# Muḥammad ibn Jābir al-Ḥarrānī al-Battānī

## Quick Facts

Intro | Muslim astronomer, astrologer, and mathematician |

A.K.A. | Al-Batani, Albategnius, Al-Battani, Muhammad al-Battani |

Is | Mathematician Astronomer Astrologer |

From | Turkey Iraq |

Type | Mathematics Science |

Gender | male |

Birth | 858, Harran, Turkey |

Death | 929, Samarra, Iraq |

## Biography

أبو عبد الله محمد بن جابر بن سنان الرقعي العراني آثاني البطاني

**Abū ʿAbd Allāh Muḥammad ibn Jābir ibn Sinān al-Raqqī al-Ḥarrānī aṣ-Ṣābiʾ al-Battānī** (Arabic: محمد بن جابر بن سنان البتاني) (Latinized as **Albategnius**, **Albategni** or **Albatenius**) (c. 858 – 929) was an Arab astronomer, astrologer, and mathematician. He introduced a number of trigonometric relations, and his *Kitāb az-Zīj* was frequently quoted by many medieval astronomers, including Copernicus.

Often called the "Ptolemy of the Arabs", al-Battani is perhaps the greatest and best known astronomer of the medieval Islamic world.

## Life

Little of al-Battānī's life is known other than his birthplace in Harran near Urfa, in Upper Mesopotamia, (today in Turkey) and his father's fame as a maker of scientific instruments. Ibn Khallikan expresses ignorance on the question of his Muslim faith, and points out that his epithet *aṣ-Ṣabi’* suggests possible Sabian-sect ancestry. Some western historians claim he had noble origins as an Arab prince, but traditional Arabic biographers make no mention of this. Between 877 and 918/19, over a forty-year period, he lived in the ancient city of Raqqa, in north central Syria, recording his astronomical observations. He is said to have died while returning to Baghdād at a fortress called *Kasr al-Hadr*, which was near either Tikrit, or Samarra.

## Astronomy

One of al-Battānī's best-known achievements in astronomy was the determination of the solar year as being 365 days, 5 hours, 46 minutes and 24 seconds, which is only 2 minutes and 22 seconds off.

The twelfth-century Egyptian encyclopedist al-Qifṭī, in his biographical history *Ta’rīkh al-Ḥukamā’*, mentions al-Battānī’s contribution to advances in astronomical observation and calculations based on Ptolemy’s *Almagest*.

Al-Battānī amended some of Ptolemy's results and compiled new tables of the Sun and Moon, long accepted as authoritative. Some of his measurements were more accurate than ones taken by Copernicus many centuries later and some ascribe this phenomenon to al-Battānī's location lying closer to the equator such that the ecliptic and the Sun, being higher in the sky, are less susceptible to atmospheric refraction. Al-Battānī observed that the direction of the Sun's apogee, as recorded by Ptolemy, was changing.

Al-Battānī's work was instrumental in the development of science and astronomy. Copernicus, in his book that initiated the Copernican Revolution, the *De Revolutionibus Orbium Coelestium*, quotes his name no fewer than 23 times, and also mentions him in the *Commentariolus*. Tycho Brahe, Riccioli, Kepler, Galileo and others frequently cited him or his observations. His data is still used in geophysics.
The major lunar crater Albategnius is named in his honor.

### Among his Innovations

- Introduction of the use of sines in calculation and partially that of tangents.
- Calculation of the values for the precession of the equinoxes (54.5" per year, or 1° in 66 years) and the obliquity of the ecliptic (23° 35').
- Use of a uniform rate for precession in his tables, choosing not to adopt the theory of trepidation attributed to his colleague Thabit ibn Qurra.

## Mathematics

In mathematics, al-Battānī produced a number of trigonometrical relationships:

- $\tan a={\frac {\sin a}{\cos a}}$

- $\sec a={\sqrt {1+\tan ^{2}a}}$

He also solved the equation sin *x* = *a* cos *x* discovering the formula:

- $\sin x={\frac {a}{\sqrt {1+a^{2}}}}$

He gives other trigonometric formulae for right-angled triangles such as:

- $b\sin(A)=a\sin(90^{\circ }-A)$

Al-Battānī used al-Marwazi's idea of tangents ("shadows") to develop equations for calculating tangents and cotangents, compiling tables of them. He also discovered the reciprocal functions of secant and cosecant, and produced the first table of cosecants, which he referred to as a "table of shadows" (in reference to the shadow of a gnomon), for each degree from 1° to 90°.

## Works

*Kitāb az-Zīj*(كتاب الزيج or زيج البتاني, "Book of Astronomical Tables"); Al-Battānī's magnum opus reflects Ptolemaic and Greco-Syriac astronomical theory, with Indo-Persian influences to a lesser degree. Al-Battānī's*zij*contains a description of a quadrant instrument. Of the many early translations into Latin and Spanish, a Latin version*De Motu Stellarum*by Plato of Tivoli (1116), was reprinted with annotations by Regiomontanus, and again at Bologna in 1645. The original manuscript is preserved at the Vatican library in Rome.

