PYTHAGORAS.

With Pythagoras and the Pythagoreans we come to a different order of things. Pythagoras, born at Samos about 572 B.C., is undoubtedly one of the greatest names in the history of science. He was a mathematician of brilliant achievements; he was also the inventor of the science of acoustics, an astronomer of great originality, a theologian and moral reformer, and the founder of a brotherhood which admits comparison with the orders of mediæval chivalry. Perhaps his most epoch-making discovery was that of the dependence of musical tones on numerical proportions, the octave representing the proportion of 2 : 1 in length of string at the same tension, the fifth 3 : 2, and the fourth 4 : 3. Mathematicians know him as the reputed discoverer of the famous theorem about the square on the hypotenuse of a right-angled triangle (= Euclid I. 47); but he was also the first to make geometry a part of a liberal education and to explore its first principles (definitions, etc.).

Pythagoras is said to have been the first to maintain that the earth is spherical in shape; on what ground, is uncertain. One suggestion is that he may have argued from the roundness of the shadow cast by the earth in the eclipses of the moon; but Anaxagoras was the first to give the true explanation of such eclipses. Probably Pythagoras attributed spherical shape to the earth for the mathematical or mathematico-æsthetical reason that the sphere is the most beautiful of all solid figures. It is probable too, and for the same reason, that Pythagoras gave the same spherical shape to the sun and moon, and even to the stars, in which case the way lay open for the discovery of the true cause of eclipses and of the phases of the moon. Pythagoras is also said to have distinguished five zones in the earth. It is true that the first declaration that the earth is spherical and that it has five zones is alternatively attributed to Parmenides (born perhaps about 516 or 514 B.C.), on the good authority of Theophrastus. It is possible that, although Pythagoras was the real author of these views, Parmenides was the first to state them in public.

Pythagoras regarded the universe as living, intelligent, spherical, enclosing the earth at the centre, and rotating about an axis passing through the centre of the earth, the earth remaining at rest.

He is said to have been the first to observe that the planets have an independent motion of their own in a direction opposite to that of the fixed stars, i.e. the daily rotation. Alternatively with Parmenides he is said to have been the first to recognise that the Morning and the Evening Stars are one and the same. Pythagoras is hardly likely to have known this as the result of observations of his own; he may have learnt it from Egypt or Chaldæa along with other facts about the planets.