...Birmingham can't understand! Get to the heart of it. Don't grant him anything. Don't be quite sure that the three angles of every triangle are equal to two right angles; and don't at all allow, until you are yourself fairly convinced, that parallel straight lines...

...ideal from are always verifiable. The skilled surveyor's measurements by triangulation assume always that the three angles of every triangle are equal to two right angles. And any one who wantsvefification can have it, either roughly and imperfectly by the use of...

...Euclidean geometry holds only on the assumption that the Constant is infinite. Only in this case is it true that the three angles of every triangle are equal to two right angles ; and this can easily be proved, as soon as we admit that the Constant is infinite." This document...

...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...

...we cannot divide it, at least in our thought). And because of these facts it can be truly asserted that the three angles of every triangle are equal to two right angles and that every body is divisible. Fifthly, \ ask my readers to spend a great deal of time and...

...we cannot divide it, at least in our thought). And because of these facts it can be truly asserted that the three angles of every triangle are equal to two right angles and that every body is divisible. Fifthly, I ask my readers to spend a great deal of time and...

...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;...

...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...

...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...