Al‐Mu˒taman ibn Hūd
Yūsuf Al‐Mu˒taman ibn Hūd was the king of the kingdom of Zaragoza in Northern Spain from 1081 until his death in 1085. He lived in the Aljafería palace in Zaragoza, which was built by his father Aḥmad al‐Muqtadir ibn Hūd (r. 1041–1081), and which is now the site of the Parliament of Aragon. Al‐Mu˒taman was interested in mathematics, optics, and philosophy. He wrote a very long mathematical work, the Kitāb al‐Istikmāl (Book of Perfection), of which large parts have recently been identified in four anonymous Arabic manuscripts in Copenhagen, Leiden, Cairo, and Damascus. A revised version of the whole Istikmāl was recently discovered.
In the Book of Perfection, al‐Mu˒taman divides most of pure mathematics according to a philosophical classification in five “species” (anwā˓). Species 1 deals with arithmetic and the theory of numbers. Al‐Mu˒taman summarizes the arithmetical books of Euclid's Elements, and he proves Thābit ibn Qurra's rule for amicable numbers. The remaining species 2–5...
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