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Books Books 1 - 7 of 7 on ... far prolonged, the same distance apart, that is, never intersect. They have the....  
" ... far prolonged, the same distance apart, that is, never intersect. They have the properties of the Euclidean parallels, and may be called and defined as such. It likewise follows, now, from the properties of triangles and rectangles, that two straight... "
Lectures on Fundamental Concepts of Algebra and Geometry - Page 26
by John Wesley Young, William Wells Denton, Ulysses Grant Mitchell - 1911 - 247 pages
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The Elements of Geometry

Webster Wells - Geometry, Plane - 1886 - 371 pages
...two of its angles, it is perpendicular to the other diagonal. 4. If two lines are cut by a third so as to make the sum of the interior angles on the same side of the secant line less than two right angles, the lines will meet if sufficiently produced. 6. If exterior...
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The Monist, Volume 14

Edward C. Hegeler - Philosophy - 1904
...properties of triangles and rectangles, that two straight lines which are cut by a third straight line so as to make the sum of the interior angles on the same side of them less than two right angles will meet on that side, but in either direction from their point of...
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Space and geometry in the light of physiological, psychological and physical ...

Ernst Mach - Geometry - 1906 - 144 pages
...properties of triangles and rectangles, that two straight lines which are cut by a third straight line so as to make the sum of the interior angles on the same side of them less than two right angles will meet on that side, but in either direction from their point of...
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Space and geometry in the light of physiological, psychological and physical ...

Ernst Mach - Mathematics - 1906 - 144 pages
...properties of triangles and rectangles, that two straight lines which are cut by a third straight line so as to make the sum of the interior angles on the same side of them less than two right angles will meet on that side, but in either direction from their point of...
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LECTURES ON FUNDAMENTAL CONCEPTS OF ALGEBRA AND GEOMETRY

JOHN WESLEY YOUNG - 1911
...up a valid geometry ? " * Gt POINCABE, loc. cit.9 p. 39. LECTURE III ON THE HISTOKY OF THE PAEALLEL POSTULATE Euclid's Attitude toward his Fifth Postulate....are cut by a transversal in such a way as to make the sum of the interior angles on the same side of the transversal less than two right angles, then...
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Mathematics and the Physical World

Morris Kline - Humor - 1981 - 482 pages
...rested. As stated by Euclid, the axiom runs as follows: 1f two lines in one plane intersect a third in such a way as to make the sum of the interior angles on one side of the third line less than two right angles, then these two lines will meet on that side...
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The Inland Educator: A Journal for the Progressive Teacher, Volumes 5-6

Education - 1897
...which the conclusion is reached. He says: If parallel lines meet at infinity, then two lines which are cut by a transversal in such a way as to make equal alternate interior angles are parallel, and he is vastly interested in establishing his conclusion,...
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