Al-Battānī

Abū ʿAbd Allāh Muḥammad ibn Jābir ibn Sinān al-Raqqī al-Ḥarrānī aṣ-Ṣābiʾ al-Battānī ( ar, 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.
Often called the "Ptolemy of the Arabs", al-Battani is perhaps one of the greatest and best known astronomer of the medieval Islamic world.

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. Jabir ibn Sinan al-Harrani was likely this famous instrument maker, although this is not something that has been proven. His epithet ''aṣ-Ṣabi’'' suggests that his family belonged to the Sabian religion of Harran, an obscure pagan belief which may have featured star worship. Although his ancestors were likely Sabian, he himself was Muslim, as can be seen from his Muslim name Abu Abd Allah Muhammad. The ''Encyclopædia Britannica Eleventh Edition'' stated that he had noble origins as an Arab prince, but traditional Arabic biographers make no mention of this. 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. He was returning from Baghdad to Raqqa after resolving a dispute on behalf of the people of Raqqa.

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.

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

Al-Battānī amended some of Ptolemy's results and compiled new tables of the Sun and Moon, long accepted as authoritative. 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. Al-Battānī observed that the direction of the Sun's apogee, as recorded by Ptolemy, was changing.

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

Among his Innovations

*Introduction of the use of sines in calculation and partially that of tangents.
*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').
*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:

::$\tan a = \frac$

::$\sec a = \sqrt$

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

::$\sin x = \frac$

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

::$b \sin (A) = a \sin (90^\circ - A)$

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°.

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. The equation he created did not give accurate directions, as it did not take into account the fact that Earth is a sphere. 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. However, it was still a widely used method at the time. The equation is as follows:

$\alpha=\arctan\frac$

Works

*''Kitāb az-Zīj'' ( or , "Book of Astronomical Tables"); Al-Battānī's magnum opus reflects Ptolemaic and Greco-Syriac astronomical theory, with Indo-Persian influences to a lesser degree.E. S. Kennedy, ''A Survey of Islamic Astronomical Tables,'' (Transactions of the American Philosophical Society, New Series, 46, 2), Philadelphia, 1956, pp. 10–11, 32–34. The word z''ij'' is a Persian word that was used to describe a rug warp. Al-Battānī's '' zij'' contains a description of a quadrant instrument. 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, and again at Bologna in 1645. The original manuscript is preserved at the Vatican library in Rome.
**
*''Kitāb az-Zīj aṣ-Ṣābi’'' () published by Carlo Alfonso Nallino (1899-1907) under the Latin title ''Al-Battānī sive Albatenii opus astronomicum: ad fidem codicis Escurialensis Arabice editum''; 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'' (, "Four discourses"); 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.
*''Maʻrifat Maṭāliʻi l-Burūj'' (, "Knowledge of the rising-places of the zodiacal signs")
*''Kitāb fī Miqdār al-Ittiṣālāt'' (); 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

* :Sabian scholars from 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, a Finestra editrice Lavis 2002
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Further reading

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External links

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PDF version

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{{DEFAULTSORT:Battani
850s births
929 deaths
Year of birth uncertain
9th-century Arabs
10th-century Arabs
9th-century astrologers
9th-century astronomers
9th-century mathematicians
9th-century people from the Abbasid Caliphate
10th-century astrologers
10th-century astronomers
10th-century mathematicians
Astronomers from the Abbasid Caliphate
Astrologers of the medieval Islamic world
People from Harran
Scientists who worked on qibla determination
Mathematicians from the Abbasid Caliphate
Sabian scholars from the Abbasid Caliphate