| John Playfair - 1819 - 333 sider
...&c. Q, ED PROP. XVII. THEOR. Jlny too angles of a triangle are together less than two right angle's. **Let ABC be any triangle ; any two of its angles together are less than two right angles. Produce** BC'to D ; and because ACD is the exterior angle of the triangle ABC, ACD is greater (16. 1.) than the... | |
| John Playfair - 1819 - 317 sider
...BCG, that is (15. 1.), the angle ACD, is greater than the angle ABC. Therefore, if one side, &c. Q, ED **PROP. XVII. THEOR. - Any two angles of a triangle are together less than' two right** angle*. Let A BC be any triangle ; any two of its angles together are less than two right angles. Produce... | |
| 1854
...proved hereafter, it is here inserted in order to facilitate the theory of parallel lines. Cor. 2. **Any two angles of a triangle are together less than two right angles.** For either is less than the supplement of the other. Cor. 3. If any angle of a triangle is right or... | |
| Euclid, John Playfair - 1826 - 320 sider
...if one Bide, <SeQED 4 PROP. XVII. t HEOR. Any two angles of a triangle are together less than twfl **right angles. Let ABC be any triangle; any two of...its angles together are less than two right angles.** Produee BC to D ; and beeause ACD is the exterior angle of the triangle ABC, ACD, is greater (16. 1.)... | |
| George Lees - 1826
...that the angle BCG, that is, ACD% is e 5. 1. greater than ABC. Therefore, if one side, &c. QED Cor. **Any two angles of a triangle, are together less than two right angles.** For, since by the proposition, the exterior angle ACD is greater than the interior and opposite angle... | |
| Pierce Morton - 1830 - 272 sider
...the one equal to the three sides of the other, each to each, are equul in all respects . . 7 (•7) **Any two angles of a triangle are together less than two right angles** 7 (A} A triangle cannot have more than one right angle, or more than one obtuse angle . . nor. 7 (i)... | |
| Augustus De Morgan - 1831
...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... | |
| Euclides - 1833
...line. For then an external angle would be = to an internal and opposite, which is absurd. PROP. 17, **THEOR. Any two angles of a triangle are together less than two right angles.** Produce any side ; then the external angle is greater than either of the internal remote angles ; but... | |
| Thomas Perronet Thompson - 1833 - 150 sider
...And by parity of reasoning, the like may be proved in every other triangle. Wherefore, universally, **any two angles of a triangle are together less than two right angles.** Which was to be demonstrated. COH. 1. A triangle cannot have more than one right angle; nor more than... | |
| Euclides - 1834
...side, &e. OED PROPOSITION XVII. THEOR. — Any two angles of a triangle are together lest than Iwo **right angles. Let 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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