PRACTICAL DIAGRAMS. 



Yicr. 6. 



ing the requisite oblique angle. Setting the instrument in b fifty links from a, with 

 one leg of the angle on the line b a, and by the other peg directing an assistant to 

 place the peg c at the distance of fifty links ; then remove to c, and so on. 



To find the center of a circle, whose circumference will 

 pass through three given points (not in a straight line), 

 connect the three points a b c (fig. 6) together ; from the 

 middle of each, erect lines perpendicular to them, and 

 where these perpendiculars cut each other is the center 

 required. 



To find the center of a circle, connect three points in 

 the circumference, and from the middle of the two lines 

 erect perpendiculars. Where these intersect each other 

 is the center required. 



To construct a hexagon, divide the circle into three equal parts ; from the middle 

 of each line erect a perpendicular ; and where these cut the circumference of the circle 

 are the points where the sides of the hexagon meet. 



To construct an octagon, divide the circle into four equal parts, by describing 

 a square within it ; erect perpendiculars from the middle of each side of the square ; 

 and where they intersect the circle are the points where the sides of the octagon meet. 



To construct a pentagon, draw a line through the center of 

 the circle, from the center of which erect a perpendicular, c d ; 

 divide the straight line from c to 6 into two equal parts ; take 

 e d as a. radius, and describe a circle, making e the center, and ^ 

 when that circle cuts the straight line at / the distance from f 

 to d is the length of the side of the pentagon. 



To describe a circle the center of which is occupied with a 

 square, say the base of the pedestal of a statue, fountain, &c., 

 tie a cord round the square, not over tight ; to that attach a line, in length equal to 

 the radius, minus half the size of the square base ; with that line describe the circle. 

 This is a plain working plan, and near enough for all practical purposes in laying out 

 grounds. The same rule may be applied when the base is circular, or of any equal 

 sided figure, a pentagon, hexagon, <fec. 



To describe a circle when the base of the fountain, statue, &c., is oblong, lay the 

 oblong correctly down on paper; find its center by drawing two lines diagonally 

 through it ; from that describe a circle of any size ; draw two lines across the circle 

 parallel to the longest sides of the oblong figure ; from these erect perpendiculars, at 

 equal distances, and note their respective lengths; on the ground draw two lines 

 parallel to the longest sides of the oblong ; erect perpendiculars as before, and measure 

 their lengths from the drawing, putting in a peg at the end of each, which will des- 

 cribe the circle required. A line applied as in the last example, will describe an 

 elliptical figure. 



describe an oval whose length is given, divide the length into three 

 let the two inner points so found be the centers of two circles, which shall 



Fig. 1. 



