'Abd al-Hamid ibn Turk
Encyclopedia
known also as was a ninth century Turkic
Turkic peoples
The Turkic peoples are peoples residing in northern, central and western Asia, southern Siberia and northwestern China and parts of eastern Europe. They speak languages belonging to the Turkic language family. They share, to varying degrees, certain cultural traits and historical backgrounds...

 Muslim mathematician
Islamic mathematics
In the history of mathematics, mathematics in medieval Islam, often termed Islamic mathematics or Arabic mathematics, covers the body of mathematics preserved and developed under the Islamic civilization between circa 622 and 1600...

. Not much is known about his biography. The two records of him, one by Ibn Nadim
Ibn al-Nadim
Abu'l-Faraj Muhammad bin Is'hāq al-Nadim , whose father was known as al-Warrāq was a Shia Muslim scholar and bibliographer. Some scholars regard him as a Persian, but this is not certain. He is famous as the author of the Kitāb al-Fihrist...

 and the other by al-Qifti
Al-Qifti
Al-Qifti or Ibn al-Qifti was a medieval Muslim writer. He is remembered today mainly for his History of Learned Men.-Life and Works:...

 are not identical. However al-Qifi mentions his name as ʿAbd al-Hamīd ibn Wase ibn Turk Jili. Jili means from Gilan.

He wrote a work on algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...

 of which only a chapter called "Logical Necessities in Mixed Equations", on the solution of quadratic equations, has survived.

He authored a manuscript entitled Logical Necessities in Mixed Equations, which is very similar to al-Khwarzimi's Al-Jabr and was published at around the same time as, or even possibly earlier than, Al-Jabr.
The manuscript gives exactly the same geometric demonstration as is found in Al-Jabr, and in one case the same example as found in Al-Jabr, and even goes beyond Al-Jabr by giving a geometric proof that if the determinant is negative then the quadratic equation has no solution. The similarity between these two works has led some historians to conclude that algebra may have been well developed by the time of al-Khwarizmi and 'Abd al-Hamid.
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