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 84
... ecliptic is a great circle which makes an angle of about 23 ° 28 with the equator . It is the path which the sun appears to describe among the stars once a year . The points in which the two great circles above defined intersect , are ...
... ecliptic is a great circle which makes an angle of about 23 ° 28 with the equator . It is the path which the sun appears to describe among the stars once a year . The points in which the two great circles above defined intersect , are ...
Page 85
... ecliptic instead of the equator . Similar measurements from and upon the celestial equator are called the declination and the right ascension , the former corresponding to the latitude , and the latter to the longitude . Longitude upon ...
... ecliptic instead of the equator . Similar measurements from and upon the celestial equator are called the declination and the right ascension , the former corresponding to the latitude , and the latter to the longitude . Longitude upon ...
Page 102
... distance apart . * Analogy is a term synonymous with proportion . The first term bears the same analogy or proportion to the second that the third does to the fourth . Let p be the pole of the ecliptic , s 102 SPHERICAL TRIGONOMETRY .
... distance apart . * Analogy is a term synonymous with proportion . The first term bears the same analogy or proportion to the second that the third does to the fourth . Let p be the pole of the ecliptic , s 102 SPHERICAL TRIGONOMETRY .
Page 103
... ecliptic , s and s ' the places of the two ce- lestial objects , then Ps and Ps ' will be their coaltitudes , and the angle P will be the difference of their longitudes , since P will be measured by that arc at a quad- rant's distance ...
... ecliptic , s and s ' the places of the two ce- lestial objects , then Ps and Ps ' will be their coaltitudes , and the angle P will be the difference of their longitudes , since P will be measured by that arc at a quad- rant's distance ...
Page 108
... ecliptic . The required part is the angle E in the figure . Of E , s and since the three are contiguous leaving out the right angle , s is the middle part , hence applying the rule of Napier , e , R sin stan e cot E We put cot E instead ...
... ecliptic . The required part is the angle E in the figure . Of E , s and since the three are contiguous leaving out the right angle , s is the middle part , hence applying the rule of Napier , e , R sin stan e cot E We put cot E instead ...
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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...