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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: With Notes - Page 172
by John Radford Young - 1827 - 208 pages
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The celebrated theory of parallels. Demonstration of the celebrated theorem ...

Matthew Ryan - 1866 - 50 pages
...lines (AB, С D) which are in the same plane, so as to make the two interior angles (BA С, A С D) ore the same side of it, taken together, less than two right angles, these two straight lines (А В, С D) shall at length meet upon that side, if sufficiently produced. Draw...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...right angles ; [I. 13. therefore the angles BGH, GHD are together less than two riglit angles. But if a straight line meet 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. [Axiom 12. Therefore the...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...two right angles ; [I. 13. therefore the angles BGH, GHD are together less than two right angles. But if a straight line meet 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. [Axiom 12. Therefore the...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1870 - 270 pages
...all right angles are equal ; and 6. That when two lines are met or crossed by a third line, so that the two interior angles on the same side of it taken together are less than two right angles, the two lines so crossed shall meet, if continually produced. — Smith's...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...another. V. That two straight lines cannot inclose a space. VI. That if a straight line meet two other straight lines, so as to make the two interior angles...angles, these straight lines being continually produced shalj. at length meet upon that side, on which are the angles, which are together less than two right...
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The Quadrature of the Circle: The Square Root of Two, and the Right-angled ...

William Alexander Myers - Circle-squaring - 1873 - 238 pages
...another. 9. The whole is greater than its part. 10. Two straight lines can not inclose a space. 12. If a straight line meet 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. ARTICLES. 1. The double...
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The Quadrature of the Circle: The Square Root of Two, and the Right-angled ...

William Alexander Myers - Circle-squaring - 1874 - 207 pages
...another. 9. The whole is greater than its part. 10. Two straight lines can not inclose a space. 12. If a straight line meet 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. ARTICLES. 1. The double...
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Pure mathematics, Volume 1

Edward Atkins - 1874 - 426 pages
...part. 10. Two straight lines cannot inclose a space. 11. All right angles are equal to one another. 12. If a straight line meet 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. Explanation of Terms and...
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Euclidian Geometry

Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...Wherefore upon the same base, &c. Euclid's Twelfth Axiom, on which his Theory of Parallels depends, is " If a straight line meet two straight lines, so as...it taken together less than two right angles, these two straight lines being continually produced, shall at length meet on that side on which are the angles...
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Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 130 pages
...Therefore the angles BGH, GHD are less than two right + z GHD incrlps ' <two right angles. _ _ angles. But if a straight line meet two straight lines, so as...than two right angles, these straight lines being Hence AB and CD meet, and are parallel. not unequal to z GHD. and ^EOB = iGHD, >lso ZBGH + i GHD =...
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