| Euclid - Geometry - 1853 - 176 pages
...lines (AB and CD), both in the same plane, and form internal angles at the same side (BGH and GHD) **equal to two right angles, the two straight lines shall be parallel.** DEMONSTRATION. Becanse the angles BGH and GHD are equal to two right angles (a), and the angles AGH... | |
| Insurance - 1853 - 394 pages
...another; (2) the exterior angle equal to the interior and remote upon the same side; and (3) the two **interior angles upon the same side together equal to two right angles.** 30. Draw through a given point between two straight lines not parallel a straight line which shall... | |
| Euclides - 1853 - 146 pages
...the third angle BAC to the third angle EDF. Therefore if two triangles, &c. QED PROP. XXVII. THEOREM. **If a straight line, falling upon two other straight lines, make the** alternate angles equal to one another, these two straight lines shall be parallel. Let the straight... | |
| Euclides - 1853 - 176 pages
...fall upon two parallel straigM lines, ii makes the aliernate angles equal to one, another ; and tlie **exterior angle equal to the interior and opposite upon the same side** ; and likewise the two interior angles upon the same side together equal to two rigM angles. LET the... | |
| Popular educator - 1854 - 1274 pages
...the preceding exercise, the straight lines AB and o D are parallel. QED PROPOSITION XXVIII.*-THEOREM. **If a straight line falling upon two other straight...exterior angle equal to the interior and opposite** angle upon the lame side of the straight line ; or make the two interior angles upon the tame side... | |
| Thomas Lund - Geometry - 1854 - 522 pages
...as already proved. COR. 2. If the two interior angles on the same side of the intersecting line are **together equal to two right angles, the two straight lines shall be parallel.** For, since / BEF ± t BEG =two right angles (30), .-. / BEF + t BEG = t BEF + L EFD, and .-. L EEG=t... | |
| William Somerville Orr - Science - 1854 - 532 pages
...straight lines (AB, CD) male the exterior angle (EGB) equal to the interior and opposite angle (GHD) **upon the same side of the line; or make the interior angles** (BGH, GHD) upon the same side together equal to tico right angles; the two straight lines (AB, CD)... | |
| Euclides - 1855 - 262 pages
...considered straight lines, aпd the figure EFDGB, a triangle, for the sake of the argument. Exercise 1.— **If a straight line falling upon two other straight lines, make the exterior** alternate angles AGE, FHD (see flg. to next proposition) equal to each other, these two straight lines... | |
| Cambridge univ, exam. papers - 1856 - 200 pages
...line fall upon two parallel straight lines, it makes the alternate angles equal to one another and **the exterior angle equal to the interior and opposite upon the same side;** and likewise the two interior angles upon the same side together equal to two right angles. If two... | |
| Cambridge univ, exam. papers - 1856 - 252 pages
...and the exterior angle equal to the interior and opposite upon the same side; and likewise the two **interior angles upon the same side together equal to two right angles.** 6. If a parallelogram and a triangle be upon the same base, and between the same parallels : the parallelogram... | |
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