 | Robert Simson - Geometry - 1838 - 434 pages
...the angles BGH, GHD ; but the angles AGH, BGH are equal (13. 1.) to two right angles; therefore the angles BGH, GHD are less than two right angles; but...the same side less than two right angles, do meet (12. ax.) * together if continually produced ; therefore the straight lines AB, CD, if produced far... | |
 | Euclides - 1838 - 264 pages
...greatert than the angles BGH, GBD: but the angles AGH, BGH are equal* to two right angles; ' therefore the angles BGH, GHD are less than two right angles ; but...line falling upon them, make the interior angles on nt . the same side less than two right angles, will meet* '- *' together if continually prolonged ;... | |
 | Euclides - Geometry - 1841 - 378 pages
...angles BGH, GHD; but * is. 1. the angles AGH, BGH are together equal* to two right angles; therefore the angles BGH, GHD are less than two right angles; but...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... | |
 | Euclides - 1845 - 546 pages
...angles BGH, GHD; fax. 4.) but the angles AGH, BGH are equal to two right angles ; (i. 13.) therefore the angles BGH, GHD are less than two right angles ; but...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
...to two right angles : wherefore the angles BGH, GHD are less than two right angles. But (I. ax. 12) those straight lines, which with another straight...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,... | |
 | Euclid - Geometry - 1845 - 218 pages
...angle AGH 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... | |
 | Euclid, Thomas Tate - 1849 - 120 pages
...the angles BGH, GHD; but the angles AGH, BGH are equal (i. 13.) to two right angles ; therefore the angles BGH, GHD are less than two right angles; but...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
...angles BGH, GHD; but the angles AGH, BGH are equal* to two right angles; • xiii. i therefore the angles BGH, GHD are less than two right angles; but...two right angles, do meet together if continually produced; therefore the straight lines AB, CD, if produced far enough, shall meet; but they never meet;... | |
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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. 
