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Abū ʿAbd Allāh Muḥammad ibn Jābir ibn Sinān al-Raqqī al-Ḥarrānī aṣ-Ṣābiʾ al-Battānī [n 1](Arabic: محمد بن جابر بن سنان البتاني) (Latinized as Albategnius, Albategni or Albatenius) (c. 858 – 929) was an astronomer and mathematician from Harran. He introduced a number of trigonometric relations, and his Kitāb az-Zīj was frequently quoted by many medieval astronomers, including Copernicus.[2] Often called the "Ptolemy of the Arabs",[3] al-Battani is perhaps one of the greatest and best known astronomer of the medieval Islamic world.[4][5][6][7]

Al-Battānī
A modern artist's impression of al-Battānī holding an astrolabe
Born	c. 858 CE Harran, the Jazira (Upper Mesopotamia) (now in Şanlıurfa Province, Turkey)
Died	929 CE Qasr al-Jiss, near Samarra
Academic background
Influences	Ptolemy
Academic work
Era	Islamic Golden Age
Main interests	Mathematics, Astronomy, Astrology
Notable works	Kitāb az-Zīj
Notable ideas	Trigonometrical relationships
Influenced	Abū al-Wafā', al-Bīrūnī, Copernicus

Life

Little of al-Battānī's life is known other than his birthplace in Harran near Urfa, in Upper Mesopotamia, (today in Turkey) and his father's fame as a maker of scientific instruments.[2] Jabir ibn Sinan al-Harrani was likely this famous instrument maker, although this is not something that has been proven.[8] His epithet aṣ-Ṣabi’ suggests that his family belonged to the Sabian religion of Harran,[9][10][11] an obscure pagan belief which may have featured star worship.[12] Although his ancestors were likely Sabian, he himself was Muslim, as can be seen from his Muslim name Abu Abd Allah Muhammad.[8] The Encyclopædia Britannica Eleventh Edition stated that he had noble origins as an Arab prince,[13] but traditional Arabic biographers make no mention of this.[2] Between 877 and 918/19, over a forty-year period, he lived in the ancient city of Raqqa, in north central Syria, recording his astronomical observations. He died at Qasr al-Jiss, which is located near Samarra, Iraq.[8] He was returning from Baghdad to Raqqa after resolving a dispute on behalf of the people of Raqqa.[8]

Astronomy

One of al-Battānī's best-known achievements in astronomy was the determination of the solar year as being 365 days, 5 hours, 46 minutes and 24 seconds, which is only 2 minutes and 22 seconds off.[10]

Another of al-Battānī's accomplishments is that he concluded how an annular solar eclipse occurs.[8] He did this by observing that the radius between the Earth and the Sun changes throughout the year.[8] This led him to arrive to the conclusion that when the Sun is farthest from the Earth, an annular solar eclipse occurs.[8][14] He was the first to make this observation and inference.

The twelfth-century Egyptian encyclopedist al-Qifṭī, in his biographical history Ta’rīkh al-Ḥukamā’, mentions al-Battānī’s contribution to advances in astronomical observation and calculations based on Ptolemy’s Almagest.[1]

Al-Battānī amended some of Ptolemy's results and compiled new tables of the Sun and Moon, long accepted as authoritative.[13] Some of his measurements were more accurate than ones taken by Copernicus many centuries later and some ascribe this phenomenon to al-Battānī's location lying closer to the equator such that the ecliptic and the Sun, being higher in the sky, are less susceptible to atmospheric refraction.[10] Al-Battānī observed that the direction of the Sun's apogee, as recorded by Ptolemy, was changing.[15] [n 2]

Al-Battānī's work was instrumental in the development of science and astronomy.[10] Copernicus, in his book that initiated the Copernican Revolution, the De Revolutionibus Orbium Coelestium, quotes his name no fewer than 23 times,[16] and also mentions him in the Commentariolus.[17] Tycho Brahe, Riccioli, Kepler, Galileo and others frequently cited him or his observations.[2] He also influenced Jewish rabbis and philosophers such as Abraham ibn Ezra, Abraham bar Hiyya, and Maimonides.[8] His data is still used in geophysics.[18] The major lunar crater Albategnius is named in his honor.[19]

Among his Innovations

• Introduction [n 3] of the use of sines in calculation and partially that of tangents.[13]
• Calculation of the values for the precession of the equinoxes (54.5" per year, or 1° in 66 years) and the obliquity of the ecliptic (23° 35').[10]
• Use of a uniform rate for precession in his tables, choosing not to adopt the theory of trepidation attributed to his colleague Thabit ibn Qurra.

