| Law - 1858 - 642 pages
...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... | |
| W. Davis Haskoll - Civil engineering - 1858 - 422 pages
...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 - 248 pages
...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. —... | |
| Robert Potts - Geometry, Plane - 1860 - 380 pages
...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 - 288 pages
...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 - 172 pages
...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... | |
| Euclides - 1862 - 140 pages
...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 - 74 pages
...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 - Education, Higher - 1863 - 316 pages
...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 - 262 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 side BC to D.... | |
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