The Info List - Abū Al-Wafā' Būzjānī

--- Advertisement ---

Abū al-Wafāʾ, Muḥammad ibn Muḥammad ibn Yaḥyā ibn Ismāʿīl ibn al-ʿAbbās al-Būzjānī or Abū al-Wafā Būzhjānī (Persian: ابوالوفا بوزجانی or بوژگانی‎)[1] (10 June 940 – 15 July 998) was a Persian[2][3] mathematician and astronomer who worked in Baghdad. He made important innovations in spherical trigonometry, and his work on arithmetics for businessmen contains the first instance of using negative numbers in a medieval Islamic text. He is also credited with compiling the tables of sines and tangents at 15 ' intervals. He also introduced the secant and cosecant functions, as well studied the interrelations between the six trigonometric lines associated with an arc.[4] His Almagest was widely read by medieval Arabic astronomers in the centuries after his death. He is known to have written several other books that have not survived.


1 Life 2 Astronomy

2.1 Almagest

3 Mathematics 4 Works 5 Legacy 6 Notes 7 References 8 External links

Life[edit] He was born in Buzhgan, (now Torbat-e Jam) in Khorasan (in today's Iran). At age 19, in 959 AD, he moved to Baghdad and remained there for the next forty years, and died there in 998.[4] He was a contemporary of the distinguished scientists Abū Sahl al-Qūhī and Al-Sijzi who were in Baghdad at the time and others like Abu Nasr ibn Iraq, Abu-Mahmud Khojandi, Kushyar ibn Labban and Al-Biruni.[5] In Baghdad, he received patronage by members of the Buyid court.[6] Astronomy[edit] Abu Al-Wafa' was the first to build a wall quadrant to observe the sky.[5] It has been suggested that he was influenced by the works of Al-Battani as the latter describes a quadrant instrument in his Kitāb az-Zīj.[5] His use of tangent helped to solve problems involving right-angled spherical triangles, and developed a new technique to calculate sine tables, allowing him to construct more accurate tables than his predecessors.[6] In 997, he participated in an experiment to determine the difference in local time between his location and that of al-Biruni (who was living in Kath, now a part of Uzbekistan). The result was very close to present-day calculations, showing a difference of approximately 1 hour between the two longitudes. Abu al-Wafa is also known to have worked with Abū Sahl al-Qūhī, who was a famous maker of astronomical instruments.[6] While what is extant from his works lacks theoretical innovation, his observational data were used by many later astronomers, including al-Biruni.[6] Almagest[edit] Among his works on astronomy, only the first seven treatises of his Almagest (Kitāb al-Majisṭī) are now extant.[7] The work covers numerous topics in the fields of plane and spherical trigonometry, planetary theory, and solutions to determine the direction of Qibla.[5][6] Mathematics[edit] He established several trigonometric identities such as sin(a ± b) in their modern form, where the Ancient Greek mathematicians had expressed the equivalent identities in terms of chords.[8]

sin ⁡ ( α ± β ) = sin ⁡ α cos ⁡ β ± cos ⁡ α sin ⁡ β

displaystyle sin(alpha pm beta )=sin alpha cos beta pm cos alpha sin beta

He also discovered the law of sines for spherical triangles:

sin ⁡ A

sin ⁡ a


sin ⁡ B

sin ⁡ b


sin ⁡ C

sin ⁡ c

displaystyle frac sin A sin a = frac sin B sin b = frac sin C sin c

where A, B, C are the sides (measured in radians on the unit sphere) and a, b, c are the opposing angles.[8] Some sources suggest that he introduced the tangent function, although other sources give the credit for this innovation to al-Marwazi.[8] Works[edit]

Almagest (كتاب المجسطي Kitāb al-Majisṭī). A book of zij called Zīj al‐wāḍiḥ (زيج الواضح), no longer extant.[6] "A Book on Those Geometric Constructions Which Are Necessary for a Craftsman", (كتاب في ما یحتاج إليه الصانع من الأعمال الهندسية Kitāb fī mā yaḥtāj ilayh al-ṣāniʿ min al-aʿmāl al-handasiyya).[9] This text contains over one hundred geometric constructions, including for a regular heptagon, which have been reviewed and compared with other mathematical treatises. The legacy of this text in Latin Europe is still debated.[10][11] "A Book on What Is Necessary from the Science of Arithmetic for Scribes and Businessmen", (كتاب في ما يحتاج إليه الكتاب والعمال من علم الحساب Kitāb fī mā yaḥtāj ilayh al-kuttāb wa’l-ʿummāl min ʾilm al-ḥisāb).[9] This is the first book where negative numbers have been used in the medieval Islamic texts.[6]

He also wrote translations and commentaries on the algebraic works of Diophantus, al-Khwārizmī, and Euclid's Elements.[6] Legacy[edit]

The crater Abul Wáfa on the Moon is named after him. on June 2015 Google has changed its logo in memory of Abu al-Wafa' Buzjani.


