Spherical Trigonometry: For the Use of Colleges and SchoolsMacmillan and Company, 1863 - 132 σελίδες |
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Σελίδα 74
... regular polygon of a given number of sides formed by arcs of great circles on the surface of a sphere ; and hence deduce that , if a be the angular radius of a small circle , its area is to that of the whole surface of the sphere as ...
... regular polygon of a given number of sides formed by arcs of great circles on the surface of a sphere ; and hence deduce that , if a be the angular radius of a small circle , its area is to that of the whole surface of the sphere as ...
Σελίδα 98
... regular when its faces are similar and equal regular polygons , and its solid angles equal to one another . 133. If S be the number of solid angles in any polyhedron , F the number of its faces , E the number of its edges , then S + FE ...
... regular when its faces are similar and equal regular polygons , and its solid angles equal to one another . 133. If S be the number of solid angles in any polyhedron , F the number of its faces , E the number of its edges , then S + FE ...
Σελίδα 99
... regular polyhedron derives its name from the number of its plane faces . m 20 S E F Name of regular Polyhedron . 3 3 4 6 4 Tetrahedron or regular Pyramid . 4 3 8 12 6 Hexahedron or Cube . 3 4 6 12 8 Octahedron . 20 5 3 20 30 12 ...
... regular polyhedron derives its name from the number of its plane faces . m 20 S E F Name of regular Polyhedron . 3 3 4 6 4 Tetrahedron or regular Pyramid . 4 3 8 12 6 Hexahedron or Cube . 3 4 6 12 8 Octahedron . 20 5 3 20 30 12 ...
Σελίδα 100
... regular polyhedron . a B E Let AB be the edge common to the two adjacent faces , C and D the centres of the faces ; bisect AB at E , and join CE and DE ; CE and DE will be perpendicular to AB , and the angle CED is the angle of ...
... regular polyhedron . a B E Let AB be the edge common to the two adjacent faces , C and D the centres of the faces ; bisect AB at E , and join CE and DE ; CE and DE will be perpendicular to AB , and the angle CED is the angle of ...
Σελίδα 101
... regular polyhedron . Let the edge AB = a , let OC = r and OA = R , so that r is the radius of the inscribed sphere , and R the radius of the circumscribed sphere . Then CEAE cot ACE = α π cot 9 2 m I r = CE tan CEO = CE tan - a π I 2 ...
... regular polyhedron . Let the edge AB = a , let OC = r and OA = R , so that r is the radius of the inscribed sphere , and R the radius of the circumscribed sphere . Then CEAE cot ACE = α π cot 9 2 m I r = CE tan CEO = CE tan - a π I 2 ...
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a+b+c angular points approximately bisecting calculated centre circle described circular measure cos b cos cos² cos³ cosb cosines Crown 8vo deduce denote equal equation Fcap Fellow of St formed formulæ given greater Hence inscribed John's College late Fellow less Let ABC limp cloth lune M.A. Fellow middle point Napier's analogies Napier's Rules obtain perpendicular plane triangle Plane Trigonometry polar triangle pole polygon preceding article primitive triangle quadrant radius regular polyhedron respectively right angles right-angled triangles School Second Edition Sermons preached shew shewn Similarly sin b sin sin² sin³ sine small circle solid angle solution sphere spherical excess spherical triangle Spherical Trigonometry St John's College suppose surface tangent tetrahedron Third Edition Treatise triangle ABC Trinity College University of Cambridge values vols
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