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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 Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Side 23
af Euclides - 1816 - 528 sider
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1881 - 236 sider
...angles PGH, GHD. But 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...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 - 272 sider
...are greater 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...two right angles, do meet together if continually "oduced ; therefore the straight lines AB, CD, if oduced far enough, shall meet ; but they never meet,...
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An introduction to geometry, consisting of Euclid's Elements, book i ..., Bind 1

Euclides - 1884 - 182 sider
...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 Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - 1885 - 538 sider
...PROPOSITION XXI. THEOREM. // two straight lines intersect a third straight line, making the sum of the interior angles on the same side less than two right angles, the two lines will meet if sufficiently produced. Let the two lines CD, IL, meet the line EF, making...
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Elements of Plane Geometry

Alan Sanders - 1901 - 260 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, Bind 13

1903 - 750 sider
...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 - 550 sider
...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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Pure Mathematics

Leslie Leland Locke - 1909 - 364 sider
...all 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 - 434 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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Monographs on Topics of Modern Mathematics, Relevant to the Elementary Field

Jacob William Albert Young - 1911 - 432 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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