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...A history of Greek philosophy, Volume 1: The earlier Presocratics and the Pythagoreans |date=1978 ...

...Ionia and the Pythagoreans" p. 43}}</ref> [[Pythagoras]] established the [[Pythagoreans|Pythagorean School]], which is credited with the first proof of the [[Pytha [[File:Square root of 2 triangle.svg|thumb|right|The Pythagoreans discovered that the sides of a triangle could have [[Commensurability (math ...

...matics being the language of [[nature]] can be found in the ideas of the [[Pythagoreans]]: the convictions that "Numbers rule the world" and "All is number",<ref>{ ...

...niverse in [[Monotheism|monotheistic]] traditions.{{sfn|Stewart|2024}} The Pythagoreans considered the numbers to be plural and therefore did not classify 1 itself ...

...very while out at sea, and was subsequently thrown overboard by his fellow Pythagoreans 'for having produced an element in the universe which denied the... doctrin ...

...'', which includes Pythagoras with a tablet of ideal ratios, sacred to the Pythagoreans.<ref name="Ladwein2006">{{cite book |last=Ladwein |first=Michael |title=Leo ...oportions, corresponding to the lengths of the lyre's strings; indeed, the Pythagoreans held that everything was arranged by Number. In the same way, in Platonic t ...

...n|2005|p=9}} | {{harvnb|Kvasz|2006|p=290}} | {{harvnb|Corry|2024|loc=§ The Pythagoreans and Euclid}} }}</ref> In the 3rd century CE, [[Diophantus]] provided a deta ...

...tion" to purify the soul, from ancient [[Babylon]] to the [[Pythagoreanism|Pythagoreans]].<ref name=":13">Ferrater Mora. 1991 p. 2054</ref> ...