 | Walter Burton Ford, Charles Ammerman - Geometry, Solid - 1913 - 176 pages
...respectively, find the sides of the polar triangle (in degrees). Why? Why? (c) § 361 367. Theorem IX. The sum of the angles of a spherical triangle is greater than 180° and less than 540°. FIG. 249 Given the spherical A ABC with the sides a, b, and c. To prove... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...Ax. 9 Ax. 9 §654 and Similarly B + b' = 180°, and C + c' = 180°. PROPOSITION XIII. THEOREM 668. The sum of the angles of a spherical triangle is greater than 180° and less than 540°. Given a spherical triangle ABC, the letter at the vertex of each angle denoting... | |
 | Horace Wilmer Marsh, Annie Griswold Fordyce Marsh - Mathematics - 1914 - 270 pages
...its point of intersection with the produced side of which that extremity is the pole. X THEOREM 29 The sum of the angles of a spherical triangle is greater than 180° and less than 540°. Draw the figure and construct its polar triangle. Formulate the sum of each... | |
 | College Entrance Examination Board - Mathematics - 1915 - 72 pages
...then it contains another element also, and the section is a parallelogram. 3. Complete and prove the theorem: The sum of the angles of a spherical triangle is greater than , and is less than The area of a spherical triangle is 100 square inches, and its angles are 100°,... | |
 | Indiana. Department of Public Instruction - Education - 1915 - 658 pages
...triangle. 6. Prove that the perpendicular is the shortest line from a point to a plane. 7. Prove that the sum of the angles of a spherical triangle is greater than 180° and less than 540°. 8. Give fully but briefly your method of conducting a recitation with a... | |
 | Horatio Scott Carslaw - Geometry - 1916 - 193 pages
...the sphere intersect all other great circles. We shall find that this analogy can be carried further. The sum of the angles of a spherical triangle is greater than two right angles. The sum of the angles of a triangle in this plane is greater than two right angles. The Sphferical... | |
 | 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... | |
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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... 
