Nayrizi, Abu Al-Abbas Al-Fadhl Bin Hatim A MATHEMATICIAN from Nayriz, a town near Shiraz. He flourished between 875 and 940 CE. Little is known of his life but we do know that he dedicated some of his works to Caliph Al-Mu'tadid (892-902 CE). So he almost certainly moved to Baghdad and worked there for the caliph. He wrote commentaries on works by Ptolemy and Euclid, compiled astronomical tables, wrote a book for Al-Mu'tadid on atmospheric phenomena. Al-Nayrizi's commentaries on Ptolemy and Euclid were translated into Latin by Gerard of Cremona. He used the so-called umbra (versa), the equivalent to the tangent, as a genuine trigonometric line. He wrote a treatise on the spherical astrolabe, which is very elaborate and seems to be the best Arabic work on the subject. Al-Nayrizi wrote a book on how to determine the direction of the Ka'ba in Makkah (it was important as Muslims face that direction five times everyday when performing the daily prayer). In this work he effectively uses the tan function, but he was not the first to use these trigonometrical ideas.
