...necessary for supporting it will be completed. Aristotle illustrates this by giving a demonstration that the angles at the base of an isosceles triangle are equal ; justifying every step in the reasoning by an appeal to some universal proposition." Again, every...

...resemblance to inductive reasoning. When in the fifth proposition of the first book of Euclid we prove that the angles at the base of an isosceles triangle are equal to each other, it is done by taking one particular -triangle as an example. A figure is given which...

...consequences, is a thing to be shunned and detested, is surely as obvious and infallible a truth, as that the angles at the base of an isosceles triangle are equal. No conceivable array of alleged or supposed proofs to the contrary,—and we may safely add, no accumulation...

...understand, but to work out for ourselves the famous fifth proposition. We are required to show : .., (1) That the angles at the base of an isosceles triangle are equal. (2) That if the equal sides are produced the angles on the other side of the base are equal. Draw an...

...observations which are essentially similar to, however superficially different from, those by which I know that the angles at the base of an isosceles triangle are equal. It is impossible, it seems to me, to have evidence greater than that which we have for the several...

...black boards to lay misshapen white eggs. 'Now, young gentlemen,' says Glanville, taking snuff, ' prove that the angles at the base of an isosceles triangle are equal.' He motioned Algy to try first. The unfortunate youngster tried, and produced a network of nonsense...

...reasoning from it resides. The assertion that all men are born equal has really no meaning. Euclid proves that the angles at the base of an isosceles triangle are equal to one another; and they are so in magnitude, which is the only attribute or quality which x an angle...

...those assigned by the examiner, and indicate the relative importance of the questions. 1875. 7. Prove that the angles at the base of an isosceles triangle are equal to one another. (8) 8. Prove that any two sides of a triangle are together greater than the third....

...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...

...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...