| Euclides - 1877
...difference of any two sides of a triangle is greater than the third side. PROPOSITION XVII. THEOREM. **Any two angles of a triangle are together less than two right angles. Let ABC be** a triangle ; then shall any two of its angles together be less than two right angles. Construction.... | |
| Scotland free church
...sides also which subtend, or are opposite to the equal angles, shall be equal to one another. Or—Any **two angles of a triangle are together less than two right angles.** 3. If a straight line be divided into any two parts, the square on the whole line is equal to the squares... | |
| Edward Atkins - 1877
...side, &c. QED Proposition 17.— Theorem. Any two angles of a triangle are together less than tworigJit **angles. Let ABC be any triangle. Any two of its angles together** shall be less than two right angles. CONSTRUCTION. — Produce BC to D. PROOF. — Because ACD is the... | |
| James Maurice Wilson - 1878
...perpendicular, OQ an oblique ; it is required to prove first that OP is less than OQ. Proof. Since **any two angles of a triangle are together less than two right angles;** (Th. 18.) therefore OPQ and OQP are together less than two right angles : but OPQ is a right angle... | |
| Thomas Hunter - 1878 - 132 sider
...BC and bisecting AB, it can be demonstrated that ABG, or its equal, DEC, is greater than CAB. Cor. **Any two angles of a triangle are together less than two right angles.** Because the exterior angle is greater than either of the interior and opposite angles; to this inequality... | |
| Euclides - 1879
...exterior angles of a triangle are together greater than two right angles. PROPOSITION XVII. THEOREM. **Any two angles of a triangle are together less than two right angles. Let ABC be** A. Then any two of its Z. s together shall be less than two rt. Z. s. ° CD Constr. Produce any side... | |
| Isaac Sharpless - 1879 - 266 sider
...greater than ABC. ANALYSIS. (By Const.), " BE= EF—f (I. 7), BA E= ECF Proposition 19. 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... | |
| Edward Harri Mathews - 1879
...contained by those sides equal to one another, they shall also have their bases or -third sides equal. 2. **Any two angles of a triangle are together less than two right angles.** 3. The opposite sides and angles of a parallelogram are equal to one another. 4. If two isosceles triangles... | |
| Rolla Rouse - 1879
...triangle be extended, the exterior angle is greater than either of the interior and opposed angles, 3 108 **Any two angles of a triangle are together less than two right angles,** 4 ... ... ... ... ... „ If one side of a triangle be greater than the second, the angle opposed to... | |
| Moffatt and Paige - 1879
...is necessary to stipulate that the given straight line must be of 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... | |
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