Spherical Trigonometry ... |
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Page 79
... terms involving r2 , and it will be seen that we are thus able to carry the approximations in the following article so far as terms involving ra . - 113. To find an approximate value of the error in ON CERTAIN APPROXIMATE FORMULE . 79.
... terms involving r2 , and it will be seen that we are thus able to carry the approximations in the following article so far as terms involving ra . - 113. To find an approximate value of the error in ON CERTAIN APPROXIMATE FORMULE . 79.
Page 80
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- note the spherical ...
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- note the spherical ...
Page 86
... error is approximately a2 + ß2 + y2 of the former area , and this denoted by the fraction 24r2 fraction is less than 0001 , if the sides do not exceed 100 miles in length . Or again , suppose we want to estimate the influence of errors ...
... error is approximately a2 + ß2 + y2 of the former area , and this denoted by the fraction 24r2 fraction is less than 0001 , if the sides do not exceed 100 miles in length . Or again , suppose we want to estimate the influence of errors ...
Page 87
... 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 88
... error of c is approximately a sin B a sin C cos A SC + SB . sin2 A sin2 A Similarly the error of b is approximately a sin C a sin B cos A SB + ISC . sin2 A sin2 A Now it is impossible to assign exactly the signs and magnitudes of the errors ...
... error of c is approximately a sin B a sin C cos A SC + SB . sin2 A sin2 A Similarly the error of b is approximately a sin C a sin B cos A SB + ISC . sin2 A sin2 A Now it is impossible to assign exactly the signs and magnitudes of the errors ...
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Common terms and phrases
A+B+C ambiguity angular points approximately bisecting Cambridge centre circular measure cloth cos b cos cos² cos³ cosine Crown 8vo deduce denote drawn equal angles equilateral example expressed Fcap formulæ formulæ of Art greater Hence hypothenuse inscribed Legendre's Theorem less Let ABC lune meet middle point Napier's analogies Napier's Rules obtained octahedron opposite angle opposite sides parallelopiped perpendicular plane angles plane triangle Plane Trigonometry polar triangle pole polygon preceding article primitive triangle prove quadrant R₁ r₂ radius regular polyhedron respectively right angle right-angled triangles Second Edition shew shewn sides and angles Similarly sin b cos sin b sin sin² sin³ sine solid angle sphere spherical excess spherical triangle Spherical Trigonometry subtended Suppose surface tangent tetrahedron Treatise triangle ABC Trigono Trinity College values π π
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