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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... "
An Elementary Treatise on Plane and Solid Geometry - Page 138
by Benjamin Peirce - 1871 - 150 pages
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Connecticut School Document, Issues 1-13

Education - 1913 - 398 pages
...plane parallel to the base is a figure of the same shape as the base (Prove for circular cone only) 7 The sum of the angles of a spherical triangle is greater than 180 but less than 540 8 The planes which bisect the dihedral angles of a trihedral angle intersect...
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Final Report of the National Committee of Fifteen on Geometry Syllabus: July ...

National Education Association of the United States. National Committee of Fifteen on Geometry Syllabus - Geometry - 1912 - 60 pages
...(a).] 2. The sum of the sides of a spherical polygon is less than 360. [O12 (b). See also (a).] 3. The sum of the angles of a spherical triangle is greater than 180 and less than 540. [K8.j 4. // A'B'C' is he polar triangle of ABC, then, reciprocally, ABC...
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Final Report of the National Committee of Fifteen on Geometry Syllabus: July ...

National Education Association of the United States. National Committee of Fifteen on Geometry Syllabus - Geometry - 1912 - 60 pages
...(a).] 2. The sum of the sides of a spherical polygon is less than 360. [Oi2 (b). See'also (a).] 3. The sum of the angles of a spherical triangle is greater than 180 and less than 540. [K8.j 4. // A'B'C' is {he polar triangle of ABC, then, reciprocally, ABC...
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Plane and Solid Geometry

Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 378 pages
...180, and Z (7+ c' = 180. The proof of (6) is left for the student. EXERCISE 302 303 367. 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...
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Solid Geometry

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...
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Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 500 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...
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Constructive Text-book of Practical Mathematics, Volume 2

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...
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Examination Questions in Mathematics: Third Series, 1911-1915

College Entrance Examination Board - Mathematics - 1915 - 60 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,...
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Annual Report of the Department of Public Instruction of the State of Indiana

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...
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The Elements of Non-Euclidean Plane Geometry and Trigonometry

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...
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