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" If a straight line meets 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 Elements of Euclid, containing the first six books, with a selection of ... - Side 6
av Euclides - 1874
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The Mystery of Space: A Study of the Hyperspace Movement in the Light of the ...

Robert T. Browne - 1919 - 395 sider
...parallel-postulate, as stated by EUCLID in his Elements of Geometry, reads as follows: "If a straight line meet two straight lines so as to make the two interior...the angles which are less than two right angles." On this postulate hang all the "law and the prophets" of the non-Euclidean Geometry. In it are the...
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Solid Geometry

Charles Austin Hobbs - 1921 - 192 sider
...corresponding angles equal, the two lines are parallel. Prop. 41. If two lines are cut by a transversal so as to make the two interior angles on the same side of the transversal supplementary, the lines are parallel. Prop. 41, Cor. II. Two lines respectively perpendicular...
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Tufts College Graduate, Volumer 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, Volum 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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Transactions of the Royal Society of New Zealand, Volum 18

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...the angles which are less than two right angles." In other words, if the angle CAH + the angle ABD < 180°, then AC and />' l> will at length meet. This...
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Non-Euclidean Geometry: A Critical and Historical Study of Its Development

Roberto Bonola - 1955 - 389 sider
...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 sider
...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 sider
...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 sider
...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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