Spherical Trigonometry, for the Use of Colleges and Schools: With Numerous Examples |
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Page 29
... elements of Co - ordinate Geometry . Suppose ABC any spherical triangle , O the centre of the sphere , take O as the origin of co - ordinates , and let the axis of z pass through C. Let x , y , z , be the co - ordinates of A , and x , y ...
... elements of Co - ordinate Geometry . Suppose ABC any spherical triangle , O the centre of the sphere , take O as the origin of co - ordinates , and let the axis of z pass through C. Let x , y , z , be the co - ordinates of A , and x , y ...
Page 32
... elements , namely , the three sides and the three angles , besides the radius of the sphere , which is supposed ... elements are given , we calculate the values of the remaining elements . It will appear , as we proceed , that when the ...
... elements , namely , the three sides and the three angles , besides the radius of the sphere , which is supposed ... elements are given , we calculate the values of the remaining elements . It will appear , as we proceed , that when the ...
Page 38
... elements of the triangle ABC as usual by a , b , c , A , B , we have in the triangle AED the hypotenuse equal to -b , the angles equal to A and to π - П 2 π as a , and the sides respectively opposite these angles equal B and 2 - C. The ...
... elements of the triangle ABC as usual by a , b , c , A , B , we have in the triangle AED the hypotenuse equal to -b , the angles equal to A and to π - П 2 π as a , and the sides respectively opposite these angles equal B and 2 - C. The ...
Page 39
... elements of the triangle BAC taken in order , beginning with the hypotenuse and omitting the right angle ; then the elements of the triangle AED taken in order , beginning with the hypotenuse and omitting the right angle , are π П α π π ...
... elements of the triangle BAC taken in order , beginning with the hypotenuse and omitting the right angle ; then the elements of the triangle AED taken in order , beginning with the hypotenuse and omitting the right angle , are π П α π π ...
Page 46
... elements can be found . ( 3 ) Suppose among the given elements of a triangle there are two sides , one of which is the supplement of the other , or two angles , one of which is the supplement of the other . Suppose , for example , that ...
... elements can be found . ( 3 ) Suppose among the given elements of a triangle there are two sides , one of which is the supplement of the other , or two angles , one of which is the supplement of the other . Suppose , for example , that ...
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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.