Ahmed Ibn Yusuf

Full name: 
Ahmed Ibn Yūsuf Ibn Ibrāhim al-Misrī Ibn ad-Dāya
Arabic name: 
أحمد بن يوسف بن إبراهيم المصري بن الداية
Latin name: 
Ametus filius Iosephi
Date of death: 

Ahmed Ibn Yusuf was born in Baghdad and moved to Damascus in 839, then to Cairo, where he died in 912 CE. He was a mathematician, like his father Yusuf Ibn Ibrahim.

Among his works that brought him fame and influence is his Risala fi 'l-nisba wa 'l-tanasub (Treatise on ratio and proportionality). This was translated into Latin by Gherard of Cremona. It influenced early European mathematicians such as Fibonacci. Further, in On similar arcs, he commented on Ptolemy's Centiloquium. He also wrote a book on the astrolabe, a predecessor of the octant and the sextant. He invented methods to solve tax problems in Liber Abaci. He was also quoted by mathematicians such as Thomas Bradwardine, Jordanus Nemorarius and Luca Pacioli.

His book On similar arcs influenced European mathematicians, as Ahmed Ibn Yusuf proves that similar arcs of circles can be equal and not equal. The proof, like that on ratio and proportion, is based on Euclid. This time it is Propositions 20 and 21 of Book III of Euclid's Elements which are the main tools used by Ahmed. The complete Arabic text of this treatise was edited by D. Schrader.

See J.J. O'Connor & E.F. Robertson, "Ahmed Ibn Yusuf al-Misri"; D. Schrader, The Epistola de proportione et proportionalitate of Ametus Filius Iosephi, PhD Dissertation, Madison, University of Wisconsin, 1961.