An Analytical Treatise on Plane and Spherical Trigonometry, and the Analysis of Angular Sections

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John Taylor, 1828 - Plane trigonometry - 317 pages
 

Contents

SECTION III
280
On the summation of certain series of sines cosines c
289
sines of
290
any tract of country involves three problems
294
arithmetical progression
295
sines of x
296
the spherical excess
300
301 To determine the sum of the errors of the angles
301
manner of computing the true angles 302 To determine the base in seconds considered as an
302
of a great circle of the earth 303 Formula by which a small arc of a great circle being
303
given in feet its sine may be found in feet and vice versa 304 Examples illustrative of these principles from
304
French geodetical operations 305 Two other methods by which the calculation of sphe
305
rical triangles is reduced to that of plane triangles 306 First method Theorem of Legendre
306
307 Application of this theorem
307
308 Advantages of Legendres method
308
general theory
309
310 Given two sides a b of a spherical triangle which
310
differ but little from quadrants to compute the difference be tween the included angle c and the opposite side c when the sides a b and either the angl...
311
triangle to determine the angle under the chords of the sides 312 Corrections to be applied in practice
312
313 On the relative practical merits of the three methods
313
for the resolution of geodetical triangles 314 On the signals Day and night signals Axis of
314
its
315
316 Description and manner of using the theodolite
316
317 To investigate the correction necessary for reducing
317
arguments of
318
tables 319 Two corrections necessary to reduce the observed
319
gles to those of a plane triangle joining three points in the axes of the three signals 320 1 To reduce the observed angles to the same plane
320
321 Investigation of the formula by which this correction
321
performed 322 Applications
322
323 2 To reduce the observed angles to the axis of
323
signals 324 Formula for performing this correction
324
325 To determine the mean surface of the earth
325
rods for performing
326
this measurement 327 Bases of verification
327
328 On the spheroidal figure of the earth 329341 Formulæ expressing the various quantities con
328

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