History of Mathematics/The Greeks

Around the seventh century BC, an active commercial intercourse sprang up between Greece and Egypt. Naturally there arose an interchange of ideas as well as of merchandise. The Greeks, thirsting for knowledge, sought the Egyptian priests for instruction. Thales, Pythagoras, Enopides, Plato, Democritus, and Eudocus all visited the land of the pyramids. Egyptian ideas were thus transplanted across the sea and there stimulated Greek thought, directed it into new lines. Not only in mathematics, but also in mythology and art, Hellas owes a debt to older countries. To Egypt, Greece is indebted, among other things, for its elementary geometry. But this does not lessen our admiration for the Greek mind. From the moment that Hellenic philosophers applied themselves to the study of Egyptian geometry, this science assumed a radically different aspect. "Whatever we Greeks receive, we improve and perfect," said Plato. The Egyptians carried geometry no further than was absolutely necessary for their practical wants. The Greeks, on the other hand, had within them a strong speculative tendency. They felt a craving to discover the reasons for things. They found pleasure in the contemplation of ideal relations, and loved science as science.

Our sources of information on the history of Greek geometry before Euclid consist merely of scattered notices in ancient writers. The early mathematicians, Thales and Pythagoras, left behind no written records of their discoveries. A full history of Greek geometry and astronomy during this period, written by Eudemus, a pupil of Aristotle, has been lost. It was well known to Proclus, who, in his commentaries on Euclid, gives a brief account of it. This abstract constitutes out most reliable information. We shall quote it frequently under the same Eudemian Summary.

The mathematician, astronomer, and philosopher Thales of Miletus (640-546 BC), often referred to as the Father of Science, was one of the "seven wise men", and was the founder of the Ionian school of philosophy. He was the first known person in Greece to make contributions to mathematics and philosophy, and he is considered important in the history of Greece, for he was the first person to look for rational and scientific explanations for things, rather than simply accepting mythological explanations. During the middle of his life he engaged in commercial pursuits, which took him to Egypt. He is said to have lived there, and to have studied the physical sciences and mathematics with the Egyptian priests. Plutarch declares that Thales soon exceeded his masters, and amazed King Amasis by measuring the heights of the pyramids from their shadows. According to Plutarch, this was done by considering that the shadow cast by a vertical staff of known length bears the same ratio to the shadow of the pyramid as the height of the staff ratio to the shadow of the pyramid as the height of the staff bears to the height of the pyramid. This solution presupposes a knowledge of proportion, and the Ahmes papyrus actually shows that the rudiments of proportion were known to the Egyptians. According to Diogenes Laertius, the pyramids were measured by Thales in a different way: by finding the length of the shadow of the pyramid at the moment when the shadow of a staff was equal to its own length.