Abu Abdallah Mohammad ibn Jabir Al-Battani

Born: about 850 in Harran (near Urfa), Mesopotamia (now Turkey)
Died: 929 in Qasr al-Jiss, Iraq

Al-Battani is sometimes known by a latinised version of his name, variants being Albategnius, Albategni or Albatenius. His full name was Abu Abdallah Mohammad ibn Jabir ibn Sinan al-Raqqi al-Harrani al-Sabi al-Battani.

Al-Battani was born in Harran, called Carrhae in earlier times by the Romans, which lies on the Balikh River, 38 km southeast of Urfa. His family had been members of the Sabian sect, a religious sect of star worshippers from Harran. Being worshipers of the stars meant that the Sabians had a strong motivation for the study of astronomy and they produced many outstanding astronomers and mathematicians such as Thabit ibn Qurra. In fact Thabit was also born in Harran and would have still have been living there at the time that al-Battani was born. Al-Battani, unlike Thabit, was not a believer in the Sabian religion, however, for "Abu Abdallah Mohammad" indicates that he was certainly a Muslim.

Although the identification is not absolutely certain, it is probable that al-Battani's father was Jabir ibn Sinan al-Harrani who had a high reputation as an instrument maker in Harran. The name certainly makes the identification fairly certain and the fact that al-Battani himself was skilled in making astronomical instruments is a good indication that he learnt these skills from his father.

Al-Battani made his remarkably accurate astronomical observations at Antioch and ar-Raqqah in Syria. The town of ar-Raqqah, where most of al-Battani's observations were made, became prosperous when Harun al-Rashid, who became the fifth Caliph of the Abbasid dynasty on 14 September 786, built several palaces there. The town had been renamed al-Rashid at that time but, by the time al-Battani began observing there, it had reverted to the name of ar-Raqqah. The town was on the Euphrates River just west of where it joins the Balikh River (on which Harran stands).

The Fihrist (Index) was a work compiled by the bookseller Ibn an-Nadim in 988. It gives a full account of the Arabic literature which was available in the 10th century and it describes briefly some of the authors of this literature. The Fihrist describes al-Battani as (see for example [1]):-

... one of the famous observers and a leader in geometry, theoretical and practical astronomy, and astrology. He composed a work on astronomy, with tables, containing his own observations of the sun and moon and a more accurate description of their motions than that given in Ptolemy's "Almagest". In it moreover, he gives the motions of the five planets, with the improved observations he succeeded in making, as well as other necessary astronomical calculations. Some of his observations mentioned in his book of tables were made in the year 880 and later on in the year 900. Nobody is known in Islam who reached similar perfection in observing the stars and scrutinising their motions. Apart from this, he took great interest in astrology, which led him to write on this subject too: of his compositions in this field I mention his commentary on Ptolemy's Tetrabiblos.

Other information about al-Battani contained in the Fihrist is that he observed between the years 877 and 918 and that his star catalogue is based on the year 880. It also describes the end of his life which seems to have occurred during a journey he made to Baghdad to protest on behalf of a group of people from ar-Raqqah because they had been unfairly taxed. Al-Battani reached Baghdad and put his arguments but died on the return journey to ar-Raqqah.

The Fihrist also quotes a number of works by al-Battani. There is his Kitab al-Zij which is his major work on astronomy with tables, referred to above. We shall examine this in more detail in a moment. There is also the commentary on Ptolemy's Tetrabiblos referred to above and two other titles: On ascensions of the signs of the zodiac and On the quantities of the astrological applications. One of the chapters of the Kitab al-Zij has the title "On ascensions of the signs of the zodiac" and so the Fihrist may be wrong in thinking this is a separate work. This point still appears unclear.

Al-Battani's Kitab al-Zij is by far his most important work and we should examine briefly the topics which it covered. The work contained 57 chapters. It begins with a description of the division of the celestial sphere into the signs of the zodiac and into degrees. The necessary background mathematical tools are then introduced such as the arithmetical operations on sexagesimal fractions and the trigonometric functions. Chapter 4 contains data from al-Battani's own observations. Chapters 5 to 26 discuss a large number of different astronomical problems following to some extent material from the Almagest. The motions of the sun, moon and five planets are discussed in chapters 27 to 31, where the theory given is that of Ptolemy but for al-Battani the theory appears less important than the practical aspects.

After giving results to allow data given for one era to be converted to another era, al-Battani then gives 16 chapters which explain how his tables are to be read. Chapters 49 to 55 cover problems in astrology, while chapter 56 discusses the construction of a sundial and the final chapter discusses the construction of a number of astronomical instruments.

What are the main achievements of al-Battani's Zij? He catalogued 489 stars. He refined the existing values for the length of the year, which he gave as 365 days 5 hours 46 minutes 24 seconds, and of the seasons. He calculated 54.5" per year for the precession of the equinoxes and obtained the value of 23° 35' for the inclination of the ecliptic.

Rather than using geometrical methods, as Ptolemy had done, al-Battani used trigonometrical methods which were an important advance. For example he gives important trigonometric formulae for right angled triangles such as

b sin(A) = a sin(90° - A).

Al-Battani showed that the farthest distance of the Sun from the Earth varies and, as a result, annular eclipses of the Sun are possible as well as total eclipses. However, as Swerdlow points out in [8], the influence of Ptolemy was remarkably strong on all medieval authors, and even a brilliant scientist like al-Battani probably did not dare to claim a different value of the distance from the Earth to the Sun from that given by Ptolemy. This was despite the fact that al-Battani could deduce a value for the distance from his own observations that differed greatly from Ptolemy's.

In [1] Hartner gives a somewhat different opinion of the way that al-Battani is influenced by Ptolemy. He writes:-

While al-Battani takes no critical attitude towards the Ptolemaic kinematics in general, he evidences ... a very sound scepticism in regard to Ptolemy's practical results. Thus, relying on his own observations, he corrects - be it tacitly, be it in open words - Ptolemy's errors. This concerns the main parameters of planetary motion no less than erroneous conclusions drawn from insufficient or faulty observations, such as the invariability of the obliquity of the ecliptic or of the solar apogee.

Al-Battani is important in the development of science for a number of reasons, but one of these must be the large influence his work had on scientists such as Tycho Brahe, Kepler, Galileo and Copernicus. In [5] there is a discussion on how al-Battani managed to produce more accurate measurements of the motion of the sun than did Copernicus. The author suggests that al-Battani obtained much more accurate results simply because his observations were made from a more southerly latitude. For al-Battani refraction had little effect on his meridian observations at the winter solstice because, at his more southerly site of ar-Raqqah, the sun was higher in the sky.

Al-Battani's Kitab al-Zij was translated into Latin as De motu stellarum (On the motion of the stars) by Plato of Tivoli. This appeared in 1116 while a printed edition of Plato of Tivoi's translation appeared in 1537 and then again in 1645. A Spanish translation was made in the 13th century and both it and Plato of Tivoli's Latin translation have survived.

Article by: J J O'Connor and E F Robertson

November 1999

MacTutor History of Mathematics