 | George Albert Wentworth - Geometry - 1877 - 416 pages
...whose sides are respectively the vertices of the given triangle. PROPOSITION XIII. THEOREM. 722. Any side of a spherical triangle is less than the sum of the other two sides. Let ABC be any spherical triangle. We are to prove BС < BA + AC. Join the vertices A, B and С with the centre... | |
 | George Albert Wentworth - Geometry - 1877 - 426 pages
...whose sides are respectively the vertices of the given triangle. PROPOSITION XIII. THEOREM. 722. Any side of a spherical triangle is less than the sum of the other two sides. Let ABС be any spherical triangle. We are to prove BС < BA + AС. Join the vertices A, B and С with... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...case the centres and the point of contact lie in one straight line. PROPOSITION III. THEOREM. . ' Any side of a spherical triangle is less than the sum of the oth' er two. Let ABC be a spherical triangle ; then .any side, as AC, is less than the sum -of the... | |
 | Cornell University - 1880 - 868 pages
...regular pyramid is equal to the product of the perimeter of its base by one half its slant height. 4. Any side of a spherical triangle is less than the sum of the other two sides. Any side of a spherical polygon is less than the sum of all the other sides. 5. The volume of a sphere... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...polygon, is called the corresponding polyedral angle of the spherical polygon. THEOREM III. 15. Any side of a spherical triangle is less than the sum of the other two. Let ABD be a spherical triangle ; then AB<^AD-\-DB. Let C be the corresponding triedral angle of the... | |
 | Elias Loomis - Conic sections - 1880 - 452 pages
...which case the centres and the point of contact lie in one straight line. PROPOSITION III. THEOREM. Any side of a spherical triangle is less than the sum of the other two. Let ABC be a spherical triangle ; then any side, as AC, is less than the sum of the other ** two, AB... | |
 | District of Columbia. Board of Education - Education - 1881 - 314 pages
...its outer extremity, is tangent to the sphere at that point. 4. Demonstrate Prop. 1, Book IX : Any side of a spherical triangle is less than the sum of the other two. ARITHMETIC. 1. What is the length of the longest curb-stones that will exactly fit each of four strips... | |
 | Webster Wells - 1883 - 298 pages
...elementary properties of spherical triangles may be found in any treatise on Solid Geometry : (a) . Any side of a spherical triangle is less than the sum of the other two. (6). If two sides of a spherical triangle are equal, the angles opposite them are equal ; and conversely.... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...will be respectively equal to the sum of two of the partial triangles minus the third. THEOREM XV. Any side of a spherical triangle is less than the sum of the other two, and greater than their difference. Let ABC be any spherical triangle on the sphere whose centre is... | |
 | Evan Wilhelm Evans - Geometry - 1884 - 170 pages
...Its planes cut the surface in arcs of great circles, which form a spherical triangle. Cor. 1.—Any side of a spherical triangle is less than the sum of the other two(?). 9. To find the surface of a material sphere. Suppose that the given sphere be of wood or iron. Let... | |
| |
Each side of a spherical triangle is less than the sum of the other two sides. Let ABC be a spherical triangle, AB the longest side. 
