YAHAYA, ABUT. or WA FA (940-998). An Arabic mathematician and as tronomer, born at Buzjan, and generally known as Abul Wela. Ile translated and commented upon works of ,everal Greek mathematicians. and calculated a table of sines at of half a degree, and also a table of tangents, which, however, was used only for determining the al sin a titude of the sun. The ratio, - ' was called ' ens a by him the 'shadow.' lie is, however, most b ilious for having made the oldest known attempt to solve geometric problem,: with only one open ing of the compatiACS, and wrote a ho(tk. contain ing 12 chapters on geometrical constructions. Our knowledge of this work is due to a Persian translation of an Arabie manuscript. written by a pupil of Abul \Vela. The problems may he divided into three groups: (1) Those deal ing with the solution of geometrical prob lems by one opening of the compasses; 12) to divide a given square in a given number of squares, and to construct a square equal to a number of given squares; this is done by juxta position, and not by the Pythagorean method; (3) problems having for aim the construction of regular polyhedra. In the problem-duel between
Tartaglia (q.v.), on one hand, and Cardan (q.v.) and Ferrari. on the other, problem, of the first group were given for solnthm and appear in the works of Leonardo da Vinci and Cardan. They also occur in several other works of the sixteenth century, but first found accurate scientific ex pression in Steiner's apoinctrischr Construe tionen, etc. (1SS3). Consult: Volpcke, Journel Asiatique, vol. v. (1855) ; Cantor. Geschichte der Mathematik, yol. i. (Leipzig, 1900).