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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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Solid Geometry Developed by the Syllabus Method

Eugene Randolph Smith - Geometry, Solid - 1918 - 232 pages
...a spherical triangle is always less than the sum of the non-adjacent interior angles, and therefore the sum of the angles of a spherical triangle is greater than a straight angle : If the exterior angle in the last figure is equal to, or less than, the interior...
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Scientific Theism Versus Materialism: The Space-time Potential

Arvid Reuterdahl - Minnesota - 1920 - 314 pages
...pangeometry can be restated in terms of Euclidean geometry. From ordinary Euclidean geometry we know that the sum of the angles of a spherical triangle is greater than two and less than six right angles. Riemann's geometry, therefore, is little more than a new version of...
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Solid Geometry

Charles Austin Hobbs - Geometry, Solid - 1921 - 216 pages
...(?) By producing BC to meet A'B' and AT' it can be proved that Z A' ? 180 - BC. Proposition 330 Theorem The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. Hypothesis. Let A, B, and C denote the numerical measures of the A...
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Bulletin, Issues 25-53

United States. Office of Education - 1921 - 1268 pages
...sum of the other two sides. 48. The sum of the sides of a spherical polygon is less than 300. 49. The sum of the angles of a spherical triangle is greater than 180 and less than 540. 50. There can not be more than five regular polyhedrons. 51. The locus of...
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Bulletin

Education - 1921 - 1198 pages
...sum of the other two sides. 48. The sum of the sides of a spherical polygon is less than 360. 49. The sum of the angles of a spherical triangle is greater than 180 and less than 540. 50. There can not be more than five regular polyhedrons. 51. The locus of...
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The Reorganization of Mathematics in Secondary Education

National Committee on Mathematical Requirements - Mathematics - 1922 - 73 pages
...sum of 'the other two sides. 48. The sum of the sides of a spherical polygon is less than 360. 49. The sum of the angles of a spherical triangle is greater than 180 and less tha'n 540. 50. There can not be more than five regular polyhedrons. 51. The locus...
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Solid Geometry

Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - Geometry, Solid - 1922 - 216 pages
...corresponding face angles are equal and the trihedrals are either symmetric or congruent. Theorem 19 661. The sum of the angles of a spherical triangle is greater than 180 and less than o40. Given the spherical triangle ABC. To prove that 180 <^A + ZB + ^C< 540...
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Plane and Spherical Trigonometry: With Stereographic Projections

James Atkins Bullard, Arthur Kiernan - Trigonometry - 1922 - 252 pages
...etc. IV. The sum of the sides of a spherical triangle is less than 360; that is, a+6+c<360. V. The sum of the angles of a spherical triangle is greater than 180 and less than 540; that is, 180<Л + +C<540. VI. In any spherical triangle the order...
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Schultze and Sevenoak's Plane and Solid Geometry; Revised by Arthur Schultze

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...ZB = 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 ZA + ZB + Z C> 180, and...
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Descriptive Geometry

Lawrence Edminster Cutter - Geometry, Descriptive - 1923 - 266 pages
...spherical polygon of three sides. THEOREMS The sum of the sides of a spherical polygon is less than 360. The sum of the angles of a spherical triangle is greater than 180 and less than 540. SOLUTION OF TRIHEDRAL ANGLES In a trihedral angle there are three face angles...
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