 | Nathan Scholfield - 1845 - 894 pages
...— cos. *' is always positive. Again, if a', V, c', be the three sides of the polar triangle, since the sum of any two sides of a spherical triangle is greater than the third side : V + c' > a' 138 .-. cos. (s' — A) is always positive, and in like manner, cos. (s1 — B), cos.... | |
 | Nathan Scholfield - Conic sections - 1845 - 244 pages
...— cos. «' is always positive. Again, if a', V, c', be the three sides of the polar triangle, since the sum of any two sides of a spherical triangle is greater than the third side : 6' + c' > a' a tan. - ^ / — cos. s' cos. (s' — A) ^ cos. (s'— B)cos. (s'— C) b tan. ¥ =... | |
 | Sir Henry Edward Landor Thuillier - Surveying - 1851 - 826 pages
...greater angle, and the less side to the less angle. 6. The sum of any two sides is greater than the third and the difference of any two sides is less than the third. 7. The triangle, is equilateral, isoscelar, or scalene according as it has its three angles all equal,... | |
 | Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...s' is always positive. Again, if af, b', c' be the three sides of the polar triangle, then, because the sum of any two sides of a spherical triangle is greater than the other side, b'+c'>a'; ... 180°— B+180°— C>180°— A; hence B+C— A<180°, and . ^(B+C— A)<90°;... | |
 | Eli Todd Tappan - Geometry - 1868 - 432 pages
...applying the principle of Art. 878 to triedrals. 3. Show, from the third of Napier's Analogies, that the sum of any two sides of a spherical triangle is greater than the third. EIGHT ANGLED SPHEKICAL TRIANGLES. 888. The foregoing formulas may be applied to right angled triangles... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...applied to spherical triangles in the same manner as to plane triangles. PROPOSITION XI. 569. Theorem.— The sum of any two sides of a spherical triangle is greater than the third side, and their difference is less than the third side. DEM.— Let ABC be any spherical triangle; then l3 BO'... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...spherical triangles in the same manner as to plane triangles. PROPOSITION XI. 56.9. Theorem.— Tlie sum of any two sides of a spherical triangle is greater than the third side, and their difference is less than the third side. DEM.— Let ABC be any spherical triangle; then is BC... | |
 | Edward Olney - Geometry - 1877 - 272 pages
...to spherical triangles in the same manner as to plane triangles. PROPOSITION XL 369. Theorem.—The sum of any two sides of a spherical triangle is greater than the third side, and their difference is less than the third side. DEM.—Let ABC be any spherical triangle; then is BC... | |
 | Simon Newcomb - Geometry - 1881 - 418 pages
...a spherical triangle the greater side and the greater angle are opposite each other (§ 656). 783. The sum of any two sides of a spherical triangle is greater than the third side (§ 659). 784. Two spherical triangles are equal when their sides are equal and similarly arranged... | |
 | Edward Olney - Geometry - 1882 - 262 pages
...to spherical triangles in the same manner as to plane triangles. PROPOSITION XI. 569. Theorem. — The sum of any two sides of a spherical triangle is greater than the third side, and their difference is less than Ihe third side. DEM.— Let ABC be any spherical triang'e; then is BC... | |
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The sum of any two sides of a spherical triangle is greater than the third side, and their difference is less than the third side. 
