 | Harvard University - Geometry - 1899 - 39 pages
...described from its vertex as a pole and included between its sides (produced if necessary). Corollary. All arcs of great circles drawn through the pole of...great circle are perpendicular to its circumference. SPHERICAL TRIANGLES AND POLYGONS. THEOREM VIII. If the first of two spherical triangles is the polar... | |
 | William James Milne - Geometry - 1899 - 398 pages
...intersection. 682. The angle between two intersecting arcs of great circles is called a Spherical Angle. 683. A portion of the surface of a sphere bounded by three or more arcs of greaI circles is called a Spherical Polygon. The bounding arcs arc the sides of the polygon ; the angles... | |
 | Arthur Schultze - 1901 - 392 pages
...But Z AOB is measured by arc AB. Hence Z DPE is measured by arc AB. QED SPHERICAL POLYGONS 710. DBF. A spherical polygon is a portion of the surface of...sphere bounded by three or more arcs of great circles. The arcs are the sides, their points of intersection are the vertices, and the spherical angles formed... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...arc AB. Hence Z DPE is measured by arc AB. QED 336 SPHERICAL POLYGONS SPHERICAL POLYGONS 710. DBF. A spherical polygon is a portion of the surface of...sphere bounded by three or more arcs of great circles. The arcs are the sides, their points of intersection are the vertices, and the spherical angles formed... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...equal to the plane angle of the diedral angle formed by their planes. SPHERICAL POLYGONS 710. DBF. A spherical polygon is a portion of the surface of...sphere bounded by three or more arcs of great circles. The arcs are the sides, their points of intersection are the vertices, and the spherical angles formed... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...vertex of the angle is the pole, intercepted between the given arcs (produced if necessary). § 615. (3) All arcs of great circles drawn through the pole of a given great circle are perpendicular to the given great circle. § 616. (4) No side of a convex spherical polygon can be greater than a semicircle.... | |
 | George Albert Wentworth - Geometry, Solid - 1902 - 248 pages
...circle (§ 779), the Z ABE is a right angle. Therefore, the arc AB is -L to the arc, CHD. QEF 782. DBF. A spherical polygon is a portion of the surface of...sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon; the angles between the sides are-the angles of the... | |
 | William Chauvenet - 1905 - 336 pages
...described from its vertex as a pole and included between its sides (produced if necessary). Corollary. All arcs of great circles drawn through the pole of...great circle are perpendicular to its circumference. PROPOSITION X. If the first of two spherical triangles is the polar triangle of the second, then, reciprocally,... | |
 | Daniel Alexander Murray - 1906 - 466 pages
...great circle is meant, unless expressly stated otherwise. ON SPHERICAL TRIANGLES. 12. Definitions. A spherical polygon is a portion of the surface of...sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the points of intersection of the sides are the vertices... | |
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...angle of the diedral angle formed by the planes of the two circles. SPHERICAL POLYGONS. DEFINITIONS 787 A spherical polygon is a portion of the surface of...sphere bounded by three or more arcs of great circles. The sides of a spherical polygon are the bounding arcs ; the vertices are the points in which the sides... | |
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A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the... 
