 | Education - 1912 - 942 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | Daniel Alexander Murray - 1906 - 466 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,... | |
 | 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... | |
 | Webster Wells - Geometry - 1908 - 336 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°.... | |
 | 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°.... | |
 | 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°... | |
 | Daniel Alexander Murray - Plane trigonometry - 1908 - 358 pages
...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... | |
| |
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... 
