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" If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles... "
The first six books of the Elements of Euclid, with numerous exercises - Seite 4
von Euclides - 1853 - 147 Seiten
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Tufts College Graduate, Bände 1-2

1901
...far from "self-evident" it is the reader may judge for himself. "If a straight line meets two other straight lines so as to make the two interior angles...it taken together less than two right angles, these sides being continually produced shall at length meet on that side on which are the angles which are...
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Popular Science Monthly, Band 68

1906
...can not enclose a space. 11. All right angles are equal to one another. 12. If a straight line meet two straight lines, so as to make the two interior...lines, being continually produced, shall at length meet on that side on which are the angles which are less than two right angles. Modern objections to these...
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Non-Euclidean Geometry: A Critical and Historical Study of Its Development

Roberto Bonola - 1955 - 389 Seiten
...make equal alternate angles, he hrings m the unwieldly postulate or axiom: " If a straight line meet two straight lines, so as to make the two interior...less than two right angles, these straight lines, heing continually produced, shall at length meet on that side on which are the angles which are less...
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Research in Educational Administration: Cooperative Research Project No. F-2

University Council for Educational Administration - 1962 - 548 Seiten
...primitive terms, for example, "point"; defined terms, for example, "triangle"; axioms, for example, "If a straight line meets two straight lines, so as to make two interior angles on the same side of it taken together less than two right angles, these straight...
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Matters Mathematical

I. N. Herstein, Irving Kaplansky - 1978 - 246 Seiten
...one another. But nothing up to this point has prepared us for the astonishing final axiom. AXIOM 12. If a straight line meets two straight lines, so as...lines, being continually produced, shall at length meet on that side on which are the angles which are less than two right angles. The axiom is illustrated...
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George Boole: Selected Manuscripts on Logic and its Philosophy

Ivor Grattan-Guinness, Gerard Bornet - 1997 - 236 Seiten
...4. And that all right angles are equal to one another. 5. And that if a straight line meet two other straight lines so as to make the two interior angles...these straight lines being continually produced shall meet on that side on which are the angles which are less than two right angles. 6. And that two straight...
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Transactions and Proceedings of the New Zealand Institute, Band 18

New Zealand Institute - 1886
...equivalence of the three forms of the parallel-axiom mentioned in my paper. Form (a), (Euclid's) is : — " If a straight line meets two straight lines, so as...than two right angles, these straight lines being I continually produced shall at length meet upon that side on which are the angles which are less than...
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The American Mathematical Monthly: Devoted to the Interests of ..., Bände 3-4

1896
...the two angles AKH and CfJK equal to two right angles. QED PROPOSITION XI. If a straight line meet two straight lines so as to make the two interior angles on the same side of it taken tdgethcr less than two light angles, these straight lines, being continually produced, shall at length...
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New Monthly Magazine, Band 30

Thomas Campbell, Samuel Carter Hall, Edward Bulwer Lytton Baron Lytton, Theodore Edward Hook, Thomas Hood, William Harrison Ainsworth - 1830
...the two interior angles on the same side of it, taken together, less than two right angles, these two straight lines, being continually produced, shall,...length, meet upon that side on which are the angles that are less than two right angles." This proposition, the author remarks, is improperly placed among...
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A short history of Greek mathematics

James Gow - 2018 - 346 Seiten
...straight lines cannot enclose a space: 11. All right angles are equal: 12. If a straight line meet two straight lines, so as to make the two interior angles on the same side of it together less than two right angles, these straight lines will meet if produced on that side. Of these...
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