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...nothing else." To quote an example which the author himself gives, the proposition that "the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides" is a categorical proposition, and is not therefore mathematical....

...achievements, one of the most profound and far-reachinghas at its origin the discovery by Pythagoras that the hypotenuse of a right-angled triangle is equal to the sum of the squares of the two sides containing the right angle. Two conditions were involved in Pythagoras'...

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...my head which seems to have inhabited some corner of my brain since that early time: "The square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides!" There it sticks, but what of it, ye gods, what of it? JESSIE B....

...strongest. Surely no one is going to deny that 2 + 2 is 4 in both China and Greece. Surely the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides, whether we call this Pythagoras' theorem, or Gou Gu. Indeed, indeed....

...procedures that deliver a conclusion whose certainty is that of a priori definition. "The square on the hypotenuse of a right-angled triangle is equal to the sum of squares on the other two sides" states a Pythagorean axiom of given truthvalue within the closed system...