...satisfactorily by an example. In the fifth proposition of Euclid's geometry, BI, it is proposed to prove that the angles at the base of an isosceles triangle are equal. The first step is to prepare the diagram by producing the two sides AB, and AC, indefinitely towards...

...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...

...through a thousand stages, if need be, till you bring it to the meaning required. Thus you may prove that the angles at the base of an isosceles triangle are equal to each other, by the music of the spheres, or the eternity of the world from the nature of cause and...

...pronounced a universal genius, but for one deficiency—he never, for the life of him, could demonstrate that the angles at the base of an isosceles triangle are equal. He bears witness of himself, "I was very dull at school, and hated arithmetic: I always had to count...

...pliiiued byan In the fifth proposition of Playfair's Geometry, BI, it is proposed example, to prove that the angles at the base of an isosceles triangle are equal. The first step is to prepare the diagram by producing the two sides, AB, and AC, indefinitely towards...

...For example, we have proved in the corollaries to Propositions 5 and 6, respectively, the proposition that the angles at the base of an isosceles triangle are equal to one another, and its con-verse. We might also proceed as follows : Pig 2I Let ABC be an isosceles...

...experience. The nature of the proof differs altogether from that by which we arrive at the certainty that the angles at the base of an isosceles triangle are equal. In the one case the result is certain under all circumstances, and arises from the nature of things....

...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...

...experience. The nature of the proof differs altogether, from that by which we arrive at the certainty that the angles at the base of an isosceles triangle are equal. In the one case the result is certain under all circumstances, and arises from the nature of things....

...satisfactorily by an example. In the fifth proposition of Euclid's geometry, BI, it is proposed to prove that the angles at the base of an isosceles triangle are equal. The first step is to prepare the diagram by producing the two sides A B. and AC, indefinitely towards...