157, in

''The Book of Bodies and Distances''

Al-Hasib conducted various observations at the Al-Shammisiyyah observatory in

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 In geometry, the circumference (from Latin ''circumferens'', meaning "carrying around") is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out t ...

: 20,160 miles (32,444 km) *Earth's

diameter In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid fo ...

: 6414.54 miles (10323.201 km) *

Earth radius Earth radius (denoted as ''R''🜨 or R_E) is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid, the radius ranges from a maximum of nearly (equatorial radius, deno ...

: 3207.275 miles (5161.609 km) ;Moon *Moon's diameter: 1886.8 miles (3036.5 km) *Moon's circumference: 5927.025 miles (9538.622 km) *Radius of closest distance of Moon: 215,208;9,9 (

sexagesimal Sexagesimal, also known as base 60 or sexagenary, is a numeral system with sixty as its base. It originated with the ancient Sumerians in the 3rd millennium BC, was passed down to the ancient Babylonians, and is still used—in a modified form ...

) miles *Half-circumference of closest distance of Moon: 676,368;28,45,25,43 (sexagesimal) miles *

Radius In classical geometry, a radius ( : radii) of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin ''radius'', meaning ray but also the ...

of furthest distance of Moon: 205,800;8,45 (sexagesimal) miles *Diameter of furthest distance of Moon: 411,600.216 miles (662,406.338 km) *Circumference of furthest distance of Moon: 1,293,600.916 miles (2,081,848.873 km) ;Sun *Sun's diameter: 35,280;1,30 miles (56,777.6966 km) *Sun's circumference: 110,880;4,43 miles (178,444.189 km) *Diameter of orbit of Sun: 7,761,605.5 miles (12,491,093.2 km) *Circumference of orbit of Sun: 24,392,571.38 miles (39,256,038 km) *One degree along orbit of Sun: 67,700.05 miles (108,952.67 km) *One minute along orbit of Sun: 1129.283 miles (1817.405 km)

Notes

References

*
PDF version

External links

*
Handbuch der Geschichte : aus den Handschriften der k.k. Hofbibliothek zu Wien, der herzoglichen Bibliothek zu Gotha und der Universitäts-Bibliothek zu Leyden (1850)
', ed.:

Ferdinand Wüstenfeld Heinrich Ferdinand Wüstenfeld (31 July 1808 – 8 February 1899) was a German orientalist, known as a literary historian of Arabic literature, born at Münden, Hanover. He studied theology and oriental languages at Göttingen and Berlin. He ...

*
An extract from Ibn Kutaiba's 'Adab al-Kâtib; or, The writer's guide (1877)
', ed.: William Oliver Sproull *
Ibn Kutaiba's Adab-al-kâtib. Nach mehreren Handschriften hrsg. von Max Grünert (1900)
', ed.: Max Grünert *
Liber poesis et poetarum (1904)
', ed.:

Michael Jan de Goeje Michael Jan de Goeje (August 13, 1836 – May 17, 1909) was a Dutch orientalist focusing on Arabia and Islam. Early life Michael Jan de Goeje was born in Dronrijp, Friesland. He devoted himself at an early age to the study of oriental lan ...

{{DEFAULTSORT:Al-Hasib Al-Marwazi, Habash 874 deaths People from Merv 9th-century Iranian mathematicians Scientists who worked on qibla determination 9th-century Iranian astronomers Year of birth unknown Men centenarians Iranian centenarians 766 births Mathematicians from the Abbasid Caliphate Astronomers from the Abbasid Caliphate

Work

''The Book of Bodies and Distances''

See also

Notes

References

External links