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Abū’l-‘Abbās al-Faḍl ibn Ḥātim al-Nairīzī (Arabic: أبو العباس الفضل بن حاتم النيريزي‎, Latin: Anaritius, Nazirius, 865–922) was a 9th-10th century Persian mathematician and astronomer from Nayriz, Fars, Iran.

He flourished under al-Mu'tadid, Caliph from 892 to 902, and compiled astronomical tables, writing a book for al-Mu'tadid on atmospheric phenomena.

Nayrizi wrote commentaries on Ptolemy and Euclid. The latter were translated by Gerard of Cremona. Nairizi used the so-called umbra (versa), the equivalent to the tangent, as a genuine trigonometric line (but he was anticipated in this by al-Marwazi).

He wrote a treatise on the spherical astrolabe, which is very elaborate and seems to be the best Persian work on the subject. It is divided into four books:

Historical and critical introduction.
Description of the spherical astrolabe; its superiority over plane astrolabes and all other astronomical instruments.

He gave a proof of the Pythagorean theorem using the Pythagorean tiling.[1]

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


^ Nelsen, Roger B. (November 2003), "Paintings, plane tilings, and proofs", Math Horizons: 5–8. Reprinted in Haunsperger, Deanna; Kennedy, Stephen (2007), The Edge of the Universe: Celebrating Ten Years of Math Horizons, Spectrum Series, Mathematical Association of America, pp. 295–298, ISBN 9780883855553. See also Alsina, Claudi; Nelsen, Roger B. (2010), Charming proofs: a journey into elegant mathematics, Dolciani mathematical expositions, 42, Mathematical Association of America, pp. 168–169, ISBN 9780883853481. Nelsen uses the for "Annairizi" of his name; for the identification of it with Anaritius, see Isis, vol. 6, p. 515.


H. Suter: Die Mathematiker und Astronomen der Araber (45, 1900)
Nachtrage (164, 1902).
O'Connor, John J.; Robertson, Edmund F., "Abu'l Abbas al-Fadl ibn Hatim Al-Nayrizi", MacTutor History of Mathematics archive, University of St Andrews.

Primary sources

The (fragmentary) text of Nairizi's commentary on Euclid I. PDF scans from the edition of Codex Leidensis 399 (Classical Arabic)

External links

Sabra, A. I. (2008) [1970-80]. "Al-Nayrīzī, Abu’l-‘Abbās Al-Faḍl Ibn Ḥātim". Complete Dictionary of Scientific Biography. Encyclopedia.com.
DeYoung, Gregg (2007). "Nayrīzī: Abū al‐ʿAbbās al‐Faḍl ibn Ḥātim al‐Nayrīzī". In Thomas Hockey et al. The Biographical Encyclopedia of Astronomers. New York: Springer. p. 823. ISBN 9780387310220. (PDF version)


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