In the mean time another sect of philosophers had arisen, who, like the Ionians, sought to explain Nature, but by a different method.  Anaximander, born 610 B.C., was one of the original mathematicians of Greece, yet, like Pythagoras and Thales, speculated on the beginning of things.  His principle was that The Infinite is the origin of all things.  He used the word [Greek:  archae] (beginning) to denote the material out of which all things were formed, as the Everlasting, the Divine.  The idea of elevating an abstraction into a great first cause was certainly a long stride in philosophic generalization to be taken at that age of the world, following as it did so immediately upon such partial and childish ideas as that any single one of the familiar “elements” could be the primal cause of all things.  It seems almost like the speculations of our own time, when philosophers seek to find the first cause in impersonal Force, or infinite Energy.  Yet it is not really easy to understand Anaximander’s meaning, other than that the abstract has a higher significance than the concrete.  The speculations of Thales had tended toward discovering the material constitution of the universe upon an induction from observed facts, and thus made water to be the origin of all things.  Anaximander, accustomed to view things in the abstract, could not accept so concrete a thing as water; his speculations tended toward mathematics, to the science of pure deduction.  The primary Being is a unity, one in all, comprising within itself the multiplicity of elements from which all mundane things are composed.  It is only in infinity that the perpetual changes of things can take place.  Thus Anaximander, an original but vague thinker, prepared the way for Pythagoras.

This later philosopher and mathematician, born about the year 600 B.C., stands as one of the great names of antiquity; but his life is shrouded in dim magnificence.  The old historians paint him as “clothed in robes of white, his head covered with gold, his aspect grave and majestic, rapt in the contemplation of the mysteries of existence, listening to the music of Homer and Hesiod, or to the harmony of the spheres.”

Pythagoras was supposed to be a native of Samos.  When quite young, being devoted to learning, he quitted his country and went to Egypt, where he learned its language and all the secret mysteries of the priests.  He then returned to Samos, but finding the island under the dominion of a tyrant he fled to Crotona, in Italy, where he gained great reputation for wisdom, and made laws for the Italians.  His pupils were about three hundred in number.  He wrote three books, which were extant in the time of Diogenes Laertius,—­one on Education, one on Politics, and one on Natural Philosophy.  He also wrote an epic poem on the universe, to which he gave the name of Kosmos.

Among the ethical principles which Pythagoras taught was that men ought not to pray for anything in particular, since they do not know what is good for them; that drunkenness was identical with ruin; that no one should exceed the proper quantity of meat and drink; that the property of friends is common; that men should never say or do anything in anger.  He forbade his disciples to offer victims to the gods, ordering them to worship only at those altars which were unstained with blood.