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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 geometry, by T. S. Davies. Conic sections, by Stephen Fenwick - Side 19
av Royal Military Academy, Woolwich - 1853
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1881
...the two angles AGH, BGH, are equal (I. 13) to two right angles. Therefore the two angles BGH, GHD, are less than two right angles. But those straight...another straight line falling upon them, make the two interior angles on the same side less than two right angles, will meet together (Ax. 12) if continually...
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Stewart's specific subjects. Euclid. [1st] (-3rd stage). [With 2 issues of ...

Stewart W. and co - 1884
...than BGH, GHD ; but the angles AGH, BGH, are equal to two right angles ; therefore the angles BGH GHD, are less than two right angles; but those straight...the same side less than two right angles, do meet together if continually "oduced ; therefore the straight lines AB, CD, if oduced far enough, shall...
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An introduction to geometry, consisting of Euclid's Elements, book ..., Volum 1

Euclides - 1884
...than BGH&nd GHD. (Ax. 4) But AGH and BGH are equal to two right angles ; (1. 13) therefore BGH and GHD are less than two right angles ; "but those straight lines which, with another falling upon them, make the interior angles on the same side of it together less than two right angles,...
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Elements of Plane Geometry

Alan Sanders - 1901 - 247 sider
...also bisected. PROPOSITION XX. THEOREM 127. If two lines are cut by a transversal, making the sum of the interior angles on the same side less than two right angles, the lines will meet if sufficiently produced. Let AB and CD be cut by EF, making Z 1 + Z 2 < 2 KA's....
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The Monist, Volum 13

1903
...to prop up the argument that proves the equality of alternate angles on parallels, viz. , that — "those straight lines which, with another straight...the same side less than two right angles, do meet if continually produced." This is exactly the point to be proved, for it is only one form of the conception...
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Introduction and books 1,2

Euclid - 1908
...right angles are equal to one another. \ 5. 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...
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Monographs on Topics of Modern Mathematics: Relevant to the Elementary Field

Jacob William Albert Young - 1911 - 416 sider
...fifth postulate of Euclid reads as follows: "If a straight line falling 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...
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Monographs on Topics of Modern Mathematics: Relevant to the Elementary Field

Jacob William Albert Young - 1911 - 416 sider
...by Euclid in his Postulate 5 as follows : " If a 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...
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Memorabilia Mathematica; Or, The Philomath's Quotation-book

Robert Édouard Moritz - 1914 - 410 sider
...2007. Euclid's Postulate 5 [The Parallel Axiom]. 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...
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The American Mathematical Monthly: The Official Journal of the ..., Volum 27

1920
...also the eleventh or twelfth axiom) states: "IS a 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 sid e on which are the angles less than...
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