THE HELLENIC PERIOD 35 



Argolis. The doctrine of Pythagoras raises as difficult 

 problems as does his life, for he has left no writing to 

 enable us to distinguish his own thought from that of 

 his disciples. We can, however, affirm that he pro- 

 fessed belief in the transmigration of souls, for the 

 testimony of Xenophanes is precise on this point. 

 " One day, it is said, as he (Pythagoras) was passing 

 by a dog which was being beaten, he cried, full of pity, 

 1 Stop, beat no more, it is the soul of a friend ; I recog- 

 nized it, hearing its complaints.' " (Diels, Vor. I, 47, 

 20). On the other hand, Pythagoras was in reality a 

 great thinker, as the testimony of Heraclitus proves. 

 " Pythagoras, the son of Mnesarchus, extended his 

 researches further than any other man, and choosing 

 from certain writings, claimed as his own wisdom what 

 was only polymathy and art of wickedness." (Diels, 

 Vor. I, 80, 14). 



As a thinker, Pythagoras was certainly struck by the 

 fact that phenomena which are heterogeneous from the 

 point of view of sensation, may nevertheless show a 

 definite numerical relationship. Figures very different 

 in shape may have the same surface. Musical sounds 

 are produced according to intervals (octave, fifth, 

 fourth) which follow a numerical law. Imbued with 

 this idea Pythagoras extended the study of arithmetic 

 beyond commercial needs (Stobaeus, I, p. 20, 1) 1 He 

 and his school came to the conclusion that number and 

 its properties constitute the basis of all things. Hence, 

 number is not a pure abstraction, it is a concrete reality, 

 although our senses cannot directly apprehend it. 

 Numbers have each spatial, physical and even spiritual 

 properties, clearly defined. By their combinations 

 they give birth to the beings and the things which we 

 see. The contributions which the Pythagorean school 

 made to arithmetic, geometry and astronomy were 

 very remarkable. They definitely directed Greek 

 1 Quoted by 8 Burnet, Aurore, p. 111. 



