Spherical Trigonometry, for the Use of Colleges and Schools: With Numerous Examples |
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Page 82
With Numerous Examples Isaac Todhunter. 113. To find an approximate value of the error in the length of a side of a spherical triangle when calculated by Legendre's Theorem . Suppose the side ẞ known and the side a required ; let 3μ de ...
With Numerous Examples Isaac Todhunter. 113. To find an approximate value of the error in the length of a side of a spherical triangle when calculated by Legendre's Theorem . Suppose the side ẞ known and the side a required ; let 3μ de ...
Page 89
... errors of the observations is 1 " 23. This total error may be distributed among the observed angles in such proportion as the opinion of the observer may suggest ; one way is to increase each of the observed angles by one - third of 1 ...
... errors of the observations is 1 " 23. This total error may be distributed among the observed angles in such proportion as the opinion of the observer may suggest ; one way is to increase each of the observed angles by one - third of 1 ...
Page 91
... error is made , in a second observation the same numerical error is made but with an opposite sign , and in the remaining observation no error is made . 126. We have hitherto proceeded on the supposition that the Earth is a sphere ; it ...
... error is made , in a second observation the same numerical error is made but with an opposite sign , and in the remaining observation no error is made . 126. We have hitherto proceeded on the supposition that the Earth is a sphere ; it ...
Page 93
... error will be introduced into one of the calculated parts of a triangle by reason of any small error which may exist in the given parts . We will here consider an example , 129. A side and the opposite angle of a spherical triangle ...
... error will be introduced into one of the calculated parts of a triangle by reason of any small error which may exist in the given parts . We will here consider an example , 129. A side and the opposite angle of a spherical triangle ...
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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.