 | Isaac Newton Failor - 1906 - 431 pàgines
...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... | |
 | Isaac Newton Failor - 1906 - 440 pàgines
...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... | |
 | Daniel Alexander Murray - 1906 - 466 pàgines
...+ C> 180° ; and A+B+C< 540° - 0°, ie A + B+G< 540°. 18. Definitions, a. The amount by which the sum of the three angles of a spherical triangle is greater than 180° is called its spherical excess. It is shown in Art. 57 that the area of a triangle depends upon... | |
 | Elmer Adelbert Lyman - 1908 - 364 pàgines
...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... | |
 | Webster Wells - 1908 - 336 pàgines
...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... | |
 | Henry Raper - 1908 - 1018 pàgines
...opposite the greater angle. The sum of the three sides of a spherical triangle is less than 360°. The sum of the three angles of a spherical triangle is greater than two right angles and less than six, or always will fall between 180° and 540°. In right-angled spherical... | |
 | Daniel Alexander Murray - 1908 - 358 pàgines
...180° ; and A + B + C< 540° - 0°, ie A + B+C< 540°. 18. Definitions, a. The amount by which the sum of the three angles of a spherical triangle is greater than 180° is called its spherical excess. It is shown in Art. 57 that the area of a triangle depends upon... | |
 | Daniel Alexander Murray - 1908 - 132 pàgines
...> 180° ; and A +B+ C< 540° - 0°, ie A + B+C< 540°. 18. Definitions, a. The amount by which the sum of the three angles of a spherical triangle is greater than 180° is called its spherical excess. It is shown in Art. 57 that the area of a triangle depends upon... | |
 | Arthur Graham Hall, Fred Goodrich Frink - 1910 - 204 pàgines
...triangle is less than 360°. The triangle may have one, two, or three sides greater than 90°. The sum of the three angles of a spherical triangle is greater than 180°, and less than 540°. The triangle may have one, two, or three angles greater than 90°. If two... | |
 | John Gale Hun, Charles Ranald MacInnes - 1911 - 234 pàgines
...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... | |
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... the sum of the three angles of a spherical triangle is greater than two right angles. 
