...and, in short, every affirmation which is either intuitively or demonstratively certain. '/'/.•"/ the square of the hypothenuse is equal to the squares of the two aides, is a proposition which expresses a relation between these figures. That three times Jive...

...a tissue/' is not less exact, not less certain, than the proposition : " In a right-angled triangle the square of the hypothenuse is equal to the squares of the two other sides." Neither proposition is self-evident; both have to be shown by experiment ; and when...

...a tissue," is not less exact, not less certain, than the proposition : " In a right-angled triangle the square of the hypothenuse is equal to the squares of the two other sides." Neither proposition is self-evident ; both have to be shown by experiment ; and when...

...conspicuous truths, which are only truths because they are identical propositions, to the inconspicuous truth that the square of the hypothenuse is equal to the squares of the sides, this also is transformed into an identical proposition; a transformation which may be effected...

...opinions that there must necessarily be hostile mathematical sects, some affirming, and some denying, thnt the square of the hypothenuse is equal to the squares of the sides. But we do not think either the one analogy or the other of the smallest value. Our way of ascertaining...

...opinions that there mast necessarily be hostile mathematical sects, some affirming and some denying, that the square of the hypothenuse is equal to the squares of the sides. But we do not think either the one analogy or the other of the smallest value. Our way of ascertaining...

...opinions that there must necessarily be hostile mathematical sects, some affirming and some denying that the square of the hypothenuse is equal to the squares of the sides. But we do not think either the one analogy or the other of the smallest value. Our way of ascertaining...

...Arithmetic, and, in short, every affirmation which is either intuitively or demonstratively certain. That the square of the hypothenuse is equal to the squares of the two sides, is a proposition which expresses a relation between these figures. That three times five...

...opinions that there must necessarily be hostile mathematical sects ; some affirming, and some denying that the square of the hypothenuse is equal to the squares of the sides. But we do not think either the one analogy or the other of the smallest value. Our way of ascertaining...

...glance all the reasons constituting the demonstration of a theorem which, like the following theorem, The square of the hypothenuse is equal to the squares of the other two sides, depends on demonstration of many other theorems. The unconscious knowledge caused by the antecedent...