# Yusuf al-Mu'taman ibn Hud

**Yusuf ibn Ahmad al-Mu'taman ibn Hūd** (Arabic: المؤتمن بالله يوسف إبن أحمد إبن هود, *al-Mutaman bi l-Lah*, died c. 1085) was an Arab mathematician and a member of the Banu Hud family. He ruled Zaragoza from 1081 to 1085, where the Banu Hūd family kept their rule until 1100. Saragossa, which encompasses modern-day Aragon, Spain, had its early influence from the Roman Empire. In medieval Islam, there was a wave of translations of ancient Greek and Roman texts. Ranging from philosophy, to medicine, to astronomy, and the more influential mathematical translations. Yusuf son to the king, Ahmad ibn Sulayman al-Muqtadir. His father Ahmad was known for philosophy, astronomy, as well as translations of mathematics. Both father and son, as well as medieval Islamic translators such as the Banū Mūsā were known for their expansions on ancient Greek and Roman ideals. There was a stigma in the periods following medieval Islam that Islamic translators only copied the ancient texts, offering no intellectual addition. Later it is proven that translators such as Ibn Sīnā and Yusuf offered copious and revolutionary input into their expansion on ancient ideas. Yusuf ibn Ahmad al-Mu'taman ibn Hūd wrote a mathematical treatise called Kitab al-Istikmāl (Arabic,كتاب الإستكمال, Perfection or Comprehensive Treatise) in mathematics, where it was edited by Maimonides (ca. 1135 – 1204).

Ceva's theorem which is often attributed to the Italian mathematician Giovanni Ceva (d. 1734) was proved much earlier by Al-Mu'taman ibn Hūd. It remains unknown whether Giovanni had discovered this geometry on his own or if he had found a translation of al-Mu'taman's treatise.^{[1]}

- What ibn Hūd proved, before Ceva's theorem.
- Ceva's parallel theorem proved by Al-Mu'taman ibn Hūd.

## Istikmāl: How the Lost Geometry of Mathematics in Medieval Islam was Perceived

"Encyclopedist Muhammad ibn Ibrahim al-AkGni says that if the Istikmāl of al-Mu’taman ibn Hūd had been completed, it would have made the existing geometrical literature superfluous." So Istikmāl is an uncompleted work but it was still revolutionary for the eleventh-century king. Especially when it was seen as something new when the seventeenth-century Italian mathematician claimed to have proven the theorem. Although it was common practice for royals to be educated both al-Mu’taman ibn Hūd and his father were exceptional mathematicians. Biographer Ibn al-Qifti said that Istikmāl was an immaculate comprehensive work. Furthermore, Ibn Aknin (ca. 1160-1226) postulated that Istikmāl needs to be read by mathematicians alongside Elements of Euclid, On the Sphere and Cylinder by Archimedes, and Conics of Apollonius to name a few. Because this was not a completed piece of work it was not appreciated nor taught to the masses like work from Euclid or Archimedes. From this lack of exposure due to ibn Hūd's lost works on geometry, during the time after his death until the eighteenth century, later mathematicians like Ceva would get credit for mathematical work that was already discovered and proven by ibn Hūd.^{[2]}

## See also

## References

- ↑ Holme, Audun (2010).
*Geometry: Our Cultural Heritage*. Springer. p. 210. ISBN 3-642-14440-3. - ↑ Hogendijk, Jan, P. (1986). "Discovery of an 11th-century geometrical compilation: The Istikmāl of Yūsuf al-Mu'taman ibn Hūd, King of Saragossa".
*Historia Mathematica*.**13**: 43–52. doi:10.1016/0315-0860(86)90227-2.