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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... "
Elements of geometry, based on Euclid, books i-iii - Side 9
av Edward Atkins - 1876 - 119 sider
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A Short Account of the History of Mathematics

Walter William Rouse Ball - 1908 - 522 sider
...usually stated iu the form that if a straight line meets two straight lines, so as to make the sum of the two interior angles on the same side of it taken together less than two right angles, then these straight lines being continually7 produced will at length meet upon that side on which are...
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Lectures on the Philosophy of Mathematics

James Byrnie Shaw - 1918 - 206 sider
...approach also, that is, in non-Euclidean geometry. Euclid had among his postulates one which read thus : If a straight line meet two straight lines so as to...lines, being continually produced, shall at length meet upon that side of the line on which are the angles which are less than two right angles. For ages mathematicians...
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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
...mankind. The parallel-postulate, as stated by EUCLID in his Elements of Geometry, reads as follows: "If a straight line meet two straight lines so as...lines being continually produced, shall at length meet upon that side on which are the angles which are less than two right angles." On this postulate hang...
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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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Transactions of the Royal Society of New Zealand, Volum 18

1886
...of the parallel-axiom mentioned in my paper. Form (a), (Euclid's) is: — "If a straight line meets two straight lines, so as to make the two interior...lines being continually produced shall at length meet upon that side on which are the angles which are less than two right angles." In other words, if the...
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Non-Euclidean Geometry: A Critical and Historical Study of Its Development

Roberto Bonola - 1955 - 389 sider
...parallels cut hy a transversal make equal alternate angles, he hrings m the unwieldly postulate or axiom: " If a straight line meet two straight lines, so as...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
...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...continually produced, shall at length meet on that side on which are the angles which are less than two right angles" (the famous "parallel postulate");...
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Matters Mathematical

I. N. Herstein, Irving Kaplansky - 1978 - 246 sider
...up to this point has prepared us for the astonishing final axiom. AXIOM 12. If a straight line meets two straight lines, so as to make the two interior...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 in Figure...
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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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