 A spherical angle is measured by the arc of a great circle described from its vertex as a pole, and included between its sides, produced if necessary.  Solid Geometry - Page 440by George C. Shutts - 1913Full view - About this book
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...circles, is equal to that formed by the tangents to these arcs at their point of intersection, and is measured by the arc of a great circle described from the vertex as a pole, and limited by the sides, produced if necesxar1/. Let the angle BAC bo formed by the two... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...between two intersecting arcs of great circles on the surface of a sphere. PROPOSITION XI. THEOREM. 648. A spherical angle is measured by the arc of a great circle described icith its vertex as a pole, included between its sides produced if necessary. Let ABC and AB'C be two... | |
 | George Albert Wentworth - 1887 - 346 pages
...the angles made by the planes of the sides. Each angle is also measured by the number of degrees in the arc of a great circle, described from the vertex of the angle as a pole, and included between its sides. The sides may have any values from 0° to 360° ; but in this work only... | |
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...important propositions may be given, which illustrate this branch of Geometry. Proposition 7. Theorem. 698. A spherical angle is measured by the arc of a great circle described with its vertex as a pole and included between its sides, produced if necessary. Hyp. Let ABC, AB'C... | |
 | George Albert Wentworth - Geometry - 1892 - 468 pages
...curves are arcs of great circles, the angle is called a spherical angle. PROPOSITION X. THEOREM. 722. A spherical angle is measured by the arc of a great circle described from its vertex as a pole and included between its sides (produced if necessary). Let AB, AC be arcs of... | |
 | Arthur Latham Baker - Geometry, Solid - 1893 - 154 pages
...they will be equivalent to^bke^sum of two triangles minus a third. PROPOSITION VII. THEOREM. *\ 263. A spherical angle is measured by the arc of a great circle described from its vertex as a pole and included between its sides (produced if necessary). Notation. Let AB, AC be... | |
 | William C. Bartol - Geometry, Solid - 1893 - 106 pages
...circle described from its vertex as a pole, included between its sides produced if necessary. Let BB' be the arc of a great circle described from the vertex of the spherical angle BAB' as a pole, included between BA and B'A, the sides of the angle ; then will BB'... | |
 | George Clinton Shutts - Geometry - 1894 - 412 pages
...intersect in the circumference of a circle. The spheres intersect in a circle. PROPOSITION XV. 655. Theorem. A spherical angle is measured by the arc of a great circle described from the intersection of the arcs as a pole and intercepted between them. Let MS and NS represent two arcs of... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 522 pages
...PROPOSITION XVII. A spherical angle is equal to the dihedral angle formed by the planes of the two arcs, and is measured by the arc of a great circle described from the intersection of the arcs as a pole, and intercepted between them. PROPOSITION XVIII. Two symmetrical... | |
 | George Albert Wentworth - Navigation - 1895 - 436 pages
...the angles made by the planes of the sides. Each angle is also measured by the number of degrees in the arc of a great circle, described from the vertex of the angle as a pole, and included between its sides. The sides may have any values from 0° to 360°; but in this work only... | |
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