# Ibn Muʿādh al-Jayyānī

Al-Jayyānī | |
---|---|

Born |
989 Cordova, Al-Andalus |

Died |
1079 Jaén, Al-Andalus |

Residence | Caliphate |

Academic background | |

Influences | Euclid, al-Khwarizmi |

Academic work | |

Era | Islamic Golden Age |

Main interests | Mathematics, Astronomy |

Influenced | Alfonso X |

**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",^{[4]} 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-Islamic 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]}

## See also

## Notes

- ↑ Latin forms include
*Abenmoat*,*Abumadh*,*Abhomadh*, or*Abumaad*, corresponding to either*Ibn Muʿādh*or*Abū ... Muʿādh*. - ↑ Calvo 2007.
- ↑ Dold-Samplonius & Hermelink 1970.
- 1 2 O'Connor, John J.; Robertson, Edmund F., "Abu Abd Allah Muhammad ibn Muadh Al-Jayyani",
*MacTutor History of Mathematics archive*, University of St Andrews. - ↑ O'Connor, John J.; Robertson, Edmund F., "Menelaus of Alexandria",
*MacTutor History of Mathematics archive*, University of St Andrews. "Book 3 deals with spherical trigonometry and includes Menelaus's theorem." - ↑ 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)

## References

- Calvo, Emilia (2007). "Ibn Muʿādh: Abū ʿAbd Allāh Muḥammad ibn Muʿādh al‐Jayyānī". In Thomas Hockey; et al.
*The Biographical Encyclopedia of Astronomers*. New York: Springer. pp. 562–3. ISBN 978-0-387-31022-0. (PDF version) - O'Connor, John J.; Robertson, Edmund F., "Abu Abd Allah Muhammad ibn Muadh Al-Jayyani",
*MacTutor History of Mathematics archive*, University of St Andrews. - Dold-Samplonius, Yvonne; Hermelink, Heinrich (1970). "Al-Jayyānī, Abū'Abd Allāh Muḥammad Ibn Mu'ādh".
*Complete Dictionary of Scientific Biography*. Encyclopedia.com.