Al-Nayrizi

Abū’l-‘Abbās al-Faḍl ibn Ḥātim al-Nairīzī (أبو العباس الفضل بن حاتم النيريزي; ; Anaritius, Nazirius, c. 865 – c. 922) was a Persian mathematician and astronomer from Nayriz, now in Fars Province, Iran.

Life
Little is known of al-Nairīzī, though his nisba refers to the town of Neyriz. He mentioned al-Mu'tadid, the Abbasid caliph, in his works, and so scholars have assumed that al-Nairīzī flourished in Baghdad during this period. Al-Nairīzī wrote a book for al-Mu'tadid on atmospheric phenomena. He died in c. 922.

Mathematics
Al-Nayrizi wrote a commentary to the translation in Arabic by Al-Ḥajjāj ibn Yūsuf ibn Maṭar of Euclid's Elements. Both the translation and the commentary have survived, as well as a 12th-century Latin translation by Gerard of Cremona. Al-Nayrizi's commentary contains unique extracts of two other commentaries on the Elements, produced by Hero of Alexandria and Simplicius of Cilicia.

Al-Nairīzī used the umbra (versa), the equivalent to the tangent, as a genuine trigonometric line, as did the Persian astronomer al-Marwazi before him. He gave a proof of the Pythagorean theorem using the Pythagorean tiling.

Al-Nayrizi gave a mathematical proof of the parallel postulate based on the assumption that parallel lines are equidistant. He wrote a treatise on an exact method for the numerical determination of the kibla and a text about a device for measuring the heights, widths, and depths.

Astronomy
Al-Nairīzī wrote a treatise on the spherical astrolabe, an elaborate work that seems to be the best Persian work on the subject. It is divided into four books:


 * 1) An historical and critical introduction of the astrolabe;
 * 2) A description of the instrument; and a comparison with other astronomical instruments;
 * 3) Applications of the instrument;
 * 4) Applications of the instrument.

Ibn al-Nadim mentions Nayrizi as a distinguished astronomer with eight works by him listed in his book al-Fihrist.

Al-Nayrizi's most important astronomical works, his commentary on Ptolemy's Almagest and both his zijes, are lost. He produced treatises on the spherical astrolabe and astrological conjunctions, both of which are extant.