| EUCLID. - 1883 - 96 sider
...on the base must fall without the triangle, towards the side on which is the obtuse angle. PROP. 17. **THEOR. Any two angles of a triangle are together less than two right angles.** Given A ABC. To prove any two of its angles, as LB + L ACB, < 2 Lr-s. Produce BC to D. •: L ACD >... | |
| J. McD. Scott - 1883 - 94 sider
...shall, if produced, meet upon that side. This, it will be seen, is the converse of the proposition, that **any two angles of a triangle are together, *less than two right angles.** Neither postulate nor axiom is needed but once ; namely, to prove that lines which are parallel to... | |
| Mathematical association - 1883
...is produced, the exterior angle is greater than either of the interior opposite angles. THEOR. 10. **Any two angles of a triangle are together less than two right angles.** COR. 1. If a triangle has one right angle or obtuse angle, its remaining angles are acute. COR. 2.... | |
| Euclid, Isaac Todhunter - 1883 - 400 sider
...or theorem; as for example, To describe an equilateral triangle on a given finite straight line, or **Any two angles of a triangle are together less than two right angles.** After the general enunciation follows the discussion of the proposition. First, the enunciation is... | |
| James Hamblin Smith - 1883
...given line ; the perpendicular will fall on the side of the acute angle. PROPOSITION XVII. THEOREM. **Any two angles of a triangle are together less than two right** angleg. c jo Let ABC be any A . Then must any two of its L s be together less than two rt. L s. Produce... | |
| Mathematical association - 1884
...of the angles of the triangle FBC is equal to the sum of the angles of the triangle ABC. TIIKOR. 10. **Any two angles of a triangle are together less than two right angles. Let ABC be** a triangle : then shall any two of its angles be together less than two right angles. Produce BC to... | |
| Association for the improvement of geometrical teaching - 1884
...of the angles of the triangle FBC is equal to the sum of the angles of the triangle ABC. THROB. 10. **Any two angles of a triangle are together less than two right angles. Let ABC be** a triangle : then shall any two of its angles be together less than two right angles. Produce BC to... | |
| Euclides - 1884
...SHEETS. PROPOSITIONS 1—26, BOOK I, ARE NOW PUBLISHED IN A SIMILAR FORM TO THIS. PEOPOSITION XVII. **Any two angles of a triangle are together less than two right angles. Let** be any triangle. Then any two of its angles together shall be less than two right angles. Produce any... | |
| Euclides - 1884
...by those sides equal to one another, they shall also have their bases or third sides equal. (8) 8. **Any two angles of a triangle are together less than two right angles.** (8) 9. The opposite sides and angles of a parallelogram are equal to one another. (9) 10. If two isosceles... | |
| Euclides - 1884
...the equal sides are opposite. Axiom 9. The whole is greater than its part. PROPOSITION XVII. THEOEEM. **Any two angles of a triangle are together less than two right angles.** GIVEN the triangle ABC ; IT is REQUIRED TO PROVE that any tioo of its angles are together less than... | |
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