Spherical Trigonometry, for the Use of Colleges and Schools: With Numerous Examples |
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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 SPHERICAL TRIANGLES . Spherical Triangles.
... 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 SPHERICAL TRIANGLES . Spherical Triangles.
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 114
... 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 . 150. 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 . 150. If S be the number of solid angles in any polyhedron , F the number of its faces , E the ...
Page 116
... faces is ( m - 2 ) π , that is Σmπ - 2FT , that is 2 ( E - F ) , that is 2 ( S - 2 ) . 153. To find the inclination of two adjacent faces of a regular polyhedron . a B E Let AB be the edge common to the two adjacent faces , C and D the ...
... faces is ( m - 2 ) π , that is Σmπ - 2FT , that is 2 ( E - F ) , that is 2 ( S - 2 ) . 153. To find the inclination of two adjacent faces of a regular polyhedron . a B E Let AB be the edge common to the two adjacent faces , C and D the ...
Page 117
... face of the polyhedron is cot m Fa2 π 4 therefore the surface of the polyhedron is cot • m , .and m Also the volume of the pyramid which has one face of the polyhedron for base and O for vertex is therefore the volume of the polyhedron ...
... face of the polyhedron is cot m Fa2 π 4 therefore the surface of the polyhedron is cot • m , .and m Also the volume of the pyramid which has one face of the polyhedron for base and O for vertex is therefore the volume of the polyhedron ...
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Common terms and phrases
ambiguity angular points approximately arcs drawn arcs which join bisecting centre circular measure cos a cos cos² cos³ cosb cosines Crown 8vo deduce denote equation equilateral escribed circles example expression faces fixed points formulæ formulæ of Art greater Hence inscribed Legendre's Theorem less Let ABC lune meet middle point Napier's analogies Napier's Rules obtain octahedron opposite angle opposite sides parallelepiped Plane Geometry plane triangle Plane Trigonometry polar triangle pole polygon position preceding Article primitive triangle quadrant r₁ regular polyhedron respectively result right angles right-angled triangles shew shewn Similarly sin b cos sin b sin sin² sin³ sine small circle described solid angles solution sphere spherical excess spherical triangle Spherical Trigonometry ß³ straight lines subtended suppose surface tangent tetrahedron Trigono
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 49 - B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G.
Page 12 - Any two sides of a spherical triangle are together greater than the third side.
Page 19 - Thus the sines of the angles of a spherical triangle are proportional to the sines of the opposite sides.
Page 30 - From this proposition, it is obvious that if one angle of a triangle be equal to the sum of the other two angles, that angle is a right angle, as is shewn in Euc.
Page 1 - A sphere is a solid bounded by a surface, every point of which is equally distant from a fixed point called the centre.
Page 62 - A circle which touches one side of a triangle and the other two sides produced, is called an escribed circle of the triangle.
Page 15 - If one angle of a spherical triangle be greater than another, the side opposite the greater angle is greater than the side opposite the less angle.