 | 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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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. 
