Al-Battani

Template:Short description Template:Redirect Template:Good article Template:Lowercase title Template:Use British English Template:Infobox academic Al-BattaniTemplate:Efn (before 858Template:Snd929), archaically Latinized as Albategnius,Template:Efn was a Muslim astronomer, astrologer, geographer and mathematician, who lived and worked for most of his life at Raqqa, now in Syria. He is considered to be the greatest and most famous of the astronomers of the medieval Islamic world.

Al-Battānī's writings became instrumental in the development of science and astronomy in the west. His Template:Transliteration (Template:Circa), is the earliest extant Template:Transliteration (astronomical table) made in the Ptolemaic tradition that is hardly influenced by Hindu or Sasanian astronomy. Al-Battānī refined and corrected Ptolemy's Almagest, but also included new ideas and astronomical tables of his own. A handwritten Latin version by the Italian astronomer Plato Tiburtinus was produced between 1134 and 1138, through which medieval astronomers became familiar with al-Battānī. In 1537, a Latin translation of the Template:Transliteration was printed in Nuremberg. An annotated version, also in Latin, published in three separate volumes between 1899 and 1907 by the Italian Orientalist Carlo Alfonso Nallino, provided the foundation of the modern study of medieval Islamic astronomy.

Al-Battānī's observations of the Sun led him to understand the nature of annular solar eclipses. He accurately calculated the Earth's obliquity (the angle between the planes of the equator and the ecliptic), the solar year, and the equinoxes (obtaining a value for the precession of the equinoxes of one degree in 66 years). The accuracy of his data encouraged Nicolaus Copernicus to pursue ideas about the heliocentric nature of the cosmos. Al-Battānī's tables were used by the German mathematician Christopher Clavius in reforming the Julian calendar, and the astronomers Tycho Brahe, Johannes Kepler, Galileo Galilei and Edmund Halley all used Al-Battānī's observations.

Al-Battānī introduced the use of sines and tangents in geometrical calculations, replacing the geometrical methods of the Greeks. Using trigonometry, he created an equation for finding the Template:Transliteration (the direction which Muslims need to face during their prayers). His equation was widely used until superseded by more accurate methods, introduced a century later by the polymath al-Biruni.

LifeEdit

Al-Battānī, whose full name was Template:Transliteration, and whose Latinized name was Template:Transliteration, was born before 858 in Harran in Bilād ash-Shām (Islamic Syria), Template:Convert southeast of the modern Turkish city of Urfa. He was the son of Jabir ibn Sinan al-Harrani, a maker of astronomical instruments.Template:Sfn The epithet Template:Transliteration suggests that his family belonged to the pagan Sabian sect of Harran,Template:Sfn<ref name="OCoRob" /> whose religion featured star worship, and who had inherited the Mesopotamian legacy of an interest in mathematics and astronomy.Template:Sfn Template:Efn His contemporary, the polymath Thābit ibn Qurra, was also an adherent of Sabianism, which died out during the 11th century.Template:Sfn

Although his ancestors were likely Sabians, al-Battānī was a Muslim, as shown by his first name.<ref name="OCoRob" /> Between 877 and 918/19 he lived in Raqqa, now in north central Syria, which was an ancient Roman settlement beside the Euphrates, near Harran. During this period he also lived in Antioch,Template:Sfn where he observed a solar and a lunar eclipse in 901. According to the Arab biographer Ibn al-Nadīm, the financial problems encountered by al-Battānī in old age forced him to move from Raqqa to Baghdad.Template:Sfn

Al-Battānī died in 929 at Qasr al-Jiss,Template:Sfn near Samarra, after returning from Baghdad where he had resolved an unfair taxation grievance on behalf of a clan from Raqqa.Template:Sfn

AstronomyEdit

Al-Battānī is considered to be the greatestTemplate:Sfn Template:Sfn<ref name=Ben-Menaḥem>Template:Cite encyclopedia</ref> and most famous of the known astronomers of the medieval Islamic world. He made more accurate observations of the night sky than any of his contemporaries,Template:Sfn and was the first of a generation of new Islamic astronomers that followed the founding of the House of Wisdom in the 8th century.Template:Sfn His meticulously described methods allowed others to assess his results, but some of his explanations about the movements of the planets were poorly written, and have mistakes.Template:Sfn

