Spherical Trigonometry, for the Use of Colleges and Schools: With Numerous Examples |
From inside the book
Results 1-5 of 7
Page 30
... supplement of the remaining angle ; or else that the triangle has two quadrants and two right angles , and then the remaining side is equal to the remaining angle . α In an equilateral triangle , shew that 2 cos 30 EXAMPLES .
... supplement of the remaining angle ; or else that the triangle has two quadrants and two right angles , and then the remaining side is equal to the remaining angle . α In an equilateral triangle , shew that 2 cos 30 EXAMPLES .
Page 31
... equilateral triangle are restricted . 8. In an equilateral triangle , shew that sec A = 1 + sec a . 9. If the three sides of a spherical triangle be halved and a new triangle formed , the angle b b between the new sides and 02 с is ...
... equilateral triangle are restricted . 8. In an equilateral triangle , shew that sec A = 1 + sec a . 9. If the three sides of a spherical triangle be halved and a new triangle formed , the angle b b between the new sides and 02 с is ...
Page 66
... equilateral triangle tan R = 2 tan r . 9 . If ABC be an equilateral spherical triangle , P the pole of the circle circumscribing it , Q any point on the sphere , shew that cos QA + cos QB + cos QC = 3 cos PA cos PQ . 10. If three small ...
... equilateral triangle tan R = 2 tan r . 9 . If ABC be an equilateral spherical triangle , P the pole of the circle circumscribing it , Q any point on the sphere , shew that cos QA + cos QB + cos QC = 3 cos PA cos PQ . 10. If three small ...
Page 73
... equilateral triangle whose area is one - fourth of that of the sphere on which it is described . 2. Find the surface of an equilateral and equiangular sphe- rical polygon of n sides , and determine the value of each of the angles when ...
... equilateral triangle whose area is one - fourth of that of the sphere on which it is described . 2. Find the surface of an equilateral and equiangular sphe- rical polygon of n sides , and determine the value of each of the angles when ...
Page 84
... equilateral triangle ABC , and P any point on the surface of the sphere , then ( tan PO tan QA ) ( cos PA + cos PB + cos PC ) 2 = cos2PA + cos2PB + cos PC - cosPAcos PB - cosPB cosPC - cosPC cosPA . 8. If ABC be a triangle having each ...
... equilateral triangle ABC , and P any point on the surface of the sphere , then ( tan PO tan QA ) ( cos PA + cos PB + cos PC ) 2 = cos2PA + cos2PB + cos PC - cosPAcos PB - cosPB cosPC - cosPC cosPA . 8. If ABC be a triangle having each ...
Other editions - View all
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.