| 1836
...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... | |
| 1836 - 472 sider
...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... | |
| George Darley - 1836 - 128 sider
...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... | |
| John Playfair - 1837 - 318 sider
...demonstrated that the angle BUG, 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...exterior angle of the triangle ABC, ACD is greater** (16. 1.) than the interior and opposite angle ABC ; to each of these add the angle ACB; therefore the... | |
| Andrew Bell - 1837 - 240 sider
...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...exterior angle of the triangle ABC, ACD is greater** than the interior and opposite angle ABC (1. 16) ; to each of these add the angle ACB ; therefore the... | |
| Euclid, James Thomson - 1837 - 390 sider
...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 together...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 - 1837 - 215 sider
...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 - 1837 - 88 sider
...= 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, Robert Simson - 1838 - 416 sider
...(15. 1.) the angle ACD, is greater than the angle ABC. Therefore, if one side, &c. QED B PROP. XVII. **THEOR. ANY two angles of a triangle are together less...exterior angle of the triangle ABC, ACD is greater** (16. 1.) than the interior and opposite angle ABC ; to each of these add the angle ACB; therefore the... | |
| Euclides - 1838
...„16 , thatis,theangle*ACD,isgreaterthantheangleABC. Therefore, if one side, &c. u. ED PROP. XVII. **THEOR. Any two angles of a triangle are together less...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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