 | George C. Shutts - 1913 - 212 pages
...g respectively. Auth. 5. Compare A ABC and EFG. Auth. Therefore— PROPOSITION XXVII. 748. THEOREM. 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... | |
 | George Clinton Shutts - Geometry - 1913 - 494 pages
...other respectively are either congruent or symmetrical and therefore equal. 748. THEOREM. Each aide 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... | |
 | Horace Wilmer Marsh - Mathematics - 1914 - 272 pages
...Diagonal of a Spherical Polygon is an arc of a great circle connecting any two non-adjacent vertices. 248. A Spherical Triangle is a spherical polygon of three sides; like a plane triangle, it may be right, oblique, equilateral, isosceles, or scalene. 249. A Bi-rectangular Triangle is a spherical triangle... | |
 | Horace Wilmer Marsh - Mathematics - 1914 - 306 pages
...sides 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 // one triangle... | |
 | Horace Wilmer Marsh, Annie Griswold Fordyce Marsh - Mathematics - 1914 - 270 pages
...sides 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 H. Williams, Kenneth P. Williams - Geometry, Solid - 1916 - 184 pages
...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 ZO-ABC,... | |
 | John Charles Stone, James Franklin Millis - Geometry, Solid - 1916 - 196 pages
...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.... | |
 | Webster Wells, Walter Wilson Hart - Geometry - 1916 - 504 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
...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.... | |
 | United States. Office of Education - 1921 - 1286 pages
...4(1. 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... | |
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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. 
