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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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Mathematics and the Roots of Postmodern Thought

Vladimir Tasi¢c, Associate Professor of Mathematics and Member of the Faculty of Interdisciplinary Studies Vladimir Tasic - 2001 - 189 σελίδες
...All right angles are mutually congruent. P5. 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 - 2001 - 602 σελίδες
...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 - 2004 - 544 σελίδες
...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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All the Mathematics You Missed: But Need to Know for Graduate School

Thomas A. Garrity - 2002 - 347 σελίδες
...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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Greek Science of the Hellenistic Era: A Sourcebook

Georgia Lynette Irby, Georgia Lynette Irby-Massie, Paul Turquand Keyser - 2002 - 392 σελίδες
...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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Companion Encyclopedia of the History and Philosophy of the ..., Τόμος 2

I. Grattan-Guinness - 2003 - 1806 σελίδες
...- 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, Cambridge University Press, Katharine Park, Lorraine Daston, Dorothy Ross, Theodore M. Porter - 2003 - 678 σελίδες
...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 - 2008 - 464 σελίδες
...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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Groundbreaking Scientific Experiments, Inventions, and Discoveries of the ...

Robert E. Krebs, Carolyn A. Krebs - 2003 - 376 σελίδες
...are given. (4) All right angles are equal. (5) 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 - 2004 - 148 σελίδες
...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, as ever...
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