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"It is certain that the Theory of Numbers originated in the school of Pythagoras."
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PythagoreanismAs the Unlimited is spatial, the Limit must be spatial too, and we sho — Pythagoreanism
"As the Unlimited is spatial, the Limit must be spatial too, and we should... expect... the point... line, and... surface were regarded as... forms of the Limit. That was the later doctrine; but the characteristic feature of Pythagoreanism is... that the point was not... a limit, but... the first product of the Limit and the Unlimited, and was identified with the arithmetical unit. According[ly]... the point has one dimension, the line two, the surface three, and the solid four... [i.e.,] Pythagorean points have magnitude... lines breadth, and... surfaces thickness. The whole theory... turns on the definition of the point as a unit “having position." ...[O]ut of such elements ...it seemed possible to construct a world."
As the Unlimited is spatial, the Limit must be spatial too, and we should... expect... the point... line, and... surface
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Pythagoreanism
Pythagoreanism
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Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans. Pythagoras established the first Pythagorean community in the ancient Greek colony of Croton, in modern Calabria (Italy) circa 530 BC. Early Pythagorean communities spread throughout Magna Graecia.
About Pythagoreanism
Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans. Pythagoras established the first Pythagorean community in the ancient Greek colony of Croton, in modern Calabria (Italy) circa 530 BC. Early Pythagorean communities spread throughout Magna Graecia.
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"Those who dwelt in the common auditorium adopted this oath: "I swear by the discoverer of the Tetraktys, which is the spring of all our wisdom; The perennial fount and root of Nature."
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PythagoreanismQuote
"[W]e have to... interpret what Aristotle tells us in the spirit of Plato, and... consider how the doctrine... is related to the systems which had preceded it. ...[This] delicate operation... has been made... safer by recent discoveries in the early history of mathematics and medicine."
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PythagoreanismQuote
"We are told that the other book which passed under the name of Pythagoras was really by Lysis."
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PythagoreanismQuote
"Whose theory is it? It is usually supposed... Plato’s... though nowadays it is... his "early theory of ideas,"... that he modified... profoundly in later life. But there are serious difficulties in this view."
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PythagoreanismQuote
"They thought they found in numbers, more than in fire, earth, or water, many resemblances to things which are and become; thus such and such an attribute of numbers is justice, another is soul and mind, another is opportunity, and so on; and again they saw in numbers the attributes and ratios of the musical scales. Since, then, all other things seemed in their whole nature to be assimilated to numbers, while numbers seemed to be the first things in the whole of nature, they supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number."
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Pythagoreanism