 | Cambridge univ, exam. papers - 1856 - 200 pages
...interior and opposite upon the same side of the line; or makes the interior angle upon the same side equal to two right angles; the two straight lines shall be parallel to each other. 3. The complements of the parallelogram, which are about the diameter of any parallelogram,... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...and AB are parallel (P. 19.) Cor. 2. If a straight line EF, meet two straight lines CD, AB, making the exterior angle EGB, equal to the interior and opposite angle GHD, the two lines will be parallel. For, to each add the angle HGB: we shall then have, EGB +HGB = GHD+HGB... | |
 | Euclides - 1860 - 288 pages
...the interior and opposite upon the same side of the line, or makes the interior angles upon the same side together equal to two right angles, the two straight lines shall be parallel to one another. Given that the straight line EF, which falls upon the two straight lines AB and CD, makes the exterior... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...l.nes, make the alternate angles equal to each other ; these two straight lines shall be parallel. Let the straight line EF, which falls upon the two straight lines A.Ji, CD, make the alternate angles AEF, EFD, equal to one another. Then AB shall be parallel to CD.... | |
 | War office - 1861 - 714 pages
...the same side of the line, or makes the interior angles on the same side of the line equal together to two right angles ; the two straight lines shall be parallel to one another. not pass through its centre, and the other straight line touches the circle, the rectangle contained... | |
 | Euclides - 1862 - 140 pages
...interior and opposite upon the tame side of the line, or make the interior angles upon the same fide together equal to two right angles, the two straight lines shall be parallel to one another. (References— Prop. I. 13, 15, 27; ax. 1, 3.) Hypothesis. — Let the straight line EF, which falls... | |
 | Euclides - 1862 - 172 pages
...lines, make the alternate angles equal to one another, then these two straight lines shall be parallel. Let the straight line EF, which falls upon the two straight lines, AB, CD, make the alternate angles, AEF, EFD, equal to one another. Then AB shall be parallel to CD. CONSTRUCTION For,... | |
 | University of Oxford - Education, Higher - 1863 - 316 pages
...the interior and opposite angle on the same side of the line, or make the interior angles on the same side together equal to two right angles, the two straight lines shall be parallel to one another. 10. If a straight line be divided into any two parts, the squares on the whole line, and on one of... | |
 | Benjamin Greenleaf - Geometry - 1863 - 502 pages
...the two lines are parallel. Let the straight line EF intersect the two straight lines AB, CD, making the exterior angle EGB equal to the interior and opposite angle, GHD ; then the lines AB, CD are parallel. For the angle AGH is equal to the angle EGB (Prop. IV.) ; F and... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...two lines are parallel. Let the straight line EF inter- E sect the two straight lines AB, CD, making the exterior angle ^ EGB equal to the interior and opposite angle, GHD ; then the lines AB, CD are parallel. c i1X For the angle AGH is equal to the angle EGB (Prop. IV.)... | |
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... upon the same side together equal to two right angles, the two straight lines shall be parallel to one another. 
