He taught publicly that the earth is the centre of the universe; but to his scholars he gave his real opinions; similar to those afterwards adopted by Copernicus, that the earth and all the planets moved round the sun, as their co-centre, and which doctrine he is presumed to have derived from either the Chaldeans or Indians. He thought that the earth is round, and everywhere inhabited. Hence, he admitted that we might have antipodes, which name is said to have been invented by Plato. Pythagoras was distinguished for his skill in music, which he first reduced to certain firm principles, and likewise for his discoveries in geometry. He first proved, that in a right-angled triangle, the square of the hypothenuse, or side subtending the right angle, is equal to the two other sides; also that of all plain figures having equal circumference, the circle is largest; and of all solids having equal surfaces, the sphere is the largest. Pythagoras likewise taught that all things were made of fire. That the Deity animated the universe, as the soul does the body; which doctrine, with that of the metempsychosis, or transmigration, he likewise taught; and which thoughts were adopted by Plato, and are most beautifully expressed by Virgil; that the sun, the moon, the planets, and fixed stars, are all actuated by some divinity, and move each in a transparent solid sphere in the order following:--next to the Earth, the Moon, then Mercury, Venus, the Sun, Mars, Jupiter, Saturn; the sphere of the fixed stars last of all; that those move with a sound inconceivably beautiful, which ears cannot comprehend. Those eight spheres he imagined to be analogous to the eight notes in music. Empedocles, the chief scholar of Pythagoras, entertained the same sentiments with his teacher, concerning astronomy. He is said to have thrown himself into the crater of Mount Etna, to make himself pass for a god; or, perhaps, which may approach nearer the truth, because he could not discover the cause of the eruption: or else in his endeavours to discover the cause. One of his iron sandals being thrown up by the volcano, revealed the mode in which he had perished. Philolaus, also a scholar of Pythagoras, first taught publicly the diurnal motion of the earth upon its axis, and its annual motion round the sun; which first suggested to Copernicus the idea of that system which he established. Meteon, born at Leuconæ, a village near Athens, first introduced into Europe the Lunar Cycle, consisting of nineteen solar years, or nineteen lunar years, and seven intercalary months. It had been first adopted by the Chaldeans. Meteon published it at the Olympic games, where it was received with so great applause that it was then universally adopted through the Grecian States, and their colonies, and got the name of the Cycle, or Golden Number, to denote its excellence, which name it still retains.