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" ... 2. I assume that this space is affected with such curvature that a right line shall always return into itself at the end of a finite and real distance... "
An Essay on the Foundations of Geometry - Page 40
by Bertrand Russell - 1897 - 201 pages
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Journal für die reine und angewandte Mathematik, Volume 83

August Leopold Crelle, Carl Wilhelm Borchardt, Leopold Kronecker, Kurt Hensel, Lazarus Fuchs, Kurt Wilhelm Sebastian Hensel, Helmut Hasse, Friedrich Schottky - Electronic journals - 1877 - 366 pages
...curvature that a right line shall always return into itself at the end of a finite and real distance 2 D without losing, in any part of its course, that symmetry...emanate from the same point, making the indefinitely small angle a with each other, their distance apart at the distance r from the point of intersection...
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Hawkins' Mechanical Dictionary: A Cyclopedia of Words, Terms, Phrases and ...

Nehemiah Hawkins - Industrial arts - 1909 - 714 pages
...always return into itself at the end of a finite and real Four Way Cock. 248 Free Burning. distance without losing in any part of its course that symmetry...which constitutes the fundamental property of our Idea of it, Four Way Cock.— A cock so designed that water or liquids may be diverted into four different...
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Theories of Parallelism: An Historical Critique

William Barrett Frankland - Parallels (Geometry). - 1910 - 116 pages
...curvature that a right line shall always return into itself at the end of a finite and real distance 2.D, without losing, in any part of its course, that symmetry...the fundamental property of our conception of it." This definition of rectilinearity and the assumption of fiuitude are faultless ; but no more needs...
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Hawkins' Electrical Dictionary: A Cyclopedia of Words, Terms, Phrases and ...

Nehemiah Hawkins - Electricity - 1910 - 570 pages
...curvature that a right fane shall always return into itself at the end of a finite and real distance without losing in any part of its course that symmetry...which constitutes the fundamental property of our idea of it. Fourth State of Matter. — A condition of matter which Sir William Crookes in his experiments...
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Journal für die reine und angewandte Mathematik, Volume 83

Helmut Hasse, Lazarus Fuchs, Carl Wilhelm Borchardt, Leopold Kronecker - Mathematics - 1877 - 380 pages
...curvature that a right line shall always return into itself at the end of a finite and real distance 2 D without losing, in any part of its course, that symmetry...emanate from the same point, making the indefinitely small angle a with each other, their distance apart at the distance r from the point of intersection...
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An Essay on the Foundations of Geometry

A. W. Russell - 2017 - 240 pages
...curvature that a right line shall always return into itself at the end of a finite and real distance 2D without losing, in any part of its course, that symmetry...emanate from the same point, making the indefinitely small angle a with each other, their distance apart at the distance r from the point -of intersection...
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Theories of Parallelism: An Historical Critique

William Barrett Frankland - Parallels (Geometry). - 1910 - 100 pages
...homogeneity of space (Crelle's Journal, Vol. 83, pages 293-299). Then : of a finite and real distance ID, without losing, in any part of its course, that symmetry...the fundamental property of our conception of it." This definition of rectilinearity and the assumption of finitude are faultless ; but no more needs...
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