| Robert Simson - 1838 - 434 sider
...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 sider
...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 - 1841 - 378 sider
...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 sider
...&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 sider
...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 - 1845 - 382 sider
...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 - 1845 - 218 sider
...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 sider
...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 - 1849 - 372 sider
...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 sider
...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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