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 Hercules 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 derived. 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 measurement 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
