Spherical Trigonometry, for the Use of Colleges and Schools: With Numerous Examples |
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Page 1
... solid bounded by a surface every point of which is equally distant from a fixed point which is called the centre of ... angle OCD is a right angle ; therefore CD = √ ( OD- OC ) . Now O and C are fixed points , so that OC is constant ...
... solid bounded by a surface every point of which is equally distant from a fixed point which is called the centre of ... angle OCD is a right angle ; therefore CD = √ ( OD- OC ) . Now O and C are fixed points , so that OC is constant ...
Page 6
... angles of the plane 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.
... angles of the plane 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 7
... solid angle will cut the sphere in arcs of great circles . Thus a figure will be formed on the surface of the sphere ... angles . If the solid angle be formed by the meeting of more than three plane angles , the corresponding figure on ...
... solid angle will cut the sphere in arcs of great circles . Thus a figure will be formed on the surface of the sphere ... angles . If the solid angle be formed by the meeting of more than three plane angles , the corresponding figure on ...
Page 8
... angle radius OA AOB so long as we keep to the same sphere . The angles of a spherical triangle are the inclinations of the plane faces which form the solid angle ; for since Ab and Ac are both perpendicular to OA , the angle bAc is the ...
... angle radius OA AOB so long as we keep to the same sphere . The angles of a spherical triangle are the inclinations of the plane faces which form the solid angle ; for since Ab and Ac are both perpendicular to OA , the angle bAc is the ...
Page 12
... angles and the sides of a spherical triangle , all expressed in circular ... solid angle at O are together greater than the third ( Euclid , x1 . 20 ) ... angles which form 12 SPHERICAL GEOMETRY .
... angles and the sides of a spherical triangle , all expressed in circular ... solid angle at O are together greater than the third ( Euclid , x1 . 20 ) ... angles which form 12 SPHERICAL GEOMETRY .
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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.