Spherical Trigonometry ... |
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Page 6
... faces which form a solid angle and the angles at which the plane faces are inclined to each other . 16. Suppose that the angular point of a solid angle is made the centre of a sphere ; then the planes which form the solid angle will cut ...
... faces which form a solid angle and the angles at which the plane faces are inclined to each other . 16. Suppose that the angular point of a solid angle is made the centre of a sphere ; then the planes which form the solid angle will cut ...
Page 8
... faces which form the solid angle ; for since Ab and Ac are both perpendicular to OA , the angle bAc is the angle of inclination of the planes OAB and OAC . 20. The letters A , B , C are generally used to denote the angles of a spherical ...
... faces which form the solid angle ; for since Ab and Ac are both perpendicular to OA , the angle bAc is the angle of inclination of the planes OAB and OAC . 20. The letters A , B , C are generally used to denote the angles of a spherical ...
Page 96
... faces . A polyhedron is said to be 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 ...
... faces . A polyhedron is said to be 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 ...
Page 97
... face of a regular poly- hedron , n the number of plane angles in each solid angle ; then the entire number of plane ... faces . m n SE F Name of regular Polyhedron . 3 3 4 CO 6 4 Tetrahedron or regular Pyramid . 4 3 8 12 6 Hexahedron or ...
... face of a regular poly- hedron , n the number of plane angles in each solid angle ; then the entire number of plane ... faces . m n SE F Name of regular Polyhedron . 3 3 4 CO 6 4 Tetrahedron or regular Pyramid . 4 3 8 12 6 Hexahedron or ...
Page 98
... faces is Σ ( m2 ) π , that is Σmπ 2 ( E - F ) , that is 2 ( S - 2 ) . - 2FT , that is 136. To find the inclination of two adjacent faces of a regular polyhedron . a 0 e B A Let AB be the edge common to the two adjacent faces , C and D ...
... faces is Σ ( m2 ) π , that is Σmπ 2 ( E - F ) , that is 2 ( S - 2 ) . - 2FT , that is 136. To find the inclination of two adjacent faces of a regular polyhedron . a 0 e B A Let AB be the edge common to the two adjacent faces , C and D ...
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Common terms and phrases
A+B+C ambiguity angular points approximately bisecting Cambridge centre circular measure cloth cos b cos cos² cos³ cosine Crown 8vo deduce denote drawn equal angles equilateral example expressed Fcap formulæ formulæ of Art greater Hence hypothenuse inscribed Legendre's Theorem less Let ABC lune meet middle point Napier's analogies Napier's Rules obtained octahedron opposite angle opposite sides parallelopiped perpendicular plane angles plane triangle Plane Trigonometry polar triangle pole polygon preceding article primitive triangle prove quadrant R₁ r₂ radius regular polyhedron respectively right angle right-angled triangles Second Edition shew shewn sides and angles Similarly sin b cos sin b sin sin² sin³ sine solid angle sphere spherical excess spherical triangle Spherical Trigonometry subtended Suppose surface tangent tetrahedron Treatise triangle ABC Trigono Trinity College values π π
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