TEE PREDECESSORS OF COPERNICUS. 317 



The views of Aristarchus on the system of the universe are reported 

 by Archimedes. "The World/' he says, "is by the greater part of 

 astronomers called a sphere whose center is the center of the earth 

 and whose radius is the distance from the earth to the sun. But 

 Aristarchus of Samos, in quoting this opinion, refutes it. According 

 to him, the world is very much greater; he supposes the sun to be 

 immovable, as also are the stars, and he believes that the earth turns 

 round the sun as a center, and that the magnitude of the sphere of 

 the fixed stars, whose center is that of the sun, is such that the cir- 

 cumference of the circle described by the earth is in proportion to the 

 distance of the fixed stars as the center of a circle is to its surface." 

 Copernicus himself did not announce and describe his system with 

 the magistral completeness and brevity of these few words. It is 

 clear that we have here not only the view of Aristarchus, but also the 

 opinion of Archimedes. We must assume that this announcement 

 was unknown to Copernicus who reports the misty theories of the 

 Pythagoreans, but makes no mention of Aristarchus in this connection.* 



Plato (428-347 B. C.) taught that the earth was the center of 

 celestial motions and that the planets and stars revolved about it 

 on eight concentric spheres or circles. He plainly states that the moon 

 shines by the sun's reflected light. Plato was not primarily an as- 

 tronomer, and in fact held astronomy to be less dignified than the 

 pure geometry that underlaid celestial motions, but his astronomical 

 opinions were always of influence, especially in the orient where he 

 held a high authority. He expressed and enforced the general idea 

 that the heavenly bodies, being perfect in their essence, must necessarily 

 revolve in circles, and with uniform, not variable, motion. 



Eudoxus of Cnidus (409-356 B. C.) elaborated the ideas of Plato 

 into a scientific system. By this time the simpler motions of the moon 

 were well known, and to account for them he found three spheres to 

 be necessary. One produced its daily motion of rising and setting, 

 another its monthly motion from west to east, while the third had 

 to do with its motions north and south of the ecliptic. The sun was 

 likewise provided with three spheres, and each of the planets had four 

 (since the planets sometimes appear to 'retrograde' from east to west, 

 though their usual progress is from west to east). The system of 

 Eudoxus thus required twenty-seven spheres; one for the fixed stars, 

 twenty for the planets, six for the sun and moon. It is not probable 

 that Eudoxus and his school regarded these spheres as material 

 crystal shells, but rather as geometrical and abstract vehicles for the 

 resolution of observed mechanical movements into intelligible parts. 

 But the notion of material crystal spheres perpetually recurs in Greek 

 astronomy after his day, and was universally held by the vulgar. 



* Copernicus had access to certain large collections of books and the cata- 

 logues of these collections exist to-day. I have had them searched and the 

 works of Archimedes are not there mentioned. 



