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6 who worked during the first half of the sixteenth century we shall here mention Peter Apianus or Bienewitz, who taught at the University of Ingolstadt. Besides other works, he published in 1540 a large book, Astronomicum Cæsareum, dedicated to Charles the Fifth. In this beautiful volume the author represented, by means of movable circles of cardboard of various colours, the epicyclical motions of the planets according to the Ptolemean system, and expected to be able in this way to find their positions without computation. The book was received with much applause, and is really in some ways to be admired, though one cannot help agreeing with Kepler in regretting the "miserable industry" of Apianus, which after all only produced a very rough approximation to the real motions of the stars, but which is eminently characteristic of the low state of science at that time. Apianus deserves more thanks for having paid much attention to comets, and for having discovered the important fact that the tails of these bodies are turned away from the sun. This was also pointed out about the same time by Fracastoro of Verona in a work published in 1538, containing an elaborate attempt to revive the theory of concentric spheres of Eudoxus, which had been pushed into the background by the Ptolemean system of the world.

Only three years after Apian's volume appeared the great work of Nicolaus Copernicus, De Revolutionibus (1543), which was destined to become the corner-stone of modern astronomy. We shall in the following so often have occasion to refer to the labours of this great man, that a few words will suffice in this place. Copernicus, who not only discovered the greatest truth in astronomy, but who even by his opponents was admitted to be an astronomer worthy of being classed with Hipparchus and Ptolemy, was born in 1473 at Thorn, on the Vistula, a town which belonged to the Hansa League, and a few years before had come under the suzerainty