12. Abul Wafa al-Buzjani
(328-387H/940-998AD)

Abu al-Wafa Muhammad Ibn Muhammad Ibn Yahya Ibn Ismail Ibn Abbas al-Buzjani was an engineer, astronomer, and mathematician. Sarton described him as one of the greatest mathematicians of Islam(77).

Abu al-Wafa was born in Buzjan in Khurasan in 328H/940 AD. He studied mathematics under his paternal uncle Abu Umar al-Maghazli and maternal uncle, known as Abu Abdullah Muhammad Ibn Ataba and studied geometry under Abu Yahya al-Marudi and Abu al-Ala' Ibn Karnib. In 348 H/ 959 AD, he moved to Iraq and lived in Baghdad until his death in 387 H/ 998 AD. Abu al-Wafa dedicated his life to writing, observing celestial bodies and teaching. He became a member of the observatory set up by Sharaf ad-Dawla in 377 H(78).

Scientific Contribution

Abu al-Wafa was one of the outstanding scholars in astronomy and mathematics. Several western scholars also acknowledged his outstanding merit in geometry(79).

Al-Buzjani made important contributions to the development of trigonometry. "Cara de Faw" acknowledged that "the services rendered by Abu al-Wafa to trigonometry can by no means be contested. Thanks to him, this science became simpler and clearer. He used the secant and cosecant and developed a new method for the calculation of the sine(80). He was also the first to demonstrate the general theorem of the sine in spherical triangles(81).

Abu al-Wafa was equally a genius in geometry; he was able to solve several geometrical problems with great dexterity.

Major Works

Al-Buzjani left several valuable books, including :

- "Kitab fima Yahtaju Ilaihi al-Kuttab wa al-Ummal min 'Ilm al-Hisab" (Book on What Is Necessary from the Science of Arithmetic for Scribes and Businessmen) a book of applied arithmetic. Two incomplete copies of this treatise are kept in Leyden in Holland and in Cairo.

- "Kitab al-Kamil"(the Complete Book)

- "Kitab fima Yahtaj Ilaih as-Suna' fi 'Amal al-Handasa" (Book on What Is Necessary from Geometric Construction for the Artisan), a book of applied geometry, written at the request of the Caliph Baha' ad-Dawla. A copy of this treatise is kept in the library of Ayasofya Mosque in Istanbul.

- "Kitab al-Majesti" (Almagest Book) is the most famous of all his books. An incomplete copy of it is kept in the National Library of Paris.

- "Kitab al-Handsa" (Applied Geometry)

Apart from these treatises, Abu al-Wafa wrote rich commentaries on Euclid, Diophantus and al-Khawarizmi, but all of these were lost.

In summary, al-Buzjani's researches and books had a significant influence of the progress of science, in particular astronomy and trigonometry. He was among the pioneers who laid the ground to the emergence of analytical geometry by finding geometric solutions to some algebraic equations(82).