Ꭼ Ꭱ Ꭱ Ꭺ Ꭲ Ꭺ. Page 179, line 20, for "hypotenuse," read "square of the hypotenuse." 255, line 9, for " diagram," read "diaphragm." 259, line 7 from bottom, for "square yards," read "solid yards." 320, line 8 from bottom, for " A F=387.55," read “386.55.” 381, line 12 from bottom, for " 45° × § 7," read “ 45° + P.S.-In the note at the bottom of page 526, it ought also to have been stated, that the last term of Mr Bailey's formula, XLIII., from which Mr Simms' table was computed, is erroneous -in place of, the true coefficient is, as correctly given in formula (1), page 527.-W. G. TREATISE ON PRACTICAL LAND-SURVEYING. SECTION FIRST. ART. I.-DEFINITIONS AND PROBLEMS. In this Treatise, which is strictly practical, the mathematical demonstrations are omitted. The Surveyor may, however, be assured that the principles upon which the problems are founded are susceptible of strict demonstration. A facility in performing these problems is of the greatest use in practice. But, before proceeding to the problems, it may be proper to lay down the following definitions: LAND-SURVEYING has for its object the determination of the extent of area contained in horizontal surfaces; for no greater number of poles could be planted perpendicularly upon the surface of a hill, than what can find room to stand upon the plane of its base. Of course, no greater number of plants or trees, all of which grow upright, could find room upon the hill's surface than what there is room for on its base. Surfaces consist of length and breadth only, and do not, like solids, infer their constitution from the three dimensions of length, breadth, and thickness. Lines, whether straight lines or curves, are the mere boundaries of surfaces, and, as such, are to be considered as having only length without breadth. A Point is the termination of a line, or the intersection of two lines, and, as such, has neither length nor breadth. A Parallel lines are lines placed equidistant from each other, and which, however far extended, can never meet; as the lines A B and C D. Angles are formed by the meeting of lines drawn in different directions. When a line, as A D, falls upon the line B C, so that the two angles on the opposite sides of the line A D, at the point D, are equal, then these two angles are cach of them right angles, and the line AD is called a perpendicular to B C. 1. A represents a right angle; 2. B is an acute angle, which is less than a right angle; 3. C is an obtuse angle, which is greater than a right angle. The space which the two lines forming 1. 2. 3. B C the angle diverge from the point where they meet, characterises the nature of the angle, as consisting of a certain number of degrees; which will be explained when the circle is treated of. It may be proper here to observe, that when only two lines, in different directions, meet at a point, and of course form only one angle at the point of junction, the angle is marked and designated by a single letter. But if three or more lines meet a point, and form two or more angles, three letters are required to mark and designate these different angles, and, in naming them, the letter at the point of junction is placed in the middle. Thus, the angle formed by the junction of the lines C A and B A, is designed the angle B A C or CAB; that formed by the lines CA and DA is named the angle D A C or CA D, and that by AB and AD the angle BAD. B C D Figures are the portions of space completely enclosed and bounded by lines, either right or curved; those bounded by the former being designated Rectilinear figures, those bounded by the latter Curvilinear. I. Rectilinear Figures comprehend Triangles, or spaces bounded by three right lines. Of these there are three kinds, as charac terised by their bounding lines: 1. The Equilateral triangle, of which all the three sides are equally represented by the triangle BCA; 2. The Isosceles triangle, of which two sides are equal; 3. The Scalene triangle, where the three sides are unequal. Triangles are also characterised by their angles. 1 All the three angles of a triangle are equal to two right angles; so that, if one angle is a right angle, (or greater than a right angle,) none of the other two can be so great as a right angle. If one of the angles is a right angle, the triangle is a right angled triangle; if one angle is obtuse, it is an obtuse angled triangle; if all the three angles are acute, it is an acute angled triangle. G H II. Quadrilateral figures are spaces bounded by four straight lines. These comprehend the Square, 1, in which all the four sides are equal, the opposite sides parallel, and all the angles are right angles; the Rectangular Parallelogram, or oblong, 2, of which the two opposite sides are equal and parallel, all the angles are right angles, but all the four sides are not equal; the Rhombus, 3, of which all the sides are equal and parallel, but none of the angles are right angles; the perfect or regular Rhombus, 3, has two of its angles of 120 degrees, and two of 60. The Rhomboid, 1, has the opposite sides equal and parallel, but the sides are not all equal, and none of the angles are right angles. |