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 AcademiesWiley & Putnam, 1838 - 307 pages |
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Page xii
... meridian altitude , 161 112. By two altitudes , 166 113. On finding the longitude by the lunar observations , 171 114. Variation of the compass , 177 PART V. ADDENDA . 115. Formulæ for the tangent of the sum and difference of two arcs ...
... meridian altitude , 161 112. By two altitudes , 166 113. On finding the longitude by the lunar observations , 171 114. Variation of the compass , 177 PART V. ADDENDA . 115. Formulæ for the tangent of the sum and difference of two arcs ...
Page 84
... meridian of a place and that meridian which passes through the sun at any given moment , is called the hour angle and converted into hours , 15 ° to the hour , will show the time of day , if we reckon from noon instead of midnight as ...
... meridian of a place and that meridian which passes through the sun at any given moment , is called the hour angle and converted into hours , 15 ° to the hour , will show the time of day , if we reckon from noon instead of midnight as ...
Page 85
... meridian of the observer and the meridian which passes through the object . 80. We are now prepared with materials for a practical application of the formulæ of spherical trigonometry , and we commence with that already demonstrated ...
... meridian of the observer and the meridian which passes through the object . 80. We are now prepared with materials for a practical application of the formulæ of spherical trigonometry , and we commence with that already demonstrated ...
Page 86
... meridian altitude . A piece of colored glass will be required for the purpose . Let p be a place on the earth ; pq its dis- tance from the equator will be the latitude ; this contains the same number of degrees as the arc za between the ...
... meridian altitude . A piece of colored glass will be required for the purpose . Let p be a place on the earth ; pq its dis- tance from the equator will be the latitude ; this contains the same number of degrees as the arc za between the ...
Page 104
... meridian through it , and the difference of siderial † time between its passage across a given meridian at the time the declination was observed and some subsequent epoch , to find its declination at the latter epoch and the dis- tance ...
... meridian through it , and the difference of siderial † time between its passage across a given meridian at the time the declination was observed and some subsequent epoch , to find its declination at the latter epoch and the dis- tance ...
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 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...