Elements of Surveying and Navigation: With Descriptions of the Instruments and the Necessary Tables

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A.S. Barnes & Company, 1866 - Navigation - 393 pages
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Page 38 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Page 45 - In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference.
Page 61 - Being on a horizontal plane, and wanting to ascertain the height of a tower, standing on the top of an inaccessible hill, there were measured, the angle of elevation of the top of the hill 40, and of the top of the tower 51 ; then measuring in a direct line 180 feet farther from the hill, the angle of 'elevation of the top of the tower was 33 45' ; required the height of the tower.
Page 92 - What must be the nominal value of 4% bonds that will yield to their owner an annual income of $720 ? 7. A owns $6000 of 5% bonds; B owns $8000 of 4% bonds. How much greater is the annual income from B's bonds than from A's ? 8. Find the area of a piece of land in the form of a rhomboid, whose base is 32 rods and whose altitude is 15 rods.
Page 39 - The secant of an arc is the line drawn from the centre of the circle through one extremity of the arc, and limited by the tangent passing through the other extremity. Thus, . 00 is the secant of the arc AB.
Page 142 - The line so determined, makes, with the true meridian, an angle equal to the azimuth of the pole-star ; and, from this line, the variation of the needle is readily determined, even without tracing the true meridian on the ground. Place the compass upon this line, turn the sights in the direction of it, and note the angle shown by the needle. Now, if the elongation, at the time of observation, was west, and the north end of the needle is on the west side of the line, the azimuth, plus the angle shown...
Page 22 - In a Right-angled Triangle, the side opposite the right angle is called the Hypothenuse ; and the other two sides are called the Legs, and sometimes the Base and Perpendicular.
Page 16 - The difference of the logarithms, as here used, means the algebraic difference ; so that, if the logarithm of the divisor have a negative characteristic, its sign must be changed to positive, after diminishing it by the unit, if any, carried in the subtraction from the decimal part of the logarithm.
Page 143 - North end of the needle on the west, angle 4 06' Variation 6 10' west. 2. Elongation west, azimuth 1 59' North end of the needle on the east, angle 4 50' Variation 2 51' east. 3. Elongation east, azimuth 2 05' North end of the needle on the west, angle 8 30' Variation 6 25
Page 10 - The logarithm of the quotient of two numbers is equal to the logarithm of the dividend minus the logarithm of the divisor.

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