| Euclides - 1855 - 262 pages
...Exercise- — 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 - 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. —... | |
| Law - 1858 - 640 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... | |
| Robert Potts - Geometry, Plane - 1860 - 380 pages
...ACD, (l. 15.) is 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... | |
| Euclides - 1860 - 288 pages
...angle ABC ; 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
...that Is, the angle 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... | |
| University of Oxford - Education, Higher - 1863 - 328 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 - 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... | |
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