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Al-Battani: the Trigonometrical Genius

Al-Battani: the Trigonometrical Genius
Al-Battani's Kitab al-Zij is by far his most important work.

Abu Abdallah Muhammad Ibn Jabir Ibn Sinan Al-Battani Al-Harrani, known in the West as Albategnius, is considered the greatest astronomer of his time and one of the greatest during the Middle Ages.

Al-Battani was born around 858 C.E. in Battan, a state of Harran, and was first educated by his father Jabir Ibn San’an Al-Battani, a well-known scientist. He then moved to Ar-Raqqa, situated on the bank of the Euphrates in Syria, where he received advanced education and began his career as a scholar.

The Fihrist (Index), compiled by the bookseller Ibn An-Nadim in 988, gives a full account of the Arabic literature available in the 10th century and briefly describes some of its authors. It depicts Al-Battani as:

… 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 scrutinizing 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.

Al-Battani’s Kitab al-Zij is by far his most important work. The book contains 57 chapters, beginning 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 Four contains data from al-Battani’s own observations. Chapters Five through 26 discuss a large number of different astronomical problems – following, to some extent, material from the Almagest. Ptolemy’s theory regarding the motions of the sun, moon, and five planets are discussed in Chapters 27 through 31; however, for al-Battani, the theory appears less important than the practical aspects.

After providing the method for converting data from one era to that of another, al-Battani then devotes 16 chapters explaining how his tables are to be read. Chapters 49 through 55 cover problems in astrology, while Chapter 56 discusses the construction of a sundial. The final chapter discusses the construction of a number of astronomical instruments.

What were al-Battani’s main achievements in Kitab Al-Zij? He catalogued 489 stars, refined the existing values for the solar year’s length (as 365 days, 5 hours, 48 minutes and 24 seconds), 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, constituting an important advance. For example, he provided important trigonometric formulas 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, Ptolemy’s influence on all medieval authors was remarkably strong so that even a brilliant scientist like Al-Battani probably did not dare claim a different value of the distance from the Earth to the Sun than that given by Ptolemy. This occurred despite the fact that Al-Battani was able to deduce a value from his own observations that differed greatly from Ptolemy’s.

Particularly in the Middle Ages, Al-Battani’s original discoveries in both Astronomy and Trigonometry were of great consequence to the development of the sciences.

He had substantial influence on scientists such as Tyco Brahe, Kepler, Galileo and Copernicus, managing to produce more accurate measurements of the motion of the sun than did Copernicus who expressed his indebtedness to Al-Battani in his book De Revolutionibus Orbium Clestium.

Beer and Madler, in their famous work Der Mond (1837), refer to one of the surface features of the moon (a plain eighty miles in diameter in Section One that is surrounded by mountains ten to fourteen thousand feet high, several craters, and several saucer-shaped pits) as Albategnius.

The printed edition of Al-Battani’s Kitab al-Zij was translated into Latin as De Motu Stellarum (On The Motion Of The Stars) by Plato of Tivoli in 1116, and appeared in 1537 and again in 1645. A Spanish translation was made in the 13th century; both it and Plato of Tivoli’s Latin translation have survived.

Al-Battani’s greatest fame came in Mathematics, with the use of trigonometric ratios as we use them today. He was the first to replace the use of Greek chords by sines, with a clear understanding of their superiority. He also developed the concept of cotangents, and furnished their tables in degrees.

According to tradition, Al-Battani died while en route to Baghdad to protest on behalf of a group of people from Ar-Raqqa who had been unfairly taxed. His memory remains strong today in the field of Islamic scientific history; he is even mentioned on modern television shows.

Al-Battani’s reputation as a premier astronomer has even worked its way into Star Trek lore. According to Star Fleet records, the first posting of newly graduated Ensign Kathryn Janeway was the USS Al-Battani. During her assignment, Janeway once knocked out power to six of its decks by misaligning positronic relays. She would survive this embarrassing mishap, however, and rise to the rank of Captain and Commander of the USS Voyager.


This article was first published in 2008 and is currently republished for its importance.

About David W. Tschanz

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