| Edward Atkins - 1877 - 72 pages
...right angles, provided that no one of the angles be included in any other angle. Proposition 16.— **Theorem. If one side of a triangle be produced, the exterior angle** shall lie greater than either of the interior opposite angles. Let ABC be a triangle, and let its side... | |
| Euclides - 1878 - 398 pages
...shew hereafter, p. 149, how this definition may be extended, so as to embrace angles greater than two **right angles. PROPOSITION XVI. THEOREM. If one side...greater than either of the interior opposite angles.** D Let the side BC of AA fiC be produced to D. Then must L ACD be greater than either L CAB or L ABC.... | |
| William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...angles is equal to R. COR. 5. In an equiangular triangle, each angle is equal to ^ of 2R = | R. XVIII. **Theorem. If one side of a triangle be produced, the exterior angle is** equal to the two interior angles not adjacent. HYPOTH. In the triangle ABC, one side, AB, is produced,... | |
| Thomas Hunter - Geometry, Plane - 1878 - 142 pages
...angles AFB and DAF are equal, the lines DE and BC are parallel (Prop. XXV.). PROPOSITION XXX.—THEOREM. **If one side of a triangle be produced, the exterior angle is** equal to the sum of the two interior and opposite angles, and the three angles of the triangle are... | |
| James Hamblin Smith - Euclid's Elements - 1879 - 378 pages
...line, and QP a line which revolves about the fixed point Q, and which at first coincides with QE. 7F **PROPOSITION XVI. THEOREM. If one side of a triangle...greater than either of the interior opposite angles.** -JSS Let the side BC of AA JRC be produced to D. Then must L ACD be greater than either i CAB or L... | |
| W J. Dickinson - Geometry - 1879 - 44 pages
...in all respects. Same proposition. Give corollaries. • Propositions XVI. -XXVI. (inclusive). 16. **If one side of a triangle be produced, the exterior...greater than either of the interior opposite angles.** • Same proposition. Show that only one perpendicular can be drawn from a given point to a given straight... | |
| Isaac Sharpless - Geometry - 1879 - 282 pages
...angles made by any number of lines meeting in a point, are equal to four right angles. Proposition 18. **Theorem. — If one side of a triangle be produced, the exterior angle is greater than either of the** opposite interior angles. Let the side BC of the triangle ABC be produced to D; then will A CD be greater... | |
| Moffatt and Paige - 1879 - 428 pages
...unlimited length. (5) Prove that any two angles of a triangle are together less than two right angles. (6) **If one side of a triangle be produced, the exterior angle is greater than either of the interior** and opposite angles. Show that only one perpendicular can be drawn from a given point to a given straight... | |
| Edward Harri Mathews - 1879 - 94 pages
...CAREFULLY SELECTED FROM THE Cambridge Mathematical Tripos Examination Papers (1867-77). Jan. 1867. 1. **If one side of a triangle be produced, the exterior angle is greater than either of the** two interior opposite angles. Any two exterior angles of a triangle are together greater than two right... | |
| Euclides - 1879 - 146 pages
...same side of a given line, draw two lines which shall meet in that line and make equal angles with it. **PROPOSITION XVI. THEOREM. If one side of a triangle be produced, the exterior angle** shall be greater than either of the interior opposite angles. Let ABC be A, and let any side BC be... | |
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