Ibn Mu'adh al-Jayyani
{{short description|Andalusian philosopher and mathematician}}
{{Redirect|Ibn Mu'adh}}
{{Infobox scholar
| image =
| image_size =
| caption =
| name = Al-Jayyānī
| birth_date = 989
| birth_place = Iraq
| death_date = 1079
| death_place = Jaén, Al-Andalus
| era = Islamic Golden Age
| school_tradition =
| main_interests = Mathematics, Astronomy
| notable_ideas =
| major_works =
| influences = Euclid, al-Khwarizmi
}}
Abū ʿAbd Allāh Muḥammad ibn Muʿādh al-JayyānīLatin forms include Abenmoat, Abumadh, Abhomadh, or Abumaad, corresponding to either Ibn Muʿādh or Abū ... Muʿādh. ({{langx|ar|أبو عبد الله محمد بن معاذ الجياني}}; 989, Cordova, Al-Andalus – 1079, Jaén, Al-Andalus) was an Arab mathematician, Islamic scholar, and Qadi from Al-Andalus (in present-day Spain).{{sfn|Calvo|2007}} Al-Jayyānī wrote important commentaries on Euclid's Elements and he wrote the first known treatise on spherical trigonometry.
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.{{sfn|Dold-Samplonius|Hermelink|1970}}
There is some evidence that he lived in Cairo from 1012/13 to 1016/17.{{cite journal |last1=Smith |first1=A. Mark |title=The Latin Version of lbn Mu c ādh's Treatise “On Twilight and the Rising of Clouds” |journal=Arabic Sciences and Philosophy |date=1992 |volume=2 |issue=1 |page=83 |doi=10.1017/s0957423900001570}}
Works
Al-Jayyānī wrote The book of unknown arcs of a sphere, which is considered "the first treatise on spherical trigonometry",{{MacTutor|id=Al-Jayyani|title=Abu Abd Allah Muhammad ibn Muadh Al-Jayyani|quote=al-Jayyani's The book of unknown arcs of a sphere, the first treatise on spherical trigonometry. The work, which is published together with a Spanish translation and a commentary in [3], contains formulae for right-handed triangles, the general law of sines, and the solution of a spherical triangle by means of the polar triangle. Proofs are sometimes only given as sketches.}} although spherical trigonometry in its ancient Hellenistic form was dealt with by earlier mathematicians such as Menelaus of Alexandria, whose treatise the Spherics included Menelaus' theorem,{{MacTutor|id=Menelaus|title=Menelaus of Alexandria}} "Book 3 deals with spherical trigonometry and includes Menelaus's theorem." still a basic tool for solving spherical geometry problems in Al-Jayyānī's time. 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.{{citation|first=E. S.|last=Kennedy|title=The History of Trigonometry|journal=31st Yearbook|publisher=National Council of Teachers of Mathematics, Washington, D.C.|year=1969|page=337}} (cf. {{citation|first=Syed Nomanul|last=Haq|title=The Indian and Persian background|page=68}}, in {{citation|title=History of Islamic Philosophy|first=Oliver Leaman|last=Seyyed Hossein Nasr|year=1996|publisher=Routledge|isbn=0-415-13159-6|pages=52–70}}) 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.
There is strong consensus in attributing the authorship of a manuscript about the duration of twilight to him.{{cite journal |last1=Sabra |first1=A.I. |title=The Authorship of the Liber de crepusculis, an Eleventh-Century Work on Atmospheric Refraction |journal=Isis |date=1967 |volume=58 |issue=1 |pages=77-85 |doi=10.1086/350185}} The short treatise On twilight was incorrectly attributed to Ibn al-Haytham for several centuries, due to a reference made by Gerard of Cremona, who translated it into Latin. The first printed edition of Cremona's translation (Allacen arabis uetustissimi liber de crepusculis, Gerardo Cremonensi interprete) was made in 1542, by the Portuguese mathematician and cosmographer Pedro Nunes.{{cite book |last1=Nunes |first1=Pedro |title=Obras |date=2003 |publisher=Fundação Calouste Gulbenkian |location=Lisboa |isbn=972-31-1084-9 |volume=II}}
See also
Notes
{{reflist}}
References
- {{cite encyclopedia | editor = Thomas Hockey| last = Calvo | first = Emilia | title=Ibn Muʿādh: Abū ʿAbd Allāh Muḥammad ibn Muʿādh al-Jayyānī | encyclopedia = The Biographical Encyclopedia of Astronomers | publisher = Springer | date = 2007 | location = New York | pages = 562–3 | url=http://islamsci.mcgill.ca/RASI/BEA/Ibn_Muadh_BEA.htm | isbn=978-0-387-31022-0 |display-editors=etal}} ([http://islamsci.mcgill.ca/RASI/BEA/Ibn_Muadh_BEA.pdf PDF version])
- {{MacTutor|id=Al-Jayyani|title=Abu Abd Allah Muhammad ibn Muadh Al-Jayyani}}
- {{cite encyclopedia | first1=Yvonne| last1=Dold-Samplonius | last2 = Hermelink | first2 = Heinrich | title=Al-Jayyānī, Abū'Abd Allāh Muḥammad Ibn Mu'ādh | url=http://www.encyclopedia.com/doc/1G2-2830902173.html | encyclopedia = Complete Dictionary of Scientific Biography | publisher = Encyclopedia.com | date=1970 |authorlink=Yvonne Dold-Samplonius}}
{{Islamic mathematics}}
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Category:Astronomers from al-Andalus
Category:Mathematicians from al-Andalus
Category:11th-century mathematicians
Category:11th-century people from al-Andalus