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
Wiley & Putnam, 1838 - 307 σελίδες
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Elements of Trigonometry, Plane and Spherical: Adapted to the Present State ...
Charles William Hackley
Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016
added adjacent altitude apparent applied becomes called celestial centre circle column comp computation considered contain correction corresponding cosine Cotang course declination departure determine diff difference difference of latitude direction dist distance divided earth east employed equal equation error EXAMPLE expressed extremity figure formed formula Geom given greater Greenwich half hence horizon hour included known latitude less logarithm manner means measured meridian method middle miles moon multiply Nautical necessary object observed obtained opposite parallax parallel pass perpendicular plane pole problem Prop proportion quadrant quantity radius remaining represent result right angled triangle rule sailing semidiameter ship sides similar sine solution spherical triangle substituting subtract supposed taken tangent tion triangle trigonometrical true altitude zenith
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 83 - An oblique equator is a great circle the plane of which is perpendicular to the axis of an oblique projection.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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
Σελίδα 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...
Σελίδα 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...