THE GOLDEN AGE OF GREECE 79 



each of the refractory planets, and at the same time a fourth and 

 fifth for the sun, in order to account for the recently discovered 

 inequality in the length of the four seasons. 



Reviewing the development of this interesting theory, Dreyer 

 says : 



But with all its imperfections as to detail, the theory of homo- 

 centric spheres proposed by Eudoxus demands our admiration as the 

 first serious attempt to deal with the apparently lawless motions of the 

 planets. . . . Scientific astronomy may really be said to date from 

 Eudoxus and Calippus, as we here for the first time meet that mutual 

 influence of theory and observation on each other which characterizes 

 the development of astronomy from century to century. Eudoxus 

 is the first to go beyond mere philosophical reasoning about the con- 

 struction of the universe ; he is the first to attempt systematically to 

 account for the planetary motions. When he has done this the next 

 question is how far this theory satisfies the observed phenomena, and 

 Calippus at once supplies the observational facts required to test the 

 theory, and modifies the latter until the theoretical and observed 

 motions agree within the limits of accuracy attainable at that time. 

 Philosophical speculation unsupported by steadily pursued obser- 

 vations is from henceforth abandoned : the science of astronomy 

 has started on its career. 



Eudoxus made the first known proposal for a leap-year, and for 

 a star catalogue. A marble celestial globe in the national museum 

 at Naples is perhaps a copy of one made by him. 



ARISTOTLE, 384-322 B.C., "the master of those who know," the 

 son of a physician, a student in Plato's Academy, and tutor of 

 Alexander the Great, exercised a mighty and lasting influence on 

 the development of Greek science and philosophy. His tenden- 

 cies were mainly non-mathematical, but the theorem that the 

 sum of the exterior angles of a plane polygon is four right angles 

 is ascribed to him. He distinguishes sharply between geodesy as 

 an art and geometry as a science ; he considers the plane sections 

 of the circular cyclinder ; he recognizes the physical reason for 

 the adoption of ten as the base number of arithmetic ; he designates 

 unknown quantities by letters. Continuity an idea so impor- 



