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2, had been introduced into Europe during the Middle Ages. Another impulse was given by the voyages of discovery, as navigators were obliged to trust entirely to the stars and the compass, and therefore required as perfect a theory as possible of the motions of the heavenly bodies. We see accordingly at the end of the fifteenth century and the beginning of the sixteenth considerable stir in the camp of science, but as yet only in Germany—a circumstance not difficult to explain. Though divided into a great number of semi-independent states, Germany bore still the proud name of the Holy Roman Empire, and on account of the claims represented by this name the Germans had for a long time been in constant intercourse with Italy, the land with the great past, and still, notwithstanding its political misery, the leader of civilisation. It was an intercourse of a peaceful and commercial as well as of a warlike character; but in both ways was this of benefit to the Germans, producing among them much knowledge of foreign affairs, and giving them greater facilities for taking up the scientific work of the ancients than were found in other parts of Europe.

The first astronomer of note was Georg Purbach (1423–1461), who studied at the University of Vienna, and afterwards for some time in Italy. His principal work on astronomy (Theoricæ Novæ Planetarum) attempted to develop the old hypothesis of material celestial spheres, and was but a mixture of Aristotelean cosmology and Ptolemean geometry; but he was the first European to make use of trigonometry, the principal legacy which astronomers owe to the Arabs. Purbach endeavoured to get beyond the rudiments of spherical astronomy, which hitherto had formed the only subject for astronomical lectures, and had been taught through the medium of a treatise written in the thirteenth century by John