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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. "
A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ... - Page 363
by John Bonnycastle - 1806 - 419 pages
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Plane and Solid Geometry

William Betz - Geometry - 1916 - 536 pages
...§232 5. Adding the equal angles A OB and A OD, or Z.AOB + Z.BOC>Z.AOC. 828. COROLLARY. The sum of two sides of a spherical triangle is greater than the third side. SPHERICAL POLYGONS PROPOSITION XIV. THEOREM 829. The sum of the face angles of any convex polyhedral...
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Third-year Mathematics for Secondary Schools

Ernst Rudolph Breslich - Logarithms - 1917 - 408 pages
...properties of spherical polygons may be inferred from a study of polyedrul angles. 3. Show that the sum of two sides of a spherical triangle is greater than the third side, Fig. 206. 4. The shortest line that can be drawn between two given points on the surface of a sphere...
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Solid Geometry Developed by the Syllabus Method

Eugene Randolph Smith, William Henry Metzler - Geometry, Solid - 1918 - 232 pages
...IV. (a) The sum of any two face angles of a trihedral angle is greater than the third face angle. (i) The sum of any two sides of a spherical triangle is greater than the third side. FIRST PROOF : Let the trihedral angle be V-ABC. Pass a plane through CV perpendicular to plane AVB,...
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Plane Geometry

Mabel Sykes, Clarence Elmer Comstock - Geometry, Modern - 1918 - 576 pages
...is a restatement of what theorem? SOME PROPERTIES OF SPHERICAL TRIANGLES 111. THEOREM 75. The sum of two sides of a spherical triangle is greater than the third side. Some theorems concerning spherical polygons bear a certain peculiar relation to the corresponding theorems...
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...tetrahedral angle are equal, the opposite dihedral angles are equal. PROPOSITION X. THEOREM 739. The sum of two sides of a spherical triangle is greater than the third side. Given ABC, a spherical triangle. To prove AB + BC > AC. Proof. Draw radii OA, OB, and 0c. Then Z AOB...
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Solid Geometry

Charles Austin Hobbs - Geometry, Solid - 1921 - 216 pages
...pyramids are said to be symmetrical when their bases are symmetrical polygons. Proposition 322 Theorem The sum of any two sides of a spherical triangle is greater than the third side. Hypothesis. ABC is a spherical A on the sphere whose centre is 0, and AC is the longest side. Conclusion....
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Solid Geometry

Mabel Sykes, Clarence Elmer Comstock - Geometry, Solid - 1922 - 236 pages
...is a restatement of what theorem? SOME PROPERTIES OF SPHERICAL TRIANGLES 111. THEOREM 75. The sum of two sides of a spherical triangle is greater than the third side. FIG. 109 Some theorems concerning spherical polygons bear, a certain peculiar relation to the corresponding...
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Plane Geometry

Walter Burton Ford, Charles Ammermann - Geometry, Modern - 1923 - 406 pages
...corresponding face angles and dihedral angles of the corresponding central polyhedral angle. 362. Theorem V. The sum of any two sides of a spherical triangle is greater than the third side. [Compare § 269.) Fio. 259 Given the spherical A ABC. To prove that AB + BC > CA. 1. Proof. Z AOB +...
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...tetrahedral angle are equal, the opposite dihedral angles are equal. PROPOSITION X. THEOREM 739. The sum of two sides of a spherical triangle is greater than the third side. THE SPHERE Given ABC, a spherical triangle. To prove AB + B~C > AC. Proof. Draw radii OA, OB, and OC....
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Trigonometry, Plane and Spherical

David Raymond Curtiss, Elton James Moulton - Trigonometry - 1927 - 426 pages
...solid geometry two theorems that are true for all spherical triangles, whether right-angled or not: 1. The sum of any two sides of a spherical triangle is greater than the third side. 2. If two angles of a spherical triangle are equal, the opposite sides are equal, and conversely. If...
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