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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 six books of the Elements of Euclid, with numerous exercises - Σελίδα 21
των Euclides - 1853 - 147 σελίδες
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Non-Euclidean Geometry: A Critical and Historical Study of Its Development

Roberto Bonola - 1955 - 389 σελίδες
...he makes use of the following Postalate (V.): Jf a straight lin-e falling on two straight lines mahe 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 Poincaré Half-plane: A Gateway to Modern Geometry

Saul Stahl - 1993 - 298 σελίδες
...paragraph introducing the Common Notions below. 5. That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles [in sum], the two straight lines, if produced indefinitely, meet on that side on which are the angles...
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An Introduction to Logic

Morris Raphael Cohen, Morris R. Cohen, Ernest Nagel - 1993 - 232 σελίδες
...is impossible. "Similarly (2) we can show that the straight line falling on the parallels does not make the interior angles on the same side less than two right angles. "But (3), if it makes them neither greater nor less than two right angles, it can only make the interior...
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Mathematics: A Concise History and Philosophy: A Concise History and Philosophy

W.S. Anglin - 1994 - 261 σελίδες
...fifth postulate is the famous Parallel Postulate: 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 'Arabick' Interest of the Natural Philosophers in Seventeenth-Century ...

G. A. Russell - 1994 - 320 σελίδες
...fifth postulate, the postulate of parallels: '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 from a Differentiable Viewpoint

John McCleary, John Mac Cleary - 1994 - 308 σελίδες
...last of his assumptions. Postulate 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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On the Shoulders of Giants

Lines M E - 1994 - 296 σελίδες
...original form as follows: 5. If a straight line falling across two straight lines makes the sum of the interior angles on the same side less than two right angles, then the two straight lines intersect, if sufficiently extended, on that side. This implies, in particular,...
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The Heritage of Thales

W.S. Anglin, J. Lambek - 1998 - 331 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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Circles: A Mathematical View

Dan Pedoe - 1995 - 102 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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Reconceiving Mathematics Instruction: A Focus on Errors

Raffaella Borasi - 1996 - 321 σελίδες
...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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