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...