*Kitāb az-Zīj aṣ-Ṣābi’*(كتاب الزيج الصابئ) published by Carlo Alfonso Nallino (1899-1907) under the Latin title*Al-Battānī sive Albatenii opus astronomicum: ad fidem codicis Escurialensis Arabice editum*; a multi-volume scientific treatise on geography and astronomical chronology from an Arabic manuscript with Latin annotations. The manuscript is held at the Escorial library.*Arbaʻu Maqālāt*(أربع مقالات, "Four discourses"); a commentary on Ptolemy’s*Quadripartitum de apotelesmatibus e judiciis astrorum*, known as the*Tetrabiblos*. The tenth-century encyclopedist Isḥāq al-Nadīm in his*Kitāb al-Fihrist*lists al-Battānī among a number of authors of commentaries on this work.*Maʻrifat Maṭāliʻi l-Burūj*(معرفة مطالع البروج, "Knowledge of the rising-places of the zodiacal signs")*Kitāb fī Miqdār al-Ittiṣālāt*(كتاب في مقدار الاتصالات); treatise on the four quarters of the sphere.

## In popular culture

A ship in *Star Trek: Voyager* is named after Al-Battānī, known as the USS Al-Batani, which Kathryn Janeway originally served on.

## Citations

- ^ Qifṭī 1903, p. 280.
**^**C.A., Nallino. "al-BATTĀNĪ". Brill. doi:10.1163/1573-3912_islam_sim_1289.**^**"Al-Battānī | Arab astronomer and mathematician".*Encyclopedia Britannica*.**^**"Al-Battani - Oxford Reference".- ^ Hartner, Willy (1970–80). "Al-Battānī, Abū ʿAbd Allāh Muḥammad Ibn Jābir Ibn Sinān al-Raqqī al-Ḥarrānī al–Ṣābi".
*Dictionary of Scientific Biography*. New York: Charles Scribner's Sons. ISBN 978-0-684-10114-9. **^**Barlow, Peter; Kater, Henry; Herschel, Sir John Frederick William (1856). The Encyclopaedia of Astronomy: Comprising Plane Astronomy. R. Griffin. p. 494.**^**Schlager, Neil; Lauer, Josh (2001). Science and Its Times: 700-1449. Gale Group. p. 291.**^**Griffin, Rosarii (2006). Education in the Muslim World: different perspectives. Symposium Books Ltd. p. 31.**^**Angelo, Joseph A. (2014). Encyclopedia of Space and Astronomy. Infobase Publishing. p. 78.**^**Ben-Menaḥem, Ari (2009). Historical Encyclopedia of Natural and Mathematical Sciences. Springer Science & Business Media. p. 541.- ^ Khallikān (ibn) 1868, p. 317.
- ^ O'Connor, John J.; Robertson, Edmund F., "Al-Battani",
*MacTutor History of Mathematics archive*, University of St Andrews. - ^ Chisholm, Hugh, ed. (1911).
*Encyclopædia Britannica*.**1**(11th ed.). Cambridge University Press. p. 491. . **^**Khallikan (ibn) 1868, p. 317.**^**Singer, Charles Joseph (1997).*A short history of science to the nineteenth century*. Courier Dover Publications. p. 135. ISBN 978-0-486-29887-0.**^**Hoskin, Michael (1999-03-18).*The Cambridge Concise History of Astronomy*. Cambridge University Press. p. 58. ISBN 9780521576000.**^**Freely, John (2015-03-30).*Light from the East: How the Science of Medieval Islam Helped to Shape the Western World*. I.B.Tauris. p. 179. ISBN 9781784531386.**^**Dalmau, W. (1997) CRITICAL REMARKS ON THE USE OF MEDIEVAL ECLIPSE RECORDS FOR THE DETERMINATION OF LONG-TERM CHANGES IN THE EARTH'S ROTATION', Surveys in Geophysics 18: 213-223.**^**Ewen A. Whitaker,*Mapping and Naming the Moon*(Cambridge University Press, 1999), p.61.**^**"trigonometry".*Encyclopædia Britannica*. Retrieved 2008-07-21.**^**E. S. Kennedy,*A Survey of Islamic Astronomical Tables,*(Transactions of the American Philosophical Society, New Series, 46, 2), Philadelphia, 1956, pp. 10–11, 32–34.**^**Moussa, Ali (2011). "Mathematical Methods in Abū al-Wafāʾ's Almagest and the Qibla Determinations".*Arabic Sciences and Philosophy*.**21**(1): 1–56. doi:10.1017/S095742391000007X.**^**Battani (al-) 1899.**^**Khallikān (ibn) 1868, pp. 318, 320.**^**Nadīm (al-), p. 640.**^**Khallikān (ibn) 1868, p. 319, n.2.