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CHAPTER NINE

AL-BATTANI CONTRIBUTIONS IN ASTRONOMY AND

MATHEMATICS

Mohammad Salah Aldin Abdullatif

Fac. of Eng., International Islamic Univ. Malaysia (IIUMj, Jalan Gombak, 53100 Kuala

Lumpur. Malaysia.

mohasalah86@gmail.com

9.1 INTRODUCTION

This chapter is talking about one of the famous and greatest Islamic astronomers and

mathematicians around the world; Al-Battani has great and significant contributions in

astronomy and mathematics. In astronomy, he has astronomical observations for more

than forty years. In addition, he did some corrections upon Ptolemy’s results and made

some new tables of the Sun and the Moon. Moreover, he determined the length of solar

year. In mathematics, he innovated new relations in trigonometric, and created a table of

cotangents, and made some formulas in spherical trigonometry.

Al-Battani wrote many books related to astronomy, and mathematics. He wrote the

following books, Kitab Al-Zij known as Al-Zij Al-Sabi. And this book is considered as the

most significant work because it covered many points that are not had taken before. In

addition, he wrote a book titled Commentary on Ptolemy’s Tetrabiblos, he corrected

numerous errors of Ptolemy’s. The purpose of his Zij was practical more than theoretical.

In mathematics, he discovered new relationships in trigonometric. He could determine the

angle of eclipse accuracy, and he also gave the length of solar year.

Al- Battani’s full name is Mohammed ibn Jabir ibn Sinan Al-Harrani Al-Battani, also

known as Albategnius or Albatenius was born in 858 in Harran near Urfa which is now in

Turkey. He lived and worked in Al-Rakka, which is now a city in Syria. Battani was born

in a family of Sabians, this religious group worship stars, and centred in Harran that has

many scholars like Thabit ibn Qurra. However, Al-Battani’s first name Mohammed and

his Kunya Abu Abdullah indicate that he was certainly Muslim. Al-Battani died in 929 in

Qasr Al-Jiss, Iraq.

The methodology adopted in this chapter is analytical. This chapter investigates what

Al-Battani did for astronomy and mathematics and show briefly his significant

contributions. The main focuses in this chapter is to provide answers of one of the greatest

scientists in astronomy, and to show some of his contributions in astronomy and

mathematics. The significant of this chapter is that there are few people who know Al-

Battani, especially among Muslims; therefore, we propose to provide enough information

about a good example of Muslim scientists who served the humanity along Islamic era.

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9.2 Astronomy

Al-Battani lived in the era of Islamic civilization, which was very rich of sciences in

that time, and astronomy was one of those sciences that Muslims made a great work for

humanity. Therefore, Al-Battani was one of those Muslim scientists who worked on

astronomy. He worked in astronomy observations for more than forty years from 877 to

918. He used some instruments as a gnomon, horizontal and vertical sundials, parallactic

rulers, an astrolabe, a new type of armillary sphere, and mural quadrant with an alidade.

He recommended sizes of more than a meter to get accurate results of the observations.

Therefore, Al-Battani has observation in Antioch for a solar and lunar eclipse

(Benno van Dalen, 2007).

Al-Battani worked on Ptolemy’s books and corrected some errors related to the length

of the year and other situations. He could put new existing values for the solar year, which

it is upon him (365 days, 5 hours, 46 minutes, and 24 seconds) is too short by 2 minutes 22

seconds (correct (365 days, 5 hours, 48 minutes, and 46 seconds) while Ptolemy’s (365

days, 5 hours, 55 minutes, and 12 seconds) is too long by 6 minutes 26 seconds

(www.encyclopedia.com) .In addition, Al-Battani calculated 54.5” per year for the

precession of the equinoxes and put the value of 23o

35’ for the inclination of the ecliptic

(O'Connor & Robertson, 1999).

Moreover, he is the first one how explored Azimuth and Nadir, and determined their

points in the sky. The Italian orientalist Carlo Alfonso Nallino said that Al-Battani has

many outstanding observations for lunar eclipse and solar eclipse that the English

astronomer Richard Dunthorne depended on these observations to specify moon

acceleration in its movement through one century. The French astronomer Lalande said

that Al-Battani is one of the astronomers’ leaders around the world (Zarkaly, 2002, p.68).

