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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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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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The Workings of Language: From Prescriptions to Perspectives

Rebecca S. Wheeler - English language - 1999 - 268 pages
...propositions appeared to require 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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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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The Rainbow of Mathematics: A History of the Mathematical Sciences

Ivor Grattan-Guinness - Mathematics - 2000 - 836 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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Geometry Civilized: History, Culture, and Technique

J. L. Heilbron - Geometry - 2000 - 344 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 straight lines. if continued indefinitely. meet on that side on which lie the angles less than...
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Methods of Geometry

James T. Smith - Mathematics - 2000 - 510 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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The Norton History of the Mathematical Sciences: The Rainbow of Mathematics

I. Grattan-Guinness - Mathematics - 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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A Course in Modern Geometries

Judith Cederberg - Mathematics - 2004 - 472 pages
...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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