 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.  Elements of Geometry and Trigonometry - Page 38by Adrien Marie Legendre - 1852 - 432 pagesFull view - About this book
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...lines meet a third line, making the sum of the inter1or angles on the same side less tl\an two ri'jltt angles, the two lines will meet if sufficiently produced. Let the two lines CD, ///, meet the line EF, making the sum of the interior angles 1IG L, G1fD, less than two right angles... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...lines, KL and CD, make with EF the two angles KGH, GHC together less than two right angles, then will KL and CD meet, if sufficiently produced. For if they do not meet, they are parallel (Def. 12). But they are not parallel ; for then the angles KGH, GHC would be equal to two right angles.... | |
 | Euclides - 1862 - 172 pages
...two right angles; but ' those straight lines which with another straight line falling upon them, make the interior angles on the same side less than two right angles, will meet together if continually produced;' (ax. 12) therefore the straight lines AB, CD, must meet... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...four obtuse angles. PROPOSITION XXI. THEOREM. If two straight lines intersect a third line, making the sum of the interior angles on the same side less than two right angles, the tioo lines will meet if sufficiently produced. Let the two lines CD, IL, meet the line JSF, making... | |
 | Euclides - 1865 - 402 pages
...two right angles; but ' those straight lines which with another straight line falling upon them, make the interior angles on the same side less than two right angles, will meet together if continually produced;' (ax. 12) therefore the straight lines AB, CD, must meet... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1869 - 470 pages
...obtuse angles: '<** PROPOSITION XXI. THEOREM. If two straight lines intersect a third line, making the sum of the interior angles on the same side less than...sufficiently produced. For, if they do not meet, they must be parallel (D. 16). But, if they were parallel, the sum of the interior angles HGL, GHD, would... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...lines, KL and CD, make with EF the two angles KGH, GHC together less than two right angles, then will KL and CD meet, if sufficiently produced. For if they do not meet, they are parallel (Def. 12). Bui they are not parallel ; for then the angles KGH, GHC wouW be equal to two right angles.... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...angles. PROPOSITION XXI. THEOREM. ' If two straight lines intersect a third straight line, making the sum of the interior angles on the same side less than...sufficiently produced For, if they do not meet, they must be parallel (D. 16). But, if they were parallel, the sum. of the interior angles HGL, £r_ZZZ>,... | |
 | Henry Major - Student teachers - 1873 - 588 pages
...two right angles ; but those straight lines which, with another straight line falling upon them, make the interior angles on the same side less than two right angles, do meet together if continually produced ; therefore the straight lines AB, CD, if produced far enough,... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...angles. PROPOSITION X2I. THEOREM. If two straight lines intersect a third straight line, making the sum of the interior angles on the same side less than...sufficiently produced. For, if they do not meet, they must be parallel (D. 16). But, if they were parallel, the sum of the interior angles HGL, GHD, would... | |
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