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), usually calledal-Battānī, a name that was in the pastLatinized asAlbategnius,^{[n 2]} (before 858 – 929) was anastronomer,astrologer,geographer andmathematician, who lived and worked for most of his life atRaqqa, now in Syria. He is considered to be the greatest and most famous of theastronomers of the medieval Islamic world.

al-Battānī
محمد بن جابر بن سنان البتاني
Afolio from aLatin translation ofKitāb az-Zīj aṣ-Ṣābi’ (c. 900), Latin 7266,Bibliothèque nationale de France
Born	Before 858 Harran,Islamic Syria (modern-day Turkey)
Died	929 Qasr al-Jiss, nearSamarra
Academic work
Era	Islamic Golden Age
Main interests	Mathematics,astronomy,astrology
Notable works	Kitāb az-Zīj
Notable ideas	Trigonometrical relationships

Al-Battānī's writings became instrumental in the development of science and astronomy in the west. HisKitāb az-Zīj aṣ-Ṣābi’ (c. 900), is the earliest extantzīj (astronomical table) made in thePtolemaic tradition that is hardly influenced by Hindu or Sasanian astronomy. Al-Battānī refined and correctedPtolemy'sAlmagest, but also included new ideas and astronomical tables of his own. A handwrittenLatin version by the Italian astronomerPlato Tiburtinus was produced between 1134 and 1138, through which medieval astronomers became familiar with al-Battānī. In 1537, a Latin translation of thezīj was printed inNuremberg. An annotated version, also in Latin, published in three separate volumes between 1899 and 1907 by the Italian OrientalistCarlo 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 ofannular solar eclipses. He accurately calculated the Earth'sobliquity (the angle between the planes of theequator and theecliptic), the solar year, and theequinoxes (obtaining a value for theprecession of the equinoxes of one degree in 66 years). The accuracy of his data encouragedNicolaus Copernicus to pursue ideas about theheliocentric nature of the cosmos. Al-Battānī's tables were used by the German mathematicianChristopher Clavius in reforming theJulian calendar, and the astronomersTycho Brahe,Johannes Kepler,Galileo Galilei andEdmund Halley all used Al-Battānī's observations.

Al-Battānī introduced the use ofsines andtangents ingeometrical calculations, replacing the geometrical methods of the Greeks. Usingtrigonometry, he created an equation for finding theqibla (the direction which Muslims need to face during theirprayers). His equation was widely used until superseded by more accurate methods, introduced a century later by thepolymathal-Biruni.

Al-Battānī, whose full name wasAbū ʿAbd Allāh Muḥammad ibn Jābir ibn Sinān al-Raqqī al-Ḥarrānī al-Ṣābiʾ al-Battānī, and whose Latinized name wasAlbategnius, was born before 858 inHarran inBilād ash-Shām (Islamic Syria), 44 kilometres (27 mi) southeast of the modern Turkish city ofUrfa. He was the son of Jabir ibn Sinan al-Harrani, a maker of astronomical instruments.^[3] Theepithetal-Ṣabi’ suggests that his family belonged to the paganSabian sect of Harran,^[4][5] whose religion featuredstar worship, and who had inherited theMesopotamian legacy of an interest in mathematics and astronomy.^{[2][n 3]} His contemporary, the polymathThābit ibn Qurra, was also an adherent of Sabianism, which died out during the 11th century.^[7]

Although his ancestors were likely Sabians, al-Battānī was a Muslim, as shown by his first name.^[5] Between 877 and 918/19 he lived inRaqqa, now in north central Syria, which was an ancient Roman settlement beside theEuphrates, near Harran. During this period he also lived inAntioch,^[3] where he observed asolar and alunar eclipse in 901. According to the Arab biographerIbn al-Nadīm, the financial problems encountered by al-Battānī in old age forced him to move from Raqqa toBaghdad.^[8]

Al-Battānī died in 929 at Qasr al-Jiss,^[2] nearSamarra, after returning from Baghdad where he had resolved an unfair taxation grievance on behalf of a clan from Raqqa.^[9]

