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. D_., iii. ii. 27.] The tendency of his speculations, obscure as they are to us, was to raise the soul to a contemplation of order and beauty and law, in the material universe, and hence to the contemplation of a supreme intelligence reigning in justice and truth. Justice and truth became therefore paramount virtues, to be practiced, to be sought as the great end of life, allied with the order of the universe, and with mathematical essences--the attributes of the deity, the sublime unity which he adored. The Ionic philosophers, and the Pythagoreans, sought to find the nature or first principle of all things in the elements, or in numbers. But the Eleatics went beyond the realm of physics to pure metaphysical inquiries. This is the second stage in the history of philosophy--an idealistic pantheism, which disregarded the sensible and maintained that the source of all truth is independent of sense. [Sidenote: Xenophanes.--God the first great cause.]