| Euclides - 1853
...The angle ACD 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...its angles together are less than two right angles.** A Produce BC to D; and because ACD is the exterior angle of the triangle ABC, (1. 16.) 1. ACD is greater... | |
| Euclides - 1853 - 147 sider
...d, is greater than the angle ab С. Therefore, if one side, &c. QED PROPOSITION XVII. — THEOREM. **Any two angles of a triangle are together less than two right angles. LET** ab С be any triangle ; any two of its angles together are less than two right angles. Produce b С... | |
| William Somerville Orr - 1854
...actually drawn. In the next place, from the property demonstrated in Proposition XVII., namely, that **any two angles of a triangle are together less than two right angles,** he knows— what he could not know at an earlier stage of his progress — an important particular... | |
| Euclides - 1855
...From a point without a straight line, only one perpendicular can be drawn to it. PROP. XVII. THEOREM. **Any two angles of a triangle are together less than two right angles. Let** ABС be any triangle ; any two of its angles are together less than two right angles. Produce B С... | |
| W. Davis Haskoll - 1858 - 324 sider
...two straight lines cut one another, the vertical or opposite angles shall be equal. The 17th, Book I. **Any two angles of a triangle are together less than two right angles.** The 18th, Book I. The greater side of every triangle is opposite to the greater angle. The 32nd, Book... | |
| Euclides - 1858
...reducing them to rectangular figures, these and similar conclusions are of great PROP. 17.— TMEOR. **Any two angles of a triangle are together less than two right angles.** CONSTRUCTION. — Pst. 2. A st. line may be produced to any length in a st. line. DEMONSTRATION. —... | |
| 1858
...truths — its general principles — unchangeable and unchanged. When we enunciate the proposition that **any two angles of a triangle are together less than two right angles,** we enunciate an absolute truth in mathematics. When we enunciate the proposition that heat is always... | |
| Robert Potts - 1860 - 361 sider
...greater than the angle ABC. Therefore, if one side of a triangle, &c. QED PKOPOSITION 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 - 1860
...therefore the exterior angle ACD is greater than either the angle CAB or ABC. PHOPOSmON XVII. THEOREM. **Any two angles of a triangle are together less than two right angles.** Given any triangle ABC ; to prove that any two of its angles together are less than two right angles.... | |
| 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... | |
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