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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. "
Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ... - Page 26
by Euclides - 1845
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Circles: A Mathematical View

Dan Pedoe - Mathematics - 1995 - 146 pages
...Euclidean geometry from other geometries, declares: 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 the side on which the angles are less than...
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The Heritage of Thales

W.S. Anglin, J. Lambek - Science - 1998 - 347 pages
...should be listed as an axiom instead. 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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Mathematics: The Science of Patterns: The Search for Order in Life, Mind and ...

Keith Devlin - Mathematics - 1996 - 228 pages
...All right angles are equal to one Postulate 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 are the angles less than...
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Reconceiving Mathematics Instruction: A Focus on Errors

Raffaella Borasi - Education - 1996 - 340 pages
...this axiom was stated by Euclid as follows: If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, then the two straight lines if extended will meet on that side of the straight line on which the angles...
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Episodes from the Early History of Mathematics, Volume 13

Asger Aaboe - Mathematics - 1963 - 154 pages
...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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Plato's Parmenides

Plato - Philosophy - 1984 - 372 pages
...Euclidean space (I, Postulate 5, trans. Heath): "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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Flavors of Geometry

Silvio Levy - Mathematics - 1997 - 212 pages
...right angles are congruent to one another. 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 extended indefinitely, meet on that side on which the angles are less than...
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Geometry: Plane and Fancy

David A. Singer - Mathematics - 1998 - 176 pages
...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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Posidonius: Volume 3, The Translation of the Fragments

Posidonius - Philosophy - 2004 - 434 pages
...controversy is Euclid's notorious fifth postulate: 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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Mathematical Expeditions: Chronicles by the Explorers

Reinhard Laubenbacher, David Pengelley - Mathematics - 2000 - 292 pages
...one another in either direction. POSTULATE 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 indefinitelv, meet on that side on which are the angles less than...
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