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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 first six books of the Elements of Euclid, with numerous exercises - Σελίδα 21
των Euclides - 1853 - 147 σελίδες
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How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to ...

William Byers - 2010 - 424 σελίδες
...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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From Clockwork to Crapshoot: A History of Physics

Roger G. Newton - 2007 - 340 σελίδες
...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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Cognitive Justice in a Global World: Prudent Knowledges for a Decent Life

Boaventura de Sousa Santos - 2007 - 446 σελίδες
...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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The Pythagorean Theorem: A 4,000-year History

Eli Maor - 2007 - 259 σελίδες
...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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Continuous Symmetry: From Euclid to Klein

William H. Barker, Roger Howe - 546 σελίδες
...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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The Nature of Statistical Evidence

Bill Thompson - 2007 - 152 σελίδες
...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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How Round is Your Circle?: Where Engineering and Mathematics Meet

John Bryant, Christopher J. Sangwin, Senior Lecturer School of Mathematics University of Birmingham Chris Sangwin - 2008 - 306 σελίδες
...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 - 2008 - 235 σελίδες
...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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