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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 ... - Σελίδα 51
των Euclides - 1852
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Circles: A Mathematical View

Dan Pedoe - 1995 - 146 σελίδες
...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 - 1998 - 347 σελίδες
...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 - 1996 - 228 σελίδες
...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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The Dialogues of Plato, Volume 4: Plato’s Parmenides, Revised Edition

Plato - 1984 - 372 σελίδες
...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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Episodes from the Early History of Mathematics, Τόμος 13

Asger Aaboe - 1963 - 154 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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Flavors of Geometry

Silvio Levy - 1997 - 212 σελίδες
...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 - 1998 - 176 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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Mathematical Expeditions: Chronicles by the Explorers

Reinhard Laubenbacher, David Pengelley - 2000 - 292 σελίδες
...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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Posidonius: Volume 3, The Translation of the Fragments

Posidonius - 2004 - 434 σελίδες
...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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Squaring the Circle: The War Between Hobbes and Wallis

Douglas M. Jesseph - 1999 - 440 σελίδες
...book 1 is the notorious parallel postulateIt asserts "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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