## ::'Abd al-Hamīd ibn Turk

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Boyer::first Category::algebra Logical::which Title::iraqi Mixed::solution Found::al-ham**ʿAbd al-Hamīd ibn Turk** (fl. 830), known also as **ʿAbd al-Hamīd ibn Wase ibn Turk Jili** was a ninth-century Turkic Muslim mathematician. Not much is known about his biography. The two records of him, one by Ibn Nadim and the other by al-Qifti are not identical. However al-Qifi mentions his name as ʿAbd al-Hamīd ibn Wase ibn Turk Jili. Jili means from Gilan.<ref>Ibn Turk in *Dāʾirat al-Maʿārif-i Buzurg-i Islāmī*, Vol. 3, no. 1001, Tehran. To be translated in Encyclopædia islamica.</ref>

He wrote a work on algebra 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*.<ref name="Boyer Ibn Turk">{{#invoke:citation/CS1|citation
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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 discriminant is negative then the quadratic equation has no solution.<ref name="Boyer Ibn Turk" /> 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.<ref name="Boyer Ibn Turk" />

**'Abd al-Hamīd ibn Turk sections**

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