 | William Chauvenet - 1893 - 340 pages
...angles of a spherical triangle are equal, the triangle is isosceles. PROPOSITION XVI.—THEOREM. 61. Any side of a spherical triangle is less than the sum of the other two. Let ABC be a spherical triangle; then any side, as AC, is less than the sum of the other two, AB and... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 522 pages
...thus: The sum of the sides of a convex spherical polygon is less than four right angles. Ex. 844. Any side of a spherical triangle is less than the sum of the other two. SuG. See Art. 388. Ex. 345. The arc of a great circle drawn from the vertex of an isosceles spherical... | |
 | John Macnie - Geometry - 1895 - 390 pages
...lateral surface is formed from a sector SOLID GEOMETRY. — BOOK IX. PROPOSITION XI. THEOREM. 625. Any side of a spherical triangle is less than the sum of the other two. Given : A spherical triangle ABC, on a sphere whose center is O ; To Prove : AB + AC is greater than... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...an 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 triangle... | |
 | Henry Dallas Thompson - Geometry, Solid - 1896 - 226 pages
...not equal, but the angle on the right of one is equal to the angle on the left of the other. 229. Any side of a spherical triangle is less than the sum of the other two sides. B For one face angle of the trihedral angle at the centre is less than the sum of the other two face... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 570 pages
...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.... | |
 | George Washington Hull - Geometry - 1897 - 408 pages
...at its point of contact passes through the centre of the sphere. PROPOSITION III. THEOREM. 576. Any side of a spherical triangle is less than the sum of the other two sides. Given—ABC a spherical triangle on the sphere whose centre is 0. To Prove— AC + BC> AB. Dem.—Draw... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 376 pages
...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.... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...may, 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... | |
 | George Albert Wentworth - Geometry, Solid - 1899 - 248 pages
...of the polygon. Thus, the planes of the sides of the polygon ABCD form the polyhedral angle O-ABCD. The face angles AOB, BOC, etc., are measured by the...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... | |
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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. 
