Yusuf al-Mu'taman ibn Hud

Al-Mu'taman was the third king of the Banu Hud dynasty, reigning from 1081 to 1085, at the height of power of Muslim Zaragoza, following the thriving period of his father Ahmad al-Muqtadir.

He knew astrology, philosophy, and especially mathematics, a discipline in which he wrote the most important treatise to come out of the al-Andalus region in the 11th century,[1] the Kitab al-Istikmal ("Book of Perfection").

Al-Mu'taman also assigned to El Cid the task of reincorporating into Zaragoza the eastern territories of his relative Mundhir, an ally of Aragon.

El Cid contained the attacks of the Aragonese until 1083, when Sancho managed to take the line of fortifications that protected Zaragoza like Graus in the east, as well as Ayerbe, Bolea, Arascués and Arguedas.

The circumstances in which he refused to continue serving al-Mu'tamin and his heir Ahmad II al-Mustaʿin are not fully clear and still debated.

The book only persists as fragments from several anonymous manuscripts, not including any preface or introduction, but it is clear from the remaining content that the intention was to organize and comprehensively describe the known results in Euclidean geometry in a single self-contained work.

[2] It is possible al-Mu'taman listed his sources in a now-lost introductory section, but none of the remaining fragments credit past authors or works for any of the content.

[2] Ibn Aknin suggested that the Istikmal should be read by mathematicians alongside such works as the Elements of Euclid, On the Sphere and Cylinder of Archimedes, and Conics of Apollonius.

[citation needed] The Kitab al-Istikmal deals with irrational numbers, conic sections, quadrature of the parabolic segment, volumes and areas of various geometric objects, and the drawing of the tangent to a circle, among other mathematical problems.