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 127by David Eugene Smith - 1911 - 339 pagesFull view - About this book
| Euclid, Sir Thomas Little Heath, Johan Ludvig Heiberg - Mathematics, Greek - 1908
...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... | |
| Jacob William Albert Young - Mathematics - 1911 - 416 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... | |
| Oswald Veblen, Thomas Franklin Holgate, Frederick Shenstone Woods, Edward Vermilye Huntington, George Abram Miller, Gilbert Ames Bliss, Leonard Eugene Dickson, David Eugene Smith - Mathematics - 1911 - 416 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... | |
| J. W. A. YOUNG - 1911
...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 - 410 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.... | |
| Cassius Jackson Keyser - Mathematics - 1922 - 466 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. Apparently convinced that this proposition could not be deduced as a theorem from... | |
| David Eugene Smith - Mathematics - 1958 - 736 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,...side on which are the angles less than the two right** angles.3 Considerable criticism of these postulates developed among the later Greeks. Zeno of Sidon... | |
| A. Szabó - History - 1978 - 358 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."** Since the appearance of Zeuthen's pioneering work, there has been little disagreement amongst scholars... | |
| Ladislaus Marton - Computers - 1980 - 492 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,...meet on that side on which are the angles less than** two right angles. Figure 3 illustrates this postulate. For a + y < 2ir the lines BB' and AA' meet on... | |
| Howard Whitley Eves - Mathematics - 1983 - 270 pages
...falling on two straight lines makes the interior angles on the same side together less than two right **angles, the two straight lines, if produced indefinitely, meet on that side on which** the angles are together less than two right angles. The Axioms or Common Notions 2. If equals be added... | |
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