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Updated: May 9, 2025
It was the aim of his school to keep this faculty alive as long as possible, and with its aid to establish a communicable world-conception. The Pythagorean teaching became the foundation of all later cosmological thinking, right up to the age which was destined to bring to birth the spectator-relationship of man's consciousness with the world.
The rule is stated in general terms, but the above representation of its effect shows that it is a piece of pure algebra. The Pythagorean contributions to geometry were even more remarkable. The most famous proposition attributed to Pythagoras himself is of course the theorem of Eucl.
At the opening of that education of modern by ancient thought which we call the Renaissance, it was the words of Aristotle which sent Columbus sailing to the New World, while a fragment of Pythagorean astronomy set Copernicus thinking on that train of reasoning which has revolutionised the whole position of our planet in the universe.
From Appius Claudius date not only the Roman aqueducts and highways, but also Roman jurisprudence, eloquence, poetry, and grammar. The publication of a table of the -legis actiones-, speeches committed to writing and Pythagorean sentences, and even innovations in orthography, are attributed to him.
Each had provided himself with a rush basket which the shikaree had woven, during the long winter nights, for other purposes; but as they were of just the size and shape to hold the Pythagorean beans they were now to be employed in that capacity.
I called it the "progressive chain of being," and wove it out of the Pythagorean philosophy. I said man's nature begins from the lowest, and ascends to the highest.
In a word, the evidence, so far as we can garner it from the remaining fragments, tends to show that all along, from the time of the early Pythagoreans, there had been an undercurrent of opinion in the philosophical world which questioned the fixity of the earth; and it would seem that the school of thinkers who tended to accept the revolutionary view centred in Asia Minor, not far from the early home of the founder of the Pythagorean doctrines.
One of them is apparently from the Pythagorean philosopher Metopos, in which the fitness of every bodily member is declared to be a virtue. The other pronounces that the virtue of a shoemaker is to make good shoes. This may also serve to explain why it is that in the ancient scheme of ethics virtues and vices are mentioned which find no place in ours.
Hippocrates, influenced as is thought by the Pythagorean doctrine of numbers, taught that they were to be expected on days fixed by certain numerical rules, in some cases on odd, in others on even numbers the celebrated doctrine of 'critical days. It follows from what has been said that prognosis, or the art of foretelling the course and event of the disease, was a strong point with the Hippocratic physicians.
It is difficult, when the political or religious feelings of men have been engaged, to ascertain the truth of events in which they have been concerned; deception, and falsehood, seem to be licensed. In the midst of the troubles befalling Italy as the consequence of these Pythagorean machinations, it is impossible to ascertain facts with certainty.
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