Mathematics

In mathematics, al-Battānī produced a number of trigonometrical relationships:

${\displaystyle \tan a={\frac {\sin a}{\cos a}}}$

${\displaystyle \sec a={\sqrt {1+\tan ^{2}a}}}$

He also solved the equation sin x = a cos x discovering the formula:

${\displaystyle \sin x={\frac {a}{\sqrt {1+a^{2}}}}}$

He gives other trigonometric formulae for right-angled triangles such as:[10]

${\displaystyle b\sin(A)=a\sin(90^{\circ }-A)}$

Al-Battānī used al-Marwazi's idea of tangents ("shadows") to develop equations for calculating tangents and cotangents, compiling tables of them. He also discovered the reciprocal functions of secant and cosecant, and produced the first table of cosecants, which he referred to as a "table of shadows" (in reference to the shadow of a gnomon), for each degree from 1° to 90°.[20]

Using these trigonometrical relationships, Al-Battānī created an equation for finding the qibla, which Muslims must face in each of the five prayers they practice every day.[21] The equation he created did not give accurate directions, as it did not take into account the fact that Earth is a sphere.[21] The relationship Al-Battānī used was fairly precise when a person is in Mecca, or close to Mecca, but resulted in more and more inaccurate results as one gets more distant from Mecca.[21] However, it was still a widely used method at the time. The equation is as follows:[21]

${\displaystyle \alpha =\arctan {\frac {\sin \Delta \lambda }{\sin \Delta \phi }}}$

Works

• Kitāb az-Zīj (كتاب الزيج or زيج البتاني, "Book of Astronomical Tables"); Al-Battānī's magnum opus reflects Ptolemaic and Greco-Syriac astronomical theory, with Indo-Persian influences to a lesser degree.[2][22] The word zij is a Persian word that was used to describe a rug warp.[8] Al-Battānī's zij contains a description of a quadrant instrument.[23] Of the many early translations into Latin and Spanish, a Latin version De Motu Stellarum by Plato of Tivoli (1116), was reprinted with annotations by Regiomontanus,[13] and again at Bologna in 1645. The original manuscript is preserved at the Vatican library in Rome.[13]
  • De scientia stellarum (in Latin). Bologna: Vittorio Benacci, eredi. 1645.
• Kitāb az-Zīj aṣ-Ṣābi’ (كتاب الزيج الصابئ) published by Carlo Alfonso Nallino (1899-1907) under the Latin title Al-Battānī sive Albatenii opus astronomicum: ad fidem codicis Escurialensis Arabice editum;[24] a multi-volume scientific treatise on geography and astronomical chronology from an Arabic manuscript with Latin annotations. The manuscript is held at the Escorial library.
• Arbaʻu Maqālāt (أربع مقالات, "Four discourses");[25] a commentary on Ptolemy’s Quadripartitum de apotelesmatibus e judiciis astrorum, known as the Tetrabiblos. The tenth-century encyclopedist Isḥāq al-Nadīm in his Kitāb al-Fihrist lists al-Battānī among a number of authors of commentaries on this work.[26][n 4]
• Maʻrifat Maṭāliʻi l-Burūj (معرفة مطالع البروج, "Knowledge of the rising-places of the zodiacal signs")[n 5][28]
• Kitāb fī Miqdār al-Ittiṣālāt (كتاب في مقدار الاتصالات); treatise on the four quarters of the sphere.

In popular culture

A ship in Star Trek: Voyager is named after Al-Battānī, known as the USS Al-Batani, on which Kathryn Janeway originally served.

Eponyms

Albategnius (crater)

See also

• Category:Sabian Scholars of the Abbasid Caliphate
• List of Arab scientists and scholars
• Thābit ibn Qurra
• Zij

