( fl. 830), known also as ( ar, ابومحمد عبدالحمید بن واسع بن ترک الجیلی) was a ninth-century Muslim mathematician. Not much is known about his life. The two records of him, one by

Ibn Nadim Abū al-Faraj Muḥammad ibn Isḥāq al-Nadīm ( ar, ابو الفرج محمد بن إسحاق النديم), also ibn Abī Ya'qūb Isḥāq ibn Muḥammad ibn Isḥāq al-Warrāq, and commonly known by the ''nasab'' (patronymic) Ibn al-Nadīm ...

and the other by

al-Qifti 'Alī ibn Yūsuf al-Qifṭī or Ali Ibn Yusuf the Qifti (of Qift, his home city) (), he was ''Jamāl al-Dīn Abū al-Ḥasan 'Alī ibn Yūsuf ibn Ibrāhīm ibn 'Abd al-Wahid al-Shaybānī'' () (ca. 1172–1248); an Egyptian Arab historian, biog ...

are not identical. Al-Qifi mentions his name as ʿAbd al-Hamīd ibn Wase ibn Turk al-Jili. Jili means from Gilan. On the other hand,

mentions his nisbah as ''khuttali'' (), which is a region located north of the Oxus and west of

Badakhshan Badakhshan is a historical region comprising parts of modern-day north-eastern Afghanistan, eastern Tajikistan, and Taxkorgan Tajik Autonomous County in China. Badakhshan Province is one of the 34 provinces of Afghanistan. Much of historic Ba ...

. In one of the two remaining manuscripts of his ''al-jabr wa al-muqabila'', the recording of his nisbah is closer to ''al-Jili''.Ibn Turk
in ''Dāʾirat al-Maʿārif-i Buzurg-i Islāmī'', Vol. 3, no. 1001, Tehran. To be translated in Encyclopædia Islamica. David Pingree / ''

Encyclopaedia Iranica An encyclopedia (American English) or encyclopædia (British English) is a reference work or compendium providing summaries of knowledge either general or special to a particular field or discipline. Encyclopedias are divided into article ...

'' states that he originally hailed from

Khuttal Khuttal, frequently also in the plural form Khuttalan (and variants such as ''Khutlan'', ''Khatlan'', in Chinese sources ''K'o-tut-lo'') was a medieval region and principality on the north bank of the river Oxus (modern Amu Darya), lying between i ...

or Gilan. He wrote a work on

algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary ...

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''. Only a chapter called "Logical Necessities in Mixed Equations", on the solution of

quadratic equations In algebra, a quadratic equation () is any equation that can be rearranged in standard form as ax^2 + bx + c = 0\,, where represents an unknown value, and , , and represent known numbers, where . (If and then the equation is linear, not quadr ...

, has survived. 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. 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.

External links

References

Sources

* * * Rev. by Jean Itard in Revue Hist. Sci. Applic., 1965, I8:123-124. Mathematicians of the medieval Islamic world Mathematicians from the Abbasid Caliphate 9th-century mathematicians 9th-century people from the Abbasid Caliphate Year of death missing {{asia-mathematician-stub