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8 the heliocentric idea. Having no materials from which to deduce the true laws of the motion of the planets in elliptic orbits, he was obliged to make use of the excentric circles and epicycles of the ancients, by which he greatly marred the beauty and simplicity of his system. He did not possess accurate instruments, and took but few observations with those he had. The idea does not seem to have struck him that it was indispensable to follow the planets through a number of years with carefully constructed instruments, and that only in that way could the true theory of planetary motion be found.

There was much to be done yet ere the reform of astronomy could be accomplished. The pressing want of new tables to take the place of the antiquated Alphonsine tables was supplied a few years after the death of Copernicus by Erasmus Reinhold, but though the positions of the planets could be computed from them with greater accuracy than from the old tables, the "Prutenic tables" (published in 1551) did not by this superiority offer any proof of the actual truth of the Copernican principle.

A century had now elapsed since the study of astronomy had commenced to revive in Italy and Germany, but as yet the work accomplished had chiefly been of a tentative and preparatory kind, Copernicus alone having attempted to make science advance along a new path. Still, much useful work had been done. The labours of the ancients had now become accessible in the originals; the Arabs and Regiomontanus had developed trigonometry, and thereby greatly facilitated astronomical computations; Copernicus had shaken the implicit conviction of the necessity of clinging to the complicated Ptolemean system, and had offered the world an alternative and simpler system, while new tables had been computed to take the place of the