"It seems to me that they do well to study mathematics, and it is not at all strange that they have correct knowledge …"

"They [the Pythagoreans] say the things themselves are Numbers and do not place the objects of mathematics between for…"

"These thinkers seem to consider that number is the principle both as matter for things and as constituting their attr…"

"They thought they found in numbers, more than in fire, earth, or water, many resemblances to things which are and bec…"

"It has fallen to the lot of one people, the ancient Greeks, to endow human thought with two outlooks on the universe …"

"None of Pythagoras' own work has survived, but the ideas fathered on him by his followers would be the most potent in…"

"In Copernicus' time Pythagoreans still believed that the only way to truth was by mathematics."

"The Pythagorean mathematical concepts, abstracted from sense impressions of nature, were... projected into nature and…"

"Ionian philosophers... had sought to identify a first principle for all things. Thales had thought to find this in wa…"

"If someone associates with a true Pythagorean, what will he will get from him, and in what quantity? I would say: sta…"