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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adjacent angle adjacent sides apply arcs is equal arith azimuth called celestial sphere centre circle circumference colatitude comp complement cosecant cosine of half cotangent course decimal declination determine diff difference of latitude difference of longitude dist distance divided ecliptic EXAMPLE expressed formula Geom given number given sides half the sum hence horizon hour angle hypothenuse included angle longitude meridian meridian altitude miles multiply Napier's rules Nautical Almanac number of degrees parallax parallel sailing perpendicular plane angle plane sailing plane triangle polar triangle Prop proportion quadrant quotient radius rectangle right angled triangle right ascension sailing secant second member semidiameter ship side opposite sine and cosine sine of half solution spherical trigonometry substituting subtracting sum rejecting TABLE OF LOGARITHMIC Tang tangent three sides tion trigonometrical lines trisolid angle true altitude unknown angle vertex zenith
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 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...