 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...  Elements of Geometry - Page 286by Andrew Wheeler Phillips, Irving Fisher - 1897 - 354 pagesFull view - About this book
 | Fletcher Durell - Geometry - 1911 - 553 pages
...spherical triangles each of which is the polar triangle of the other. PROPOSITION XIV. THEOREM 783. The sum of the angles of a spherical triangle is greater than 180°, and less than 540°. \b <*] ^0 ' a' Given the spherical triangle ABO. To prove A + B + 0 > 180°... | |
 | Charles Davison - Geometry, Solid - 1905 - 140 pages
...angles, .'. L HOK + L B'OC' = two right angles, .'. A + a' = two right angles, etc. 106. PROP. 70. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. Since A+a' = B + 6' = C + c' = two right angles, .'. A + B + C = six right angles — (a + b' + c').... | |
 | 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... | |
 | Education - 1912 - 914 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 about an axis in its plane. 58.... | |
 | 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 of the polar triangle A'B'C'.... | |
 | 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, on adding, A + B + C+a' + V... | |
 | 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 sides of the polar triangle A'B'C'.... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...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°. Proof. 1. Let A'B'C' be polar A of... | |
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