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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. "
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Page 23
by Euclides - 1816 - 528 pages
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The Cambridge History of Eighteenth-century Philosophy, Volume 1

Knud Haakonssen - Electronic reference sources - 2006 - 790 pages
...intuition about arbitrarily distant space: 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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How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to ...

William Byers - Mathematics - 2010 - 424 pages
...Parallel Postulate: Postulate 5 (Parallel Postulate)6: 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 the side on which the angles are less than...
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The Nature of Statistical Evidence

Bill Thompson - Mathematics - 2007 - 152 pages
...right angles are equal to one another. V. 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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The Pythagorean Theorem: A 4,000-year History

Eli Maor - Mathematics - 2007 - 296 pages
...right angles are equal to one another. 5. 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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From Clockwork to Crapshoot: A History of Physics

Roger G. Newton - Science - 2007 - 366 pages
...last one, which he stated this way: "If a straight line crossing two straight lines makes the sum of the interior angles on the same side less than two right angles, the two straight lines, if continued indefinitely will meet on that side on which the two angles add...
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Continuous Symmetry: From Euclid to Klein

William H. Barker, Roger Howe - Mathematics - 574 pages
...Here is an English translation of what it said. 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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Cognitive Justice in a Global World: Prudent Knowledges for a Decent Life

Boaventura de Sousa Santos - Law - 2007 - 472 pages
...postulate for geometry in the plane states 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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How Round is Your Circle?: Where Engineering and Mathematics Meet

John Bryant, Christopher J. Sangwin - Mathematics - 2008 - 352 pages
...right angles are equal to one another, and 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 extended indefinitely, meet on that side on which the angles are less than...
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Impossible?: Surprising Solutions to Counterintuitive Conundrums

Julian Havil - Mathematics - 2008 - 249 pages
...the fifth postulate was at least cumbersome: 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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