Al-Battani

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.[5] Ibn Khallikan expresses ignorance on the question of his Muslim faith, and points out that his epithet aṣ-Ṣabi’ suggests possible Sabian-sect ancestry.[11][12] Some western historians claim he had noble origins as an Arab prince,[13] but traditional Arabic biographers make no mention of this.[5] 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.[14]

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.[12]

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.[1]

Al-Battānī amended some of Ptolemy's results and compiled new tables of the Sun and Moon, long accepted as authoritative.[13] 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.[12] Al-Battānī observed that the direction of the Sun's apogee, as recorded by Ptolemy, was changing.[15] [n 2]

Al-Battānī's work was instrumental in the development of science and astronomy.[12] Copernicus, in his book that initiated the Copernican Revolution, the De Revolutionibus Orbium Coelestium, quotes his name no fewer than 23 times,[16] and also mentions him in the Commentariolus.[17] Tycho Brahe, Riccioli, Kepler, Galileo and others frequently cited him or his observations.[5] His data is still used in geophysics.[18] The major lunar crater Albategnius is named in his honor.[19]

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

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

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

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

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

He gives other trigonometric formulae for right-angled triangles such as:[12]

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

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°.[20]

• 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.[5][21] Al-Battānī's zij contains a description of a quadrant instrument.[22] 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,[13] and again at Bologna in 1645. The original manuscript is preserved at the Vatican library in Rome.[13]

• 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 [23]; 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")[24]; 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.[25][n 4]
• Maʻrifat Maṭāliʻi l-Burūj (معرفة مطالع البروج, "Knowledge of the rising-places of the zodiacal signs")[n 5][11]
• Kitāb fī Miqdār al-Ittiṣālāt (كتاب في مقدار الاتصالات); treatise on the four quarters of the sphere.

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

• List of Arab scientists and scholars
• Zij

• Al-Battānī sive Albatenii, Opus Astronomicum. Ad fidem codicis escurialensis arabice editum, ed. by Carlo Alfonso Nallino. Milan, Ulrico Hoepli, 1899-1907 [= Pubblicazioni del Reale Osservatorio di Brera in Milano, nr. XL], 412 + 450 + 288 pp. (anast.: I-III, [La Finestra editrice], Lavis 2002 ISBN 978-8888097-26-8

• Battani (al-), Muḥammad ibn Jabir (1899). Nallino, Carlo Alfonso (ed.). Al-Battānī sive Albatenii opus astronomicum: ad fidem codicis Escurialensis Arabice editum (Kitāb Zīj al-Ṣābī’) (in Arabic). 3. Milan: Mediolani Insubrum: Prostat apud Urlichum Hoeplium. ISBN 978-8888097-26-8.CS1 maint: ref=harv (link)
• Khallikān (ibn), Aḥmad i. M (1868). Mac Guckin de Slane, William (ed.). Wafayāt al-A’yān wa Anbā’ (Ibn Khallian’s Biographical Dictionary). III. Paris & London: W.H. Allen. p. 317.CS1 maint: ref=harv (link)
• Nadīm (al-), Abū al-Faraj Muḥammad ibn Isḥāq Abū Ya’qūb al-Warrāq (1970). Dodge, Bayard (ed.). The Fihrist of al-Nadim; a tenth-century survey of Muslim culture. New York & London: Columbia University Press.CS1 maint: ref=harv (link)

• Qifṭī (al-), Jamāl al-Dīn Abū al-Ḥasan ‘Alī ibn Yūsuf (1903). Lippert, Julius (ed.). Ta’rīkh al-Ḥukamā’ (in Arabic). Leipzig: Theodor Weicher. p. 280.CS1 maint: ref=harv (link)

• Sarton, George (1947). Introduction to the History of Science. I. Baltimore: Williams and Wilkins. p. 602.CS1 maint: ref=harv (link)

• Smith, David Eugene (1925) [1923]. History of Mathematics. I. Boston: Ginn. p. 175.CS1 maint: ref=harv (link)

• 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.
• O'Connor, John J.; Robertson, Edmund F., "Abu Abdallah Mohammad ibn Jabir Al-Battani", MacTutor History of Mathematics archive, University of St Andrews.

• Dalen, Benno van (2007). "Battānī: Abū ʿAbd Allāh Muḥammad ibn Jābir ibn Sinān al‐Battānī al‐Ḥarrānī al‐Ṣābiʾ". In Thomas Hockey; et al. (eds.). The Biographical Encyclopedia of Astronomers. New York: Springer. pp. 101–3. ISBN 978-0-387-31022-0. (PDF version)
• Weisstein, Eric Wolfgang (ed.). "Albategnius (ca. 858–929)". ScienceWorld.
• Texts on Wikisource:
  • Gilman, D. C.; Peck, H. T.; Colby, F. M., eds. (1905). "al-Battani, Mohammed ibn Jabir ibn Sinan". New International Encyclopedia (1st ed.). New York: Dodd, Mead.
  • "Albategnius". Encyclopædia Britannica. 1 (11th ed.). 1911. p. 491.
  • "al-Battani". New International Encyclopedia. 1920.