 | John Gale Hun, Charles Ranald MacInnes - Trigonometry - 1911 - 234 pages
...angle A is greater than 180° if the side opposite to it, BDC, is greater than 180°, and conversely. The sum of any two sides of a spherical triangle is greater than the third side. This follows from the corresponding theorem concerning the face angles of a convex triedral angle.... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Solid - 1911 - 208 pages
...+ BD, (3) ED < BD, (4) Z ECD < Z BCD. Hence, Z 4CD < Z ^CB + Z BCD. j 228. COROLLARY 1. The sum of two sides of a spherical triangle is greater than the third side. 229. COROLLARY 2. The sum of the three sides of a spherical triangle is less than a great circle. Proof:... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry - 1912 - 504 pages
...corresponding known properties of the polyhedral angle, as in §§ 941 and 942. PROPOSITION IX. THEOREM 941. The sum of any two sides of a spherical triangle is greater than the third side. Given spherical A ABC. To prove AB + BC> CA. ARGUMENT 1. Z AOB + Z BOC > Z COA. 2. Z AOB oc AB, Z BOC*... | |
 | Clara Avis Hart, Daniel D. Feldman, Virgil Snyder - Geometry, Solid - 1912 - 230 pages
...corresponding known properties of the polyhedral angle, as in §§ 941 and 942. PROPOSITION IX. THEOREM 941. The sum of any two sides of a spherical triangle is greater than the third side. Given spherical A ABC. To prove AB + BC > CA. ARGUMENT 1. Z AOB + Z BOC > Z COA. 2. Z. AOB oc AB, Z... | |
 | William Herschel Bruce, Claude Carr Cody - Geometry, Solid - 1912 - 134 pages
...in position such that each is the vertical of the other. PROPOSITION VIII. THEOREM. 761. The sum of two sides of a spherical triangle is greater than the third side. Given the spherical A ABC. To prove AB + BC > AC. Proof. Draw radii OA, OB, and 0(7. Then in the trihedral... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 376 pages
...terminated by the sides. See §§ 358, 359. 298 VIII, §363] TRIANGLES AND POLYGONS 362. Theorem V. The sum of any two sides of a spherical triangle is greater than the third side. [Compare § 272.] FIG. 244 Given the spherical A ABC. To prove that AB + BC > CA. Proof. Z AOB + Z... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Solid - 1913 - 176 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 § 272.] Fio. 244 Given the spherical A ABC. To prove that AB + BC > CA. Proof. Z AOB + Z... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 490 pages
...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 OC. Then Z AOB... | |
 | Sophia Foster Richardson - Geometry, Solid - 1914 - 236 pages
...70°. 3. a = 100°, ft = 75°, c = 84°. 4. A = 80°, B = 100°, C = 110°. 397. THEOREM. The sum of two sides of a spherical triangle is greater than the third side. Given the spherical triangle ABC on a sphere whose center is O To prove AB+BC> AC. Proof. 1. In the... | |
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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. 
