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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. "
A Popular Course of Pure and Mixed Mathematics ...: With Tables of ... - Page 177
by Peter Nicholson - 1825 - 372 pages
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The Dialogues of Plato, Volume 4: Plato’s Parmenides, Revised Edition

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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Squaring the Circle: The War Between Hobbes and Wallis

Douglas M. Jesseph - Mathematics - 1999 - 440 pages
...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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Space from Zeno to Einstein: Classic Readings with a Contemporary Commentary

Nick Huggett - Philosophy - 1999 - 292 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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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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Posidonius: Volume 3, The Translation of the Fragments

Posidonius - Literary Criticism - 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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The Norton History of the Mathematical Sciences: The Rainbow of Mathematics

I. Grattan-Guinness - History - 1998 - 846 pages
...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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Using History to Teach Mathematics: An International Perspective

Victor J. Katz - Mathematics - 2000 - 284 pages
...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 - Islamic civilization - 2000 - 192 pages
...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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