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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 ... - الصفحة 179
بواسطة Peter Nicholson - 1825 - عدد الصفحات: 372
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An Introduction to Logic

Morris Raphael Cohen, Morris R. Cohen, Ernest Nagel, John Corcoran - 1993 - عدد الصفحات: 232
...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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The Poincaré Half-plane: A Gateway to Modern Geometry

Saul Stahl - 1993 - عدد الصفحات: 298
...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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The 'Arabick' Interest of the Natural Philosophers in Seventeenth-Century ...

G. A. Russell - 1994 - عدد الصفحات: 320
...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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Mathematics: A Concise History and Philosophy: A Concise History and Philosophy

W.S. Anglin - 1994 - عدد الصفحات: 261
...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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On the Shoulders of Giants

Lines M E - 1994 - عدد الصفحات: 296
...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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Geometry from a Differentiable Viewpoint

John McCleary - 1994 - عدد الصفحات: 308
...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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Circles: A Mathematical View

Dan Pedoe - 1995 - عدد الصفحات: 102
...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 - عدد الصفحات: 331
...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 - عدد الصفحات: 224
...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 - 1996 - عدد الصفحات: 321
...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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