Jabir ibn Aflah
Encyclopedia
Abū Muḥammad Jābir ibn Aflaḥ was a Muslim astronomer
and mathematician
from Seville
, who was active in 12th century Andalusia
. His work Iṣlāḥ al-Majisṭi (Correction of the Almagest) influenced Islamic, Jewish and Christian
astronomers.
This work is a commentary and reworking of Ptolemy
's Almagest
and is the first criticism of it in the Islamic West. He particularly criticized the mathematical basis of the work. For example he replaced the use of Menelaus' theorem
with ones based on spherical trigonometry
, in what seems to be an attempt to increase the mathematical precision of the work. These theorems had been developed by a group of 10th century Islamic mathematicians who included Abū al-Wafā' Būzjānī and then also by Abu Abd Allah Muhammad ibn Muadh Al-Jayyani
who worked in Andalusia during the 11th century. Jābir doesn't credit any of these authors and doesn't refer to a single Islamic author in this work.
One substantial change Jābir made to Ptolemy's account is that he placed the orbits of Venus
and Mercury
, the minor planets, outside that of the Sun
, rather than between the Moon
and the Sun as had been the case in the original work.
He invented an observational instrument known as the torquetum
, a mechanical device to transform between spherical coordinate systems.
Several later Islamic authors were influenced by Jābir, including Ibn Rushd
(Averroes) and Nur ad-Din al-Betrugi, both of whom worked in Andalusia. The work was transmitted to Egypt
in the 12th century by Maimonides
and further east by the end of the 13th century.
The work was translated from the Arabic into both Hebrew and Latin
, the latter by Gerard of Cremona
, who Latinized his name as "Geber". Through that channel it had a wide influence on later Europe
an mathematicians and astronomers and helped to promote trigonometry
in Europe.
Much of the material on spherical trigonometry in Regiomontanus
' On Triangles (c.1463) was taken directly and without credit from Jābir's work, as noted in the 16th century by Gerolamo Cardano
.
The trigonometry that Nicholas Copernicus (1473–1543) outlined in the first part of his epochal work De revolutionibus was also apparently inspired by Jābir.
Islamic astronomy
Islamic astronomy or Arabic astronomy comprises the astronomical developments made in the Islamic world, particularly during the Islamic Golden Age , and mostly written in the Arabic language. These developments mostly took place in the Middle East, Central Asia, Al-Andalus, and North Africa, and...
and mathematician
Islamic mathematics
In the history of mathematics, mathematics in medieval Islam, often termed Islamic mathematics or Arabic mathematics, covers the body of mathematics preserved and developed under the Islamic civilization between circa 622 and 1600...
from Seville
Seville
Seville is the artistic, historic, cultural, and financial capital of southern Spain. It is the capital of the autonomous community of Andalusia and of the province of Seville. It is situated on the plain of the River Guadalquivir, with an average elevation of above sea level...
, who was active in 12th century Andalusia
Al-Andalus
Al-Andalus was the Arabic name given to a nation and territorial region also commonly referred to as Moorish Iberia. The name describes parts of the Iberian Peninsula and Septimania governed by Muslims , at various times in the period between 711 and 1492, although the territorial boundaries...
. His work Iṣlāḥ al-Majisṭi (Correction of the Almagest) influenced Islamic, Jewish and Christian
Christian
A Christian is a person who adheres to Christianity, an Abrahamic, monotheistic religion based on the life and teachings of Jesus of Nazareth as recorded in the Canonical gospels and the letters of the New Testament...
astronomers.
This work is a commentary and reworking of Ptolemy
Ptolemy
Claudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...
's Almagest
Almagest
The Almagest is a 2nd-century mathematical and astronomical treatise on the apparent motions of the stars and planetary paths. Written in Greek by Claudius Ptolemy, a Roman era scholar of Egypt,...
and is the first criticism of it in the Islamic West. He particularly criticized the mathematical basis of the work. For example he replaced the use of Menelaus' theorem
Menelaus' theorem
Menelaus' theorem, named for Menelaus of Alexandria, is a theorem about triangles in plane geometry. Given a triangle ABC, and a transversal line that crosses BC, AC and AB at points D, E and F respectively, with D, E, and F distinct from A, B and C, thenThis equation uses signed lengths of...
with ones based on spherical trigonometry
Spherical trigonometry
Spherical trigonometry is a branch of spherical geometry which deals with polygons on the sphere and the relationships between the sides and the angles...
