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 ix
... complement of an arc or angle , 24. Its definition , 25. Its Algebraic sign , 26. Its variations of value , 27. Negative arcs , THE COSINE . B 14 14 15 16 17 828 18 20 20 21 21 2223 2233 ARTICLE THE COTANGENT AND COSECANT . 28. Values ...
... complement of an arc or angle , 24. Its definition , 25. Its Algebraic sign , 26. Its variations of value , 27. Negative arcs , THE COSINE . B 14 14 15 16 17 828 18 20 20 21 21 2223 2233 ARTICLE THE COTANGENT AND COSECANT . 28. Values ...
Page x
... complement , 63. Example in the measurement of distances , 535 59 60 61 3953528 8 85 43 45 47 49 51 Solution of oblique - angled triangles by logarithms , 64. A side and the opposite angle being two of the given parts , 65. Two angles ...
... complement , 63. Example in the measurement of distances , 535 59 60 61 3953528 8 85 43 45 47 49 51 Solution of oblique - angled triangles by logarithms , 64. A side and the opposite angle being two of the given parts , 65. Two angles ...
Page 21
... complement of the arc or angle . Thus 40 ° is the complement of 50 ° ; 60 ° is the complement of 30 ° ; and in general 90 ° -a is the complement of the arc a . The cosine , cotangent and cosecant , are the sine , tangent , and secant of ...
... complement of the arc or angle . Thus 40 ° is the complement of 50 ° ; 60 ° is the complement of 30 ° ; and in general 90 ° -a is the complement of the arc a . The cosine , cotangent and cosecant , are the sine , tangent , and secant of ...
Page 22
... complement of the arc AM ; and мQ being a perpendicular from one extremity м of of the arc DM upon the diameter which passes through the other ex- tremity D , is the sine of the arc DM . There- fore by the definition THE COSINE . Q M A ...
... complement of the arc AM ; and мQ being a perpendicular from one extremity м of of the arc DM upon the diameter which passes through the other ex- tremity D , is the sine of the arc DM . There- fore by the definition THE COSINE . Q M A ...
Page 23
... 4th quadrant will apply with this modification , that when the trigonometrical line is in the fourth quad- TRIGONOMETRICAL LINES . 23 Definition of the complement of an arc or angle, ARTICLE THE COTANGENT AND COSECANT.
... 4th quadrant will apply with this modification , that when the trigonometrical line is in the fourth quad- TRIGONOMETRICAL LINES . 23 Definition of the complement of an arc or angle, ARTICLE THE COTANGENT AND COSECANT.
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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...