Notes

References

Citations

Cited sources

• Al-Battānī sive Albatenii, Opus Astronomicum. Ad fidem codicis escurialensis arabice editum, ed. by Carlo Alfonso Nallino. Milan, Ulrico Hoepli, 1899-1907 [= Pubblicazioni del Reale Osservatorio di Brera in Milano, nr. XL], 412 + 450 + 288 pp. (anast.: I-III, [La Finestra editrice], Lavis 2002 ISBN 978-8888097-26-8
• Battani (al-), Muḥammad ibn Jabir (1899). Nallino, Carlo Alfonso (ed.). Al-Battānī sive Albatenii opus astronomicum: ad fidem codicis Escurialensis Arabice editum (Kitāb Zīj al-Ṣābī') (in Arabic). Vol. 3. Milan: Mediolani Insubrum: Prostat apud Urlichum Hoeplium. ISBN 978-8888097-26-8.
• Khallikān (ibn), Aḥmad i. M (1868). Mac Guckin de Slane, William (ed.). Wafayāt al-A'yān wa Anbā' (Ibn Khallian's Biographical Dictionary). Vol. III. Paris & London: W.H. Allen. p. 317.
• Nadīm (al-), Abū al-Faraj Muḥammad ibn Isḥāq Abū Ya’qūb al-Warrāq (1970). Dodge, Bayard (ed.). The Fihrist of al-Nadim; a tenth-century survey of Muslim culture. New York & London: Columbia University Press.
• Qifṭī (al-), Jamāl al-Dīn Abū al-Ḥasan ‘Alī ibn Yūsuf (1903). Lippert, Julius (ed.). Ta'rīkh al-Ḥukamā' (in Arabic). Leipzig: Theodor Weicher. p. 280.

Further reading

• Sarton, George (1947). Introduction to the History of Science. Vol. I. Baltimore: Williams and Wilkins. p. 602.
• Smith, David Eugene (1925) [1923]. History of Mathematics. Vol. I. Boston: Ginn. p. 175.
• Hartner, Willy (1970–1980). "Al-Battānī, Abū ʿAbd Allāh Muḥammad Ibn Jābir Ibn Sinān al-Raqqī al-Ḥarrānī al–Ṣābi". Dictionary of Scientific Biography. New York: Charles Scribner's Sons. ISBN 978-0-684-10114-9.
• O'Connor, John J.; Robertson, Edmund F., "Abu Abdallah Mohammad ibn Jabir Al-Battani", MacTutor History of Mathematics archive, University of St Andrews

External links

• Dalen, Benno van (2007). "Battānī: Abū ʿAbd Allāh Muḥammad ibn Jābir ibn Sinān al‐Battānī al‐Ḥarrānī al‐Ṣābiʾ". In Thomas Hockey; et al. (eds.). The Biographical Encyclopedia of Astronomers. New York: Springer. pp. 101–3. ISBN 978-0-387-31022-0. (PDF version)
• Weisstein, Eric Wolfgang (ed.). "Albategnius (ca. 858–929)". ScienceWorld.
• Texts on Wikisource:
  • Gilman, D. C.; Peck, H. T.; Colby, F. M., eds. (1905). "al-Battani, Mohammed ibn Jabir ibn Sinan". New International Encyclopedia (1st ed.). New York: Dodd, Mead.
  • "Albategnius". Encyclopædia Britannica. Vol. 1 (11th ed.). 1911. p. 491.
  • "al-Battani". New International Encyclopedia. 1920.

На других языках

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[de] Al-Battani

Mohammed ibn Dschābir al-Battānī (أبو عبد الله محمد بن جابر بن سنان الحراني الصابي البتاني Abū ʿAbdullāh Muhammad ibn Dschābir ibn Sinān al-Harrānī as-Sābī al-Battānī, DMG Abū ʿAbdullāh Muḥammad ibn Ǧābir ibn Sinān al-Ḥarrānī aṣ-Ṣābī al-Battānī), latinisiert Albategnius oder Albatanius (* etwa zwischen 850 und 869 in Harran nahe Şanlıurfa – heute Türkei; † 929 auf der Reise von Bagdad nach Raqqa in Qasr al-Dschiss bei Samarra) war ein arabischer Gelehrter und gilt als einer der größten Astronomen im Nahen Osten.

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- [en] Al-Battani

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[es] Al-Battani

Al-Batani (c. 858–929), fue un príncipe, astrónomo, astrólogo y matemático árabe. Su nombre completo es Abū `Abd Allāh Muḥammad ibn Jābir ibn Sinān al-Raqqī al-Ḥarrānī aṣ-Ṣābi` al-Battānī (en idioma árabe أبو عبد الله محمد بن جابر بن سنان الحراني الصابي البتاني), latinizado como Albategnius, Albategni o Albatenius y deriva de su ciudad natal Harrán, cerca de Urfa (Mesopotamia), en la actual Turquía.

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[ru] Аль-Баттани

Абу Абдулла́х Муха́ммад ибн Джаби́р ибн Синан ар-Ракки аль-Харрани ас-Саби аль-Батта́ни (араб. أبو عبد الله محمد بن جابر بن سنان الحراني الصابي البتاني‎, Харран, 858 — Самарра, 929) — выдающийся средневековый арабский астроном и математик. В средневековой Европе был известен под латинизированным именем Альбатений (лат. Albategnius).

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