...wanted into consciousness, ie, our general assertion is confirmed here too. Eg, if I want to prove that the angles at the base of an isosceles triangle are equal to one another, I only need to remember the general proposition that in every triangle equal angles...

...equally distant the one from the other — can never meet, let them be continued even into infinity ; or that the angles at the base of an isosceles triangle are equal, the one to the other ; the three angles of any triangle equal to two right angles ; the square of the...

...wanted into consciousness, ie, our general assertion is confirmed here too. Eg, if I want to pro.ve that the angles at the base of an isosceles triangle are equal to one another, I only need to remember the general proposition that in every triangle equal angles...

...always consists in showing a valid reason why the assertion should deserve belief. So again, to prove that the angles at the base of an isosceles triangle are equal to one another, means to establish the truth of that proposition ; and the manner of performing the...

...question. Or when we take for granted any principle which requires proof. In proving, for example, that the angles at the base of an isosceles triangle are equal to each other, if we assume that the angles on the other side of the base are equal to each other,...

...least sometimes called the Pans Asinarutti), will agree that though it may be more difficult to prove that the angles at the base of an isosceles triangle are equal, and that if the equal sides be produced, the angles on the other side of the base shall be equal, than...

...least sometimes called the Pons Asinantm), will agree that though it may be more difficult to prove that the angles at the base of an isosceles triangle are equal, and that if the equal sides be produced, the angles on the other side of the base shall be equal, than...

...truths which would be true here and everywhere in all past and all future time, as much as it is true that the angles at the base of an isosceles triangle are equal and were equal before there was a human being in existence. Lastly, there remains the so-called evolution...

...convince a Drainage Commissioner that the angle of incidence is equal to the angle of reflection, or that the angles at the base of an isosceles triangle are equal, however apparent it may be. Life is too short. Moreover he would probably only query in his mind what...

...think, in the words, " He that walketh with wise men shall be wise." The boy that has learned to prove that the angles at the base of an isosceles triangle are equal to one another — especially if he has learned it after Euclid — has made a certain gain in mental...