 | William Betz - Geometry - 1916 - 536 pages
...there congruence theorems for triangles in plane geometry corresponding to all of these cases? 844. The sum of the angles of a spherical triangle is greater than two and less than six right angles. Given the spherical triangle ABC, in which A, B, and C respectively... | |
 | John Charles Stone, James Franklin Millis - Geometry, Solid - 1916 - 196 pages
...their polar triangles are mutually equilateral ; and conversely. The proof is left to the student. 474. Theorem. — The sum of the angles of a spherical triangle is greater than 180° and less than 540°. Hypothesis. A ABC is any spherical triangle. Conclusion. ZA + ZB + Z C>... | |
 | William Betz, Harrison Emmett Webb - Geometry, Solid - 1916 - 214 pages
...are respectively equal, and they are either congruent or symmetric. PROPOSITION XVIII. THEOREM 844. The sum of the angles of a spherical triangle is greater than two and less than six right angles. Given the spherical triangle ABC, in which A, J5, and C respectively... | |
 | Claude Irwin Palmer, Charles Wilbur Leigh - Logarithms - 1916 - 348 pages
...E-OD-C, and ¿CAB and C-OE-D. 110. The sum of the sides of a spherical triangle is less than 360°. The sum of the angles of a spherical triangle is greater than 180° and less than 540°. It is evident that the sides and angles of a spherical triangle can be greater... | |
 | John H. Williams, Kenneth P. Williams - Geometry, Solid - 1916 - 184 pages
...are 84°, 100°, and 110°, what are the angles of the polar triangle? PROPOSITION XIV. THEOREM 750. The sum of the angles of a spherical triangle is greater than 180° and less than 540°. a' Let ABC be a spherical triangle and A'B'C' its polar triangle. To prove... | |
 | Edward Richard Cary - Geodesy - 1916 - 302 pages
...where e is the difference above stated. o±|+6±|-+c±|•+d±J=360'> FIG. 47. 57. Spherical Excess. The sum of the angles of a spherical triangle is greater than 180°. The excess becomes appreciable when the sides are from 4 to 5 miles long. The equation* for... | |
 | Fletcher Durell, Elmer Ellsworth Arnold - Geometry, Solid - 1917 - 220 pages
...circumference of a great circle of the sphere. PROPOSITION XVI. THEOREM 1. Post. 1. 2. Why? 3. § 677. QED 691. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. Given the spherical triangle ABC. To prove A + B + C > 180° and <... | |
 | Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry - 1918 - 460 pages
...is opposite the greater angle; and conversely. Proof of theorem is similar to that of § 184. 858. Theorem. The sum of the angles of a spherical triangle is greater than 180° and less than 540°. Given the spherical AABC with the letter at each vertex of an angle denoting... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...= 80°, prove that Z C> 10°. II INT. 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. A' K Given ABC, a spherical triangle. To prove ZA + ZB + Z C> 180°,... | |
 | Claude Irwin Palmer - Geometry, Solid - 1918 - 192 pages
...equal, the triangle is isosceles. 3. If a spherical triangle is equiangular it is equilateral. 858. Theorem. The sum of the angles of a spherical triangle is greater than 180° and less than 540°. Given the spherical AABC with the letter at each vertex of an angle denoting... | |
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The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC... 