Sometimes referred to as the "Ptolemy of the Arabs",Template:Sfn al-Battānī's works reveal him to have been a devout believer in Ptolemy's geocentric model of the cosmos. He refined the observations found in Ptolemy's {{#invoke:Lang|lang}},Template:Sfn and compiled new tables of the Sun and the Moon, previously long accepted as authoritative.<ref name="OCoRob" /> Al-Battānī established his own observatory at Raqqa. He recommended that the astronomical instruments there were greater than Template:Convert in size.Template:Sfn Such instruments, being larger—and so having scales capable of measuring smaller values—were capable of greater precision than had previously been achieved.Template:Sfn Some of his measurements were more accurate than those taken by the Polish astronomer and mathematician Nicolaus Copernicus during the Renaissance. One reason for this is thought to be that al-Battānī's location for his observations at Raqqa was closer to the Earth's equator, so that the ecliptic and the Sun, being higher in the sky, were less susceptible to atmospheric refraction.<ref name="OCoRob" /> The careful construction and alignment of his astronomical instruments enabled him to achieve an accuracy of observations of equinoxes and solstices that had previously been unknown.Template:Sfn

Template:Multiple image Al-Battānī was one of the first astronomers to observe that the distance between the Earth and the Sun varies during the year, which led him to understand the reason why annular solar eclipses occur.Template:Sfn<ref name="Gal">Template:Cite journal</ref>Template:Sfn He saw that the position in the sky at which the angular diameter of the Sun appeared smallest was no longer located where Ptolemy had stated it should be,Template:Sfn and that since Ptolemy's time, the longitudinal position of the apogee had increased by 16°47'.Template:R

Al-Battānī was an excellent observer.Template:Sfn He improved Ptolemy's measurement of the obliquity of the ecliptic (the angle between the planes of the equator and the ecliptic),Template:Sfn producing a value of 23° 35';<ref name="OCoRob" />Template:Efn the accepted value is around 23°.44.<ref name="Inf">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> Al-Battānī obtained the criterion for observation of the lunar crescent—i.e., if the longitude difference between the Moon and the Sun is greater than 13° 66˝ and the Moon's delay after sunset is more than 43.2 minutes, the crescent will be visible.Template:Sfn His value for the solar year of 365 days, 5 hours, 46 minutes and 24 seconds, is 2 minutes and 22 seconds from the accepted value.<ref name="OCoRob">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

Al-Battānī observed changes in the direction of the Sun's apogee, as recorded by Ptolemy,Template:Sfn and that as a result, the equation of time was subject to a slow cyclical variation.Template:Sfn His careful measurements of when the March and September equinoxes took place allowed him to obtain a value for the precession of the equinoxes of 54.5" per year, or 1 degree in 66 years,<ref name="OCoRob" />Template:Sfn a phenomenon that he realised was altering the Sun's annual apparent motion through the zodiac constellations.Template:Sfn

It was impossible for al-Battānī, who adhered to the ideas of a stationary Earth and geocentricism, to understand the underlying scientific reasons for his observations or the importance of his discoveries.Template:Sfn

MathematicsEdit

Template:Multiple image

One of al-Battani's greatest contributions was his introduction of the use of sines and tangents in geometrical calculations, especially spherical trigonometric functions, to replace Ptolemy's geometrical methods. Al-Battānī's methods involved some of the most complex mathematics developed up to that time.Template:Sfn He was aware of the superiority of trigonometry over geometrical chords, and demonstrated awareness of a relation between the sides and angles of a spherical triangle, now given by the expression:Template:R

Al-Battānī produced a number of trigonometrical relationships:<ref name="Mao" />

<math>\tan \alpha = \frac{\sin \alpha}{\cos \alpha}</math>

<math>\sec \alpha = \sqrt{1 + \tan^2 \alpha }</math>, where <math>\sec \alpha = \frac{1}{\cos \alpha}</math>.

He also solved the equation

<math>\sin x = y\cos x</math>,

discovering the formula

Al-Battānī used the Iranian astronomer Habash al-Hasib al-Marwazi's idea of tangents to develop equations for calculating and compiling tables of both tangents and cotangents. He discovered their reciprocal functions, the secant and cosecant, and produced the first table of cosecants for each degree from 1° to 90°, which he referred to as a "table of shadows", in reference to the shadow produced on a sundial.<ref name=Mao>Template:Cite book</ref>

File:Qibla diagram 2.svg

A geometrical representation of the method used by al-Battānī to determine the Template:Transliteration, shown as q from O (the observer) to M (Mecca)Template:Sfn Template:Efn

Using these trigonometrical relationships, al-Battānī created an equation for finding the {{#invoke:Lang|lang}}, which Muslims face in each of the five prayers they practice every day.Template:Sfn 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 he used was precise enough only for a person located in (or close to) Mecca, but was still a widely used method at the time. Al-Battānī's equation for <math>q</math>, the angle of the direction of a place towards Mecca is given by:Template:Sfn

<math>\tan q=\frac{\sin\Delta\lambda}{\sin\Delta\phi}</math>

where <math>\Delta\lambda</math> is the difference between the longitude of the place and Mecca, and <math>\Delta\phi</math> is the difference between the latitude of the place and Mecca.