, in what seems to be an attempt to increase the mathematical precision of the work. These theorems had been developed by a group of 10th century Islamic mathematicians who included Abū al-Wafā' Būzjānī and then also by Abu Abd Allah Muhammad ibn Muadh Al-Jayyani
Al-Jayyani
Abū ʿAbd Allāh Muḥammad ibn Muʿādh al-Jayyānī was a mathematician, Islamic scholar, and Qadi from Al-Andalus...
who worked in Andalusia during the 11th century. Jābir doesn't credit any of these authors and doesn't refer to a single Islamic author in this work.
One substantial change Jābir made to Ptolemy's account is that he placed the orbits of Venus
Venus
Venus is the second planet from the Sun, orbiting it every 224.7 Earth days. The planet is named after Venus, the Roman goddess of love and beauty. After the Moon, it is the brightest natural object in the night sky, reaching an apparent magnitude of −4.6, bright enough to cast shadows...
and Mercury
Mercury (planet)
Mercury is the innermost and smallest planet in the Solar System, orbiting the Sun once every 87.969 Earth days. The orbit of Mercury has the highest eccentricity of all the Solar System planets, and it has the smallest axial tilt. It completes three rotations about its axis for every two orbits...
, the minor planets, outside that of the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
, rather than between the Moon
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...
and the Sun as had been the case in the original work.
He invented an observational instrument known as the torquetum
Torquetum
The torquetum or turquet is a medieval astronomical instrument designed to take and convert measurements made in three sets of coordinates: Horizon, equatorial, and ecliptic...
, a mechanical device to transform between spherical coordinate systems.
Influence
Averroes
' , better known just as Ibn Rushd , and in European literature as Averroes , was a Muslim polymath; a master of Aristotelian philosophy, Islamic philosophy, Islamic theology, Maliki law and jurisprudence, logic, psychology, politics, Arabic music theory, and the sciences of medicine, astronomy,...
(Averroes) and Nur ad-Din al-Betrugi, both of whom worked in Andalusia. The work was transmitted to Egypt
Egypt
Egypt , officially the Arab Republic of Egypt, Arabic: , is a country mainly in North Africa, with the Sinai Peninsula forming a land bridge in Southwest Asia. Egypt is thus a transcontinental country, and a major power in Africa, the Mediterranean Basin, the Middle East and the Muslim world...
in the 12th century by Maimonides
Maimonides
Moses ben-Maimon, called Maimonides and also known as Mūsā ibn Maymūn in Arabic, or Rambam , was a preeminent medieval Jewish philosopher and one of the greatest Torah scholars and physicians of the Middle Ages...
and further east by the end of the 13th century.
The work was translated from the Arabic into both Hebrew and Latin
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...
, the latter by Gerard of Cremona
Gerard of Cremona
Gerard of Cremona was an Italian translator of Arabic scientific works found in the abandoned Arab libraries of Toledo, Spain....
, who Latinized his name as "Geber". Through that channel it had a wide influence on later Europe
Europe
Europe is, by convention, one of the world's seven continents. Comprising the westernmost peninsula of Eurasia, Europe is generally 'divided' from Asia to its east by the watershed divides of the Ural and Caucasus Mountains, the Ural River, the Caspian and Black Seas, and the waterways connecting...
an mathematicians and astronomers and helped to promote trigonometry
Trigonometry
Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...
in Europe.
Much of the material on spherical trigonometry in Regiomontanus
Regiomontanus
Johannes Müller von Königsberg , today best known by his Latin toponym Regiomontanus, was a German mathematician, astronomer, astrologer, translator and instrument maker....
' On Triangles (c.1463) was taken directly and without credit from Jābir's work, as noted in the 16th century by Gerolamo Cardano
Gerolamo Cardano
Gerolamo Cardano was an Italian Renaissance mathematician, physician, astrologer and gambler...
.
The trigonometry that Nicholas Copernicus (1473–1543) outlined in the first part of his epochal work De revolutionibus was also apparently inspired by Jābir.