| 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... | |
| Stewart W. and co - 1884
...angle BCG is greater than ABC. PROP. XVII., BOOK I.— With a paper triangle show practically that **any two angles of a triangle are together less than two right angles.** PROP. XXII., BOOK I. — Why cannot a triangle be described of which the sides shall be respectively... | |
| 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... | |
| John Veitch - 1885 - 551 sider
...thereafter speak of the propositions expressing truths regarding them as embodying their properties — eg, **any two angles of a triangle are together less than two right angles.** 1 Hoblyn's Briti*h Plants, p. 7. Given our conception of a particular metal, we may add on, by observation... | |
| Richard Anthony Proctor - 1887 - 180 sider
...respects, or else the angles B and C together make up two right angles. But the angles B and C, being **two angles of a triangle, are together less than two right angles.** Hence the triangles ABD, ACD are equal in all respects. Therefore AB is equal to A C. PROP. XII. —... | |
| H. Freeman Wood - 1888 - 398 sider
...be produced, the exterior angle shall be greater than either of the interior opposite angles; that **any two angles of a triangle are together less than two right angles;** and that the greater angle of every triangle is subtended by the greater side. He had been interrupted... | |
| George William Usill - 1889 - 272 sider
...the exterior angle, A c D, is greater than either of the interior opposite angles, CAB and ABC. 8. **Any two angles of a triangle are together less than two right angles.** 9. If one side of a triangle, A c, be greater than a second, AB, the angle, ABC, opposite the first... | |
| Edward Mann Langley, W. Seys Phillips - 1890 - 515 sider
...equal. Ex. 21. — The three medians of an equilateral triangle are equal. PROPOSITION 17. THEOREM. **Any two angles of a triangle are together less than two right angles. Let ABC be** a A, any two of its ^s are together less than two rt. L s. Produce BC to D. Then ext. L ACD > int.... | |
| Euclid - 1890 - 400 sider
...by producing CB to F, it could be shown that ABF (which = CBD) > BAG. i Proposition 17. THEOREM — **Any two angles of a triangle are together less than two right angles.** This proposition is omitted because it is — i°, included in i. 32 : 2°, not referred to in anything... | |
| James Andrew Blaikie, William Thomson - 1891
...the exterior angle thus formed shall be greater than either of the two interior opposite angles. 17. **Any two angles of a triangle are together less than two right angles.** 18. If one side of a triangle be greater than another side, the angle opposite to the greater side... | |
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