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" That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles. "
Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ... - Page 26
by Euclides - 1845
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Cognitive Dimensions of Social Science

Mark Turner Professor of English and Member of the Doctoral Faculty in Neuroscience and Cognitive Science University of Maryland - Language Arts & Disciplines - 2001 - 194 pages
...propositions, he made use of the parallel axiom: "If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which the angles are less than...
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A Mathematics Sampler: Topics for the Liberal Arts

William P. Berlinghoff, Kerry E. Grant, Dale Skrien - Mathematics - 2001 - 672 pages
...Euclid's Fifth Postulate, which says: If a straight line falling on two straight lines makes the sum of the interior angles on the same side less than two right angles, then the two straight lines, if extended indefinitely, meet on that side on which the angle sum is...
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Mathematics and Its History

John Stillwell - Mathematics - 2004 - 576 pages
...all right angles are equal to one another. 5. That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than...
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Greek Science of the Hellenistic Era: A Sourcebook

Georgia Lynette Irby-Massie, Paul Turquand Keyser - History - 2002 - 440 pages
...equal one to another, [space is homogenous] 5. If a straight line intersecting two straight lines makes the interior angles on the same side less than two right angles, die two straight lines, extended indefinitely, intersect on die side of die angles less than two right...
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All the Mathematics You Missed: But Need to Know for Graduate School

Thomas A. Garrity - Mathematics - 2002 - 378 pages
...Euclid's beginnings. Fifth Postulate: That, if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than...
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Companion Encyclopedia of the History and Philosophy of the ..., Volume 2

I. Grattan-Guinness - Mathematics - 2003 - 980 pages
...- the parallel postulate. This is the claim 'that, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which the angles are less than...
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The Cambridge History of Science: Volume 5, The Modern Physical and ...

David C. Lindberg, Mary Jo Nye, Roy Porter, Ronald L. Numbers - Mathematics - 2003 - 714 pages
...fifth, or paralled postulate, which states: "That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than...
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The Way We Think: Conceptual Blending And The Mind's Hidden Complexities

Gilles Fauconnier, Mark Turner - Psychology - 2008 - 464 pages
...require what is known as the parallel axiom: "If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which the angles are less than...
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The Foundations of Mathematics

Paul Carus - Mathematics - 2004 - 149 pages
...as follows: "But those straight lines which, with another straight * aJriif/iare. * Ktnva.1 trmuu. line falling upon them, make the interior angles on the same side less than two right angles, do meet if continually produced." Now this is exactly a point that calls for proof. Proof was then,...
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A Long Way from Euclid

Constance Reid - Mathematics - 2004 - 306 pages
...The famous fifth postulate stated as follows: 7/ a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, will meet on that side on which the angles are less...
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