 | 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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Wherefore, if a straight line, &c. QB D. PROPOSITION XXVIII. THEOB.—-If a straight line, falling upon two other straight lines, make the exterior angle equal to... 
