 | Noah Porter - 1869 - 758 pages
...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... | |
 | 1870 - 484 pages
...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... | |
 | William Stanley Jevons - 1870 - 420 pages
...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... | |
 | Noah Porter - 1871 - 604 pages
...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... | |
 | Henry William Watson - 1871 - 320 pages
...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... | |
 | John Benn Walsh (Baron Ormathwaite.), John Benn Walsh Baron Ormathwaite - 1872 - 220 pages
...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.... | |
 | John Benn Walsh (Baron Ormathwaite.), John Benn Walsh Baron Ormathwaite - 1872 - 184 pages
...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.... | |
 | George Grote - 1872 - 508 pages
...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... | |
 | Noah Porter - 1873 - 726 pages
...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... | |
 | Edward James Mortimer Collins - 1874 - 312 pages
...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 that... | |
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