 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 Teaching of Geometry - Page 129by David Eugene Smith - 1911 - 339 pagesFull view - About this book
 | Euclid - Mathematics, Greek - 1908 - 550 pages
...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,...on that side on which are the angles less than the ht'fl right angles. Although Aristotle gives a clear idea of what he understood by a postulate, he... | |
 | Leslie Leland Locke - Mathematics - 1909 - 364 pages
...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,...which are the angles less than the two right angles. It will be noticed that the plane geometry is built on three elements, the point, the straight line... | |
 | Jacob William Albert Young - Mathematics - 1911 - 432 pages
...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,...are the angles less than the two right angles." This is a consequence of our assumption, for let the rays AC and BD be such that the sum of the ~k 5 angles... | |
 | Jacob William Albert Young - Mathematics - 1911 - 434 pages
...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,...are the angles less than the two right angles." This is a consequence of our assumption, for let the rays AC and BD be such that the sum of the angles 2^CAB... | |
 | Jacob William Albert Young - Mathematics - 1911 - 427 pages
...on two straight lines makes the interior angles on the same side less than two right angles, the two lines, if produced indefinitely, meet on that side on which are the angles less than two right angles." Under the term non-Euclidean geometry we shall understand a system of geometry which... | |
 | Robert Édouard Moritz - Mathematics - 1914 - 434 pages
...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,...which are the angles less than the two right angles. — EUCLID. The Thirteen Books of Euclid's Elements [TL Heath] Vol. 1 (Cambridge, 1908), p. 202. 2008.... | |
 | Duncan M'Laren Young Sommerville - Geometry, Non-Euclidean - 1914 - 291 pages
...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 two right angles." 3. Attempts to prove the parallel-postulate. It seems impossible to suppose that... | |
 | Mathematics - 1915 - 830 pages
...on two straight lines makes the interior angles on the same side less than two right angles, the two lines, if produced indefinitely, meet on that side on which are the angles less than two right angles." The idea of a non-Euclidean geometry came into being after many years of futile... | |
 | Horatio Scott Carslaw - Geometry - 1916 - 193 pages
...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,...are the angles less than the two right angles. This hypothesis we shall refer to as Euclid's Parallel Postulate. It is true that in some of the MSS. it... | |
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