...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...

...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...

...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 >...

...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...

...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...

...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...

...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...

...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...

...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...

...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...