Plane and Spherical Trigonometry, Surveying and Tables

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Ginn, 1895 - Surveying - 367 pages

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Page 50 - ... y) = sin x' cos y + cos x' sin y, cos (x' + y) = cos x' cos y — sin x
Page 61 - EXERCI8E XII. 1. What do the formulas of § 36 become when one of the angles is a right angle ? 2. Prove by means of the Law of Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Page 24 - Geometry that the area of a triangle is equal to one-half the product of the base by the altitude. Therefore, if a and b denote the legs of a right triangle, and F the area...
Page 83 - A pole is fixed on the top of a mound, and the angles of elevation of the top and the bottom of the pole are 60° and 30° respectively.
Page 116 - For, 2Р = (а")' = а"г. . • . loga (N") = np=plog„N. 7. The logarithm of the real positive value of a root of a positive number is found by dividing the logarithm of the number by the index of the root.
Page 172 - Azimuth of a point in the celestial sphere is the angle at the zenith between the meridian of the observer and the vertical circle passing through the point; it may also be regarded as the arc of the horizon intercepted between those circles.
Page 28 - From the top of a hill the angles of depression of two objects situated in the...
Page 50 - ... cos y + cos x sin y cos x cos y — sin x sin y tan a- + tan y 1 — tan x tan y sin (x — y) = sin x cos y — cos x...
Page 115 - Any positive number being selected as a base, the logarithm of any other positive number is the exponent of the power to which the base must be raised to produce the given number. Thus, if a
Page ii - If the number is less than 1 , make the characteristic of the logarithm negative, and one unit more than the number of zeros between the decimal point and the first significant figure of the given number.

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