 | 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... | |
 | 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° < A + B + C < 540°. Hence, on... | |
 | 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°. Proof: Construct the polar A A'B'C'... | |
 | 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 a spherical triangle ABC : I. .4... | |
 | Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...polyhedral angle at the center of the sphere is less than 360°, etc. THEOREM IX 687. The sum of tlie angles of a spherical triangle is greater than two, and less than six, right angles. Given : Spherical A ABC. To Prove : ZA + ZB + ZO 180° and < 540°. Proof: Construct the polar A A'B'C'... | |
 | Eugene Randolph Smith - Geometry, Plane - 1909 - 424 pages
...opposite sides are equal. (Use the polar triangles.) State this for a trihedral angle. 277. Theorem XVI. The sum of the angles of a spherical triangle is greater than one, and less than three, straight angles. Let the angles be A, B, C, the opposite sides be a, 6, c,... | |
 | Levi Leonard Conant - Trigonometry - 1909 - 320 pages
...equal sides are opposite equal angles. III. Any angle of a spherical triangle is less than 180°. IV. The sum of the angles of a spherical triangle is greater than 180° and less than 540° ; ie 180° < A + B + C< 540°. V. Any side of a spherical triangle is less... | |
 | John Gale Hun, Charles Ranald MacInnes - Trigonometry - 1911 - 234 pages
...MN is the measure of the angle A, (page 68 ). Therefore a' + A = 180°, or A = 180° - a', etc. 71. The sum of the angles of a spherical triangle is greater than two and less than six right angles. Let ABC be a spherical triangle. To prove that 180° < A + B + С < 540°. Construct the polar triangle.... | |
 | John Gale HUN (and MAC INNES (Charles Ranald)), Charles Ranald MacInnes - Trigonometry - 1911 - 234 pages
...MN is the measure of the angle A, (page 68). Therefore a' + A = 180°, or A = 180° - a', etc. 71. The sum of the angles of a spherical triangle is greater than two and less than six right angles. Let ABC be a spherical triangle. To prove that 180° < A + B + С < 540°. Construct the polar triangle.... | |
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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... 
