Books Books 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 ## 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... ## 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... ## 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... ## 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... ## 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... ## 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... ## 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°... ## 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 + ß+C<540°. VI. In any spherical triangle the order... ## 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... 