Pythagoras was another scholar of Thales. The place of his nativity is uncertain; but having settled in the island of Samos, he is generally reckoned of that place. He travelled in search of knowledge through Phœnicia, Chaldea, Egypt, and India; however, meeting with little encouragement on his return to Samos, he passed over to Italy, in the time of Tarquin the Proud, and opened a school at Croto, a city in the Gulf of Tarentum, where he had a number of students, and gained much reputation. His pupils were obliged to listen in silence for at least two years; if talkative, longer; sometimes, for five years, before they were permitted to ask him any questions; for which time they were mathematicoi, because they were set to study geometry, dialling, music, and other high sciences, called by the Greeks mathemata. But the name of mathematici was commonly applied to those who cultivated the stellary science, and who predicted the fortunes of men, by observing the stars under which they were born.
This luminary of science first assumed the appellation of philosopher; before him, those whose pursuits have now that title, were called sages or wise men; he was the founder of the sect called the Italic. He was so much honoured whilst living, and his memory honoured when dead, by the Romans, that they attributed to him the learning of Numa, who lived much earlier. About the year of the city 411, the Delphian oracle having directed the Romans to erect statues to the bravest and wisest of the Greeks, they conferred that honour upon Alcibiades and Pythagoras.
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.
It was also called the Great Year; which name was likewise applied to various spaces of time by different authors; by Virgil, to the solar year, to distinguish it from the monthly revolution of the moon; by Cicero and others, to the revolution of six hundred years, or three thousand six hundred years; called also several ages, when all the stars shall come to the same position, with respect to one another, as they were in at a certain time before; called likewise Annus Mundanus, or Vertens.
The lunar cycle begun four hundred and thirty-two years before the commencement of our era, and according to it, the Greek calendars, which determined the celebration of their annual feasts, &c. were adjusted. Meteon is said to have derived his knowledge of this subject from Chaldea.
The opinions of the subsequently registered astronomer, Xonophanes, founder of the Eleatic school, are so truly monstrous, that after the light which had appeared, he must have travelled with his eyes shut; or else the rage for novelty alike affected the scientific of Greece, as it did their literati; choosing to travel a long way for new thoughts, when they might have found much better at hand. Xonophanes, among other whimsical opinions, maintained that the stars were extinguished every morning, and illuminated every evening; that the sun is an inflamed cloud; that eclipses happen by the extinction of the sun, which is afterwards lighted up; that the moon is ten times larger than the earth; that there are many suns and moons to illumine different climates.