 | Webster Wells - Trigonometry - 1887 - 200 pages
...following properties of spherical triangles may be found in any treatise on Solid Geometry : (a) Either side of a spherical triangle is less than the sum of the other two sides. (b) If two sides of a spherical triangle are unequal, the angles opposite them are unequal,... | |
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...Uie same relation between the face, and diedral, angles of a polyedral angle. Therefore: 704. Each side of a spherical triangle is less than the sum of the other two sides (565). 705. The sum of the sides of a spherical polygon is less than a circumference (566). 706.... | |
 | William Chauvenet - 1893 - 340 pages
...mutually equiangular, they are mutually equilateral, and are either equal or symmetrical. PROPOSITION XVI. Any side of a spherical triangle is less than the sum of the other two. PROPOSITION XVII. The sum of the sides of a convex spherical polygon is less than the circumference... | |
 | William C. Bartol - Geometry, Solid - 1893 - 112 pages
...mutually equilateral, their polar triangles are mutually equiangular. PROPOSITION XXXIII. 209. THEOREM. Any side of a spherical triangle is less than the sum of the other two sides. In the spherical triangle ABC let the side BC be greater than either AC or AB; then will BC... | |
 | Arthur Latham Baker - Geometry, Solid - 1893 - 154 pages
...property of polyhedral angles, infer an analogous property of spherical polygons. 268. COR. 4. Eai.h side of a spherical triangle is less than the sum of the other two, § 91. 269. COR. 5. Any side of a polygon Is less than the sum of the of her sitIes. 270. COR. 6. The... | |
 | William Chauvenet - Geometry - 1894 - 380 pages
...triangle A'B'C', the sides AB and AC axe equal in its polar triangle ABC. PROPOSITION XXV.—THEOREM. 82. Any side of a spherical triangle is less than...triedral angle / formed at the centre O of the sphere, we / _ have the angle AOC less than the sum of Q &(** the angles A OB and BOC (VI. 69); and since the... | |
 | George Clinton Shutts - Geometry - 1894 - 412 pages
...sphere can be inscribed in any tetrahedron. (§ 458.) Can more than one be inscribed? § 459. Ex. 390. Any side of a spherical triangle is less than the sum of the other two. Suggestion. Sec §656 (c). PROPOSITION XXI. 671. Theorem. Two triangles on the same sphere, or equal... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 522 pages
...triangle, prove that the second triangle is isosceles. PROPOSITION VIII. THEOREM. 67. Any side of a triangle is less than the sum of the other two. Let ABC represent any triangle. To prove' that any side, as AB, is less than the sum of the other two. SuG.... | |
 | John Macnie - Geometry - 1895 - 390 pages
...lateral surface is formed from a sector SOLID GEOMETRY. — BOOK IX. PROPOSITION XI. THEOREM. 625. Any side of a spherical triangle is less than the sum of the other two. Given : A spherical triangle ABC, on a sphere whose center is O ; To Prove : AB + AC is greater than... | |
 | Henry Dallas Thompson - Geometry, Solid - 1896 - 226 pages
...are not equal, but the angle on the right of one is equal to the angle on the left of the other. 229. Any side of a spherical triangle is less than the sum of the other two sides. B For one face angle of the trihedral angle at the centre is less than the sum of the other... | |
| |
Any side of a spherical triangle is less than the sum of the other two. 
