 | William Nicholson - Natural history - 1809 - 684 pages
...makes the exterior angle equal to the interior and opposite one on the same side of the line ; or makes the interior angles on the same side equal to two right angles , the two straight lines shall be parallel to one another. I'M; M, 1,1 j. planes, are such planes ai have all... | |
 | William Nicholson - 1809 - 716 pages
...exterior angle equal to the interior and opposite one on the same side of tin- line ; or makes tile interior angles on the same side equal to two right angles ; the two straight lines shall be parallel to one another. PARALLEL planet, are such planes a* have all the perpendiculars... | |
 | William Nicholson - Natural history - 1821 - 406 pages
...makes the exterior angle equal to the interior and opposite one on the same side of the line ; or makes the interior angles on the same side equal to two right angles ; the two straight lines shall be parallel to one another. 1' niAL'.ci. planes, are such planes as have all the... | |
 | Adrien Marie Legendre - Geometry - 1828 - 346 pages
...proposition. For a strictly rigorous demonstration we refer to the second Note. THEOREM. •<; 0 _ €0. If two straight lines meet a third line, making the sum of the interior angles, on the same side of the line met, equal to two right angles, the two lines will be parallel. Let the two lines AC and... | |
 | Adrien Marie Legendre - Geometry - 1830 - 344 pages
...of the proposition. For a strictly rigorous demonstration we refer to the second Note. THEOREM. 60. If two straight lines meet a third line, making the sum of the interior angles, on tlie game side of the line met, equal to two right angles, the two lines will be parallel. •Let the... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...fall from the same point on the same straight line; which is impossible (Prop. XIV.). PROPOSITION XIX. THEOREM. If two straight lines meet a third line,...making the sum of the interior angles on the same side of the Km met, equal to twe right angles, the two lines will be parallel. > . Let the two lines EC,... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...fall from the same point on the same straight line; which is impossible (Prop. XIV.). PROPOSITION XIX. THEOREM. If two straight lines meet a third line,...making the sum of the interior angles on the same side of the line met, equal to two right angles, the two lines will be parallel. the third line BA, making... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...the same point on the AC same straight line ; which is impossible (P. 14). PROPOSITION XIX, THEOEEM. If two straight lines meet a third line, making the...same side equal to two right angles, the two' lines are parallel. Let the two lines KG, HD, meet the line BA, making the angles BAC, ABD, together equal... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...four acute angles are equal to each other, and so also are the four obtuse angles. PROPOSITION XXI. THEOREM. If two straight lines meet a third line,...making the sum of the interior angles on the same side less than two right angles, the two lines will meet if sufficiently produced. Let the two lines CD,... | |
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...interior angles. THEOREM XvII. If two straight lines are cut ly a third line, making the sum of the two interior angles on the same side equal to two right angles, the two lines will T)e parallel. For we have BGH + BGE = 2 right E angles (TI), therefore BGH + DHG G / = BGH + BGE; taking... | |
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A straight line falling on parallel straight lines makes the alternate angles equal to one another, the exterior angle equal to the interior and opposite angle, and the interior angles on the same side equal to two right angles... 
