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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 Teaching of Geometry - Page 127
by David Eugene Smith - 1911 - 339 pages
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Introduction and books 1,2

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...
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Monographs on Topics of Modern Mathematics: Relevant to the Elementary Field

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...
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Monographs on topics of modern mathematics: relevant to the elementary field

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...
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MODERN MATIIEMATICS

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...
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Memorabilia mathematica: or, The philomath's quotation-book

Robert ╔douard 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. Ś EUCLID. The Thirteen Books of Euclid's Elements [TL Heath] Vol. 1 (Cambridge, 1908), p. 202. 2008....
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Mathematical Philosophy: A Study of Fate and Freedom; Lectures for Educated ...

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...
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History of Mathematics, Volume 2

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...
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The Beginnings of Greek Mathematics

A. Szabˇ - 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...
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ADV ELECTRONICS ELECTRON PHYSICS, Volume 50

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...
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Great Moments in Mathematics (before 1650)

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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