| 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... | |
| John Playfair - 1832 - 333 sider
...the angle ACD, is greater than the angle ABC. Therefore if one side, &c. QED PROP. XVII. THEOR. Jlny **two angles of a triangle are together less than two...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 - 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... | |
| John Playfair - 1835 - 316 sider
...that the angle BCG, that is (8. 1.) the angle ACD, is greater than the angle ABC. PROP. X. THEOR. Aw) **two angles of a triangle are together less than two...Produce BC to D ; and because ACD is the exterior** ano-le of the triangle ABC, ACD is greater (9. 1.) than the interior and opposite angle ABC ; to each... | |
| Euclid - 1835 - 513 sider
...d 15. 1. greater than the angle ABC. Therefore, " if one side" &c. QED PROP. XVII. THEOR. Any tico **angles of a triangle are together less than two right...right angles. Produce BC to D ; and because ACD is the** exteriorangle of the triangle ABC, ACD is greater3 than the interior and , opposite angle ABC; to each... | |
| 1835
...Therefore, Sic. Cor. The two triangles are equal in every respect. (4. & 4 Cor.) PROP. 8. (Eue. i. 17.) **Any two angles of a triangle are together less than two right angles. Let** А В С be any triangle : any two of its angles, ABC and ACB, shall be together less than two right... | |
| John Playfair - 1836 - 471 sider
...that is1', 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.** Book I. Let ABC be any triangle ; any two of its angles together are less than two right angles. Produce... | |
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