M 23, 24] The Pythagoreans 25 



Greek thought, and was in later times an established part 

 of Greek systems, whence it has been handed down, 

 almost unchanged, to modern times. This belief is thus 

 2,000 years older than the belief in the rotation of 

 the earth and its revolution round the sun (chapter iv.), 

 doctrines which we are sometimes inclined to couple with 

 it as the foundations of modern astronomy. 



In Pythagoras occurs also, perhaps for the first time, an 

 idea which had an extremely important influence on ancient 

 and mediaeval astronomy. Not only were the stars supposed 

 to be attached to a crystal sphere, which revolved daily 

 on an axis through the earth, but each of the seven 

 planets (the sun and moon being included) moved on a 

 sphere of its own. The distances of these spheres from 

 the earth were fixed in accordance with certain speculative 

 notions of Pythagoras as to numbers and music ; hence 

 the spheres as they revolved produced harmonious sounds 

 which specially gifted persons might at times hear: this 

 is the origin of the idea of the music of the spheres which 

 recurs continually in mediaeval speculation and is found 

 occasionally in modern literature. At a later stage these 

 spheres of Pythagoras were developed into a scientific 

 representation of the motions of the celestial bodies, which 

 remained the basis of astronomy till the time of Kepler 

 (chapter VIL). 



24. The Pythagorean Philolaus, who lived about a 

 century later than his master, introduced for the first time 

 the idea of the motion of the earth : he appears to have 

 regarded the earth, as well as the sun, moon, and five 

 planets, as revolving round some central fire, the earth 

 rotating on its own axis as it revolved, apparently in order 

 to ensure that the central fire should always remain in- 

 visible to the inhabitants of the known parts of the earth. 

 That the scheme was a purely fanciful one, and entirely 

 different from the modern doctrine of the motion of the 

 earth, with which later writers confused it, is sufficiently 

 shewn by the invention as part of the scheme of a purely 

 imaginary body, the counter-earth (avrt^wi/), which brought 

 the number of moving bodies up to ten, a sacred Pytha- 

 gorean number. The suggestion of such an important 

 idea as that of the motion of the earth, an idea so 



