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Abū ʿAbd Allāh Muḥammad ibn Muʿādh al-Jayyānī[1] (Arabic: 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).[2] Al-Jayyānī wrote important commentaries on Euclid's Elements and he wrote the first known treatise on spherical trigonometry.

"Ibn Mu'adh" redirects here. For other uses, see Ibn Mu'adh (disambiguation).
Al-Jayyānī
Born989
Cordova, Al-Andalus
Died1079
Jaén, Al-Andalus
Academic background
InfluencesEuclid, al-Khwarizmi
Academic work
EraIslamic Golden Age
Main interestsMathematics, 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


  1. Latin forms include Abenmoat, Abumadh, Abhomadh, or Abumaad, corresponding to either Ibn Muʿādh or Abū ... Muʿādh.
  2. Calvo 2007.
  3. Dold-Samplonius & Hermelink 1970.
  4. O'Connor, John J.; Robertson, Edmund F., "Abu Abd Allah Muhammad ibn Muadh Al-Jayyani", MacTutor History of Mathematics archive, University of St Andrews, 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.
  5. 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."
  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)

References


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На других языках

[de] Ibn Muʿādh al-Dschaiyānī

Ibn Muʿādh al-Dschaiyānī oder el-Dschajjani (arabisch ابن معاذ الجياني, DMG Ibn Muʿāḏ al-Ǧaiyānī, spanisch Yayyani de Jaén el Joven) war ein aus Spanien (al-Andalus) stammender arabischer Astronom, Jurist und Mathematiker des 11. Jahrhunderts. Er schrieb die erste bekannte Abhandlung über sphärische Trigonometrie.
- [en] Ibn Mu'adh al-Jayyani

[fr] Ibn Muʿādh al-Jayyānī

Abū ʿAbd Allāh Muḥammad ibn Muʿādh al-Jayyānī (en arabe ابن معاذ الجياني, né vers 989, mort après 1079 à Jaén) est un mathématicien, ouléma et cadi arabe[1],[2] du califat de Cordoue. Il est à l'origine de travaux important sur les éléments d'Euclide et d'un des plus anciens traités de trigonométrie sphérique de l'ouest médiéval, comme discipline indépendante de l'astronomie.

[it] Ibn Mu'adh al-Jayyani

Abū ʿAbd Allāh Muḥammad ibn Muʿādh al-Jayyānī, أبو عبد الله محمد بن معاذ الجياني, noto nel mondo cristiano latino come Abenmoat, Abumadh, Abhomadh o Abumaad (Cordova, 989 – Jaén, 1079), è stato un matematico e astronomo arabo di al-Andalus, un illustre scienziato e un dotto giurisperito, tanto da essere nominato dalle autorità omayyadi andaluse Qāḍī.

[ru] Ибн Муаз аль-Джайяни

Абу Абд-Аллах Мухаммад ибн Юсуф ибн Ахмад ибн Му‘аз ал-Джайяни (англ. Abu Abd Allah Muhammad Al-Jayyani, Кордова, 989 — Хаэн, 1050 ?) — западноарабский математик, астроном и законовед. В 1012—1016 жил в Египте. Впоследствии был судьей и везиром в Севилье. В Европе был известен как Abhomadi Malfegeyr.


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