...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 effort...

...a quadrilateral have two of its opposite sides parallel, and the two others equal but not parallel, any two of its opposite angles are together equal to two right angles. In quad. ABCD let AD || BC and AB = DC. AD is not equal to BC, for then AB would be both equal to and...

...quadrilateral be inscribable in two ellipses whose major axes are parallel or perpendicular to one another, any two of its opposite angles are together equal to two right angles. 4. A weight is supported by two pistons which are rigidly connected together, and which work in two...

...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,...

...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...

...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;...