 | Elias Loomis - Conic sections - 1858 - 256 pages
...AC, the other two sides of the triangle. Produce BD until it meets the side AC BC in E ; and, because one side of a triangle is less than the sum of the other two (Prop. VIII.). the side CD of the triangle CDE is less than the sum of CE and ED. To each of these... | |
 | Elias Loomis - Conic sections - 1861 - 254 pages
...each, and the angle A to the angle D. Therefore, if two triangles, dsc. PROPOSITION VIII. THEOREM. Any side of a triangle is less than the sum of the other two For the straight line AB is the shortest path between the points A and B (Def. 3) ; hence AB is less... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...61. Cor. Therefore every equiangular triangle is equilateral. PROPOSITION IX. — THEOREM. 62. Any side of a triangle is less than the sum of the other two. In the triangle ABC, any one side, as AB, is less than the sum of the other two sides, AC and C B.... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...61. Cor. Therefore every equiangular triangle is equilateral. PROPOSITION IX. — THEOREM. 62. Any side of a triangle is less than the sum of the other two. In the triangle ABC, any one side, C as AB,is less than the sum of the other two sides, AC and C B.... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...61. Cor. Therefore every equiangular triangle is equilateral. PROPOSITION IX. — THEOREM. 62. Any side of a triangle is less than the sum of the other two. In the triangle ABC, any one side, as AB,is less than the sum of the other two sides, AC and C B. For... | |
 | Edward Brooks - Geometry - 1868 - 284 pages
...straight line can be drawn parallel to a given line. Corollary. Prom axiom 10, it is evident that either side of a triangle is less than the sum of the other two sides. POSTULATES. 32. The following postulates are self-evident problems resulting from the preceding definitions:—... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...61. Cor. Therefore every equiangular triangle is equilateral. PROPOSITION IX. — THEOREM. 62. Any side of a triangle is less than the sum of the other two. In the triangle ABC, any one side, as AB, is less than the sum of the other two sides, AC and C B.... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...AC, the other two sides of the triangle. Produce BD until it meets the side AC BC in E ; and, because one side of a triangle is less than the sum of the other two (Prop. VIII.), the side CD of the triangle CDE is less than the sum of CE and ED. To each of these... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...vertex upon the base is then called the altitude of the triangle. PROPOSITION XVII.— THEOREM. 66. Any side of a triangle is less than the sum of the other two. Let BC be any side of a triangle whose other two sides are AB and AC; then BC < AB + AC. For, the straight... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...of the other sides. The figure will suggest the demonstration, which is based on the fact that any side of a triangle is less than the sum of the other two. Fio. 923. TJieo. — The difference between the distances from two points on opposite sides of a fixed... | |
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Any side of a triangle is less than the sum of the other two sides... 
