| Euclid - 1837 - 410 Seiten
...to two right angles ; therefore the angles BGH, GHD are less than two right angles. But (I. ax. 12.) **those straight lines which, with another straight...them, make the interior angles on the same side less** that two right angles, meet together, if continually produced ; therefore the straight lines AB, CD,... | |
| Euclides - 1838 - 264 Seiten
...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 those straight...line falling upon them, make the interior angles on** nt . the same side less than two right angles, will meet* '- *' together if continually prolonged ;... | |
| Robert Simson - 1838 - 434 Seiten
...two right angles: but straight lines which with another straight line make the interior angles upon **the same side less than two right angles do 'meet (12. Ax.)** if produced far enough : therefore EB, FD shall meet, if produced towards B, D: let them meet in G,... | |
| Euclides - 1841 - 378 Seiten
...* 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 those straight...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 - 320 Seiten
...&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 - 544 Seiten
...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 those straight...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 - 380 Seiten
...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 Seiten
...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... | |
| Euclides - 1846 - 292 Seiten
...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 Seiten
...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 those straight...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,... | |
| |