| Euclides - 1853 - 146 pages
...the angles BGH, GHD; but the angles AGH, BGH, are equal (I. 13,) to two right angles ; therefore 2. **The angles BGH, GHD, are less than two right angles;...the same side less than two right angles, will meet** (Ai. 12.) together if continually produced ; therefore 3. The straight lines AB, CD, shall meet, if... | |
| Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...GHD; but the angles AGH, BGH are equal (13. i.) to two right angles; therefore the angles BGH, GIID, **are less than two right angles ; but those straight...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... | |
| Euclides - Geometry - 1853 - 176 pages
...angles a.gh, bgh, are equal (i. 13) to two right • • f angles ; therefore the angles bgh, ghci **are less than two right angles ; but those straight...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... | |
| Charles Davies - Geometry - 1854 - 436 pages
...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 two right angles,** the two lines will meet if sufficiently produced. Let the two lines CD, IL, meet the line EF, making... | |
| Euclides - 1862 - 172 pages
...the angles AGH, BGH, are equal to two right angles ; (i. 13) therefore the angles BGH, GHD, must be **less than two right angles; but ' those straight lines...produced;' (ax. 12) therefore the straight lines AB, CD,** must meet if produced far enough. but they never meet, since they are parallel by the hypothesis ;... | |
| Euclides - 1863 - 122 pages
...nngles. Therefore the two angles t _V j> angles. But those straight lines, which with j.make the two **interior angles on the same side less than two right angles, will meet together** (Ax. 12) if continually produced. Therefore the two straight lines AB, CD, if produced far enough,... | |
| Euclides - 1865 - 402 pages
...the angles AGH, BGH, are equal to two right angles ; (i. 13) therefore the angles BGH, GHD, must be **less than two right angles; but ' those straight lines...produced;' (ax. 12) therefore the straight lines AB, CD,** must meet if produced far enough. but they never meet, since they are parallel by the hypothesis ;... | |
| Robert Potts - 1868 - 434 pages
...angles ; but those straight lines, which with another straight line falling upon them, make the two **interior angles on the same side less than two right...continually produced; (ax. 12.) therefore the straight** fines AB, CD, if produced far enough, will meet towards B, D ; but they never meet, since they are... | |
| Charles Davies - Geometry - 1872 - 464 pages
...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 two right angles,** the two lines will meet if sufficiently produced. Let the two lines CD, IL, meet the line EF, making... | |
| Henry Major - Student teachers - 1873 - 592 pages
...angles AGH, BGH, 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 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,... | |
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