PRACTICAL DIAGRAMS. 



721 



the oblong ; erect perpendiculars as be- 

 fore, and measure their lengths from the 

 drawing, putting in a peg at the end of 

 each, which will describe the circle re- 

 quired. A line applied as in the last 

 example, will describe an elliptical figure. 



To describe an Oval whose length is 

 given. — Divide the length into three 

 equal parts; let 

 the two inner 

 points so found 

 be the centres^ 

 of two circles, 

 which shall 

 form the ends 

 of the oval : 

 the intersecting 

 points of these 

 circles will be 

 centres to the two segments required to 

 complete the figure 1019. 



To describe an Oval, when the length 

 and breadth are both given. — Lay down 

 the length and breadth perpendicular to 

 each other ; combine a and d ; measure 

 the "distance from c d, on the line a c from 

 c, which will give c n ; measure the dis- 

 tance from n a, on the line d a, which will 

 give / ; divide / a into two equal parts, at 

 the middle of which erect a perpendicular, 

 and where that perpendicular cuts the 

 line a b will be the centre k, for the end 



Fig. 1020. 



the pegs i e and c, with the addition of 

 the space from a to e, describe the figure 

 with the peg c. (Fig. 1021.) 



Fig. 1021. 



\ — v 



c 



V \ 



9 



of the oval ; and where it cuts the line d i 

 at g, is the centre for the side, (fig. 1020.) 



The Gardener's Oval, when both the 

 length and breadth are given, is thus 

 formed : Set off the length a b, and breadth 

 c d, perpendicular to each other ; take 

 half the long diameter, and measure from 

 c, to the line a b, with that length ; when 

 that line cuts the line a b, put in a peg ; 

 do the same on the other side, and the 

 point e will be found ; stick in there also 

 a peg ; then, with a cord passing round 



VOL. I. 



To form an egg-shaped figure (fig. 

 1022.) — The line a b being given, divide 



Fig. 1022. 



f 



N~ -^^^ 







d 



\ / 



it into two equal parts ; from the point 

 c, where these lines intersect each other, 

 construct a circle with the radius c a or 

 c b ; draw the line c d perpendicular to 

 a b ; taking a and b as centres, describe 

 two arcs ; draw a line from b through d, 

 till it cuts the arc at /; then, with df 

 as a radius, complete the figure. 



To set off a walk perpendicular to the 

 line c d. — From 



Fig. 102; 



the centre e, on 

 the line c d, set 

 off e g and e h, 

 at equal distan- 

 ces. From the 

 points h g draw 

 two arcs of dif- 

 ferent radii \ 

 if, where these 

 arcs bisect each 

 other, a line 

 4 Y 



