| Euclides - 1862
...ACD, (r, 15) ls greater than the angle ABC. Therefore, if one side, &c. QED PROP. XVII. — THEOREM. **Any two angles of a triangle are together less than two right angles** (References — Prop. i. 13, 16; ax. 4.) Let ABC be any triangle. Then any two of its angles shall... | |
| Euclides - 1862
...that the angle BCG (or Us equal ACD), is greater than the angle ABC. PROPOSITION 17.— THEOREM. A ny **two angles of a triangle are together less than two right angles.** (References— Prop. I. 13, 16; ax. 4.) Hypothesis. — Let ABC be any triangle. Sequence. — Any... | |
| Euclides - 1863
...Therefore if one side of a triangle be produced, &e. QED Pitop. 17. — THEOE. (converse of Ax. 12.) **Any two angles of a triangle are together less than two right angles.** Con.— Pst. 2, DEJI.— P. 10, Ax. 4, P. 18. Let ABC be a triangle ; then any two /.s in it, as A... | |
| University of Oxford - 1863
...line perpendicular to a given straight line of an unlimited length, from a given point without it. 3. **Any two angles of a triangle are together less than, two right angles.** 4. At a given point in a given straight line make a rectilineal angle equal to a given rectilineal... | |
| Euclides - 1864
...greater than the angle ABC. Therefore, if one side of a triangle, &c. QED PROPOSITION XVII. 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. Produce any side BC to D.... | |
| Euclides - 1864
...greater than the angle ABC. Therefore, if one side of a triangle, &c. QED PROPOSITION XVII. 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. Produce any side BC to D.... | |
| Euclides - 1865
...demonstrated that the angle BCG, that is (7) the angle ACD, is greater than the angle ABC. PROPOSITION XVH. **THEOR. Any two angles of a triangle are together less...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... | |
| Euclides - 1865
...prodnced, the exterior angle is greater than either of the interior opposite angles . . .1. 16. 7. **Any two angles of a triangle are together less than two right angles** . . . . . . . . . I. 17. 8. If a side of any triangle be prodnced, the exterior angle is equal to the... | |
| William Harris JOHNSTON - 1865
...right angle ¡ it cannot have more than one, as it is proved in Euclid, Book I., Prop. 17, that « **Any two angles of a triangle are together less than two right angles.** An obtuse-angled triangle has one of its angles an obtuse angle. An acute-angled triangle has all its... | |
| Euclid, Isaac Todhunter - 1867 - 400 sider
...ACD, is greater than the angle ABC. [I. 15. Wherefore, if one side &c. QED PROPOSITION 17. THEOREM. **Any two angles of a triangle are together less than two right angles. Let ABC be** a triangle : any two of its angles are together less than two right angles. Produce BC to D. Then because... | |
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