 | Mathematics - 1836 - 352 pages
...than two right angles, is not an assumption but a consequence of his proposition, which shews that any two angles of a triangle are together less than two right angles, and which is established before any mention is made of parallels. It has been found by the experience... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...be demonstrated that the angle BCG, that is (1. 15), the angle ACD, is greater than the angle ABC. PROPOSITION XVII. THEOREM. Any two angles of a triangle...are together less than two right angles. Let ABC be any triangle ; any two of its angles together are less than two right angles. Produce BC to D ; and... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...ECF)jba*e ^ = base Fc, 'land ZBAC = Z ACF, 2 3. that Z ACD > Z BAC, that similarly Z BCG or ACD > Z ,IBC. PROPOSITION XVII. Theorem. Any two angles of a triangle are together less than two right angles. Steps of the Demonstration. 1. Prove that Zs DCA + ACB > Zs ACB + CBA, 2. that Zs ACB + CBA < 2 right... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...greater than the interior and remote right angle, which (I. def. 10.) is impossible. PROP. XVII. THEOR.* ANY two angles of a triangle are together less than two right angles. Let ABC be any triangle ; any two of its angles are together less than two right angles. ing the equality of CEB... | |
 | Charles Reiner - Geometry - 1837 - 254 pages
...12 \ a / rt. £s; and .'. the sum of the 9 ext. /.s = 10 rt. /.s. SUBSTANCE OF SECTION III. / \ 1. Any two angles of a triangle are together less than two right angles. 2. The interior angles of every triangle are together equal to two right angles. 3. A right-angled... | |
 | Euclides - 1838 - 264 pages
...thatis,theangle*ACD,isgreaterthantheangleABC. Therefore, if one side, &c. u. ED PROP. XVII. THEOR. Any two angles of a triangle are together less than two right angles. Let ABC be any triangle ; any two of its angles together shall be less than two right angles. Produce BC to D... | |
 | Euclides - 1840 - 82 pages
...produced, the external angle is greater than either of the internal remote angles. PROP. XVII. THEOR. Any two angles of a triangle are together less than two right angles. cu PROP. XVIII. THEOR. If two sides of a triangle are unequal, the angle subtended by the greater side... | |
 | Euclides - Geometry - 1841 - 378 pages
...' the angle ACD, is greater than the angle ABC. Therefore, if one side, &c. QED PROP. XVII. THEOR. Any two angles of a triangle are together less than two right angles. Let ABC be any triangle; any two of its angles together shall be less than two right angles. Produce BC to D;... | |
 | Euclides - 1842 - 316 pages
...1.), the angle ACD, is greater than the angle ABC. Therefore, if one side, &c. QED PROP. XVII. THEOR. ANY two angles of a triangle are together less than two right angles. Let ABC be any triangle; any two of its angles together are less than two right angles. Produce B c to D ; and... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...that the angle BCG, that is (15. 1.), the angle ACD, is greater than the angle ABC. PROP. XVII. THEOR. Any two angles of a triangle are together less than two right angles. Let ABO be any triangle ; any two of its angles together are less than two right angles. Produce BC to... | |
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Any two angles of a triangle are together less than two right angles. 
