 | William Betz - 1916 - 536 páginas
...§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... | |
 | Ernst Rudolph Breslich - 1917 - 408 páginas
...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... | |
 | Eugene Randolph Smith, William Henry Metzler - 1918 - 232 páginas
...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,... | |
 | Mabel Sykes, Clarence Elmer Comstock - 1918 - 576 páginas
...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... | |
 | Arthur Schultze, Frank Louis Sevenoak - 1918 - 486 páginas
...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... | |
 | Charles Austin Hobbs - 1921 - 216 páginas
...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.... | |
 | Mabel Sykes, Clarence Elmer Comstock - 1922 - 236 páginas
...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... | |
 | Walter Burton Ford, Charles Ammermann - 1923 - 406 páginas
...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 +... | |
 | Arthur Schultze, Frank Louis Sevenoak - 1913 - 484 páginas
...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.... | |
 | David Raymond Curtiss, Elton James Moulton - 1927 - 426 páginas
...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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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. 
