## Euclid's Parallel Postulate: Its Nature, Validity, and Place in Geometrical Systems ... |

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Euclid's Parallel Postulate: Its Nature, Validity, and Place in Geometrical ... John William Withers Ingen forhåndsvisning tilgjengelig - 2016 |

Euclid's Parallel Postulate: Its Nature, Validity, and Place in Geometrical ... John Withers Ingen forhåndsvisning tilgjengelig - 2017 |

Euclid's Parallel Postulate: Its Nature, Validity, and Place in Geometrical ... John William Withers Ingen forhåndsvisning tilgjengelig - 2016 |

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abstract actual already analytic appear assumed assumption axioms becomes body called certain certainly chapter character claims Cloth completely conception conclusion consider construction continuous course curvature curved defined definition determined difficulty dimensions direction distance empirical equal essential establish Euclid Euclidean exist experience expression facts figures follow geometry give given Hence hold idea important impossible interesting involved judgment known Leipzig less limit Lobatchewsky logical manifold Math Mathematics matter meaning measurement meet method metrical nature necessary necessity non-Euclidean notion objects observation origin Pages parallel postulate perception philosophical plane position possible present principle priori problem properties propositions prove pure question reality reason regarded relations remains requires Riemann right angles Science seems sense shown shows side similar simply space spatial standard straight line suggested surface taken theorems theory thought tion triangle true validity

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Side 4 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...

Side 11 - Assuming as an axiom that two straight lines which cut one another cannot both be parallel to the same straight line ; deduce Euclid's twelfth axiom as a corollary of Euc.

Side 25 - AF, to the not-cutting lines, as AG, we must come upon a line AH, parallel to DC, a boundary line, upon one side of which all lines AG are such as do not meet the line DC, while upon the other side every straight line AF cuts the line DC. The angle HAD between the parallel HA and the perpendicular AD is called the parallel angle (angle of parallelism), which we will here designate by f] (p) for AD = p. If H (p) is a right angle, so will the prolongation AE...

Side 13 - CD are crossed by a transversal (see figure on page 42), if the sum of the interior angles on one side of the transversal is...

Side 194 - THE ETHICAL PROBLEM. Second edition, revised and enlarged. 351 pages. Cloth, $1.25 (6s. 6d.) FUNDAMENTAL PROBLEMS. Second edition, revised and enlarged.

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Side 44 - Whitehead in his Universal Algebra, § 262, recurs to this important point, saying, "The idea of a space of one type as a locus in space of another type, and of dimensions higher by one, is due partly to J. Bolyai, and partly to Beltrami. Bolyai points out that the relations between lines formed by great circles on a two-dimensional limit-surface are the same as those of straight lines in a Euclidean plane of two dimensions. "Beltrami proves, by the use of the pseudosphere, that a...

Side 195 - Cloth, 11.75 (7S. 6d.). RIBOT, TH. THE PSYCHOLOGY OF ATTENTION. THE DISEASES OF PERSONALITY. THE DISEASES OF THE WILL.

Side 6 - The state of the exact sciences proves, says Mr. Gladstone, that, as respects religion " the association of these two ideas...

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