 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...the radius of the inscribed sphere. SOLID GEOMETRY PROPOSITION VIII. THEOREM 708. A spherical angle is measured by the arc of a great circle described...included between its sides, produced if necessary. Hyp. DPE is the spherical angle formed by the great circles PAC and PBC. AB is an arc of a great circle... | |
 | 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 - 246 pages
...called a spherical angle. PROPOSITION IX. THEOREM. 779. A spherical angle is measured by the arc of the great circle described from its vertex as a pole and...included between its sides (produced if necessary). Let AB, AC be arcs of great circles intersecting at A; AB' and AC', the tangents to these arcs at A;... | |
 | Education - 1904 - 738 pages
...of a cone is a circle, every section parallel to the base is a circle. 6 Prove that a spheric angle is measured by the arc of a great circle described...included between its sides produced if necessary. NOTE — Use w Instead of Its approximate value 3.1410. Second •, Find the surface of a sphere whose... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...called a spherical angle. PROPOSITION IX. THEOREM. 779. A spherical angle is measured by the arc of the great circle described from its vertex as a pole and...included between its sides (produced if necessary). Let AB, AC be arcs of great circles intersecting at A; AB' and AC', the tangents to these arcs at A;... | |
 | William Chauvenet - 1905 - 336 pages
...line. PROPOSITION IX. The angle of two arcs of great circles is equal to the angle of their planes, and is measured by the arc of a great circle described...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,... | |
 | Education - 1911 - 946 pages
...sphere may be inscribed in or circumscribed about any given tetrahedron. [H5.] p. A spherical angle is measured by the arc of a great circle described...included between its sides (produced if necessary). [K5.] V. Spherical Triangles and Polygons. (Every theorem stated here may also be stated as n theorem... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...circles of a sphere. PROPOSITION VIII. THEOREM 785 A spherical angle is measured by the arc of the great circle described from its vertex as a pole and...included between its sides, produced if necessary. HYPOTHESIS. PAP' and PBP' are great circles to which PS and PT are tangents at P, and AB is an arc... | |
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...circles of a sphere. PROPOSITION VIII. THEOREM 785 A spherical angle is measured by the arc of the great circle described from its vertex as a pole and...included between its sides, produced if necessary. HYPOTHESIS. PAP' and PBP' are great circles to which PS and PT are tangents at P, and AB is an arc... | |
 | Wisconsin. Department of Public Instruction - Education - 1906 - 124 pages
...at the point. 24. The angle between two arcs of great circles is equal to the angle of their planes and is measured by the arc of a great circle described from its vertex as pole and included between its sides. 25. The sum of two face angles of a trihedral angle is greater... | |
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The angle of two arcs of great circles is equal to the angle of their planes, and is measured by the arc of a great circle described from its vertex as a pole and included between its sides (produced if necessary). 
