 | Euclides - 1865 - 80 pages
...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 than two right angles. Let ABC be any triangle, any two of its angles are together less than two right angles. Produce BC to D, and because... | |
 | Robert Potts - 1865 - 528 pages
...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... | |
 | William Harris Johnston - 1865 - 478 pages
...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... | |
 | Euclides - 1865 - 402 pages
...(L 15) is 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... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...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...Produce BC to D. Then because A CD is the exterior angle of the triangle ABC, it is greater than the interior opposite angle ABC. [I.16. To each of these add... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...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... | |
 | Robert Potts - 1868 - 434 pages
...greater than the angle ABC. Therefore, if one side of a triangle, &e. 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. A Produce any... | |
 | Henry Raper - 1870 - 968 pages
...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... | |
 | Euclides - 1871 - 136 pages
...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 - Geometry - 1871 - 320 pages
...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... | |
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Any two angles of a triangle are together less than two right angles. 
