Tag Archives: geometry

The Ionian Greeks, who lived on the coast of Asia Minor and the adjoining islands, had produced some of the leading poets and thinkers of the Greek world. Thales of Miletus (640-546 B.C.) predicted an eclipse of the sun and introduced geometry to the Greeks. Pythagoras of Samos (c. 500) won fame as a philosopher and mathematician, although it is not now thought that he discovered the geometrical truth which bears his name (i.e. that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides). Thales was interested in politics as well as mathematics and tried to unite the cities of Ionia into a federation. Each city-state would have renamed independent but would have sent representatives to a council to discuss affairs of common interest. This scheme did not succeed. The Ionian cities of the mainland (except for the largest, Miletus) became subject to Lydia and later, when Cyrus conquered Croesus (p. 21), they all became subject to Persia. Even some of the islands succumbed. Polycrates, the fabulously wealthy tyrant of Samos, whose position was such that he could enter into a treaty with the king of Egypt, was enticed by the Persians onto the mainland and killed (522). In the year 522 a pretender had seized the throne of Persia and some nobles, of whom Darius was one, joined in assassinating him. They then decided that they would ride out early in the morning and that the one whose horse neighed first after the sun rose should be King. Darius’s groom saw to it that his master’s horse neighed first and Darius became King of Persia. Neither fate nor the other nobles punished him for cheating in this way. He ruled Persia until 485, by no means …

In the last years of the fourth century B. C., Greek citizens going about their business in the stoas or the shops sometimes stopped and wondered what was wrong. Everything seems strange. They themselves had not changed and their cities looked the same as before, but the world around them was so different that they could hardly recognize themselves. The little poleis on the mainland looked out at an enormous empire, which stretched across Asia and Egypt. They shipped their olive oil and pottery across the Mediterranean. Their corn came from fields beside the Black Sea and the Nile. Merchants who crowded their market places now did business in Antioch and their sculptors had gone to Alexandria. There were new Greek cities, thousands of miles from Greece, where Asians spoke Greek and Greeks began to dress like the barbarians. There were no barbarians now, only the many sorts of people who shared a world which Alexandria had conquered for  the Greeks. As the world the Greeks knew became larger, a man and his city seemed to become smaller. The Greeks began to wonder if there was a Greece at all any more. Athenians who travelled on business saw Athens in a new way when they came home. It was not very big and not very busy. When they went to the Assembly, the fine speeches had a hollow ring. In the old days, when Pericles or Themistocles spoke to the Assembly, things happened and the world felt the difference. Now, a man who spoke out in Athens might as well have dropped a pebble in an ocean. Alexander’s empire was much too big to be run by a group of citizens who talked over their problems in an Assembly. One man could rule it, if he was a king like …