DISCOVERIES IN THE CELESTIAL SPACES. 315 



parent revolution of the heaven of the fixed stars by the di- 

 urnal rotation of the earth round its axis ; and by its annual 

 movement round the sun he had afforded an equally perfect 

 solution of the most striking movements of the planets (their 

 stationary conditions and their retrogressions), and thus given 

 the true reason of the so-called second inequality of the plan-, 

 ets. The first inequality, or the unequal movement of the 

 planets in their orbits, he left unexplained. True to the an- 

 cient Pythagorean principle of the perfectibility inherent in 

 circular movements, Copernicus thought that he required for 

 his structure of the universe some of the epicycles of Apollo- 

 nius of Perga, besides the eccentric circles having a vacuum 

 in their center. However bold was the path adventured on, 

 the human mind could not at once emancipate itself from all 

 earlier views. 



The equal distance at which the stars remained, while the 

 whole vault of heaven seemed to move from east to west, had 

 led to the idea of a firmament and a solid crystal sphere, in 

 which Anaximenes (who was probably not much later than 

 Pythagoras) had conjectured that the stars were riveted like 

 nails.* Geminus of Rhodes, the cotemporary of Cicero, doubt- 

 ed whether the constellations lay in one uniform plane, being 

 of opinion that some were higher and others lower than the 

 rest. The idea formed of the heaven of the fixed stars was 

 extended to the planets, and thus arose the theory of the ec- 

 centric intercalated spheres of Eudoxus and Menaechmus, and 

 of Aristotle, who was the inventor of retrograde spheres. The 

 theory of epicycles a construction which adapted itself most 

 readily to the representation and calculation of the planetary 

 movements was,, a century afterward, made by the acute 

 mind of Apollonius to supersede solid spheres. However much 

 I may incline to mere ideal abstraction, I here refrain from 

 attempting to decide historically whether, as Ideler believes, 

 it was not until after the establishment of the Alexandrian 

 Museum that " a free movement of the planets in space was 

 regarded as possible," or whether, before that period, the in- 

 tercalated transparent spheres (of which there were twenty- 

 seven according to Eudoxus, and fifty-five according to Aris- 

 totle), as well as the epicycles which passed from Hipparchus 

 and Ptolemy to the Middle Ages, were regarded generally not 



* Plat., De plac. Philos., ii., 14; Aristot., Meteorol., xi., 8; De Ceelo, 

 ii., 8. On the theory of spheres generally, and on the retrograding 

 spheres of Aristotle in particular, see Ideler's Vorlesung.uber Eudoxus, 

 1828, s. 49-60. 



