Spherical Trigonometry, for the Use of Colleges and Schools: With Numerous Examples |
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Page 18
... b cos c + sin b sin c cos A , cos b = cos c cos a + sin c sin a cos B , cos c = cos a cos b + sin a sin b cos C. These may be considered as the fundamental equations of Spheri- 18 RELATIONS BETWEEN THE TRIGONOMETRICAL FUNCTIONS.
... b cos c + sin b sin c cos A , cos b = cos c cos a + sin c sin a cos B , cos c = cos a cos b + sin a sin b cos C. These may be considered as the fundamental equations of Spheri- 18 RELATIONS BETWEEN THE TRIGONOMETRICAL FUNCTIONS.
Page 19
With Numerous Examples Isaac Todhunter. These may be considered as the fundamental equations of Spheri- cal Trigonometry ; we shall proceed to deduce various formulæ from them . 40. To express the sine of an angle of a spherical triangle ...
With Numerous Examples Isaac Todhunter. These may be considered as the fundamental equations of Spheri- cal Trigonometry ; we shall proceed to deduce various formulæ from them . 40. To express the sine of an angle of a spherical triangle ...
Page 67
... considered as a lune with an angle equal to four right angles , we have for a lune with an angle of which the circular measure is A , Suppose area of lune surface of sphere = A · 2π the radius of the sphere , then the surface is 4πr2 ...
... considered as a lune with an angle equal to four right angles , we have for a lune with an angle of which the circular measure is A , Suppose area of lune surface of sphere = A · 2π the radius of the sphere , then the surface is 4πr2 ...
Page 78
... considered equal to the area of the plane triangle which can be formed with sides of the same length . 107. Legendre's Theorem may be used for the approximate solution of spherical triangles in the following manner . ( 1 ) Suppose the ...
... considered equal to the area of the plane triangle which can be formed with sides of the same length . 107. Legendre's Theorem may be used for the approximate solution of spherical triangles in the following manner . ( 1 ) Suppose the ...
Page 86
... considered known very approximately ; let this radius be denoted by r , then if a be the length of any arc the circular measure of the angle which the arc subtends at the centre of the earth is a The formulæ of Spherical Trigonometry ...
... considered known very approximately ; let this radius be denoted by r , then if a be the length of any arc the circular measure of the angle which the arc subtends at the centre of the earth is a The formulæ of Spherical Trigonometry ...
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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.