Spherical Trigonometry, for the Use of Colleges and Schools: With Numerous Examples |
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Page 13
... + π - B + π- C is less than 2π ; A + B + C is greater than π . And since each of the angles A , B , C is less than A + B + C is less than 3π . c ' π , the sum 33. The angles at the base of an isosceles spherical SPHERICAL GEOMETRY . 13.
... + π - B + π- C is less than 2π ; A + B + C is greater than π . And since each of the angles A , B , C is less than A + B + C is less than 3π . c ' π , the sum 33. The angles at the base of an isosceles spherical SPHERICAL GEOMETRY . 13.
Page 14
... base of the spherical triangle . The figure supposes AC and BC to be less than quadrants ; if they are greater than quadrants the tangents to AC and BC will meet on CO produced through O instead of through C , and the demonstration may ...
... base of the spherical triangle . The figure supposes AC and BC to be less than quadrants ; if they are greater than quadrants the tangents to AC and BC will meet on CO produced through O instead of through C , and the demonstration may ...
Page 28
... bases will be equal . We may shew that the bases are equal by applying the first formula in Art . 39 to each triangle ... base of that which has the greater angle will be greater than the 28 RELATIONS BETWEEN THE TRIGONOMETRICAL FUNCTIONS.
... bases will be equal . We may shew that the bases are equal by applying the first formula in Art . 39 to each triangle ... base of that which has the greater angle will be greater than the 28 RELATIONS BETWEEN THE TRIGONOMETRICAL FUNCTIONS.
Page 29
... base of the other ; and conversely . Let b and c denote the sides which are equal in the two tri- angles ; let a be the base and A the opposite angle of one triangle , and a ' and A ' similar quantities for the other . Then cos a = cos ...
... base of the other ; and conversely . Let b and c denote the sides which are equal in the two tri- angles ; let a be the base and A the opposite angle of one triangle , and a ' and A ' similar quantities for the other . Then cos a = cos ...
Page 46
... base , the triangle is divided into two equal right - angled triangles ; by the solution of one of these right - angled triangles the required elements can be found . ( 3 ) Suppose among the given elements of a triangle there are two ...
... base , the triangle is divided into two equal right - angled triangles ; by the solution of one of these right - angled triangles the required elements can be found . ( 3 ) Suppose among the given elements of a triangle there are two ...
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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.