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
... obtained from the scale , describe with the other an arc of a circle on the side towards which the line is to be drawn ; then from A draw the line in the proper direction , terminating it at the arc before described , and it will be the ...
... obtained from the scale , describe with the other an arc of a circle on the side towards which the line is to be drawn ; then from A draw the line in the proper direction , terminating it at the arc before described , and it will be the ...
Page 4
... obtained by its being said that one is seven feet or yards , and the other nine . Or the just conception of the length of a single line is had by being told how many feet , yards or miles it contains . The mind compares it with one of ...
... obtained by its being said that one is seven feet or yards , and the other nine . Or the just conception of the length of a single line is had by being told how many feet , yards or miles it contains . The mind compares it with one of ...
Page 9
... obtain the length of the required side ex- tending from the light - house to the salient of the fort . A somewhat rude instrument for the purpose of observing such 2 SEMI - CIRCULAR PROTRACTOR . Use of the protractor,
... obtain the length of the required side ex- tending from the light - house to the salient of the fort . A somewhat rude instrument for the purpose of observing such 2 SEMI - CIRCULAR PROTRACTOR . Use of the protractor,
Page 26
... obtain the last R X sin a tan a = COS a If R that is the tangent of any arc is equal to radius multiplied by the sine divided by the cosine of the same arc . be made equal to 1 , then sin tan = COS 33. In the same similar triangles we ...
... obtain the last R X sin a tan a = COS a If R that is the tangent of any arc is equal to radius multiplied by the sine divided by the cosine of the same arc . be made equal to 1 , then sin tan = COS 33. In the same similar triangles we ...
Page 31
... obtained α = 1 x 15 sin 35 ° * They are under the form of a proportion , but may be converted into equa- tions . This remark is here made because we have spoken of equations only as being called formula . Proportions are no less so . + ...
... obtained α = 1 x 15 sin 35 ° * They are under the form of a proportion , but may be converted into equa- tions . This remark is here made because we have spoken of equations only as being called formula . Proportions are no less so . + ...
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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 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 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 sine and cosine solution spherical triangle spherical trigonometry substituting subtract tance 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 126 - The latitude of a place is its distance from the equator, measured on the meridian of the place, and is north or south according as the place lies north or south of the equator.
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 83 - An oblique equator is a great circle the plane of which is perpendicular to the axis of an oblique projection.
Page 17 - The minutes in the left-hand column of each page, increasing downwards, belong to the degrees at the top ; and those increasing upwards, in the right.hand column, belong to the degrees below.
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 174 - A' . cos z =— .- — ;t cos A cos A ' and in the triangle mzs, cos d — sin « sin a' cos z = cos a cos a hence, for the determination of D, we have this equation, viz., cos D — sin A sin A' cos d — sin a sin a
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 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...