| Eugene Randolph Smith - Geometry, Plane - 1909 - 192 pages
...opposite sides are equal. (Use the polar triangles.) State this for a trihedral angle. 277. Theorem XVI. **The sum of the angles of a spherical triangle is greater than** one, and less than three, straight angles. Let the angles be A, B, C, the opposite sides be a, 6, c,... | |
| Levi Leonard Conant - Trigonometry - 1909 - 316 pages
...equal sides are opposite equal angles. III. Any angle of a spherical triangle is less than 180°. IV. **The sum of the angles of a spherical triangle is greater than** 180° and less than 540° ; ie 180° < A + B + C< 540°. V. Any side of a spherical triangle is less... | |
| John Gale Hun, Charles Ranald MacInnes - Trigonometry - 1911 - 236 pages
...MN is the measure of the angle A, (page 68 ). Therefore a' + A = 180°, or A = 180° - a', etc. 71. **The sum of the angles of a spherical triangle is greater than two** and less than six right angles. Let ABC be a spherical triangle. To prove that 180° < A + B + С <... | |
| David Eugene Smith - Geometry - 1911 - 339 pages
...concave, with its base 359°, and its other two sides each 90°, the sum of the sides being 539°. '<f- **THEOREM. The sum of the angles of a spherical triangle is greater than** 180° and less than 540°. It is for th'e purpose of proving this important fact that polar triangles... | |
| George Clinton Shutts - Geometry - 1912 - 392 pages
...side or diagonal of a convex spherical polygon is as great as 180° of arc. PROPOSITION XXIX. 750. **THEOREM. The sum of the angles of a spherical triangle is greater than** 180° and less than 540°. cGiven A ABC. To Prove ZA + Z-B+ZO 180° and ZA + LB + ZC < 540°. Proof.... | |
| Clara Avis Hart, Daniel D. Feldman, Virgil Snyder - Geometry, Solid - 1912 - 220 pages
...9f,8 54, 2. 988. 54, 2. 985. 8. §309. 9. 10. § § 54, 54, 8 a. 3. 991. In § 949 it was proved that **the sum of the angles of a spherical triangle is greater than** 180° and less than 540°. Hence the spherical excess of a spherical triangle may vary from 0° to... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 488 pages
...B = 80°, prove that Z C > 10°. HINT. Construct the polar A A'B'C'. PROPOSITION XVII. THEOREM 754. **The sum of the angles of a spherical triangle is greater than two** and less than six right angles. Given ABC, a spherical triangle. To prove Z A + ZB + Z C> 180°, and... | |
| George C. Shutts - 1913 - 212 pages
...spherical triangle are equal, the triangle is isosceles. 454 SOLID CiEOMETRY PROPOSITION XXIX. 752. **THEOREM. The sum of the angles of a spherical triangle is greater than** 180° and less than 540°. Given A ABC. To Prove ZA+Z#+ZC> 180° and Z A + Z B + Z C < 540°. Proof.... | |
| Alfred Monroe Kenyon, Louis Ingold - Trigonometry - 1913 - 132 pages
...triangles can be changed into a new theorem by applying it first to the polar triangle ; thus from " **The sum of the angles of a spherical triangle is greater than** 180° " follows " The sum of the sides of a spherical triangle is less than 360°." (25) It may be... | |
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