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" The sum of any two sides of a spherical triangle is greater than the third side, and their difference is less than the third side. "
A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ... - Page 363
by John Bonnycastle - 1806 - 419 pages
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Elementary Geometry: Including Plane, Solid, and Spherical Geometry, with ...

Edward Olney - Geometry - 1883 - 352 pages
...to spherical triangles in the same manner as to plane triangles. PROPOSITION XIV. 689. Theorem. — The sum of any two sides of a spherical triangle is greater than the third side, and their difference is less than the third side. DEMONSTRATION. Let ABC be any spherical triangle. Then...
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Elementary Geometry: Including Plane, Solid, and Spherical Geometry, with ...

Edward Olney - Geometry - 1883 - 344 pages
...triangle considered will be the one which is less than a hemisphere. PROPOSITION XIV. 689. Theorem.—The sum of any two sides of a spherical triangle is greater than the third side, and their difference is less than the third side. DEMONSTRATION. Let ABC be any spherical triangle. Then...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 400 pages
...arc DE. (§ 603.) Therefore, A + a' = 180°. Whence, A = 180° — a'. PROPOSITION XIV. THEOREM. 620. The sum of any two sides of a spherical triangle is greater than the third side. A Let ABC be a spherical triangle on the surface of a sphere whose centre is O. To prove AB + AC >...
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Elements of Geometry

George Cunningham Edwards - Geometry - 1895 - 330 pages
...circle. But a great circle cannot be tangent to another great circle. 120. THEOREM. — The sum of two sides of a spherical triangle is greater than the third side. Let ABC represent the spherical triangle, AC being the largest side. Analysis. — If AC be less than...
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Examination Papers: A Supplement to the University Calendar

1897 - 674 pages
...ALGKBRA. 1. Show that the sum of any two sides of u triangle is greater than the third side, and that the difference of any two sides is less than the third side. 3. Construct a rectangle equal in area to a given triangle. 4. Given two lines, a and b, and two other...
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Plane and Solid Geometry: Inductive Method

Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...Compare a face angle of any triedral angle with the sum of the other two. [§449.] Can you prove that the sum of any two sides of a spherical triangle is greater than the third side? 656. Cor. Can you prove that any side of a spherical triangle is greater than the difference of the...
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Elements of Plane and Spherical Trigonometry

James William Nicholson - Trigonometry - 1898 - 204 pages
...whose parts are each less than 180°. Of these the following properties are proved in Geometry : 1. The sum of any two sides of a spherical triangle is greater than the third side. 8. ln any spherical triangle, the greater side lies opposite the greater angle ; and, conversely, the...
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Plane and Solid Geometry

William James Milne - Geometry - 1899 - 404 pages
...the third side ? 2. How does any side compare with the difference of the other two sides ? Theorem. The sum of any two sides of a spherical triangle is greater than the third side. To prove the sum of any two sides, as AC + BC, greater than the third side AJB. Proof. In the corresponding...
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Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...derived directly from known properties of the corresponding polyhedral angles. PROPOSITION VII 621. The sum of any two sides of a spherical triangle is greater than the third side. SUGGESTIONS FOR PROOF. The sum of any two face angles of a trihedral angle is greater than the third...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...sides of a spherical polygon are usually measured in degrees. PROPOSITION IX. THEOREM 716. The sum of two sides of a spherical triangle is greater than the third side. Hyp. ABC is a spherical triangle. To prove AB + BC> AC. Proof. Draw radii OA, OB, and 0C. Then Z AOB...
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