Euclid's Parallel Postulate: Its Nature, Validity, and Place in Geometrical Systems ...Open Court Publishing Company, 1905 - 192 σελίδες |
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Σελίδα 2
... propositions , the introduction of formal logic and the powerful influence of the dialectics of Socrates and the Sophists , all contributed to make possible that re- markable outburst of mathematical genius which has been fittingly ...
... propositions , the introduction of formal logic and the powerful influence of the dialectics of Socrates and the Sophists , all contributed to make possible that re- markable outburst of mathematical genius which has been fittingly ...
Σελίδα 3
... propositions is his . He chose the theorems and demonstrations which should form a part of his system . Many available demonstrations were cer- 4 tainly rejected . We may attribute to his delib- erate choice the distinctive ...
... propositions is his . He chose the theorems and demonstrations which should form a part of his system . Many available demonstrations were cer- 4 tainly rejected . We may attribute to his delib- erate choice the distinctive ...
Σελίδα 5
... proposition 4. He also gives the parallel " axiom " as postulate 5 , but claims that it , too , should be proved , and ... propositions which involve this assumption were first demonstrated by Euclid him- 9 Discovered by Napoleon in Rome ...
... proposition 4. He also gives the parallel " axiom " as postulate 5 , but claims that it , too , should be proved , and ... propositions which involve this assumption were first demonstrated by Euclid him- 9 Discovered by Napoleon in Rome ...
Σελίδα 6
... Proposition 29 where it is introduced to support the proof of the equality of the alternate angles of parallel lines ... propositions more obvious by far . He even demonstrates that two a sides of a triangle are greater than the third 6 ...
... Proposition 29 where it is introduced to support the proof of the equality of the alternate angles of parallel lines ... propositions more obvious by far . He even demonstrates that two a sides of a triangle are greater than the third 6 ...
Σελίδα 7
... proposition which the Epicureans derided as being manifest even to asses . ' 66 11 The position of the postulate seems to indicate that Euclid struggled on as far as possible without it and postulated it finally only because he could ...
... proposition which the Epicureans derided as being manifest even to asses . ' 66 11 The position of the postulate seems to indicate that Euclid struggled on as far as possible without it and postulated it finally only because he could ...
Άλλες εκδόσεις - Προβολή όλων
Euclid's Parallel Postulate: Its Nature, Validity, and Place in Geometrical ... John William Withers Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Euclid's Parallel Postulate: Its Nature, Validity, and Place in Geometrical ... John William Withers Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Euclid's Parallel Postulate: Its Nature, Validity, and Place in Geometrical ... John Withers Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
Συχνά εμφανιζόμενοι όροι και φράσεις
absolute abstract ALFRED BINET analytical anguli apodeictic assumed assumption body Bolyai certainly Cloth conception consider construction Crelle's Journal curved defined definition determined direction distance Edition Elliptic geometry empirical ence equal essential etry Euclid Euclidean geometry Euclidean plane Euclidean space Euclidean system facts figures Foundations of Geometry free mobility G. B. Halsted Gauss geodesics geom Grundlagen der Geometrie Helmholtz Hence homogeneity idea intuition involved judgment Kant Kant's Klein Leipzig Lobatchewsky logical manifold Math Mathematics meaning measure of curvature nature of space necessary non-Euclid Non-Euclidean Geometry non-Euclidean systems notion Pages parallel lines parallel postulate PAUL CARUS Peano peculiar perception philosophical plane possible principle priori problem Proclus projective geometry propositions prove Psychology question reality regarded relations Riemann right angles Russell Saccheri Science sense sensory Sophus Lie spatial straight line surface synthetic theorems theory of parallels three dimensions tion triangle triangle's angle sum true two-dimensional validity
Δημοφιλή αποσπάσματα
Σελίδα 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...
Σελίδα 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.
Σελίδα 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...
Σελίδα 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...
Σελίδα 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...
Σελίδα 6 - The state of the exact sciences proves, says Mr. Gladstone, that, as respects religion " the association of these two ideas...