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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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School Science and Mathematics, Volume 12

Education - 1912 - 944 pages
...spherical triangle is measured by the supplement of the opposite side of its polar triangle. Corollary i. The sum of the angles of a spherical triangle is greater than one, and less than three straight angles. Corollary 2. The sum of the dihedral angles of a trihedral...
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Manual of the Free High Schools of Wisconsin

Wisconsin. Department of Public Instruction - Education - 1906 - 124 pages
...triangles each angle of one is measured by the supplement of the side lying opposite it in the other. 56. The sum of the angles of a spherical triangle is greater than two and less than six right angles, 57. The area of the surface generated by a straight line revolving...
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Plane and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 431 pages
...by a plane 4 in. from the center. Find the diameter of the small circle. PROPOSITION XV. THEOREM 801 The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. HYPOTHESIS. ABC is a spherical triangle, and a', 6', c', are the sides...
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Plane and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 440 pages
...plane 4 in. from the center. Find the diameter of the small circle. 380 * PROPOSITION XV. THEOREM 801 The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. m HYPOTHESIS. ABC is a spherical triangle, and a', b', c', are the...
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Plane Trigonometry

Daniel Alexander Murray - 1906 - 472 pages
...between the parts of the original triangle. This will be exemplified in later articles. 17. Proposition. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. Let ABC be any spherical triangle ; it is required to show that Hence,...
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Plane and Solid Geometry

Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...centers of the spherical surfaces of given radius, that contain two given points ? SOLID GEOMETRY (760.) THEOREM. The sum of the angles of a spherical triangle is greater than 180 and less than 540. Given: A spherical A ABC. To Prove: I. Z4 + ZB + ZO 180; II. ZA + B...
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Spherical Trigonometry: For Colleges and Secondary Schools

Daniel Alexander Murray - Spherical trigonometry - 1908 - 132 pages
...the parts of the original triangle. This will be exemplified in later articles. / 17. Proposition. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. Let ABC be any spherical triangle ; it is required to show that 180...
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Plane and Solid Geometry

Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...the center of the sphere is less than 360, etc. Give the complete demonstration. THEOREM IX 687. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. Given : Spherical A ABC. To Prove : ZA + Zs + Zo 180 and < 540....
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New Plane and Solid Geometry

Webster Wells - Geometry - 1908 - 338 pages
...B Given convex spherical polygon ABCD. To Prove AB + BC + CD + DA < 360. PROP. XIV. THEOREM 551. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. a' Given spherical A ABC. To Prove A + B + C > ISO0, and < 540....
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Plane [and Spherical] Trigonometry for Colleges and Secondary Schools

Daniel Alexander Murray - Plane trigonometry - 1908
...triangles each angle of the one is the supplement of the side opposite to it in the other. 17. Show that the sum of the angles of a spherical triangle is greater than two, and less than six, right angles. 18. Discuss the following cases, in which A, a, and 6 are given in...
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