Abū’l-‘Abbās al-Faḍl ibn Ḥātim al-Nairīzī (Arabic: أبو العباس الفضل بن حاتم النيريزي‎, Latin: Anaritius, Nazirius, c. 865–922) was a Persian[1] mathematician and astronomer from Nayriz, Fars Province, 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:

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

He gave a proof of the Pythagorean theorem using the Pythagorean tiling.[2]

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


  1. ^ Hamilton Alexander Rosskeen Gibb (1993). The Encyclopaedia of Islam: MIF-NAZ. Brill. p. 1050. AL-NAYRIZI, ABU 'L-CABBAS AL-FADL B. HATIM, Persian geometer and astronomer
  2. ^ Nelsen, Roger B. (November 2003), "Paintings, plane tilings, and proofs" (PDF), Math Horizons, 11 (2): 5–8, doi:10.1080/10724117.2003.12021741, S2CID 126000048. 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 978-0-88385-555-3. 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 978-0-88385-348-1. Nelsen uses the "Annairizi" form of his name; for the identification of it with Anaritius, see Isis, vol. 6, p. 515.


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