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 3
... direction , terminating it at the arc before described , and it will be the line required . Another line of 42 being measured from the scale and laid down upon the paper , the two lines will be in the ratio of 56 to 42. If they are ...
... direction , terminating it at the arc before described , and it will be the line required . Another line of 42 being measured from the scale and laid down upon the paper , the two lines will be in the ratio of 56 to 42. If they are ...
Page 19
... direction to that of the tangent of an arc in the first quadrant , is negative . When the arc is 180 ° , the negative tangent which became shorter and short- M Thus A T is A T er , as the second extremity of the arc approached this ...
... direction to that of the tangent of an arc in the first quadrant , is negative . When the arc is 180 ° , the negative tangent which became shorter and short- M Thus A T is A T er , as the second extremity of the arc approached this ...
Page 19
... direction . he principle which it is necessary to observe , we have before spoken , the secant must in these considered as negative . In the fourth quadrant again estimated towards the second extremity of s therefore positive . al ...
... direction . he principle which it is necessary to observe , we have before spoken , the secant must in these considered as negative . In the fourth quadrant again estimated towards the second extremity of s therefore positive . al ...
Page 21
... direction . According to the principle which it is necessary to observe , and of which we have before spoken , the secant must in these quadrants be considered as negative . In the fourth quadrant the secant is again estimated towards ...
... direction . According to the principle which it is necessary to observe , and of which we have before spoken , the secant must in these quadrants be considered as negative . In the fourth quadrant the secant is again estimated towards ...
Page 22
... directions in these two cases must have opposite signs . It is therefore positive in the 1st and 4th quadrants , and negative in the 2d and 3d . It will be recollected that the positive were separated from the negative secants , as the ...
... directions in these two cases must have opposite signs . It is therefore positive in the 1st and 4th quadrants , and negative in the 2d and 3d . It will be recollected that the positive were separated from the negative secants , as the ...
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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...