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...holds good only under the presupposition, that the constant is infinitely great. Only then is it true, that the three angles of every triangle are equal to two right angles ; also this can be easily proven if one takes as given the proposition, that the constant is infinitely...

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...built up. Nothing is taken on trust ; every step is understood and commands our intellectual assent. That the three angles of every triangle are equal to two right angles is a proposition which cannot be denied by anyone who has assented to the definitions and axioms which...

...certainty. In mathematical reasoning our knowledge is greater than our ignorance. When, you have proved that the three angles of every triangle are equal to two right angles , there is an end of doubt; because there are no materials for ignorance to work up into phantoms;...

...We wish to recall that proposition. Arbitrary association of ideas immediately suggests the words, 'The three angles of every triangle are equal to two right angles.' But at first these are words only : our mind runs along an established train of sounds. By well-formed,...

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