Al-Battani
Al-Battani, archaically Latinized as Albategnius, was a Arab 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 one of 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 , is the earliest extant 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 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 solar year, and the equinoxes. 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 . His equation was widely used until superseded by more accurate methods, introduced a century later by the polymath al-Biruni.
Life
Al-Battānī, whose full name was, and whose Latinized name was, was born before 858 in Harran in Bilād ash-Shām, southeast of the modern Turkish city of Urfa. He was the son of Jabir ibn Sinan al-Harrani, a maker of astronomical instruments. The epithet suggests that his family belonged to the pagan Sabian sect of Harran, whose religion featured star worship, and who had inherited the Mesopotamian legacy of an interest in mathematics and astronomy. His contemporary, the polymath Thābit ibn Qurra, was also an adherent of Sabianism, which died out during the 11th century.Although his ancestors were likely Sabians, al-Battānī was a Muslim, as shown by his first name. 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, 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.
Al-Battānī died in 929 at Qasr al-Jiss, near Samarra, after returning from Baghdad where he had resolved an unfair taxation grievance on behalf of a clan from Raqqa.
Astronomy
Al-Battānī is considered to be the greatest 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, and was the first of a generation of new Islamic astronomers that followed the founding of the House of Wisdom in the 8th century. 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.Sometimes referred to as the "Ptolemy of the Arabs", 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 Almagest, and compiled new tables of the Sun and the Moon, previously long accepted as authoritative. Al-Battānī established his own observatory at Raqqa. He recommended that the astronomical instruments there were greater than in size. Such instruments, being larger—and so having scales capable of measuring smaller values—were capable of greater precision than had previously been achieved. 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. 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.
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. 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, and that since Ptolemy's time, the longitudinal position of the apogee had increased by 16°47'.
Al-Battānī was an excellent observer. He improved Ptolemy's measurement of the obliquity of the ecliptic, producing a value of 23° 35'; the accepted value is around 23°.44. 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. 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.
Al-Battānī observed changes in the direction of the Sun's apogee, as recorded by Ptolemy, and that as a result, the equation of time was subject to a slow cyclical variation. 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, a phenomenon that he realised was altering the Sun's annual apparent motion through the zodiac constellations.
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.
Mathematics
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. 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:Al-Battānī produced a number of trigonometrical relationships:
He also solved the equation
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.
Using these trigonometrical relationships, al-Battānī created an equation for finding the qibla, which Muslims 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 he used was precise enough only for a person located in Mecca, but was still a widely used method at the time. Al-Battānī's equation for, the angle of the direction of a place towards Mecca is given by:
where is the difference between the longitude of the place and Mecca, and 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.
A small work on trigonometry, is known. Once attributed to the Iranian astronomer Kushyar Gilani by the German orientalist Carl Brockelmann, it is a fragment of al-Battānī's. The manuscript is extant in Istanbul as MS Carullah 1499/3. The authenticity of this work has been questioned, as scholars believe al-Battānī would have not have included for "sines" in the title.
Works
Al-Battānī's , written in around 900, and also known as the , is the earliest extant made in the Ptolemaic tradition that is hardly influenced by Hindu or Sasanian–Iranian astronomy. It corrected mistakes made by Ptolemy and described instruments such as horizontal and vertical sundials, the triquetrum, the mural instrument, and a quadrant instrument. Ibn al-Nadim wrote that al-Battānī's existed in two different editions, "the second being better than the first". In the west, the work was sometimes called the Sabean Tables.The work, consisting of 57 chapters and additional tables, is extant, copied in Al-Andalus during the 12th or 13th century. Incomplete copies exist in other western European libraries. 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.
Other based on include those written by Kushyar Gilani, Alī ibn Ahmad al-Nasawī, Abū Rashīd Dāneshī, and Ibn al-Kammad.
The first version in Latin from the Arabic was made by the English astronomer Robert of Ketton; this version is now lost. A Latin edition was also produced by the Italian astronomer Plato Tiburtinus between 1134 and 1138. Medieval astronomers became quite familiar with al-Battānī through this translation, renamed De motu stellarum. 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.
The appears to have been widely used until the early 12th century. One 11th-century, 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 , but then discovered the data he used had been superseded by more accurately made calculations.
File:Al-Battani, Muhammad – De scientia stellarum frontispiece.jpg|thumb|The frontispiece of De scientia stellarum
The invention of movable type in 1436 made it possible for astronomical works to be circulated more widely, and a Latin translation of the 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. The was reprinted in Bologna in 1645; the original document is preserved at the Vatican Library in Rome.
The Latin translations, including the printed edition of 1537, made the influential in the development of European astronomy. A chapter of the also appeared as a separate work, .
Al-Battānī's work was published in three volumes, in 1899, 1903, and 1907, by the Italian Orientalist Carlo Alfonso Nallino, who gave it the title Al-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.