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
| Euclid - Geometry - 1845 - 218 pages
...the angle GHD, add to each of them the angle BGH ; therefore the angles AGH, falling upon them, make **the interior angles on the same side less than two right angles,** do meetJ together if con- I « AX. tinually produced ; therefore the straight lines AB, CD, if produced... | |
| Euclides, James Thomson - Geometry - 1845 - 382 pages
...angles. But (I. ax. 12) those straight lines, which with another straight line falling upon them, make **the interior angles on the same side less than two right angles,** meet together, if continually produced : therefore the straight fines AB, CD, if produced far enough,... | |
| Charles Davies - Trigonometry - 1849 - 372 pages
...obtuse angles. PROPOSITION XXI. THEOREM. If a straight line meet two other straight lines, making the **sum of the interior angles on the same side less than...the two lines will meet if sufficiently produced.** Letthe line EFmeet the two lines CD, IH, making the sum of the interior angles OGH, GOD, less than... | |
| Euclid, Thomas Tate - 1849 - 120 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 (Ax. 12.) together if continually produced; therefore the straight lines AB, CD, if produced... | |
| Euclides - 1852 - 152 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,... | |
| Euclides - Geometry - 1853 - 176 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 (12 ax.) together if continually produced ; therefore the straight lines ab, С d, if produced... | |
| Euclides - 1853 - 146 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 (Ai. 12.) together if continually produced ; therefore 3. The straight lines AB, CD, shall... | |
| Royal Military Academy, Woolwich - Mathematics - 1853 - 400 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 (12 Ax.) together if continually produced ; therefore the straight lines AB, CD, if produced... | |
| Charles Davies - Geometry - 1854 - 436 pages
...the four obtuse angles. PROPOSITION XXI. THEOREM. If two straight lines meet a third line, making the **sum of the interior angles on the same side less than...produced. For, if they do not meet they are parallel** (D. 16). But they are not parallel, for if they were, the sum of the interior angles LGH, GHD, would... | |
| Elias Loomis - Conic sections - 1857 - 242 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.... | |
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