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seemed divine oracles, and the sacred obscurity in which he veiled them, attracted great numbers of disciples. But as his ideas embraced politics, the structure of society, and the science of government, as well as religion and philosophy, and desiring probably to apply his theories to a practical result, he left Samos and established himself at Crotona, in Magna Græcia. Here he established his secret brotherhood, which was organized after the Ideal, and in harmony with those political principles which he wished to see realized in all civilized institutions. It was an aristocratic republic, although all who became members united their property in one common stock for the good of the whole. The most influential citizens of Crotona were numbered among its members.

Candidates for initiation were subjected to a severe discipline and examination before they were admitted to all the Mysteries. They were required to practice the greatest simplicity of manners. A silence of two to five years was imposed upon them. He alone who had passed through the appointed series of severe trials, was allowed to hear the word of the master, in his immediate presence. Whoever was terrified by the difficulties of initiation, might withdraw without opposition, and his contributions to the common stock were repaid, a tomb was erected to his memory, as if he were dead, and he was no more thought of. To the illuminated

the doctrines were not delivered as to others, under the veil of images and symbols. As soon as they had made sufficient progress in geometry, they were introduced to the study of Nature, to the investigation of fundamental principles, and to the knowledge of God and religious ideas. They were instructed in morals, economics, or politics, and afterward employed either in managing the affairs of the order, or sent abroad to inculcate and bring into practice these principles of philosophy and government in the other Grecian states.

It appears, therefore, that the secret fraternity of Pythagoras was intended as a propaganda of new ideas and social relations, as a means of fashioning society after a higher and better idea of justice and right. The members lived together, with their wives and children, in buildings, in perfect harmony, as one family. Each morning it was decided how the day should be spent, and every evening a review was made of all that had been done. They rose before the sun for religious worship; verses from Homer and other poets were then recited, or music was introduced, to arouse the mental powers, and fit them for the duties of the day. Several hours were then spent in serious study. A pause for recreation followed, in which a solitary walk was usually taken, to indulge in contemplation; a conversation then took place. Before dinner, various gymnastic exercises were performed.

The common meal consisted principally of bread, honey, and water. The remainder of the day was devoted to public and domestic affairs, conversation, and religious performances.

Such was the character of this famous confrérie, which was to achieve the social regeneration of Magna Græcia. Previous to, and at the time of its establishment there, the inhabitants were notorious for the looseness of their manners. They were licentious and vicious to the last degree. Lawlessness, disorder, and crime, prevailed on one hand, and despotism on the other. But the influence of the Pythagorean Brotherhood was not long in showing itself. Sobriety, temperance, justice, and virtue, soon predominated over the prevailing dissoluteness. Justice and equity appeared in the administration of the laws, and society rapidly advanced to a high degree of prosperity.

Unfortunately, the social Ideal of the order did not reach far enough. The society was republican, but it retained the aristocratic element. In progress of time a struggle arose between this and the democratic element. The fault of the society was, that it did not provide for the unlimited development of social ideas, nor for their application to life. It did not yield readily to the progress of the democratic principle, and as nobles and princes were active members of the order, it was suspected of too great a leaning in that direction. The rejection of

one Cylon, an influential citizen, who had made application for initiation, was made the occasion of an attack on the institution, which ended in the breaking up of the establishment at Crotona. But this turned to the advantage of the order at large; for the members dispersing, carried the ideas of the society into all lands, and Pythagorean lodges or clubs-to use modern appellations for want of better-were established in all quarters of the globe, and flourished through many ages.

The objects of the associations were mutual aid, social communion, intellectual cultivation, and social and personal progress. The scope of the Pythagorean Mysteries was therefore as wide as the circle of human wants and human science. By an admirable system of education, they led the neophyte gradually, step by step, through the mazes of science, up to the sublimest secrets of philosophy. In this progress of the human mind, the first step was the study of

THE MATHEMATICS.-The doctrine of numbers was considered the foundation of the mathematics, according to Pythagoras. They are, as it were, the model by which the world is formed in all its parts. The odd numbers are limited and perfect; the even unlimited and imperfect. The monad, or unity, is the source of all numbers. The dyad is imperfect and passive, and the cause of increase and division.

The triad, compounded of the monad and dyad, partakes of the nature of both. The tetras, or number four, is, in the highest degree, perfect. The decad, which contains the sum of the four prime numbers, and is therefore called the tetractys, comprehends all musical and arithmetical proportions, and denotes the system of the world.

The real meaning of this Pythagorean doctrine of numbers is not well understood. It is probable, however, that numbers were considered the symbolical or allegorical representations of the first principles or forms of nature. As Pythagoras could not express abstract ideas in simple language, he seems to have made use of numbers, as geometers do of a diagram, to assist the comprehension of his scholars. He perceived some analogies between numbers and the attributes of the Divine understanding, and made the former the symbols of the latter. As the numbers proceed from the monad, or unity, undergo various combinations, and, with progress, assume new properties, so he regarded the pure and simple essence of the Deity as the common source of all the forms of nature, which, according to their various modifications, possess different properties. Here, as in all the philosophical systems of antiquity, God is presented as the basis of all existence, and interpenetrates all things.

The second preparatory step, in the pursuit of wisdom, was

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