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TWO:In designing supports for shafts the strains are easily defined and followed, while the vertical and lateral adjustment, lubrication of bearings, symmetry of supports and hangers, and so on, will furnish grounds for endless modification, both as to arrangement and mechanism.We have not here to examine the scientific achievements of Pythagoras and his school; they belong to the history of science, not to that of pure thought, and therefore lie outside the present discussion. Something, however, must be said of Pythagoreanism as a scheme of moral, religious, and social reform. Alone among the pre-Socratic systems, it undertook to furnish a rule of conduct as well as a theory of being. Yet, as Zeller has pointed out,11 it was only an apparent anomaly, for the ethical teaching of the Pythagoreans was not based on their physical theories, except in so far as a deep reverence for law and order was common to both.13 Perhaps, also, the separation of soul and body, with the ascription of a higher dignity to the former, which was a distinctive tenet of the school, may be paralleled with the position given to number as a kind of spiritual power creating and controlling the world of sense. So also political power was to be entrusted to an aristocracy trained in every noble accomplishment, and fitted for exercising authority over others by self-discipline, by mutual fidelity, and by habitual obedience to a rule of right. Nevertheless, we must look, with Zeller, for the true source of Pythagoreanism as a moral movement in that great wave of religious enthusiasm which swept over Hellas during the sixth century before Christ, intimately associated with the importation of Apollo-worship from Lycia, with the concentration of spiritual authority in the oracular shrine of Delphi, and the political predominance of the Dorian race, those Normans of the ancient world. Legend has thrown this connexion into a poetical form by making Pythagoras the son of Apollo; and the Samian sage, although himself an Ionian, chose the Dorian cities of Southern Italy as a favourable field for his new teaching, just as Calvinism found a readier acceptance in the advanced posts of the Teutonic race than among the people whence its founder sprang. Perhaps the nearest parallel, although on a far more extensive scale, for the religious movement of which we are speaking, is the spectacle offered by mediaeval Europe during the twelfth and thirteenth centuries of our era, when a series of great Popes had concentrated all spiritual power in their own hands, and were sending forth army after army of Crusaders to the East; when all Western Europe had awakened to the consciousness of its common Christianity, and each individual was thrilled by a sense of the tremendous alternatives committed to his choice; when the Dominican and Franciscan orders were founded; when Gothic architecture and Florentine painting arose; when the Troubadours and Minnes?ngers were pour14ing out their notes of scornful or tender passion, and the love of the sexes had become a sentiment as lofty and enduring as the devotion of friend to friend had been in Greece of old. The bloom of Greek religious enthusiasm was more exquisite and evanescent than that of feudal Catholicism; inferior in pure spirituality and of more restricted significance as a factor in the evolution of humanity, it at least remained free from the ecclesiastical tyranny, the murderous fanaticism, and the unlovely superstitions of mediaeval faith. But polytheism under any form was fatally incapable of coping with the new spirit of enquiry awakened by philosophy, and the old myths, with their naturalistic crudities, could not long satisfy the reason and conscience of thinkers who had learned in another school to seek everywhere for a central unity of control, and to bow their imaginations before the passionless perfection of eternal law.

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