 | Euclides - Geometry - 1853 - 176 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 anotlier. £ LET the straight line ef, which falls upon the two straight lines ab, Сd, make the exterior... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...lines, makes the. alternate angles equal to one another, 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 ; AB is parallel to CD. For, if it be not parallel,... | |
 | Euclides - 1853 - 146 pages
...lines, make the alternate angles equal to one another, 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 ; AB is parallel to CD. / V For, if it be not parallel,... | |
 | 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... | |
 | William Somerville Orr - Science - 1854 - 534 pages
...PROPOSITION XXVIII.— THEOREM. If a straight line (EF) falling upon two other 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... | |
 | Thomas Lund - Geometry - 1854 - 520 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... | |
 | Popular educator - 1852 - 1272 pages
...the exterior alternate angles equal to each other, then two itraight lines are parallel. In Bg. 28, let the straight line EF, which falls upon the two straight lines AB and c D, make the tico exterior alternate angles AGE and PUD equal to one another ; then AB is parallel... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...parallel (P. 19.) BOOK I. 87 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... | |
 | John Playfair - Euclid's Elements - 1855 - 340 pages
...the alternate ingles equal to one another, these two straight lines are parallel. Let the straiglg line EF, which falls upon the two straight lines AB, CD make the alternate angles AEF, EFD equal to one another ; AB is parallel to CD. For, if it be not parallel,... | |
 | Euclides - 1855 - 270 pages
...straight lines, make the alternate angles equal to each other ; these two straight lines are parallel. Let the straight line EF, which falls upon the two straight lines AB, СD, make the alternate angles AEF, EFD, equal to one another. Then AB / shall be parallel to С D.... | |
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... upon the same side together equal to two right angles, the two straight lines shall be parallel to one another. 