^ "بوزجانی". Encyclopaediaislamica.com. Archived from the original on 2008-10-25. Retrieved 2009-08-30.  ^ Ben-Menahem, A. (2009). Historical encyclopedia of natural and mathematical sciences (1st ed.). Berlin: Springer. p. 559. ISBN 978-3-540-68831-0. 970 CE Abu al-Wafa al-Buzjani (940–998, Baghdad). Persian astronomer and mathematician.  ^ Sigfried J. de Laet (1994). History of Humanity: From the seventh to the sixteenth century. UNESCO. p. 931. ISBN 978-92-3-102813-7. The science of trigonometry as known today was established by Islamic mathematicians. One of the most important of these was the Persian Abu' l-Wafa' Buzjani (d. 997 or 998), who wrote a work called the Almagest dealing mostly with trigonometry  ^ a b O'Connor, John J.; Robertson, Edmund F., "Mohammad Abu'l-Wafa Al-Buzjani", MacTutor History of Mathematics archive, University of St Andrews . ^ a b c d Moussa, Ali (2011). "Mathematical Methods in Abū al-Wafāʾ's Almagest and the Qibla Determinations". Arabic Sciences and Philosophy. Cambridge University Press. 21 (1). doi:10.1017/S095742391000007X.  ^ a b c d e f g h Hashemipour 2007. ^ Kennedy, E. S. (1956). Survey of Islamic Astronomical Tables. American Philosophical Society. p. 12.  ^ a b c Jacques Sesiano, "Islamic mathematics", p. 157, in Selin, Helaine; D'Ambrosio, Ubiratan, eds. (2000), Mathematics Across Cultures: The History of Non-western Mathematics, Springer, ISBN 1-4020-0260-2  ^ a b Youschkevitch 1970. ^ Raynaud 2012. ^ Gamwell, Lynn (2 December 2015). "Why the history of maths is also the history of art". The Guardian. Retrieved 3 December 2015. 


O'Connor, John J.; Robertson, Edmund F., "Mohammad Abu'l-Wafa Al-Buzjani", MacTutor History of Mathematics archive, University of St Andrews . Hashemipour, Behnaz (2007). "Būzjānī: Abū al‐Wafāʾ Muḥammad ibn Muḥammad ibn Yaḥyā al‐Būzjānī". In Thomas Hockey; et al. The Biographical Encyclopedia of Astronomers. New York: Springer. pp. 188–9. ISBN 978-0-387-31022-0.  (PDF version) Raynaud, D. (2012), "Abū al-Wafāʾ Latinus? A Study of Method", Historia Mathematica, 39 (1): 34–83, doi:10.1016/j.hm.2011.09.001  (PDF version) Youschkevitch, A.P. (1970). "Abū'l-Wafāʾ Al-Būzjānī, Muḥammad Ibn Muḥammad Ibn Yaḥyā Ibn Ismāʿīl Ibn Al-ʿAbbās". Dictionary of Scientific Biography. 1. New York: Charles Scribner's Sons. pp. 39–43. ISBN 0-684-10114-9. 

External links[edit]

v t e

Mathematics in medieval Islam


9th century

'Abd al-Hamīd ibn Turk Sind ibn Ali al-Jawharī Al-Ḥajjāj ibn Yūsuf Al-Kindi Al-Mahani al-Dinawari Banū Mūsā Hunayn ibn Ishaq al-Khwārizmī Yusuf Al-Khuri ibn Qurra Na'im ibn Musa Sahl ibn Bishr al-Marwazi Abu Said Gorgani

10th century

al-Sufi Abu al-Wafa al-Khāzin Abū Kāmil Al-Qabisi al-Khojandi Ahmad ibn Yusuf Aṣ-Ṣaidanānī al-Uqlidisi Al-Nayrizi Al-Saghani Brethren of Purity Ibn Sahl Ibn Yunus Ibrahim ibn Sinan Al-Battani Sinan ibn Thabit Al-Isfahani Nazif ibn Yumn al-Qūhī Abu al-Jud al-Majriti al-Jabali

11th century

al-Zarqālī Abu Nasr Mansur Said al-Andalusi Ibn al-Samh Al-Biruni Alhazen ibn Fatik Al-Sijzi al-Nasawī Al-Karaji Avicenna Muhammad al-Baghdadi ibn Hud al-Jayyānī Kushyar Gilani Al-Muradi Al-Isfizari Abu Mansur al-Baghdadi

12th century

Al-Samawal al-Maghribi Avempace Al-Khazini Omar Khayyam Jabir ibn Aflah al-Hassar Al-Kharaqī Sharaf al-Dīn al-Ṭūsī Ibn al-Yasamin

13th century

al-Hanafi al-Abdari Muhyi al-Dīn al-Maghribī Ibn 'Adlan Nasir al-Din al-Tusi Shams al-Dīn al-Samarqandī Ibn al‐Ha'im al‐Ishbili Ibn Abi al-Shukr al-Hasan al-Marrakushi

14th century

al-Umawī Ibn al-Banna' Ibn Shuayb Ibn al-Shatir Kamāl al-Dīn al-Fārisī Al-Khalili Qutb al-Din al-Shirazi Ahmad al-Qalqashandi Ibn al-Durayhim

15th century

al-Qalaṣādī Ali Qushji al-Wafa'i al-Kāshī al-Rūmī Ulugh Beg Ibn al-Majdi Sibt al-Maridini al-Kubunani

16th century

Al-Birjandi Muhammad Baqir Yazdi Taqi ad-Din Ibn Hamza al-Maghribi Ibn Ghazi al-Miknasi Ahmad Ibn al-Qadi

Mathematical works

The Compendious Book on Calculation by Completion and Balancing De Gradibus Principles of Hindu Reckoning Book of Optics The Book of Healing Almanac Encyclopedia of the Brethren of Purity Toledan Tables Tabula Rogeriana Zij


Alhazen's problem Islamic geometric patterns


Al-Azhar University Al-Mustansiriya University House of Knowledge House of Wisdom Constantinople observatory of Taqi al-Din Madrasa Maktab Maragheh observatory University of Al Quaraouiyine


Babylonian mathematics Greek mathematics Indian mathematics


Byzantine mathematics European mathematics Indian mathematics

Authority control

WorldCat Identities VIAF: 90065177 LCCN: n89120201 ISNI: 0000 0000 8454 3125 GND: 102419213 SUDOC: 118702882 BNF: