of Draioing Hyperbolas, 



73 



being- similar triangles, 



or 



BO : AB : : EC : DE, 

 BC.DE = AB.EC. 

 Kir. 1. 



+y 



A 













D 



-x 



-y 



1 



3 1 



3 C +Jr 



But by tbe construction, AB and EC are constant ; 

 and also BC=OE=a?; 



and 



Therefore if ED 



EC = OB. 



.r?/=OB . BA = a constant, 



and D is a point on the hyperbola. 



It is scarcely necessary to point out that this construction 

 applies also to hyperbolas other than rectangular, since the 

 lines AB and ED are drawn parallel to Oy, the other 

 asymptote. 



In practice, when it is required to plot several curves, 

 the simplest plan is to draw the asymptotes on a piece of 

 stout paper and then cut it into the shape of a modified 

 T-square, as shown in P, fig. 2, where the edge OBE forms 

 part of the asymptote 0#, the continuation of which is ruled 

 on the paper and represented by the dotted line, and the edge 

 DE is parallel to the asymptote Oy. 



A distance EC equal to OP is measured along the line Ejp, 

 and a fine pin-hole made at C. 



