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 43
... diff . of logs . 2421 Before explaining other operations by means of logarithms , we shall exhibit some principles derived from those just de- monstrated . 50. The base of the common system being 10 , the common logarithm of 10 is 1 ...
... diff . of logs . 2421 Before explaining other operations by means of logarithms , we shall exhibit some principles derived from those just de- monstrated . 50. The base of the common system being 10 , the common logarithm of 10 is 1 ...
Page 46
... diff . of logs . diff of logs . .000051 diff . of num . :: 42 : X .000051 x 42 X = = .00002142 100 adding this to the logarithm of 843700 which is 5.926188 the sum , rejecting the last two places 42 which go beyond the usual number is ...
... diff . of logs . diff of logs . .000051 diff . of num . :: 42 : X .000051 x 42 X = = .00002142 100 adding this to the logarithm of 843700 which is 5.926188 the sum , rejecting the last two places 42 which go beyond the usual number is ...
Page 47
... diff . of num . 100 : diff . of logs . 000051 :: diff . of num . 42 diff . of logs . 000021 * We add 1 for the 55 rejected which is more tha 100 Instead of the 42 being given and the 000021 required TABLES OF LOGARITHMS . 47.
... diff . of num . 100 : diff . of logs . 000051 :: diff . of num . 42 diff . of logs . 000021 * We add 1 for the 55 rejected which is more tha 100 Instead of the 42 being given and the 000021 required TABLES OF LOGARITHMS . 47.
Page 49
... diff . and divide by the number in co- lumn D which is 59 . 59 ) 2700 ( 45 236 340 295 Annex the quotient 45 to the number 7392 before found , and you have the number required corresponding to the given logarithm , namely 739245. This ...
... diff . and divide by the number in co- lumn D which is 59 . 59 ) 2700 ( 45 236 340 295 Annex the quotient 45 to the number 7392 before found , and you have the number required corresponding to the given logarithm , namely 739245. This ...
Page 79
... diff . of the sides 16 - log . -1 1.204120 :: tan . of sum op . angs . = ( 180 ° — 40 ° 33 ′ 12 ′′ ) = - 69 ° 43 ' 24 " log - 1 = : tan . of diff . of op . angs . log . of which is sum rejec . 10 = 10.432446 137 yds 9.174168 = log . tan ...
... diff . of the sides 16 - log . -1 1.204120 :: tan . of sum op . angs . = ( 180 ° — 40 ° 33 ′ 12 ′′ ) = - 69 ° 43 ' 24 " log - 1 = : tan . of diff . of op . angs . log . of which is sum rejec . 10 = 10.432446 137 yds 9.174168 = log . tan ...
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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...