Indian Mathematics c11.13

c11.13

28. From the time of M. b. Mūsā onwards the Muhammadan mathematicians made remarkable progress. To illustrate this fact we need only mention a few of their distinguished writers and their works on mathematics. ‘Tābit b. Qorra b. Merwān (826-901) wrote on Euclid, the Almagest, the arithmetic of Nicomachus, the right-angle triangle the parabola, magic squares, amicable numbers, etc. Qosṭā b. Lūka el-Ba’albekī (died c. A.D. 912) translated Diophantus and wrote on the sphere and cylinder, the rule of two errors, etc. El-Battānī (M. b. Gābir b. Sinān, A.D. 877-919) wrote a commentary on Ptolemy and made notable advances in trigonometry. Abū Kāmil Shogā b. Aslam (c. 850-930) wrote on algebra and geometry, the pentagon and decagon, the rule of two errors, etc. Abū 'l-Wefā el-Būzgānī, 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-siǧzī (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-Karchī (M. b. el-Hasan, 1016 A.D.) wrote on arithmetic and indeterminate equations after Diophantus. Alberuni (M. b. Aḥmed, Abū'l-Riḥān el-Bīrūnī) 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. Ibrāhīm el-Chaijāmī, 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.