 Pythagoras
(582?-500? BC), Greek philosopher and mathematician, whose doctrines
strongly influenced Plato. Born on the island of Sámos, Pythagoras
was instructed in the teachings of the early Ionian philosophers Thales,
Anaximander, and Anaximenes. Pythagoras is said to have been driven from
Sámos by his disgust for the tyranny of Polycrates. About 530 BC
Pythagoras settled in Crotona, a Greek colony in southern Italy, where
he founded a movement with religious, political, and philosophical aims,
known as Pythagoreanism. The philosophy of Pythagoras is known only through
the work of his disciples. Basic Doctrines The Pythagoreans adhered to
certain mysteries, similar in many respects to the Orphic mysteries (see
Mysteries; Orphism). Obedience and silence, abstinence from food, simplicity
in dress and possessions, and the habit of frequent self-examination were
prescribed. The Pythagoreans believed in immortality and in the transmigration
of souls. Pythagoras himself was said to have claimed that he had been
Euphorbus, a warrior in the Trojan War, and that he had been permitted
to bring into his earthly life the memory of all his previous existences.
Theory of Numbers Among the extensive mathematical investigations carried
on by the Pythagoreans were their studies of odd and even numbers and of
prime and square numbers (see Number Theory). From this arithmetical standpoint
they cultivated the concept of number, which became for them the ultimate
principle of all proportion, order, and harmony in the universe. Through
such studies they established a scientific foundation for mathematics.
In geometry the great discovery of the school was the hypotenuse theorem,
or Pythagorean theorem, which states that the square of the hypotenuse
of a right triangle is equal to the sum of the squares of the other two
sides. Astronomy The astronomy of the Pythagoreans marked an important
advance in ancient scientific thought, for they were the first to consider
the earth as a globe revolving with the other planets around a central
fire. They explained the harmonious arrangement of things as that of bodies
in a single, all-inclusive sphere of reality, moving according to a numerical
scheme. Because the Pythagoreans thought that the heavenly bodies are separated
from one another by intervals corresponding to the harmonic lengths of
strings, they held that the movement of the spheres gives rise to a musical
sound-the "harmony of the spheres." Source: Microsoft
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