 | Richard Wilson - Logarithms - 1831 - 372 pages
...polygon is a portion of the surface of a sphere contained by several arcs of great circles. 32. PROP. The sum of the sides of a spherical polygon is less than the circumference of a great circle. Let a, ß, y, S, &c. be the sides of the polygon subtending plane... | |
 | John Radford Young - Astronomy - 1833 - 308 pages
...circles are perpendicular to each other, or the spherical angle at Q is a right angle. (38.) Any one side of a spherical triangle is less than the sum of the other two. Let ABC be any spherical triangle, and О the centre of die sphere; draw the radii OA, OB, ОС, then... | |
 | Benjamin Peirce - Geometry - 1837 - 216 pages
...spherical sector. The base of the sector is the zone generated by the arc DP, or FH. 438. Theorem, Either side of a spherical triangle is less than the sum of the other two. Demonstration. From the centre O (fig. 179) of the sphere draw the radii OA, OB, OC to the vertices... | |
 | Benjamin Peirce - Geometry - 1847 - 204 pages
...spherical sector. The base of the sector is the zone generated by the arc DF, or FH. 438. Theorem. Either side of a spherical triangle is less than the sum of the other two. Proof. From the centre O (fig. 179) of the sphere draw the radii OA, OB, OCto the vertices .5, B, C... | |
 | Thomas Grainger Hall - Trigonometry - 1848 - 192 pages
...the triangle, is always less than the circumference of a great circle. COR. Hence it is obvious that the sum of the sides of a spherical polygon is less than the circumference of a great circle. The Polar TriangU. 12. Let ABC be a spherical triangle. With points,... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...be out of the arc of a ijreat circle ADB. Therefore, the shortest path, &c. PROPOSITION IV. THEOREM. The sum of the sides of a spherical polygon, is less than the circumference of a great circle. Let ABCD be any spherical polygon; then will the sum of the sides... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...angles forming a polyedral angle is less than the sum of the two other angles (B. vL, P. 19); hence, any side of a spherical triangle is less than the sum of the two other sides. PROPOSITION II. THEOEEM. The sum of all the sides of any spherical polygon is less... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...which bound a polyedral angle is less than the sum of the two other angles (B. v1., P. 19) ; hence, any side of a spherical triangle is less than the sum of the two other sides. PROPOSITION II. THEOREM. The sum of all the sides of any spherical polygon is less... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...which bound a polyedral angle is less than the sum of the two other angles (B. VL, p. 19) ; hence, any side of a spherical triangle is less than the sum of the two other sides. PROPOSITION II. THEOREM. The sum of all the sides of any spherical polygon is less... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...be out of the arc of a great circle ADB. Therefore, the shortest path, &c. PROPOSITION IV. THEOREM. The sum of the sides of a spherical polygon, is less than the circumference of a great circle. Let ABCD be any spherical polygon ; then will the sum of the sides... | |
| |
The sum of the face angles of any convex polyhedral angle is less than four right angles. 
