| Henry Raper - 1870
...and bisecting AB, it would be proved that the angle ABG, or its equal CBD, is greater than A. 122. **Any two angles of a triangle are together less than two right angles.** Produce the side BC of the triangle ABC, to D. Then the exterior angle AC D of the triangle is greater... | |
| Henry William Watson - 1871 - 285 sider
...producing any one side of a triangle, is greater than either of the interior and non-adjacent angles, and **any two angles of a triangle are together less than two right angles.** p. , Let ABC be a triangle, and let the side BC be produced to D, then i st. The exterior angle ACD... | |
| Euclides - 1871
...perpendicular be drawn to the given line; the perpendicular will fall on the side of the acute angle. **Any two angles of a triangle are together less than two right angles.** , 3 c -D Let ABC be any A . Then must any two of its L s be together less than two rt. L», Produce... | |
| Henry William Watson - 1872 - 285 sider
...producing any one side of a triangle, is greater than either of the interior and non-adjacent angles, and **any two angles of a triangle are together less than two right angles. Let ABC be** a triangle, and let the side BC be produced to D, then 1 st. The exterior angle AC D shall be greater... | |
| Euclides, James Hamblin Smith - 1872 - 349 sider
...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 angles.** 3 CU Let ABC be any A . ' Then must any two of its is be together less than two rt, L s. Produce BC... | |
| Henry Major - 1873
...bisected, it may be demonstrated that the angle BOG, that is the angle ACD, is greater than ABC. XVII. — **Any two angles of a triangle are together less than...angles. Let ABC be any triangle; any two of its angles** are together less than two right angles. Produce BC to D ; and because ACD is the exterior angle of... | |
| 1874
...equal ACD), is greater than the angle ABC. Therefore, if one side, &c. QED Proposition 17. — Theorem. **Any two angles of a triangle are together less than two right angles. Let ABC be any triangle.** CONSTRUCTION. — Produce BC to D. PROOF. — Because ACD is the ex- A ^ ABC terior angle of the triangle... | |
| Euclides - 1874
...greater than the angle ABC. Therefore, if one side of a triangle, &c. QED PROPOSITION 17.— Theorem. **Any two angles of a triangle are together less than two right angles. Let ABC be any triangle.** Then any two of its angles together shall be less than two right angles. B c D Construction. Produce... | |
| Francis Cuthbertson - 1874 - 349 sider
...shewn, if AC be produced to G, that L BCG is > the L ABC. But /^CZ?is= LBCG; (1.6) Hence it follows that **Any two angles of a triangle are together less than two right angles. Let** ^.5C be a A. Then shall any two of its angles, as ABC »nd ACB, be together < two right angles. Produce... | |
| Euclides - 1874
...mentioned at the end of the proposition, and show that ACD is greater than ABCPROPOSITION 17. THEOREM. **Any two angles of a triangle are together less than two right angles.** i Let ABC be any triangle : any two of its angles ' • are together loss than two right angles. 0... | |
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