Al-Battānī's equation was superseded a century after it was first used, when the polymath al-Biruni summarized several other methods to produce results that were more accurate than those that could be obtained using al-Battānī's equation.Template:Sfn

A small work on trigonometry, Template:Transliteration ("Summary of the principles for establishing sines") is known. Once attributed to the Iranian astronomer Kushyar Gilani by the German orientalist Carl Brockelmann, it is a fragment of al-Battānī's Template:Transliteration. The manuscript is extant in Istanbul as MS Carullah 1499/3.Template:Sfn The authenticity of this work has been questioned, as scholars believe al-Battānī would have not have included Template:Transliteration for "sines" in the title.Template:Sfn

WorksEdit

Template:TransliterationEdit

Al-Battānī's Template:Transliteration ({{#invoke:Lang|lang}} or {{#invoke:Lang|lang}}, "Book of Astronomical Tables"), written in around 900, and also known as the Template:Transliteration ({{#invoke:Lang|lang}}),Template:Sfn is the earliest extant Template:Transliteration made in the Ptolemaic tradition that is hardly influenced by Hindu or Sasanian–Iranian astronomy.Template:Sfn It corrected mistakes made by Ptolemy and described instruments such as horizontal and vertical sundials, the triquetrum, the mural instrument,Template:Sfn and a quadrant instrument.Template:Sfn Ibn al-Nadim wrote that al-Battānī's Template:Transliteration existed in two different editions, "the second being better than the first".Template:Sfn In the west, the work was sometimes called the Sabean Tables.Template:Sfn

The work, consisting of 57 chapters and additional tables, is extant (in the manuscript árabe 908, held in El Escorial), copied in Al-Andalus during the 12th or 13th century. Incomplete copies exist in other western European libraries.Template:Sfn Much of the book consists of instructions for using the attached tables. Al-Battānī used an Arabic translation of the Almagest made from Syriac, and used few foreign terms. He copied some data directly from Ptolemy's Handy Tables, but also produced his own. His star table of 880 used around half the stars found in the then 743-year-old Almagest. It was made by increasing Ptolemy's stellar longitudes, to allow for the different positions of the stars, now known to be caused by precession.Template:Sfn

Other Template:Transliteration based on Template:Transliteration include those written by Kushyar Gilani, Alī ibn Ahmad al-Nasawī, Abū Rashīd Dāneshī, and Ibn al-Kammad.Template:Sfn

The first version in Latin from the Arabic was made by the English astronomer Robert of Ketton; this version is now lost.Template:Sfn Template:Sfn A Latin edition was also produced by the Italian astronomer Plato Tiburtinus between 1134 and 1138.Template:Sfn Medieval astronomers became quite familiar with al-Battānī through this translation, renamed {{#invoke:Lang|lang}} ("On stellar motion").Template:Sfn It was also translated from Arabic into Spanish during the 13th century, under the orders of Alphonso X of Castile; a part of the manuscript is extant.Template:Sfn

The Template:Transliteration appears to have been widely used until the early 12th century. One 11th-century Template:Transliteration, now lost, was compiled by al-Nasawī. That it was based on al-Battānī can be inferred from the matching values for the longitudes of the solar and planetary apogees. Al-Nasawī had as a young man written astronomical tables using data obtained from al-Battānī's Template:Transliteration, but then discovered the data he used had been superseded by more accurately made calculations.<ref name="Moz">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

File:Al-Battani, Muhammad – De scientia stellarum frontispiece.jpg

The frontispiece of De scientia stellarum (Bologna, 1645)

The invention of movable type in 1436 made it possible for astronomical works to be circulated more widely, and a Latin translation of the Template:Transliteration was printed in Nuremberg in 1537 by the astronomer Regiomontanus, which enabled Al-Battānī's observations to become accessible at the start of the scientific revolution in astronomy.Template:Sfn Template:Sfn The Template:Transliteration was reprinted in Bologna in 1645;Template:Sfn the original document is preserved at the Vatican Library in Rome.<ref name="Dig">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

The Latin translations, including the printed edition of 1537, made the Template:Transliteration influential in the development of European astronomy.Template:Sfn A chapter of the Template:Transliteration also appeared as a separate work, Template:Transliteration ("On the accurate determination of the quantities of conjunctions [according to the latitudes of the planets]").Template:Sfn

Al-Battānī's work was published in three volumes, in 1899, 1903, and 1907, by the Italian Orientalist Carlo Alfonso Nallino,Template:Sfn who gave it the title {{#invoke:Lang|lang}}. Nallino's edition, although in Latin, is the foundation of the modern study of medieval Islamic astronomy.Template:Sfn

Template:TransliterationEdit

Template:Transliteration ({{#invoke:Lang|lang}}, “The book of the science of the ascensions of the signs of the zodiac in the spaces between the quadrants of the celestial sphere”)Template:Sfn may have been about calculations relating to the zodiac. The work is mentioned in a work by Ibn al-Nadim, and is probably identical with chapter 55 of al-Battānī's Template:Transliteration. It provided methods of calculation needed in the astrological problem of finding Template:Transliteration (directio).Template:Sfn

