## Elements of Surveying: Including a Description of the Instruments and the Necessary Tables |

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Page 32 - 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 39 - In any triangle, the sum of the two sides containing eithei 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 108 - B, from B to C, from C to D, from D to E, and from E to A ; and measure the distances AB, BC, CD, DE, and EA.

Page 33 - 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 12 - Find from the table the logarithm of the first four figures, and to it prefix a characteristic less by unity than all the places of figures in the given number. Take from the last column on the right of the page, marked D, the number on the same horizontal line with the logarithm, and multiply this number by the figures that have been considered as ciphers : then cut off from the right hand as many places for decimals as there are figures in the multiplier, and add the product so obtained to the...

Page 32 - In every plane triangle there are six parts : three sides and three angles. These parts are so related to each other, that if a certain number of them are known or given, the remaining ones can be determined.

Page 120 - 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 82 - Multiply the half sum and the three remainders together, and extract the square root of the product. EXAMPLES. 1. What is the area of a triangle whose sides are respectively 30, 40, and 50 feet ? 30 + 40 + 50 = 120.

Page 81 - Then, add together the logarithms of the two sides and the logarithmic sine of their included angle; from this sum subtract the logarithm of the radius, which is 10, and the remainder will be the logo.ritiim of double the area of the triangle.

Page 159 - NB In the following table, in the last nine columns of each page, where the first or leading figures change from 9's to O's, points or dots are introduced instead of the...