What are the contributions of Johann muller in trigonometry?

Answer 1

REGIOMONTANUS (1436-1476), German astronomer, was born at Konigsberg in Franconia on the 6th of June 1436. The son of a miller, his name originally was Johann Muller, but he called himself, from his birthplace, Joh. de Monteregio, an appellation which became gradually modified into Regiomontanus. At Vienna, from 1452, he was the pupil and associate of George Purbach (1423-1461), and they jointly undertook a reform of astronomy rendered necessary by the errors they detected in the Alphonsine Tables. In this they were much hindered by the lack of correct translations of Ptolemy's works; and in 1462 Regiomontanus accompanied Cardinal Bessarion to Italy in search of authentic manuscripts. He rapidly mastered Greek at Rome and Ferrara, lectured on Alfraganus at Padua, and completed at Venice in 1463 Purbach's Epitome in Cl. Ptolemaei magnam compositionem (printed at Venice in 1496), and his own De Triangulis (Nuremberg, 1533), the earliest work treating of trigonometry as a substantive science. A quarrel with George of Trebizond, the blunders in whose translation of the Almagesthe had pointed out, obliged him to quit Rome precipitately in 1468. He repaired to Vienna, and was thence summoned to Buda by Matthias Corvinus, king of Hungary, for the purpose of collating Greek manuscripts at a handsome salary. He also finished his Tabulae Directionum(Nuremberg, '475), essentially an astrological work, but containing a valuable table of tangents. An outbreak of war, meanwhile, diverted the king's attention from learning, and in 1471 Regiomontanus settled at Nuremberg. Bernhard Walther, a rich patrician, became his pupil and patron; and they together equipped the first European observatory, for which Regiomontanus himself constructed instruments of an improved type (described in his posthumous Scripta, Nuremberg, 1544). His observations of the great comet of January 1472 supplied the basis of modern cometary astronomy. At a printing-press established in Walther's house by Regiomontanus, Purbach's Theoricae planetarum novaewas published in 1472 or 1473; a series of popular calendars issued from it, and in 1474 a volume ofEphemerides calculated by Regiomontanus for thirty-two years (1474-1506), in which the method of "lunar distances," for determining the longitude at sea, was recommended and explained. In 1472 Regiomontanus was summoned to Rome by Pope Sixtus IV. to aid in the reform of the calendar; and there he died, most likely of the plague, on the 6th of July 1476.