...method of superposition, as in the case of plane triangles. THEOREMS AND DEMONSTRATIONS THEOREM. One side of a spherical triangle is less than the sum of the other two. Given : (?). To Prove : AB < AC + BC. Proof : Draw radii OA, OB, OC. In the trihedral Z o, Z AOB <...

...analogous property of spherical polygons can be inferred, and vice versa. 15. Propositions. (1) Any side of a spherical triangle is less than the sum of the other two sides. This follows from Arts. 14 and 4. a. COR. Any side of a spherical polygon is less than the sum of the...

...homologous sides of the polar A are supplements of equal A, and therefore equal. PROP. XII. THEOREM 549. 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 § 406, Z AOB < Z AOC + Z BOC; these...

...analogous property of spherical polygons can be inferred, and vice versa. 15. Propositions. (1) Any side of a spherical triangle is less than the sum of the other two sides. This follows from Arts. 14 and 4. a. COB. Any side of a spherical polygon is less than the sum of the...

...and 126°. How many degrees in each side of its polar triangle ? PROPOSITION XII. THEOREM 1113. One side of a spherical triangle is less than the sum of the otlwr two sides. Let ABC be any spherical triangle. To Prove AB + BC > AC. Proof. Draw the radii of...

...the vertices of a triangle which is in another plane. Use locus. PROPOSITION XXVII. 746. THEOREM. I. Each side of a spherical triangle is less than the sum of the other two. SUG. Construct the subtended trihedral angle at the center of the sphere and use § 509. PROPOSITION...

...applied, one to the other, so as to coincide, they are said to be congruent. PBOPOSITION IX. THEOREM 663. Each side of a spherical triangle is less than the sum of the other two sides. Given a spherical triangle ARC, CA being the longest side, To prove that CA<AB + BC. Proof. In the...

...right, obtuse, or acute. It may also be equilateral, isosceles, or scalene. PROPOSITION IX. THEOREM 663. Each side of a spherical triangle is less than the sum of the other two sides. Given a spherical triangle ABC, CA being the longest side. To prove that CA<AB + BC. Proof. In the...

...and Polygons. (Every theorem stated here may also be stated as a theorem on polyhedral angles.) I. Each side of a spherical triangle is less than the sum of the other two sides. [On (b). See also (a).] 2. The sum of the sides of a spherical polygon is less than 360°. [Oia (b)....

...Triangles and Polygons (Every theorem stated here may also be stated as a theorem on polyhedral angles.) 1. Each side of a spherical triangle is less than the sum of the other two sides. [On (b). See also (a).] 2. The sum of the sides of a spherical polygon is less than 360°. [O12 (b)....