# Elements of Trigonometry, Plane and Spherical: Adapted to the Present State of Analysis : to which is Added, Their Application to the Principles of Navigation and Nautical Astronomy : with Logarithmic, Trigonometrical, and Nautical Tables, for Use of Colleges and Academies

Wiley & Putnam, 1838 - 307 sider

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 ARTICLE Page 28 Values of the cotangent 24 Algebraic notation of the trigonometrical lines 25 Expression for the secant 27 Relation of tangent and cotangent 28 39 40 and 41 Applications of these formulae 31 Advantage of logarithms 35 Logarithms of the base and unity 36 Method of calculating tables of logarithms 37
 ARticlf Page 96 Definitions 125 Plane sailing 129 Traverse sailing 132 Parallel sailing 138 Middle latitude sailing 141 Mercators sailing 145 Example of the last 147 NAUTICAL ASTRONoMY 103 Introductory 149

### Populĉre avsnitt

Side 201 - 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.
Side 78 - In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Side 35 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
Side 14 - SINE of an arc, or of the angle measured by that arc, is the perpendicular let fall from one extremity of the arc, upon the diameter passing through the other extremity. The COSINE is the distance from the centre to the foot of the sine.
Side 66 - FH is the sine of the arc GF, which is the supplement of AF, and OH is its cosine ; hence, the sine of an arc is equal to the. sine of its supplement ; and the cosine of an arc is equal to the cosine of its supplement* Furthermore...
Side 193 - Given the Angles of Elevation of Any Distant object, taken at Three places in a Horizontal Right Line, which does not pass through the point directly below the object ; and the Respective Distances between the stations ; to find the Height of the Object, and its Distance from either station. Let...
Side 162 - S"Z and declination S"E, and it is north. We have here assumed the north to be the elevated pole, but if the south be the elevated pole, then we must write south for north, and north for south. Hence the following rule for all cases. Call the zenith distance north or south, according as the zenith is north or south of the object. If the zenith distance and declination be of the same name, that is, both north or both south, their sum will be the latitude ; but, if of different names, their difference...
Side 1 - NB In the following table, in the last nine columns of each page, where the first or leading figures change from 9's to O's, points or dots are introduced instead of the O's...
Side 151 - ... the surface of the celestial sphere. The Zenith of an observer is that pole of his horizon which is exactly above his head. Vertical Circles are great circles passing through the zenith of an observer, and perpendicular to his horizon.
Side 143 - Then, along the horizontal line, and under the given difference of latitude, is inserted the proper correction to be added to the middle latitude to obtain the latitude in which the meridian distance is accurately equal to the departure. Thus, if the middle latitude be 37°, and the difference of latitude 18°, the correction will be found on page 94, and is equal to 0° 40'. EXAMPLES. 1. A ship, in latitude 51° 18...