 | Euclides - 1846 - 292 pages
...angle equal to the interior and opposite upon the same side, and also the two interior angles upon the same side together equal to two right angles. Let the straight line EF fall upon the parallel straight lines AB, CD : it makes the alternate jt angles AGH, GHD, equal... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...equal to each other; also, any exterior angle equal to the interior and opposite on the same side; and the two interior angles on the same side together equal to two right angles. Let the straight line EF intersect the two parallel lines AB, CD; the alternate angles AGH, GHD are gle EGB is equal to the... | |
 | Euclides - 1852 - 152 pages
...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. Let the straight line EF fall upon the parallel straight lines AB, CD; (1.) the alternate angles AGH,* GHD are equal to one... | |
 | Euclides - Geometry - 1853 - 334 pages
...this straight line bisects FD at right angles : therefore <JR, DF, which are cut by this line, make the two interior angles on the same side together equal to two right angles, and are therefore parallel (i. 28). Hence QDFR is a parallelogram (Def. A) ; and it may be shewn as... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...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. Let the straight line EF fall upon the parallel straight lines AB, CD ; the alternate angles AGH, GIII), are E equal to one... | |
 | Euclides - 1853 - 146 pages
...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. Let the straight line EF fall upon the parallel straight lines AB, CD; the alternate angles AGH, GHD, are equal to one another;... | |
 | Dugald Stewart - 1854 - 454 pages
...asserted, for example, that " if one straight line falls on two other straight lines, so as to make the two interior angles on the same side together equal to two right angles, these two straight lines, though indefinitely produced, will never meet ; " is not the boundless immensity... | |
 | Dugald Stewart - 1854 - 452 pages
...asserted, for example, that " if one straight line falls on two other straight lines, so as to make the two interior angles on the same side together equal to two right angles, these two straight lines, though indefinitely produced, will never meet ;" is not the boundless immensity... | |
 | War office - 1858 - 578 pages
...other, and the exterior angle equal to the interior and opposite angle on the same side, and likewise the two interior angles on the same side together equal to two right angles. 3. If a straight line be divided into any two parts, the rectangle contained by the whole and one of... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...lines, &c. PROPOSITION XXI. THEOREM. If a straight line, meeting two other straight lines, makes the interior angles on the same side, together equal to two right angles, the two lines are parallel. Let the straight line AB, which A. EC meets the two straight lines AC,... | |
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... if a straight line, &c. QED PROPOSITION 29. — Theorem. If a straight 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 ;... 
