 | John Playfair - Euclid's Elements - 1836 - 488 pages
...the same manner, if the side BC be bisected, it may be demonstrated that the angle BCG, that is1', the angle ACD, is greater than the angle ABC. Therefore,...triangle are together less than two right angles. Book I. Let ABC be any triangle ; any two of its angles together are less than two right angles. Produce... | |
 | 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... | |
 | George Darley - Euclid's Elements - 1836 - 172 pages
...together. Hence the angles BCA, ABC, BAC together are equal to -^ \* v two right angles. This, &c. ART. 38. Any two angles of a triangle are together less than two right angles ; and if any angle of a triangle be obtuse or right, the other two are acute ; also, if two angles... | |
 | Mathematics - 1836 - 488 pages
...be produced, the exterior angle is greater than either of the interior, and opposite angles. XVII. Any two angles of a triangle are together less than two right angles. XVIII. The greater side of every triangle has the greater angle opposite to it. XIX. The greater angle... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...angle would be greater than the interior and remote right angle, which (I. def. 10.) is impossible. PROP. XVII. THEOR.* ANY two angles of a triangle are...angles. Let ABC be any triangle ; any two of its angles are together less than two right angles. ing the equality of CEB and AED, either AEC or BED may be... | |
 | 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 - Euclid's Elements - 1837 - 112 pages
...= 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... | |
 | Euclides - 1838 - 264 pages
...angle BCG, „16 , thatis,theangle*ACD,isgreaterthantheangleABC. Therefore, if one side, &c. u. ED PROP. XVII. THEOR. Any two angles of a triangle are...ABC be any triangle ; any two of its angles together shall be less than two right angles. Produce BC to D ; and because ACD is the exterior angle of the... | |
 | Euclides - 1840 - 82 pages
...of a triangle is 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
...be bisected, and AC be produced to 6, it may be demonstrated that the angle BCG, that is,* * 15. ' the angle ACD, is greater than the angle ABC. Therefore,...ABC be any triangle; any two of its angles together shall be less than two right angles. Produce BC to D; and because ACD is the exterior angle of the... | |
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ANY two angles of a triangle are together less than two right angles. 
