**Al-Jayyani** was an Islamic mathematician working in Spain. He wrote important commentaries on Euclid's Elements and he wrote the first treatise on spherical trigonometry.

- Even the identification of al-Jayyani the mathematician with al-Jayyani the Spanish scholar who was born in Cordoba in 989 is not absolutely certain.
- Al-Jayyani, the mathematician, is described as a judge and a jurist in one of his treatises.
- The only possible problem to the identification is that al-Jayyani wrote a treatise on the total solar eclipse which occurred in Jaén on 1 July 1079.
- The only other facts known about al-Jayyani's life are that he lived in Cairo from 1012 to 1017 and that he must have undertaken most of his work in Jaén, the city at the centre of the Moorish principality of Jayyan.
- This cannot only be deduced from his name "al-Jayyani" which means "from Jaén", but also from the fact that the astronomical tables that he produced were for the longitude of Jaén.
- Al-Jayyani's work On ratio is almost certainly his most interesting mathematical work.
- In this work al-Jayyani sets out to defend Euclid's Elements Book V.
- There are five magnitudes that, according to al-Jayyani, are used in geometry; number, line, surface, angle, and solid.
- Neither Euclid nor any other Greek mathematician would have considered "number" as a geometrical magnitude, but al-Jayyani needs the notion for his definition of ratio which follows the Arabic idea of number.
- After assuming that every intelligent person has a basic understanding of ratio, al-Jayyani deduces further properties based on this "commonly understood definition".
- Another work of great importance is al-Jayyani's The book of unknown arcs of a sphere, the first treatise on spherical trigonometry.
- Al-Jayyani was to have a strong influence on European mathematics.
- Among the similarities between al-Jayyani's treatise and that of Regiomontanus are the definition of ratios as numbers, the lack of a tangent function, and a similar method of solving a spherical triangle when all sides are unknown.
- Although it is certain that Regiomontanus based his treatise on Arabic works on spherical trigonometry it may well be that al-Jayyani's work was only one of many such sources.
- Work by al-Jayyani on astronomy was also important.
- In the Tabulae Jahen al-Jayyani gave data to enable the calculation of the time of day, the calendar, the new moon, eclipses and information required for the timing and direction for prayers.
- Al-Jayyani seems to have considerable respect for al-Khwarizmi's astronomical data, which he freely used, but he rejects the ideas of al-Khwarizmi on astrology.
- Much of al-Jayyani's astrology is based on Hindu sources.

Born 989, Cordoba, Andalusia (now Spain). Died after 1079, possibly Jaén, Andalusia (now Spain).

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Astronomy, Origin Spain

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive