 | Horace Wilmer Marsh - Mathematics - 1914 - 272 pages
...if necessary. Prove the angle formed by the two radii, equal to the plane angle. X THEOREM 25 Each side of a spherical triangle is less than the sum of the other two sides. • X THEOREM 26 The sum of the sides of a spherical polygon is less than 360°. X THEOREM 27 X THEOREM... | |
 | Horace Wilmer Marsh, Annie Griswold Fordyce Marsh - Mathematics - 1914 - 270 pages
...if necessary. Prove the angle formed by the two radii, equal to the plane angle. X THEOREM 25 Each side of a spherical triangle is less than the sum of the other two X THEOREM 26 The sum of the sides of a spherical polygon is less than 360°. X THEOREM 27 // one triangle... | |
 | John Charles Stone, James Franklin Millis - Geometry, Solid - 1916 - 196 pages
...polyedral angle has the same measure as the corresponding angle of the spherical polygon. 466. Theorem. — Any side of a spherical triangle is less than the sum of the other two sides. The proof is left to the student. See § 342 and § 425 (1). Write the proof in full. 467. Theorem. —... | |
 | John H. Williams, Kenneth P. Williams - Geometry, Solid - 1916 - 184 pages
...also have the same numerical measure as the angles of the polygon, respectively. § 729 742. THEOREM. Any side of a spherical triangle is less than the sum of the other two sides. Let AB be the longest side of spherical AABC. To prove AB<AC+CB. Now in the corresponding trihedral... | |
 | Webster Wells, Walter Wilson Hart - Geometry - 1916 - 490 pages
...distance from the center of each sphere. Suggestion. — Recall § 313. PROPOSITION XXI. THEOREM 701. Any side of a spherical triangle is less than the sum of the other two. A Hypothesis. AB is any side of spherical A ABC. Conclusion. AB < AC + BC. Suggestions. — 1. Compare... | |
 | Fletcher Durell, Elmer Ellsworth Arnold - Geometry, Solid - 1917 - 220 pages
...equal to a given spherical angle on the sphere. SOLID GEOMETRY. BOOK IX PROPOSITION XIV. THEOREM 688. Any side of a spherical triangle is less than the sum of the other two sides. Given the spherical triangle ABC, of which no side is larger than A C. To prove AC < AB + BC. Proof.... | |
 | John William Norie, J. W. Saul - Nautical astronomy - 1917 - 642 pages
...is called an isosceles triangle, etc., as in plane trigonometry. The following properties relate to. spherical triangles — (a) Any side of a spherical triangle is less than a semicircle, and any angle is less than two right angles. (b) The sum of the three angles is greater... | |
 | United States. Office of Education - 1921 - 1286 pages
...The sum of the face angles of any convex polyhedral angle is less than four right angles. 47. Each side of a spherical triangle is less than the sum of the other two sides. 48. The sum of the sides of a spherical polygon is less than 300°. 49. The sum of the angles of a... | |
 | Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - Geometry, Solid - 1922 - 216 pages
...the sides of a convex spherical polygon is less than a great circle. HINT. Apply §§ 629, 572. 632. Any side of a spherical triangle is less than the sum of the other two sides. HINT. Apply § 570. 633. Congruence. Two spherical triangles are congruent if their sides and their... | |
 | National Committee on Mathematical Requirements - Mathematics - 1922 - 84 pages
...The sum of the face angles of any convex polyhedral angle is less than four right angles. 47. Each side of a spherical triangle is less than the sum of 'the other two sides. 48. The sum of the sides of a spherical polygon is less than 360°. 49. The sum of the angles of a... | |
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Each side of a spherical triangle is less than the sum of the other two sides. 
