Spherical Trigonometry, for the Use of Colleges and Schools: With Numerous Examples |
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Page 12
... remain true when the angles are changed into the supplements of the corresponding sides and the sides into the supplements of the corresponding angles . We shall see several examples of this principle in the next Chapter . 29. Any two ...
... remain true when the angles are changed into the supplements of the corresponding sides and the sides into the supplements of the corresponding angles . We shall see several examples of this principle in the next Chapter . 29. Any two ...
Page 23
... remain true when the angles and sides are changed into the supplements of the cor- responding sides and angles respectively ; it will be found , how- ever , that no new formulæ are thus obtained , but only the same formulæ over again ...
... remain true when the angles and sides are changed into the supplements of the cor- responding sides and angles respectively ; it will be found , how- ever , that no new formulæ are thus obtained , but only the same formulæ over again ...
Page 32
... remain- ing three can generally be found . We begin with the right - angled triangle : here two elements , in addition to the right angle , will be supposed known . 62. The formulæ requisite for the solution of right - 32 SOLUTION OF ...
... remain- ing three can generally be found . We begin with the right - angled triangle : here two elements , in addition to the right angle , will be supposed known . 62. The formulæ requisite for the solution of right - 32 SOLUTION OF ...
Page 93
... remain constant : determine the connexion between the small varia- tions of any other pair of elements , Suppose C and c to remain constant . ( 1 ) Required the connexion between the small variations of the other sides . We suppose a ...
... remain constant : determine the connexion between the small varia- tions of any other pair of elements , Suppose C and c to remain constant . ( 1 ) Required the connexion between the small variations of the other sides . We suppose a ...
Page 95
... remain constant while a and b receive the small increments Sa and 86 respectively , shew that δα - √ ( 1 − n2 sin3 a ) - бъ √ ( 1 − n2 sin3 b ) = 0 where n = · sin C sin c 2. If C and c remain constant , and a small change be made ...
... remain constant while a and b receive the small increments Sa and 86 respectively , shew that δα - √ ( 1 − n2 sin3 a ) - бъ √ ( 1 − n2 sin3 b ) = 0 where n = · sin C sin c 2. If C and c remain constant , and a small change be made ...
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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.