 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 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 OC. Then Z AOB... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 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 OC. Then ZAOB... | |
 | Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...often not so suggestive of properties as the polyhedral angle. PROPOSITION X. THEOREM 775. The sum of two sides of a spherical triangle is greater than the third side. Given the spherical triangle ABC, of which no side is larger than AB. To prove AC+BO AB. Proof. From... | |
 | Fletcher Durell - Geometry - 1911 - 553 pages
...often not so suggestive of properties as the polyhedral angle. PROPOSITION X. THEOREM 775. The sum of two sides of a spherical triangle is greater than the third side. Given the spherical triangle ABC, of which no side is larger than AB. To prove AG+ BC > AB, Proof .... | |
 | Walter Nelson Bush, John Bernard Clarke - Geometry - 1905 - 378 pages
...angles of tJie polyhedral and whose angles are the measures of the dihedrals of the polyhedrals. (b) The sum of any two sides of a spherical triangle is greater than the third. (XXII. (b) 3.) (c) The sum of the sides of a spherical polygon {ie the perimeter) is less than the... | |
 | Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...is isosceles. SUGGESTION. Construct the polar triangle of ABC. Then A'B' = A'C'. Use Ex. 4, etc. 7. The sum of any two sides of a spherical triangle is greater than the third side. SUGGESTION. The sum of any two face angles of the corresponding trihedral angle at the center of the... | |
 | Eugene Randolph Smith - Geometry, Plane - 1909 - 424 pages
...IV. (a) The sum of any two face angles of a trihedral angle is greater than the third face angle. (b) The sum of any two sides of a spherical triangle is greater than the third side. VA FIRST PROOF : Let the trihedral angle be V-ABC. Pass a plane through CV perpendicular to plane A... | |
 | Levi Leonard Conant - Trigonometry - 1909 - 320 pages
...respectively. THEOREMS. The following theorems on spherical triangles were proved in solid geometry. I. The sum of any two sides of a spherical triangle is greater than the third side.* II. In any spherical triangle the greatest side is opposite the greatest angle, and conversely. Also,... | |
 | Walter Nelson Bush, John Bernard Clarke - Geometry - 1909 - 376 pages
...angles of the polyhedral and whose angles are the measures of the dihedrals of the polyhedrals. (b) The sum of any two sides of a spherical triangle is greater than tiie third. (XXII. (6) 3.) (c) The sum of the sides of a spherical polygon (ie the perimeter) is less... | |
 | Arthur Graham Hall, Fred Goodrich Frink - Trigonometry - 1910 - 204 pages
...less than 180°. The following theorems, proved in elementary geometry, are restated without proof : The sum of any two sides of a spherical triangle is greater than the third side. The sum of the three sides of a spherical triangle is less than 360°. The triangle may have one, two,... | |
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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. 
