...the triangle in which it is contained are equal to two right angles, and to the fact that the angles at the base of an isosceles triangle are equal to one another, and shows now only that the angle in the semicircle must therefore necessarily be equal to the other two...

...clearer if we consider a false negative and a true affirmative judgement. It is true that 'the angles at the base of an isosceles triangle are equal to one another/ because (I presume) in the real counterpart of our judgement the angles are really united by the relation...

...thought of the past. If Euclid were alive to-day (and I dare say he is), he would not say "the angles at the base of an isosceles triangle are equal to one another." He would say, "To me (a very frail and fallible being, remember) it does somehow seem that these two...

...seat, has proven to us all that the angles at the base of an isosceles triangle are not equal, and that if the equal sides be produced the angles on the other side of the base are not equal either. Therefore, Mr. Speaker, may I be allowed to ask what I am to do about the matter....

...thought of the past. If Euclid were alive to-day (and I dare say he is) he would not say, " The angles at the base of an isosceles triangle are equal to one another." He would say, "To me (a very frail and fallible being, remember) it does somehow seem that these two...

...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 it was to describe an equilateral triangle on a given finite straight line; yet no one but an...

...demonstrate, for example, 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 are equal also; or that the square on the hypotenuse of a right-angled triangle is equal to the sum...

...demonstrate, for example, 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 are equal also; or that the square on the hypotenuse of a right-angled triangle is equal to the sum...

...Euclid in itself is not of much practical use — no one wants to prove in everyday life that the angles at the base of an isosceles triangle are equal to one another or that the three angles of a triangle are equal to two right angles, but you learn Euclid in order...

...according to Euclid's description in the proof. Proposition 5: The angles opposite the equal sides of an isosceles triangle are equal to one another; and, if the equal sides are extended further, the angles made with the third side will be equal. Proof: Let ABC be an isosceles...