GEOMETRY. 367 



Draw the diagonals AC and B D, intersecting 

 at e. Upon the points A, B, C, D, as centres, 

 with a radius e C, describe the arcs h e /, k e n, 

 m e g,fe i. Join J n, m h, k /, / «', and it will be the 

 required octagon. 



Prob. 17* In a given circle, to describe any re- 

 gular polygon. 



Divide the circumference into as many parts as 

 there are sides in the polygon to be drawn, and 

 join the points of division. 



Prob. 18. Upon a given line AB, to construct 

 an equilateral triangle. 



Upon the points A, and B, with a radius equal 

 to A B, describe arches cutting each other at C. 

 Draw A C and B C, and ABC will be the triangle 

 required. 



Prob. 19. To make a triangle, whose sides shall 

 be equal to three given lines, D, E, F, any two of 

 them being greater than the third. 



Draw A B equal to the line D. Upon A, with 

 the radius F, describe an arc C D. Upon B, with 

 the radius E, describe another arc intersecting the 

 former at C. Draw A C and C B, and ABC will 

 be the triangle required. 



Prob. 20. To make a trapezium equal and simi- 

 lar to a given trapezium A B C D. 



Divide the given trapezium ABCD into two 

 triangles by the diagonal D B. Make E F equal 

 to A B J upon E F construct the triangle E F PI, 

 whose sides shall be respectively equal to those of 

 the triangle A B D by the last problem. Upon 

 H F, which is equal to D B, construct the triangle 

 HFG, whose sides are respectively equal to DBC ; 

 then EFGH will be the trapezium required. 



By the help of this problem any plan may be 

 copied J as every figure, however irregular, may 



