# Muḥammad ibn Jābir al-Ḥarrānī al-Battānī

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 |

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 = sin a cos a {displaystyle tan a={frac {sin a}{cos a}}} sec a = 1 + tan 2 a {displaystyle sec a={sqrt {1+tan ^{2}a}}} He also solved the equation sin x = a cos x discovering the formula: sin x = a 1 + a 2 {displaystyle 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 ∘ − A ) {displaystyle bsin(A)=asin(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

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