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altitude azimuth base bearing Calculation called celestial concave circle contained cosec decimal declination determine difference divide drawn earth east equal equator EXAMPLES expression feet former formula fraction given given angle given sides Given the sun's haversines headland heavenly body hill horizon hour angle known latitude latter length less logarithm longitude means measured meridian miles namely natural number object observed opposite passing perpendicular plane triangle pole position problems proportion quantity reduced remaining represents required angle required the distance required the height required the latitude result right angled triangle root rules sailing ship sides sine spherical triangle ABC stations subtract sun's declination supposed tables taken tangent term third tower Trigonometry versine yards zenith
Page 62 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Page 79 - Wanting to know the breadth of a river, I , measured a base of 500 yards in a straight line close by one side of it ; and at each end of this line I found the angles subtended by the other end and a tree, close to the bank on the other side of the river, to be 53° and 79° 12'.
Page 11 - Hence, if we find the logarithm of the dividend, and from it subtract the logarithm of the divisor, the remainder will be the logarithm of the quotient. This additional caution may be added. The difference of the logarithms, as here used, means the algebraic difference ; so that, if the logarithm of the divisor...
Page 97 - The hour angle of a heavenly body, is the angle at the pole between the celestial meridian and the circle of declination passing through the place of the body ; thus, zpx is the hour angle of x.
Page 114 - Paris, and extended northward ; the result of the measurement gave, as the length of a degree in latitude 49J°, 121,627 yards, which differs only 35 yards from what is now considered as the most exact length ; an accuracy which is justly supposed to be quite accidental. Since this period arcs of meridian lines have been measured in various countries, as well in intermediate latitudes between the equator and the north pole, as near both the equator and the pole. The following table represents the...
Page 21 - The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor.
Page 73 - A ladder, 40 feet long, may be so placed as to reach a window 33 feet from the ground on one side of the street; and by only turning it over, without moving the foot out of its place, it will do the same by a window 21 feet high on the other side. Required the breadth of the street?
Page 73 - A ladder 70 feet long is so planted as to reach a window 40 feet from the ground, on one side of the street, and without moving it at the foot, will reach a window 30 feet high on the other side ; what is the breadth of the street ? Ans.
Page 75 - From the top of a ship's mast, which was 80 feet above the water, the angle of depression of another ship's hull was found to be 20°.