Other worksEdit

Template:Transliteration ("On the astrological indications of conjunctions and eclipses") is a treatise on horoscopes and astrology in connection with conjunctions of Saturn and Jupiter that occurred during the earliest period of Islam. The extant manuscript is held in the İsmail Saib Library at Ankara University.Template:Sfn
Template:Transliteration ({{#invoke:Lang|lang}}, "Commentary on Ptolemy's Tetrabiblos") is a commentary on the Template:Transliteration in the version of Abu as-Salt. Al-Battānī mentions two earlier treatises that are likely identical to two chapters of the Template:Transliteration.<ref name="Loh">{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref> It is extant in the manuscripts Berlin Spr. 1840 (Ahlwardt #5875) and Escorial árabe 969/2.Template:Sfn

Template:Transliteration ({{#invoke:Lang|lang}}, "Four discourses") was a commentary on Ptolemy's {{#invoke:Lang|lang}}, known as the {{#invoke:Lang|lang}}.Template:Sfn The 10th-century encyclopedist Ibn Nadim in his Template:Transliteration, lists al-Battānī among a number of authors of commentaries on this work.Template:Sfn Template:Sfn Template:Efn
Template:Transliteration ({{#invoke:Lang|lang}}, "Knowledge of the rising-places of the zodiacal signs").Template:Sfn
Template:Transliteration ({{#invoke:Lang|lang}}), an astrological treatise on the four "quarters of the sphere".Template:Sfn

LegacyEdit

Medieval periodEdit

The Template:Transliteration was renowned by medieval Islamic astronomers; the Arab polymath al-Bīrūnī wrote Template:Transliteration ("Elucidation of genius in al-Battānī's Zīj"), now lost.Template:Sfn

Al-Battānī's work was instrumental in the development of science and astronomy in the west.<ref name="OCoRob" /> Once it became known, it was used by medieval European astronomers and during the Renaissance.Template:Sfn He influenced Jewish rabbis and philosophers such as Abraham ibn Ezra and Gersonides.<ref name="Gal" /> The 12th-century scholar Moses Maimonides, the intellectual leader of medieval Judaism, closely followed al-Battānī.Template:Sfn Hebrew editions of the Template:Transliteration were produced by the 12th-century Catalan astronomer Abraham bar Hiyya and the 14th-century French mathematician Immanuel Bonfils.Template:Sfn

Copernicus referred to "al-Battani the Harranite" when discussing the orbits of Mercury and Venus. He compared to his own value for the sidereal year with those obtained by al-Battānī, Ptolemy and a value he attributed to the 9th-century scholar Thabit ibn Qurra.Template:Sfn The accuracy of al-Battānī's observations encouraged Copernicus to pursue his ideas about the heliocentric nature of the cosmos,Template:Sfn and in the book that initiated the Copernican Revolution, the {{#invoke:Lang|lang}}, al-Battānī is mentioned 23 times.Template:Sfn

16th and 17th centuriesEdit

Al-Battānī's tables were used by the German mathematician Christopher Clavius in reforming the Julian calendar, leading to it being replaced by the Gregorian calendar in 1582.Template:Sfn The astronomers Tycho Brahe, Giovanni Battista Riccioli, Johannes Kepler and Galileo Galilei cited Al-Battānī or his observations.<ref name="OCoRob"/> His almost exactly correct value obtained for the Sun's eccentricity is better than the values determined by both Copernicus and Brahe.Template:Sfn

The lunar crater Albategnius was named in his honour during the 17th century. Like many of the craters on the Moon's near side, it was given its name by Riccioli, whose 1651 nomenclature system has become standardized.Template:Sfn

In the 1690s, the English physicist and astronomer Edmund Halley, using Plato Tiburtius's translation of al-Battānī's Template:Transliteration, discovered that the Moon's speed was possibly increasing.Template:Sfn Halley researched the location of Raqqa, where al-Battānī's observatory had been built, using the astronomer's calculations for the solar obliquity, the interval between successive autumnal equinoxes and several solar and lunar eclipses seen from Raqqa and Antioch. From this information, Halley derived the mean motion and position of the Moon for the years 881, 882, 883, 891, and 901. To interpret his results, Halley was dependent upon on knowing the location of Raqqa, which he was able to do once he had corrected the accepted value for the latitude of Aleppo.Template:Sfn

18th century – presentEdit

Al-Battānī's observations of eclipses were used by the English astronomer Richard Dunthorne to determine a value for the increasing speed of the Moon in its orbit, he calculated that the lunar longitude was changing at a rate of 10 arcseconds per century.Template:Sfn Template:Sfn

Al-Battānī's data is still used by geophysicists.Template:Sfn