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 xii
... third side directly , 201 128. Rules relative to ambiguous cases , 127. Two angles and the interjacent side being given to find the third angle , 202 203 129. Additional formulæ where three sides or three angles of a spherical triangle ...
... third side directly , 201 128. Rules relative to ambiguous cases , 127. Two angles and the interjacent side being given to find the third angle , 202 203 129. Additional formulæ where three sides or three angles of a spherical triangle ...
Page 16
... third time 0 . Beyond 360 ° we pursue the same round again , and no new variations are deve- loped . 17. The least value of the sine , is 0 . value at 0 ° , at 360 . It has this 180 , and at M The greatest value of the sine is R. It has ...
... third time 0 . Beyond 360 ° we pursue the same round again , and no new variations are deve- loped . 17. The least value of the sine , is 0 . value at 0 ° , at 360 . It has this 180 , and at M The greatest value of the sine is R. It has ...
Page 19
... third quadrant , the tangent is cut off above the origin again . Thus A T in the annexed diagram , is the tangent of the arc A B M. The tangent of an arc in the third quadrant is , there- fore , positive . When the arc is 270 ° or 3 ...
... third quadrant , the tangent is cut off above the origin again . Thus A T in the annexed diagram , is the tangent of the arc A B M. The tangent of an arc in the third quadrant is , there- fore , positive . When the arc is 270 ° or 3 ...
Page 20
... third , two diagonal quadrants , and negative in the second and fourth , the other two diagonal quadrants . The tangent is co at the top and bottom of the circle , and 0 on the right and left . THE SECANT . 21. The secant of an arc is a ...
... third , two diagonal quadrants , and negative in the second and fourth , the other two diagonal quadrants . The tangent is co at the top and bottom of the circle , and 0 on the right and left . THE SECANT . 21. The secant of an arc is a ...
Page 21
... third quadrants it is estimated in the opposite 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 ...
... third quadrants it is estimated in the opposite 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 ...
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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...