 | Euclides - Geometry - 1841 - 378 pages
...are less than 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 * 12 Ax. angles meet,* if far enough produced; therefore the straight lines AB, CD, if produced far... | |
 | Euclides - 1842 - 316 pages
...&c. is made to depend upon an assumption that, if a line falling upon two other lines makes with them the interior angles on the same side less than two right angles, those lines must meet if produced. Now this is evidently a theorem which ought to have been previously... | |
 | Euclid - Geometry - 1845 - 218 pages
...is greater than 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 - 1845 - 546 pages
...are less than 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, if produced... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...than two right 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,... | |
 | Euclides - 1846 - 292 pages
...it together less than two right angles, these straight lines, being produced, shall meet (Ax. 12) ; therefore the straight lines AB, CD, if produced far...meet — but they never meet, since they are parallel (Hyp.) : Therefore the angle AGH is not unequal to the angle GHD, that is, it is equal to it : But... | |
 | Euclid, Thomas Tate - 1849 - 120 pages
...are less than 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 far enough,... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...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 two right angles, the two lines will meet if sufficiently produced. Letthe line EFmeet the two lines CD, IH, making the... | |
 | Euclides - 1852 - 152 pages
...are less than 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, shall... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...obtuse angles. PROPOSITION XXI. THEOEEM. If two straight lines meet a third line, raaking tlie 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... | |
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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. 
