counter-earth, possibly invented to explain the eclipses of the moon, 

 and that of Olympus, as a source of light, were soon discredited 

 and gave way to a much more important and interesting theory. 

 Ecphantus, one of the youngest of the Pythagoreans, held that the 

 earth turned of itself in a definite direction (that is, turned upon 

 its axis), and for this reason Copernicus, in the sixteenth century, 

 was able to claim that his system was not a new one but was a 

 revival of the theory held by the Pythagoreans. The marked 

 difference in the luminosities of the different planets, and the differ- 

 ences, indeed, in the intensity of one planet at different times s^>on 

 suggested that these were at different distances from the earth, and 

 so a blow was given to the ancient notion of the one dome of 

 heaven supporting the heavenly bodies all at a fixed distance from 

 the earth. 



Eudoxus of Cnidus, 370 B.C., unable to tear himself away en- 

 tirely from the notion of the spherical vault of heaven, but seeing 

 the insufficiency of the theory of one dome, postulated one for each 

 separate motion, but the increasing number of vaults was becoming 

 unintelligible, and a hundred years later Aristarchus of Samos, 

 having learned from Eudoxus that the sun was considerably larger 

 than the earth, was able to advance a new theory which had none 

 of the intricacies and complexities and absurdities of the old sup- 

 position; the earth had to lay down its sceptre, geocentricity was 

 superseded by heliocentricity and Aristarchus became the Coperni- 

 cus of antiquity. But the new theory was not to be accorded a 

 hearty welcome, for Hipparchus, the next astronomer of note, went 

 back to the geocentric view. Notwithstanding this, Hipparchus 

 holds an important place in the pages of the history of astronomy, 

 because he assisted materially in coordinating that science with the 

 mathematics of his day. He was able to compute the length of the 

 year differing by only four minutes from present day calculation; 

 he observed and made a catalogue of 1080 stars, dividing them into 

 six classes of brightness or magnitude, a work which is one of the 

 finest monuments of ancient astronomy. Because he supposed the 

 earth to be fixed, he found it necessary to assume that the centre, 

 around which the sun revolved, was a point a little distance from 

 the earth, which point he called the eccentric. Ptolemy, writing 

 250 years later, expounded the work of Hipparchus, adopting his 



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