# Ibn Muʿādh al-Jayyānī

"Ibn Mu'adh" redirects here. For other uses, see Ibn Mu'adh (disambiguation).
Born 989 Cordova, Al-Andalus 1079 Jaén, Al-Andalus Islamic Golden Age Caliphate Mathematics, Astronomy Influenced by Influenced

Abū ʿAbd Allāh Muḥammad ibn Muʿādh al-Jayyānī[1] (989, Cordova, Al-Andalus – 1079, Jaén, Al-Andalus) was a mathematician, Islamic scholar, and Qadi from Al-Andalus (in present-day Spain).[2] Al-Jayyānī wrote important commentaries on Euclid's Elements and he wrote the first known treatise on spherical trigonometry as a discipline independent from astronomy.

## Life

Little is known about his life. Confusion exists over the identity of al-Jayyānī of the same name mentioned by ibn Bashkuwal (died 1183), Qur'anic scholar, Arabic Philologist, and expert in inheritance laws (farāʾiḍī). It is unknown whether they are the same person.[3]

## The book of unknown arcs of a sphere

Al-Jayyānī wrote The book of unknown arcs of a sphere, which is considered "the first treatise on spherical trigonometry" in its modern form,[4][not in citation given] although spherical trigonometry in its ancient Hellenistic form was dealt with by earlier mathematicians such as Menelaus of Alexandria, who developed Menelaus' theorem to deal with spherical problems.[5] However, E. S. Kennedy points out that while it was possible in pre-lslamic mathematics to compute the magnitudes of a spherical figure, in principle, by use of the table of chords and Menelaus' theorem, the application of the theorem to spherical problems was very difficult in practice.[6] Al-Jayyānī's work on spherical trigonometry "contains formulae for right-handed triangles, the general law of sines, and the solution of a spherical triangle by means of the polar triangle." This treatise later had a "strong influence on European mathematics", and his "definition of ratios as numbers" and "method of solving a spherical triangle when all sides are unknown" are likely to have influenced Regiomontanus.[4]

## Notes

1. ^ Latin forms include Abenmoat, Abumadh, Abhomadh, or Abumaad, corresponding to either Ibn Muʿādh or Abū ... Muʿādh.
2. ^
3. ^
4. ^ a b
5. ^ . "Book 3 deals with spherical trigonometry and includes Menelaus's theorem."
6. ^ Kennedy, E. S. (1969), "The History of Trigonometry", 31st Yearbook (National Council of Teachers of Mathematics, Washington, D.C.): 337 (cf. Haq, Syed Nomanul, The Indian and Persian background, p. 68, in Seyyed Hossein Nasr, Oliver Leaman (1996), History of Islamic Philosophy, Routledge, pp. 52–70, ISBN 0-415-13159-6)