 | George Washington Hull - Geometry - 1807 - 408 pages
...sphere at equal distances from the centre of a sphere are equal. PROPOSITION IV. THEOREM. 579. TJie sum, of the sides of a spherical polygon is less than the circumference of a great circle. Given — ABCD a spherical polygon on the sphere whose centre is 0. To Prove — AB + BC + CD + DA... | |
 | Daniel Cresswell - Geometry - 1816 - 352 pages
...of a great circle of the sphere. (75.) COR. In the same manner, it may be shewn, that the aggregate of the sides of a spherical polygon, is less than the circumference of a great circle of the sphere, if the polygon be bounded by arches of great circles, each of which is less than the... | |
 | Dionysius Lardner - Plane trigonometry - 1828 - 434 pages
...sum of the three sides is less than the circumference of a great circle. (130.) Cor. The periphery of a spherical polygon is less than the circumference of a great circle. ( 131.) Eight triangles formed by three great circles. , (132.) Cor. 1. Given any one of these eight... | |
 | 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 angles at the centre of the sphere... | |
 | Benjamin Peirce - Geometry - 1837 - 216 pages
...AB, ACj BC; and, therefore, each of these arcs is less than the sum of the other two. 439. Theorem. The sum of the sides of a spherical polygon is less than the circumference of a great circle. Polar Triangle. Demonstration. From the centre O (fig. ISO) of the sphere draw the radii OA, OB, OC,... | |
 | Benjamin Peirce - Geometry - 1847 - 204 pages
...AB, AC, BC ; and, therefore, each of these arcs is less than the sum of the other two. 439. Theorem. The sum of the sides of a spherical polygon is less than the circumference of a great circle. Sum of the Sides of a Spherical Polygon. Proof. From the centre O (fig. 180) of the sphere draw the... | |
 | Charles William Hackley - Geometry - 1847 - 248 pages
...Show how to construct a spherical triangle with any three parts given. 10. Prove that the sum of all the sides of a spherical polygon is less than the circumference of a great circle. 11. Make a sphere pass through four given points, or prove that every tetrahedron may he circumscribed... | |
 | 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 AB, BC, CD, DA be less than the circumference... | |
 | Elias Loomis - Conic sections - 1857 - 242 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 tIia circumference of a great circle. Let ABCD be any spherical polygon ; then will the sum of the... | |
 | 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 AB, BC, CD, DA be less than the... | |
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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 spherical triangle is greater than 180° and less tha'n 540°. 
