 | 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... | |
 | Euclid, Isaac Todhunter - 1867 - 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... | |
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ANY two angles of a triangle are together less than two right angles. 