Al-Battānī is considered to be the greatest^[10][11][12] and most famous of the knownastronomers of the medieval Islamic world. He made more accurate observations of the night sky than any of his contemporaries,^[3] and was the first of a generation of new Islamic astronomers that followed the founding of theHouse of Wisdom in the 8th century.^[13] 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.^[14]

Sometimes referred to as the "Ptolemy of the Arabs",^[15] al-Battānī's works reveal him to have been a devout believer inPtolemy'sgeocentric model of the cosmos. He refined the observations found in Ptolemy'sAlmagest,^[3] and compiled new tables of the Sun and the Moon, previously long accepted as authoritative.^[5] Al-Battānī established his own observatory at Raqqa. He recommended that the astronomical instruments there were greater than one metre (3 ft 3 in) in size.^[8] Such instruments, being larger—and so having scales capable of measuring smaller values—were capable of greaterprecision than had previously been achieved.^[16] Some of his measurements were more accurate than those taken by the Polish astronomer and mathematicianNicolaus Copernicus during theRenaissance. One reason for this is thought to be that al-Battānī's location for his observations at Raqqa was closer to the Earth'sequator, so that theecliptic and the Sun, being higher in the sky, were less susceptible toatmospheric refraction.^[5] The careful construction and alignment of his astronomical instruments enabled him to achieve an accuracy of observations ofequinoxes andsolstices that had previously been unknown.^[8]

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 whyannular solar eclipses occur.^[3][17][18] He saw that the position in the sky at which theangular diameter of the Sun appeared smallest was no longer located where Ptolemy had stated it should be,^[3] and that since Ptolemy's time, thelongitudinal position of the apogee had increased by 16°47'.^[12]

Al-Battānī was an excellent observer.^[19] He improved Ptolemy's measurement of theobliquity of the ecliptic (the angle between the planes of the equator and the ecliptic),^[9] producing a value of 23° 35';^{[5][n 4]} the accepted value is around 23°.44.^[20] 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.^[2] His value for thesolar year of 365 days, 5 hours, 46 minutes and 24 seconds, is 2 minutes and 22 seconds from the accepted value.^[5]

Al-Battānī observed changes in the direction of the Sun'sapogee, as recorded by Ptolemy,^[21] and that as a result, theequation of time was subject to a slow cyclical variation.^[22] His careful measurements of when theMarch andSeptember equinoxes took place allowed him to obtain a value for theprecession of the equinoxes of 54.5" per year, or 1degree in 66 years,^[5][9] a phenomenon that he realised was altering the Sun's annual apparent motion through the zodiacconstellations.^[23]

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.^[23]

One of al-Battani's greatest contributions was his introduction of the use ofsines andtangents ingeometrical calculations, especiallyspherical trigonometric functions, to replace Ptolemy's geometrical methods. Al-Battānī's methods involved some of the most complex mathematics developed up to that time.^[23] He was aware of the superiority of trigonometry overgeometrical chords, and demonstrated awareness of a relation between the sides and angles of a spherical triangle, now given by the expression:^[12]

${\displaystyle \cos a=\cos b\cos c+\sin b\sin c\cos A}$ 

Al-Battānī produced a number oftrigonometrical relationships:^[24]

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

${\displaystyle \sec \alpha =\sqrt{1+{\tan }^2\alpha }}$ , where${\displaystyle \sec \alpha =\frac{1}{\cos \alpha }}$ .

He also solved the equation

${\displaystyle \sin x=y\cos x}$ ,

discovering the formula

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

Al-Battānī used the Iranian astronomerHabash al-Hasib al-Marwazi's idea oftangents to develop equations for calculating and compiling tables of both tangents and cotangents. He discovered theirreciprocal 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 asundial.^[24]

Using these trigonometrical relationships, al-Battānī created an equation for finding theqibla, which Muslims face in each of the fiveprayers they practice every day.^[26] 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${\displaystyle q}$ , the angle of the direction of a place towards Mecca is given by:^[25]

${\displaystyle \tan q=\frac{\sin \mathrm{\Delta }\lambda }{\sin \mathrm{\Delta }\varphi }}$ 

where${\displaystyle \mathrm{\Delta }\lambda }$  is the difference between the longitude of the place and Mecca, and${\displaystyle \mathrm{\Delta }\varphi }$  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 thepolymathal-Biruni summarized several other methods to produce results that were more accurate than those that could be obtained using al-Battānī's equation.^[27]

