Aristoteles, Pytagoreerne og [rot][/rot]2
Lagt inn: 06/04-2005 16:42
Fra Aristoteles "Prior Analytics":
"For all who argue per impossibile infer by syllogism a false conclusion, and prove the original conclusion hypothetically when something impossible follows from a contradictory assumption, as, for example, that the diagonal [of a square] is incommensurable [with the side] because odd numbers are equal to even if it is assumed to be commensurate. It is iferred by syllogism that odd numbers are equal to even, and proved hypothetically that the diagonal is incommensurate, since a false conclusion follows from the contradictory assumption."
Man mener at Aristoteles i dette sitatet redegjorde for at Pytagoreerne viste at [rot][/rot]2 er irrasjonal og hvordan de fant dette ut.
Kan noen forklare meg hvordan Pytagoreerne fant ut dette?[rot][/rot]
"For all who argue per impossibile infer by syllogism a false conclusion, and prove the original conclusion hypothetically when something impossible follows from a contradictory assumption, as, for example, that the diagonal [of a square] is incommensurable [with the side] because odd numbers are equal to even if it is assumed to be commensurate. It is iferred by syllogism that odd numbers are equal to even, and proved hypothetically that the diagonal is incommensurate, since a false conclusion follows from the contradictory assumption."
Man mener at Aristoteles i dette sitatet redegjorde for at Pytagoreerne viste at [rot][/rot]2 er irrasjonal og hvordan de fant dette ut.
Kan noen forklare meg hvordan Pytagoreerne fant ut dette?[rot][/rot]