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 |
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Page xi
... included angle being given , the method of solu- tion , with examples , 78 PART II . SPHERICAL TRIGONOMETRY . 77. Definitions and general principles , 81 78. The hypothenuse of a right - angled triangle , being either given or required ...
... included angle being given , the method of solu- tion , with examples , 78 PART II . SPHERICAL TRIGONOMETRY . 77. Definitions and general principles , 81 78. The hypothenuse of a right - angled triangle , being either given or required ...
Page xii
... included angle of a spherical triangle being given to find the third side directly , 201 127. Two angles and the interjacent side being given to find the third angle , 202 128. Rules relative to ambiguous cases , 203 199. Additional ...
... included angle of a spherical triangle being given to find the third side directly , 201 127. Two angles and the interjacent side being given to find the third angle , 202 128. Rules relative to ambiguous cases , 203 199. Additional ...
Page 2
... included angle of a triangle being given , let it be required to find the remaining side and the other two angles . Let A and B be the two given sides , and c the gi- ven included angle . Draw two lines DH and G of indefinite length ...
... included angle of a triangle being given , let it be required to find the remaining side and the other two angles . Let A and B be the two given sides , and c the gi- ven included angle . Draw two lines DH and G of indefinite length ...
Page 4
... included between their sides , the arcs being described with equal radii , and it is also there stated that hence such arcs are properly the measures of angles . So that if an arc included between two sides of one angle be double , or ...
... included between their sides , the arcs being described with equal radii , and it is also there stated that hence such arcs are properly the measures of angles . So that if an arc included between two sides of one angle be double , or ...
Page 5
... included between the sides of the angle , bear the same relation to each other as the radii , . ( Geom . B. 5 , Prop . 11 , Cor . ) and since the entire circumferences are also proportional to their radii , it follows that two ...
... included between the sides of the angle , bear the same relation to each other as the radii , . ( Geom . B. 5 , Prop . 11 , Cor . ) and since the entire circumferences are also proportional to their radii , it follows that two ...
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Other editions - View all
Elements of Trigonometry, Plane and Spherical: Adapted to the Present State ... Charles William Hackley No preview available - 2016 |
Elements of Trigonometry, Plane and Spherical: Adapted to the Present State ... Charles William Hackley No preview available - 2016 |
Common terms and phrases
adjacent apparent altitude applied arith called celestial object celestial sphere centre chord circle colatitude comp complement correction cosecant decimal declination departure determine diff difference of latitude difference of longitude direct course dist divided ecliptic equation EXAMPLE expressed formula Geom given number given side Greenwich hence horizon hour angle hypothenuse included angle meridian altitude method middle latitude miles multiply Napier's rules Nautical Almanac number of degrees observed altitude obtained parallax in altitude parallel parallel sailing perpendicular plane sailing plane triangle polar triangle pole Prop proportion quadrant quantity quotient radius right angled triangle right ascension secant second member semidiameter ship side opposite sin a sin solution spherical triangle spherical trigonometry substituting subtract tance Tang tangent three sides tion trigonometrical lines true altitude tude
Popular passages
Page 199 - 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 76 - 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 33 - 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 64 - 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 191 - 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 160 - 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 207 - 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 149 - ... 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 141 - 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...