A small work on trigonometry,Tajrīd uṣūl tarkīb al-juyūb ("Summary of the principles for establishing sines") is known. Once attributed to the Iranian astronomerKushyar Gilani by the German orientalistCarl Brockelmann, it is a fragment of al-Battānī'szīj. The manuscript is extant inIstanbul as MS Carullah 1499/3.^[2] The authenticity of this work has been questioned, as scholars believe al-Battānī would have not have includedal-juyūb for "sines" in the title.^[8]

Al-Battānī'sKitāb az-Zīj (كتاب الضد orالضد البتاني, "Book of Astronomical Tables"), written in around 900, and also known as the al-Zīj al-Ṣābī (كتاب الزيج الصابئ),^[2] is the earliest extant zīj made in the Ptolemaic tradition that is hardly influenced by Hindu or Sasanian–Iranian astronomy.^[8] It corrected mistakes made by Ptolemy and described instruments such as horizontal and vertical sundials, thetriquetrum, themural instrument,^[2] and aquadrant instrument.^[28] Ibn al-Nadim wrote that al-Battānī'szīj existed in two different editions, "the second being better than the first".^[8] In the west, the work was sometimes called theSabean Tables.^[6]

The work, consisting of 57 chapters and additional tables, is extant (in the manuscript árabe 908, held inEl Escorial), copied inAl-Andalus during the 12th or 13th century. Incomplete copies exist in other western European libraries.^[8] Much of the book consists of instructions for using the attached tables. Al-Battānī used an Arabic translation of the Almagest made fromSyriac, and used few foreign terms. He copied some data directly from Ptolemy'sHandy 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.^[8]

Otherzījes based on Kitāb az-Zīj aṣ-Ṣābi’ include those written by Kushyar Gilani,Alī ibn Ahmad al-Nasawī, Abū Rashīd Dāneshī, andIbn al-Kammad.^[2]

The first version in Latin from the Arabic was made by the English astronomerRobert of Ketton; this version is now lost.^[2][22] A Latin edition was also produced by the Italian astronomerPlato Tiburtinus between 1134 and 1138.^[29] Medieval astronomers became quite familiar with al-Battānī through this translation, renamedDe motu stellarum ("On stellar motion").^[9] It was also translated from Arabic into Spanish during the 13th century, under the orders ofAlphonso X of Castile; a part of the manuscript is extant.^[22]

The zīj appears to have been widely used until the early 12th century. One 11th-centuryzīj, 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 zīj, but then discovered the data he used had been superseded by more accurately made calculations.^[30]

The invention ofmovable type in 1436 made it possible for astronomical works to be circulated more widely, and aLatin translation of theKitāb az-Zīj aṣ-Ṣābi’ was printed inNuremberg in 1537 by the astronomerRegiomontanus, which enabled Al-Battānī's observations to become accessible at the start of the scientific revolution in astronomy.^[9][29] Thezīj was reprinted inBologna in 1645;^[29] the original document is preserved at theVatican Library in Rome.^[31]

The Latin translations, including the printed edition of 1537, made thezīj influential in the development of European astronomy.^[19] A chapter of theṢābiʾ Zīj also appeared as a separate work,Kitāb Taḥqīq aqdār al-ittiṣālāt [bi-ḥasab ʿurūḍ al-kawākib] ("On the accurate determination of the quantities of conjunctions [according to the latitudes of the planets]").^[8]

Al-Battānī's work was published in three volumes, in 1899, 1903, and 1907, by the ItalianOrientalistCarlo Alfonso Nallino,^[2] who gave it the titleAl-Battānī sive Albatenii opus astronomicum: ad fidem codicis Escurialensis Arabice editum. Nallino's edition, although in Latin, is the foundation of the modern study of medieval Islamic astronomy.^[19]

