Al-Khwârizmî, Ibn Turk, and the Liber Mensurationum : On the Origins of Islamic Algebr

Authors : Jens HOYRUP

Pages : 445-484

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Publication Date : 1986-05-01

Article Type : Research Paper

Abstract :A close investigation o f O ld Babylonian second-degree algebra shows that its method and conceptualization are not arithm etical and rhetorical, as is grosso modo the al-jabr presented by A l-K hw ârizm î. Instead, it appears to be based on a “ naive” geom etry o f areas very similar to that used by lbn T urk and A l-K hw ârizm î in their justifications o f the algorithms used in al-jabr to solve the basic mixed second-degree equations. This raises in a new light the question whether the early Islam ic use o f geometric justifications was a graft o f Greek methods upon a “ sub-scientific” m athem atical tradition, as often maintained, or the relation o f early Islam ic algebra to its sources must be seen differently.
Keywords : Al Khwârizmî, Ibn, Turk