 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...arc of a great circle through a given point perpendicular to a given arc of a great circle. 731. Each side of a spherical triangle is less than the sum of the other two sides. 732. The sum of the sides of a spherical polygon is less than 360°. 734. If A'B'C' is the polar... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 570 pages
...angles of a triedral angle are equal, the three face angles are equal. PROPOSITION XXII. THEOREM 864. Any side of a spherical triangle is less than the sum of the two others. Hint. — Form the corresponding triedral angle. Then apply §§ 843, 593. 865. COR. I.... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 376 pages
...angles of a triedral angle are equal, the three face angles are equal. PROPOSITION XIII. THEOREM 781. Any side of a spherical triangle is less than the sum of the two others. /lint. — Construct the corresponding triedral angle. Then apply S;§ 760, 565. 783. COR.... | |
 | William Chauvenet - Geometry - 1898 - 376 pages
...polar triangle ABC. PROPOSITION XXV.—THEOREM. 82. Any side of a spherical triangle is less than tlie sum of the other two. Let ABC be a spherical triangle;...AC, is less than the sum of the other two, AB and BC. For, in the corresponding triedral angle formed at the centre 0 of the sphere, we have the angle... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...from any property of polyedral angles, infer an analogous property of spherical polygons. 504. Each side of a spherical triangle is less than the sum of the other two. (384) 505. Any side of a polygon is less than the sum of the other sides. 506. The sum of the sides... | |
 | Webster Wells - Geometry - 1899 - 180 pages
...- a'. In like manner, the theorem may be proved for any Z. of either A. PROP. XVIII. THEOREM. 594. Any side of a spherical triangle is less than the sum of the other two sides. Given AB any side of spherical A ABC. To Prove AB<AO + BC. (By § 457, Z.AOB<^AOO+^BOC; and... | |
 | Webster Wells - Geometry - 1899 - 450 pages
...is the measure of ZA (§ 584) .-. A + a' = 180°, or A = 180° - a'. 340 PROP. XVIII. THEOREM. 594. Any side of a spherical triangle is less than the sum of the other two sides. Given AB any side of spherical A ABC. To Prove AB < AC + BC. (By § 457, ^AOB<ZAOC + ^BOC; and... | |
 | Harvard University - Geometry - 1899 - 39 pages
...mutually equiangular, they are mutually equilateral, and are either equal or symmetrical. THEOREM XIV. Any side of a spherical triangle is less than the sum of the other two. THEOREM XV. The sum of the sides of a convex spherical polygon is less than the circumference of a... | |
 | George Albert Wentworth - Geometry - 1899 - 496 pages
...be right, obtuse, or acute : equilateral, isosceles, or scalene. PROPOSITION XI. THEOREM. 789. Each side of a spherical triangle is less than the sum of the other two sides. Let ABC be a spherical triangle, AB the longest side. To prove that AB < AC + EC. Proof. In... | |
 | George Albert Wentworth - Geometry, Solid - 1899 - 248 pages
...obtuse, or acute ; equilateral, isosceles, or scalene. THE SPHERE. PROPOSITION XI. THEOREM. 789. Each side of a spherical triangle is less than the sum of the other two sides. Let ABC be a spherical triangle, AB the lengest side. To prove that AB < AC + BC. Proof. In... | |
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Any side of a spherical triangle is less than the sum of the other two. 
