THE ASTRONOMICAL WHITINGS OF SCOT 101 



corrected the observations of Ptolemy here, and 

 showed that the retrograde movement amounted to 

 one degree, not in a century as the Greek philosopher 

 had said, but in a shorter period which is variously 

 stated as sixty-six or seventy years. Alfargan re- 

 peated this calculation, and amended that relating 

 to the declination of the ecliptic, which he computed 

 at 23 35". 



This was the progress and these the data which 

 led the Moorish astronomers to abandon the earlier 

 and simpler theories of the sphere as inconsistent 

 with ascertained facts. They were aware of 

 motions among the heavenly bodies not to be 

 explained by the mere supposition that round the 

 earth as a centre moved the concentric spheres 

 on the axes of their poles. It is true that 

 even Ptolemy himself had felt something of this 

 difficulty and had endeavoured to meet it by a 

 theory of eccentrics and epicycles. As knowledge 

 increased, however, this primitive explanation was 

 felt to be cumbrous and unsatisfactory. Aboasar 1 

 and Azarchel gained fame by boldly striking out in 

 new paths, and later Moorish astronomers eagerly 

 followed the lead thus given them, each adding 

 some modification of his own. 



Thus then we return to the preface of Alpetrongi 

 prepared to understand his position when he 

 declares himself obliged to depart from previous 

 traditions. He proceeds to avow himself a scholar 

 of Azarchel, but when we examine his work we find 

 that the theory he proposes differs considerably 

 even from that taught by his immediate master. 



1 For the unfavourable judgment of Mirandola on this astronomer, 

 see infra, p. 143. 



