 | 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...AC, is less than the sum of the other ** two, AB and BC. Let D be the centre of the sphere, and draw the radii AD, BD, CD. Conceive the planes ADB,BDC,... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...spherical 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 triangle... | |
 | 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... | |
 | District of Columbia. Board of Education - Education - 1881 - 314 pages
...sphere at 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... | |
 | William Chauvenet - Geometry - 1884 - 384 pages
...the angles B' and C' are equal (78). But since the angles B' and C" are equal in the triangle A'B'C', the sides AB and AC are equal in its polar triangle...side of a spherical triangle is less than the sum of tht other two. Let ABC be a spherical triangle; then, any side, as AC, is less than the sum of the... | |
 | Evan Wilhelm Evans - Geometry - 1884 - 242 pages
...sphere. 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 (?). Cor. 2. — The perimeter of a spherical triangle is less than a great circle (?). 9. To find... | |
 | 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... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...great circle joining the vertices of any two angles which are not consecutive. PROPOSITION I. THEOREM. side of a spherical triangle is less than the sum of the two others. Let ABC be a spherical triangle situated on a sphere whose centre is O: then is any side,... | |
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Any side of a spherical triangle is less than the sum of the other two. 
