1 64 TEE POPULAR SCIENCE MONTHLY 



its origin to Cecrops, the Egyptian ; the Peloponnesus derived its name 

 from Pelops, of Phrygia; Argos was settled by Danaus, of Egypt; and 

 Thebes by Cadmus, of Phoenicia. Even their religion was borrowed 

 from more ancient nations. For example, the twelve labors of Her- 

 cules rests upon the ancient idea of the sun performing its cycle 

 through the twelve signs of the zodiac. 



With the general shifting of the tribes which succeeded the Trojan 

 War, the Dorians and Ionians came to be the dominant races of Greece. 

 The Dorian band which invaded Lacedemon, called also Sparta from 

 its grain fields, was at first forced by the scantiness of its numbers to 

 be constantly on the defensive, which developed in them the warlike 

 and hardy spirit which finally made the Spartans dominant in the 

 Peloponnesus. The Ionians inhabited Attica, where the contending 

 geographic factors of plain, coast and mountain transformed their 

 original monarchy into a democracy, and their little fortress upon a 

 rock into the mighty Acropolis of Athens, for centuries the synonym 

 of learning and democracy. " The Athenians," said Herodotus, " then 

 grew mighty, and it became plain that liberty is a brave thing." 



No phase of Greek culture was more expressive of their national 

 characteristics than their mathematical attainments. Heterogeneity, 

 which formed the basal element of their national character, was here 

 apparent in the diverse sources from which their mathematics was de- 

 rived. Thales, the first great Greek mathematician and the founder of 

 the Ionian School, was a native of Miletus, but spent much of his life 

 in Egypt as a merchant, where he studied geometry and astronomy. 

 Pythagoras, who was a contemporary of Thales and founder of the 

 Pythagorean School, was of Phoenician origin, and in his early life 

 studied for several years in Egypt and traveled extensively in Asia 

 Minor. The Ionian and Pythagorean schools were jointly the founders 

 of Greek mathematics, which took the form of an abstract deductive 

 geometry, as distinguished from the practical empirical geometry of 

 the Egyptians. It was, in fact, the boast of the Pythagoreans that they 

 sought knowledge and not power, and had raised mathematics above 

 the needs of merchants. One of their maxims was, " a figure and a step 

 forward ; not a figure to gain three oboli." The disciples of Pythagoras 

 were required to pass through a preliminary training, consisting in a 

 moral and religious preparation for life, which included the elements 

 of music and mathematics. In fact Pythagoras made the science of 

 numbers the basis of his philosophy in the belief that accurate meas- 

 urement was essential to the definition of form, and consequently that 

 the entire universe was founded upon a numerical basis. Thus among 

 other attributes of number, the cause of color was the number 5; the 

 origin of fire was to be found in the pyramid ; the four elements, earth, 

 air, fire and water were represented by the tetrad ; 8 was the symbol of 



