## 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 (Google eBook) |

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### Common terms and phrases

annexed apparent altitude applied arcs is equal arith becomes called celestial sphere centre circle circumference column marked common logarithm comp complement correction cosecant Cosine Sine cotangent decimal declination departure determine diagram diff difference of latitude difference of longitude divided ecliptic equation EXAMPLE expressed figures formula Geom given number given side Greenwich half the sum hence horizon hour angle hypothenuse included angle meridian meridian altitude method middle latitude miles multiply Napier's rules Nautical Almanac number of degrees observed altitude obtained parallax parallel parallel sailing perpendicular plane sailing plane triangle pole Prop proportion quadrant quantity quotient radius right angled triangle right ascension sailing secant second member semidiameter ship side opposite sine and cosine solution spherical triangle spherical trigonometry substituting subtract Tang tangent three sides tion trigonometrical lines true altitude tude

### Popular passages

Page 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.

Page 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.

Page 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.

Page 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.

Page 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...

Page 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...

Page 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...

Page 209 - 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...

Page 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.

Page 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...