The Fihrist was a work compiled by the bookseller Ibn an-Nadim in 988. It gives brief

information about 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

(O'Connor & Robertson, 1999):

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.

Finally we can show some of the chapters of Al-Battani’s book Al-Zij which contains

57 chapters, however, we will show only some chapters. It contained the necessary

background mathematical tools. In addition, it describes many astronomical problems

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related to the, sun, moon, and 5 planets. It also contained tables and how to read these

tables (O'Connor & Robertson, 1999).

9.3 Mathematics

Al-Battani was an astronomer, however, he has some significant contributions in

mathematics that served the astronomy in his era, and after that these contributions were

not only for astronomy but also for many applications in engineering specially.

Al-Battani made a number of important trigonometric functions. He used the sine which

was innovated before him, however, he innovated cosine, tangent, and cotangent.

Moreover, he wrote accurate tables for cotangents for angles from 00 to 90

0. He found the

cotangents in his tables by the following functions (Al-Difa, 1981, p.47):

Florian Cajori says in his book Mathematics History: Al-Battani didn’t follow the

Greek in many of their Geometry solutions, he instead solve the problems by another way

(Al-Difa, 1981, p.47):

but

√

So he could find the angle value x

Al-Battani, in addition, provides other important formulas (O'Connor & Robertson,

1999):

( ) ( ) Al-Battani used the surfaced triangle to calculate sun height according to the height of

the ground h and its tangent m (Al-Difa, 1981, p.49)

( )

Figure 1 (adopted from Al-Difa, 1981, p.49)

In Britannica Encyclopedia we can find some of the contributions by Al-Battani

(www.britannica.com):

h

a m

48

Al-Battani gave a rule for finding the elevation θ of the Sun above the

horizon in terms of the length s of the shadow cast by a vertical gnomon of

height h. Al- Battani’s rule, s = h sin (90° − θ)/sin θ, is equivalent to the

formula s = h cot θ. Based on this rule he constructed a “table of shadows”

-essentially a table of cotangents- for each degree from 1° to 90°.

9.4 Conclusion

The findings of this chapter are showing one example of Muslim scientists who served

the humanity by his outstanding contributions in astronomy and mathematics. What I

found through my research is that there is little importance from Muslims and Arabs about

their scientists. Not only that but also they don’t know the basic information about them

and their contributions. Therefore, I recommend making more researches about Muslim

and Arabic scientists in order to know more about them. I recommend about our research

is to be tested that I can avoided in the future.

9.5 References

Ali Abdullah Al-Difa, 1981, Arab and Muslim scientists in developing astronomy.

Muhammad Ibn Jabir Ibn Sinan Al-Raqqi Al-Ḥarrani Al-Ṣabi Al-Battani, Al-Zij Al-Sabi,

1899.

"Al-Battani, Abu Abd Allah Muhammad Ibn Jabir Ibn Sinan Al-Raqqi Al-Ḥarrani Al-

Ṣabi’." Complete Dictionary of Scientific Biography. 2008. Retrieved November 04, 2011

from Encyclopedia.com:

http://www.encyclopedia.com/doc/1G2-2830900300.html

"Battani: Abu Abd Allah Muḥammad ibn Jabir ibn Sinan al-Battani al-Harran al-Ṣabi".

Benno van Dalen. The Biographical Encyclopedia of Astronomers. Springer

Science+Business Media, LLC. 2007

http://www.springerlink.com/content/l205655556361547/

J J O'Connor and E F Robertson. "Abu Abdallah Mohammad ibn Jabir Al-Battani".

School of Mathematics and Statistics, University of St Andrews, Scotland

http://www-history.mcs.st-andrews.ac.uk/Biographies/Al-Battani.html

N Swerdlow, Al-Battani 's determination of the solar distance, Centaurus 17 (2) (1972),

97-105.

Britannica Encyclopedia

http://www.britannica.com/EBchecked/topic/605281/trigonometry

W Hartner, Biography in Dictionary of Scientific Biography (New York 1970-1990).