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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 two books of the Elements of Euclid, with additional figures ... - Pagina 51
door Euclides - 1852
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Space from Zeno to Einstein: Classic Readings with a Contemporary Commentary

Nick Huggett - 1999 - 292 pagina’s
...are greater than the angles BGH, GHD. But the angles AGH, BGH are equal to two right angles [1. 13]; therefore the angles BGH, GHD are less than two right angles. But straight lines produced indefinitely from angles less than two right angles meet [Post. 5]; therefore...
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Using History to Teach Mathematics: An International Perspective

Victor J. Katz - 2000 - 284 pagina’s
...also in Heath's translation from Heiberg: 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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Great Muslim Mathematicians

Mohaini Mohamed - 2000 - 192 pagina’s
...postulate as stated in most manuscript is as follows: 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 will, if produced indefinitely, meet on that side on which are the angles less...
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The Rainbow of Mathematics: A History of the Mathematical Sciences

Ivor Grattan-Guinness, I. Grattan-Guinness - 2000 - 836 pagina’s
...formulated a postulate in terms of «o«-parallelism: 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 Norton History of the Mathematical Sciences: The Rainbow of Mathematics

I. Grattan-Guinness - 1998 - 846 pagina’s
...formulated a postulate in terms of «o«-parallelism: 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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Methods of Geometry

James T. Smith - 2000 - 510 pagina’s
...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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Geometry Civilized: History, Culture, and Technique

J. L. Heilbron - 2000 - 344 pagina’s
...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 straight lines. if continued indefinitely. meet on that side on which lie the angles less than...
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A Course in Modern Geometries

Judith Cederberg - 2004 - 472 pagina’s
...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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Cognitive Dimensions of Social Science

Mark Turner Professor of English and Member of the Doctoral Faculty in Neuroscience and Cognitive Science University of Maryland - 2001 - 194 pagina’s
...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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Mathematics and the Roots of Postmodern Thought

Vladimir Tasić - 2001 - 208 pagina’s
...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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