The German astronomer and mathematician Regiomontanus (1436-1476) constructed the first European observatory and established trigonometry as a separate area of study in mathematics.
Regiomontanus, called after the Latinized form of his birthplace, Königsberg, in the duchy of Coburg, was born Johann Müller on June 6, 1436, the son of a miller. At the age of 12 he began the study of classical languages and mathematics at the University of Leipzig. In 1452 he moved to Vienna and became the favorite pupil of Georg Peurbach, astronomer and mathematician, who interested Regiomontanus in securing a truly reliable version of Ptolemy's Almagest.
A year after Peurbach's death in 1461, Regiomontanus went to Italy and established close contacts with Cardinal Bessarion, the leading Greek scholar of the time. Regiomontanus made quick progress in Greek and studied various Greek mathematical and astronomical texts in addition to Ptolemy's Almagest. The study of this latter work enabled him to complete Peurbach's Epitome in Cl. Ptolemaei magnam compositionem, but it saw print only in 1496.
The most important work of Regiomontanus, completed in 1464 but printed in 1533, was the first fullfledged monograph on trigonometry, De triangulis omnimodis libri quinque (Five Books on All Kinds of Triangles). The first two books dealt with plane trigonometry, while the rest were largely devoted to spherical trigonometry. Although Regiomontanus relied heavily on Arabic and Greek sources, such as al-Battani, Nasir al-Din al-Tusi, Menealos, Theodosius, and Ptolemy, his work was the starting point of a new development leading to modern trigonometry.
In 1468 Regiomontanus went to the court of King Matthias Corvinus of Hungary at Buda to serve as librarian of one of the richest collections of codices in existence in Europe. There he completed his Tabulae directionum et projectionum, the first European study of Diophantes' Algebra.
In 1471 Regiomontanus went to Nuremberg at the invitation of Bernhard Walther, a rich citizen who provided him with the means to set up the first observatory in Europe. It was equipped with instruments of Regiomontanus's own making, which he described in Scripta de torqueto, astrolabio armillari, first printed in 1544. His most important observations concerned the great comet of 1472 (probably Halley's comet). Walther also set up a printing press and published Regiomontanus's calendars and pamphlets. Regiomontanus published Peurbach's planetary theory, Theoricae novae planetarum, and his own ephemerides for 1474-1506, which contained a method of calculating longitudes at sea on the basis of the motion of the moon. The book was used by the leading navigators of the times.
At the summons of Pope Sixtus IV, Regiomontanus, a newly appointed titular bishop of Ratisbon, journeyed to Italy in the fall of 1475 to undertake the reform of the calendar. He died on July 6, 1476, probably the victim of an epidemic.
There is a chapter on Regiomontanus in Lynn Thorndike, Science and Thought in the Fifteenth Century (1929). Also useful are J. L. E. Dreyer, A History of Astronomy from Thales to Kepler (1905; rev. ed. 1953); Lynn Thorndike, A History of Magic and Experimental Science vols. 5 and 6 (1941); and A. C. Crombie, Augustine to Galileo: The History of Science A.D. 400-1650 (1953).