Page:Indian mathematics, Kaye (1915).djvu/59

 and wrote on the sphere and cylinder, the rule of two errors, etc. El-Battāni (M. b. Gabir b. Sinān, A.D. 877–919) wrote a commentary on Ptolemy and made notable advances in trigonometry. Abū Kāmil ShogāShogâ [sic] b. Aslam (c. 850–930) wrote on algebra and geometry, the pentagon and decagon, the rule of two errors, etc. Abū '1-Wefā el-Būzgāni, born in A.D. 940, wrote commentaries on Euclid, Diophantus, Hipparchus. and M. b. Mūsā, works on arithmetic, on the circle and sphere, etc.. etc. Abū Sa 'id, el-sigzi (Ahmed b. M. b. Abdelgalil, A.D., 951–1024) wrote on the trisection of an angle, the sphere, the intersection of the parabola and hyperbola, the Lemmata of Archimedes, conic sections, the hyperbola and its asymptotes, etc., etc. Abū Bekr. el-Karchi (M. b. el-Hasan, 1016 A.D.) wrote on arithmetic and indeterminate equations after Diophantus. Alberuni (M. b. Ahmed, Abū'l-Rihān el-Bīrunī) was born in A.D. 973 and besides works on history, geography, chronology and astronomy wrote on mathematics generally, and in particular on tangents, the chords of the circle, etc. Omār b. Ibrāhim el-Chaijāmi, the celebrated poet, was born about A.D. 1046 and died in A.D. 1123 a few years after Bhāskara was born. He Wrote an algebra in which he deals with cubic equations, a commentary on the difficulties in the postulates of Euclid: on mixtures of metals; and on arithmetical difficulties. This very brief and incomplete resumé of Arabic mathematical works written during the period intervening between the time of Brahmagupta and Bhāskara indicates at least considerable intellectual activity and a great advance on the Indian works of the period in all branches of mathematics except, perhaps, indeterminate equations.