THE HELLENIC PERIOD 57 



for measuring the air. For you must know that the 

 air is formed like an oven. This is why applying the 

 top of this curved rule, then placing the compass, 

 I shall use a straight rule and I shall take my dimen- 

 sions so well that I shall make a squared circle." 

 This Meton, whom Aristophanes introduces, seems to 

 have been a good astronomer. He rediscovered the 

 so-called cycle of Saros, which henceforward bore his 

 name, and which helped to reform the calendar and 

 fix religious rites. A short time after the sophists, 

 there appeared the works of the schools of Athens 

 and Cnidus, which were so closely united that it is 

 difficult to separate them. According to tradition 

 Hippocrates, Plato, and Theaetetus belong to the 

 school of Athens, whilst Eudoxus, Menaechmus and 

 Aristo represent that of Cnidus. 



Hippocrates of Chios was born in 470 B.C. 

 Despoiled of his wealth by the Athenian customs, 

 according to Eudemus, by pirates, according to 

 Philoponus (Diels, Vor. I, p. 231, 27, 30) he came to 

 Athens to beg for justice and the recovery of his 

 property. Having been unable to gain his cause, he 

 devoted himself to philosophy and opened a school 

 of geometry. He was the first to compile a treatise of 

 geometry, thus breaking away from the Pythagorean 

 tradition, which kept secret all mathematical know- 

 ledge ; hereby he provided a solid basis for instruction 

 and foreshadowed the Elements of Euclid. He also 

 introduced the use of letters to indicate lines and 

 figures, and it was really he who created the geometry 

 of the circle by means of the two following propositions : 

 Circles are to one another in the ratio of the squares 

 of their diameters. Similar segments are to one 

 another in the ratio of the squares of their chords. 



Hippocrates also recognized that the duplication of 

 the cube leads to the investigation of mean pro- 

 portionals : 



