Abul Wafa Muhammad Ibn Muhammad Ibn Yahya Ibn Ismail al-Buzjani was born in Buzjan, Nishapur in 940 C.E. He flourished as a large mathematician and astronomer at Baghdad and died in 997/998 C.E. He learnt numbers in Baghdad. In 959 C.E. he migrated to Iraq and dwelled there till his death.
Abul Wafa’s major assistance lies in some parts of mathematics, especially geometry and trigonometry. In geometry his assistance comprises solution of geometrical problems with unfastening of the compass; construction of a square matching to other squares; normal polyhedra; construction of normal hectagon taking for its edge half the edge of the equilateral triangle inscribed in the identical around; buildings of parabola by points and geometri- cal answer of the formulas:
x4 = a and x4 + ax3 = b
Abul Wafa’s contribution to the development of trigonometry was extensive. He was the first to display the generality of the sine theorem relative to spherical triangles. He developed a new procedure of constructing sine tables, the worth of sin 30′ being correct to the eighth decimal location. He furthermore evolved relations for sine (a+b) and the formula:
2 sin2 (a/2) = 1 – cos a , and
sin a = 2 sin (a/2) cos (a/2)
In supplement, he made a special study of the tangent and calculated a table of tangents. He presented the secant and cosecant for the first time, knew the relatives between the trigonometric lines, which are now used to characterise them, and undertook comprehensive investigations on conics.
Apart from being a mathematician, Abul Wafa furthermore assisted to astronomy. In this area he discussed distinct movements of the moon, and discovered ‘variation’. He was furthermore one of the last Arabic translators and commentators of Greek works.
He composed a large number of publications on mathematics and other subjects, most of which have been lost or live in changed types. His contribution encompasses Kitab ‘Ilm al-Hisab, a functional book of arithmetic, al-Kitab al-Kamil (the Complete Book), Kitab al-Handsa (Applied Geometry). Apart from this, he composed rich commentaries on Euclid, Diophantos and al-Khawarizmi, but all of these have been lost. His publications now extant include Kitab ‘Ilm al-Hisab, Kitab al- Handsa and Kitab al-Kamil.
His astronomical information on the movements of the moon has been admonished in that, in the case of variety’ the third inequality of the moon as he considered was the second part of the ‘evection’. But, according to Sedat, what he discovered was the identical that was found out by Tycho Brache six centuries later. Nonetheless, his assistance to trigonometry was extremely important in that he evolved the knowledge on the tangent and presented the secant and cosecant for the first time; in detail a sizeable part of today’s trigonometry can be traced back to him.
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