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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 - Seite 21
von Euclides - 1853 - 147 Seiten
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Mathematics and Its History

John Stillwell - 2004 - 576 Seiten
...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 - 378 Seiten
...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-Massie, Paul Turquand Keyser - 2002 - 440 Seiten
...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 ..., Band 2

I. Grattan-Guinness - 2003 - 980 Seiten
...- 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 - 2003 - 714 Seiten
...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 Seiten
...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 - 2004 - 149 Seiten
...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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A Long Way from Euclid

Constance Reid - 2004 - 306 Seiten
...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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Real Analysis and Applications: Including Fourier Series and the Calculus of ...

Frank Morgan - 218 Seiten
...¡aspr] EIOIV at icov ouo opucov EXaaaoveç. [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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Philosophy in the Ancient World: An Introduction

James A. Arieti - 2005 - 420 Seiten
...other. The fifth postulate is quite different: 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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