Elements of Surveying, and Navigation: With a Description of the Instruments and the Necessary Tables

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A.S. Barnes & Company, 1846 - Navigation - 288 pages
 

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Page 12 - FRACTION is a negative number, and is one more than the number of ciphers between the decimal point and the first significant Jigure.
Page 41 - 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 40 - THEOREM I. The sides of a plane triangle are proportional to the sines of their opposite angles.
Page 34 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Page 35 - 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, OC is the secant of the arc AB.
Page 19 - Two lines are said to be parallel, when being situated in the same plane, they cannot meet, how far soever, either way, both of them be produced. 13. A plane figure is a plane terminated on all sides by lines, either straight or curved. If the lines are straight, the space they enclose is called a rectilineal figure, or polygon, and the lines themselves, taken together, form the contour, or perimeter of the polygon. 14. The polygon of three sides, the simplest of all, is called a triangle; that of...
Page 132 - Now, if the elongation, at the time of observation, were west, and the north end of the needle on the west side of the line, the azimuth, plus the angle shown by the needle, is the true variation. But should the north end of the needle be found on the east side of the line, the elongation being west, the difference between the azimuth and the angle would show the variation : and the reverse when the elongation is east. 1. Elongation west, azimuth . . 2° 04' North end of the needle on the west, angle...
Page 34 - Mathematics which treats of the solution of plane triangles. In every plane triangle there are six parts : three sides and three angles. When three of these parts are given, one being a side, the remaining parts may be found by computation.
Page 132 - The line so determined makes, with the true meridian, an angle equal to the azimuth of the polestar; 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 by...
Page 21 - AXIOM is a self-evident truth ; such as, — 1. Things which are equal to the same thing, are equal to each other. 2. If equals be added to equals, the sums will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added to unequals, the sums will be unequal. 5. If equals be taken from unequals, the remainders will be unequal. 6.

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