He is also credited with compiling the tables ofsines andtangents at 15' intervals. He also introduced thesecant and cosecant functions, as well studied the interrelations between the sixtrigonometric lines associated with an arc.[2] HisAlmagest 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.
Abu al-Wafa' was the first to build a wallquadrant to observe the sky.[6] It has been suggested that he was influenced by the works ofal-Battani as the latter described a quadrant instrument in hisKitāb az-Zīj.[6] His use of the concept of thetangent helped solve problems involving right-angledspherical triangles. He developed a new technique to calculatesine tables, allowing him to construct more accurate tables than his predecessors.[7]
In 997, he participated in an experiment to determine the difference in local time between his location, Baghdad, and that of al-Biruni (who was living in Kath, now a part ofUzbekistan).[8] 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 withAbū Sahl al-Qūhī, who was a famous maker of astronomical instruments.[7] While what is extant from his works lacks theoretical innovation, his observational data were used by many later astronomers, including al-Biruni.[7]
Among his works on astronomy, only the first seven treatises of hisAlmagest (Kitāb al-Majisṭī) are now extant.[9] The work covers numerous topics in the fields of plane andspherical trigonometry, planetary theory, and solutions to determine the direction ofQibla.[6][7]
He defined the tangent function, and he established severaltrigonometric identities in their modern form, where theancient Greek mathematicians had expressed the equivalent identities in terms of chords.[10] The trigonometric identities he introduced were:
A book ofzij calledZīj al-wāḍiḥ (زيج الواضح), no longer extant.[7]
"A Book on Those Geometric Constructions Which Are Necessary for a Craftsman", (كتاب في ما یحتاج إليه الصانع من الأعمال الهندسيةKitāb fī mā yaḥtāj ilayh al-ṣāniʿ min al-aʿmāl al-handasiyya).[13] This text contains over one hundred geometric constructions, including for a regularheptagon, which have been reviewed and compared with other mathematical treatises. The legacy of this text in Latin Europe is still debated.[14][15]
"A Book on What Is Necessary from the Science of Arithmetic for Scribes and Businessmen", (كتاب في ما يحتاج إليه الكتاب والعمال من علم الحسابKitāb fī mā yaḥtāj ilayh al-kuttāb wa’l-ʿummāl min ʾilm al-ḥisāb).[13] This is the first book wherenegative numbers have been used in the medieval Islamic texts.[7]
^Sigfried J. de Laet (1994).History of Humanity: From the seventh to the sixteenth century.UNESCO. p. 931.ISBN978-92-3-102813-7.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
^Subtelny, Maria E. (2007).Timurids in Transition. BRILL. p. 144.ISBN9789004160316.Persian mathematician Abu al-Wafa Muhammad al-Buzjani
^S. Frederick Starr (2015).Lost Enlightenment: Central Asia's Golden Age from the Arab Conquest to Tamerlane. Princeton University Press. p. 177.ISBN9780691165851.
