This philosopher and mathematician, born about the year B.C. 570, is 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, wrapt in the contemplation of the mysteries of existence, listening to the music of Homer and Hesiod, or to the harmony of the spheres." [Footnote: Lewes, Biog. Hist. Phil.] To him is ascribed the use of the word philosopher rather than sophos, a lover of wisdom, not wise man. He taught his doctrines to a select few, the members of which society lived in common, and venerated him as an oracle. His great doctrine is, that number is the essence of things, by which is understood the form and not the matter of the sensible. The elements of numbers are theodd and even, the former being regarded as limited, the latter unlimited. Diogenes Laertius thus sums up his doctrines, which were that "the monad is - the beginning of every thing. From the monad proceeds an indefinite duad. From the monad and the duad proceed numbers, and from numbers signs, and from these lines, of which plain figures consist. And from plain figures are derived solid bodies, and from these sensible bodies, of which there are four elements, fire, water, earth, and air. The world results from a combination of these elements." [Footnote: Diog. Laert., Lives of Phil.] All this is unintelligible or indefinite. We cannot comprehend how the number theory will account for the production of corporeal magnitude any easier than we can identify monads with mathematical points. But underlying this mysticism is the thought that there prevails in the phenomena of nature a rational order, harmony, and conformity to law, and that these laws can be represented by numbers. Number or harmony is the principle of the universe, and order holds together the world. Like Anaximander, he passes from the region of physics to metaphysics, and thus opens a new world of speculation. His method was purely deductive, and his science mathematical. "The Infinite of Anaximander became the One of Pythagoras." Assuming that number is the essence of the world, he deduced that the world is regulated by numerical proportions, in other words, by a system of laws, and these laws, regular and harmonious in their operation, may have suggested to the great mind of Pythagoras, so religious and lofty, the necessity for an intelligent creator of the universe. It was in moral truth that he delighted as well as metaphysical, and his life and the lives of his disciples were disciplined to a severe virtue, as if he recognized in numbers or order the necessity of a conformity to all law, and saw in obedience to it both harmony and beauty. But we have no direct and positive evidence of the kind or amount of knowledge which this great intellect acquired. All that can be affirmed is, that he was a man of extensive attainments; that he was a great mathematician, that he was very religious, that he devoted himself to doing good, that he placed happiness in the virtues of the soul or the perfect science of numbers, and made a likeness to the Deity the object of all endeavors. He believed that the soul was incorporeal, [Footnote: Ritter, b. iv. chap i.] and is put into the body by the means of number and harmonical relation, and thus subject to a divine regulation. Every thing was regarded by him in a moral light. The order of the universe is only a harmonical development of the first principle of all things to virtue and wisdom. [Footnote: Our knowledge of Pythagoras is chiefly derived from Aristotle. Both Ritter and Brandis have presented his views elaborately, but with more clearness than was to be expected.] He attached great value to music, as a subject of precise mathematical calculation, and an art which has a great effect on the affections. Hence morals and mathematics were linked together in his mind. As the heavens were ordered in consonance with number, they must move in eternal order. "The spheres" revolved in harmonious order around the great centre of light and heat - the sun - "the throne of the elemental world." Hence the doctrine of "the music of the spheres." Pythagoras ad harmoniam canere mundum existimat. [Footnote: Cicero, De Nat.