Kitāb maʿrifat maṭāliʿ al-burūd̲j̲ fī mā baina arbāʿ al-falak (معرفة مطالع البروج, “The book of the science of the ascensions of the signs of the zodiac in the spaces between the quadrants of the celestial sphere”)^[22] may have been about calculations relating to thezodiac. The work is mentioned in a work by Ibn al-Nadim, and is probably identical with chapter 55 of al-Battānī'szīj. It provided methods of calculation needed in the astrological problem of findingal-tasyīr (directio).^[8]

• Kitāb fī dalāʾil al-qirānāt wa-l-kushūfāt ("On the astrological indications of conjunctions and eclipses") is a treatise onhoroscopes 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 atAnkara University.^[8]
• Sharḥ kitāb al-arbaʿa li-Baṭlamiyūs (شرح كتاب الأربع مقالات في أحكام علم النجوم, "Commentary on Ptolemy's Tetrabiblos") is a commentary on the Kitāb al-Arbaʿ maqālāt in the version ofAbu as-Salt. Al-Battānī mentions two earlier treatises that are likely identical to two chapters of the Ṣābiʾ Zīj.^[32] It is extant in the manuscripts Berlin Spr. 1840 (Ahlwardt #5875) and Escorial árabe 969/2.^[8]
• Arbaʻ maqālāt (أربع مقالات, "Four discourses") was a commentary on Ptolemy'sQuadripartitum de apotelesmatibus e judiciis astrorum, known as theTetrabiblos.^[33] The 10th-century encyclopedistIbn Nadim in hisKitāb al-Fihrist, lists al-Battānī among a number of authors of commentaries on this work.^{[8][34][n 6]}
• Maʻrifat maṭāliʻ al-burūj (معرفة مطالع البروج, "Knowledge of the rising-places of the zodiacal signs").^[35]
• Kitāb fī miqdār al-ittiṣālāt (كتاب في مقدار الاتصالات), an astrological treatise on the four "quarters of the sphere".^[35]

The al-Zīj al-Ṣābī was renowned by medieval Islamic astronomers; the Arab polymathal-Bīrūnī wroteJalā' al-adhhān fī zīj al-Battānī ("Elucidation of genius in al-Battānī's Zīj"), now lost.^[8]

Al-Battānī's work was instrumental in the development of science and astronomy in the west.^[5] Once it became known, it was used by medieval European astronomers and during the Renaissance.^[8] He influenced Jewishrabbis and philosophers such asAbraham ibn Ezra andGersonides.^[17] The 12th-century scholarMoses Maimonides, the intellectual leader of medieval Judaism, closely followed al-Battānī.^[36]Hebrew editions of the al-Zīj al-Ṣābī were produced by the 12th-centuryCatalan astronomerAbraham bar Hiyya and the 14th-century French mathematicianImmanuel Bonfils.^[8]

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 scholarThabit ibn Qurra.^[6] The accuracy of al-Battānī's observations encouraged Copernicus to pursue his ideas about theheliocentric nature of the cosmos,^[3] and in the book that initiated theCopernican Revolution, theDe Revolutionibus Orbium Coelestium, al-Battānī is mentioned 23 times.^[37]

Al-Battānī's tables were used by the German mathematicianChristopher Clavius in reforming theJulian calendar, leading to it being replaced by theGregorian calendar in 1582.^[9] The astronomersTycho Brahe,Giovanni Battista Riccioli,Johannes Kepler andGalileo Galilei cited Al-Battānī or his observations.^[5] His almost exactly correct value obtained for the Sun'seccentricity is better than the values determined by both Copernicus and Brahe.^[8]

Thelunar craterAlbategnius 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 1651nomenclature system has become standardized.^[38]

In the 1690s, the Englishphysicist and astronomerEdmund Halley, using Plato Tiburtius's translation of al-Battānī'szīj, discovered that the Moon's speed was possibly increasing.^[39] 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 ofAleppo.^[40]

Al-Battānī's observations of eclipses were used by the English astronomerRichard Dunthorne to determine a value for the increasing speed ofthe Moon in its orbit, he calculated that the lunar longitude was changing at a rate of 10arcseconds per century.^[8][41]

Al-Battānī's data is still used bygeophysicists.^[42]

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• c. 1245–1250 –Gerard of AbbevilleManuscript: Latin 16657 (Liber Albategni. – Almagesti minoris libri VI. – Tabule stellarum fixarum)
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