20 THE HISTORY OF SCIENCE 



great philosopher's point of view. The story is told 

 that one of his pupils, arrived perhaps at the pons 

 asinorum, asked, " What do I get by learning these 

 things?' Euclid, calling his servant, said, "Give 

 him sixpence, since he must make gain out of what 

 he learns." Adults were also found, even among the 

 nimble-witted Greeks, to whom abstract reasoning 

 was not altogether congenial. This is attested by the 

 fainiliar story of Ptolemy, King of Egypt, who once 

 asked Euclid whether geometry could not be learned 

 in some easier way than by studying the geometer's 

 book, The Elements. To this the schoolmaster re- 

 plied, "There is no royal road to geometry." For 

 the academic intelligence abstract and abstruse 

 mathematics are tonic and an end in themselves. As 

 already stated, their ultimate practical value is also 

 immense. One of Plato's associates, working under 

 his direction, investigated the curves produced by 

 cutting cones of different kinds in a certain plane. 

 These curves the ellipse, the parabola, hyperbola 

 play a large part in the subsequent history of 

 astronomy and mechanics. Another Platonist made 

 the first measurement of the earth's circumference. 

 Aristotle, the greatest pupil of Plato, was born at 

 Stagira in 384 B.C. He came of a family of physi- 

 cians, was trained for the medical profession, and 

 had his attention early directed to natural phenomena. 

 He entered the Academy at Athens about 367 B.C., 

 and studied there till the death of Plato twenty 

 years later. He was a diligent but, as was natural, 

 considering the character of his early education, by 

 no means a passive student. Plato said that Aristotle 

 reacted against his instructor as a vigorous colt kicks 



